Approximation of Large Probabilistic Networks by Structured Population Protocols

2013 ◽  
pp. 199-210
Author(s):  
Michel de Rougemont ◽  
Mathieu Tracol
Keyword(s):  
Probabilistic Networks ◽  
Population Protocols ◽  
Structured Population

Causal Probabilistic Network and Power Spectral Estimation Used in Sleep Stage Classification

1997 ◽  
Vol 36 (04/05) ◽  
pp. 41-46
Author(s):  
A. Kjaer ◽  
W. Jensen ◽  
T. Dyrby ◽  
L. Andreasen ◽  
J. Andersen ◽  
...  
Keyword(s):  
Sleep Stage ◽  
Spectral Estimation ◽  
Interrater Agreement ◽  
Probabilistic Networks ◽  
Probabilistic Network ◽  
Spectral Bands ◽  
Power Spectral ◽  
Stage Classification ◽  
Sleep Stage Classification ◽  
The Brain

Abstract.A new method for sleep-stage classification using a causal probabilistic network as automatic classifier has been implemented and validated. The system uses features from the primary sleep signals from the brain (EEG) and the eyes (AOG) as input. From the EEG, features are derived containing spectral information which is used to classify power in the classical spectral bands, sleep spindles and K-complexes. From AOG, information on rapid eye movements is derived. Features are extracted every 2 seconds. The CPN-based sleep classifier was implemented using the HUGIN system, an application tool to handle causal probabilistic networks. The results obtained using different training approaches show agreements ranging from 68.7 to 70.7% between the system and the two experts when a pooled agreement is computed over the six subjects. As a comparison, the interrater agreement between the two experts was found to be 71.4%, measured also over the six subjects.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

Causal Probabilistic Networks With Learning: A Diagnosis Decisional Tool

1994 ◽  
Vol 4 (1) ◽  
pp. 31-52 ◽  
Author(s):  
F. Casciati ◽  
L. Faravelli
Keyword(s):  
Probabilistic Networks

scholarly journals Towards efficient verification of population protocols

2021 ◽  
Author(s):  
Michael Blondin ◽  
Javier Esparza ◽  
Stefan Jaax ◽  
Philipp J. Meyer
Keyword(s):  
Linear Constraints ◽  
Computational Power ◽  
High Complexity ◽  
Reachability Problem ◽  
Population Protocols ◽  
Finite State ◽  
State Agents ◽  
Efficient Verification ◽  
Primitive Recursive ◽  
Very High

AbstractPopulation protocols are a well established model of computation by anonymous, identical finite-state agents. A protocol is well-specified if from every initial configuration, all fair executions of the protocol reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is -hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class $${ WS}^3$$ WS 3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that $${ WS}^3$$ WS 3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for $${ WS}^3$$ WS 3 reduce to solving boolean combinations of linear constraints over $${\mathbb {N}}$$ N . This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.

scholarly journals A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽  
1974 ◽  
Vol 76 (2) ◽  
pp. 367-377
Author(s):  
Takeo Maruyama
Keyword(s):  
Genetic Variation ◽  
Markov Process ◽  
Diffusion Process ◽  
Gene Frequency ◽  
Transition Probabilities ◽  
Large Population ◽  
Sample Path ◽  
Time Parameter ◽  
Frequency Change ◽  
Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

scholarly journals Time-Optimal Self-Stabilizing Leader Election in Population Protocols

2021 ◽  
Author(s):  
Janna Burman ◽  
Ho-Lin Chen ◽  
Hsueh-Ping Chen ◽  
David Doty ◽  
Thomas Nowak ◽  
...  
Keyword(s):  
Leader Election ◽  
Population Protocols ◽  
Time Optimal

Enhanced Phase Clocks, Population Protocols, and Fast Space Optimal Leader Election

2021 ◽  
Vol 68 (1) ◽  
pp. 1-21
Author(s):  
Leszek Gąsieniec ◽  
Grzegorz Stachowiak
Keyword(s):  
Leader Election ◽  
Population Protocols
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