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This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…
In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
Low decoding latency and complexity are two important requirements of channel codes used in many applications, like machine-to-machine communications. In this paper, we show how these requirements can be fulfilled by using some special…
Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a…
Spatially coupled codes have been shown to universally achieve the capacity for a large class of channels. Many variants of such codes have been introduced to date. We discuss a further such variant that is particularly simple and is…
In this paper we study the optimality of the certainty equivalence approximation in robust finite-horizon optimization problems with expected cost. We provide an algorithm for determining the subset of the state-space for which the…
It is well known that {\em superposition coding}, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. In this paper we prove an upper bound on the minimal…
A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how…
We study sheaf codes, a type of linear codes with a fixed hierarchical collection of local codes, viewed as a sheaf of vector spaces on a finite topological space we call coded space. Many existing codes, such as tensor product codes,…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…