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In this letter we present a new construction of interleavers for turbo codes from 3-regular Hamiltonian graphs. The interleavers can be generated using a few parameters, which can be selected in such a way that the girth of the interleaver…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We explore the well-known Jaeger's directed cycle double cover conjecture which is equivalent to the assertion that every cubic bridgeless graph has an embedding on a closed orientable surface with no dual loop. We associate each cubic…
We study thick subcategories of derived categories of gentle algebras. Any thick subcategory of a derived category of a gentle algebra is generated by a set of string objects or a set of band objects. We show the thick subcategories…
We are interested in unsupervised reconstruction of complex near-capillary vasculature with thousands of bifurcations where supervision and learning are infeasible. Unsupervised methods can use many structural constraints, e.g. topology,…
We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…
Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the individual sheaves. We also prove a similar result in the…
Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic side length 2
In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar…
We consider post-selection inference for high-dimensional (generalized) linear models. Data carving (Fithian et al., 2014) is a promising technique to perform this task. However, it suffers from the instability of the model selector and…
We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford process and the twisted tensor…
Hypergraph expanders are hypergraphs with surprising, non-intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of $3$-uniform hypergraph expanders with polylogarithmic…
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…
Motivated by a conjecture of Xiao, we study supporting divisors of fibred surfaces. On the one hand, after developing a formalism to treat one-dimensional families of varieties of any dimension, we give a structure theorem for fibred…
A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and…
In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph~$G$ with adjacency matrix…
We study projective surfaces in $\mathbb{P}^3$ which can be written as Hadamard product of two curves. We show that quadratic surfaces which are Hadamard product of two lines are smooth and tangent to all coordinate planes, and such…
Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for…
We prove derived invariance of the cap product for associative algebras projective over a commutative ring.
We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pairwise cross at most $k$ times.