Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure

Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value

We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge $Z\alpha=2/\pi$.Comment: LaTeX2e, 12 page

The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic

We study the dynamics of a backtracking procedure capable of proving uncolourability of graphs, and calculate its average running time T for sparse random graphs, as a function of the average degree c and the number of vertices N. The analysis is carried out by mapping the history of the search process onto an out-of-equilibrium (multi-dimensional) surface growth problem. The growth exponent of the average running time is quantitatively predicted, in agreement with simulations.Comment: 5 figure

Characterisation and outcome of idiopathic pyogranulomatous lymphadenitis in 64 English springer spaniel dogs

Objectives To describe the history, clinicopathological abnormalities, diagnostic imaging findings, lymph node cytological/histological appearance, treatment and outcome of English springer spaniels diagnosed with idiopathic pyogranulomatous lymphadenitis. Materials and Methods In this retrospective UK‐based multicentre study, 64 dogs were recruited from 10 referral centres, 32 first‐opinion practices and three histopathology/cytology laboratories, between 2010 and 2016. Results The median age at presentation was 6 years (range: 0.17 to 11.75). Neutered females were frequently affected. Pyrexia (83.8%), peripheral lymphadenomegaly (78.4%), dermatological lesions (72.9%), lethargy (67.6%), hyporexia (54%), diarrhoea (29.7%), coughing (24.3%), epistaxis, sneezing or nasal discharge (21.6%), ocular signs (21.6%) and vomiting (16.2%) were reported in dogs for which the history and physical examination records were available. Popliteal (45.3%), superficial cervical (35.9%) and submandibular (37.5%) lymphadenomegaly were frequently reported. Haematology and serum biochemistry revealed non‐specific changes. When undertaken, testing for infectious diseases was negative in all cases. Lymph node cytology, histopathology or both demonstrated mixed inflammatory (27%), pyogranulomatous (24%), neutrophilic (20%) or granulomatous (11%) lymphadenitis. Treatment details were available for 38 dogs, with 34 receiving prednisolone for a median duration of 15 weeks (range: 1 to 28 weeks). A good to excellent clinical response was reported in all but one case. Ten dogs relapsed after discontinuing prednisolone. Clinical Significance Idiopathic pyogranulomatous lymphadenitis should be considered as a differential diagnosis for lymphadenopathy and pyrexia in English springer spaniels. The characteristics of the disease, absence of identifiable infectious aetiology and response to glucocorticoid therapy suggest an immune‐mediated aetiology

Laboratory, field and airborne spectroscopy for monitoring organic carbon content in agricultural soils

This study explains the potential and the limits of a field ASD spectrometer and a CASI airborne instrument to assess the Soil Organic Carbon, in the context of soil carbon mapping

C-axis lattice dynamics in Bi-based cuprate superconductors

We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A2u eigenfrequencies and the experimental values of the c axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Gamma-point A1g symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is based on the published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.Comment: 29 pages, 13 figure

Algebraic Comparison of Partial Lists in Bioinformatics

The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or just within a meta-analysis comparison, instead of one list it is often the case that sets of alternative feature lists (possibly of different lengths) are obtained. Here we introduce a method, based on the algebraic theory of symmetric groups, for studying the variability between lists ("list stability") in the case of lists of unequal length. We provide algorithms evaluating stability for lists embedded in the full feature set or just limited to the features occurring in the partial lists. The method is demonstrated first on synthetic data in a gene filtering task and then for finding gene profiles on a recent prostate cancer dataset

Differential co-expression framework to quantify goodness of biclusters and compare biclustering algorithms

<p>Abstract</p> <p>Background</p> <p>Biclustering is an important analysis procedure to understand the biological mechanisms from microarray gene expression data. Several algorithms have been proposed to identify biclusters, but very little effort was made to compare the performance of different algorithms on real datasets and combine the resultant biclusters into one unified ranking.</p> <p>Results</p> <p>In this paper we propose differential co-expression framework and a differential co-expression scoring function to objectively quantify quality or goodness of a bicluster of genes based on the observation that genes in a bicluster are co-expressed in the conditions belonged to the bicluster and not co-expressed in the other conditions. Furthermore, we propose a scoring function to stratify biclusters into three types of co-expression. We used the proposed scoring functions to understand the performance and behavior of the four well established biclustering algorithms on six real datasets from different domains by combining their output into one unified ranking.</p> <p>Conclusions</p> <p>Differential co-expression framework is useful to provide quantitative and objective assessment of the goodness of biclusters of co-expressed genes and performance of biclustering algorithms in identifying co-expression biclusters. It also helps to combine the biclusters output by different algorithms into one unified ranking i.e. meta-biclustering.</p