Article
Statistics & Probability
Jui-Lin Chi, Jyy- Hong
Summary: In this paper, we study a simple branching random walk model and show that the set of occupied positions eventually becomes an interval almost surely when the individuals do not go extinct.
STATISTICS & PROBABILITY LETTERS
(2023)
Article
Mathematics
Miguel Gonzalez, Cristina Gutierrez, Rodrigo Martinez
Summary: A two-type two-sex branching process is used to model the evolution of carriers and mutations of a Y-linked gene, with limiting growth rates of couples and males on different genotype sets obtained. Results are illustrated through simulated studies contextualized in problems of population genetics.
Article
Statistics & Probability
Tianyi Bai, Yijun Wan
Summary: By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, the authors establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
ANNALS OF APPLIED PROBABILITY
(2022)
Article
Physics, Multidisciplinary
Pierre Le Doussal
Summary: This study reveals the equivalence between the mean-field theory of avalanches in the dynamics of elastic interfaces (BFM) and the super-Brownian motion (SBM) in probability theory, along with some results that can be transferred between the two fields.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Biology
Jochen Blath, Felix Hermann, Martin Slowik
Summary: This article aims to contribute towards understanding the evolutionary benefits of microbial populations maintaining a seed bank of dormant individuals in fluctuating environmental conditions. By discussing branching processes and comparing different strategies, a fitness map is generated to determine unique supercritical switching strategies under varying environmental regimes.
JOURNAL OF MATHEMATICAL BIOLOGY
(2021)
Article
Physics, Mathematical
Tianyi Bai, Pierre Rousselin
Summary: This paper investigates a pruned Galton-Watson tree and its branching random walk, providing an explicit probability measure for the first n generations of the tree and the asymptotic tail behavior of span and gap statistics of its k particles. This study extends the work of Ramola et al. (Chaos Solitons Fractals 74:79-88, 2015) to arbitrary offspring and displacement distributions with moment constraints.
JOURNAL OF STATISTICAL PHYSICS
(2021)
Article
Statistics & Probability
Souvik Ray, Rajat Subhra Hazra, Parthanil Roy, Philippe Soulier
Summary: We study the extremes of branching random walks where the underlying Galton-Watson tree has infinite progeny mean. The displacements are either regularly varying or have lighter tails. In the regularly varying case, we find that the sequence of normalized extremes converges to a Poisson random measure. We also analyze the scaled position of the rightmost particle in the nth generation when the tail of the displacement behaves like exp(-K(x)), and identify the exact scaling of the maxima in all cases.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2023)
Article
Computer Science, Information Systems
Jayson Rook, Chi-Hao Cheng
Summary: This article applies two contextual anomaly detection techniques based on Hidden Markov Models (HMM) and Long Short-Term Memories (LSTM) to detect changes in the behavior of multifunction radars (MFRs). The techniques are trained on known radar modes and can identify an anomaly radar mode when the emitted signal sequence does not match the prediction based on known modes. This is important for enhancing the survivability of electrical warfare (EW) systems in the face of unknown radar behaviors.
Article
Polymer Science
Rolf Bachmann, Marcel Klinger, Jan Meyer
Summary: This study investigates cross-linking and branching of primary polymer molecules using the Galton-Watson (GW) process. Analytical expressions are derived for the bivariate probability generating functions (pgfs) of branched polymers based on the primary molecular weight distribution (MWD). The bivariate MWDs are then obtained as Taylor expansions, with consideration of the number of branch points. The study covers three cases of random branching: X-shaped, T-shaped, and H-shaped.
MACROMOLECULAR THEORY AND SIMULATIONS
(2023)
Proceedings Paper
Engineering, Electrical & Electronic
Maria Luz Gil Heras, Alvaro Cubillo Garcia, Jose Correcher Soriano, Jose Luis Galan de la Haba, Isabelle Le Roy-Naneix, Stephane Kemkemian, Mattias Thorsell, Michael Brandfass, Philippe Brouard, Tomas Boman, Sebastian Durst, Antonio Nanni, Jacco J. M. de Wit, Ubaldo Calfa, Mantas Sakalas
Summary: The CROWN project aims to develop high-performance and compact multifunction RF systems to meet the requirements of complex battlefields. Technological challenges in the project include the development of broadband antennas, digital beam forming, and smart resource management.
2022 IEEE INTERNATIONAL SYMPOSIUM ON PHASED ARRAY SYSTEMS & TECHNOLOGY (PAST)
(2022)
Article
Statistics & Probability
Thomas Duquesne, Robin Khanfir, Shen Lin, Niccole Torri
Summary: This article discusses a branching random walk (BRW) on a b-ary rooted tree and proves various theoretical results on its properties. It also establishes a convergence relationship with a variant of the Brownian cactus.
ELECTRONIC JOURNAL OF PROBABILITY
(2022)
Article
Engineering, Aerospace
Francesco Carravetta, Langford B. White
Summary: This article discusses the problem of defining statistical models for languages derived from context-free grammars, introduces the concept of stochastic syntactic processes, and demonstrates embedding an SSP into a Markov random field for advanced machine learning algorithms. Extensions to context-sensitive grammars are also discussed.
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
(2021)
Article
Statistics & Probability
Matyas Barczy, Fanni K. Nedenyi, Gyula Pap
Summary: This article provides a generalization of Theorem 1 in Bartkiewicz et al. (2011) by giving sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a strongly stationary sequence to the corresponding finite dimensional distributions of a non-Gaussian stable process. It also applies the results to the asymptotic behavior of finite dimensional distributions of aggregation of independent copies of a strongly stationary subcritical Galton-Watson branching process.
BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS
(2022)
Article
Statistics & Probability
David Clancy
Summary: The papers demonstrated that the area under a normalized Brownian motion minus one-half the integral of its total local time squared is a centered normal random variable with variance 1/12. This result was extended to Brownian bridges with combinatorial interpretation using random forests and process level generalization for a certain infinite forest model. Analogous results were also shown for various related models using stochastic calculus.
JOURNAL OF THEORETICAL PROBABILITY
(2021)
Article
Mathematics, Applied
Matija Vidmar
Summary: By identifying the relevant harmonic functions of X-q, it is possible to determine the Laplace transforms of the first passage times downwards and of the explosion time for X. This can only be done when the killing rate is sufficiently large, but is always achievable when the branching mechanism is not supercritical or if there is no culling.
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
(2022)