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1. A.G. Zippo. NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS.

Degree: 2010, Università degli Studi di Milano

URL: http://hdl.handle.net/2434/150077

Neuronal cells (neurons) mainly transmit signals by action potentials or spikes. Neuronal electrical activity is recorded from experimental animals by microelectrodes placed in specific brain areas. These electrochemical fast phenomena occur as all-or-none events and can be analyzed as boolean sequences. Following this approach, several computational analyses reported most variable neuronal behaviors expressed through a large variety of firing patterns. These patterns have been modeled as symbolic strings with a number of different techniques. As a rule, single neurons or neuronal ensembles are manageable as unknown discrete symbol sources S = <Σ, P> where Σ is the source alphabet
and P is the unknown symbol probability distribution.
Within the hierarchy of Markov Models (MMs), Markov Chains and Hidden MMs have been profusely employed to model neuronal recording data. However, due to the highly complex dynamic profiles of single neuron (SN) and neuronal ensemble (NE) firing patterns, those models failed to capture biologically relevant dynamical features. K-Order MMs could overcome these failures,
but their time and space computational complexity turned them into unfeasibility. Variable Order MMs (VOMMs) meet with these restrictions confining modeling to the effective symbols of a given sequence up to a D maximum order. Formally a VOMM is characterized by a couple s, D where s ∈ Σ^∗ is the training sequence and the returned P is an estimation of P from source S. Given an arbitrary finite sequence s ∈ Σ^∗ , delivered by a generic source S, a VOMM builds a structure for S. Once a structure has been captured (or learnt) it may undergo tasks like prediction or compression or, again, analysis. Thus, a lossless compression algorithm originated from a VOMM can perform prediction tasks and every prediction algorithm can perform compression tasks.
Statistically Based Compression Algorithms (SBCAs) build a prefix tree to estimate the symbol probability by combining conditional probability of a symbol with a chain rule, given d previous symbols (d ≤ D). In particular, just on the track of previously discussed issues, I took into consideration three SBCAs: Prediction by Partial Matching (PPM), Context-Tree Weighting (CTW) and Probabilistic Suffix Tree (PST).
Prediction capability of these algorithms can be exploited in at least two ways: i)
to draw a similarity function between experiments and ii) to analyze the changes
of stationary phase of specific experiment dynamics from SN or NE datasets.
The predictive accuracy can be measured by functions like the average log-loss
(self-information). The average log-loss function measures the average compression rate of s assuming its P distribution and so the P prediction accuracy.
Once the VOMM is trained with a given sequence source A, the average log-loss between the obtained VOMM model and another arbitrary sequence source B approximates their similarity measure μ(A, B). Where the sequences represent whole recording experiments, the VOMMs identify the similarity between…
*Advisors/Committee Members: tutor: Bruno Apolloni, relatore: Gabriele E.M. Biella, coordinatore: Vincenzo Capasso, APOLLONI, BRUNO, CAPASSO, VINCENZO.*

Subjects/Keywords: Variable Order Markov Models; Neuronal signals; Lossless Compression Algorithms; Cortical Spontaneous Activity; Chronic Pain; Settore INF/01 - Informatica; Settore ING-INF/05 - Sistemi di Elaborazione delle Informazioni; Settore ING-INF/06 - Bioingegneria Elettronica e Informatica

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APA (6^{th} Edition):

Zippo, A. (2010). NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS. (Thesis). Università degli Studi di Milano. Retrieved from http://hdl.handle.net/2434/150077

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Zippo, A.G.. “NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS.” 2010. Thesis, Università degli Studi di Milano. Accessed November 18, 2019. http://hdl.handle.net/2434/150077.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Zippo, A.G.. “NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS.” 2010. Web. 18 Nov 2019.

Vancouver:

Zippo A. NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS. [Internet] [Thesis]. Università degli Studi di Milano; 2010. [cited 2019 Nov 18]. Available from: http://hdl.handle.net/2434/150077.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zippo A. NEURONAL ENSEMBLE MODELING AND ANALYSIS WITH VARIABLE ORDER MARKOV MODELS. [Thesis]. Università degli Studi di Milano; 2010. Available from: http://hdl.handle.net/2434/150077

Not specified: Masters Thesis or Doctoral Dissertation