Search results for "Near space"

Ein Axiomensystem f�r partielle affine R�ume

1994

A partial linear space with parallelism is called partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. These partial affine spaces will be characterized by a system of three axioms for partial linear spaces with parallelism.

Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six

2017

We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.

Entropic Profiles, Maximal Motifs and the Discovery of Significant Repetitions in Genomic Sequences

2014

The degree of predictability of a sequence can be measured by its entropy and it is closely related to its repetitiveness and compressibility. Entropic profiles are useful tools to study the under- and over-representation of subsequences, providing also information about the scale of each conserved DNA region. On the other hand, compact classes of repetitive motifs, such as maximal motifs, have been proved to be useful for the identification of significant repetitions and for the compression of biological sequences. In this paper we show that there is a relationship between entropic profiles and maximal motifs, and in particular we prove that the former are a subset of the latter. As a furt…

On semi-fredholm properties of a boundary value problem inR + n

1988

The paper considers a boundary value problem with the help of the smallest closed extensionL ∼ :H k →H k 0×B h 1×...×B h N of a linear operatorL :C (0) ∞ (R + n ) →L(R + n )×L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) ∞ (R + n )) denotes the linear space of smooth functionsR n →C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 ∞ , resp.),L(R n−1) is the Schwartz class of functionsR n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ∼) and for the uniqueness of solutionsL ∼ U=F are expressed. In addition, ana prio…

Finite semiaffine linear spaces

1985

Adaptive learning of compressible strings

2020

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm needs to ask the oracle $\sigma n/4 -O(n)$ queries in order to be able to reconstruct the hidden string, where $\sigma$ is the size of the alphabet of $S$ and $n$ its length, and gave an algorithm that spends $(\sigma-1)n+O(\sigma \sqrt{n})$ queries to reconstruct $S$. The main contribution of our paper is to improve the above upper-bound in the context where the string is compressible. We first present a universal algorithm that, given a (computable) compre…

Parallel and Space-Efficient Construction of Burrows-Wheeler Transform and Suffix Array for Big Genome Data

2016

Next-generation sequencing technologies have led to the sequencing of more and more genomes, propelling related research into the era of big data. In this paper, we present ParaBWT, a parallelized Burrows-Wheeler transform (BWT) and suffix array construction algorithm for big genome data. In ParaBWT, we have investigated a progressive construction approach to constructing the BWT of single genome sequences in linear space complexity, but with a small constant factor. This approach has been further parallelized using multi-threading based on a master-slave coprocessing model. After gaining the BWT, the suffix array is constructed in a memory-efficient manner. The performance of ParaBWT has b…

Spaces of holomorphic functions in regular domains

2009

AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.

Uncountable classical and quantum complexity classes

2018

It is known that poly-time constant-space quantum Turing machines (QTMs) and logarithmic-space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (A.C. Cem Say and A. Yakaryılmaz, Magic coins are useful for small-space quantum machines. Quant. Inf. Comput. 17 (2017) 1027–1043). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough for PTMs on unary languages in sweeping reading mode or logarithmic space for one-way head. On unary languages, for quantum models, we obtain middle logarithmic space for counter machines. For binary la…

On Representing Concepts in High-dimensional Linear Spaces

2017

Producing a mathematical model of concepts is a very important issue in artificial intelligence, because if such a model were found this, besides being a very interesting result in its own right, would also contribute to the emergence of what we could call the ‘mathematics of thought.’ One of the most interesting attempts made in this direction is P. Gardenfors’ theory of conceptual spaces, a ¨ theory which is mostly presented by its author in an informal way. The main aim of the present article is contributing to Gardenfors’ theory of conceptual spaces ¨ by discussing some of the advantages which derive from the possibility of representing concepts in high-dimensional linear spaces.