An ordinal shapley value for economic environments (Revised version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

Accuracy vs. simplicity: a complex trade-off

Inductive learning aims at finding general rules that hold true in a database. Targeted learning seeks rules for the predictions of the value of a variable based on the values of others, as in the case of linear or non-parametric regression analysis. Non-targeted learning finds regularities without a specific prediction goal. We model the product of non-targeted learning as rules that state that a certain phenomenon never happens, or that certain conditions necessitate another. For all types of rules, there is a trade-off between the rule's accuracy and its simplicity. Thus rule selection can be viewed as a choice problem, among pairs of degree of accuracy and degree of complexity. However, one cannot in general tell what is the feasible set in the accuracy-complexity space. Formally, we show that finding out whether a point belongs to this set is computationally hard. In particular, in the context of linear regression, finding a small set of variables that obtain a certain value of R2 is computationally hard. Computational complexity may explain why a person is not always aware of rules that, if asked, she would find valid. This, in turn, may explain why one can change other people's minds (opinions, beliefs) without providing new information.

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Data size sufficiency analyses of haplotype inference algortihms

We present experimental and theoretical analyses of data requirements for haplotype inference algorithms. Our experiments include a broad range of problem sizes under two standard models of tree distribution and were designed to yield statistically robust results despite the size of the sample space. Our results validate Gusfield's conjecture that a population size of n log n is required to give (with high probability) sufficient information to deduce the n haplotypes and their complete evolutionary history. The experimental results inspired our experimental finding with theoretical bounds on the population size. We also analyze the population size required to deduce some fixed fraction of the evolutionary history of a set of n haplotypes and establish linear bounds on the required sample size. These linear bounds are also shown theoretically.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Violence: les femmes font confiance au milieu médical [Partner violence: women trust health professionals]

In 2008, the department of gynaecology and obstetrics of a university hospital centre implemented a program addressing interpersonal partner violence (screening, prevention and care of the patient victims). A qualitative survey was conducted to identify the needs and feelings of patients. The results show that patients are in favour of being actively and directly questioned about violence during the consultation and that they trust medical doctors and nurses to help and support them.

New York City: "gilt cage" or "promised land" ? : representations of urban space in Edith Wharton and Anzia Yezierska

This thesis explores the importance of literary New York City in the urban narratives of Edith Wharton and Anzia Yezierska. It specifically looks at the Empire City of the Progressive Period when the concept of the city was not only a new theme but also very much a typical American one which was as central to the American experience as had been the Western frontier. It could be argued, in fact, that the American city had become the new frontier where modern experiences like urbanization, industrialization, immigration, and also women's emancipation and suffrage, caused all kinds of sensations on the human scale from smoothly lived assimilation and acculturation to deeply felt alienation because of the constantly shifting urban landscape. The developing urban space made possible the emergence of new female literary protagonists like the working girl, the reformer, the prostitute, and the upper class lady dedicating her life to 'conspicuous consumption'. Industrialization opened up city space to female exploration: on the one hand, upper and middle class ladies ventured out of the home because of the many novel urban possibilities, and on the other, lower class and immigrant girls also left their domestic sphere to look for paid jobs outside the home. New York City at the time was not only considered the epicenter of the world at large, it was also a city of great extremes. Everything was constantly in flux: small brownstones made way for ever taller skyscrapers and huge waves of immigrants from Europe pushed native New Yorkers further uptown on the island, adding to the crowdedness and intensity of the urban experience. The city became a polarized urban space with Fifth Avenue representing one end of the spectrum and the Lower East Side the other. Questions of space and the urban home greatly mattered. It has been pointed out that the city setting functions as an ideal means for the display of human nature as well as social processes. Narrative representations of urban space, therefore, provide a similar canvas for a protagonist's journey and development. From widely diverging vantage points both Edith Wharton and Anzia Yezierska thus create a polarized city where domesticity is a primal concern. Looking at all of their New York narratives by close readings of exterior and interior city representations, this thesis shows how urban space greatly affects questions of identity, assimilation, and alienation in literary protagonists who cannot escape the influence of their respective urban settings. Edith Wharton's upper class "millionaire" heroines are framed and contained by the city interiors of "old" New York, making it impossible for them to truly participate in the urban landscape in order to develop outside of their 'Gilt Cages'. On the other side are Anzia Yezierska's struggling "immigrant" protagonists who, against all odds, never give up in their urban context of streets, rooftops, and stoops. Their New York City, while always challenging and perpetually changing, at least allows them perspectives of hope for a 'Promised Land' in the making. Central for both urban narrative approaches is the quest for a home as an architectural structure, a spiritual resting place, and a locus for identity forming. But just as the actual city embraces change, urban protagonists must embrace change also if they desire to find fulfillment and success. That this turns out to be much easier for Anzia Yezierska's driven immigrants rather than for Edith Wharton's well established native New Yorkers is a surprising conclusion to this urban theme.

Addressing the net balances problem as a prerequisite for EU budget reform: a proposal

Conflict among member states regarding the distribution of net financial burdens has been allowed to contaminate the entire design of the EU budget with very negative consequences in terms of equity, efficiency and transparency. To get around this problem and pave the way for a substantive budget reform, we propose to decouple distributional negotiations from the rest of the budget process by linking member state net balances in a rigid manner to relative prosperity. This would be achieved through the introduction of a system of compensating horizontal transfers that would take to its logical conclusion the Commission's proposal for a generalized compensation mechanism. We discuss the impact of the proposed scheme on member states? incentives and illustrate its financial implications using revenue and expenditure projections for 2013 that are based on the current Financial Perspectives and Own Resources Decision.

Label Space Reduction in All-Optical Label Switchiing Networks

Report for the scientific sojourn at the Department of Information Technology (INTEC) at the Ghent University, Belgium, from january to june 2007. All-Optical Label Swapping (AOLS) forms a key technology towards the implementation of All-Optical Packet Switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the wayin which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This project studies and proposes All-Optical Label Stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this project, an Integer Lineal Program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more.