Related papers: "Barcodes" for continuous maps and a brief introdu…
A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and…
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…
In a former paper the authors introduced two new systematic authentication codes based on the Gray map over a Galois ring. In this paper, it is proved the one-to-one onto correspondence between keys and encoding maps for the second…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…
We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classes. These new invariants are as simple, but more discerning…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings. In this work, we introduce sub-barcodes and…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove…
An $n$-valued map is a set-valued continuous function $f$ such that $f(x)$ has cardinality $n$ for every $x$. Some $n$-valued maps will "split" into a union of $n$ single-valued maps. Characterizations of splittings has been a major theme…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. In this system, messages from two correlated sources are jointly encoded, and…
Polar code is a breakthrough in coding theory. Using list successive cancellation decoding with large list size L, polar codes can achieve excellent error correction performance. The L partial decoded vectors are stored in the path memory…
Bar charts are among the most frequently used visualizations, in part because their position encoding leads them to convey data values precisely. Yet reproductions of single bars or groups of bars within a graph can be biased. Curiously,…
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of…
We improve the method in \cite{Seidl:10} for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for…
In this paper we propose a new class of spatially coupled codes based on repeat-accumulate protographs. We show that spatially coupled repeat-accumulate codes have several advantages over spatially coupled low-density parity-check codes…