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 »
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 »
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 »
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 »
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 »
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 »
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 »
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 consider equations of the type: (Formula presented) , for general linear operators R in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localised solutions. Singularities can even form in settings where solutions dissipate an… 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 »