Search results for "Combinatorics"
showing 10 items of 1770 documents
The b-chromatic number of power graphs
2003
The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.
A simulation function approach for best proximity point and variational inequality problems
2017
We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
Normal, Abby Normal, Prefix Normal
2014
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number \(\textit{pnw}(n)\) of prefix normal words of length n, showing that \(\textit{pnw}(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)\) for some c and \(\textit{pnw}(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)\). We introduce efficient algorithms for testing the prefix normal property and a “mechanical algorithm” for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes t…
Skinning Measures with Potential on CAT(–1) Spaces
2019
In this chapter, we introduce skinning measures as weighted pushforwards of the Patterson{Sullivan densities associated with a potential to the unit normal bundles of convex subsets of a CAT(–1) space.
Multi-dimensional pattern matching with dimensional wildcards
1995
We introduce a new multi-dimensional pattern matching problem, which is a natural generalization of the on-line search in string matching. We are given a text matrix A[1: n1, ..., 1:n d ] of size N= n1×n2×...×n d , which we may preprocess. Then, we are given, online, an r-dimensional pattern matrix B[1:m1,...,1:m r ] of size M= m1×m2×...×m r , with 1≤r≤d. We would like to know whether B*=B*[*, 1:m1,*, ...,1: mr, *] occurs in A, where * is a dimensional wildcard such that B* is any d-dimensional matrix having size 1 × ... × m1×...1×m r ×...1 and containing the same elements as B. Notice that there might be (d/r)≤2d occurrences of B* for each position of A. We give CRCW-PRAM algorithms for pr…
Real-time data processing in the ALICE High Level Trigger at the LHC
2019
At the Large Hadron Collider at CERN in Geneva, Switzerland, atomic nuclei are collided at ultra-relativistic energies. Many final-state particles are produced in each collision and their properties are measured by the ALICE detector. The detector signals induced by the produced particles are digitized leading to data rates that are in excess of 48 GB/$s$. The ALICE High Level Trigger (HLT) system pioneered the use of FPGA- and GPU-based algorithms to reconstruct charged-particle trajectories and reduce the data size in real time. The results of the reconstruction of the collision events, available online, are used for high level data quality and detector-performance monitoring and real-tim…
On the calculation of derived variables in the analysis of multivariate responses
1992
AbstractThe multivariate regression of a p × 1 vector Y of random variables on a q × 1 vector X of explanatory variables is considered. It is assumed that linear transformations of the components of Y can be the basis for useful interpretation whereas the components of X have strong individual identity. When p ≥ q a transformation is found to a new q × 1 vector of responses Y∗ such that in the multiple regression of, say, Y1∗ on X, only the coefficient of X1 is nonzero, i.e. such that Y1∗ is conditionally independent of X2, …, Xq, given X1. Some associated inferential procedures are sketched. An illustrative example is described in which the resulting transformation has aided interpretation.
Transversal competences and character education in Latvia: needs analysis report
2018
The national report “Transversal competences and character education in Latvia: Needs analysis report” is a part of the transnational intellectual output 1 “Needs analysis report” elaborated within the Erasmus+ project “Supporting teachers for developing intra-personal competences and character education at school (ARETE CATALYST)”, 2017-1-LV01-KA201-035435. The research report is structured in four parts as follows: 1) A detailed description of transversal competences and character education in Latvia; 2) Case studies of best practices in Latvia; 3) Benchmarking of transversal competences and character education in UK and USA; 4) Developing pupils’ intrapersonal competencies and character …
ChemInform Abstract: Nb4Te17I4, a New Pseudo One-Dimensional Solid-State Polytelluride.
2010
The new ternary compound Nb4Te17I4 has been prepared and structurally characterized. It crystallizes in the monoclinic system, space group C2/c with unit-cell parameters a = 16.199(4), b = 8.128(2), c = 27.355(6) A, β = 110.84(2)°, Z = 4. The structure consists of infinite one-dimensional niobium/tellurium chains running parallel to the crystallographic c direction. The chains are separated by iodine atoms. Short and long metal–metal distances alternate in the sequence of three consecutive short bonds ([d ≈ 3.1 – 3.2 A) and one long (d = 4.268 A) metal–metal separation. Each Nb atom is eight-coordinate. The composition of the chain is ∞11[(Nb5+)2(Nb4+)2(Te22−)4(Te32−)3(I−)4].
The pedagogy of multiliteracies as a code breaker : A suggestion for a transversal approach to computing education in basic education
2021
While computing has been (re)introduced into the basic education curricula in various countries, its actual implementation appears to be inconsistent. There are schools in which computing education is commonplace, while the implementation seems to be lagging behind in others. There is emerging evidence that some teachers do not consider computing education relevant, meaningful and important and, thus, intentionally neglect its provision. This is problematic as understanding the principles of code and computing is crucial for agentic citizenship in the post-digital era. This paper argues that one main reason for these teachers' reluctance is the economy-driven discursive framing of computing…