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Moment functions of higher rank on some types of hypergroups
We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The...
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Constrained optimization of rank-one functions with indicator variables
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision...
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A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions
Polynomial approximation of smooth functions is becoming increasingly important in fields like numerical analysis and scientific computing. These...
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Moment functions of higher rank on polynomial hypergroups
In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial...
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Furnas rank
In the original publication by Furnas [52], the Furnas rank (also sometimes referred to as Furnas’ R statistic) was introduced as a tool for sampling...
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Morrey’s Conjecture for the Planar Volumetric-Isochoric Split: Least Rank-One Convex Energy Functions
We consider Morrey’s open question whether rank-one convexity already implies quasiconvexity in the planar case. For some specific families of...
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Around the log-rank conjecture
The log-rank conjecture states that the communication complexity of a boolean matrix A is bounded by a polynomial in the log of the rank of A ....
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Deviation of the rank and crank modulo 11
In this paper, we build on the recent results of Frank Garvan and Rishabh Sarma as well as classical results of Bruce Berndt in order to establish...
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A two-phase rank-based algorithm for low-rank matrix completion
Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target...
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Monogenic Functions with Values in Commutative Algebras of the Second Rank with Unit and the Generalized Biharmonic Equation with Double Characteristic
We prove that any commutative and associative algebra 𝔹 * of the second rank with unit over the field of complex numbers ℂ contains bases { e 1 , e 2 }...
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Evaluation of Hecke–Rogers series and expansions of the rank function
A formula is established for the evaluation of double series of Hecke–Rogers type in terms of theta functions and Appell–Lerch functions. This...
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A new perspective on low-rank optimization
A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple...
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Integral representations of rank two false theta functions and their modularity properties
False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the...
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Monogenic functions with values in algebras of the second rank over the complex field and a generalized biharmonic equation with a triple characteristic
The statement that any two-dimensional algebra 𝔹 * of the second rank with unity over the field of complex numbers contains such a basis { e 1 ; e 2 }...
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Schmidt Rank and Singularities
We revisit Schmidt’s theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of...
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Graph coloring and semidefinite rank
This paper considers the interplay between semidefinite programming, matrix rank, and graph coloring. Karger et al. (J ACM 45(2):246–265, 1998) give...
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New symmetries for Dyson’s rank function
At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan’s mock theta functions analogous to...
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Nonlocal Matrix Rank Minimization Method for Multiplicative Noise Removal
Multiplicative noise removal is a challenging problem in image denoising. In this paper, we develop a nonlocal matrix rank minimization method for...
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On solving a rank regularized minimization problem via equivalent factorized column-sparse regularized models
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can...
