Article
Mathematics
Sayan Das, Evgeni Dimitrov
Summary: This paper introduces discrete beta-ensembles and establishes a large deviation principle for the rightmost particle. The general results are applied to two classes of measures related to Jack symmetric functions.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mechanics
Cecile Monthus
Summary: This paper revisits the inference of Markov models from stochastic dynamical trajectories data using large deviations at level 2.5, focusing on obtaining the large deviations properties for the probability distribution of inferred Markov parameters. The explicit rate functions are provided for different settings such as discrete-time Markov chains, continuous-time Markov jump processes, and diffusion processes in dimension d, with applications to random walks in disordered media described.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Physics, Fluids & Plasmas
Hugo Cui, Luca Saglietti, Lenka Zdeborova
Summary: In semisupervised community detection, knowing the membership of a set of revealed nodes can lead to better inference accuracies. This study focuses on correlated subsets in the dense stochastic block model, showing a nonmonotonic relationship between reconstruction accuracy and free energy. The findings have potential implications for active learning applications in community detection.
Article
Statistics & Probability
Stefan Gerhold, Christoph Gerstenecker, Archil Gulisashvili
Summary: We study non-Gaussian fractional stochastic volatility models where the volatility is described by a fractional transform of the solution to an SDE satisfying the Yamada-Watanabe condition. These models are generalizations of a fractional version of the Heston model. We establish sample path and small-noise large deviation principles for the log-price process in a non-Gaussian model and illustrate how to compute the second order Taylor expansion of the rate function in a simplified example.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Mathematics
Liangzhen Lei, Yutao Ma
Summary: This paper investigates the properties of beta-Jacobi ensembles under certain conditions. It provides the large deviation of p1+p2/p1 max(1 <= i <= n) lambda i when gamma > 0, and the large deviation of the corresponding empirical measure and a direct estimate when gamma = 0.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Computer Science, Artificial Intelligence
Changqin Huang, Ming Li, Dianhui Wang
Summary: Studies have shown that stochastic configuration networks (SCNs) have potential for rapid data modeling with good test performance, however, more theoretical analysis is needed for enhanced generalization capacities. A novel framework is proposed for building SCN ensembles by selecting appropriate base models and utilizing a new algorithm to improve generalization performance.
Article
Mathematics
Zdzislaw Brzezniak, Ben Goldys, Martin Ondrejat, Nimit Rana
Summary: We study the stochastic wave map equation with solutions on a d-dimensional compact Riemannian manifold. We prove the existence of a unique, global, and strong solution in local Sobolev spaces. The main contribution of this paper is the proof of the Large Deviations Principle for solutions when the noise vanishes.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Ecology
Gonche Danesh, Emma Saulnier, Olivier Gascuel, Marc Choisy, Samuel Alizon
Summary: Stochastic population dynamics simulations play a crucial role in ecological and epidemiological studies as they can generate time series and genealogies that capture the relatedness between individuals. However, current software packages for simulating phylogenetic trees often have simplified population dynamics models and are not suitable for simulating a large number of trees. To address these limitations, this study introduces TiPS, an R package that can generate trajectories and phylogenetic trees associated with a compartmental model. TiPS uses different simulation algorithms and a backwards-in-time approach to simulate trajectories and trees, respectively. It combines the flexibility of R for model definition and the speed of C++ for simulations execution. Benchmarking analyses show that TiPS is faster than existing packages and it is particularly useful for population genetics and phylodynamics studies that require a large number of phylogenies for population dynamics analysis.
METHODS IN ECOLOGY AND EVOLUTION
(2023)
Article
Mathematics, Applied
Yu Tao Ma
Summary: In this paper, the characteristics of beta-Jacobi ensembles with parameters p1, p2, n, and beta are studied. The weak convergence of empirical measures and the strong law of large numbers for extremal eigenvalues are proved.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
Article
Statistics & Probability
Archil Gulisashvili
Summary: This paper introduces time-inhomogeneous stochastic volatility models and obtains sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model. These results are then used to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Mathematics
David Alonso-Gutierrez, Joscha Prochno, Christoph Thaele
Summary: This work explores the connection between the KLS conjecture and the deviations of random vectors, as well as the projections in a ball. The study shows that the rate function undergoes a phase transition under different conditions.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mechanics
Cecile Monthus
Summary: In this study, large deviations at level 2.5 were applied to Markov processes with absorbing states to obtain the explicit extinction rate of metastable quasi-stationary states. This rate was determined based on the empirical time-averaged density and empirical flows over a large time-window T. The research revealed that the standard spectral problem for the slowest relaxation mode could be recovered through the optimization of the extinction rate using all these empirical observables. The study also demonstrated the derivation of large deviation properties of any time-additive observable of the Markov trajectory before extinction from the level 2.5, by decomposing the observable in terms of the empirical density and empirical flows. The general formalism described in this research has important theoretical implications and practical applications for continuous-time Markov chains and diffusion processes.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Biochemistry & Molecular Biology
Jinglei Lv, Maria Di Biase, Robin F. H. Cash, Luca Cocchi, Vanessa L. Cropley, Paul Klauser, Ye Tian, Johanna Bayer, Lianne Schmaal, Suheyla Cetin-Karayumak, Yogesh Rathi, Ofer Pasternak, Chad Bousman, Christos Pantelis, Fernando Calamante, Andrew Zalesky
Summary: The study found widespread brain structural abnormalities in patients with schizophrenia, including reductions in white matter tracts and cortical regions. However, the locations of these structural abnormalities are highly inconsistent between individuals, with most patients not matching the group-consensus pathological maps.
MOLECULAR PSYCHIATRY
(2021)
Article
Physics, Multidisciplinary
Nahuel Freitas, Gianmaria Falasco, Massimiliano Esposito
Summary: This method provides an effective expression for determining probability distribution away from equilibrium and accurately approximates the rate function through linear response theory at the level of the rate function, applicable to various physical and chemical systems. The approach can be extended to transient probabilities and non-autonomous dynamics, creating a virtual flow in probability space to determine the steady state rate function far from equilibrium.
NEW JOURNAL OF PHYSICS
(2021)
Article
Mathematics, Applied
Wen Xuan Chen, Fu Qing Gao
Summary: We study precise deviations for discrete ensembles. For the case of beta=2, we establish an asymptotic formula for the Christoffel-Darboux kernel of the discrete orthogonal polynomials on an infinite regular lattice with weight e(-NV(x)). Using this asymptotic formula, we obtain the precise deviations of the extreme value for the corresponding ensemble.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
