Asymptotic estimate for the mathematical expectation of the number of elements in the Pareto set

Cybernetics ◽  
1976 ◽  
Vol 11 (1) ◽  
pp. 108-113 ◽  
Author(s):  
V. M. Ivanin
Keyword(s):  
Mathematical Expectation ◽  
Asymptotic Estimate ◽  
Pareto Set

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

PROCEDURES OF AGGREGATION OF THE INDICATОRS OF SUSTAINABLE DEVELOPMENT OF THE HIGHER SCHOOL INSTITUTIONS

2020 ◽  
pp. 28-31
Author(s):  
Д.В. Довгая ◽  
М.Х. Мальсагов
Keyword(s):  
Sustainable Development ◽  
Pareto Set

В статье описан подход к оценке функционирования высших учебных заведений на уровне кафедры, факультета и университета в целом. Он включает в себя - агрегирование показателей с помощью специальных функций; построение множества Парето в пространстве индексов; выбор наилучшей точки множества Парето с помощью скаляризации. In this paper we describe an approach to the evaluation of the higher school institutions on the levels of a chair, a faculty, and the whole university. The approach includes - an aggregation of the indicators by means of specific functions; building of Pareto set in the space of the research, teaching, and innovative criteria; a choice of the best point in the Pareto set by scalarization.

Pareto Set as a Model for Dispatching Resources in Emergency Centres

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarc�sio Pequeno ◽  
Joel Rodrigues
Keyword(s):  
Pareto Set

Pareto Set as a Model for Dispatching Resources in Emergency Centres (Preprint)

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues
Keyword(s):  
Operational Research ◽  
Real Data ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Four Dimensions ◽  
Multi Objective ◽  
The Best Approximation ◽  
One Year ◽  
The Cost

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.

scholarly journals On the Number of Quadratic Twists with a Rational Point of Almost Minimal Height

2020 ◽  
Author(s):  
Joachim Petit
Keyword(s):  
Asymptotic Formula ◽  
Elliptic Curve ◽  
Asymptotic Estimate ◽  
Rational Point ◽  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Quadratic Twists ◽  
The Family ◽  
Minimal Height ◽  
Real Quadratic

Abstract We investigate the number of curves having a rational point of almost minimal height in the family of quadratic twists of a given elliptic curve. This problem takes its origin in the work of Hooley, who asked this question in the setting of real quadratic fields. In particular, he showed an asymptotic estimate for the number of such fields with almost minimal fundamental unit. Our main result establishes the analogue asymptotic formula in the setting of quadratic twists of a fixed elliptic curve.

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