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University of Waterloo
1.
Vu, Thi Xuan.
Homotopy algorithms for solving structured determinantal systems.
Degree: 2020, University of Waterloo
URL: http://hdl.handle.net/10012/16566 
► Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such…
(more)
▼ Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems.
In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the
number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials.
In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method.
Subjects/Keywords: symbolic computation; polynomial systems solving; symbolic homotopy continuation; determinantal systems; invariant algebraic systems
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APA (6th Edition):
Vu, T. X. (2020). Homotopy algorithms for solving structured determinantal systems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16566
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Vu, Thi Xuan. “Homotopy algorithms for solving structured determinantal systems.” 2020. Thesis, University of Waterloo. Accessed January 23, 2021.
http://hdl.handle.net/10012/16566.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Vu, Thi Xuan. “Homotopy algorithms for solving structured determinantal systems.” 2020. Web. 23 Jan 2021.
Vancouver:
Vu TX. Homotopy algorithms for solving structured determinantal systems. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10012/16566.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Vu TX. Homotopy algorithms for solving structured determinantal systems. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16566
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Colorado State University
2.
Ihde, Steven L.
Preconditioning polynomial systems for homotopy continuation.
Degree: MS(M.S.), Mathematics, 2011, Colorado State University
URL: http://hdl.handle.net/10217/51875
► Polynomial systems are ubiquitous in today's scientific world. These systems need to be solved quickly and efficiently. One key solution method comes from Numerical Algebraic…
(more)
▼ Polynomial systems are ubiquitous in today's scientific world. These
systems need to be solved quickly and efficiently. One key solution method comes from Numerical Algebraic Geometry, specifically Homotopy Continuation. This method involves following paths from the solutions of a simpler system to the solutions of the target system. If we can follow fewer or better conditioned paths to the solution set, the result is better efficiency. Our goal is to precondition the original system in order to achieve such efficiency. Using dual spaces and H-bases, we are able to remove poorly conditioned paths and at worst replace them with, possibly more, better conditioned paths. At best we can trim the system down so that we track only the paths that lead to solutions. These techniques require only numerical linear algebra and are therefore easily computed. In this thesis we will introduce H-bases and dual spaces, show some promising preliminary results, and discuss further work in this area.
Advisors/Committee Members: Bates, Dan (advisor), Peterson, Chris (committee member), Young, Peter (committee member).
Subjects/Keywords: dual basis; polynomial systems; numerical algebraic geometry; homotopy continuation; H-basis
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APA (6th Edition):
Ihde, S. L. (2011). Preconditioning polynomial systems for homotopy continuation. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/51875
Chicago Manual of Style (16th Edition):
Ihde, Steven L. “Preconditioning polynomial systems for homotopy continuation.” 2011. Masters Thesis, Colorado State University. Accessed January 23, 2021.
http://hdl.handle.net/10217/51875.
MLA Handbook (7th Edition):
Ihde, Steven L. “Preconditioning polynomial systems for homotopy continuation.” 2011. Web. 23 Jan 2021.
Vancouver:
Ihde SL. Preconditioning polynomial systems for homotopy continuation. [Internet] [Masters thesis]. Colorado State University; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10217/51875.
Council of Science Editors:
Ihde SL. Preconditioning polynomial systems for homotopy continuation. [Masters Thesis]. Colorado State University; 2011. Available from: http://hdl.handle.net/10217/51875
University of Miami
3.
Masterjohn, Joseph.
Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves.
Degree: MS, Computer Science (Arts and Sciences), 2017, University of Miami
URL: https://scholarlyrepository.miami.edu/oa_theses/699
► One of the fundamental concepts in computational geometry is deducing the combinatorial structure, or interactions, of a group of static geometric objects. In two…
(more)
▼ One of the fundamental concepts in computational geometry is deducing the combinatorial structure, or interactions, of a group of static geometric objects. In two dimensions, the objects in question include, but are not limited to: points, lines, line segments, polygons, and non-linear curves. There are various properties of interest describing a collection of such objects; examples include: distances, adjacencies, and most notably, intersections of these objects. Well studied, robust, and highly efficient algorithms exist for linear geometry and parametric curves. Problems involving non-linear, implicit, and high-dimensional objects however are an active area of research. Algebraic curves and algebraic surfaces arise frequently in numerous applications: GIS software, CAD software, VLSI design, computational chemistry and biology, dynamics, and robotics. We present a novel algorithm for finding all intersections of two semi-algebraic curves in a convex polygonal region and describe its prospective analog in 3 dimensions. We "encase'' the curves in the convex region by repeatedly splitting the region until each cell contains at most two intersecting segments, thus detecting and isolating all of the intersections. The advantage of using encasement is that the running time is proportional to the size of the convex region when it is small and yet comparable to existing techniques when it is large.
Advisors/Committee Members: Victor J. Milenkovic, Hüseyin Koçak, Elisha Sacks.
Subjects/Keywords: computational geometry; arrangements; algebraic curves; algorithms; intersections; polynomial systems
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APA (6th Edition):
Masterjohn, J. (2017). Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves. (Thesis). University of Miami. Retrieved from https://scholarlyrepository.miami.edu/oa_theses/699
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Masterjohn, Joseph. “Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves.” 2017. Thesis, University of Miami. Accessed January 23, 2021.
https://scholarlyrepository.miami.edu/oa_theses/699.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Masterjohn, Joseph. “Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves.” 2017. Web. 23 Jan 2021.
Vancouver:
Masterjohn J. Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves. [Internet] [Thesis]. University of Miami; 2017. [cited 2021 Jan 23].
Available from: https://scholarlyrepository.miami.edu/oa_theses/699.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Masterjohn J. Encasement: A Robust Method for Finding Intersections of Semi-algebraic Curves. [Thesis]. University of Miami; 2017. Available from: https://scholarlyrepository.miami.edu/oa_theses/699
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Melbourne
4.
SLEIGH, CALLUM.
Eynard-Orantin theory of the A-polynomial.
Degree: 2013, University of Melbourne
URL: http://hdl.handle.net/11343/38442
► This thesis studies the Eynard-Orantin invariants of an important knot invariant: the A-polynomial. In particular, period integrals of the Eynard-Orantin invariants are studied. First, formulae…
(more)
▼ This thesis studies the Eynard-Orantin invariants of an important knot invariant: the A-polynomial. In particular, period integrals of the Eynard-Orantin invariants are studied. First, formulae for the period integrals are derived in the case of a general elliptic curve, and relations to the Gauss-Manin connection and integrable systems are shown. These constructions are then elaborated to the case of the A-polynomial of a knot. In the specific case of the figure eight knot, explicit formula are given.
Subjects/Keywords: A-polynomial; Chern-Simons Theory; integrable systems; topological recursion
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APA ·
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APA (6th Edition):
SLEIGH, C. (2013). Eynard-Orantin theory of the A-polynomial. (Doctoral Dissertation). University of Melbourne. Retrieved from http://hdl.handle.net/11343/38442
Chicago Manual of Style (16th Edition):
SLEIGH, CALLUM. “Eynard-Orantin theory of the A-polynomial.” 2013. Doctoral Dissertation, University of Melbourne. Accessed January 23, 2021.
http://hdl.handle.net/11343/38442.
MLA Handbook (7th Edition):
SLEIGH, CALLUM. “Eynard-Orantin theory of the A-polynomial.” 2013. Web. 23 Jan 2021.
Vancouver:
SLEIGH C. Eynard-Orantin theory of the A-polynomial. [Internet] [Doctoral dissertation]. University of Melbourne; 2013. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/11343/38442.
Council of Science Editors:
SLEIGH C. Eynard-Orantin theory of the A-polynomial. [Doctoral Dissertation]. University of Melbourne; 2013. Available from: http://hdl.handle.net/11343/38442
Laurentian University
5.
Wang, Zhenheng.
Model based fault detection for two-dimensional systems
.
Degree: 2014, Laurentian University
URL: https://zone.biblio.laurentian.ca/dspace/handle/10219/2186
► Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for…
(more)
▼ Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial
systems. Extensive research has been carried out on FDI for one dimensional (1-D)
systems, where variables vary only with time. The existing FDI strategies are mainly focussed
on 1-D systems and can generally be classified as model based and process history data based
methods. In many industrial systems, the state variables change with space and time (e.g., sheet
forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter
systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented
by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems
represent a great challenge in both theoretical development and applications and only limited
research results are available.
In this thesis, model based fault detection strategies for 2-D systems have been investigated
based on the F-M and the Roesser models. A dead-beat observer based fault detection has been
available for the F-M model. In this work, an observer based fault detection strategy is investigated
for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique,
a dead-beat observer is developed and the state estimate from the observer is then input to a
residual generator to monitor occurrence of faults. An enhanced realization technique is combined
to achieve efficient fault detection with reduced computations. Simulation results indicate
that the proposed method is effective in detecting faults for systems without disturbances as well
as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems
but strict conditions are required in order for an observer and a residual generator to exist. These
strict conditions may not be satisfied for some systems. The effect of process noises are also not
considered in the observer based fault detection approaches for 2-D systems. To overcome the
disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation
error variances. Based on the state estimate from the Kalman filter, a residual is generated
reflecting fault information. A model is formulated for the relation of the residual with faults
over a moving evaluation window. Simulations are performed on two F-M models and results
indicate that faults can be detected effectively and efficiently using the Kalman filter based fault
detection.
In the observer based and Kalman filter based fault detection approaches, the residual signals
are used to determine whether a fault occurs. For systems with complicated fault information
and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault
detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component
analysis (DPCA). Based…
Subjects/Keywords: Two dimensional systems;
Fault detection;
Kalman filter;
Polynomial theory
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APA ·
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Export
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Manager
APA (6th Edition):
Wang, Z. (2014). Model based fault detection for two-dimensional systems
. (Thesis). Laurentian University. Retrieved from https://zone.biblio.laurentian.ca/dspace/handle/10219/2186
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Wang, Zhenheng. “Model based fault detection for two-dimensional systems
.” 2014. Thesis, Laurentian University. Accessed January 23, 2021.
https://zone.biblio.laurentian.ca/dspace/handle/10219/2186.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Wang, Zhenheng. “Model based fault detection for two-dimensional systems
.” 2014. Web. 23 Jan 2021.
Vancouver:
Wang Z. Model based fault detection for two-dimensional systems
. [Internet] [Thesis]. Laurentian University; 2014. [cited 2021 Jan 23].
Available from: https://zone.biblio.laurentian.ca/dspace/handle/10219/2186.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Wang Z. Model based fault detection for two-dimensional systems
. [Thesis]. Laurentian University; 2014. Available from: https://zone.biblio.laurentian.ca/dspace/handle/10219/2186
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Virginia Tech
6.
Hinkelmann, Franziska Babette.
Algebraic theory for discrete models in systems biology.
Degree: PhD, Mathematics, 2011, Virginia Tech
URL: http://hdl.handle.net/10919/28509
► This dissertation develops algebraic theory for discrete models in systems biology. Many discrete model types can be translated into the framework of polynomial dynamical systems…
(more)
▼ This dissertation develops algebraic theory for discrete models in
systems biology. Many discrete model types can be translated into the framework of
polynomial dynamical
systems (PDS), that is, time- and state-discrete dynamical
systems over a finite field where the transition function for each variable is given as a
polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods. Formal definitions and theorems for PDS and the concept of PDS as models of biological
systems are introduced in section 1.3.
Constructing a model for given time-course data is a challenging problem. Several methods for reverse-engineering, the process of inferring a model solely based on experimental data, are described briefly in section 1.3. If the underlying dependencies of the model components are known in addition to experimental data, inferring a "good" model amounts to parameter estimation.
Chapter 2 describes a parameter estimation algorithm that infers a special class of polynomials, so called nested canalyzing functions. Models consisting of nested canalyzing functions have been shown to exhibit desirable biological properties, namely robustness and stability. The algorithm is based on the parametrization of nested canalyzing functions. To demonstrate the feasibility of the method, it is applied to the cell-cycle network of budding yeast.
Several discrete model types, such as Boolean networks, logical models, and bounded Petri nets, can be translated into the framework of PDS. Section 3 describes how to translate agent-based models into
polynomial dynamical
systems.
Chapter 4, 5, and 6 are concerned with analysis of complex models. Section 4 proposes a new method to identify steady states and limit cycles. The method relies on the fact that attractors correspond to the solutions of a system of polynomials over a finite field, a long-studied problem in algebraic geometry which can be efficiently solved by computing Gröbner bases. Section 5 introduces a bit-wise implementation of a Gröbner basis algorithm for Boolean polynomials. This implementation has been incorporated into the core engine of Macaulay2. Chapter 6 discusses bistability for Boolean models formulated as
polynomial dynamical
systems.
Advisors/Committee Members: Laubenbacher, Reinhard C. (committeechair), Tyler, Brett M. (committee member), Herdman, Terry L. (committee member), Jarrah, Abdul Salam (committee member).
Subjects/Keywords: systems biology; discrete models; Mathematical biology; finite fields; reverse-engineering; polynomial dynamical systems
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APA ·
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APA (6th Edition):
Hinkelmann, F. B. (2011). Algebraic theory for discrete models in systems biology. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/28509
Chicago Manual of Style (16th Edition):
Hinkelmann, Franziska Babette. “Algebraic theory for discrete models in systems biology.” 2011. Doctoral Dissertation, Virginia Tech. Accessed January 23, 2021.
http://hdl.handle.net/10919/28509.
MLA Handbook (7th Edition):
Hinkelmann, Franziska Babette. “Algebraic theory for discrete models in systems biology.” 2011. Web. 23 Jan 2021.
Vancouver:
Hinkelmann FB. Algebraic theory for discrete models in systems biology. [Internet] [Doctoral dissertation]. Virginia Tech; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10919/28509.
Council of Science Editors:
Hinkelmann FB. Algebraic theory for discrete models in systems biology. [Doctoral Dissertation]. Virginia Tech; 2011. Available from: http://hdl.handle.net/10919/28509
7.
Dehornoy, Pierre.
Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field.
Degree: Docteur es, Mathématiques, 2011, Lyon, École normale supérieure
URL: http://www.theses.fr/2011ENSL0626
► Cette thèse se situe à l’interface entre théorie des nœuds et théorie des systèmes dynamiques. Le thème central consiste, étant donné un champ de vecteurs…
(more)
▼ Cette thèse se situe à l’interface entre théorie des nœuds et théorie des systèmes dynamiques. Le thème central consiste, étant donné un champ de vecteurs dans une variété de dimension 3, à considérer ses orbites périodiques, et à s’interroger sur les informations qu’elles donnent sur le champ de vecteurs et la variété initiaux.La première partie est consacrée au flot géodésique défini sur le fibré unitaire tangentd’une surface, ou d’une orbiface, à courbure constante. L’observation de certains exemples (sphère, tore, surface modulaire) suggère la conjecture suivante, due à Étienne Ghys : l’enlacement entre deux familles homologiquement nulles quelconques d’orbites périodiques est toujours négatif. En d’autres termes, le flot géodésique serait lévogyre. Quand la courbure est négative, par les travaux de David Fried sur les flots d’Anosov, cette conjecture implique une propriété étonnante et très particulière : n’importe quelle collection homologiquement nulle d’orbites périodiques borde une section de Birkhoff pour le flot géodésique, et est par conséquent la reliure d’un livre ouvert. En ce sens, cette conjecture propose une généralisation de la construction de Norbert A’Campo de livres ouverts sur les fibrés unitaires tangents. Nous proposons la démonstration de cette conjecture dans les cas du tore, des orbifolds de type (2, q, infini), et de l’orbifold de type (2, 3, 7). La seconde partie est consacrée au comportement asymptotique des invariants des nœuds formés par les orbites périodiques d’un champ de vecteur, quand la longueur de l’orbite tend vers l’infini. Le but est de définir des invariants de champs de vecteurs stables par difféomorphisme. Dans le cas particulier des nœuds de Lorenz, nous montrons que les racines du polynôme d’Alexander admettent un comportement particulier : elles s’accumulent au voisinage du cercle-unité.
This thesis deals with interactions between knot theory and dynamical systems. Givena vector field on a 3-manifold, the main idea is to study its periodic orbits from the knottheoretical point of view, and to deduce informations about the vector field and the initial manifold. The first part is devoted to the study of the geodesic flow defined on the unit tangent bundle of a surface, or an orbiface, with constant curvature. Simple examples (sphere, torus, modular surface) suggest the following conjecture, due to Ghys : the linking number of two homologically zero collections of periodic orbits is always negative. In other words, the geodesic flow on any orbiface with constant curvature is left-handed. In the negatively curved case, the work of Fried imply another surprising property : any homologically trivial collection of periodic orbits bound a Birkhoff section for the geodesic flow, and is therefore the binding of an open book decomposition. In this setting, the conjecture is a generalization of A’Campo’s construction of open book decompositions on unit tangent bundles. In our work, we prove the conjectre for the torus, for the orbifolds of type (2, q, oo), and for the orbifold…
Advisors/Committee Members: Ghys, Étienne (thesis director).
Subjects/Keywords: Noeud fibré; Noeud de Lorenz; Dynamical systems; Topology; Fibered knot; Lorenz knot; Alexander polynomial
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APA ·
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Export
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APA (6th Edition):
Dehornoy, P. (2011). Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2011ENSL0626
Chicago Manual of Style (16th Edition):
Dehornoy, Pierre. “Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field.” 2011. Doctoral Dissertation, Lyon, École normale supérieure. Accessed January 23, 2021.
http://www.theses.fr/2011ENSL0626.
MLA Handbook (7th Edition):
Dehornoy, Pierre. “Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field.” 2011. Web. 23 Jan 2021.
Vancouver:
Dehornoy P. Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2011. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2011ENSL0626.
Council of Science Editors:
Dehornoy P. Invariants topologiques des orbites périodiques d'un champ de vecteurs : Topological invariants of the periodic orbits of a vector field. [Doctoral Dissertation]. Lyon, École normale supérieure; 2011. Available from: http://www.theses.fr/2011ENSL0626
University of Illinois – Chicago
8.
Bliss, Nathan R.
Computing Series Expansions of Algebraic Space Curves.
Degree: 2018, University of Illinois – Chicago
URL: http://hdl.handle.net/10027/22682
► We work towards a series-based computational approach for polynomial systems having positive-dimensional solution sets. The tropical variety gives information on the exponents of the leading…
(more)
▼ We work towards a series-based computational approach for
polynomial systems having positive-dimensional solution sets. The tropical variety gives information on the exponents of the leading terms of the series; we provide insight into when the purely polyhedral and more easily computed tropical prevariety is sufficient. When it is not sufficient and hidden cones exist, we give an alternative to known symbolic algorithms based on polyhedral end games. We develop an effective method to apply the Gauss-Newton algorithm over power or Laurent series, using linearization and a lower triangular echelon form; we can thus extend the information obtained tropically with quadratic convergence. We also characterize when tropical methods can be avoided entirely. Finally we give applications to several problems in view of extending current approaches to homotopy continuation to allow for starting from singular solutions. We also provide a result related to the Backelin component of the cyclic-16 roots
polynomial system.
Advisors/Committee Members: Verschelde, Jan (advisor), Awanou, Gerard (committee member), Hampton, Marshall (committee member), Reyzin, Lev (committee member), Tucker, Kevin (committee member), Verschelde, Jan (chair).
Subjects/Keywords: computational algebraic geometry; puiseux series; gauss-newton algorithm; tropical geometry; polynomial systems; homotopy continuation
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APA (6th Edition):
Bliss, N. R. (2018). Computing Series Expansions of Algebraic Space Curves. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/22682
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Thesis, University of Illinois – Chicago. Accessed January 23, 2021.
http://hdl.handle.net/10027/22682.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Web. 23 Jan 2021.
Vancouver:
Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10027/22682.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/22682
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Notre Dame
9.
Timothy M McCoy.
Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>.
Degree: Applied and Computational Mathematics and
Statistics, 2014, University of Notre Dame
URL: https://curate.nd.edu/show/6395w66528z
► Algorithms from the field of numerical algebraic geometry provide robust means to compute all isolated solutions of arbitrary systems of polynomials and to give…
(more)
▼ Algorithms from the field of numerical
algebraic geometry provide robust means to compute all isolated
solutions of arbitrary
systems of polynomials and to give a
thorough numerical description of positive-dimensional solution
components. However, the number of isolated complex solutions tends
to grow exponentially with respect to the number N of equations
and variables, limiting the size of tractable
systems. This is a
particular problem for
systems arising from discretizations of
ordinary differential equations because N is directly related to
mesh size, and finer meshes are generally more desirable. On the
other hand, the number of interesting solutions is often far
smaller than the total count, and much effort is wasted on complex
solutions with no physical interpretation.In the first part of this
thesis, a general method is given for constructing a homotopy that
directly relates solutions on grids of different resolutions. This
enables iterative generation of solutions on increasingly fine
meshes, and makes it possible to filter out some non-physical
solutions to substantially reduce wasted computation time. In the
second part, a new algorithm is given to compute the numerical
irreducible decomposition of a general
polynomial system over a
finite algebraic extension of Q by projecting the solution set
onto a line and deducing the exact defining
polynomial of the
projection.
Advisors/Committee Members: Bei Hu, Committee Member, Andrew Sommese, Committee Chair, Jonathan Hauenstein, Committee Member, Yongtao Zhang, Committee Member.
Subjects/Keywords: algebraic computation; numerical algebraic geometry; homotopy continuation; computational mathematics; polynomial systems; boundary value problems
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APA (6th Edition):
McCoy, T. M. (2014). Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/6395w66528z
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
McCoy, Timothy M. “Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>.” 2014. Thesis, University of Notre Dame. Accessed January 23, 2021.
https://curate.nd.edu/show/6395w66528z.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
McCoy, Timothy M. “Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>.” 2014. Web. 23 Jan 2021.
Vancouver:
McCoy TM. Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>. [Internet] [Thesis]. University of Notre Dame; 2014. [cited 2021 Jan 23].
Available from: https://curate.nd.edu/show/6395w66528z.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
McCoy TM. Mesh-Expanding Homotopies and Numerical Irreducible
Decomposition Over a Number Field</h1>. [Thesis]. University of Notre Dame; 2014. Available from: https://curate.nd.edu/show/6395w66528z
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Waterloo
10.
Melczer, Stephen.
Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration.
Degree: 2017, University of Waterloo
URL: http://hdl.handle.net/10012/12039
► The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of…
(more)
▼ The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics and the natural sciences. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions represented by diagonals of multivariate rational functions. This thesis examines the methods of ACSV from a computer algebra viewpoint, developing rigorous algorithms and giving the first complexity results in this area under conditions which are broadly satisfied. Furthermore, this thesis gives several new applications of ACSV to the enumeration of lattice walks restricted to certain regions. In addition to proving several open conjectures on the asymptotics of such walks, a detailed study of lattice walk models with weighted steps is undertaken.
Subjects/Keywords: Analytic Combinatorics; Enumerative Combinatorics; Singularity Analysis; Computer Algebra; Lattice Paths; Rational Diagonals; Polynomial Systems
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APA (6th Edition):
Melczer, S. (2017). Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/12039
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Melczer, Stephen. “Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration.” 2017. Thesis, University of Waterloo. Accessed January 23, 2021.
http://hdl.handle.net/10012/12039.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Melczer, Stephen. “Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration.” 2017. Web. 23 Jan 2021.
Vancouver:
Melczer S. Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration. [Internet] [Thesis]. University of Waterloo; 2017. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10012/12039.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Melczer S. Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration. [Thesis]. University of Waterloo; 2017. Available from: http://hdl.handle.net/10012/12039
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Northeastern University
11.
Brunet, Pascal Maurice.
Nonlinear system modeling and identification of loudspeakers.
Degree: PhD, Department of Electrical and Computer Engineering, 2014, Northeastern University
URL: http://hdl.handle.net/2047/d20004964
► This dissertation considers modeling and identification of nonlinear systems pertinent to loudspeakers with nonlinear distortion effects. It is well known that when loudspeakers are driven…
(more)
▼ This dissertation considers modeling and identification of nonlinear systems pertinent to loudspeakers with nonlinear distortion effects. It is well known that when loudspeakers are driven at high playback levels the nonlinear characteristics of these speakers become a major source of sound degradations. Nonlinear distortion not only diminishes listening pleasure but more importantly impairs speech intelligibility. Consequently it is essential to find a good model that matches to the loudspeaker response for the purpose of predicting and preventing the nonlinear distortion. This becomes particularly important for the purpose of improving sound quality of mobile phones. This report analyzes the loudspeaker operation and provides nonlinear modeling techniques that can reliably be used for its identification process. Frequency domain and state-space modeling are considered and emphasis is given towards model that mix polynomial nonlinear state-space models and fractional order state-space models.
Subjects/Keywords: fractional order systems; loudspeakers; nonlinear systems; polynomial state-space model; system identification; Acoustics, Dynamics, and Controls; Electrical and Computer Engineering
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CSE |
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APA (6th Edition):
Brunet, P. M. (2014). Nonlinear system modeling and identification of loudspeakers. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/d20004964
Chicago Manual of Style (16th Edition):
Brunet, Pascal Maurice. “Nonlinear system modeling and identification of loudspeakers.” 2014. Doctoral Dissertation, Northeastern University. Accessed January 23, 2021.
http://hdl.handle.net/2047/d20004964.
MLA Handbook (7th Edition):
Brunet, Pascal Maurice. “Nonlinear system modeling and identification of loudspeakers.” 2014. Web. 23 Jan 2021.
Vancouver:
Brunet PM. Nonlinear system modeling and identification of loudspeakers. [Internet] [Doctoral dissertation]. Northeastern University; 2014. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2047/d20004964.
Council of Science Editors:
Brunet PM. Nonlinear system modeling and identification of loudspeakers. [Doctoral Dissertation]. Northeastern University; 2014. Available from: http://hdl.handle.net/2047/d20004964
Université de Grenoble
12.
Ben Sassi, Mohamed Amin.
Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems.
Degree: Docteur es, Mathématiques appliquées, 2013, Université de Grenoble
URL: http://www.theses.fr/2013GRENM005
► Cette thèse présente une étude des systèmes dynamiques polynomiaux motivée à la fois par le grand spectre d'applications de cetteclasse (modèles de réactions chimiques, modèles…
(more)
▼ Cette thèse présente une étude des systèmes dynamiques polynomiaux motivée à la fois par le grand spectre d'applications de cetteclasse (modèles de réactions chimiques, modèles de circuits électriques ainsi que les modèles biologiques) et par la difficulté (voire incapacité)de la résolution théorique de tels systèmes. Dans une première partie préliminaire, nous présentons les polynômes multi-variés et nous introduisons les notions de forme polaire d'un polynôme (floraison) et de polynômes de Bernstein qui seront d'un grand intérêt par la suite. Dans une deuxième partie, nous considérons le problème d'optimisation polynomial dit POP. Nous décrivons dans un premier temps les principales méthodes existantes permettant de résoudre ou d'approcher la solution d'un tel problème. Puis, nous présentons deux relaxations linéaires se basant respectivement sur le principe de floraison ainsi que les polynômes de Bernstein permettant d'approcher la valeur optimale du POP. La dernière partie de la thèse sera consacré aux applications de nos deux méthodes de relaxation dans le cadre des systèmes dynamiques polynomiaux. Une première application s'inscrit dans le cadre de l'analyse d'atteignabilité: en effet, on utilisera notre relaxation de Bernsteinpour pouvoir construire un algorithme permettant d'approximer les ensembles atteignables d'un système dynamique polynomial discrétisé. Une deuxième application sera la vérification et le calcul d'invariants pour un système dynamique polynomial. Une troisième application consiste à calculer un contrôleur et un invariant pour un système dynamique polynomial soumis à des perturbations. Dans le contexte de l'invariance, on utilisera la relaxation se basant sur le principe de floraison.Enfin, une dernière application sera d'exploiter les principales propriétés de la forme polaire pour pouvoir étudier des systèmes dynamiques polynomiaux dans des rectangles.
This thesis presents a study of polynomial dynamical systems motivated by both thewide spectrum of applications of this class (chemical reaction models, electrical modelsand biological models) and the difficulty (or inability) of theoretical resolutionof such systems.In a first preliminary part, we present multivariate polynomials and we introducethe notion of polar form of a polynomial (blossoming) and Bernstein polynomialswhich will be of great interest thereafter.In a second part, we consider the polynomial optimization problem said POP.We first describe existing methods allowing us to solve or approximate the solution5TABLE DES MATI`ERES 6of such problems. Then, we present two linear relaxations based respectively on theblossoming principle and the Bernstein polynomials allowing us to approximate theoptimal value of the POP.The last part of the thesis is devoted to applications of the two relaxation methodsin the context of polynomial dynamical systems. A first application is in thecontext of reachability analysis. In fact, we use our Bernstein relaxation in order tobuild an algorithm allowing us to approximate the reachable sets of a…
Advisors/Committee Members: Girard, Antoine (thesis director), James, Guillaume (thesis director).
Subjects/Keywords: Systèmes dynamiques; Optimisation polynomiale; Programmation linéaire; Contrôle; Abstraction; Dynamical systems; Polynomial optimization; Linear programming; Control; Abstraction; 620
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Ben Sassi, M. A. (2013). Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2013GRENM005
Chicago Manual of Style (16th Edition):
Ben Sassi, Mohamed Amin. “Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems.” 2013. Doctoral Dissertation, Université de Grenoble. Accessed January 23, 2021.
http://www.theses.fr/2013GRENM005.
MLA Handbook (7th Edition):
Ben Sassi, Mohamed Amin. “Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems.” 2013. Web. 23 Jan 2021.
Vancouver:
Ben Sassi MA. Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems. [Internet] [Doctoral dissertation]. Université de Grenoble; 2013. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2013GRENM005.
Council of Science Editors:
Ben Sassi MA. Analyse et contrôle des systèmes dynamiques polynomiaux : Analysis and Control of Polynomial Dynamical Systems. [Doctoral Dissertation]. Université de Grenoble; 2013. Available from: http://www.theses.fr/2013GRENM005
Delft University of Technology
13.
Perkó, Z.
Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors.
Degree: 2015, Delft University of Technology
URL: http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
;
urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
;
urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
;
http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
► This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics.…
(more)
▼ This thesis presents novel adjoint and spectral methods for the sensitivity and uncertainty (S&U) analysis of multi-physics problems encountered in the field of reactor physics. The first part focuses on the steady state of reactors and extends the adjoint sensitivity analysis methods well established for pure neutron transport problems to coupled criticality calculations, where feedbacks are present between neutronics and other phenomena (e.g. thermalhydraulics or fission product poisoning). The second part presents novel spectral techniques, namely grid and basis adaptive
Polynomial Chaos (PC) methods for the S&U analysis of generic problems, together with a large scale application of the developed Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm for the sensitivity and uncertainty analysis of a transient. Following a short introduction in Chapter 1 to some of the most frequently used S&U analysis techniques Chapter 2 presents the theory for the adjoint based sensitivity analysis of coupled criticality problems. This enables the computation of first order changes in responses of interest due to variations of both neutronic input parameters (such as cross sections) and those describing augmenting phenomena (e.g. thermal-hydraulics). The chapter also presents a very efficient procedure for calculating the necessary neutronics and augmenting adjoint functions that relies on using Krylov algorithms together with the individual neutron transport and augmenting codes to perform the required matrix-vector multiplications and inversions during preconditioning. As a proof of principle study a one-dimensional slab model is investigated, where two-group diffusion theory is coupled with heat-conduction and xenon-poisoning. In Chapter 3 the larger scale applicability of the coupled adjoint theory is studied. A deeper look into the exact form of the adjoint operators reveals that for the most common cases of coupling neutron transport to thermal-hydraulics and fission product poisoning the effects of the operators can easily be calculated by routines present in the adjoint capable neutron transport and augmenting codes. This enables their reuse with little code modifications, therefore the main challenge lies in the coupling scheme rather than in dedicated code development (once both codes are already suited for solving the individual adjoint problems). As a more realistic application the S&U analysis of a coupled model of an infinite array of fuel pins was performed employing a purpose made thermal-hydraulics code and a general purpose discrete ordinates neutron transport solver. The results confirmed that the preconditioned Krylov algorithm provides excellent performance in calculating the necessary adjoint functions and these properly provide the first order changes of responses of interest due to perturbations in any of the system input parameters. In Chapter 4 the development of novel adaptive
Polynomial Chaos techniques is detailed aimed at the S&U analysis of generic problems. Two types of adaptivity is…
Advisors/Committee Members: Van der Hagen, T.H.J.J..
Subjects/Keywords: sensitivity analysis; uncertainty quantification; adjoint; polynomial chaos; coupled systems
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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APA (6th Edition):
Perkó, Z. (2015). Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
Chicago Manual of Style (16th Edition):
Perkó, Z. “Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors.” 2015. Doctoral Dissertation, Delft University of Technology. Accessed January 23, 2021.
http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c.
MLA Handbook (7th Edition):
Perkó, Z. “Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors.” 2015. Web. 23 Jan 2021.
Vancouver:
Perkó Z. Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors. [Internet] [Doctoral dissertation]. Delft University of Technology; 2015. [cited 2021 Jan 23].
Available from: http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c.
Council of Science Editors:
Perkó Z. Sensitivity and Uncertainty Analysis of Coupled Reactor Physics Problems: Method Development for Multi-Physics in Reactors. [Doctoral Dissertation]. Delft University of Technology; 2015. Available from: http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; urn:NBN:nl:ui:24-uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c ; http://resolver.tudelft.nl/uuid:2a55e581-acc0-4cbf-a8cf-9675986b9a0c
University of Notre Dame
14.
Jonathan David Hauenstein.
Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>.
Degree: Mathematics, 2009, University of Notre Dame
URL: https://curate.nd.edu/show/w3763487g2w
► Algorithms in the field of numerical algebraic geometry provide numerical methods for computing and manipulating solution sets of polynomial systems. One of the main…
(more)
▼ Algorithms in the field of numerical
algebraic geometry provide numerical methods for computing and
manipulating solution sets of
polynomial systems. One of the main
algorithms in this field is the computation of the numerical
irreducible decomposition. This algorithm has three main parts:
computing a witness superset, filtering out the junk points to
create a witness set, and decomposing the witness set into
irreducible components. New and efficient algorithms are presented
in this thesis to address the first two parts, namely regeneration
and a local dimension test. Regeneration is an equation-by-equation
solving method that can be used to efficiently compute a witness
superset for a
polynomial system. The local dimension test
algorithm presented in this thesis is a numerical-symbolic method
that can be used to compute the local dimension at an approximated
solution to a
polynomial system. This test is used to create an
efficient algorithm that filters out the junk points. The
algorithms presented in this thesis are applied to problems arising
in kinematics and partial differential
equations.
Advisors/Committee Members: Charles W. Wampler, Committee Member, Andrew J. Sommese, Committee Chair, Jason McLachlan, Committee Co-Chair, Bei Hu, Committee Member, Chris Peterson, Committee Member.
Subjects/Keywords: regeneration; polynomial systems; numerical algebraic geometry; local dimension; Bertini
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Manager
APA (6th Edition):
Hauenstein, J. D. (2009). Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/w3763487g2w
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Hauenstein, Jonathan David. “Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>.” 2009. Thesis, University of Notre Dame. Accessed January 23, 2021.
https://curate.nd.edu/show/w3763487g2w.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Hauenstein, Jonathan David. “Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>.” 2009. Web. 23 Jan 2021.
Vancouver:
Hauenstein JD. Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>. [Internet] [Thesis]. University of Notre Dame; 2009. [cited 2021 Jan 23].
Available from: https://curate.nd.edu/show/w3763487g2w.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hauenstein JD. Regeneration, local dimension, and applications in numerical
algebraic geometry</h1>. [Thesis]. University of Notre Dame; 2009. Available from: https://curate.nd.edu/show/w3763487g2w
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Lund
15.
Ask, Erik.
Methods for Optimal Model Fitting and Sensor
Calibration.
Degree: 2014, University of Lund
URL: https://lup.lub.lu.se/record/4628179
;
https://portal.research.lu.se/ws/files/3876001/4628235.pdf
► The problem of fitting models to measured data has been studied extensively, not least in the field of computer vision. A central problem in this…
(more)
▼ The problem of fitting models to measured data has
been studied extensively, not least in the field of computer
vision. A central problem in this field is the difficulty in
reliably find corresponding structures and points in different
images, resulting in outlier data. This thesis presents theoretical
results improving the understanding of the connection between model
parameter estimation and possible outlier-inlier partitions of data
point sets. Using these results a multitude of applications can be
analyzed in respects to optimal outlier inlier partitions, optimal
norm fitting, and not least in truncated norm sense. Practical
polynomial time optimal solvers are derived for several
applications, including but not limited to multi-view triangulation
and image registration. In this thesis the problem of sensor
network self calibration is investigated. Sensor networks play an
increasingly important role with the increased availability of
mobile, antenna equipped, devices. The application areas can be
extended with knowledge of the different sensors relative or
absolute positions. We study this problem in the context of
bipartite sensor networks. We identify requirements of solvability
for several configurations, and present a framework for how such
problems can be approached. Further we utilize this framework to
derive several solvers, which we show in both synthetic and real
examples functions as desired. In both these types of model
estimation, as well as in the classical random samples based
approaches minimal cases of polynomial systems play a central role.
A majority of the problems tackled in this thesis will have solvers
based on recent techniques pertaining to action matrix solvers. New
application specific polynomial equation sets are constructed and
elimination templates designed for them. In addition a general
improvement to the method is suggested for a large class of
polynomial systems. The method is shown to improve the
computational speed by significant reductions in the size of
elimination templates as well as in the size of the action
matrices. In addition the methodology on average improves the
numerical stability of the solvers.
Subjects/Keywords: Mathematics; Computer Vision and Robotics (Autonomous
Systems); Model Fitting; Sensor Networks; Computer Vision; Polynomial Equations; Action Matrix Methods
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APA ·
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MLA ·
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CSE |
Export
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Manager
APA (6th Edition):
Ask, E. (2014). Methods for Optimal Model Fitting and Sensor
Calibration. (Doctoral Dissertation). University of Lund. Retrieved from https://lup.lub.lu.se/record/4628179 ; https://portal.research.lu.se/ws/files/3876001/4628235.pdf
Chicago Manual of Style (16th Edition):
Ask, Erik. “Methods for Optimal Model Fitting and Sensor
Calibration.” 2014. Doctoral Dissertation, University of Lund. Accessed January 23, 2021.
https://lup.lub.lu.se/record/4628179 ; https://portal.research.lu.se/ws/files/3876001/4628235.pdf.
MLA Handbook (7th Edition):
Ask, Erik. “Methods for Optimal Model Fitting and Sensor
Calibration.” 2014. Web. 23 Jan 2021.
Vancouver:
Ask E. Methods for Optimal Model Fitting and Sensor
Calibration. [Internet] [Doctoral dissertation]. University of Lund; 2014. [cited 2021 Jan 23].
Available from: https://lup.lub.lu.se/record/4628179 ; https://portal.research.lu.se/ws/files/3876001/4628235.pdf.
Council of Science Editors:
Ask E. Methods for Optimal Model Fitting and Sensor
Calibration. [Doctoral Dissertation]. University of Lund; 2014. Available from: https://lup.lub.lu.se/record/4628179 ; https://portal.research.lu.se/ws/files/3876001/4628235.pdf
University of Lund
16.
Kuang, Yubin.
Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks.
Degree: 2014, University of Lund
URL: https://lup.lub.lu.se/record/4393456
;
https://portal.research.lu.se/ws/files/5374142/4393481.pdf
► Given images of a scene taken by a moving camera or recordings of a moving smart phone playing a song by a microphone array, how…
(more)
▼ Given images of a scene taken by a moving camera or
recordings of a moving smart phone playing a song by a microphone
array, how hard is it to reconstruct the scene structure or the
moving trajectory of the phone? In this thesis, we study and solve
several fundamental geometric problems in order to provide
solutions to these problems. The key underlying technique for
solving such geometric problems is solving systems of polynomial
equations. In this thesis, several general techniques are
developed. We utilize numerical schemes and explore symmetric
structures of polynomial equations to enable fast and stable
polynomial solvers. These enable fast and robust techniques for
reconstruction of the scene structures using different
measurements. One of the examples is structure from sound. By
measuring the time-of-arrivals of specific time instances of a song
played on a phone, one can reconstruct the trajectory of the phone
as well as the positions of the microphones up to precision of
centimeters.
Subjects/Keywords: Computer Vision and Robotics (Autonomous
Systems); Mathematics; polynomial solver; geometric problems; computer vision; sensor networks; symmetry
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APA (6th Edition):
Kuang, Y. (2014). Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks. (Doctoral Dissertation). University of Lund. Retrieved from https://lup.lub.lu.se/record/4393456 ; https://portal.research.lu.se/ws/files/5374142/4393481.pdf
Chicago Manual of Style (16th Edition):
Kuang, Yubin. “Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks.” 2014. Doctoral Dissertation, University of Lund. Accessed January 23, 2021.
https://lup.lub.lu.se/record/4393456 ; https://portal.research.lu.se/ws/files/5374142/4393481.pdf.
MLA Handbook (7th Edition):
Kuang, Yubin. “Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks.” 2014. Web. 23 Jan 2021.
Vancouver:
Kuang Y. Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks. [Internet] [Doctoral dissertation]. University of Lund; 2014. [cited 2021 Jan 23].
Available from: https://lup.lub.lu.se/record/4393456 ; https://portal.research.lu.se/ws/files/5374142/4393481.pdf.
Council of Science Editors:
Kuang Y. Polynomial Solvers for Geometric Problems - Applications
in Computer Vision and Sensor Networks. [Doctoral Dissertation]. University of Lund; 2014. Available from: https://lup.lub.lu.se/record/4393456 ; https://portal.research.lu.se/ws/files/5374142/4393481.pdf
Universidad de Extremadura
17.
García Zapata, Juan Luis.
Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
.
Degree: 2015, Universidad de Extremadura
URL: http://hdl.handle.net/10662/3658
► Los polinomios tienen una larga historia en matemáticas, ciencia e ingeniería. Es conocido que las raíces de polinomios de grado 2, 3 y 4 pueden…
(more)
▼ Los polinomios tienen una larga historia en matemáticas, ciencia e ingeniería. Es conocido que las raíces de polinomios de grado 2, 3 y 4 pueden obtenerse con ciertas fórmulas, y que no existen (usando radicales) para grados superiores. En la práctica se recurre a métodos numéricos para aproximar raíces. Los polinomios que aparecen en aplicaciones científicas y de ingeniería pueden ser de grado superior al centenar, por ejemplo en procesamiento digital de señal .
Los métodos se pueden clasificar en iterativos y geométricos. Los iterativos están basados en una sucesión de estimaciones de error y corrección que conduce a un punto del plano complejo tan cerca de una raíz como se quiera. Estos métodos son rápidos (convergencia más que lineal) y su análisis, es decir, la prueba de su corrección como algoritmo y la determinación de los recursos necesarios, se basa en técnicas numéricas bien conocidas. Por el contrario, los métodos geométricos se basan en la distribución de raíces en el plano complejo. Por ejemplo, acotan el módulo de las raíces, o las separan (es decir, definen regiones del plano que contienen precisamente una raíz).
Sin embargo los métodos iterativos no son fácilmente aplicables en la práctica a los polinomios que aparecen en las aplicaciones de procesamiento de señal. El objetivo de esta tesis es desarrollar, analizar y comparar un método geométrico de cálculo de raíces adecuado para polinomios de alto grado. Se basa en el índice de curvas planas (el número de vueltas).
Advisors/Committee Members: Díaz Martín, Juan Carlos (advisor).
Subjects/Keywords: Aproximación numérica;
Proceso lineal de señal;
Análisis de algoritmos;
Signal and systems;
Polynomial models;
Recursive algorithms
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APA (6th Edition):
García Zapata, J. L. (2015). Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
. (Thesis). Universidad de Extremadura. Retrieved from http://hdl.handle.net/10662/3658
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
García Zapata, Juan Luis. “Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
.” 2015. Thesis, Universidad de Extremadura. Accessed January 23, 2021.
http://hdl.handle.net/10662/3658.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
García Zapata, Juan Luis. “Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
.” 2015. Web. 23 Jan 2021.
Vancouver:
García Zapata JL. Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
. [Internet] [Thesis]. Universidad de Extremadura; 2015. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10662/3658.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
García Zapata JL. Métodos geométricos para aproximar raíces de polinomios, con aplicaciones a procesamiento de señal
. [Thesis]. Universidad de Extremadura; 2015. Available from: http://hdl.handle.net/10662/3658
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
18.
El Hilany, Boulos.
Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems.
Degree: Docteur es, Mathématiques, 2016, Université Grenoble Alpes (ComUE)
URL: http://www.theses.fr/2016GREAM037
► Les systèmes polynomiaux réels sont omniprésents dans de nombreux domaines des mathématiques pures et appliquées. A. Khovanskii a fourni une borne fewnomiale supérieure sur le…
(more)
▼ Les systèmes polynomiaux réels sont omniprésents dans de nombreux domaines des mathématiques pures et appliquées. A. Khovanskii a fourni une borne fewnomiale supérieure sur le nombre de solutions positives non-dégénérées d'un système
polynomial réel de n équations à n variables qui ne dépend que du nombre de monômes apparaissant dans les équations. Cette dernière borne a été récemment améliorée par F. Bihan et F. Sottile, mais la borne résultante peut être encore améliorée, même dans certains cas simples.Le but de ce travail est d'aborder trois problèmes importants dans la théorie des Fewnomials. Considérons une famille de systèmes polynomiaux réels avec une structure donnée (par exemple, support ou le nombre de monômes). Un problème est de trouver de bonnes bornes supérieures pour leurs nombres de solutions réelles (ou positives). Un autre problème est de construire des systèmes dont le nombre de solutions réelles (ou positives) sont proches de la meilleure borne supérieure connue. Lorsqu'une borne supérieure optimale est bien connue, qu'est ce qu'on peut dire dans le cas où elle est atteinte?Dans cette thèse, nous affinons un résultat de M. Avendaño en démontrant que le nombre de points d'intersection réels d'une droite réelle avec une courbe réelle plane définie par un polynôme avec au plus t monômes est soit infini ou ne dépasse pas 6t -7. En outre, on montre que notre borne est optimale pour t=3 en utilisant les dessins d'enfant réels de Grothendieck. Cela montre que le nombre maximal de points d'intersection réels d'une droite réelle avec une courbe trinomiale réelle plane est onze.Nous considérons ensuite le problème de l'estimation du nombre maximal de points d'intersection transverses positifs d'une courbe plane trinomiale et d'une courbe plane t-nomiale. T-Y Li, J.-M. Rojas et X. Wang ont montré que ce nombre est borné par 2 t - 2, et récemment P. Koiran, N. Portier et S. Tavenas ont trouvé la borne supérieure 2t 3/3 +5t. Nous fournissons la borne supérieure 3*2 (t-2) - 1 qui est optimale pour t = 3 et est la plus petite pour t=4,...,9. Ceci est réalisé en utilisant la notion de dessins d'enfant réels. De plus, nous étudions en détail le cas t = 3 et nous donnons une restriction sur les supports des systèmes atteignant la borne optimale cinq.Un circuit est un ensemble de n+ 2 points dans mathbb{R}^n qui sont minimalement affinement dépendants. Il est connu qu'un système supporté sur un circuit a au plus n+1 solutions positives non dégénérées, et que cette borne est optimale. Nous utilisons les dessins d'enfant réels et le patchwork combinatoire de Viro pour donner une caractérisation complète des circuits supportant des systèmes polynomiaux avec le nombre maximal de solutions positives non dégénérées.Nous considérons des systèmes polynomiaux de deux équations à deux variables avec cinq monômes distincts au total. Ceci est l'un des cas les plus simples où la borne supérieure optimale sur le nombre de solutions positives non dégénérées n'est pas connue. F. Bihan et F. Sottile ont prouvé que cette borne…
Advisors/Committee Members: Bihan, Frédéric (thesis director).
Subjects/Keywords: Géométrie Algébrique Réelle; Théorie des Fewnomials; Géométrie Tropicale; Systèmes Polynomiaux; Real Algebraic Geometry; Theory of Fewnomials; Tropical Geometry; Polynomial Systems; 516
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APA ·
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MLA ·
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CSE |
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Manager
APA (6th Edition):
El Hilany, B. (2016). Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2016GREAM037
Chicago Manual of Style (16th Edition):
El Hilany, Boulos. “Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems.” 2016. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed January 23, 2021.
http://www.theses.fr/2016GREAM037.
MLA Handbook (7th Edition):
El Hilany, Boulos. “Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems.” 2016. Web. 23 Jan 2021.
Vancouver:
El Hilany B. Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2016. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2016GREAM037.
Council of Science Editors:
El Hilany B. Géométrie tropicale et systèmes polynomiaux : Tropical geometry and polynomial systems. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2016. Available from: http://www.theses.fr/2016GREAM037
Virginia Tech
19.
Oremland, Matthew Scott.
Optimization and Optimal Control of Agent-Based Models.
Degree: MS, Mathematics, 2011, Virginia Tech
URL: http://hdl.handle.net/10919/78119
► Agent-based models are computer models made up of agents that can exist in a finite number of states. The state of the system at any…
(more)
▼ Agent-based models are computer models made up of agents that can exist in a finite number of states. The state of the system at any given time is determined by rules governing agents' interaction. The rules may be deterministic or stochastic. Optimization is the process of finding a solution that optimizes some value that is determined by simulating the model. Optimal control of an agent-based model is the process of determining a sequence of control inputs to the model that steer the system to a desired state in the most efficient way. In large and complex models, the number of possible control inputs is too large to be enumerated by computers; hence methods must be developed for use with these models in order to find solutions without searching the entire solution space. Heuristic algorithms have been applied to such models with some success. Such algorithms are discussed; case studies of examples from biology are presented. The lack of a standard format for agent-based models is a major issue facing the study of agent-based models; presentation as
polynomial dynamical
systems is presented as a viable option. Algorithms are adapted and presented for use in this framework.
Advisors/Committee Members: Laubenbacher, Reinhard C. (committeechair), Loehr, Nicholas A. (committee member), Zietsman, Lizette (committee member).
Subjects/Keywords: optimization; optimal control; individual-based model; polynomial dynamical system; agent-based model; bioinformatics; heuristic algorithm; discrete model; systems biology
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APA (6th Edition):
Oremland, M. S. (2011). Optimization and Optimal Control of Agent-Based Models. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/78119
Chicago Manual of Style (16th Edition):
Oremland, Matthew Scott. “Optimization and Optimal Control of Agent-Based Models.” 2011. Masters Thesis, Virginia Tech. Accessed January 23, 2021.
http://hdl.handle.net/10919/78119.
MLA Handbook (7th Edition):
Oremland, Matthew Scott. “Optimization and Optimal Control of Agent-Based Models.” 2011. Web. 23 Jan 2021.
Vancouver:
Oremland MS. Optimization and Optimal Control of Agent-Based Models. [Internet] [Masters thesis]. Virginia Tech; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10919/78119.
Council of Science Editors:
Oremland MS. Optimization and Optimal Control of Agent-Based Models. [Masters Thesis]. Virginia Tech; 2011. Available from: http://hdl.handle.net/10919/78119
Virginia Tech
20.
Wise, Steven M.
POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations.
Degree: MS, Mathematics, 1998, Virginia Tech
URL: http://hdl.handle.net/10919/36933
► Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years…
(more)
▼ Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to
polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. This thesis describes the theory behind and performance of the new code POLSYS_PLP, which consists of Fortran 90 modules for finding all isolated solutions of a complex coefficient
polynomial system of equations by a probability-one homotopy method. The package is intended to be used in conjunction with HOMPACK90, and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP)
polynomial system structure. PLP structure is a generalization of m-homogeneous structure, whereby each component of the system can have a different m-homogeneous structure. POLSYS_PLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different PLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.
Advisors/Committee Members: Watson, Layne T. (committeechair), Rossi, John F. (committee member), Beattie, Christopher A. (committee member).
Subjects/Keywords: Numerical Analysis; Homotopy Methods; Polynomial Systems of Equations; Zeros
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APA (6th Edition):
Wise, S. M. (1998). POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/36933
Chicago Manual of Style (16th Edition):
Wise, Steven M. “POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations.” 1998. Masters Thesis, Virginia Tech. Accessed January 23, 2021.
http://hdl.handle.net/10919/36933.
MLA Handbook (7th Edition):
Wise, Steven M. “POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations.” 1998. Web. 23 Jan 2021.
Vancouver:
Wise SM. POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations. [Internet] [Masters thesis]. Virginia Tech; 1998. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10919/36933.
Council of Science Editors:
Wise SM. POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations. [Masters Thesis]. Virginia Tech; 1998. Available from: http://hdl.handle.net/10919/36933
21.
Bender, Matias Rafael.
Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants.
Degree: Docteur es, Informatique, 2019, Sorbonne université
URL: http://www.theses.fr/2019SORUS029
► La résolution de systèmes polynomiaux est l’un des problèmes les plus anciens et importants en mathématiques informatiques et a des applications dans plusieurs domaines des…
(more)
▼ La résolution de systèmes polynomiaux est l’un des problèmes les plus anciens et importants en mathématiques informatiques et a des applications dans plusieurs domaines des sciences et de l’ingénierie. C'est un problème intrinsèquement difficile avec une complexité au moins exponentielle du nombre de variables. Cependant, dans la plupart des cas, les systèmes polynomiaux issus d'applications ont une structure quelconque. Dans cette thèse, nous nous concentrons sur l'exploitation de la structure liée à la faible densité des supports des polynômes; c'est-à-dire que nous exploitons le fait que les polynômes n'ont que quelques monômes à coefficients non nuls. Notre objectif est de résoudre les systèmes plus rapidement que les estimations les plus défavorables, qui supposent que tous les termes sont présents. Nous disons qu'un système creux est non mixte si tous ses polynômes ont le même polytope de Newton, et mixte autrement. La plupart des travaux sur la résolution de systèmes creux concernent le cas non mixte, à l'exception des résultants creux et des méthodes d'homotopie. Nous développons des algorithmes pour des systèmes mixtes. Nous utilisons les résultantes creux et les bases de Groebner. Nous travaillons sur chaque théorie indépendamment, mais nous les combinons également: nous tirons parti des propriétés algébriques des systèmes associés à une résultante non nulle pour améliorer la complexité du calcul de leurs bases de Groebner; par exemple, nous exploitons l’exactitude du complexe de Koszul pour déduire un critère d’arrêt précoce et éviter tout les réductions à zéro. De plus, nous développons des algorithmes quasi-optimaux pour décomposer des formes binaires.
Solving polynomial systems is one of the oldest and most important problems in computational mathematics and has many applications in several domains of science and engineering. It is an intrinsically hard problem with complexity at least single exponential in the number of variables. However, in most of the cases, the polynomial systems coming from applications have some kind of structure. In this thesis we focus on exploiting the structure related to the sparsity of the supports of the polynomials; that is, we exploit the fact that the polynomials only have a few monomials with non-zero coefficients. Our objective is to solve the systems faster than the worst case estimates that assume that all the terms are present. We say that a sparse system is unmixed if all its polynomials have the same Newton polytope, and mixed otherwise. Most of the work on solving sparse systems concern the unmixed case, with the exceptions of mixed sparse resultants and homotopy methods. In this thesis, we develop algorithms for mixed systems. We use two prominent tools in nonlinear algebra: sparse resultants and Groebner bases. We work on each theory independently, but we also combine them to introduce new algorithms: we take advantage of the algebraic properties of the systems associated to a non-vanishing resultant to improve the complexity of computing their Groebner…
Advisors/Committee Members: Faugère, Jean-Charles (thesis director), Tsigaridas, Elias (thesis director).
Subjects/Keywords: Résolution de systèmes polynomiaux; Systèmes polynomiaux creux; Systèmes multi-homogènes; Résultant; Base de Gröbner; Décomposition du tenseur; Solving polynomial systems; Sparse polynomial systems; Multi-homogenous systems; Resultant; Groebner base; Tensor decomposition; 004.0151
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APA (6th Edition):
Bender, M. R. (2019). Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants. (Doctoral Dissertation). Sorbonne université. Retrieved from http://www.theses.fr/2019SORUS029
Chicago Manual of Style (16th Edition):
Bender, Matias Rafael. “Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants.” 2019. Doctoral Dissertation, Sorbonne université. Accessed January 23, 2021.
http://www.theses.fr/2019SORUS029.
MLA Handbook (7th Edition):
Bender, Matias Rafael. “Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants.” 2019. Web. 23 Jan 2021.
Vancouver:
Bender MR. Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants. [Internet] [Doctoral dissertation]. Sorbonne université; 2019. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2019SORUS029.
Council of Science Editors:
Bender MR. Algorithms for sparse polynomial systems : Gröbner bases and resultants : Algorithmes pour les systèmes polynomiaux creux : bases de Gröbner et résultants. [Doctoral Dissertation]. Sorbonne université; 2019. Available from: http://www.theses.fr/2019SORUS029
22.
Nechak, Lyes.
Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems.
Degree: Docteur es, Automatique et Mécanique, 2011, Mulhouse
URL: http://www.theses.fr/2011MULH6253
► Cette thèse traite de l’analyse robuste du comportement dynamique des systèmes frottants. Ces derniers constituent une classe particulière des systèmes non linéaires et sont caractérisés…
(more)
▼ Cette thèse traite de l’analyse robuste du comportement dynamique des systèmes frottants. Ces derniers constituent une classe particulière des systèmes non linéaires et sont caractérisés par des comportements dynamiques très sensibles aux variations des paramètres de conception en particulier aux dispersions des lois de frottement. Cette sensibilité se traduit par des variations qualitatives importantes du comportement dynamique (stabilité, niveaux vibratoire) qui peuvent alors affecter négativement les performances des systèmes frottants. Il est ainsi important, voire indispensable, de pouvoir tenir compte de la dispersion des lois de frottement dans l’étude et l’analyse du comportement dynamique des systèmes frottants afin d’en garantir la robustesse et, dans une perspective plus générale, d’asseoir une démarche de conception robuste des systèmes frottants. Des méthodes spectrales basées sur le concept du chaos polynomial sont proposées dans cette thèse pour traiter de l’analyse robuste du comportement dynamique des systèmes frottants. Pouvant modéliser les fonctions et processus stochastiques, ces méthodes sont adaptées au problème en particulier à l’analyse de la stabilité et à la prédiction des niveaux vibratoires en tenant compte de la dispersion des lois de frottement. Différentes procédures sont proposées et développées pour traiter de ces deux questions. Une efficacité importante a été illustrée à travers l’évaluation des différentes méthodes proposées (chaos polynomial généralisé, chaos polynomial multi-éléments, chaos de Wiener-Haar) en les appliquant sur un exemple de système frottant. En effet, il est montré que ces méthodes offrent une alternative très intéressante à la méthode prohibitive, mais référentielle, de Monte Carlo puisque, pour des niveaux de précision et de confiance similaires, le coût en nombre, en volume et nécessairement en temps de calcul occasionné par les méthodes spectrales sur les différentes analyses (de la stabilité et des niveaux vibratoire) est largement inférieur à celui requis par la technique de Monte Carlo.
This thesis deals with the robust analysis of the dynamic behaviour of dry friction systems. These are a special class of nonlinear systems and are characterized by dynamic behaviors very sensitive to changes in design parameters in particular to dispersions of friction laws. This sensitivity results in important qualitative changes (stability, vibration levels) that can adversely affect the performances of friction systems. It is thus important, even essential, to take account of the dispersion laws of friction in the study and analysis of the dynamic behavior of friction systems in order to ensure robustness and, in a more general perspective, to establish a robust design approach for friction systems. Spectral methods based on the concept of polynomial chaos are proposed in this thesis to address these problems. The spectral methods can model random functions and stochastic processes so they have been adapted to deal with the robust analysis of the dynamic behavior…
Advisors/Committee Members: Aubry-Barottin, Evelyne (thesis director).
Subjects/Keywords: Approches robustes; Chaos polynomial; Chaos multiéléments; Ondelettes de Haar; Systèmes dynamiques; Stabilité et cycle limites; Systèmes frottant; Incertitudes; Robust approaches; Polynomial chaos; Chaos multielements; Haar wavelet; Dynamic systems; Stability and limit cycle; Friction systems; Uncertainties
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APA (6th Edition):
Nechak, L. (2011). Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems. (Doctoral Dissertation). Mulhouse. Retrieved from http://www.theses.fr/2011MULH6253
Chicago Manual of Style (16th Edition):
Nechak, Lyes. “Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems.” 2011. Doctoral Dissertation, Mulhouse. Accessed January 23, 2021.
http://www.theses.fr/2011MULH6253.
MLA Handbook (7th Edition):
Nechak, Lyes. “Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems.” 2011. Web. 23 Jan 2021.
Vancouver:
Nechak L. Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems. [Internet] [Doctoral dissertation]. Mulhouse; 2011. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2011MULH6253.
Council of Science Editors:
Nechak L. Approches robustes du comportement dynamique des systèmes non linéaires : Application aux systèmes frottants : Robust approaches of dynamic behaviour of nonlinear systems : Application to friction systems. [Doctoral Dissertation]. Mulhouse; 2011. Available from: http://www.theses.fr/2011MULH6253
Virginia Tech
23.
Dimitrova, Elena Stanimirova.
Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics.
Degree: PhD, Mathematics, 2006, Virginia Tech
URL: http://hdl.handle.net/10919/28490
► Systems biology aims at system-level understanding of biological systems, in particular cellular networks. The milestones of this understanding are knowledge of the structure of the…
(more)
▼ Systems biology aims at system-level understanding of biological
systems, in particular cellular networks. The milestones of this understanding are knowledge of the structure of the system, understanding of its dynamics, effective control methods, and powerful prediction capability. The complexity of biological
systems makes it inevitable to consider mathematical modeling in order to achieve these goals.
The enormous accumulation of experimental data representing the activities of the living cell has triggered an increasing interest in the reverse engineering of biological networks from data. In particular, construction of discrete models for reverse engineering of biological networks is receiving attention, with the goal of providing a coarse-grained description of such networks. In this dissertation we consider the modeling framework of
polynomial dynamical
systems over finite fields constructed from experimental data. We present and propose solutions to two problems inherent in this modeling method: the necessity of appropriate discretization of the data and the selection of a particular
polynomial model from the set of all models that fit the data.
Data discretization, also known as binning, is a crucial issue for the construction of discrete models of biological networks. Experimental data are however usually continuous, or, at least, represented by computer floating point numbers. A major challenge in discretizing biological data, such as those collected through microarray experiments, is the typically small samples size. Many methods for discretization are not applicable due to the insufficient amount of data. The method proposed in this work is a first attempt to develop a discretization tool that takes into consideration the issues and limitations that are inherent in short data time courses. Our focus is on the two characteristics that any discretization method should possess in order to be used for dynamic modeling: preservation of dynamics and information content and inhibition of noise.
Given a set of data points, of particular importance in the construction of
polynomial models for the reverse engineering of biological networks is the collection of all polynomials that vanish on this set of points, the so-called ideal of points.
Polynomial ideals can be represented through a special finite generating set, known as Gröbner basis, that possesses some desirable properties. For a given ideal, however, the Gröbner basis may not be unique since its computation depends on the choice of leading terms for the multivariate polynomials in the ideal. The correspondence between data points and uniqueness of Gröbner bases is studied in this dissertation. More specifically, an algorithm is developed for finding all minimal sets of points that, added to the given set, have a corresponding ideal of points with a unique Gröbner basis. This question is of interest in itself but the main motivation for studying it was its relevance to the construction of
polynomial dynamical
systems.
This research…
Advisors/Committee Members: Laubenbacher, Reinhard C. (committeechair), Beattie, Christopher A. (committee member), Mendes, Pedro J. P. (committee member), Burns, John A. (committee member).
Subjects/Keywords: Biochemical Networks; Polynomial Rings; Polynomial Dynamical Systems; Gr\"{o}bner Bases; Systems Biology; Discrete Modeling; Data Discretization; Finite Fields
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APA (6th Edition):
Dimitrova, E. S. (2006). Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/28490
Chicago Manual of Style (16th Edition):
Dimitrova, Elena Stanimirova. “Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics.” 2006. Doctoral Dissertation, Virginia Tech. Accessed January 23, 2021.
http://hdl.handle.net/10919/28490.
MLA Handbook (7th Edition):
Dimitrova, Elena Stanimirova. “Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics.” 2006. Web. 23 Jan 2021.
Vancouver:
Dimitrova ES. Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics. [Internet] [Doctoral dissertation]. Virginia Tech; 2006. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10919/28490.
Council of Science Editors:
Dimitrova ES. Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics. [Doctoral Dissertation]. Virginia Tech; 2006. Available from: http://hdl.handle.net/10919/28490
Université de Lorraine
24.
Meddeb Mimouni, Houda.
Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems.
Degree: Docteur es, Automatique, Traitement du signal et des images, Génie informatique, 2017, Université de Lorraine
URL: http://www.theses.fr/2017LORR0149
► Dans ce mémoire, nous avons proposé une nouvelle approche pour la stabilisation des polytopes de systèmes SISO LTI avec un contrôleur d’ordre fixe. En utilisant…
(more)
▼ Dans ce mémoire, nous avons proposé une nouvelle approche pour la stabilisation des polytopes de systèmes SISO LTI avec un contrôleur d’ordre fixe. En utilisant le théorème des segments étendus, nous avons montré que, pour stabiliser un polytope de systèmes LTI, il suffit de stabiliser simultanément tous ses sommets en considérant une condition supplémentaire associée à ces derniers. Nous avons présenté également dans ce mémoire des méthodes originales pour la synthèse des contrôleurs simultanés en combinant les techniques polynomiales et l’optimisation linéaire. Avec les méthodes de synthèse proposées, nous avons montré non seulement que le contrôleur stabilise simultanément les sommets du polytope de systèmes (commande simultanée), mais également tous les systèmes appartenant au polytope (commande robuste). Il s’agit donc de contrôleur simultané et robuste pour les polytopes de systèmes. Avant de pouvoir énoncer des résultats concernant la commande simultanée de l’ensemble des segments d’un polytope de systèmes, nous avons étudié la commande d’un segment de systèmes avec un contrôleur LTI. Ce segment de systèmes est défini par les deux systèmes situés à chacune de ses extrémités et par un paramètre appartenant à un intervalle donné. La question de la stabilisation de cette classe de systèmes incertains a été formulée comme celle d’un problème de commande simultanée de deux systèmes situés aux extrémités avec une contrainte d’égalité des parties paires de chacun des deux polynômes caractéristiques en boucle fermée. Des conditions d’existence d’un régulateur stabilisant un segment de systèmes ont été données en utilisant deux critères de stabilité polynomiaux : le critère d’Hermite-Fujiwara et le critère d’Hermite-Biehler. Les résultats obtenus pour la commande simultanée d’un segment de systèmes ont été étendus à la stabilisation d’un polytope de systèmes. Ce problème a été réduit à la stabilisation des sommets du polytope avec un contrôleur simultané générant des polynômes caractéristiques en boucle fermée ayant la même partie paire (ou impaire). Des conditions d’existence de ces contrôleurs simultanés robustes d’ordre fixe sont données en utilisant les deux critères de stabilité mentionnés ci-dessus. Des algorithmes de synthèse sont également développés pour calculer ces régulateurs
In this manuscript, a new approach is proposed for the stabilization of polytopes of SISO LTI systems with a fixed order controller. Using the extended segment theorem, we have shown that to stabilize a polytope of LTI systems, it is sufficient to simultaneously stabilize all its vertices by considering an additional condition associated with them. In this paper, we have also presented original methods for the synthesis of simultaneous controllers by combining polynomial techniques and linear optimization. With the proposed synthesis methods, we have shown not only that the controller simultaneously stabilizes the vertices of the system polytope (simultaneous control), but also all systems belonging to the polytope (robust control).…
Advisors/Committee Members: Zasadzinski, Michel (thesis director), Fonte, Christophe (thesis director).
Subjects/Keywords: Stabilisation simultanée; Segment de systèmes; Polytope de systèmes; Approche polynomiale; Optimisation linéaire; Simultaneous stabilization; Segment of systems; Polytope of systems; Polynomial approach; Linear optimization; 629.8; 620.001 1
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APA (6th Edition):
Meddeb Mimouni, H. (2017). Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2017LORR0149
Chicago Manual of Style (16th Edition):
Meddeb Mimouni, Houda. “Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems.” 2017. Doctoral Dissertation, Université de Lorraine. Accessed January 23, 2021.
http://www.theses.fr/2017LORR0149.
MLA Handbook (7th Edition):
Meddeb Mimouni, Houda. “Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems.” 2017. Web. 23 Jan 2021.
Vancouver:
Meddeb Mimouni H. Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems. [Internet] [Doctoral dissertation]. Université de Lorraine; 2017. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2017LORR0149.
Council of Science Editors:
Meddeb Mimouni H. Contribution à la commande simultanée des systèmes linéaires : Contribution to simultaneous stabilization of linear systems. [Doctoral Dissertation]. Université de Lorraine; 2017. Available from: http://www.theses.fr/2017LORR0149
25.
Verron, Thibaut.
Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery.
Degree: Docteur es, Informatique, 2016, Université Pierre et Marie Curie – Paris VI
URL: http://www.theses.fr/2016PA066355
► La résolution de systèmes polynomiaux est un problème aux multiples applications, et les bases de Gröbner sont un outil important dans ce cadre. Il est…
(more)
▼ La résolution de systèmes polynomiaux est un problème aux multiples applications, et les bases de Gröbner sont un outil important dans ce cadre. Il est connu que de nombreux systèmes issus d'applications présentent une structure supplémentaire par rapport à des systèmes arbitraires, et que ces structures peuvent souvent être exploitées pour faciliter le calcul de bases de Gröbner.Dans cette thèse, on s'intéresse à deux exemples de telles structures, pour différentes applications. Tout d'abord, on étudie les systèmes homogènes avec poids, qui sont homogènes si on calcule le degré en affectant un poids à chaque variable. Cette structure apparaît naturellement dans de nombreuses applications, dont un problème de cryptographie (logarithme discret). On montre comment les algorithmes existants, efficaces pour les polynômes homogènes, peuvent être adaptés au cas avec poids, avec des bornes de complexité générique divisées par un facteur polynomial en le produit des poids.Par ailleurs, on étudie un problème de classification de racines réelles pour des variétés définies par des déterminants. Ce problème a une application directe en théorie du contrôle, pour l'optimisation de contraste de l'imagerie à résonance magnétique. Ce système particulier s'avère insoluble avec les stratégies générales pour la classification. On montre comment ces stratégies peuvent tirer profit de la structure déterminantielle du système, et on illustre ce procédé en apportant des réponses aux questions posées par le problème d'optimisation de contraste.
Polynomial system solving is a problem with numerous applications, and Gröbner bases are an important tool in this context. Previous studies have shown that systèmes arising in applications usually exhibit more structure than arbitrary systems, and that these structures can be used to make computing Gröbner bases easier.In this thesis, we consider two examples of such structures. First, we study weighted homogeneous systems, which are homogeneous if we give to each variable an arbitrary degree. This structure appears naturally in many applications, including a cryptographical problem (discrete logarithm). We show how existing algorithms, which are efficient for homogeneous systems, can be adapted to a weighted setting, and generically, we show that their complexity bounds can be divided by a factor polynomial in the product of the weights.Then we consider a real roots classification problem for varieties defined by determinants. This problem has a direct application in control theory, for contrast optimization in magnetic resonance imagery. This specific system appears to be out of reach of existing algorithms. We show how these algorithms can benefit from the determinantal structure of the system, and as an illustration, we answer the questions from the application to contrast optimization.
Advisors/Committee Members: Faugère, Jean-Charles (thesis director), Safey El Din, Mohab (thesis director).
Subjects/Keywords: Systèmes polynomiaux; Bases de Gröbner; Systèmes structurés; Systèmes homogènes avec poids; Systèmes déterminantiels; Géométrie réelle; Polynomial systems; Gröbner bases; Structured systems; 518.1
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APA ·
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CSE |
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Verron, T. (2016). Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2016PA066355
Chicago Manual of Style (16th Edition):
Verron, Thibaut. “Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery.” 2016. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed January 23, 2021.
http://www.theses.fr/2016PA066355.
MLA Handbook (7th Edition):
Verron, Thibaut. “Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery.” 2016. Web. 23 Jan 2021.
Vancouver:
Verron T. Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2016. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2016PA066355.
Council of Science Editors:
Verron T. Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale : Regularisation of Gröbner basis computations for weighted and determinantal systems, and application to medical imagery. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2016. Available from: http://www.theses.fr/2016PA066355
26.
Grenet, Bruno.
Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds.
Degree: Docteur es, Informatique, 2012, Lyon, École normale supérieure
URL: http://www.theses.fr/2012ENSL0769
► La complexité algorithmique est l'étude des ressources nécessaires — le temps, la mémoire, … — pour résoudre un problème de manière algorithmique. Dans ce cadre,…
(more)
▼ La complexité algorithmique est l'étude des ressources nécessaires — le temps, la mémoire, … — pour résoudre un problème de manière algorithmique. Dans ce cadre, la théorie de la complexité algébrique est l'étude de la complexité algorithmique de problèmes de nature algébrique, concernant des polynômes.Dans cette thèse, nous étudions différents aspects de la complexité algébrique. D'une part, nous nous intéressons à l'expressivité des déterminants de matrices comme représentations des polynômes dans le modèle de complexité de Valiant. Nous montrons que les matrices symétriques ont la même expressivité que les matrices quelconques dès que la caractéristique du corps est différente de deux, mais que ce n'est plus le cas en caractéristique deux. Nous construisons également la représentation la plus compacte connue du permanent par un déterminant. D'autre part, nous étudions la complexité algorithmique de problèmes algébriques. Nous montrons que la détection de racines dans un système de n polynômes homogènes à n variables est NP-difficile. En lien avec la question « VP = VNP ? », version algébrique de « P = NP ? », nous obtenons une borne inférieure pour le calcul du permanent d'une matrice par un circuit arithmétique, et nous exhibons des liens unissant ce problème et celui du test d'identité polynomiale. Enfin nous fournissons des algorithmes efficaces pour la factorisation des polynômes lacunaires à deux variables.
Computational complexity is the study of the resources — time, memory, …— needed to algorithmically solve a problem. Within these settings, algebraic complexity theory is the study of the computational complexity of problems of algebraic nature, concerning polynomials. In this thesis, we study several aspects of algebraic complexity. On the one hand, we are interested in the expressiveness of the determinants of matrices as representations of polynomials in Valiant's model of complexity. We show that symmetric matrices have the same expressiveness as the ordinary matrices as soon as the characteristic of the underlying field in different from two, but that this is not the case anymore in characteristic two. We also build the smallest known representation of the permanent by a determinant.On the other hand, we study the computational complexity of algebraic problems. We show that the detection of roots in a system of n homogeneous polynomials in n variables in NP-hard. In line with the “VP = VNP ?”question, which is the algebraic version of “P = NP?” we obtain a lower bound for the computation of the permanent of a matrix by an arithmetic circuit, and we point out the links between this problem and the polynomial identity testing problem. Finally, we give efficient algorithms for the factorization of lacunary bivariate polynomials.
Advisors/Committee Members: Koiran, Pascal (thesis director).
Subjects/Keywords: Complexité algébrique; Déterminant; Permanent; Théorie de Valiant; Bornes inférieures; Corps finis; Test d'identité polynomiale; Factorisation; Circuits arithmétiques; Systèmes polynomiaux; Algebraic complexity; Determinant; Permanent; Valiant's theory; Lower bounds; Finite fields; Polynomial identity testing; Factorization; Arithmetic circuits; Polynomial systems
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APA ·
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APA (6th Edition):
Grenet, B. (2012). Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2012ENSL0769
Chicago Manual of Style (16th Edition):
Grenet, Bruno. “Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds.” 2012. Doctoral Dissertation, Lyon, École normale supérieure. Accessed January 23, 2021.
http://www.theses.fr/2012ENSL0769.
MLA Handbook (7th Edition):
Grenet, Bruno. “Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds.” 2012. Web. 23 Jan 2021.
Vancouver:
Grenet B. Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2012. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2012ENSL0769.
Council of Science Editors:
Grenet B. Représentations des polynômes, algorithmes et bornes inférieures : Representations of polynomials, algorithms and lower bounds. [Doctoral Dissertation]. Lyon, École normale supérieure; 2012. Available from: http://www.theses.fr/2012ENSL0769
Indian Institute of Science
27.
Devaraj, G.
Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.
Degree: PhD, Faculty of Engineering, 2017, Indian Institute of Science
URL: http://etd.iisc.ac.in/handle/2005/2719
► This thesis deals with smooth discretization schemes and inverse problems, the former used in efficient yet accurate numerical solutions to forward models required in turn…
(more)
▼ This thesis deals with smooth discretization schemes and inverse problems, the former used in efficient yet accurate numerical solutions to forward models required in turn to solve inverse problems. The aims of the thesis include, (i) development of a stabilization techniques for a class of forward problems plagued by unphysical oscillations in the response due to the presence of jumps/shocks/high gradients, (ii) development of a smooth hybrid discretization scheme that combines certain useful features of Finite Element (FE) and Mesh-Free (MF) methods and alleviates certain destabilizing factors encountered in the construction of shape functions using the
polynomial reproduction method and, (iii) a first of its kind attempt at the joint inversion of both static and dynamic source parameters of the 2004 Sumatra-Andaman earthquake using tsunami sea level anomaly data. Following the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as having two parts, viz., the first part constituting the development and use of smooth discretization schemes in the possible presence of destabilizing factors (Chapters 2 and 3) and the second part involving solution to the inverse problem of tsunami source recovery (Chapter 4).
In the context of stability requirements in numerical solutions of practical forward problems, Chapter 2 develops a new stabilization scheme. It is based on a stochastic representation of the discretized field variables, with a view to reduce or even eliminate unphysical oscillations in the MF numerical simulations of
systems developing shocks or exhibiting localized bands of extreme plastic deformation in the response. The origin of the stabilization scheme may be traced to nonlinear stochastic filtering and, consistent with a class of such filters, gain-based additive correction terms are applied to the simulated solution of the system, herein achieved through the Element-Free Galerkin (EFG) method, in order to impose a set of constraints that help arresting the spurious oscillations. The method is numerically illustrated through its application to a gradient plasticity model whose response is often characterized by a developing shear band as the external load is gradually increased.
The potential of the method in stabilized yet accurate numerical simulations of such
systems involving extreme gradient variations in the response is thus brought forth.
Chapter 3 develops the MF-based discretization motif by balancing this with the widespread adoption of the FE method. Thus it concentrates on developing a 'hybrid' scheme that aims at the amelioration of certain destabilizing algorithmic issues arising from the necessary condition of moment matrix invertibility en route to the generation of smooth shape functions. It sets forth the hybrid discretization scheme utilizing bivariate simplex splines as kernels in a
polynomial reproducing approach adopted over a conventional FE-like domain discretization based on Delaunay…
Advisors/Committee Members: Roy, Debasish (advisor).
Subjects/Keywords: Smooth Discretization; Inverse Geodetic Problems; Strain Gradient Platicity Systems; Polynomial Reproducing Simplex Splines; Earthquake Source Parameters; Sumatra-Andaman Earthquake Source Parameters-2004; Tsunami Source Recovery; Tsunami Numerical Modeling; Polynomial Shape Functions; Mesh Free Method; Finite Element Method; Inverse Problems; Civil Engineering
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APA ·
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APA (6th Edition):
Devaraj, G. (2017). Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2719
Chicago Manual of Style (16th Edition):
Devaraj, G. “Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed January 23, 2021.
http://etd.iisc.ac.in/handle/2005/2719.
MLA Handbook (7th Edition):
Devaraj, G. “Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters.” 2017. Web. 23 Jan 2021.
Vancouver:
Devaraj G. Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Jan 23].
Available from: http://etd.iisc.ac.in/handle/2005/2719.
Council of Science Editors:
Devaraj G. Schemes for Smooth Discretization And Inverse Problems - Case Study on Recovery of Tsunami Source Parameters. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2719
28.
Masucci, Antonia Maria.
Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil.
Degree: Docteur es, Télécommunications (STIC), 2011, Supélec
URL: http://www.theses.fr/2011SUPL0011
► Dans cette thèse, on étudie l'application de la méthode des moments pour les télécommunications. On analyse cette méthode et on montre son importance pour l'étude…
(more)
▼ Dans cette thèse, on étudie l'application de la méthode des moments pour les télécommunications. On analyse cette méthode et on montre son importance pour l'étude des matrices aléatoires. On utilise le cadre de probabilités libres pour analyser cette méthode. La notion de produit de convolution/déconvolution libre peut être utilisée pour prédire le spectre asymptotique de matrices aléatoires qui sont asymptotiquement libres. On montre que la méthode de moments est un outil puissant même pour calculer les moments/moments asymptotiques de matrices qui n'ont pas la propriété de liberté asymptotique. En particulier, on considère des matrices aléatoires gaussiennes de taille finie et des matrices de Vandermonde al ?eatoires. On développe en série entiére la distribution des valeurs propres de differents modèles, par exemple les distributions de Wishart non-centrale et aussi les distributions de Wishart avec des entrées corrélées de moyenne nulle. Le cadre d'inference pour les matrices des dimensions finies est suffisamment souple pour permettre des combinaisons de matrices aléatoires. Les résultats que nous présentons sont implémentés en code Matlab en générant des sous-ensembles, des permutations et des relations d'équivalence. On applique ce cadre à l'étude des réseaux cognitifs et des réseaux à forte mobilité. On analyse les moments de matrices de Vandermonde aléatoires avec des entrées sur le cercle unitaire. On utilise ces moments et les détecteurs à expansion polynomiale pour décrire des détecteurs à faible complexité du signal transmis par des utilisateurs mobiles à une station de base (ou avec deux stations de base) représentée par des réseaux linéaires uniformes.
In this thesis, we focus on the analysis of the moments method, showing its importance in the application of random matrices to wireless communication. This study is conducted in the free probability framework. The concept of free convolution/deconvolution can be used to predict the spectrum of sums or products of random matrices which are asymptotically free. In this framework, we show that the moments method is very appealing and powerful in order to derive the moments/asymptotic moments for cases when the property of asymptotic freeness does not hold. In particular, we focus on Gaussian random matrices with finite dimensions and structured matrices as Vandermonde matrices. We derive the explicit series expansion of the eigenvalue distribution of various models, as noncentral Wishart distributions, as well as correlated zero mean Wishart distributions. We describe an inference framework so flexible that it is possible to apply it for repeated combinations of random ma- trices. The results that we present are implemented generating subsets, permutations, and equivalence relations. We developped a Matlab routine code in order to perform convolution or deconvolution numerically in terms of a set of input moments. We apply this inference framework to the study of cognitive networks, as well as to the study of wireless networks with high mobility. We…
Advisors/Committee Members: Debbah, Mérouane (thesis director).
Subjects/Keywords: Méthode des moments; Matrices aléatoires; Probabilités libres; Systèmes MIMO; Réseaux cognitifs; Convolution/déconvolution; Détecteur à expansion polynomial; Réseaux linéaires uniformes; Moments method; Random matrices; Free probability; MIMO systems; Cognitive networks; Convolution/deconvolution; Polynomial expansion detector; Uniform linear arrays; 378.242
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APA (6th Edition):
Masucci, A. M. (2011). Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil. (Doctoral Dissertation). Supélec. Retrieved from http://www.theses.fr/2011SUPL0011
Chicago Manual of Style (16th Edition):
Masucci, Antonia Maria. “Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil.” 2011. Doctoral Dissertation, Supélec. Accessed January 23, 2021.
http://www.theses.fr/2011SUPL0011.
MLA Handbook (7th Edition):
Masucci, Antonia Maria. “Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil.” 2011. Web. 23 Jan 2021.
Vancouver:
Masucci AM. Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil. [Internet] [Doctoral dissertation]. Supélec; 2011. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2011SUPL0011.
Council of Science Editors:
Masucci AM. Moments method for random matrices with applications to wireless communication. : La méthode des moments pour les matrices aléatoires avec application à la communication sans fil. [Doctoral Dissertation]. Supélec; 2011. Available from: http://www.theses.fr/2011SUPL0011
University of Michigan
29.
Lacy, Seth LaRoe.
System identification.
Degree: PhD, Applied Sciences, 2002, University of Michigan
URL: http://hdl.handle.net/2027.42/129833
► In this dissertation, we present research on identifying Wiener systems with known, noninvertible nonlinearities; on identifying multi-input multi-output nonlinear systems that are linear in unmeasured…
(more)
▼ In this dissertation, we present research on identifying Wiener
systems with known, noninvertible nonlinearities; on identifying multi-input multi-output nonlinear
systems that are linear in unmeasured states; on identifying finite impulse response Wiener
systems with
polynomial nonlinearities; and on guaranteeing stable solutions in the context of subspace identification methods. Wiener
systems consist of a linear dynamic system followed by a static non-linearity. They are often used to model a linear system with a nonlinear sensor. We develop a method for identifying
systems with known, not necessarily invertible, nonlinearities based on the minimization of a nonlinear cost function. Next, we identify multi-input multi-output nonlinear
systems that are linear in unmeasured states. My approach allows for the identification of nonlinear
systems in which the arguments of the system nonlinearities are measured. We write the nonlinearities as a sum of basis functions, and then we simultaneously estimate the coefficients of the basis functions and the linear system. Then we return to the Wiener identification problem and develop a two-stage direct computation approach for the identification of Wiener
systems with finite impulse response and
polynomial nonlinearities. My approach is based on multi-index notation. Finally, we present a method for guaranteeing stability in the context of subspace identification methods for linear
systems. We write the problem as a minimization of a least squares cost function
subject to a convex constraint. The constraint is sufficient to ensure stability, but is not necessary. Existing optimization algorithms can be used to solve the resulting convex optimization problem.
Advisors/Committee Members: Bernstein, Dennis S. (advisor).
Subjects/Keywords: Multi-index Notation; Polynomial Nonlinearity; Subspace Identification; System Identification; Weiner Systems
Record Details
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Record Details
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APA (6th Edition):
Lacy, S. L. (2002). System identification. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/129833
Chicago Manual of Style (16th Edition):
Lacy, Seth LaRoe. “System identification.” 2002. Doctoral Dissertation, University of Michigan. Accessed January 23, 2021.
http://hdl.handle.net/2027.42/129833.
MLA Handbook (7th Edition):
Lacy, Seth LaRoe. “System identification.” 2002. Web. 23 Jan 2021.
Vancouver:
Lacy SL. System identification. [Internet] [Doctoral dissertation]. University of Michigan; 2002. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2027.42/129833.
Council of Science Editors:
Lacy SL. System identification. [Doctoral Dissertation]. University of Michigan; 2002. Available from: http://hdl.handle.net/2027.42/129833
North Carolina State University
30.
Teachey, Angela Lynne.
Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students.
Degree: PhD, Mathematics Education, 2003, North Carolina State University
URL: http://www.lib.ncsu.edu/resolver/1840.16/4836
► This study investigated the achievement of gifted students on mathematics problems that were designed to assess both conceptual and procedural knowledge of polynomial functions, and…
(more)
▼ This study investigated the achievement of gifted students on mathematics problems that were designed to assess both conceptual and procedural knowledge of
polynomial functions, and it attempted to determine the impact of the students? mathematical belief
systems on this achievement. The students were enrolled in a three-week Algebra II course at a summer program for gifted mathematics students. Data sources were belief scales, in-class examinations, and in-depth interviews. Qualitative and quantitative analyses indicated that the students were able to make a variety of connections among concepts related to polynomials and functions, and they easily applied their mathematical knowledge to real world phenomena. The participants suffered, however, from several misconceptions relating to the understanding of the roles of the independent and dependent variables in functions. They also struggled with the concept of symmetry and how it relates to
polynomial functions. Statistical analyses suggested that belief
systems were correlated with achievement, but the conclusions from this study were ambiguous since the correlations were unexpectedly negative. Through its identification of potential conceptual difficulties that gifted students may encounter in their learning of
polynomial functions, this study suggested specific topics that teachers of gifted students should consider when planning their instructional activities.
Advisors/Committee Members: Karen S. Norwood, Ed.D., Committee Chair (advisor).
Subjects/Keywords: polynomial functions; conceptual understanding; mathematical belief systems; gifted education; mathematics education
Record Details
Similar Records
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Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Teachey, A. L. (2003). Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4836
Chicago Manual of Style (16th Edition):
Teachey, Angela Lynne. “Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students.” 2003. Doctoral Dissertation, North Carolina State University. Accessed January 23, 2021.
http://www.lib.ncsu.edu/resolver/1840.16/4836.
MLA Handbook (7th Edition):
Teachey, Angela Lynne. “Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students.” 2003. Web. 23 Jan 2021.
Vancouver:
Teachey AL. Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students. [Internet] [Doctoral dissertation]. North Carolina State University; 2003. [cited 2021 Jan 23].
Available from: http://www.lib.ncsu.edu/resolver/1840.16/4836.
Council of Science Editors:
Teachey AL. Investigations in Conceptual Understanding of Polynomial Functions and the Impact of Mathematical Belief Systems on Achievement in an Accelerated Summer Program for Gifted Students. [Doctoral Dissertation]. North Carolina State University; 2003. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4836
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Open Access Theses and Dissertations