23 papers · ranked by Valyu relevance
Xu Yang
Asymptotic analysis is one of the classical tools for bridging models across scales. Behind many such derivations lies a common symbolic structure: an ansatz, a substitution, an order-by-order matching procedure, and the extraction of effective equations or interface conditions. This article revisits that structure…
Benoit Cloitre
Two linear recurrences exhibit mirror symmetry connecting the constants e and π. When parametrized, their asymptotic connection constants extend to meromorphic functions satisfying additive functional equations with rational coefficients. We call such functions additive Gamma functions (AGFs), recognizing Euler's Γ(z)…
David Berenstein, Paula Garcia Martinez
We propose an asymptotic bootstrap method to evaluate moment integrals that arise in problems related to hermitian matrix models. These are normalized integrals of the form $a_n=\int^{\infty}_{-\infty} x^n \exp(-V(x)) dx$ where $V(x)$ is a polynomial of $x$. The method is applicable even when the coupling constants in…
Madhuparna Das, Nicolas Robles
where ∆ f (n) = f(n + 1) − f(n). In this article, we establish a central limit theorem for the number of summands in such partitions when f(n) = σr(n) denotes the generalised divisor function, defined as σr(n) = P d|n d r for integer r ≥ 2. This can be considered as a generalisation of the work of Lipnik, Madritsch…
Emine Atıcı Endes, Neslihan Nesliye Pelen
Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the specific conditions that convert stable plaques into unstable ones remain unclear. To provide insight into the conditions for this…
Aaron J. Moston-Duggan, C. J. Howls, Christopher J. Lustri
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not present in the continuous Airy function and is typically only encountered in solutions to third-order or higher linear homogeneous, or…
Damian Clancy
We consider stochastic population processes that are almost surely absorbed at the origin within finite time. Our interest is in the quasistationary distribution, ${\varvec{u}}$, and the expected time, $\tau$, from quasistationarity to extinction, both of which we study via WKB approximation. This approach involves…
Bing He, Guanting Liu
Integer partitions have fascinated people for centuries, from Ramanujan's groundbreaking congruences to the modern theory of modular forms. This paper investigates the statistical properties of odd unimodal sequences--a natural refinement where sequences rise to a peak and then fall, but with the constraint that all…
Nicholas Pischke, Thomas Powell
We provide abstract, general and highly uniform rates of asymptotic regularity for a generalized stochastic Halpern-style iteration, which incorporates a second mapping in the style of a Krasnoselskii-Mann iteration. This iteration is general in two ways: First, it incorporates stochasticity completely abstractly…
Liangrong Peng, Liu Hong, José María Amigó
We present a systematic derivation of asymptotic expansions of nonequilibrium thermodynamics for chemical reaction networks (CRNs) based on singular perturbation theory. For a general reversible CRN with fast-slow kinetics, we obtain the first and second laws of thermodynamics for the asymptotic expansion model. We…
Sean P. Svihla, Manuel E. Lladser
Haar-like wavelets sparsify the phylogenetic covariance matrices of large, uniformly random k-regular trees with overwhelmingly high probability. This motivates the Haar-like distance, a β-diversity metric that implicitly ranks the splits of a reference phylogeny by their relevance in differentiating two microbial…
Ibrahim A. Nafisah, Mohamed Kayid, Alessandro Mazzoccoli
The identification of aging behavior in reliability and survival data is a central problem with important implications for risk assessment, system reliability, and decision-making in applied fields. The exponential model serves as the standard benchmark corresponding to the absence of aging, making the detection of…
Qiyue Huang, Anyin Feng, Qiang Wu, Xingwei Tong
This study develops estimation methods for a deep partially linear Cox proportional hazards model with a change point under current status data, aiming to accommodate complex change-point effects. Prior work has largely relied on linear models, which may inadequately capture relationships among multivariate covariates…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz, Gerhard Schindl
We prove several improved versions of the Borel-Ritt theorem about the surjectivity of the asymptotic Borel mapping in classes of functions with M-uniform asymptotic expansion on an unbounded sector of the Riemann surface of the logarithm. While in previous results the weight sequence M of positive numbers is supposed…
E. G. Cooch, D. I. MacKenzie, J. A. Royle
Data augmentation is now a standard device across capture–recapture and occupancy analysis: adding a fixed number M of all-zero encounter histories replaces a model of unknown dimension with one of fixed dimension. Although M is often treated as a computational tuning choice, it also specifies a finite superpopulation…
Łukasz Płociniczak, Marek Teuerle, Hubert Woszczek
We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of Lévy walks, in which transport is driven by a convex combination of fractional material derivatives and a source term. Using techniques of Fourier-Laplace transforms, we first prove the…
Yamaan Attwa, Albert López Vidal, Patrick J. Morris
The Ramsey number r(t; ℓ) is the smallest n such that every ℓ-coloring of the edges of Kn gives a monochromatic Kt. In recent years, there have been several improvements on asymptotic lower bounds for these numbers when ℓ ≥ 3. This started with a breakthrough result of Conlon and Ferber, followed by further…
Metehan Kara, Murat Tuğrul
Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that…
Authors not listed
The twin property of aromaticity and antiaromaticity is one of the most important and well-known concepts in chemical structure and bonding, but it is also an over-a-century enigma as the necessary and sufficient conditions of aromaticity and antiaromaticity have not been fully understood yet, and the relationships…
Authors not listed
Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been…
Rudra Prakash, Shaunak Sen
The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To…
Authors not listed
Bonkowski and De Souza [Sol. Stat. Ionics 429, 116967 (2025)] provide a guide for performing molecular dynamics simulations of ion transport, including methods for estimating diffusion coefficients and their uncertainties from mean-squared displacement (MSD) data. The discussion of uncertainty in estimated diffusion…