Collaborative multi-agent reinforcement learning based on experience propagation

For multi-agent reinforcement learning in Markov games, knowledge extraction and sharing are key research problems. State list extracting means to calculate the optimal shared state path from state trajectories with cycles. A state list extracting algorithm checks cyclic state lists of a current state in the state trajectory, condensing the optimal action set of the current state. By reinforcing the optimal action selected, the action policy of cyclic states is optimized gradually. The state list extracting is repeatedly learned and used as the experience knowledge which is shared by teams. Agents speed up the rate of convergence by experience sharing. Competition games of preys and predators are used for the experiments. The results of experiments prove that the proposed algorithms overcome the lack of experience in the initial stage, speed up learning and improve the performance.     

Analysis for Influence of Market Information on Firms＇ Optimal Strategies in Multidimensional Bertrand Game

The Bertrand model of two firms‘ static multidimensional game with incomplete information for two kinds of product with certain substitution is discussed in the paper,and analyzes influences of the firms‘ forecasting results of total market demands on their optimal strategies according to marxet information. The conclusions are that the more a firm masters market information, the greater differences of forecasted values and expected values of market demands for products have influence upon equilibrium strategies; conversely, the less they have influence upon equilibrium strategies.     

Some Open Problems on Simultaneous Stabilization of Linear Systems

Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory,and is of theoretical and practical significance.In this paper,the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems.Especially,the authors list the ever best results on the parameters involved in the well known "French Champagne Problem" and "Belgian Chocolate Problem" from the point of view of mathematical theoretical analysis and numerical calculation.And the authors observed that Boston claimed the lower bound of δ can be enlarged to 0.976461 in 2012 is not accurate.The authors hope it will inspire further study on simultaneous stabilization of several linear systems.     

ON AN ELLIPTIC PROBLEM INVOLVING CRITICAL AND SUBLINEAR GROWTH

In this paper, the author considers an elliptic problem with critical and sub-linear growth. Some results about the multiplicity and uniqueness of the positive solutions are given by making use of variational method and bifurcation theory.     

A New Method with High Confidence for Validation of Computer Simulation Models of Flight Systems

Computer simulation models may by used to gain further information about missile performance variability. Model validation is an important aspect of the test program for a missile system. Validation provides a basis for confidence in the model's results and is a necessary step if the model is to be used to draw inference about the behavior of the real missile. This paper is a review of methods useful for validation of computer simulation models of missile systems and provides a new method with high degree of confidence for validation of computer simulation models of missile systems. Some examples of the use of the new method in validating computer simulation models are given.     

The Numerical Simulation of Flow Field of Jet System

In this paper, the internal fluid motion of a jet system is described by the Navier Stokes mechanics equations. For the simulation of the motion, the penalty function finite element method is used, and the velocity vectors and stream function curves are obtained. Using the Prandtl theory, this paper derives the free jet velocity and the jet bunch width in a half-space, the latter of which is amended by experiment. The results obtained in this paper are applied to micro-type high pressure water jet cleaner and the ejector of rocket engine.     

A simplified decoding algorithm for multi-CRC polar codes

Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.     

A New Algorithm for Unconstrained Min-Max Optimization

We have structured the new differential approximation,V_α-approximation,about themaximum function max{f_i(x)}.On the basis of which the kind of minimax algorithms and itsconvergence are proved.Some numerical examples are tested.The results show that the algorithmis better than Madsen's algorithm when the problem is singular     

COURSE TIMETABLING AT A TUNISIAN UNIVERSITY： A CASE STUDY

This paper deals with the Course Timetabling Problem at an institution in a Tunisian University. We introduce a heuristic procedure to construct a feasible timetable for all lectures and tutorials taken by different groups of each sub-section of any section. We describe the timetabling problem using a list of all specific hard and soft constraints. We formulate the problem as a set of linear constraints using two sets of binary variables corresponding to lectures and tutorials, respectively. This heuristic is illustrated with real data for a sub-section of the Faculty of Economics and Management Sciences of Sfax in Tunisia, and the resulting timetables are compared with those generated manually. The results of another full section have confirmed the good quality of the proposed heuristic when compared with the hand made solution.     

Hilbert Problem 15 and Ritt-Wu Method(Ⅰ)

Hilbert problem 15 requires to understand Schubert's book. In this book, there is a theorem in §23, about the relation of the tangent lines from a point and the singular points of cubed curves with cusp near a 3-multiple straight line, which was obtained by the so called main trunk numbers, while for these numbers, Schubert said that he obtained them by experiences. So essentially Schubert even did not give any hint for the proof of this theorem. In this paper, by using the concept of generic point in the framework of Van der Waerden and Weil on algebraic geometry, and realizing Ritt-Wu method on computer, the authors prove that this theorem of Schubert is completely right.     

柔性路面损坏状况评价与养护决策的系统方法

On the basis of domestic and foreign research results about flexible pavement evaluation,this article sets forth a set of indices for evaluating flexible pavement distress condi-tion, and adopts the AHP method to construct hierarchy analysis model for determining the weight of each index in the evaluation of flexible pavement distress condition. Finally,a o一1 programming model for deciding flexible pavement maintenance strategics is presented.     

Series expansion feasibility of singular integral in method of moments

When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.     

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.     

Stock loan valuation under a regime-switching model with mean-reverting and finite maturity

<正> Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the loan.Since the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation problem.This paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian motionstates.Numerical examples are reported to illustrate the results.     

Image separation using wavelet-complex shearlet dictionary

This paper presents a new method for image separation through employing a combined dictionary consisting of wavelets and complex shearlets. Because the combined dictionary sparsely represents points and curvilinear singularities respectively, the image can be decomposed into pointlike and curvelike parts as accurate as possible. The proposed method based on the geo- metric separation theory introduced by Donoho in 2005 shows that accurate geometric separation of the morphologically distinct fea- tures of points and curves can be achieved by l1 minimization. The experimental results show that the proposed method can not only be effective but also greatly reduce the computing time.     

4/2随机波动率模型下的期权定价

The existing stochastic volatility models have such a problem: A single-factor volatility model can generate steep curves or flat curves at a given volatility, but it cannot generate both for given parameters, which is inconsistent with the actual observed data. To precisely describe the market implied volatility curve, this paper studied a two-factor 4/2 stochastic volatility model that includes, as special instances, the Heston model and the 3/2 model. Besides, it applied Lewis’s fundamental transform approach to deduce the partial differential equation(PDE). In addition, by adopting the data on S&P 500, it estimated the parameters of the 4/2 model. Furthermore, it investigated the 4/2 model along with the Heston model and the 3/2 model, and compare their different performances. The results indicate that the option price fitting error of the 4/2 model is smaller than that of other two models.     

Azimuth space-variant properties of BiSAR with nonequal velocities

Bistatic SAR possesses characteristic of the azimuth space-variant when the velocities of transmitter and receiver are not equal. The geometric model of BiSAR with the parallel trajectories and the nonequal platform velocities is presented. Analyzing the motion relationship of transmitter and receiver, the formula of azimuth spacevariant is derived in time domain. Via Taylor polynomial expansions, the azimuth space-variant is factorized by four terms： zero-order, first-order, second-order, and third-order term. And, their impacts on impulse response are illuminated. Some characteristics about azimuth space-variant of airborne BiSAR case are exhibited by simulation experiments, and these simulated results are coincident with the formulae of azimuth space-variant.     

Identification of linear continuous-time system using wavelet modulating filters

An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.     

Stability Analysis of Ranking Alternatives Based on Subjective and Objective Weight

1　 IntroductionWeights of criteria are used to assess the relative importance of the different criteria inmulticriteria analysis,which can influence ranking result more or less depending on themulticriteria decision-making( MCDM) method used.Determining the weights ofcriteria isusually a difficult task due to the decision-maker( DM) is not always clear about how toweightfor each criterion and is noteasy to understand thatthe change of weightinfluencesthe ranking results from qualitative mea…     

Optimal antenna placement in distributed antenna systems

To minimize the outage probability of the cell (OPC) in downlink distributed antenna systems with selection transmission, a complex-encoding genetic algorithm (GA) is proposed to find the optimal locations of the antenna elements (AEs). First, the outage probability at a fixed location in the cell is investigated. Next, an analytical expression of the OPC is derived, which is a function of the AE locations. Then the OPC is used as the objective function of the antenna placement optimization problem, and the complexencoding GA is used to find the optimal AE locations in the cell. Numerical results show that the optimal AE locations are symmetric about the cell center, and the outage probability contours are also given with the optimal antenna placement. The algorithm has a good convergence and can also be used to determine the number of AEs which should be installed in order to satisfy the certain OPC value. Lastly, verification of the OPC’s analytical expression is carried out by Monte Carlo simulations. The OPC with optimal AE locations is about 10% lower than the values with completely random located AEs.