Linear-time list recovery of high-rate expander codes

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as well as explicit constructions of matrices for compressive sensing and group testing. Previous list recoverable codes with linear-time decoding algorithms have all had rate at most 1/2; in contrast, our codes can have rate $1 - \epsilon$ for any $\epsilon > 0$. We can plug our high-rate codes into a construction of Meir (2014) to obtain linear-time list recoverable codes of arbitrary rates, which approach the optimal trade-off between the number of non-trivial lists provided and the rate of the code. While list-recovery is interesting on its own, our primary motivation is applications to list-decoding. A slight strengthening of our result would implies linear-time and optimally list-decodable codes for all rates, and our work is a step in the direction of solving this important problem

Population size impacts host-pathogen coevolution

Ongoing host–pathogen interactions are characterized by rapid coevolutionary changes forcing species to continuously adapt to each other. The interacting species are often defined by finite population sizes. In theory, finite population size limits genetic diversity and compromises the efficiency of selection owing to genetic drift, in turn constraining any rapid coevolutionary responses. To date, however, experimental evidence for such constraints is scarce. The aim of our study was to assess to what extent population size influences the dynamics of host–pathogen coevolution. We used Caenorhabditus elegans and its pathogen Bacillus thuringiensis as a model for experimental coevolution in small and large host populations, as well as in host populations which were periodically forced through a bottleneck. By carefully controlling host population size for 23 host generations, we found that host adaptation was constrained in small populations and to a lesser extent in the bottlenecked populations. As a result, coevolution in large and small populations gave rise to different selection dynamics and produced different patterns of host–pathogen genotype-by-genotype interactions. Our results demonstrate a major influence of host population size on the ability of the antagonists to co-adapt to each other, thereby shaping the dynamics of antagonistic coevolution

Spectral approach to linear programming bounds on codes

We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces.Comment: 11 pages, submitte

EVALUACIÓN DE LAS COMPETENCIAS COGNITIVAS Y SOCIALES DE NIÑOS QUE HAN ESTADO EN SITUACIÓN DE CALLE

The following study is an exploratory approach to the population of street children of Montevideo. It involves 27 children of both sexes between 7 and 13 years. Sociodemographic variables were considered and it was evaluated the neuropsychological development, including the use of oral language, the relationship with the writing code, logical-mathematical reasoning skills, cognitive functioning and exploring some psychopathological indicators. The results show that this is a population with high levels of weaknesses and vulnerabilities, and a significant presence of behavioral disorders. In the cognitive aspect, there is some level of effectiveness in the implementation of intellectual nonverbal operations. In the verbal tasks, significant deficits for the low overall development of language were found. This would have a negative impact on school integration as well as on the capacity for self-regulation of behavior.En el siguiente estudio se busca una aproximación exploratoria a la población de los niños y niñas en situación de calle de Montevideo. Se trabajo con 27 niños de ambos sexos de entre 7 y 13 años. Se consideraron las variables sociodemográficas y se evaluó el desarrollo neuropsicológico, incluyendo la utilización del lenguaje oral, la relación con el código escrito, las habilidades de razonamiento lógico-matemático, el funcionamiento cognitivo general y la exploración de algunos indicadores psicopatológicos. Los resultados muestran que se trata de una población con un alto nivel de carencias y vulnerabilidades, y una importante presencia de trastornos comportamentales. En el aspecto cognitivo, se encuentra algún nivel de efectividad en la ejecución intelectual de operaciones no verbales. En las  tareas verbales, se comprobaría un déficit significativo por el escaso desarrollo general del lenguaje. Esto tendría consecuencias negativas en la inserción escolar así como en la capacidad de auto-regulación del comportamiento

Type 2 Diabetes Susceptibility Gene TCF7L2 and Its Role in β-Cell Function

Type 2 diabetes is associated with impaired insu-lin secretion. Both 1st- and 2nd-phase insulinsecretion are reduced, but the effect is particu-larly pronounced for the 1st phase. The pro-cesses culminating in impaired insulin secretion are not fully understood, but both genetic and environmental factors are thought to play a role. Over the past 2 years, genome-wide association scans have transformed the ge-netic landscape of type 2 diabetes susceptibility, with the current gene count close to 20 (1). A couple of common themes have emerged from these studies. First, the major-ity of the genes identified thus far seem to affect diabetes susceptibility through -cell dysfunction (2). Second, the risk alleles tend to be common in the population, but their effect on diabetes risk is relatively small (3,4). TCF7L2, the susceptibility gene with the largest effect on disease susceptibility discovered to date, was iden-tified pre–genome-wide association by Grant et al. i

Random subcubes as a toy model for constraint satisfaction problems

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.Comment: 21 pages, 4 figure