Information-Geometric Measure for Neural Spikes

2002 ◽  
Vol 14 (10) ◽  
pp. 2269-2316 ◽  
Author(s):  
Hiroyuki Nakahara ◽  
Shun-ichi Amari
Keyword(s):  
Information Geometry ◽  
Higher Order ◽  
Neural Firing ◽  
Firing Patterns ◽  
Neural Spikes ◽  
Geometric Measure ◽  
Leibler Divergence ◽  
Novel Method ◽  
Account Information ◽  
Spike Firing

This study introduces information-geometric measures to analyze neural firing patterns by taking not only the second-order but also higher-order interactions among neurons into account. Information geometry provides useful tools and concepts for this purpose, including the orthogonality of coordinate parameters and the Pythagoras relation in the Kullback-Leibler divergence. Based on this orthogonality, we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders. As a result, purely pairwise, triple-wise, and higher-order interactions are singled out. We also demonstrate the benefits of our proposal by using several examples.

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

2009 ◽  
Vol 19 (02) ◽  
pp. 453-485 ◽  
Author(s):  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
LI LI ◽  
YULIN XU ◽  
HONGJV LIU ◽  
...  
Keyword(s):  
Time Series ◽  
Limit Cycle ◽  
Stochastic Dynamics ◽  
Nonlinear Time Series ◽  
Special Importance ◽  
Neuronal System ◽  
Neural Firing ◽  
Firing Patterns ◽  
Theoretical Simulation ◽  
Definition Of

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

scholarly journals Distributions of Hyper-Local Configuration Elements to Characterize, Compare, and Assess Landscape-Level Spatial Patterns

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 420
Author(s):  
Tarmo K. Remmel
Keyword(s):  
A Priori ◽  
Simulated Data ◽  
Generic Model ◽  
Regular Grid ◽  
First Order ◽  
Local Configuration ◽  
Leibler Divergence ◽  
Common Framework ◽  
Novel Method ◽  
The Many

Even with considerable attention in recent decades, measuring and working with patterns remains a complex task due to the underlying dynamic processes that form these patterns, the influence of scales, and the many further implications stemming from their representation. This work scrutinizes binary classes mapped onto regular grids and counts the relative frequencies of all first-order configuration components and then converts these measurements into empirical probabilities of occurrence for either of the two landscape classes. The approach takes into consideration configuration explicitly and composition implicitly (in a common framework), while the construction of a frequency distribution provides a generic model of landscape structure that can be used to simulate structurally similar landscapes or to compare divergence from other landscapes. The technique is first tested on simulated data to characterize a continuum of landscapes across a range of spatial autocorrelations and relative compositions. Subsequent assessments of boundary prominence are explored, where outcomes are known a priori, to demonstrate the utility of this novel method. For a binary map on a regular grid, there are 32 possible configurations of first-order orthogonal neighbours. The goal is to develop a workflow that permits patterns to be characterized in this way and to offer an approach that identifies how relatively divergent observed patterns are, using the well-known Kullback–Leibler divergence.

scholarly journals A Novel Method for Predicting Disease-Associated LncRNA-MiRNA Pairs Based on the Higher-Order Orthogonal Iteration

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Zhanwei Xuan ◽  
Xiang Feng ◽  
Jingwen Yu ◽  
Pengyao Ping ◽  
Haochen Zhao ◽  
...  
Keyword(s):  
Higher Order ◽  
System Level ◽  
Cell Proliferation And Differentiation ◽  
Proliferation And Differentiation ◽  
Great Insight ◽  
Novel Method ◽  
Global And Local ◽  
Novel Model ◽  
Insight Into ◽  
Orthogonal Iteration

A lot of research studies have shown that many complex human diseases are associated not only with microRNAs (miRNAs) but also with long noncoding RNAs (lncRNAs). However, most of the current existing studies focus on the prediction of disease-related miRNAs or lncRNAs, and to our knowledge, until now, there are few literature studies reported to pay attention to the study of impact of miRNA-lncRNA pairs on diseases, although more and more studies have shown that both lncRNAs and miRNAs play important roles in cell proliferation and differentiation during the recent years. The identification of disease-related genes provides great insight into the underlying pathogenesis of diseases at a system level. In this study, a novel model called PADLMHOOI was proposed to predict potential associations between diseases and lncRNA-miRNA pairs based on the higher-order orthogonal iteration, and in order to evaluate its prediction performance, the global and local LOOCV were implemented, respectively, and simulation results demonstrated that PADLMHOOI could achieve reliable AUCs of 0.9545 and 0.8874 in global and local LOOCV separately. Moreover, case studies further demonstrated the effectiveness of PADLMHOOI to infer unknown disease-related lncRNA-miRNA pairs.

Analysis of Firing Patterns in Single Neurons

Science ◽  
1960 ◽  
Vol 131 (3416) ◽  
pp. 1811-1812 ◽  
Author(s):  
George L. Gerstein
Keyword(s):  
Spontaneous Activity ◽  
Digital Computer ◽  
High Speed ◽  
High Sensitivity ◽  
Single Neurons ◽  
Neural Firing ◽  
Firing Patterns ◽  
Stimulus Response

The use of a high-speed digital computer for investigation of neural firing patterns is described. The high sensitivity of the method permits detection of stimulus-response relations buried in a background of spontaneous activity.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

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