Classification of Temporal Patterns in Dynamic Biological Networks

1998 ◽  
Vol 10 (7) ◽  
pp. 1831-1846 ◽  
Author(s):  
Patrick D. Roberts
Keyword(s):  
Graph Theory ◽  
Metric Space ◽  
Biological Networks ◽  
Temporal Patterns ◽  
State Transitions ◽  
Synaptic Connections ◽  
Functional Differences ◽  
Algebraic Properties ◽  
General Method

A general method is presented to classify temporal patterns generated by rhythmic biological networks when synaptic connections and cellular properties are known. The method is discrete in nature and relies on algebraic properties of state transitions and graph theory. Elements of the set of rhythms generated by a network are compared using a metric that quantifies the functional differences among them. The rhythms are then classified according to their location in a metric space. Examples are given, and biological implications are discussed.

scholarly journals Rule based Classification of Graph Theory Concepts by Use Case Analysis

2016 ◽  
Vol 9 (48) ◽  
Author(s):  
Anuja Bokhare ◽  
P. S. Metkewar ◽  
R. S. Walse
Keyword(s):  
Graph Theory ◽  
Case Analysis ◽  
Use Case ◽  
Rule Based

scholarly journals Analysis of Spatial Patterns of Phase in Neocortical Gamma EEGs in Rabbit

2000 ◽  
Vol 84 (3) ◽  
pp. 1266-1278 ◽  
Author(s):  
Walter J. Freeman ◽  
John M. Barrie
Keyword(s):  
Spatial Coherence ◽  
Sensory Information ◽  
State Transitions ◽  
Wave Form ◽  
Conditioned Stimuli ◽  
Phase Gradient ◽  
Gamma Range ◽  
Sensory Cortices ◽  
Half Power

Arrays of 64 electrodes (8 × 8, 7 × 7 mm) were implanted epidurally on the surface of the visual, auditory or somatosensory cortex of rabbits trained to discriminate conditioned stimuli in the corresponding modality. The 64 electroencephalographic (EEG) traces at all times displayed a high degree of spatial coherence in wave form, averaging >90% of the variance in the largest principal components analysis component. The EEGs were decomposed with the fast Fourier transform (FFT) to give the spatial distributions of amplitude and phase modulation (AM and PM) in segments 128 ms in duration. Spatial (2-dimensional) and temporal (1-dimensional) filters were designed to optimize classification of the spatial AM patterns in the gamma range (20–80 Hz) with respect to discriminative conditioned stimuli. No evidence was found for stimulus-dependent classification of the spatial PM patterns. Instead some spatial PM distributions conformed to the pattern of a cone. The location and sign (maximal lead or lag) of the conic apex varied randomly with each recurrence. The slope of the phase gradient varied in a range corresponding to that of the conduction velocities reported of axons to extend parallel to the cortical surfaces. The durations and times of recurrence of the phase cones corresponded to those of the optimally classified spatial AM patterns. The interpretation is advanced that the phase cones are manifestations of state transitions in the mesoscopic dynamics of sensory cortices by which the intermittent AM patterns are formed. The phase cones show that the gamma EEG spatial coherence is not due to volume conduction from a single deep-lying dipole generator nor to activity at the site of the reference lead on monopolar recording. The random variation of the apical sign shows that gamma AM patterns are self-organized and are not imposed by thalamic pacemakers. The half-power radius of the phase gradient provides a useful measure of the soft boundary condition for the formation and read-out of cooperative cortical domains responsible for binding sensory information into the context of prior experience in the process of perception.

scholarly journals Graph Theory-Based Characterization and Classification of Household Photovoltaics

2021 ◽  
Vol 11 (22) ◽  
pp. 10999
Author(s):  
Jesús M. Ceresuela ◽  
Daniel Chemisana ◽  
Nacho López
Keyword(s):  
Graph Theory ◽  
Power Production ◽  
Expected Value ◽  
Maximum Power ◽  
Solar Panels ◽  
Zero Energy ◽  
Photovoltaic Panel ◽  
Clear Goal ◽  
Zero Energy Buildings

With the clear goal of improving photovoltaic (PV) technology performance towards nearly-zero energy buildings, a graph theory-based model that characterizes photovoltaic panel structures is developed. An algorithm to obtain all possible configurations of a given number of PV panels is presented and the results are exposed for structures using 3 to 7 panels. Two different classifications of all obtained structures are carried out: the first one regarding the maximum power they can produce and the second according to their capability to produce energy under a given probability that the solar panels will fail. Finally, both classifications are considered simultaneously through the expected value of power production. This creates structures that are, at the same time, reliable and efficient in terms of production. The parallel associations turn out to be optimal, but some other less expected configurations prove to be rated high.

scholarly journals Classification of mini-dimmings associated with extreme ultraviolet eruptions by using graph theory

2016 ◽  
Vol 16 (2) ◽  
pp. 217-223
Author(s):  
S Bazargan ◽  
H Safari ◽  
H Kaashisaaz ◽  
◽  
◽  
...  
Keyword(s):  
Graph Theory ◽  
Extreme Ultraviolet

Introduction

2021 ◽  
pp. 1-36
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Biological Networks ◽  
Real Life ◽  
Scale Free ◽  
Graph Theoretic ◽  
Life Problems ◽  
Scale Free Networks ◽  
Web Graph ◽  
The Web

This chapter gives a brief overview of selected applications of graph theory, many of which gave rise to the development of graph theory itself. A range of such applications extends from puzzles and games to serious scientific and real-life problems, thus illustrating the diversity of applications. The first section is devoted to the six earliest applications of graph theory. The next section introduces so-called scale-free networks, which include the web graph, social and biological networks. The last section describes a number of graph-theoretic algorithms, which can be used to tackle a number of interesting applications and problems of graph theory.

Protein Interactions for Functional Genomics

2012 ◽  
Vol 3 (4) ◽  
pp. 15-30
Author(s):  
Pablo Minguez ◽  
Joaquin Dopazo
Keyword(s):  
Graph Theory ◽  
Protein Interactions ◽  
Biological Networks ◽  
State Of The Art ◽  
Protein Protein Interactions ◽  
Pairwise Interactions ◽  
Novel Approach ◽  
Functional Profiling ◽  
Available Resources

Here the authors review the state of the art in the use of protein-protein interactions (ppis) within the context of the interpretation of genomic experiments. They report the available resources and methodologies used to create a curated compilation of ppis introducing a novel approach to filter interactions. Special attention is paid in the complexity of the topology of the networks formed by proteins (nodes) and pairwise interactions (edges). These networks can be studied using graph theory and a brief introduction to the characterization of biological networks and definitions of the more used network parameters is also given. Also a report on the available resources to perform different modes of functional profiling using ppi data is provided along with a discussion on the approaches that have typically been applied into this context. They also introduce a novel methodology for the evaluation of networks and some examples of its application.

scholarly journals On the maximal connected algebraic subgroups of the Cremona group I

1982 ◽  
Vol 88 ◽  
pp. 213-246 ◽  
Author(s):  
Hiroshi Umemura
Keyword(s):  
Cremona Group ◽  
Group I ◽  
Group Ii ◽  
General Method

This paper is a continuation of the two preceding papers [12], [13] where the classification of the de Jonquières type subgroups in the Cremona group of 3 variables is promised. However the classification of such subgroups is postponed until the article in preparation “On the maximal connected algebraic subgroups of the Cremona group II”. The purpose of this paper is to establish a general method to study algebraic subgroups in the Cremona group of n variables and to illustrate how it works and leads to the classification of Enriques (Theorem (2.25)) when applied to the 2 variable case. This method gives us also the classification of the maximal connected algebraic subgroups of the Cremona group of 3 variables.

Sign in / Sign up

Export Citation Format

Share Document