196 research outputs found
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 . 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 -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 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
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