The Experts below are selected from a list of 9525 Experts worldwide ranked by ideXlab platform
Matthew Junge - One of the best experts on this subject based on the ideXlab platform.
-
COVER TIME FOR THE Frog Model ON TREES
Forum of Mathematics Sigma, 2019Co-Authors: Christopher Hoffman, Tobias Johnson, Matthew JungeAbstract:The Frog Model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\mu$ on the full $d$-ary tree of height $n$. If $\mu= \Omega( d^2)$, all of the vertices are visited in time $\Theta(n\log n)$ with high probability. Conversely, if $\mu = O(d)$ the cover time is $\exp(\Theta(\sqrt n))$ with high probability.
-
Infection spread for the Frog Model on trees
Electronic Journal of Probability, 2019Co-Authors: Christopher Hoffman, Tobias Johnson, Matthew JungeAbstract:The Frog Model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $\Omega(d^2)$, the set of visited sites contains a linearly expanding ball and the number of visits to the root grows linearly with high probability.
-
The Frog Model on trees with drift
arXiv: Probability, 2018Co-Authors: Erin Beckman, Matthew Junge, Natalie Frank, Yufeng Jiang, Si TangAbstract:We provide a uniform upper bound on the minimal drift so that the one-per-site Frog Model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for Frog Models on nested sequences of graphs is known to be difficult. The upper bound comes from combining the coupling with a new, simpler proof that the Frog Model on a binary tree is recurrent when the drift is sufficiently strong. Additionally, we describe a coupling between Frog Models on trees for which the degree of the smaller tree divides that of the larger one. This implies that the critical drift has a limit as $d$ tends to infinity along certain subsequences.
-
Stochastic orders and the Frog Model
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2018Co-Authors: Tobias Johnson, Matthew JungeAbstract:The Frog Model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove that certain Frog Model statistics are monotone in the initial configuration for two nonstandard stochastic dominance relations: the increasing concave and the probability generating function orders. This extends many canonical theorems. We connect recurrence for random initial configurations to recurrence for deterministic configurations. Also, the limiting shape of activated sites on the integer lattice respects both of these orders. Other implications include monotonicity results on transience of the Frog Model where the number of Frogs per vertex decays away from the origin, on survival of the Frog Model with death, and on the time to visit a given vertex in any Frog Model.
-
Asymptotic behavior of the Brownian Frog Model
arXiv: Probability, 2017Co-Authors: Erin Beckman, Emily Dinan, Rick Durrett, Ran Huo, Matthew JungeAbstract:We introduce an extension of the Frog Model to Euclidean space and prove properties for the spread of active particles. The new geometry introduces a phase transition that does not occur for the Frog Model on the lattice. Fix $r>0$ and place a particle at each point $x$ of a unit intensity Poisson point process $\mathcal P \subseteq \mathbb R^d - \mathbb B(0,r)$. Around each point in $\mathcal{P}$, put a ball of radius $r$. A particle at the origin performs Brownian motion. When it hits the ball around $x$ for some $x \in \mathcal P$, new particles begin independent Brownian motions from the centers of the balls in the cluster containing $x$. Subsequent visits to the cluster do nothing. This waking process continues indefinitely. For $r$ smaller than the critical threshold of continuum percolation, we show that the set of activated sites in $\mathcal P$ behaves like a linearly expanding ball. Moreover, in any fixed ball the set of active particles converges to a unit intensity Poisson point process. Lastly, we prove that the Model expands at rate at least $t^{2- \epsilon}$ when $d=2$ and $r$ equals the critical threshold in continuum percolation.
Nicolas Pollet - One of the best experts on this subject based on the ideXlab platform.
-
Characterization of a novel Xenopus tropicalis cell line as a Model for in vitro studies
Genesis, 2012Co-Authors: Ludivine Sinzelle, Raphaël Thuret, Ho-yon Hwang, Bérénice Herszberg, Elodie Paillard, Odile J. Bronchain, Derek L. Stemple, Sophie Pollet, Nicolas PolletAbstract:Cell lines are useful tools to facilitate in vitro studies of many biological and molecular processes. We describe a new permanent fibroblast-type cell line obtained from disaggregated Xenopus tropicalis limb bud. The cell line population doubling time was _ 24 h. Its karyotype was genetically stable with a chromosome number of 2n 5 21 and a chromosome 10 trisomy. These cells could be readily transfected and expressed transgenes faithfully. We obtained stable transformants using transposon-based gene transfer technology. These cells responded to thyroid hormone and thus can provide a complementary research tool to study thyroid hormone signaling events. In conclusion, this cell line baptized ‘‘Speedy’’ should prove useful to couple in vitro and in vivo biological studies in the X. tropicalis Frog Model.
Daniel R Buchholz - One of the best experts on this subject based on the ideXlab platform.
-
Frogs Model man: In vivo thyroid hormone signaling during development.
Genesis (New York N.Y. : 2000), 2017Co-Authors: Laurent M Sachs, Daniel R BuchholzAbstract:Thyroid hormone (TH) signaling comprises TH transport across cell membranes, metabolism by deiodinases, and molecular mechanisms of gene regulation. Proper TH signaling is essential for normal perinatal development, most notably for neurogenesis and fetal growth. Knowledge of perinatal TH endocrinology needs improvement to provide better treatments for premature infants and endocrine diseases during gestation and to counteract effects of endocrine disrupting chemicals. Studies in amphibians have provided major insights to understand in vivo mechanisms of TH signaling. The Frog Model boasts dramatic TH-dependent changes directly observable in free-living tadpoles with precise and easy experimental control of the TH response at developmental stages comparable to fetal stages in mammals. The hormones, their receptors, molecular mechanisms, and developmental roles of TH signaling are conserved to a high degree in humans and amphibians, such that with respect to developmental TH signaling "Frogs are just little people that hop." The Frog Model is exceptionally illustrative of fundamental molecular mechanisms of in vivo TH action involving TH receptors, transcriptional cofactors, and chromatin reModeling. This review highlights the current need, recent successes, and future prospects using amphibians as a Model to elucidate molecular mechanisms and functional roles of TH signaling during post-embryonic development.
-
more similar than you think Frog metamorphosis as a Model of human perinatal endocrinology
Developmental Biology, 2015Co-Authors: Daniel R BuchholzAbstract:Hormonal control of development during the human perinatal period is critically important and complex with multiple hormones regulating fetal growth, brain development, and organ maturation in preparation for birth. Genetic and environmental perturbations of such hormonal control may cause irreversible morphological and physiological impairments and may also predispose individuals to diseases of adulthood, including diabetes and cardiovascular disease. Endocrine and molecular mechanisms that regulate perinatal development and that underlie the connections between early life events and adult diseases are not well elucidated. Such mechanisms are difficult to study in uterus-enclosed mammalian embryos because of confounding maternal effects. To elucidate mechanisms of developmental endocrinology in the perinatal period, Xenopus laevis the African clawed Frog is a valuable vertebrate Model. Frogs and humans have identical hormones which peak at birth and metamorphosis, have conserved hormone receptors and mechanisms of gene regulation, and have comparable roles for hormones in many target organs. Study of molecular and endocrine mechanisms of hormone-dependent development in Frogs is advantageous because an extended free-living larval period followed by metamorphosis (1) is independent of maternal endocrine influence, (2) exhibits dramatic yet conserved developmental effects induced by thyroid and glucocorticoid hormones, and (3) begins at a developmental stage with naturally undetectable hormone levels, thereby facilitating endocrine manipulation and interpretation of results. This review highlights the utility of Frog metamorphosis to elucidate molecular and endocrine actions, hormone interactions, and endocrine disruption, especially with respect to thyroid hormone. Knowledge from the Frog Model is expected to provide fundamental insights to aid medical understanding of endocrine disease, stress, and endocrine disruption affecting the perinatal period in humans.
Ludivine Sinzelle - One of the best experts on this subject based on the ideXlab platform.
-
Characterization of a novel Xenopus tropicalis cell line as a Model for in vitro studies
Genesis, 2012Co-Authors: Ludivine Sinzelle, Raphaël Thuret, Ho-yon Hwang, Bérénice Herszberg, Elodie Paillard, Odile J. Bronchain, Derek L. Stemple, Sophie Pollet, Nicolas PolletAbstract:Cell lines are useful tools to facilitate in vitro studies of many biological and molecular processes. We describe a new permanent fibroblast-type cell line obtained from disaggregated Xenopus tropicalis limb bud. The cell line population doubling time was _ 24 h. Its karyotype was genetically stable with a chromosome number of 2n 5 21 and a chromosome 10 trisomy. These cells could be readily transfected and expressed transgenes faithfully. We obtained stable transformants using transposon-based gene transfer technology. These cells responded to thyroid hormone and thus can provide a complementary research tool to study thyroid hormone signaling events. In conclusion, this cell line baptized ‘‘Speedy’’ should prove useful to couple in vitro and in vivo biological studies in the X. tropicalis Frog Model.
Josh Rosenberg - One of the best experts on this subject based on the ideXlab platform.
-
The Frog Model on non-amenable trees.
arXiv: Probability, 2019Co-Authors: Marcus Michelen, Josh RosenbergAbstract:We examine an interacting particle system on trees commonly referred to as the Frog Model. For its initial state, it begins with a single active particle at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles at each non-root vertex. Active particles perform discrete time simple random walk and in the process activate any inactive particles they encounter. We show that for $\textit{every}$ non-amenable tree with bounded degree there exists a phase transition from transience to recurrence (with a non-trivial intermediate phase sometimes sandwiched in between) as $\lambda$ varies.
-
The Frog Model on Galton-Watson trees
arXiv: Probability, 2019Co-Authors: Marcus Michelen, Josh RosenbergAbstract:We consider an interacting particle system on trees known as the Frog Model: initially, a single active particle begins at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles are placed at each non-root vertex. Active particles perform discrete time simple random walk and activate the inactive particles they encounter. We show that for Galton-Watson trees with offspring distributions $Z$ satisfying $\mathbf{P}(Z \geq 2) = 1$ and $\mathbf{E}[Z^{4 + \epsilon}] 0$, there is a critical value $\lambda_c\in(0,\infty)$ separating recurrent and transient regimes for almost surely every tree, thereby answering a question of Hoffman-Johnson-Junge. In addition, we also establish that this critical parameter depends on the entire offspring distribution, not just the maximum value of $Z$, answering another question of Hoffman-Johnson-Junge and showing that the Frog Model and contact process behave differently on Galton-Watson trees.
-
The nonhomogeneous Frog Model on ℤ
Journal of Applied Probability, 2018Co-Authors: Josh RosenbergAbstract:Abstract We examine a system of interacting random walks with leftward drift on ℤ, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become activated when landed on by other particles, and all particles beginning at the same point possess equal leftward drift. Once activated, the trajectories of distinct particles are independent. This system belongs to a broader class of problems involving interacting random walks on rooted graphs, referred to collectively as the Frog Model. Additional conditions that we impose on our Model include that the number of Frogs (i.e. particles) at positive integer points is a sequence of independent random variables which is increasing in terms of the standard stochastic order, and that the sequence of leftward drifts associated with Frogs originating at these points is decreasing. Our results include sharp conditions with respect to the sequence of random variables and the sequence of drifts that determine whether the Model is transient (meaning the probability infinitely many Frogs return to the origin is 0) or nontransient. We consider several, more specific, versions of the Model described, and a cleaner, more simplified set of sharp conditions will be established for each case.
-
The nonhomogeneous Frog Model on $\mathbb{Z}$
arXiv: Probability, 2017Co-Authors: Josh RosenbergAbstract:We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become activated when landed on by other particles, and all particles beginning at the same point posses equal leftward drift. Once activated, the trajectories of distinct particles are independent. This system belongs to a broader class of problems involving interacting random walks on rooted graphs, referred to collectively as the Frog Model. Additional conditions that we impose on our Model include that the number of Frogs (i.e. particles) at positive integer points is a sequence of independent random variables which is increasing in terms of the standard stochastic order, and that the sequence of leftward drifts associated with Frogs originating at these points is decreasing. Our results include sharp conditions with respect to the sequence of random variables and the sequence of drifts, that determine whether the Model is transient (meaning the probability infinitely many Frogs return to the origin is $0$) or non-transient. Several, more specific, versions of the Model described will also be considered, and a cleaner, more simplified set of sharp conditions will be established for each case.
-
the nonhomogeneous Frog Model on mathbb z
arXiv: Probability, 2017Co-Authors: Josh RosenbergAbstract:We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become activated when landed on by other particles, and all particles beginning at the same point posses equal leftward drift. Once activated, the trajectories of distinct particles are independent. This system belongs to a broader class of problems involving interacting random walks on rooted graphs, referred to collectively as the Frog Model. Additional conditions that we impose on our Model include that the number of Frogs (i.e. particles) at positive integer points is a sequence of independent random variables which is increasing in terms of the standard stochastic order, and that the sequence of leftward drifts associated with Frogs originating at these points is decreasing. Our results include sharp conditions with respect to the sequence of random variables and the sequence of drifts, that determine whether the Model is transient (meaning the probability infinitely many Frogs return to the origin is $0$) or non-transient. Several, more specific, versions of the Model described will also be considered, and a cleaner, more simplified set of sharp conditions will be established for each case.
