Related papers: On the Symmetric Difference Property in Difference…
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the $q$-analogues of projective systems and blocking sets. We also illustrate how to associate a classical…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which the $v_i$ are the rows. We characterize properties of $v$ in…
In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a…
Symmetry is a ubiquitous and fundamental property in the visual world, serving as a critical cue for perception and structure interpretation. This paper investigates the detection of 3D reflection symmetry from a single RGB image, and…
We give a framework for generalizing LDPC code constructions that use Transversal Designs or related structures such as mutually orthogonal Latin squares. Our construction offers a broader range of code lengths and codes rates. Similar…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
The $k$-th symmetric product of a graph $G$ with vertex set $V$ with edge set $E$ is a graph with vertices as $k$-sets of $V$, where two $k$-sets are connected by an edge if and only if their symmetric difference is an edge in $E$. Using…
Let $M$ be a free module of rank $m$ over a commutative unital ring $R$ and let $N$ be its free submodule. We consider the problem when a given element of the exterior product $\Lambda^pM$ is divisible, in a sense, over elements of the…
Self-orthogonal codes have been of interest due to there rich algebraic structures and wide applications. Euclidean self-orthogonal codes have been quite well studied in literature. Here, we have focused on Hermitian self-orthogonal codes.…
It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with commuting and normal block entries of dimension $d$, the separability of such a block matrices is equivalent to its semi-positive definity. The separability…
A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been known for a long time, attracting recent interest due to…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
The monomial basis for polynomials in N variables is labeled by compositions. To each composition there is associated a hook-length product, which is a product of linear functions of a parameter. The zeroes of this product are related to…
An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…
Clustering is spotting pattern in a group of objects and resultantly grouping the similar objects together. Objects have attributes which are not always numerical, sometimes attributes have domain or categories to which they could belong…
We explore the application of generating symmetries, i.e. symmetries that depend on a parameter, to integrable hyperbolic third order equations, and in particular to consistent pairs of such equations as introduced by Adler and Shabat (AS).…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
Step skew products with interval fibres and a subshift as a base are considered. It is proved that if the fibre maps are continuous, piecewise monotone, expanding and surjective and the subshift has the specification property and a periodic…