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 »
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 »
Abstract 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… 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 »
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 »
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 »
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 »
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 »
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 »
The stein variational gradient descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the… 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 »
We study long-term behavior and stationary distributions for stochastic heat equations forced simultaneously by a multiplicative noise and an independent additive noise with the same distribution. We prove that nontrivial space-time translation-invariant measures exist for all values of the… read more about this publication »
Ramsey’s theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdős conjectured that the random 2-edge-coloring minimizes the number of monochromatic copies of Kk, and the conjecture was extended by Burr… read more about this publication »
We study the mixing time of a recently proposed efficiently implementable Lindbladian designed to prepare the Gibbs states in the setting of weakly interacting fermionic systems. We show that at any temperature, the Lindbladian spectral gap for even parity observables is lower bounded by a constant… read more about this publication »
Many fundamental problems in extremal combinatorics are equivalent to proving certain polynomial inequalities in graph homomorphism densities. In 2011, a breakthrough result by Hatami and Norine showed that it is undecidable to verify polynomial inequalities in graph homomorphism densities.… read more about this publication »
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application of the techniques of [DS22]. We also provide effective upper bounds for Betti numbers of compact quaternionic- and… read more about this publication »
The accurate quantification of symmetry is a key goal in biological inquiries because symmetry can affect biological performance and can reveal insights into development and evolutionary history. Recently, we proposed a versatile measure of symmetry, transformation information (TI), which provides… read more about this publication »
Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is desired. We introduce a new time-dependent Hamiltonian… read more about this publication »
In this paper, we investigate the instability of growing tumors by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al. (Z Angew Math Phys 74:107, 2023). Building upon the insights derived from… read more about this publication »