Search results for "Computation"
showing 10 items of 7362 documents
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Exact Quantum Query Complexity of $$\text {EXACT}_{k,l}^n$$
2017
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly k or l of the n input bits given by an oracle are 1. We find an optimal algorithm (for some cases), and a nontrivial general lower and upper bound on the minimum number of queries to the black box.
Quantum Query Complexity for Some Graph Problems
2004
The paper [4] by H. Buhrman and R. de Wolf contains an impressive survey of solved and open problems in quantum query complexity, including many graph problems. We use recent results by A.Ambainis [1] to prove higher lower bounds for some of these problems. Some of our new lower bounds do not close the gap between the best upper and lower bounds. We prove in these cases that it is impossible to provide a better application of Ambainis’ technique for these problems.
Structured Frequency Algorithms
2015
B.A. Trakhtenbrot proved that in frequency computability (introduced by G. Rose) it is crucially important whether the frequency exceeds \(\frac{1}{2}\). If it does then only recursive sets are frequency-computable. If the frequency does not exceed \(\frac{1}{2}\) then a continuum of sets is frequency-computable. Similar results for finite automata were proved by E.B. Kinber and H. Austinat et al. We generalize the notion of frequency computability demanding a specific structure for the correct answers. We show that if this structure is described in terms of finite projective planes then even a frequency \(O(\frac{\sqrt{n}}{n})\) ensures recursivity of the computable set. We also show that …
Y-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4
2012
Abstract Let F be a field of characteristic 0. We consider the upper triangular matrices with entries in F of size 2, 3 and 4 endowed with the grading induced by that of Vasilovsky. In this paper we give explicit computation for the multiplicities of the Y -proper graded cocharacters and codimensions of these algebras.
Quantum Identification of Boolean Oracles
2004
The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…
Fast and Simple Approximation of the Diameter and Radius of a Graph
2006
The increasing amount of data to be processed by computers has led to the need for highly efficient algorithms for various computational problems. Moreover, the algorithms should be as simple as possible to be practically applicable. In this paper we propose a very simple approximation algorithm for finding the diameter and the radius of an undirected graph. The algorithm runs in $O(m\sqrt{n})$ time and gives an additive error of $O(\sqrt{n})$ for a graph with n vertices and m edges. Practical experiments show that the results of our algorithm are close to the optimum and compare favorably to the 2/3-approximation algorithm for the diameter problem by Aingworth et al [1].
Towards next generation diagnostics for tuberculosis: identification of novel molecular targets by large-scale comparative genomics
2019
AbstractTuberculosis remains one of the main causes of death worldwide. The long and cumbersome process of culturingMycobacterium tuberculosiscomplex (MTBC) bacteria has encouraged the development of specific molecular tools for detecting the pathogen. Most of these tools aim to become novel tuberculosis diagnostics, and big efforts and resources are invested in their development, looking for the endorsement of the main public health agencies. Surprisingly, no study had been conducted where the vast amount of genomic data available is used to identify the best MTBC diagnostic markers. In this work, we use large-scale comparative genomics to provide a catalog of 30 characterized loci that ar…
CALANGO: a phylogeny-aware comparative genomics tool for discovering quantitative genotype-phenotype associations across species
2023
The increasing availability of high-quality genomic, annotation and phenotypic data for different species contrasts with the lack of general software for comparative genomics that integrates these data types in a statistically sound framework in order to produce biologically meaningful knowledge. In this work, we present CALANGO (Comparative AnaLysis with ANnotation-based Genomic cOmponentes), a first-principles comparative genomics tool to search for annotation terms, such as GO terms or Pfam domain IDs, associated with a quantitative variable used to rank species data, after correcting for phylogenetic relatedness. This information can be used to annotate genomes at any level, including p…
The Relative Efficacy of Price Announcements and Express Communication for Collusion: Experimental Findings
2014
Collusion is when firms coordinate on suppressing competition, and coordination typically requires that firms communicate in some manner. This study conducts experiments to determine what modes of communication are able to produce and sustain collusion and how the efficacy of communication depends on firm heterogeneity and the number of firms. We consider two different communication treatments: non-binding price announcements and unrestricted written communication. Our main findings are that price announcements allow subjects to coordinate on a high price but only under duopoly and when firms are symmetric. While price announcements do result in higher prices when subjects are asymmetric, t…