相关论文: Convex expansion for finite distributive lattices …

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…

Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary…

Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets of discrete valuations. Over purely transcendental field extensions of fields that…

A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…

Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…

For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices $xx^{\mathrm{H}}$, where the elements of $x \in \mathbb{C}^n$ are $m$th unit roots. These polytopes have applications in ${\text{MAX-3-CUT}}$, digital…

An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…

We generalise structure tree theory, which is based on removing finitely many edges, to removing finitely many vertices. This gives a significant generalization of Tutte's tree decomposition of 2-connected graphs into 3-connected blocks.…

The direct application of the definition of sorting in lattices is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a…

We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…

In the present paper, we propose a novel generalization of the celebrated MMP algorithm in order to find the wavefront propagation and the cut-locus on a convex polyhedron with an emphasis on actual implementation for instantaneous…

In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…

Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…

Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors proved the converse. In…