On-Line Load Balancing with Task Buffer

On-line load balancing is one of the most important problems for applications with resource allocation. It aims to assign tasks to suitable machines and balance the load among all of the machines, where the tasks need to be assigned to a machine upon arrival. In practice, tasks are not always required to be assigned to machines immediately. In this paper, we propose a novel on-line load balancing model with task buffer, where the buffer can temporarily store tasks as many as possible. Three algorithms, namely LPTCP1_α, LPTCP2_α, and LPTCP3_β, are proposed based on the Longest Processing Time (LPT) algorithm and a variety of planarization algorithms. The planarization algorithms are proposed for reducing the difference among each element in a set. Experimental results show that our proposed algorithms can effectively solve the on-line load balancing problem and have good performance in large scale experiments

Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results

The Convergence of a Cooperation Markov Decision Process System

In a general Markov decision progress system, only one agent’s learning evolution is considered. However, considering the learning evolution of a single agent in many problems has some limitations, more and more applications involve multi-agent. There are two types of cooperation, game environment among multi-agent. Therefore, this paper introduces a Cooperation Markov Decision Process (CMDP) system with two agents, which is suitable for the learning evolution of cooperative decision between two agents. It is further found that the value function in the CMDP system also converges in the end, and the convergence value is independent of the choice of the value of the initial value function. This paper presents an algorithm for finding the optimal strategy pair (πk0,πk1) in the CMDP system, whose fundamental task is to find an optimal strategy pair and form an evolutionary system CMDP(πk0,πk1). Finally, an example is given to support the theoretical results

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers

The Phase Transition Analysis for the Random Regular Exact 2-(d, k)-SAT Problem

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d<d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d>d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results

Application of machine learning on the modelling of diffusion Magnetic Resonance Imaging signal

International audienceAbstract The modelling of diffusion Magnetic Resonance Imaging (dMRI) signals is very important for medical clinical application. However, the traditional method is to use a fixed mathematical model to make assumptions about the diffusion-weighted (DW) signals of all regions of human organ, which is unreasonable. In this paper, Convolutional Neural Network (CNN), a machine learning based method is used for learning the different characteristics of the signals, and finally intelligently give multi-model predictions for different regions of human livers. The performance of the proposed method is verified on both simulation and real liver data. The results show that the multi-model predicted by CNN method has high performance in distinguishing normal liver from diseased liver, and has great clinical application prospect

Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System

This paper proposes a new delay-depended stability criterion for a class of delayed Lur'e systems with sector and slope restricted nonlinear perturbation. The proposed method employs an improved Wirtinger-type inequality for constructing a new Lyapunov functional with triple integral items. By using the convex expression of the nonlinear perturbation function, the original nonlinear Lur'e system is transformed into a linear uncertain system. Based on the Lyapunov stable theory, some novel delay-depended stability criteria for the researched system are established in terms of linear matrix inequality technique. Three numerical examples are presented to illustrate the validity of the main results