Related papers: A combinatorial characterization of tight fusion f…
Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of…
We introduce an FFT-based solver for the combinatorial continuous maximum flow discretization applied to computing the minimum cut through heterogeneous microstructures. Recently, computational methods were introduced for computing the…
Joint analysis of data from multiple sources has the potential to improve our understanding of the underlying structures in complex data sets. For instance, in restaurant recommendation systems, recommendations can be based on rating…
In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex $T^{2}$ in $\mathbb{R}^{2}$. We give the framelet transforms -- decomposition and reconstruction of the coefficients for framelets of a…
We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…
We propose high-order FDTD schemes based on the Correction Function Method (CFM) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an…
Deriving the Yukawa couplings and the resulting fermion masses and mixing angles of the Standard Model (SM) from a more fundamental theory remains one of the central outstanding problems in theoretical high-energy physics. It has long been…
We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too…
We give a detailed discussion of the recently developed Generalized Dynamical Mean-Field Theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is non-perturbative and exact in infinite dimensions and…
We study some combinatorial properties of the word metric of Thompson's group F in the standard two generator finite presentation. We explore connections between the tree pair diagram representing an element w of F, its normal form in the…
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally…
Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large…
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods…
Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two…
We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of…
Our research focuses on few-shot fine-grained image classification, which faces two major challenges: appearance similarity of fine-grained objects and limited number of samples. To preserve the appearance details of images, traditional…
We present a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as…
We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…
Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call…
We study a one-dimensional two-component Fermi gas in a harmonic trapping potential using finite temperature lattice quantum Monte Carlo methods. We are able to compute observables in the canonical ensemble via an efficient projective…