An axiomatization of the τ-value

The τ-value is characterized by three axioms. It is shown that the τ-value is the unique solution concept which is efficient and has the minimal right property and the restricted proportionality property. The minimal right property is weaker than the additivity property, which plays a role in the axiomatic characterization of the Shapley value: together with individual rationality and efficiency additivity implies the minimal right property. The restricted proportionality property says that for games with minimal right vector zero, the dividend given to the players is proportional to the marginal contribution of the players to the grand coalition.     

Convexity results and sharp error estimates in approximate multivariate integration

An interesting property of the midpoint rule and the trapezoidal rule, which is expressed by the so-called Hermite-Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite-Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. In particular, for simplices of arbitrary dimension, we present two families of integration formulae which both contain a multivariate analogue of the midpoint rule and the trapezoidal rule as boundary cases. The first family also includes a multivariate analogue of a Maclaurin formula and of the two-point Gaussian quadrature formula; the second family includes a multivariate analogue of a formula by P.C. Hammer and of Simpson's rule. In both families, we trace out those formulae which satisfy a Hermite-Hadamard inequality. As an immediate consequence of the latter, we obtain sharp error estimates for twice continuously differentiable functions.

     

Littlewood–Richardson polynomials

We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are polynomials in the parameters which we call the Littlewood–Richardson polynomials. We give a combinatorial rule for their calculation by modifying an earlier result of B. Sagan and the author. The new rule provides a formula for these polynomials which is positive in the sense of W. Graham. We apply this formula for the calculation of the product of equivariant Schubert classes on Grassmannians which implies a stability property of the structure coefficients. The first manifestly positive formula for such an expansion was given by A. Knutson and T. Tao by using combinatorics of puzzles while the stability property was not apparent from that formula. We also use the Littlewood–Richardson polynomials to describe the multiplication rule in the algebra of the Casimir elements for the general linear Lie algebra in the basis of the quantum immanants constructed by A. Okounkov and G. Olshanski.     

The reverse Talmud family of rules for bankruptcy Problems: A characterization

We characterize the reverse Talmud family of  rules for bankruptcy problems using consistency and additivity on a restricted domain of problems. The family includes several standard rules such as the constrained equal awards, constrained equal losses and reverse Talmud rules. This last rule is characterized by further imposing the mid-point property. Furthermore, each member of the RTAL-family is characterized using consistency and additivity on a domain in which that member is additive.     

基于纵向数据下连续型单参数指数族参数的经验贝叶斯检验(英文)

本文讨论了在纵向数据下,运用非参数估计方法构造了连续型单参数指数族参数的经验贝叶斯检验函数,证明了所提出的经验贝叶斯检验函数的渐近最优性,并获得了它的收敛速度.     

A Theory of Status-Mediated Inequity Aversion

We introduce a new social utility function which relates inequity aversion to social status, effort, and ability. The basic idea is as follows: Actors do not suffer from inequality but from inequity relative to a fair share that reflects some normative orientation the actors have internalized. In this regard we advocate the rule of proportionality which states that rewards should be proportional to some standard of comparison. We apply this social utility function to various games from non-cooperative and cooperative game theory and interpret the results with respect to the effects of social status on behavioral outcomes.     

The Number of Lattice Rules of Specified Upper Class and Rank

The upper class of a lattice rule is a convenient entity for classification and other purposes. The rank of a lattice rule is a basic characteristic, also used for classification. By introducing a rank proportionality factor and obtaining certain recurrence relations, we show how many lattice rules of each rank exist in any prime upper class. The Sylow p-decomposition may be used to obtain corresponding results for any upper class.     

基于近邻方法下分布参数的贝叶斯分析

本文基于近邻方法下,构造了连续型单参数指数族参数的经验Bayes(EB)检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的大样本性质.     

Merge-proofness in minimum cost spanning tree problems

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called merge-proofness. This property says that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using merge-proofness.     

The fuzzy intersection rule in variational analysis with applications

The fuzzy intersection rule for Fréchet normal cones in Asplund spaces was established by Mordukhovich and the author using the extremal principle, which appears more convenient to apply in some applications. In this paper, we present a complete discussion of this rule in various aspects. We show that the fuzzy intersection rule is another characterization of the Asplund property of the space. Various applications are considered as well. In particular, a complete set of fuzzy calculus rules for general lower semicontinuous functions are established.     

Analysis and Construction of Multivariate Interpolating Refinable Function Vectors

In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and analyze the underlying sum rule structure of its generalized interpolatory matrix mask. We also discuss the symmetry property of multivariate interpolating refinable function vectors. Based on these results, we construct a family of univariate generalized interpolatory matrix masks with increasing orders of sum rules and with symmetry for interpolating refinable function vectors. Such a family includes several known important families of univariate refinable function vectors as special cases. Several examples of bivariate interpolating refinable function vectors with symmetry will also be presented.     

排序对策的一个新的收益分配准则

针对一个机器的排序问题,给出了排序问题中成本增加量的表达式,提出了收益分配的不小于成本增加量准则。针对一类特殊的排序问题,给出一个符合不小于成本增加量分配准则的解,并证明了它满足有效性,哑元性和单调性。结合一个算例,对本文的提出的方法进行了分析验证。     

Drop out monotonic rules for sequencing situations

This note introduces a new monotonicity property for sequencing situations. A sequencing rule is called drop out monotonic if no player will be worse off whenever one of the players decides to drop out of the queue before processing starts. This intuitively appealing property turns out to be very strong: we show that there is at most one rule satisfying both stability and drop out monotonicity. For the standard model of linear cost functions, the existence of this rule is established.     

Dynamic adjustment: an electoral method for relaxed double proportionality

We describe an electoral system for distributing seats in a parliament. It gives proportionality for the political parties and close to proportionality for constituencies. The system suggested here is a version of the system used in Sweden and other Nordic countries with permanent seats in each constituency and adjustment seats to give proportionality on the national level. In the national election of 2010 the current Swedish system failed to give proportionality between parties. We examine here one possible cure for this unwanted behavior. The main difference compared to the current Swedish system is that the number of adjustment seats is not fixed, but rather dynamically determined to be as low as possible and still insure proportionality between parties.     

Sustainability in bankruptcy problems

This paper focuses on a new property for bankruptcy rules, calledsustainability, which requires that the agents with small enough claims be fully reimbursed. We show that the constrained equal-awards rule is the only rule that satisfies path independence and sustainability. Exploiting duality relations, we also provide a characterization of the constrained equal-losses rule, as the only one that satisfies composition and independence of residual claims (the dual property of sustainability).     

A composite run-to-the-bank rule for multi-issue allocation situations

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations. We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency.     

Control aspects in proportionality Markov manpower systems

In this paper, the control aspects of a hierarchical organization under the influence of “proportionality” policies are analyzed. Proportionality policies are those that restrict the recruitment to every level of the hierarchy (except the bottom most level or base level) to be in strict proportion to the promotions into that level. Both long term and short term control analysis have been discussed. In long term control the specific roles of the parameters of the system with regard to control of the shape and size of the system have been analyzed and yield suitable control strategies. In short term control, the attainability of a target or goal structure within a specific time from a given initial structure has been analyzed and yields the required recruitment strategies. The theoretical analyses have been illustrated with computational examples and also with real world data.The control of such proportionality systems is then compared with that of the general systems (which do not follow such policies) with some significant conclusions. The control relations of such proportionality systems are found to be simpler and more practically feasible than those of general Markov systems, which do not have such restrictions. Such proportionality systems thus not only retain and match the flexibility of general Markov systems but also have the added advantage of simpler and more practically feasible controls. The proportionality policies hence act as an alternative and more practicably feasible means of control.     

渐近最优的经验贝叶斯决策

本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性.     

Classifier fusion in the Dempster-Shafer framework using optimized t-norm based combination rules

When combining classifiers in the Dempster-Shafer framework, Dempster’s rule is generally used. However, this rule assumes the classifiers to be independent. This paper investigates the use of other operators for combining non independent classifiers, including the cautious rule and, more generally, t-norm based rules with behavior ranging between Dempster’s rule and the cautious rule. Two strategies are investigated for learning an optimal combination scheme, based on a parameterized family of t-norms. The first one learns a single rule by minimizing an error criterion. The second strategy is a two-step procedure, in which groups of classifiers with similar outputs are first identified using a clustering algorithm. Then, within- and between-cluster rules are determined by minimizing an error criterion. Experiments with various synthetic and real data sets demonstrate the effectiveness of both the single rule and two-step strategies. Overall, optimizing a single t-norm based rule yields better results than using a fixed rule, including Dempster’s rule, and the two-step strategy brings further improvements.