The minimum sum representation as an index of voting power

We propose a new power index based on the minimum sum representation (MSR) of a weighted voting game. The MSR offers a redesign of a voting game, such that voting power as measured by the MSR index becomes proportional to voting weight. The MSR index is a coherent measure of power that is ordinally equivalent to the Banzhaf, Shapley–Shubik and Johnston indices. We provide a characterization for a bicameral meet as a weighted game or a complete game, and show that the MSR index is immune to the bicameral meet paradox. We discuss the computation of the MSR index using a linear integer program and the inverse MSR problem of designing a weighted voting game with a given distribution of power.     

Correlation and Entanglement

In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance.     

Generating random correlation matrices based on vines and extended onion method

We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.G. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276–294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, Journal of Multivariate Analysis 97 (2006) 2177–2189] based on partial correlations. The latter is based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions.     

Common volatility and correlation clustering in asset returns

We present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations. Our approach assumes return innovations with time dependent covariances. A Cholesky decomposition of the asset covariance matrix, with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t. As in Christodoulakis and Satchell [Christodoulakis, G.A., Satchell, S.E., 2002. Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139 (2), 350–369] correlation is generated by conditionally autoregressive processes, thus allowing for an autocorrelation structure for correlation. Our approach allows for explicit out-of-sample forecasting and is consistent with stylized facts as time-varying correlations and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). The latter two are shown to depend on correlation and volatility persistence. Empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield supports our theoretical arguments.     

Border collision bifurcations and power spectral density of chaotic signals generated by one-dimensional discontinuous piecewise linear maps

Recently, many papers have appeared which study the power spectral density (PSD) of signals issued from some specific maps. This interest in the PSD is due to the importance of frequency in the telecommunications and transmission security. With the large number of wireless systems, the availability of frequencies for transmission and reception is increasingly uncommon for wireless communications. Also, guided media have limitations related to the bandwidth of a signal. In this paper, we investigate some properties associated to the border-collision bifurcations in a one-dimensional piecewise-linear map with three slopes and two parameters. We derive analytical expressions for the autocorrelation sequence, power spectral density (PSD) of chaotic signals generated by our piecewise-linear map. We prove the existence of strong relation between different types of the power spectral density (low-pass, high-pass or band-stop) and the parameters. We also find a relation between the type of spectrum and the order of attractive cycles which are located after the border collision bifurcation between chaos and cycles.     

Generating multivariate correlated samples

Summary  Generating random samples from multivariate distributions is a common, requirement in many fields of study. Often the complete joint distribution is not specified to the scientist. This paper addresses the situation where only the marginals and the correlation matrix are specified. We suggest a deterministic algorithm, PERMCORR, to approximately achieve the required correlation structure that can be used to get good initial values to standard stochastic algorithms. In many situations the output of PERMCORR is already accurate enough to preempt any need for running an expensive stochastic algorithm. We provide some theoretical justification for our method as well as simulation studies. We also provide a bootstrap technique based on PERMCORR.     

基于FDI收益分成视角的FTA网络演化

本文假定双边自由贸易协定(bilateral free trade agreement,简称FTA)包含着无限制对外直接投资(foreign direct investment,简称FDI),并且通过FDI销售到非FTA伙伴国的收益按照一定比例在母国和东道国之间进行分配。基于Goyal和Joshi^[1],本文构建了FTA网络形成博弈模型。本文发现,FTA网络演化过程分为两个阶段:第一阶段,从空FTA网络到星状FTA网络,存在一条路径使得个体国家福利、世界总福利均改善,在此过程中,国家福利存在不对称性;第二阶段,从星状FTA网络到全连接FTA网络,存在一条路径使得个体国家福利改善,在此过程中,世界总福利不变,国家福利不对称性逐步消除。     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

Measures of pseudorandomness for binary sequences constructed using finite fields

We extend the results of Goubin, Mauduit and Sárközy on the well-distribution measure and the correlation measure of order k of the sequence of Legendre sequences with polynomial argument in several ways. We analyze sequences of quadratic characters of finite fields of prime power order and consider in each case two, in general, different definitions of well-distribution measure and correlation measure of order k, respectively.     

Testing procedures for detection of linear dependencies in efficiency models

The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausmann-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.     

Mean–variance asset–liability management with asset correlation risk and insurance liabilities

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.     

Optimality of myopic strategies for multi-stock discrete time market with management costs

The paper studies multi-stock discrete time market models with serial correlations and with some management costs. We found a market structure that ensures that the optimal strategy is myopic for the case of either power or log utility function.     

The credit risk+ model with general sector correlations

We consider an enhancement of the credit risk⁺ model to incorporate correlations between sectors. We model the sector default rates as linear combinations of a common set of independent variables that represent macro-economic variables or risk factors. We also derive the formula for exact VaR contributions at the obligor level.     

On mixing properties of compact group extensions of hyperbolic systems

We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing properties of such extensions with accessibility properties of their stable and unstable laminations. We show that generically the correlations decay faster than any power of time. In particular, this is always the case for ergodic semisimple extensions as well as for stably ergodic extensions of Anosov diffeomorphisms of infranilmanifolds.     

Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere

The steady state boundary layer equations around rotating pure hydrocarbon droplet are solved numerically. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method where Thomas algorithm solves the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hexane droplet concluded. The thickness of the boundary layer is unknown for this model and therefore, it is determined. Further, this work proposes correlations of Nusselt and Sherwood numbers for monocomponent hydrocarbon droplets in evaporation. These correlations consider the rotation phenomena and further, the variation of the thermophysical and transport properties in the vapour phase.     

Relative efficiencies of estimates using patterned covariances or correlations in the multivariate normal estimation problem

Summary The relative efficiency of maximum likelihood estimates is studied when taking advantage of underlying linear patterns in the covariances or correlations when estimating covariance matrices. We compare the variances of estimates of the covariance matrix obtained under two nested patterns with the assumption that the more restricted pattern is the true state. Formulas for the asymptotic variances are given which are exact for linear covariance patterns when explicit maximum likelihood estimates exist. Several specific examples are given using complete symmetry, circular symmetry and general covariance patterns as well as an example involving a covariance matrix with a linear pattern in the correlations.     

Vanishing quantum discord and complete entropy exchange between subsystems in a bipartite system

Vanishing quantum discord and the entropy correlations between subsystems in a bipartite system are investigated. We numerically verify that there exists a condition of complete entropy exchange between the two subsystems, and it is found that the condition is in excellent agreement with that of the nullity of quantum discord in a certain range of parameters of the bipartite system.     

Maps on Ultrametric Spaces,Hensel's Lemma,and Differential Equations Over Valued Fields

We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multidimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued differential fields, for both valued D-fields in the sense of Scanlon, and differentially valued fields in the sense of Rosenlicht. We modify the approach so that it also covers logarithmic-exponential power series fields. Finally, we give a criterion for a sum of spherically complete subgroups of a valued abelian group to be spherically complete. This in turn can be used to determine elementary properties of power series fields in positive characteristic.     

Jacobians of Symmetric Polynomials

Annals of Combinatorics - We give the Jacobian of any family of complete symmetric functions, or of power sums, in a finite number of variables.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.