Search results for "Crete"
showing 10 items of 2495 documents
Information potential for some probability density functions
2021
Abstract This paper is related to the information theoretic learning methodology, whose goal is to quantify global scalar descriptors (e.g., entropy) of a given probability density function (PDF). In this context, the core concept is the information potential (IP) S [ s ] ( x ) : = ∫ R p s ( t , x ) d t , s > 0 of a PDF p(t, x) depending on a parameter x; it is naturally related to the Renyi and Tsallis entropies. We present several such PDF, viewed also as kernels of integral operators, for which a precise relation exists between S[2](x) and the variance Var[p(t, x)]. For these PDF we determine explicitly the IP and the Shannon entropy. As an application to Information Theoretic Learning w…
Adjacent vertices can be hard to find by quantum walks
2018
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element. We show that if the search space contains more than one marked element, their placement may drastically affect the performance of the search. More specifically, we study search by quantum walks on general graphs and show a wide class of configurations of marked vertices, for which search by quantum walk needs Ω(N) steps, that is, it has no speed-up over the classical exhaustive search. The demonstrated configurations occur for certain placements of two or more adjace…
Aggregation of Risk Level Assessments Based on Fuzzy Equivalence Relation
2017
The paper deals with the problem of aggregation of risk level assessments. We describe the technique of a risk level evaluation taking into account values of the risk level obtained for objects which are in some sense equivalent. For this purpose we propose to use the construction of a general aggregation operator based on the corresponding fuzzy equivalence relation. Numerical example of the investment risk level aggregation using an equivalence relation obtained on the basis of different macroeconomic factors for countries of one region is considered.
From fuzzy metric spaces to modular metric spaces: a fixed point approach
2017
We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.
An exact method for graph coloring
2006
International audience; We are interested in the graph coloring problem. We propose an exact method based on a linear-decomposition of the graph. The complexity of this method is exponential according to the linearwidth of the entry graph, but linear according to its number of vertices. We present some experiments performed on literature instances, among which COLOR02 library instances. Our method is useful to solve more quickly than other exact algorithms instances with small linearwidth, such as mug graphs. Moreover, our algorithms are the first to our knowledge to solve the COLOR02 instance 4-Inser_3 with an exact method.
Longest Motifs with a Functionally Equivalent Central Block
2004
International audience; This paper presents a generalization of the notion of longest repeats with a block of k don't care symbols introduced by [Crochemore et al., LATIN 2004] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [Crochemore et al., LATIN 2004] and extend to the case of regular expressions with no Kleene closure or …
The Steiner Traveling Salesman Problem and its extensions
2019
Abstract This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.
Distance graphs and the T-coloring problem
1999
Abstract The T-coloring problem is, given a graph G = (V, E), a set T of nonnegative integers containing 0, and a ‘span’ bound s ⩾ 0, to compute an integer coloring f of the vertices of G such that |f(ν) − f(w)| ∉ T ∀νw ∈ E and max f − min f ⩽ s. This problem arises in the planning of channel assignments for broadcast networks. When restricted to complete graphs, the T-coloring problem boils down to a number problem which can be solved efficiently for many types of sets T. The paper presents results indicating that this is not the case if the set T is arbitrary. To these ends, the class of distance graphs is introduced, which consists of all graphs G : G ≅ G(A) for some (finite) set of posi…
Thin and fat sets for doubling measures in metric spaces
2011
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.
A function whose graph has positive doubling measure
2014
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that the doubling constant of the measure can be chosen to be arbitrarily close to the doubling constant of the Lebesgue measure.