Related papers: Range Algebra for Safe Array Splits
In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naive height tends to infinity. Let $I \subset \mathbb{R}$ be an arbitrary bounded interval, and $Q$ be a sufficiently large number. We…
Classifying orthogonal arrays is a well known important class of problems that asks for finding all non-isomorphic, non-negative integer solutions to a class of systems of constraints. Solved instances are scarce. We develop two new methods…
In the first part of this paper we develop some theorems in linear algebra applicable to information theory when all random variables involved are linear functions of the individual bits of a source of independent bits. We say that a…
We investigate the class of completely regular codes in graphs with a distance partition C_0,..., C_\rho, where each set C_i, for 0<=i<=r-1, is an independent set. This work focuses on the existence problem for such codes in the…
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Most existing algorithms for dictionary learning assume that all entries of the (high-dimensional) input data are fully observed. However, in several practical applications (such as hyper-spectral imaging or blood glucose monitoring), only…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in…
In this short article I introduce the spray package, which provides some functionality for handling sparse arrays. The package uses the C++ Standard Template Library's map class to store and retrieve elements. One natural application for…
This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an $(n-1,w)$-difference triangle set are used as supports of the columns of rate…
The rational index of a context-free language $L$ is a function $f(n)$, such that for each regular language $R$ recognized by an automaton with $n$ states, the intersection of $L$ and $R$ is either empty or contains a word shorter than…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
For many tracking and surveillance applications, background subtraction provides an effective means of segmenting objects moving in front of a static background. Researchers have traditionally used combinations of morphological operations…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and…
There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…