The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform

Anthony G. Pakes - One of the best experts on this subject based on the ideXlab platform.

Anyue Chen - One of the best experts on this subject based on the ideXlab platform.

Servet Martinez - One of the best experts on this subject based on the ideXlab platform.

Arnab Sen - One of the best experts on this subject based on the ideXlab platform.

  • Branching Process Approach for 2-Sat Thresholds
    Journal of Applied Probability, 2010
    Co-Authors: Elchanan Mossel, Arnab Sen
    Abstract:

    It is well known that, as n tends to ∞, the probability of satisfiability for a random 2-SAT formula on n variables, where each clause occurs independently with probability α / 2n, exhibits a sharp threshold at α = 1. We study a more general 2-SAT model in which each clause occurs independently but with probability α i / 2n, where i ∈ {0, 1, 2} is the number of positive literals in that clause. We generalize the Branching Process arguments used by Verhoeven (1999) to determine the satisfiability threshold for this model in terms of the maximum eigenvalue of the Branching matrix.

  • Branching Process approach for 2-SAT thresholds
    arXiv: Probability, 2008
    Co-Authors: Elchanan Mossel, Arnab Sen
    Abstract:

    It is well known that, as $n$ tends to infinity, the probability of satisfiability for a random 2-SAT formula on $n$ variables, where each clause occurs independently with probability $\alpha/2n$, exhibits a sharp threshold at $\alpha=1$. We study a more general 2-SAT model in which each clause occurs independently but with probability $\alpha_i/2n$ where $i \in \{0,1,2\}$ is the number of positive literals in that clause. We generalize Branching Process arguments by Verhoeven(99) to determine the satisfiability threshold for this model in terms of the maximum eigenvalue of the Branching matrix.

Carmen Minuesa - One of the best experts on this subject based on the ideXlab platform.

  • a predator prey two sex Branching Process
    Mathematics, 2020
    Co-Authors: Cristina Gutierrez, Carmen Minuesa
    Abstract:

    In this paper, we present the first stochastic Process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled Branching model. This Process is a two-type Branching Process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex Branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. In view of their potential for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them. Moreover, the description of the present predator–prey two-sex Branching Process on the fixation events can be performed in terms of the behaviour of a one-type two-sex Branching Process with a random control on the number of individuals, which is also introduced and analysed.

  • a predator prey two sex Branching Process
    arXiv: Probability, 2019
    Co-Authors: Cristina Gutierrez, Carmen Minuesa
    Abstract:

    In this paper, we introduce a two-sex controlled Branching model to describe the interaction between predator and prey populations with sexual reproduction. This Process is a two-type Branching Process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex Branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. We provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of the species and the coexistence of both of them. Moreover, the description of the present predator-prey two-sex Branching Process on the fixation events can be performed in terms of the behaviour of a one-type two-sex Branching Process with a random control on the number of individuals, which is also introduced and analysed.

  • An inhomogeneous controlled Branching Process
    Lithuanian Mathematical Journal, 2015
    Co-Authors: Miguel González, Carmen Minuesa, Manuel Mota, Inés M. Del Puerto, Alfonso Ramos
    Abstract:

    We consider a discrete-time Branching Process in which the offspring distribution is generation-dependent and the number of reproductive individuals is controlled by a random mechanism. This model is a Markov chain, but, in general, the transition probabilities are nonstationary. Under not too restrictive hypotheses, this model presents the classical duality of Branching Processes: it either becomes extinct or grows to infinity. Sufficient conditions for the almost sure extinction and for a positive probability of indefinite growth are given. Finally, the rates of growth of the Process are studied, provided that there is no extinction.