Clustering, Hamming Embedding, Generalized LSH and the Max Norm

We study the convex relaxation of clustering and hamming embedding, focusing on the asymmetric case (co-clustering and asymmetric hamming embedding), understanding their relationship to LSH as studied by (Charikar 2002) and to the max-norm ball, and the differences between their symmetric and asymmetric versions.Comment: 17 page

Existential witness extraction in classical realizability and via a negative translation

We show how to extract existential witnesses from classical proofs using Krivine's classical realizability---where classical proofs are interpreted as lambda-terms with the call/cc control operator. We first recall the basic framework of classical realizability (in classical second-order arithmetic) and show how to extend it with primitive numerals for faster computations. Then we show how to perform witness extraction in this framework, by discussing several techniques depending on the shape of the existential formula. In particular, we show that in the Sigma01-case, Krivine's witness extraction method reduces to Friedman's through a well-suited negative translation to intuitionistic second-order arithmetic. Finally we discuss the advantages of using call/cc rather than a negative translation, especially from the point of view of an implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS), 201

Zipf's law in Multifragmentation

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition

Realizability Interpretation and Normalization of Typed Call-by-Need λ\lambda-calculus With Control

We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need \lambda$-$calculus with control due to Ariola et al. Indeed, in such call-by-need calculus, substitutions have to be delayed until knowing if an argument is really needed. In a second step, we extend the proof to a call-by-need \lambda$$-calculus equipped with a type system equivalent to classical second-order predicate logic, representing one step towards proving the normalization of the call-by-need classical second-order arithmetic introduced by the second author to provide a proof-as-program interpretation of the axiom of dependent choice

Polarizing Double Negation Translations

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the polarization of the formul{\ae}{} and adapt those translation to the different connectives and quantifiers. We show that the embedding results still hold, using a customized version of the focused classical sequent calculus. We also prove the latter equivalent to more usual versions of the sequent calculus. This polarization process allows lighter embeddings, and sheds some light on the relationship between intuitionistic and classical connectives

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

ASMs and Operational Algorithmic Completeness of Lambda Calculus

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family of computable functions (taken as primitive tools, i.e., kind of oracle functions for the algorithm), for every constant K big enough, each computation step of the algorithm can be simulated by exactly K successive reductions in a natural extension of lambda calculus with constants for functions in the above considered family. The proof is based on a fixed point technique in lambda calculus and on Gurevich sequential Thesis which allows to identify sequential deterministic algorithms with Abstract State Machines. This extends to algorithms for partial computable functions in such a way that finite computations ending with exceptions are associated to finite reductions leading to terms with a particular very simple feature.Comment: 37 page

Strongly damped nuclear collisions: zero or first sound ?

The relaxation of the collective quadrupole motion in the initial stage of a central heavy ion collision at beam energies $E_{lab}=5\div20$ AMeV is studied within a microscopic kinetic transport model. The damping rate is shown to be a non-monotonic function of E_{lab} for a given pair of colliding nuclei. This fact is interpreted as a manifestation of the zero-to-first sound transition in a finite nuclear system.Comment: 15 pages, 4 figure

Hepatitis B infection in HIV-1-infected patients receiving highly active antiretroviral therapy in Lomé, Togo: Prevalence and molecular consequences

Background. No data are available on HIV/hepatitis B virus (HBV) or hepatitis C virus coinfection in Togo, and patients are not routinely tested for HBV infection.Objectives. To determine the prevalence of HBV and the risk of HBV drug resistance during antiretroviral treatment in HIV-coinfected patients in Togo.Method. This cross-sectional study was carried out in Lomé, Togo, from January 2010 to December 2011 among HIV-infected patients who had been on antiretroviral therapy (ART) for at least 6 months.Results. In total, 1 212 patients (74.9% female) living with HIV/AIDS and treated with ART were included in the study. The seroprevalence of hepatitis B surface antigen (HBsAg) was 9.7% (117/1 212; 95% confidence interval (CI) 8.04 - 11.45). Of these 117 HBsAg-positive patients, 16 (13.7%) were hepatitis B e antigen (HBeAg)-positive, and 115 (98.3%) were on lamivudine. The HBV DNA load was >10 IU/ mL in 33/117 patients overall (38%), and in 87.5% of 16 HBeAg positive patients (p<0.0001). In multivariate analysis, factors associated with HBV DNA load >10 IU/mL were HBeAg positivity (adjusted odds ratio (aOR) 6.4; p=0.001) and a higher level of education (aOR 6.5; p=0.026). The prevalence of HBV resistance to lamivudine was 13.0% (15/115; 95% CI 7.0 - 19.0). The detected resistance mutations were rtL180M (14/15 patients) and rtM204V/I (15/15).Conclusion. The seroprevalence of HBV among ART-treated HIV-infected patients in Togo was 9.7%. The prevalence of HBV lamivudine resistance mutations after 2 years of ART was 13.0%. These results suggest that HBV screening before ART initiation can be based on HBsAg testing

Conditional Bigraphs

Bigraphs are a universal graph based model, designed for analysing reactive systems that include spatial and non-spatial (e.g. communication) relationships. Bigraphs evolve over time using a rewriting framework that finds instances of a (sub)-bigraph, and substitutes a new bigraph. In standard bigraphs, the applicability of a rewrite rule is determined completely by a local match and does not allow any non-local reasoning, i.e. contextual conditions. We introduce conditional bigraphs that add conditions to rules and show how these fit into the matching framework for standard bigraphs. An implementation is provided, along with a set of examples. Finally, we discuss the limits of application conditions within the existing matching framework and present ways to extend the range of conditions that may be expressed