Related papers: A combinatorial characterization of tight fusion f…

In this paper, uniqueness properties of a coupled tensor model are studied. This new coupled tensor model is used in a new method called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D. This method performs estimation of…

In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $\mathcal F$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F$ by a finite family of vectors with…

We systematically develop the formalism necessary for ensuring that boundary conditions of flavon fields in extra dimensions are consistent with heterotic string theory. Having developed a set of consistency conditions on the boundary…

Herein we propose a new numerical technique for solving field theories: the large momentum frame (LMF). This technique combines several advantages of lattice gauge theory with the simplicity of front form quantisation. We apply the LMF on…

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…

Though high redundancy rate of a tight frame can improve performance in applications, as the dimension increases, it also makes the computational cost skyrocket and the storage of frame coefficients increase exponentially. This seriously…

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the…

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a…

In this article, a Probability Mass Function (PMF) estimation method which tames the curse of dimensionality is proposed. This method, called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D, has for principle to partially…

Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of…

We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion…

In the first of this two-part series, we find `fixed point factorisation' formulas, towards an understanding of the fusion ring of WZW models. Fixed-point factorisation refers to the simplifications in the data of a CFT involving primary…

We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main…

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell-Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial…

Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…

A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…

Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear…

In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…