相关论文: A Simple Optimal Binary Representation of Mosaic F…

Which polygons admit two (or more) distinct lattice tilings of the plane? We call such polygons double tiles. It is well-known that a lattice tiling is always combinatorially isomorphic either to a grid of squares or to a grid of regular…

Computational methods to compute similarities between floor plans can help architects explore floor plans in large datasets to avoid duplication of designs and to search for existing plans that satisfy their needs. Recently, LayoutGMN…

A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…

We observe that a standard transformation between \emph{ordinal} trees (arbitrary rooted trees with ordered children) and binary trees leads to interesting succinct binary tree representations. There are four symmetric versions of these…

A multiple group rack is a rack which is a disjoint union of groups equipped with a binary operation satisfying some conditions. It is used to define invariants of spatial surfaces, i.e., oriented compact surfaces with boundaries embedded…

The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…

We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to…

Geometric objects are primarily represented using curves and surfaces and the subdivision schemes are the basic tools for these representations. This study is based on a new thought that there is a special relation between the binary and…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted to small cluster sizes or rely on various simplifying approximations. We have recently shown that the…

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope…

In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…

Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…

Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…

A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes the set of arbitrary plane partitions in a box and the set of symmetric plane partitions as bases of linear representations of Lie groups. We extend this method by…

We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in…

Building blocks containing strongly coupled posts offer new possibilities for advanced coaxial (comb-line) filter designs. Equivalent circuits based on the individual resonances of the posts cannot be used to reliably describe the behavior…