Search results for "Linear space"
showing 10 items of 16 documents
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…
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.
The Influence of H. Grassmann on Italian Projective N-Dimensional Geometry
1996
On May 29, 1883, Corrado Segre took his doctorate in Turin (Torino), under Enrico D’Ovidio’s guidance. His thesis (Segre 1884a,b) was published one year later in the Journal of the local Academy of Science, and after a short time it became a fundamental starting point for the development of Italian projective n-dimensional geometry.
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…
A remark on weakly convex continuous mappings in topological linear spaces
2009
Abstract Let C be a compact convex subset of a Hausdorff topological linear space and T : C → C a continuous mapping. We characterize those mappings T for which T ( C ) is convexly totally bounded.
Finite linear spaces in which any n-gon is euclidean
1986
Abstract An n-gon of a linear space is a set S of n points no three of which are collinear. By a diagonal point of S we mean a point p off S with the property that at least two lines through p intersect S in two points. The number of diagonal points is called the type of S. For example, a 4-gon has at most three diagonal points. We call an n-gon euclidean if (roughly speaking) it contains the maximal possible number of 4-gons of type 3. In this paper, we characterize all finite linear spaces in which, for a fixed number n ⩾ 5, any n-gon is euclidean. It turns out that these structures are essentially projective spaces or punctured projective spaces.
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…
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…
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.
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…