Related papers: Duality and LP Bounds for Codes with Locality

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…

We show how deviations from the dimensional scaling laws for exclusive processes may be related to a breakdown in the locality of quark-hadron duality. The essential principles are illustrated in a pedagogic model of a composite system with…

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…

Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…

We generalize the fundamental bounds of Delsarte thesis (1973) on codes of given degree and designs of given strength in the new setting of Bannai et al. (2025). We assume the scheme is weakly metric in the sense of (Sol\'e, 1989). We give…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we…

We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal operator that recovers the classical boundary integral,…

With the help of the newly developed S-lemma with interval bounds, we show that strong duality holds for the interval bounded generalized trust region subproblem under some mild assumptions, which answers an open problem raised by Pong and…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…

The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S.…

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…

Generalizing the known results on graded rings and modules, we formulate and prove the equivariant version of the local duality on schemes with a group action. We also prove an equivariant analogue of Matlis duality.

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space. In this article, we review the last developments concerning…

We provide a procedure to determine if a given nonlocal operator in a large N holographic CFT is dual to a local bulk operator on the geometry associated with a particular code subspace of the CFT. This procedure does not presuppose…

The relations and differences between various classification problems arising in the context of local two-dimensional conformal QFT, modular invariants, and subfactors are discussed. The extent to which locality implies modular invariance,…

Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries. The S-duality of the bulk gauge theory can be extended in a natural fashion to act on such half-BPS…

A locally testable code (LTC) is an error-correcting code that has a property-tester. The tester reads $q$ bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter $q$ is…