Branching Process Research Papers - Academia.edu (original) (raw)

2025, Physical Review E

Mutations not only alter allele frequencies in a genetic pool but may also determine the fate of an evolutionary process. Here we study which allele fixes in a one-step, one-way model including the wild type and two adaptive mutations. We study the effect of the four basic evolutionary mechanisms-genetic drift, natural selection, mutation, and gene flow-on mutant fixation and its kinetics. Determining which allele is more likely to fix is not simply a question of comparing fitnesses and mutation rates. For instance, if the allele of interest is less fit than the other, then not only must it have a greater mutation rate, but also its mutation rate must exceed a specific threshold for it to prevail. We find exact expressions for such conditions. Our conclusions are based on the mathematical description of two extreme but important regimes, as well as on simulations.

2025, Theory of Probability and Mathematical Statistics

We investigate the problem of estimation of the unknown drift parameter in the stochastic differential equations driven by fractional Brownian motion, with the coefficients supplying standard existence-uniqueness demands. We consider a particular case when the ratio of drift and diffusion coefficients is non-random, and establish the asymptotic strong consistency of the estimator with different ratios, from many classes of non-random standard functions. Simulations are provided to illustrate our results, and they demonstrate the fast rate of convergence of the estimator to the true value of a parameter.

2025, Stochastic Models

We consider a stochastic system in which Markovian customer attribute processes are initiated at customer arrivals in a discrete batch Markovian arrival process (D-BMAP). We call the aggregate a Markovian branching D-BMAP. Each customer attribute process is an absorbing discrete time Markov chain whose parameters depend both on the phase transition, of the driving D-BMAP, and the number of arrivals taking place at the customer's arrival instant. We investigate functionals of Markovian branching D-BMAPs that may be interpreted as cumulative rewards collected over time for the various customers that arrive to the system, in the transient and asymptotic cases. This is achieved through the derivation of recurrence relations for expected values and Laplace transforms in the former case, and Little's law in the latter case.

2025, Applied Mathematics and Computation

In this paper, we consider the problem of finding reliably and with certainty all zeros of an interval equation within a given search interval for continuously differentiable functions over real numbers. We propose a new formality of interval arithmetic which is treated in a theoretical manner to develop and prove a new method, lying on the context of interval Newton methods. Some important theoretical aspects of the new method are stated and proved. Finally, an algorithmic realization of our method is proposed to be applied on a set of test functions, where the promising theoretical results are verified.

2025, Zenodo (CERN European Organization for Nuclear Research)

This paper presents a branching schema for the solving of a wide range of interval constraint satisfaction problems defined on any domain of computation, finite or infinite, provided the domain forms a lattice. After a formal definition of the branching schema, useful and interesting properties, satisfied by all instances of the schema, are presented. Examples are then used to illustrate how a range of operational behaviors can be modelled by means of different schema instantiations. It is shown how the operational procedures of many constraint systems (including cooperative systems) can be viewed as instances of this branching schema. Basic directives to adapt this schema to solving constraint optimization problems are also provided.

2025, The Annals of Statistics

When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the observation locations. This paper explores conditions on the observation locations and the process model under which an asymptotic screening effect holds. A series of examples shows the difficulty in formulating a general result, especially for processes with different degrees of smoothness in different directions, which can naturally occur for spatial-temporal processes. These examples lead to a general conjecture and two special cases of this conjecture are proven. The key condition on the process is that its spectral density should change slowly at high frequencies. Models not satisfying this condition of slow high-frequency change should be used with caution.

2025, Archivum mathematicum

The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic... more

2025, Archivum Mathematicum

2025, arXiv (Cornell University)

Consider the representative task of designing a distributed coin-tossing protocol for n processors such that the probability of heads is X0 ∈ [0, 1]. This protocol should be robust to an adversary who can reset one processor to change the distribution of the final outcome. For X0 = 1/2, in the information-theoretic setting, no adversary can deviate the probability of the outcome of the well-known Blum's "majority protocol" by more than 1 √ 2πn , i.e., it is 1 √ 2πn insecure. In this paper, we study discrete-time martingales (X0, X1, . . . , Xn) such that Xi ∈ [0, 1], for all i ∈ {0, . . . , n}, and Xn ∈ {0, 1}. These martingales are commonplace in modeling stochastic processes like coin-tossing protocols in the information-theoretic setting mentioned above. In par- Mathematics of computing → Markov processes; Security and privacy → Information-theoretic techniques; Security and privacy → Mathematical foundations of cryptography Keywords and phrases Discrete-time Martingale, Coin-tossing and Dice-rolling Protocols, Discrete Control Processes, Fair Computation, Black-box Separation

2025, arXiv (Cornell University)

We present a general approach to a broad class of asymptotic problems related to the long-time influence of small perturbations, of both the deterministic and stochastic type. The main characteristic of this influence is a limiting motion on the simplex of invariant probability measures of the non-perturbed system in an appropriate time scale. We consider perturbations of dynamical systems in R n , linear and nonlinear perturbations of PDE's, wave fronts in the reaction-diffusion equations, homogenization problems and perturbations caused by small time delay. The main tools we use in these problems are limit theorems for large deviations, modified averaging principle and diffusion approximation.

2025, Physical Review E

The branching aftershock sequence ͑BASS͒ model is a self-similar statistical model for earthquake aftershock sequences. A prescribed parent earthquake generates a first generation of daughter aftershocks. The magnitudes and times of occurrence of the daughters are obtained from statistical distributions. The first generation daughter aftershocks then become parent earthquakes that generate second generation aftershocks. The process is then extended to higher generations. The key parameter in the BASS model is the magnitude difference ⌬m* between the parent earthquake and the largest expected daughter earthquake. In the application of the BASS model to aftershocks ⌬m* is positive, the largest expected daughter event is smaller than the parent, and the sequence of events ͑aftershocks͒ usually dies out, but an exponential growth in the number of events with time is also possible. In this paper we explore this behavior of the BASS model as ⌬m* varies, including when ⌬m* is negative and the largest expected daughter event is larger than the parent. The applications of this self-similar branching process to biology and other fields are discussed.

2025, Annales De L Institut Henri Poincare-probabilites Et Statistiques

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2025, HAL (Le Centre pour la Communication Scientifique Directe)

Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at random. The resulting dynamics is called Fleming-Viot process. We show that for each N there exists a unique invariant measure for the Fleming-Viot process, and that its stationary empirical distribution converges, as N goes to infinity, to the minimal quasi-stationary distribution of the Galton-Watson process conditioned on non-extinction.

2025, Computational Statistics & Data Analysis

The problem of statistical inference from a Bayesian outlook is studied for the multitype Galton-Watson branching process, considering a non-parametric framework. The only data assumed to be available are each generation's population size vectors. The Gibbs sampler is used in estimating the posterior distributions of the main parameters of the model, and the predictive distributions for as yet unobserved generations. The algorithm provided is independent of whether the process becomes extinct or not. The method is illustrated with simulated examples.

2025

This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub-and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors.

2025, arXiv (Cornell University)

We study a generalization of the model introduced in that interpolates between the random energy model (REM) and the branching random walk (BRW). More precisely, we are interested in the asymptotic behaviour of the extremal process associated to this model. In , Kistler and Schmidt show that the extremal process of the GREM (N α ), α ∈ [0, 1) converges weakly to a simple Poisson point process. This contrasts with the extremal process of the branching random walk (α = 1) which was shown to converge toward a decorated Poisson point process by Madaule . In this paper we propose a generalized model of the GREM (N α ), that has the structure of a tree with kn levels, where (kn ≤ n) is a non-decreasing sequence of positive integers. We study a generalized case, where the position of the particles are not necessarily Gaussian variables and the reproduction law is not necessarily binary. We show that as long as bn = ⌊ n kn ⌋ →n→∞ ∞ in the Gaussian case (with the assumption bn log(n) 2 → ∞ as n → ∞ in the non Gaussian case) the decoration disappears and we have convergence to a simple Poisson point process.

2025, arXiv (Cornell University)

We study the asymptotic behaviour of the extremal process of a cascading family of branching Brownian motions. This is a particle system on the real line such that each particle has a type in addition to his position. Particles of type 1 move on the real line according to Brownian motions and branch at rate 1 into two children of type 1. Furthermore, at rate α, they give birth to children too of type 2. Particles of type 2 move according to standard Brownian motion and branch at rate 1, but cannot give birth to descendants of type 1. We obtain the asymptotic behaviour of the extremal process of particles of type 2.

2025

In this thesis, we are interested in extreme values of certain spatial branching processes such as the branching random walk and the branching Brownian motion. The branching random walk is a particle system that can be described as follows. It starts with an unique particle at generation 000. It gives birth to a random number of children positioned with respect to their parent according to a point process. Then, each child repeats the same process to that of his parent and independently of the rest of particles. The branching Brownian motion can be described similarly. It starts with an unique particle at the origin. It moves according to a standard Brownian motion. After an exponential time, it dies giving birth to two children on its current position. Then, each child starts an independent branching Brownian motion.In the first part of this thesis, we study a model that interpolates between the branching random walk and a model linked to statistical physics which called \textit{Ra...

2025, arXiv (Cornell University)

2025

We present a version of the stochastic maximum principle (SMP) for ergodic control problems. In particular we give necessary (and sufficient) conditions for optimality for controlled dissipative systems in finite dimensions. The strategy we employ is mainly built on duality techniques. We are able to construct a dual process for all positive times via the analysis of a suitable class of perturbed linearized forward equations. We show that such a process is the unique bounded solution to a Backward SDE on infinite horizon from which we can write a version of the SMP.

2025

2000 Mathematics Subject Classification: 60J80, 62P05.The randomly indexed Galton-Watson branching process has been used for the model of daily stock prices. Using this stock price process we derive a new formula for the price of European... more

2025, HAL (Le Centre pour la Communication Scientifique Directe)

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2025

Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet de traiter des non linéarités très proches de la croissance critique. Les résultats obtenus nous ont motivé de travailler sur des équations polyharmoniques (-Δ)ku = f(x; u) avec notamment k = 2 et 3. Avec des hypothèses semblables à Yang [1998] sur f et des conditions au bord convenables, on obtient pour la première fois des estimations explicites de solution des équations polyha...

2025, Journal of Applied Ecology

1. There exists a continuing dilemma in prioritizing conservation actions for large carnivores. Habitat loss, poaching, and prey depletion have often been cited as the three primary threats, but there is debate over the relative importance of each. 2. We assess the relative importance of poaching and prey depletion rates, and use existing information in the literature and multi-type branching process and deterministic felid population models to address four lines of evidence used to infer that tiger populations are inherently resilient to high mortality rates. 3. Our results suggest that tigers, more so than leopards or cougars, require large populations to persist, are quite susceptible to modest increases in mortality, and less likely to recover quickly after population declines. Demographic responses that would ensure population persistence with mortality rates that are sustainable for cougars or leopards are biologically unrealistic for tigers. 4. We propose alternative interpretations of evidence used to suggest that tigers are inherently resilient to high mortality rates. In contrast to other solitary felids, tigers breed later and their inter-birth interval is larger, making them less resilient to poaching. A model used to support the contention that prey depletion has greater impact on population persistence than poaching appears to be based on false premises. Camera-trapping data that suggest positive population growth despite low survival rate cannot differentiate mortality from emigration, and does not differentiate the impact of varying survival rate on different sex-age classes; for example, low survival rate of dispersers is tolerable if survival rate of adult breeding females is high. 5. Synthesis and applications. While high prey numbers are essential to sustain tiger populations, our results suggest prey recovery efforts will not be sufficient if mortality rates reach 15%. Extrapolating demographic responses from other, even closely related species to develop conservation strategies can be misleading. Reduction of human-caused mortality, especially of resident breeding females, appears to be the most essential short-term conservation effort that must be made. Since mortality rates are usually unknown and generally stochastic in nature, any management policy that might reduce survival rates should be firmly avoided.

2025, Journal of Applied Ecology

2025, Annals of Probability

This paper considers some measure-valued processes {X t : t ∈ [0, T ]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Φ of the process are given that imply that the expectations E(Φ(X T )) are comparable to the constant branching case. Applications to hitting estimates and regularity of solutions are discussed. The result is established via the martingale optimality principle of stochastic control theory. Key steps, which are of independent interest, are the proof of a version of Ito's Lemma for Φ(X t ), suitable for a large class of functions of measures (Theorem 3) and the proof of various smoothing properties of the Dawson-Watanabe transition semigroup (section 3).

2025, Georgetown Environmental Law Review

In recent years, federal courts have increasingly assessed the legality of regulatory action by considering its antecedents, or lack thereof, in prior agency actions. In several Supreme Court decisions-including the Court's recent opinions in which it expressly applied the major questions doctrine-a majority of justices have expressed skepticism of agency authority when "an agency claims to discover in a long-extant statute an unheralded power to regulate a significant portion of the American economy." District and appellate courts have relied on this language to strike down numerous agency actions dating back to 2014, and judicial scrutiny of regulatory antecedents has grown since the Supreme Court formalized the major questions doctrine in West Virginia v. Environmental Protection Agency in 2022. Yet federal agencies have insufficiently adapted to this increased judicial focus on regulatory antecedents. While significant agency rulemakings typically include extensive dockets with many different types of analysis, they have generally provided limited analysis of regulatory antecedents. When agencies do provide relevant analysis, as they have for several recent proposals that have met objections under the major questions doctrine, such analysis often fails to catalog key regulatory antecedents or is insufficiently targeted at legal objections from opponents of the policy. In some actions, the only explicit discussion of the Supreme Court’s emphasis on agency exercise of “unheralded power” comes from dissenting commissioners on a multi-member agency. This Article recommends that agencies more extensively catalog regulatory antecedents at all stages of the rulemaking process, from drafting to promulgation. By assessing antecedents in regulatory proposals, agencies can more fully lay the foundation for their authority and facilitate targeted comments that consider whether the antecedents offered by the agency support the proposed action. This will enable an even more complete analysis of regulatory antecedents in the final rulemaking, which will provide government litigators with a roadmap for responding to claims that the agency action lacks precedent and thereby reduce the vulnerability of agency action under the major questions doctrine.

2025, Nucleic Acids Research

With the availability of next-generation sequencing (NGS) technology, it is expected that sequence variants may be called on a genomic scale. Here, we demonstrate that a deeper understanding of the distribution of the variant call frequencies at heterozygous loci in NGS data sets is a prerequisite for sensitive variant detection. We model the crucial steps in an NGS protocol as a stochastic branching process and derive a mathematical framework for the expected distribution of alleles at heterozygous loci before measurement that is sequencing. We confirm our theoretical results by analyzing technical replicates of human exome data and demonstrate that the variance of allele frequencies at heterozygous loci is higher than expected by a simple binomial distribution. Due to this high variance, mutation callers relying on binomial distributed priors are less sensitive for heterozygous variants that deviate strongly from the expected mean frequency. Our results also indicate that error rates can be reduced to a greater degree by technical replicates than by increasing sequencing depth.

2025, In Vitro Cellular & Developmental Biology - Animal

Dear Editor: The functions of lacrimal gland are mainly to secrete proteins and electrolytes to supply them into the aqueous layer of the preocular tear film, which contributes to the maintenance of a healthy ocular surface (6). A lacrimal gland dysfunction can cause a fall in lacrimal fluid secretion that results in ocular surface diseases, such as dry eye. Even though the incidence of dry eye has increased to become one of the most serious clinical problems in ophthalmology, our knowledge of the cell biology of lacrimal glands lags behind that of the other exocrine glands. A better understanding of lacrimal gland physiology depends on having an in vitro cell culture system that mimics the in vivo condition. Primary monolayer culture systems were reported for rat (3,7) and rabbit lacrimal epithelial cells (5,8). However, the morphology described in these culture systems is quite different from the in situ condition. Their main limitation is that they did not exhibit any branching tubular structures that are characteristic of compound tubuloalveolar glands in situ. Therefore, to understand the physiology and pathophysiology of the lacrimal glands, it is important to establish a lacrimal epithelial cell culture system that resembles the in situ morphology and biochemistry of lacrimal epithelial cells. For this, we determined the importance of various extracellular matrix proteins on the morphology of rabbit lacrimal epithelial cells in culture. We describe here a culture system for rabbit lacrimal epithelial cells in which morphologic features are formed that closely resemble the in situ condition. Such a system provides a meaningful approach to a better understanding of the physiology and pathophysiology of the lacrimal gland. Lacrimal gland epithelial cells from albino rabbits weighing 2 to 3 kg (Kitayama Labes, Kyoto, Japan) were prepared and cultured by a modification of described procedures (3,7). Briefly, the intraorbital lacrimal glands were excised and placed in Dulbecco's modified Eagle's medium (DMEM) containing 0.1 mg/ml of soybean trypsin inhibitor (STI solution), and the surrounding tissues were removed. The glands were then cut into small pieces (1-4 mm 2) with a razor blade, and rinsed with calcium-magnesium-free Hanks' balanced salt solution (HBSS). The fragments were incubated in DMEM containing 0.76 mg/ml of ethylenediaminetetraacetic acid (EDTA), pH 7.4 (EDTA solution) at 37 ~ C for 15 min. After incubation, the fragments were further incubated in DMEM containing 200 units/ml of collagenase, 700 units/ml of hyaluronidase, and 10 units/ml of DNase I (CHD solution) at 37 ~ C for 15 rain. The resulting fragments were repeatedly treated with these EDTA and CHD solutions. After treatment, the resulting cell suspension was passed through a 230-p,m stainless steel mesh to remove the undigested fragments. After centrifugation, the cell pellet was suspended in DMEM containing 20% fetal bovine serum (FBS), and was layered over a Ficoll gradient (2%, 3%, and 4% in DMEM). The resulting cell pellet was

2025

We propose two systems of ordinary differential equations modeling the assembly of intermediate filament networks. The first one describes the in vitro intermediate filament assembly dynamics. The second one deals with the in vivo evolution of cytokeratin, which is the intermediate filament protein expressed by epithelial cells. The in vitro model is then briefly analyzed

2025, Journal of Theoretical Biology

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of * These authors contributed equally. † corresponding author A c c e p t e d m a n u s c r i p t Simulating the formation of keratin filament networks by a PDMP piecewise-deterministic Markov processes to the modeling of keratin network formation in high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, mostly depends on lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

2025, arXiv (Cornell University)

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector has a different dependence structure from the usual one. By applying the bounds to sequences of weighted branching processes, we derive sufficient conditions for the convergence in the Kantorovich-Rubinstein distance of linear functions. We focus on the case where the limits are endogenous fixed points of suitable smoothing transformations.

2025, COVENANT JOURNAL OF PHYSICAL AND LIFE SCIENCES VOL.12, NO.2, DECEMBER 2024

This study explores the impact of pipeline conflicts on processor reliability and performance, focusing specifically on data hazards, one of three primary types of pipeline conflicts (the others being control hazards and structural conflicts). Data hazards arise from dependencies between instructions, causing stalls that reduce pipeline efficiency. The research applies machine learning to detect and mitigate these conflicts, using a dataset of artificial instruction sequences, each labeled as either conflict-free or containing one of three data hazard types: Read After Write (RAW), Write After Read (WAR), or Write After Write (WAW). Two machine learning models-logistic regression and Support Vector Machine (SVM)-were evaluated for their effectiveness in identifying pipeline conflicts. The logistic regression model achieved 96% accuracy and high precision, recall, and F1-scores across all categories, indicating its strong ability to accurately classify pipeline conflicts. In contrast, the SVM model achieved lower accuracy (83%) and performed inconsistently across classes, excelling in some but struggling with others, suggesting difficulties in recognizing certain conflict patterns.

2025

This paper deals with the pointwise estimation of the drift function of an ergodic diffusion using the absolute error loss. The optimal convergence rate and the sharp asymptotic lower bound are found for the minimax risk. An... more

2025, Probability Theory and Related Fields

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset of the boundary consisting of all ends of the tree in which the population survives, called the limit set of the process, is shown to have Hausdorff dimension no larger than one half the Hausdorff dimension of the entire geometric boundary. Moreover, there is strict inequality at the phase separation point between weak and strong survival except when the branching random walk is isotropic. It is further shown that in all cases there is a distinguished probability measure µ supported by such that the Hausdorff dimension of ∩ µ , where µ is the set of µ-generic points of , converges to one half the Hausdorff dimension of µ at the phase separation point. Exact formulas are obtained for the Hausdorff dimensions of and ∩ µ , and it is shown that the log Hausdorff dimension of has critical exponent 1/2 at the phase separation point.

2025, arXiv (Cornell University)

We consider a two-type stochastic competition model on the integer lattice Z d . The model describes the space evolution of two "species" competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The spread mechanism for both species is the same: each particle produces offspring independently of other particles and can place them only at the neighboring sites that are either unoccupied, or occupied by particles of the opposite type. In the second case, the old particle is killed by the newborn. The rate of birth for each particle is equal to the number of neighboring sites available for expansion. The main problem we address concerns the possibility of the long-term coexistence of the two species. We have shown that if we start the process with finitely many representatives of each type, then, under the assumption that the limit set in the corresponding first passage percolation model is uniformly curved, there is positive probability of coexistence.

2025, Probability Theory and Related Fields

2025, Electronic proceedings in theoretical computer science

We show a cancellation property for probabilistic choice. If µ ⊕ ρ and ν ⊕ ρ are branching probabilistic bisimilar, then µ and ν are also branching probabilistic bisimilar. We do this in the setting of a basic process language involving non-deterministic and probabilistic choice and define branching probabilistic bisimilarity on distributions. Despite the fact that the cancellation property is very elegant and concise, we failed to provide a short and natural combinatorial proof. Instead we provide a proof using metric topology. Our major lemma is that every distribution can be unfolded into an equivalent stable distribution, where the topological arguments are required to deal with uncountable branching.

2025, arXiv (Cornell University)

Recent progress in microdissection and in DNA sequencing has enabled subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led to the construction of genealogies of the primary, secondary, tertiary and so forth, foci of the tumor. These studies have led to diverse conclusions concerning the Darwinian (selective) or neutral evolution in cancer. Mathematical models of development of multifocal tumors have been developed to support these claims. We report a model of development of a multifocal tumor, which is a mathematically rigorous refinement of a model of . Guided by numerical studies and simulations, we show that the rigorous model, in the form of an infinite-type branching process, displays distributions of tumors size which have heavy tails and moments that become infinite in finite time. To demonstrate these points, we obtain bounds on the tails of the distributions of the process and infinite-series expression for the first moments. In addition to its inherent mathematical interest, the model is corroborated by recent reports of apparent super-exponential growth in cancer metastases.

2025, Advances in Applied Probability

Recent progress in microdissection and in DNA sequencing has facilitated the subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led to the construction of genealogies of the primary, secondary, tertiary, and so forth, foci of the tumor. These studies have led to diverse conclusions concerning the Darwinian (selective) or neutral evolution in cancer. Mathematical models of the development of multi-focal tumors have been devised to support these claims. We offer a model for the development of a multifocal tumor: it is a mathematically rigorous refinement of a model of . Guided by numerical studies and simulations, we show that the rigorous model, in the form of an infinite-type branching process, displays distributions of tumor size which have heavy tails and moments that become infinite in finite time. To demonstrate these points, we obtain bounds on the tails of the distributions of the process and an infinite series expansion for the first moments. In addition to its inherent mathematical interest, the model is corroborated by recent literature on apparent super-exponential growth in cancer metastases.

2025, Frontiers in oncology

We present a stochastic model of driver mutations in the transition from severe congenital neutropenia to myelodysplastic syndrome to acute myeloid leukemia (AML). The model has the form of a multitype branching process. We derive equations for the distributions of the times to consecutive driver mutations and set up simulations involving a range of hypotheses regarding acceleration of the mutation rates in successive mutant clones. Our model reproduces the clinical distribution of times at diagnosis of secondary AML. Surprisingly, within the framework of our assumptions, stochasticity of the mutation process is incapable of explaining the spread of times at diagnosis of AML in this case; it is necessary to additionally assume a wide spread of proliferative parameters among disease cases. This finding is unexpected but generally consistent with the wide heterogeneity of characteristics of human cancers.

2025, Advances in Applied Probability

Recent progress in microdissection and in DNA sequencing has facilitated the subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led to the construction of genealogies of the primary, secondary, tertiary, and so forth, foci of the tumor. These studies have led to diverse conclusions concerning the Darwinian (selective) or neutral evolution in cancer. Mathematical models of the development of multi-focal tumors have been devised to support these claims. We offer a model for the development of a multi-focal tumor: it is a mathematically rigorous refinement of a model of Linget al.(2015). Guided by numerical studies and simulations, we show that the rigorous model, in the form of an infinite-type branching process, displays distributions of tumor size which have heavy tails and moments that become infinite in finite time. To demonstrate these points, we obtain bounds on t...

2025, arXiv (Cornell University)

Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered include a stochastic version of the Kermack & McKendrick model, the Reed-Frost model, and the Volz configuration model.

2025, Теория вероятностей и ее применения

Рассматривается версия многотипного максимального ветвящегося процесса, введенного недавно А. В. Лебедевым. Основным результатом работы является предельная теорема для эмпирических частот типов. Показано, как изменяется со временем первоначальное распределение типов под воздействием механизма селекции среди соревнующихся индивидуумов максимального ветвящегося процесса. Ключевые слова и фразы: многотипные максимальный ветвящийся процесс, максимальный ветвящийся процесс, асимптотическое поведение цепей Маркова, аддитивные функционалы на цепях Маркова.

2025, Journal of the ACM

In the concurrent language CCS, two programs are considered the same if they are bisimilar . Several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice. However, bisimulation makes too many distinctions between programs. We consider the problem of adding operations to CCS to make bisimulation fully abstract. We define the class of GSOS operations, generalizing the style and technical advantages of CCS operations. We characterize GSOS congruence in as a bisimulation-like relation called ready-simulation . Bisimulation is strictly finer than ready simulation, and hence not a congruence for any GSOS language.

2025, International Journal of Theoretical and Applied Finance

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

2025, Applied Sciences

Tracking information diffusion is a non-trivial task and it has been widely studied across different domains and platforms. The advent of social media has led to even more challenges, given the higher speed of information propagation and the growing impact of social bots and anomalous accounts. Nevertheless, it is crucial to derive a trustworthy information diffusion graph that is capable of highlighting the importance of specific nodes in spreading the original message. The paper introduces the interaction strength, a novel metric to model retweet cascade graphs by exploring users’ interactions. Initial findings showed the soundness of the approaches based on this new metric with respect to the state-of-the-art model, and its ability to generate a denser graph, revealing crucial nodes that participated in the retweet propagation. Reliable retweet graph generation will enable a better understanding of the diffusion path of a specific tweet.

2025, Probability Theory and Related Fields

We consider a class of systems of particles of k types in R d undergoing spatial diffusion and critical multitype branching, where the diffusions, the particle lifetimes and the branching laws depend on the types. We prove persistence criteria for such systems and for their corresponding high density limits known as multitype Dawson-Watanabe processes. The main tool is a representation of the Palm distributions for a general class of inhomogeneous critical branching particle systems, constructed by means of a "backward tree".

2025, Stochastic Processes and their Applications

We study here by stochastic calculus methods some martingale properties of a general class of measurevalued branching processes. The form of the cumulant semigroup determines their local characteristics and the explosion time. Finally, by the infinite divisibility property of these processes, we obtain a L&y-Khintchine representation on the paths space and we propose an interpretation of the canonical measures in terms of entrance laws.