Minimal half-spaces and external representation of tropical polyhedra

We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently represented internally (in terms of extreme points and rays) or externally (in terms of half-spaces containing it). A canonical external representation of a polyhedron turns out to be provided by the extreme elements of its tropical polar. We characterize these extreme elements, showing in particular that they are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures improved, references update

The economic implications of HLA matching in cadaveric renal transplantation.

Abstract Background: The potential economic effects of the allocation of cadaveric kidneys on the basis of tissue-matching criteria are controversial. We analyzed the economic costs associated with the transplantation of cadaveric kidneys with various numbers of HLA mismatches and examined the potential economic benefits of a local, as compared with a national, system designed to minimize HLA mismatches between donor and recipient in first cadaveric renal transplantations. Methods: All data were supplied by the U.S. Renal Data System. Data on all payments made by Medicare from 1991 through 1997 for the care of recipients of a first cadaveric renal transplant were analyzed according to the number of HLA-A, B, and DR mismatches between donor and recipient and the duration of cold ischemia before transplantation. Results: Average Medicare payments for renal-transplant recipients in the three years after transplantation increased from $60,436 per patient for fully HLA-matched kidneys (those with no HLA-A, B, or DR mismatches) to$80,807 for kidneys with six HLA mismatches between donor and recipient, a difference of 34 percent (P\u3c0.001). By three years after transplantation, the average Medicare payments were $64,119 for transplantations of kidneys with less than 12 hours of cold-ischemia time and$74,997 for those with more than 36 hours (P\u3c0.001). In simulations, the assignment of cadaveric kidneys to recipients by a method that minimized HLA mismatching within a local geographic area (i.e., within one of the approximately 50 organ-procurement organizations, which cover widely varying geographic areas) produced the largest cost savings ($4,290 per patient over a period of three years) and the largest improvements in the graft-survival rate (2.3 percent) when the potential costs of longer cold-ischemia time were considered. Conclusions: Transplantation of better-matched cadaveric kidneys could have substantial economic advantages. In our simulations, HLA-based allocation of kidneys at the local level produced the largest estimated cost savings, when the duration of cold ischemia was taken into account. No additional savings were estimated to result from a national allocation program, because the additional costs of longer cold-ischemia time were greater than the advantages of optimizing HLA matching

New representation of orbital motion with arbitrary angular momenta

A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total angular momentum $L$, and thereby needs no explicit coupling of partial waves between particles. A simple generating function for the correlated Gaussian is exploited to derive the matrix elements. The formulation is applied to various Coulomb three-body systems such as $e^-e^-e^+, tt\mu, td\mu$, and $\alpha e^-e^-$ up to $L=4$ in order to show its usefulness and versatility. A stochastic selection of the basis functions gives good results for various angular momentum states.Comment: Revte

Why Global Inequality Matters: Derivative Global Egalitarianism

This article integrates empirical and normative discussions about why global economic inequalities matter in critically examining an approach known as derivative global egalitarianism (DGE). DGE is a burgeoning perspective that opposes excessive global economic inequality not based on the intrinsic value of equality but inequality\u27s negative repercussions on other values. The article aims to advance the research agenda by identifying and critically evaluating four primary varieties of DGE arguments from related but distinct literatures, which span a number of disciplines, including economics, international relations, and political philosophy. Overall, DGE offers a number of persuasive arguments as to why current levels of global inequality are of concern, but aspects of DGE beg further philosophical and empirical examination. By situating DGE within the wider theoretical and empirical contexts, this article provides resources for its critical assessment and theoretical development

Partnerships and Public Service: Normative Issues for Journalists in Converged Newsrooms

As media companies test and implement newsroom “convergence,” growing numbers of journalists are producing content not only for their own employer but also for other media outlets with which that employer has a business relationship. This article, based on case studies in four converged news markets, explores journalists’ perceptions of normative pressures in this new media environment, particularly in relation to the overarching concept of public service. The findings suggest that although journalists do not see convergence itself as posing significant ethical problems, they do raise concerns related to specific components of public service, including a devotion to accuracy, an avoidance of sensationalism, and independence from economic pressures

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Schwannoma of the vagus nerve, a rare middle mediastinal neurogenic tumor: case report

Schwannoma originating from the vagus nerve within the mediastinum is a rare, usually benign tumor. A 44-year old male was presented with chest pain. Chest radiography, CT scan and MRI showed a well circumscribed mass, 5 × 4 cm located in the aortopulmonary window. The mass was found at surgery to be in close proximity with the aortic arch and the left pulmonary hilum, alongside the left vagus nerve. The encapsulated tumor was completely resected through a left thoracotomy incision and it was found to be a benign schwannoma in pathology. The patient is free of recurrence 6 years after surgery

Endogenous fantasy and learning in digital games.

Many people believe that educational games are effective because they motivate children to actively engage in a learning activity as part of playing the game. However, seminal work by Malone (1981), exploring the motivational aspects of digital games, concluded that the educational effectiveness of a digital game depends on the way in which learning content is integrated into the fantasy context of the game. In particular, he claimed that content which is intrinsically related to the fantasy will produce better learning than that which is merely extrinsically related. However, this distinction between intrinsic and extrinsic (or endogenous and exogenous) fantasy is a concept that has developed a confused standing over the following years. This paper will address this confusion by providing a review and critique of the empirical and theoretical foundations of endogenous fantasy, and its relevance to creating educational digital games. Substantial concerns are raised about the empirical basis of this work and a theoretical critique of endogenous fantasy is offered, concluding that endogenous fantasy is a misnomer, in so far as the "integral and continuing relationship" of fantasy cannot be justified as a critical means of improving the effectiveness of educational digital games. An alternative perspective on the intrinsic integration of learning content is described, incorporating game mechanics, flow and representations

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

The Precursors and Products of Justice Climates: Group Leader Antecedents and Employee Attitudinal Consequences

Drawing on the organizational justice, organizational climate, leadership and personality, and social comparison theory literatures, we develop hypotheses about the effects of leader personality on the development of three types of justice climates (e.g., procedural, interpersonal, and informational), and the moderating effects of these climates on individual level justice- attitude relationships. Largely consistent with the theoretically-derived hypotheses, the results showed that leader (a) agreeableness was positively related to procedural, interpersonal and informational justice climates, (b) conscientiousness was positively related to a procedural justice climate, and (c) neuroticism was negatively related to all three types of justice climates. Further, consistent with social comparison theory, multilevel data analyses revealed that the relationship between individual justice perceptions and job attitudes (e.g., job satisfaction, commitment) was moderated by justice climate such that the relationships were stronger when justice climate was high