Following the approach of Eckhaus, Mielke, and Schneider for reaction–diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg–Landau approximation. Notably, our analysis includes higher-order,… read more about this publication »
This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation in three dimensions, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives stability estimates for identifying the… read more about this publication »
We study “V-shaped” solutions to the KPZ equation, those having opposite asymptotic slopes θ and -θ, with θ>0, at positive and negative infinity, respectively. Answering a question of Janjigian, Rassoul-Agha, and Seppäläinen, we show that the spatial increments of V-shaped solutions cannot be… read more about this publication »
Oxidative stress occurs when there is an imbalance between oxidants and antioxidants, leading to the accumulation of reactive oxygen species (ROS). Excessive ROS can damage lipids, proteins, and DNA, contributing to cellular dysfunction and disease. Interestingly, premenopausal females tend to have… read more about this publication »
Microtubules are dynamic biopolymers whose lengths are continuously regulated by the concerted actions of polymerization, depolymerization, and motor-protein activity. While numerous mathematical models have explored the regulation of filament length, most have been formulated in the context of… read more about this publication »
A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with… read more about this publication »
In this paper, we propose two approaches to derive the discrete Poincaré inequality for the B-schemes, a family of finite volume discretization schemes, for the one-dimensional Fokker-Planck equation in full space. We study the properties of the spatially discretized Fokker-Planck equation in the… read more about this publication »
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines attracting monocytes to fight invading bacteria. Another… read more about this publication »
Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction–diffusion systems, we justify rigorously by Lyapunov–Schmidt reduction the formal amplitude (complex Ginzburg–Landau) equations describing Turing-type bifurcations of general reaction–diffusion–convection… read more about this publication »
Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p -adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant, then after a rational change of basis on the left and right,… read more about this publication »
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to… read more about this publication »
The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of Nakayama's lemma; complete theories of minimal and dense… read more about this publication »
We prove a quenched version of the large deviation principle for Birkhoff-like sums along a sequence of random quantum measurements driven by an ergodic process. We apply the result to the study of entropy production in the two-time measurement framework. read more about this publication »
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale systems is mitigating the large errors that arise when… read more about this publication »
BACKGROUND AND AIMS: Elevated hepatic homocysteine (Hcy) contributes to hepatic inflammation and fibrogenesis in metabolic dysfunction-associated steatotic liver disease (MASLD). We aimed to evaluate the association between serum Hcy levels and the risk of MASLD and hepatic fibrosis in a large,… read more about this publication »
AbstractAs environmental change accelerates globally, understanding concurrent organismal, species, and community responses is increasingly vital. Here, we examine these collective responses by incorporating genotype-specific thermal reaction norms into an eco-evolutionary predator-prey model,… read more about this publication »
Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases, and the nucleation of new filaments is believed to be… read more about this publication »
We study the solution theory of the whole-space static (elliptic) Hamilton--Jacobi--Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the discount factor is sufficiently large, there exists a… read more about this publication »
Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction. In this work, we extend the investigation initiated by Kiselev and Ryzhik [Comm. Partial Differential Equations, 37 (… read more about this publication »
The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solutions of this bow representation are in one-to-one correspondence with the instantons. We also prove that this… read more about this publication »
This work investigates the ambient potential identification problem in inverse mean-field games (MFGs), where the goal is to recover the unknown potential from the value function at equilibrium. We propose a simple yet effective iterative strategy, equilibrium correction iteration (ECI), that… read more about this publication »
We study the inviscid Burgers equation on the circle T := R/Z forced by the spatial derivative of a Poisson point process on R × T. We construct global solutions with mean θ simultaneously for all θ ∈ R, and in addition construct their associated global shocks (which are unique except on a… read more about this publication »