Analytical Method for Mechanism Design in Partially Observable Markov Games

A theme that become common knowledge of the literature is the difficulty of developing a mechanism that is compatible with individual incentives that simultaneously result in efficient decisions that maximize the total reward. In this paper, we suggest an analytical method for computing a mechanism design. This problem is explored in the context of a framework, in which the players follow an average utility in a non-cooperative Markov game with incomplete state information. All of the Nash equilibria are approximated in a sequential process. We describe a method for the derivative of the player’s equilibrium that instruments the design of the mechanism. In addition, it showed the convergence and rate of convergence of the proposed method. For computing the mechanism, we consider an extension of the Markov model for which it is introduced a new variable that represents the product of the mechanism design and the joint strategy. We derive formulas to recover the variables of interest: mechanisms, strategy, and distribution vector. The mechanism design and equilibrium strategies computation differ from those in previous literature. A numerical example presents the usefulness and effectiveness of the proposed method.

Mathetical problem of banking assets diversification

In article we consider a problem of optimal investment strategy by a commercial bank building. This task is actual and the development of a procedure to solve it can help in making investment banking decisions. The general formulation of the problem consists of two criteria. The first one is to maximize the expected return, and the second is to minimize the risk of the investment transaction. Mathematical formulation of the problem is considered as a problem of nonlinear programming under constraints. The procedure for solving such a two-criteria optimization problem allows to obtain many solutions, which requires further steps to make a single optimal solution. According to the algorithm proposed in the work, the problem is divided into two separate problems of single-criteria optimization. Each of these tasks allows to obtain the optimal values of the investment vector both in terms of its expected return and in terms of investment risk. Additional constraints in the mathematical formulation of the problem, make it possible to take into account factors that, from the point of view of the investor, may influence decision-making. The procedures presented in this work allow to obtain analytical representations of formulas that describe the optimal values of the investment distribution vector for both mathematical formulations of the problem.

A Note on Migration Perturbation and Convergence Rates to a Steady State

Using tools developed in the Markov chains literature, we study convergence times in the Leslie population model in the short and middle run. Assuming that the population is in a steady-state and reproduces itself period after period, we address the following question: how long will it take to get back to the steady-state if the population distribution vector was affected by some shock as, for instance, the “brain drain”? We provide lower and upper bounds for the time required to reach a given distance from the steady-state.

A Generator of Bivariate Distributions: Properties, Estimation, and Applications

In 2020, El-Morshedy et al. introduced a bivariate extension of the Burr type X generator (BBX-G) of distributions, and Muhammed presented a bivariate generalized inverted Kumaraswamy (BGIK) distribution. In this paper, we propose a more flexible generator of bivariate distributions based on the maximization process from an arbitrary three-dimensional baseline distribution vector, which is of interest for maintenance and stress models, and expands the BBX-G and BGIK distributions, among others. This proposed generator allows one to generate new bivariate distributions by combining non-identically distributed baseline components. The bivariate distributions belonging to the proposed family have a singular part due to the latent component which makes them suitable for modeling two-dimensional data sets with ties. Several distributional and stochastic properties are studied for such bivariate models, as well as for its marginals, conditional distributions, and order statistics. Furthermore, we analyze its copula representation and some related association measures. The EM algorithm is proposed to compute the maximum likelihood estimations of the unknown parameters, which is illustrated by using two particular distributions of this bivariate family for modeling two real data sets.

On Certain Classes of Irregular Languages

Objective of this paper is to prove certain regularity and irregularity conditions in languages determined by a set of integer vectors called distribution vectors of the number of letters in words over a finite alphabet. Each language over the finite alphabet uniquely determines its proprietary set of distribution vectors and vice versa, i.e., each set of vectors is associated with a language having this set of distribution vectors. A single necessary condition for the language regularity was considered associated with the concept of Z+-plane (sets of points with non-negative integer coordinates lying on a plane in the affine space). The condition is that a set of distribution vectors determined by any regular language could be represented as a finite union of the Z+-planes. Certain sufficient irregularity conditions associated with the distribution vector properties were proven. Based on this, classes of irregular languages could be identified. These classes are determined by a set of vectors (points) that could not be represented as a finite union of the Z+-planes; by a set of vectors containing vectors with arbitrarily high values of each coordinate and having certain restrictions on the difference between maximum and minimum values of the coordinates; by a set of vectors called the sparse sets. A method is proposed for building such sets using strictly convex and strictly increasing numerical sequences. These sufficient irregularity conditions are based on the Myhill --- Nerode theorem, which is known in the formal languages' theory. Examples of applying the proved theorems to the analysis of languages' regularity/irregularity are presented

Cross-Season Visual Route Classification Using a Domain-Invariant Next-Best-View Planner

This paper addresses the problem of active visual place recognition (VPR) from a novel perspective of long-term autonomy. In our approach, a next-best-view (NBV) planner plans an optimal action-observation-sequence to maximize the expected cost-performance for a visual route classification task. A difficulty arises from the fact that the NBV planner is trained and tested in different domains (times of day, weather conditions, and seasons). Existing NBV methods may be confused and deteriorated by the domain-shifts, and require significant efforts for adapting them to a new domain. We address this issue by a novel deep convolutional neural network (DNN) -based NBV planner that does not require the adaptation. Our main contributions in this paper are summarized as follows: (1) We present a novel domain-invariant NBV planner that is specifically tailored for DNN-based VPR. (2) We formulate the active VPR as a POMDP problem and present a feasible solution to address the inherent intractability. Specifically, the probability distribution vector (PDV) output by the available DNN is used as a domain-invariant observation model without the need to retrain it. (3) We verify efficacy of the proposed approach through challenging cross-season VPR experiments, where it is confirmed that the proposed approach clearly outperforms the previous single-view-based or multi-view-based VPR in terms of VPR accuracy and/or action-observation-cost.

INDIKATOR ENTOMOLOGI DAN RISIKO PENULARAN DEMAM BERDARAH DENGUE (DBD) DI PULAU JAWA, INDONESIA

One of dengue hemorrhagic fever (DHF) transmission risk factors is presence of vectors, especially Aedes aegypti. Vector surveillance is carried out to determine vectors distribution, vector density and risk of transmission. The larva survey is a common and easy vector surveillance method. This study aims to describe the cases and deaths due to DHF and entomological indicators in Java. This study was further analysis of Special Research Disease of Vector and Reservoir (Rikhus Vektora). Data collection was conducted in 2016 - 2018. The study locations were five provinces on Java Island i.e. East Jawa, West Jawa, Banten, DI Yogyakarta, DKI Jakarta and three districts were each taken. The data of DHF cases and entomology were analyzed descriptively. The results of the study show that the last two years were 50% districts experienced an increase in DHF cases and 38.9% an increase in deaths. The highest house index was 50% and lowest was 9%, highest larval free rate was 91% and lowest was 50%. The highest container index was 26.48%, lowest was 3.68%, and the highest breteau index was 67, lowest was 11. As many as 73.3% districts have the most water containers were buckets and 26.7% most water containers were bathtubs. Java Island has a medium to high potential region toward DHF transmission occurs. Increased knowledge and skills for eradication mosquito correctly by individually and community needs to be planned and implemented sustainable, to increase community participation as well.