Bell inequalities stronger than the CHSH inequality for 3-level isotropic states

We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3 \otimes 3 isotropic states in the sense that they are violated by some isotropic states in the 3 \otimes 3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I_3322 Bell inequality for 3 \otimes 3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2 \otimes 2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.Comment: 9 pages, 1 figure. v2: organization improved; less references to the cut polytope to make the main results clear; references added; typos corrected; typesetting style change

Efficiently Clustering Very Large Attributed Graphs

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes and to the structure of the graph. However, time and space complexities of state of the art algorithms limit their scalability to medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a fast and scalable algorithm for partitioning large attributed graphs. The approach is robust, being compatible both with categorical and with quantitative attributes, and it is tailorable, allowing the user to weight the semantic and topological components. Further, the approach does not require the user to guess in advance the number of clusters. SToC relies on well known approximation techniques such as bottom-k sketches, traditional graph-theoretic concepts, and a new perspective on the composition of heterogeneous distance measures. Experimental results demonstrate its ability to efficiently compute high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an appendix with validation of our attribute model and distance function, omitted in the converence version for lack of space. Please refer to the published versio

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Universality-class dependence of energy distributions in spin glasses

We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price algorithms. By tuning the exponent of the power-law interactions we are able to scan several universality classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution. We compare the results of the disordered one-dimensional Ising chain to results for a disordered two-leg ladder, for which large system sizes can be studied, and find a qualitative agreement between the disordered one-dimensional Ising chain in the short-range universality class and the disordered two-leg ladder. We show that the mean and the standard deviation of the ground-state energy distributions scale with a power of the system size. In the mean-field universality class the skewness does not follow a power-law behavior and converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick model seem to be acceptably well fitted by a modified Gumbel distribution. Finally, we discuss the distribution of the internal energy of the Sherrington-Kirkpatrick model at finite temperatures and show that it behaves similar to the ground-state energy of the system if the temperature is smaller than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl

Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes

We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundant constraints that forces the central path to take at least 2n − 2 sharp turns. This fact sug-gests that any feasible path-following interior-point method will take at least O(2n) iterations to solve this problem, whereas in practice typically only a few iterations (e.g., 50) suffices to obtain a high-quality solution. Thus, the construction potentially exhibits the worst-case iteration-complexity known to date which almost matches the theoretical iteration-complexity bound for this type of methods. In addition, this construction gives a counterexample to a conjecture that the total central path curvature is O(n)

Arbitration between model-free and model-based control is not affected by transient changes in tonic serotonin levels

Background: Serotonin has been suggested to modulate decision-making by influencing the arbitration between model-based and model-free control. Disruptions in these control mechanisms are involved in mental disorders such as drug dependence or obsessive-compulsive disorder. While previous reports indicate that lower brain serotonin levels reduce model-based control, it remains unknown whether increases in serotonergic availability might thus increase model-based control. Moreover, the mediating neural mechanisms have not been studied yet. Aim: The first aim of this study was to investigate whether increased/decreased tonic serotonin levels affect the arbitration between model-free and model-based control. Second, we aimed to identify the underlying neural processes. Methods: We employed a sequential two-stage Markov decision-task and measured brain responses during functional magnetic resonance imaging in 98 participants in a randomized, double-blind cross-over within-subject design. To investigate the influence of serotonin on the balance between model-free and model-based control, we used a tryptophan intervention with three intervention levels (loading, balanced, depletion). We hypothesized that model-based behaviour would increase with higher serotonin levels. Results: We found evidence that neither model-free nor model-based control were affected by changes in tonic serotonin levels. Furthermore, our tryptophan intervention did not elicit relevant changes in Blood-Oxygenation-Level Dependent activity

A generalization of the concept of distance based on the simplex inequality

We introduce and discuss the concept of n-distance, a generalization to n elements of the classical notion of distance obtained by replacing the triangle inequality with the so-called simplex inequality d(x1,…,xn)≤K∑i=1nd(x1,…,xn)zi,x1,…,xn,z∈X, where K=1. Here d(x1,…,xn)zi is obtained from the function d(x1,…,xn) by setting its ith variable to z. We provide several examples of n-distances, and for each of them we investigate the infimum of the set of real numbers K∈]0,1] for which the inequality above holds. We also introduce a generalization of the concept of n-distance obtained by replacing in the simplex inequality the sum function with an arbitrary symmetric function

Identificación molecular de bacterias asociadas a la filosfera de plantas de arroz (Oryza sativa L), mediante técnicas de cultivo microbiano

Las plantas albergan una gran diversidad de microorganismos, como hongos, bacterias, etc., que interactúan con ella y tienen una funcionalidad que va desde la patogenicidad, hasta la protección de la misma. Se ha estudiado parte de esta diversidad microbiana a nivel de la filosfera en plantas de Oryza sativa (L) “arroz”; mediante microbiología molecular se ha caracterizado siete especies bacterianas entre las cuales sobresalieron especies Uncultured, es decir no cultivadas, además de Bacillus amyloliquefafaciens, Enterobacter asburiae, Klebsiella pneumoniae y Pantoea sp., todas ellas con un alto porcentaje de identidad; asimismo, mediante metagenómica dirigida se caracterizó trecientos ochenta y cinco especies bacterianas, de las que sobresalen pertenecen a los generos Bacillus, Rhizobium, Pseudomonas, Mycobacterium, Nocardioides, Clostridium, Methylobacterium y Pantoea. Las faamilias que más destacan son Enterobacteriaceae, Rhizobiaceae, Microbacteriaceae, Bacillaceae, Flavobacteriaceae, Pseudomonadaceae, Nocardiaceae, Mycobacteriaceae, Clostridiaceae y Methylobacteriaceae; no se encontró Burkholderia glumae

Excreción prolongada de Escherichia coli productor de toxina Shiga en niños que concurren a jardines maternales de Argentina

En el presente trabajo se describe la detección y el tiempo de excreción de Escherichia coli productor de toxina Shiga (STEC) O157 y no-O157 en casos sintomáticos y asintomáticos durante cuatro eventos ocurridos en jardines maternales de Argentina. En cada evento se identificaron los casos entre los niños, sus familiares y el personal del jardín. Los aislamientos fueron caracterizados por técnicas feno-genotípicas y de subtipificación. La excreción de STEC fue, en general, prolongada e intermitente. Cepas STEC O157:H7 (1er evento); O26:H11 (2do evento); O26:H11 (3er evento) y O145:NM (4to evento) fueron excretadas durante 23-30, 37, 31 y 19 días, respectivamente. Dadas las características de la excreción, no debe permitirse el reingreso a la institución de todo niño o adulto con infección por STEC, sintomático o asintomático, hasta no tener dos coprocultivos negativos sucesivos, con intervalos de 48 horas entre ellos.In this report we describe the detection and duration of fecal shedding of Shiga toxin-producing Escherichia coli (STEC) O157 and non-O157 in symptomatic and asymptomatic cases during four events occurred among children in day-care centers in Argentina. In each event, the cases were identified among children, family contacts and staff members of the Institution. The isolates were characterized by pheno-genotyping and subtyping methods. The STEC fecal shedding was prolonged and intermittent. Strains O157:H7 (1st event); O26:H11 (2nd event); O26:H11 (3rd event) and O145:NM (4th event) were shed during 23-30, 37, 31 and 19 days, respectively. Considering the possibility of STEC intermittent long-term shedding, symptomatic and asymptomatic individuals should be excluded from the Institution until two consecutive stool cultures obtained at least 48 h apart, test negative.Instituto de Genética Veterinari