Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.Comment: 8 page

A Frobenius variant of Seshadri constants

We define and study a version of Seshadri constant for ample line bundles in positive characteristic. We prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle. As a consequence, we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual Seshadri constants holds also in positive characteristic.Comment: 16 page

Dividend Policy as Mediation of the Influence of Management Ownership and Institutional Ownership on Company’s Financial Performance

The purposes of this research are: (1) to examine if management ownership influences significantly positive on dividend policy (2) to examine if institutional ownership influences significantly positive on dividend policy, and (3) to examine if dividend policy influences significantly positive on company’s financial performance. This is an explanatory research since it aims to explain the influence among variables after testing research hypotheses based on the underlying theory. The data of this research are financial reports of go public manufacture companies which have been audited at Indonesian Stock Exchange (IDX) from 2003 – 2012. This is a census research that is by using all population, 36 manufacture companies. Since this is a census research by using pooling data technique for 10 years so there were 360 observation data. This research used path analysis technique to test hypotheses. The research finding shows that management ownership doesn’t influence significantly positive on dividend policy, institutional ownership doesn’t influence significantly positive on dividend policy, dividend policy doesn’t influence significantly positive on company’s financial performance,

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

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

Low autocorrelated multi-phase sequences

The interplay between the ground state energy of the generalized Bernasconi model to multi-phase, and the minimal value of the maximal autocorrelation function, $C_{max}=\max_K{|C_K|}$, $K=1,..N-1$, is examined analytically and the main results are: (a) The minimal value of $\min_N{C_{max}}$ is $0.435\sqrt{N}$ significantly smaller than the typical value for random sequences $O(\sqrt{\log{N}}\sqrt{N})$. (b) $\min_N{C_{max}}$ over all sequences of length N is obtained in an energy which is about 30% above the ground-state energy of the generalized Bernasconi model, independent of the number of phases m. (c) The maximal merit factor $F_{max}$ grows linearly with m. (d) For a given N, $\min_N{C_{max}}\sim\sqrt{N/m}$ indicating that for m=N, $\min_N{C_{max}}=1$, i.e. a Barker code exits. The analytical results are confirmed by simulations.Comment: 4 pages, 4 figure

Multi-Player and Multi-Choice Quantum Game

We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we provide a strategy with which players can always avoid the worst outcome. Also, by changing the value of the parameter of the initial state, the probabilities for players to obtain the best payoff will be much higher that in its classical version.Comment: 4 pages, 1 figur

The influence of feature selection methods on accuracy, stability and interpretability of molecular signatures

Motivation: Biomarker discovery from high-dimensional data is a crucial problem with enormous applications in biology and medicine. It is also extremely challenging from a statistical viewpoint, but surprisingly few studies have investigated the relative strengths and weaknesses of the plethora of existing feature selection methods. Methods: We compare 32 feature selection methods on 4 public gene expression datasets for breast cancer prognosis, in terms of predictive performance, stability and functional interpretability of the signatures they produce. Results: We observe that the feature selection method has a significant influence on the accuracy, stability and interpretability of signatures. Simple filter methods generally outperform more complex embedded or wrapper methods, and ensemble feature selection has generally no positive effect. Overall a simple Student's t-test seems to provide the best results. Availability: Code and data are publicly available at http://cbio.ensmp.fr/~ahaury/

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Predictive gene lists for breast cancer prognosis: A topographic visualisation study

<p>Abstract</p> <p>Background</p> <p>The controversy surrounding the non-uniqueness of predictive gene lists (PGL) of small selected subsets of genes from very large potential candidates as available in DNA microarray experiments is now widely acknowledged <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>. Many of these studies have focused on constructing discriminative semi-parametric models and as such are also subject to the issue of random correlations of sparse model selection in high dimensional spaces. In this work we outline a different approach based around an unsupervised patient-specific nonlinear topographic projection in predictive gene lists.</p> <p>Methods</p> <p>We construct nonlinear topographic projection maps based on inter-patient gene-list relative dissimilarities. The Neuroscale, the Stochastic Neighbor Embedding(SNE) and the Locally Linear Embedding(LLE) techniques have been used to construct two-dimensional projective visualisation plots of 70 dimensional PGLs per patient, classifiers are also constructed to identify the prognosis indicator of each patient using the resulting projections from those visualisation techniques and investigate whether <it>a-posteriori </it>two prognosis groups are separable on the evidence of the gene lists.</p> <p>A literature-proposed predictive gene list for breast cancer is benchmarked against a separate gene list using the above methods. Generalisation ability is investigated by using the mapping capability of Neuroscale to visualise the follow-up study, but based on the projections derived from the original dataset.</p> <p>Results</p> <p>The results indicate that small subsets of patient-specific PGLs have insufficient prognostic dissimilarity to permit a distinction between two prognosis patients. Uncertainty and diversity across multiple gene expressions prevents unambiguous or even confident patient grouping. Comparative projections across different PGLs provide similar results.</p> <p>Conclusion</p> <p>The random correlation effect to an arbitrary outcome induced by small subset selection from very high dimensional interrelated gene expression profiles leads to an outcome with associated uncertainty. This continuum and uncertainty precludes any attempts at constructing discriminative classifiers.</p> <p>However a patient's gene expression profile could possibly be used in treatment planning, based on knowledge of other patients' responses.</p> <p>We conclude that many of the patients involved in such medical studies are <it>intrinsically unclassifiable </it>on the basis of provided PGL evidence. This additional category of 'unclassifiable' should be accommodated within medical decision support systems if serious errors and unnecessary adjuvant therapy are to be avoided.</p