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.

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.

Diagnostic d'embolie pulmonaire: problématique résiduelle des D-dimères faussement positifs [The unresolved issue of false-positive D-dimer results in the diagnostic workup of pulmonary embolism].

The unresolved issue of false-positive D-dimer results in the diagnostic workup of pulmonary embolism Pulmonary embolism (PE) remains a difficult diagnosis as it lacks specific symptoms and clinical signs. After the determination of the pretest PE probability by a validated clinical score, D-dimers (DD) is the initial blood test in the majority of patients whose probability is low or intermediate. The low specificity of DD results in a high number of false-positives that then require thoracic angio-CT. A new clinical decision rule, called the Pulmonary Embolism Rule-out criteria (PERC), identifies patients at such low risk that PE can be safely ruled-out without a DD test. Its safety has been confirmed in US emergency departments, but retrospective European studies showed that it would lead to 5-7% of undiagnosed PE. Alternative strategies are needed to reduce the proportion of false-positive DD results.

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.

Orbit decidability and the conjugacy problem for some extensions of groups

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The generic Hanna Neumann conjecture and post correspondence problem

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The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.

High-magnification vascular imaging to reject false-positive sites in situ during Hexvix® fluorescence cystoscopy.

Fluorescence imaging for detection of non-muscle-invasive bladder cancer is based on the selective production and accumulation of fluorescing porphyrins-mainly, protoporphyrin IX-in cancerous tissues after the instillation of Hexvix®. Although the sensitivity of this procedure is very good, its specificity is somewhat limited due to fluorescence false-positive sites. Consequently, magnification cystoscopy has been investigated in order to discriminate false from true fluorescence positive findings. Both white-light and fluorescence modes are possible with the magnification cystoscope, allowing observation of the bladder wall with magnification ranging between 30× for standard observation and 650×. The optical zooming setup allows adjusting the magnification continuously in situ. In the high-magnification (HM) regime, the smallest diameter of the field of view is 600 microns and the resolution is 2.5 microns when in contact with the bladder wall. With this cystoscope, we characterized the superficial vascularization of the fluorescing sites in order to discriminate cancerous from noncancerous tissues. This procedure allowed us to establish a classification based on observed vascular patterns. Seventy-two patients subject to Hexvix® fluorescence cystoscopy were included in the study. Comparison of HM cystoscopy classification with histopathology results confirmed 32?33 (97%) cancerous biopsies and rejected 17?20 (85%) noncancerous lesions.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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