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View article: Random walks on Z with Gaussian metastable distribution caused by linear drift with application to the contact process on the complete graph
Random walks on Z with Gaussian metastable distribution caused by linear drift with application to the contact process on the complete graph Open
Contains fulltext : 320505.pdf (Publisher’s version ) (Open Access)
View article: The SIS process on Erdös-Rényi graphs: determining the infected fraction
The SIS process on Erdös-Rényi graphs: determining the infected fraction Open
There are many methods to estimate the quasi-stationary infected fraction of the SIS process on (random) graphs. A challenge is to adequately incorporate correlations, which is especially important in sparse graphs. Methods typically are e…
View article: Random walks on $\mathbb{Z}$ with metastable Gaussian distribution caused by linear drift with application to the contact process on the complete graph
Random walks on $\mathbb{Z}$ with metastable Gaussian distribution caused by linear drift with application to the contact process on the complete graph Open
We study random walks on $\mathbb{Z}$ which have a linear (or almost linear) drift towards 0 in a range around 0. This drift leads to a metastable Gaussian distribution centered at zero. We give specific, fast growing, time windows where w…
View article: Extremal Binary PFAs with Small Number of States
Extremal Binary PFAs with Small Number of States Open
The largest known reset thresholds for DFAs are equal to [Formula: see text], where [Formula: see text] is the number of states. This is conjectured to be the maximum possible. PFAs (with partial transition function) can have exponentially…
View article: Extremal Binary PFAs in a Cerny Family
Extremal Binary PFAs in a Cerny Family Open
The largest known reset thresholds for DFAs are equal to (n-1)^2, where n is the number of states. This is conjectured to be the maximum possible. PFAs (with partial transition function) can have exponentially large reset thresholds. This …
View article: Extremal Binary PFAs with Small Number of States
Extremal Binary PFAs with Small Number of States Open
The largest known reset thresholds for DFAs are equal to $(n-1)^2$, where $n$ is the number of states. This is conjectured to be the maximum possible. PFAs (with partial transition function) can have exponentially large reset thresholds. T…
View article: A lower bound for point-to-point connection probabilities in critical percolation
A lower bound for point-to-point connection probabilities in critical percolation Open
Consider critical site percolation on Zd with d ≥ 2. We prove a lower bound of order n-d 2 for point-to-point connection probabilities, where n is the distance between the points. Most of the work in our proof concerns a ‘construction’ whi…
View article: A lower bound for point-to-point connection probabilities in critical percolation
A lower bound for point-to-point connection probabilities in critical percolation Open
Consider critical site percolation on $\mathbb{Z}^d$ with $d \geq 2$. We prove a lower bound of order $n^{- d^2}$ for point-to-point connection probabilities, where $n$ is the distance between the points. Most of the work in our proof conc…
View article: Lower Bounds for Synchronizing Word Lengths in Partial Automata
Lower Bounds for Synchronizing Word Lengths in Partial Automata Open
It was conjectured by Černý in 1964, that a synchronizing DFA on [Formula: see text] states always has a synchronizing word of length at most [Formula: see text], and he gave a sequence of DFAs for which this bound is reached. Until now a …
View article: Lower Bounds for Synchronizing Word Lengths in Partial Automata
Lower Bounds for Synchronizing Word Lengths in Partial Automata Open
It was conjectured by Černý in 1964, that a synchronizing DFA on [Formula: see text] states always has a synchronizing word of length at most [Formula: see text], and he gave a sequence of DFAs for which this bound is reached. Until now a …
View article: Counting Symbol Switches in Synchronizing Automata
Counting Symbol Switches in Synchronizing Automata Open
Instead of looking at the lengths of synchronizing words as in \v{C}ern\'y's conjecture, we look at the switch count of such words, that is, we only count the switches from one letter to another. Where the synchronizing words of the \v{C}e…
View article: Counting symbol switches in synchronizing automata
Counting symbol switches in synchronizing automata Open
Instead of looking at the lengths of synchronizing words as in Černý's conjecture, we look at the switch count of such words, that is, we only count the switches from one letter to another. Where the synchronizing words of the Černý automa…
View article: Explicit bounds for critical infection rates and expected extinction times of the contact process on finite random graphs
Explicit bounds for critical infection rates and expected extinction times of the contact process on finite random graphs Open
We introduce a method to prove metastability of the contact process on Erdős-Rényi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed number of …
View article: Metastability of the contact process on Erd\"os-R\'enyi and configuration model graphs
Metastability of the contact process on Erd\"os-R\'enyi and configuration model graphs Open
We introduce a method to prove metastability of the contact process on Erdos-Renyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed number of …
View article: Synchronizing Non-Deterministic Finite Automata
Synchronizing Non-Deterministic Finite Automata Open
In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that \v{C}ern\'y's conjecture generalizes to CNFAs and that any upper bound for the synchronizing wor…
View article: Synchronizing non-deterministic finite automata
Synchronizing non-deterministic finite automata Open
In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that Černý's conjecture generalizes to CNFAs and that the general upper bound for the length of a sho…
View article: DFAs and PFAs with Long Shortest Synchronizing Word Length
DFAs and PFAs with Long Shortest Synchronizing Word Length Open
It was conjectured by Černý in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of …
View article: Self-averaging sequences which fail to converge
Self-averaging sequences which fail to converge Open
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is m…
View article: Self-averaging sequences which fail to converge
Self-averaging sequences which fail to converge Open
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is m…
View article: Approximating general SIS using non-negative matrix factorization
Approximating general SIS using non-negative matrix factorization Open
In this paper we consider the SIS model with general infectionrate matrix A. Using a nonnegative matrix factorization to approximate A, we are able to identify when a metastable state can be expected, and that the metastable distribution, …
View article: Estimating the covariance structure of heterogeneous SIS epidemics on networks
Estimating the covariance structure of heterogeneous SIS epidemics on networks Open
Heterogeneous Markovian Susceptible-Infected-Susceptible (SIS) epidemics with a general infection rate matrix $\widetilde{A}$ are considered. Using a non-negative matrix factorization to approximate $\widetilde{A}$, we are able to identify…
View article: Slowly synchronizing automata with fixed alphabet size
Slowly synchronizing automata with fixed alphabet size Open
It was conjectured by Černý in 1964 that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. In this paper, we investigate …
View article: Finding DFAs with maximal shortest synchronizing word length
Finding DFAs with maximal shortest synchronizing word length Open
It was conjectured by Cerny in 1964 that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. In 2006 Trahtman conjectured t…
View article: The Černý Conjecture and 1-Contracting Automata
The Černý Conjecture and 1-Contracting Automata Open
A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with $n$ states has a synchronizing word of length …
View article: Conditioned multi-type Galton−Watson trees
Conditioned multi-type Galton−Watson trees Open
Contains fulltext : 162966.pdf (Publisher’s version ) (Open Access) Contains fulltext : 162966.pdf (Author’s version preprint ) (Open Access)
View article: The Cerny conjecture and 1-contracting automata
The Cerny conjecture and 1-contracting automata Open
A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. Černý conjectured in 1964 that a synchronizing automaton with $n$ states has a synchronizing word of length …