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 »
ABSTRACT For a finite graph $$ F $$ and a value $$ p\in \left[0,1\right] $$, let $$ I\left(F,p\right) $$ denote the largest $$ y $$ for which there is a sequence of graphs of edge density approaching $$ p $$ so that the induced $$ F $$-density of the sequence approaches $$ y $$. We show that for… 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 »
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 »
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 »
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 »
In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such non-Gaussian phenomena calls for Lévy noise, which accommodates jumps and extreme variations. We propose the Random… read more about this publication »
Alon and Shikhelman initiated the systematic study of a generalization of the extremal function. Motivated by algorithmic applications, the study of the extremal function (Formula presented.), that is, the number of cliques of order (Formula presented.) in (Formula presented.) -minor free graphs on… read more about this publication »
We present a new strategy for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions with the help of observation data from leading-order moments. A stochastic-statistical modeling framework is designed to enable systematic theoretical analysis… read more about this publication »
For each configuration of rational points on the affine line, we define an operation on the group of unstable motivic homotopy classes of endomorphisms of the projective line. We also derive an algebraic formula for the image of such an operation under Cazanave and Morel's unstable degree map,… read more about this publication »
We develop a computer-assisted symbolic method to show that a linearized Boussinesq flow in self-similar coordinates gives rise to an invertible operator. read more about this publication »
This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the H1 norm. For the spatial discretization, we consider the finite element method with quadrature using Pk basis on a… read more about this publication »
The microtubule cytoskeleton is comprised of dynamic, polarized filaments that facilitate transport within the cell. Polarized microtubule arrays are key to facilitating cargo transport in long cells such as neurons. Microtubules also undergo dynamic instability, where the plus and minus ends of… read more about this publication »
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold… read more about this publication »
We prove the equality of three conjectural formulas for Brumer–Stark units. The first formula has essentially been proven, so this paper also verifies the validity of the other two formulas. read more about this publication »
We consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. The model is derived by taking the incompressible limit of porous medium type equations, and the boundary instability of this model was recently studied in [16] using asymptotic analysis. In this paper, we further… read more about this publication »
BACKGROUND: Oropharyngeal cancer (OPC) exhibits varying responses to chemoradiation therapy, making treatment outcome prediction challenging. Traditional imaging-based methods often fail to capture the spatial heterogeneity within tumors, which influences treatment resistance and disease… read more about this publication »
For any Legendrian knot or link in (Formula presented.), we construct an (Formula presented.) algebra that can be viewed as an extension of the Chekanov–Eliashberg differential graded algebra. The (Formula presented.) structure incorporates information from rational symplectic field theory and can… read more about this publication »
We present examples of Legendrian knots in $\mathbb{R}^3$ that have linearized Legendrian contact homology over $\mathbb{Z}$ containing torsion. As a consequence, we show that there exist augmentations of Legendrian knots over $\mathbb{Z}$ that are not induced by exact Lagrangian fillings, even… read more about this publication »
Let ρ be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into SL2(C) expressed in terms of the Wirtinger generators of a diagram D. This diagram also determines an ideal triangulation of the complement called the octahedral decomposition. ρ induces… read more about this publication »