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You searched for subject:( zero norm). Showing records 1 – 3 of 3 total matches.

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1. Jain, Vibhor. Zero-norm optimization: Models and applications.

Degree: Industrial Engineering, 2010, Texas Tech University

A zero-norm optimization model is a mathematical program in which one either minimizes or restricts the number of certain sets of variables to being non-zero. Zero-norm optimization arises in various applications, such as compressive sensing, metabolic engineering, portfolio optimization and data mining. In these examples we find the most common form of zero-norm optimization: we minimize or restrict the number of allowed activities by minimizing or restricting the number of the respective {\em activity variables} that are allowed to being non-zero. In this thesis we study recent applications of zero-norm and models related to these optimization problems. We first discuss the applications and thereafter study the problem statement of the applications. Once the problem statement is understood we then see how the zero-norm model can be tackled to solve the problem. Advisors/Committee Members: Farias, Ismael R. d. (Committee Chair), Matis, Timothy I. (committee member), Simonton, James L. (committee member).

Subjects/Keywords: Zero-norm; NP-hard constraints

…the vector x. The zero-norm of the vector x, x 0 , is also called the support or the… …problem of minimizing the zero-norm of the decision variables vector, subject to a number of… …constraints, has become of great importance. The zero-norm minimization drifts, for example, in… …of zero-norm optimization. Specifically, we review the use of zero-norm optimization in: 1… …Vibhor Jain, Dec 2010 4. Data Mining and Statistics. Zero-norm with signal processing, more… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Jain, V. (2010). Zero-norm optimization: Models and applications. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/ETD-TTU-2010-12-1056

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):

Jain, Vibhor. “Zero-norm optimization: Models and applications.” 2010. Thesis, Texas Tech University. Accessed April 11, 2021. http://hdl.handle.net/2346/ETD-TTU-2010-12-1056.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Jain, Vibhor. “Zero-norm optimization: Models and applications.” 2010. Web. 11 Apr 2021.

Vancouver:

Jain V. Zero-norm optimization: Models and applications. [Internet] [Thesis]. Texas Tech University; 2010. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/2346/ETD-TTU-2010-12-1056.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jain V. Zero-norm optimization: Models and applications. [Thesis]. Texas Tech University; 2010. Available from: http://hdl.handle.net/2346/ETD-TTU-2010-12-1056

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Adam, Stavros. Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς.

Degree: 2016, University of Patras; Πανεπιστήμιο Πατρών

This dissertation deals with the development of methods and algorithms offering reliable neural computation. An important part of the research has focused on providing the necessary theoretical basis for these developments. More specifically, research in this thesis focuses on handling uncertainty issues inherent in the data processing, that is, the algorithms used in neural computing. The questions that highlight and qualify the uncertainty in the data processing level are related to matters such as, the initial and boundary values of the algorithms, the robustness of the algorithms against computation or data errors, the multitude of heuristics which substitute mathematical modeling of unknown parameters etc. For modeling and resolving issues such as the above, we, mainly, adopted concepts and methods of Interval Analysis. We also used mathematical approaches such as global optimization and the zero norm of a vector. For specific analysis purposes we used clustering and data mining techniques. In this thesis we study neural networks such as multi-layer perceptrons. Formulation of reliable algorithms implies dealing with uncertainty on matters such as the following: a) initialization of synaptic weights, b) optimization of the network architecture, c) determining the search space where a global minimizer is located for the global optimization procedure when training a network, and d) reliable estimation of a neural network’s domain of validity.

Το αντικείμενο της διδακτορικής διατριβής αϕορά στην ανάπτυξη και στη θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς. Ένα σημαντικό τμήμα της διατριβής είναι αφιερωμένο στη μαθηματική θεμελίωση των μεθόδων. Ειδικότερα, η διατριβή εστιάζει στη διαχείριση της αβεβαιότητας που είναι σύμϕυτη με την επεξεργασία των δεδομένων δηλαδή με τους αλγορίθμους επεξεργασίας. Τα ζητήματα που αναδεικνύουν και χαρακτηρίζουν την αβεβαιότητα σε επίπεδο επεξεργασίας των δεδομένων σχετίζονται με τις αρχικές και τις οριακές τιμές των αλγορίθμων, τη σθεναρότητα των αλγορίθμων σε σϕάλματα των υπολογισμών ή των δεδομένων, την πληθώρα των ευρετικών που υποκαθιστούν τη μαθηματική μοντελοποίηση άγνωστων παραμέτρων κλπ. Για τη μοντελοποίηση και την επίλυση ζητημάτων, όπως τα ανωτέρω, χρησιμοποιήθηκαν κύρια οι έννοιες και οι μέθοδοι της Ανάλυσης Διαστημάτων καθώς και μαθηματικές προσεγγίσεις όπως η ολική βελτιστοποίηση και η μηδενική στάθμη διανυσμάτων. Επί πλέον, αξιοποιήθηκαν κάποιες τεχνικές ομαδοποίησης και εξόρυξης δεδομένων για συγκεκριμένες περιπτώσεις ανάλυσης δεδομένων. Στα πλαίσια της διατριβής μελετώνται, κυρίως, πολυστρωματικά δίκτυα τύπου perceptron. Η διατύπωση αξιόπιστων αλγορίθμων σχετίζεται με τη διαχείριση της αβεβαιότητας στα ακόλουθα ζητήματα: α) αρχικοποίηση των συναπτικών βαρών, β) βελτιστοποίηση της σχεδίασης του δικτύου, γ) καθορισμός του χώρου εντός του οποίου εγγυημένα βρίσκεται κάποιος ολικός ελάχιστοποιητής της συνάρτησης κόστους της εξόδου του δικτύου, και δ) αξιόπιστη εκτίμηση του πεδίου εγκυρότητας ενός δικτύου.

Subjects/Keywords: Νευρωνικοί υπολογισμοί; Υπολογιστική νοημοσύνη; Αλγόριθμοι; Αξιόπιστοι αλγόριθμοι και υπολογισμοί; Ανάλυση διαστημάτων; Νοημοσύνη σμήνους; Νευρωνικά δίκτυα; Ομαδοποίηση δεδομένων; Δίκτυα Kohonen; Πολυστρωματικά δίκτυα perceptron; Αρχικοποίηση συναπτικών βαρών; Διευθέτηση πολυπλοκότητας; Μηδενική στάθμη; Καθολική βελτιστοποίηση; ΕΚΠΑΙΔΕΥΣΗ ΝΕΥΡΩΝΙΚΩΝ ΔΙΚΤΥΩΝ; Αντιστροφή νευρωνικών δικτύων; Στατιστική ανάλυση δεδομένων; Reliable algorithms and computations; Interval analysis; Swarm intelligence; Neural networks; Clustering; Kohonen networks; Multilayer perceptrons; Complexity regularization; Zero norm; Global optimization; NEURAL NETWORK TRAINING; Neural network inversion; Statistical data analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Adam, S. (2016). Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς. (Thesis). University of Patras; Πανεπιστήμιο Πατρών. Retrieved from http://hdl.handle.net/10442/hedi/38490

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):

Adam, Stavros. “Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς.” 2016. Thesis, University of Patras; Πανεπιστήμιο Πατρών. Accessed April 11, 2021. http://hdl.handle.net/10442/hedi/38490.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Adam, Stavros. “Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς.” 2016. Web. 11 Apr 2021.

Vancouver:

Adam S. Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς. [Internet] [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2016. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10442/hedi/38490.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Adam S. Ανάπτυξη και θεμελίωση μεθόδων για αξιόπιστους νευρωνικούς υπολογισμούς. [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2016. Available from: http://hdl.handle.net/10442/hedi/38490

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of Otago

3. Lee, Au-Chen. Dipolar Bose-Einstein Condensate with a Vortex .

Degree: University of Otago

We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes. Advisors/Committee Members: Blakie, Blair (advisor).

Subjects/Keywords: Bose-einstein condensates; BEC; nonlinear; condensate; Gross-Pitaevskii; nonlinear Schrödinger equation; vortices; Collective excitations; vortex self-bound droplets; dipolar BEC; dipolar quantum; quantum fluctuations; Bogoliubov-de Gennes; instability; quadrupolar modes; dynamical stability; dipole interaction; density approximation; dipolar Bose-Einstein condensate; quasi-particle excitations; vortex; Hankel Transformation; Bessel function; cosine transformation; Cylindrical; BdG; Bogoliubov-de Gennes Equation; numerical calculations; DDI; dipole-dipole interactions; phonon dispersion; dynamical instability; eigenvalue problem; eigenvector; imaginary time evolution; laplacian operator; GPE; Gross–Pitaevskii equation; zero-norm; Kohn modes; Bessel grid; DDIs; numerical techniques; dipolar; dipolar BECs; LHY term; local density treatment; vortex stationary states; Kelvin wave (helical) excitations; stabilized from collapse; quasi-particle; leading order quantum fluctuation correction; lanthanides dysprosium; dysprosium; Dy; s-wave interaction; many-body physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lee, A. (n.d.). Dipolar Bose-Einstein Condensate with a Vortex . (Masters Thesis). University of Otago. Retrieved from http://hdl.handle.net/10523/9254

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Chicago Manual of Style (16th Edition):

Lee, Au-Chen. “Dipolar Bose-Einstein Condensate with a Vortex .” Masters Thesis, University of Otago. Accessed April 11, 2021. http://hdl.handle.net/10523/9254.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

MLA Handbook (7th Edition):

Lee, Au-Chen. “Dipolar Bose-Einstein Condensate with a Vortex .” Web. 11 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

Lee A. Dipolar Bose-Einstein Condensate with a Vortex . [Internet] [Masters thesis]. University of Otago; [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10523/9254.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Council of Science Editors:

Lee A. Dipolar Bose-Einstein Condensate with a Vortex . [Masters Thesis]. University of Otago; Available from: http://hdl.handle.net/10523/9254

Note: this citation may be lacking information needed for this citation format:
No year of publication.

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