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While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The…
Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design…
Recently, implicit neural representations (INRs) have attracted increasing attention for multi-dimensional data recovery. However, INRs simply map coordinates via a multi-layer perception (MLP) to corresponding values, ignoring the inherent…
This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and…
We study disjunctive conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce…
Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer…
We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…
We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson groups called Pythagorean. For each natural number d we…
In this work we prove constructively that the complement ${\mathbb R}^n\setminus{\mathcal K}$ of an $n$-dimensional unbounded convex polyhedron ${\mathcal K}\subset{\mathbb R}^n$ and the complement ${\mathbb R}^n\setminus{\rm Int}({\mathcal…
We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in $\RP^n$ is maximal. That is, there exist generic configurations of real linear spaces such…
It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…
We study properties of 3-restricted min-wise independent sets of permutations and prove that the class of these sets is isomorphic to the class of subsets of vertices of multi-dimentional hypercube of certain size with certain pair-wise…
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
Fast and accurate large-scale energy system models are needed to investigate the potential of storage to complement the fluctuating energy production of renewable energy systems. However, standard Mixed-Integer Programming (MIP) models that…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
Many rotational invariants for crystal structure representations have been used to describe the structure-property relationship by machine learning. The machine learning interatomic potential (MLIP) is one of the applications of rotational…