Although real-coded evolutionary algorithms (EAs) have been applied to optimization problems for over thirty years, the convergence properties of these methods remain poorly understood. We discuss the use of discrete random variables to perform search in real-valued EAs. Although most real-valued EAs perform mutation with continuous random variables, we argue that EAs using discrete random vari...

We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse transformation from the separation variables to the discrete lattice variables may be factorised as a sequence of canonical transformations, following the procedure out...

We discuss the classical efficiency criteria in density estimation and propose some variants. The context is a general density estimation scheme that contains the cases of i.i.d. or dependent random variables, in discrete or continuous time. Unbiased estimation, optimality and asymptotic optimality are considered. An example of a density estimator that satisfies some suggested criteria is given...

We describe a framework and an algorithm for solving hybrid influence diagrams with discrete, continuous, and deterministic chance variables, and discrete and continuous decision variables. A continuous chance variable in an influence diagram is said to be deterministic if its conditional distributions have zero variances. The solution algorithm is an extension of Shenoy’s fusion algorithm for ...

in this paper at rst, a history of mathematical models is given.next, some basic information about random variables, stochastic processesand markov chains is introduced. as follows, the entropy for a discrete timemarkov process is mentioned. after that, the entropy for sis stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

Instrumental variable models for discrete outcomes are set, not point, identifying. The paper characterises identi…ed sets of structural functions when endogenous variables are discrete. Identi…ed sets are unions of large numbers of convex sets and may not be convex nor even connected. Each of the component sets is a projection of a convex set that resides in a much higher dimensional space ont...

1 Stochastic processes A stochastic process is an indexed collection of random variables, {Xt}, t ∈ T . If the index set T is discrete, we will often write t ∈ {1, 2, . . .}, to represent discrete time steps. For a finite number of variables, we will assume t ∈ 1 : d as usual, where d is the length of the sequence. If the state space X is finite, we will write Xt ∈ {1, 2, . . . ,K}, where K is ...

This paper proposes a probabilistic power flow (PPF) method considering continuous and discrete variables (continuous and discrete power flow, CDPF) for power systems. The proposed method—based on the cumulant method (CM) and multiple deterministic power flow (MDPF) calculations—can deal with continuous variables such as wind power generation (WPG) and loads, and discrete variables such as fuel...

This paper proposes a modified sine cosine algorithm (MSCA) for discrete sizing optimization of truss structures. The original sine cosine algorithm (SCA) is a population-based metaheuristic that fluctuates the search agents about the best solution based on sine and cosine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical function...