On Minimum Violations Ranking in Paired Comparisons

Ranking a set of objects from the most dominant one to the least, based on the results of paired comparisons, proves to be useful in many contexts. Using the rankings of teams or individuals players in sports to seed tournaments is an example. The quality of a ranking is often evaluated by the number of violations, cases in which an object is ranked lower than another that it has dominated in a comparison, that it contains. A minimum violations ranking (MVR) method, as its name suggests, searches specifically for rankings that have the minimum possible number of violations which may or may not be zero. In this paper, we present a method based on statistical physics that overcomes conceptual and practical difficulties faced by earlier studies of the problem.Comment: 10 pages, 10 figures; typos corrected (v2

A network-based ranking system for American college football

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional playoff system to decide which those teams are. Instead, ranking of teams is based on their record of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well-founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.Comment: 15 pages, 3 figure

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks

The semi-presidential system of Cape Verde: the relationship between the executive and the legislative powers = O sistema semi-presidencialista caboverdiano: a relação entre os poderes executivo e legislativo

e article analyses the relationship established between the executive and legislative powers in the Cape Verdean government system where researchers seek to understand it, taking into account their theoretical and constitutional setting practice. It should be noted the prominence of the debate and studies undertaken to understand how the scienti c academy seeks to eradicate this problem. Two issues are relevant in this debate: the rst reporting to the theoretical and constitutional con guration of Cape Verdean government system and the other to its policy and legislative practice. Keywords: Cape Verde. Semi-presidential System. Systems of Government. Legislative and Executive Powers.O artigo procura analisar a relação que se estabelece entre o poder executivo e legislativo no sistema de governo cabo-verdiano, onde Investigadores buscam compreendê-lo, tendo em conta a sua con guração prática, teórica e constitucional. Há que realçar a proeminência do debate e dos estudos realizados no sentido de compreender como é que a academia cientí ca procura debelar esta problemática. Duas questões são pertinentes neste debate: a primeira refere-se à con guração teórico-constitucional do sistema de governo cabo-verdiano e a outra à prática política e legislativa. Palavras-chave: Cabo Verde. Sistema Semi-presidencialista. Sistemas de Governo. Poder legislativo e Poder Executivo

Element-Specific Depth Profile of Magnetism and Stoichiometry at the La0.67Sr0.33MnO3/BiFeO3 Interface

Depth-sensitive magnetic, structural and chemical characterization is important in the understanding and optimization of novel physical phenomena emerging at interfaces of transition metal oxide heterostructures. In a simultaneous approach we have used polarized neutron and resonant X-ray reflectometry to determine the magnetic profile across atomically sharp interfaces of ferromagnetic La0.67Sr0.33MnO3 / multiferroic BiFeO3 bi-layers with sub-nanometer resolution. In particular, the X-ray resonant magnetic reflectivity measurements at the Fe and Mn resonance edges allowed us to determine the element specific depth profile of the ferromagnetic moments in both the La0.67Sr0.33MnO3 and BiFeO3 layers. Our measurements indicate a magnetically diluted interface layer within the La0.67Sr0.33MnO3 layer, in contrast to previous observations on inversely deposited layers. Additional resonant X-ray reflection measurements indicate a region of an altered Mn- and O-content at the interface, with a thickness matching that of the magnetic diluted layer, as origin of the reduction of the magnetic moment.Comment: 13 pages, 4 figures, supplemental material include

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

A comparison of transgenic rodent mutation and in vivo comet assay responses for 91 chemicals.

A database of 91 chemicals with published data from both transgenic rodent mutation (TGR) and rodent comet assays has been compiled. The objective was to compare the sensitivity of the two assays for detecting genotoxicity. Critical aspects of study design and results were tabulated for each dataset. There were fewer datasets from rats than mice, particularly for the TGR assay, and therefore, results from both species were combined for further analysis. TGR and comet responses were compared in liver and bone marrow (the most commonly studied tissues), and in stomach and colon evaluated either separately or in combination with other GI tract segments. Overall positive, negative, or equivocal test results were assessed for each chemical across the tissues examined in the TGR and comet assays using two approaches: 1) overall calls based on weight of evidence (WoE) and expert judgement, and 2) curation of the data based on a priori acceptability criteria prior to deriving final tissue specific calls. Since the database contains a high prevalence of positive results, overall agreement between the assays was determined using statistics adjusted for prevalence (using AC1 and PABAK). These coefficients showed fair or moderate to good agreement for liver and the GI tract (predominantly stomach and colon data) using WoE, reduced agreement for stomach and colon evaluated separately using data curation, and poor or no agreement for bone marrow using both the WoE and data curation approaches. Confidence in these results is higher for liver than for the other tissues, for which there were less data. Our analysis finds that comet and TGR generally identify the same compounds (mainly potent mutagens) as genotoxic in liver, stomach and colon, but not in bone marrow. However, the current database content precluded drawing assay concordance conclusions for weak mutagens and non-DNA reactive chemicals

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font