Related papers: Linear programming duality for geometers
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…
Large language models (LLMs) have shown remarkable capabilities across diverse coding tasks. However, their adoption requires a true understanding of program execution rather than relying on surface-level patterns. Existing benchmarks…
We generalize our previous lattice construction of the abelian bosonization duality in $2+1$ dimensions to the entire web of dualities as well as the $N_f=2$ self-duality, via the lattice implementation of a set of modular transformations…
We present a new kind of nontermination argument, called geometric nontermination argument. The geometric nontermination argument is a finite representation of an infinite execution that has the form of a sum of several geometric series.…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the…