Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Semilattices, Canonical Embeddings and Representing Measures

We provide conditions under which a modular function defined on a semilattice $X$ and with values in a commutative group is homomorphic to a modular function on a lattice $L$ for any embedding $X\hookrightarrow L$

Maharam-type kernel representation for operators with a trigonometric domination

[EN] Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in L2[0, 1] by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals.This research has been supported by MTM2016-77054-C2-1-P (Ministerio de Economia, Industria y Competitividad, Spain).Sánchez Pérez, EA. (2017). Maharam-type kernel representation for operators with a trigonometric domination. Aequationes Mathematicae. 91(6):1073-1091. https://doi.org/10.1007/s00010-017-0507-6S10731091916Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Generalized perfect spaces. Indag. Math. 19(3), 359–378 (2008)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Delgado, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Dodds, P.G., Huijsmans, C.B., de Pagter, B.: Characterizations of conditional expectation type operators. Pacific J. Math. 141(1), 55–77 (1990)Flores, J., Hernández, F.L., Tradacete, P.: Domination problems for strictly singular operators and other related classes. Positivity 15(4), 595–616 (2011). 2011Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87–106 (1974)Hu, G.: Weighted norm inequalities for bilinear Fourier multiplier operators. Math. Ineq. Appl. 18(4), 1409–1425 (2015)Halmos, P., Sunder, V.: Bounded Integral Operators on $$L^2$$ L 2 Spaces. Springer, Berlin (1978)Kantorovitch, L., Vulich, B.: Sur la représentation des opérations linéaires. Compositio Math. 5, 119–165 (1938)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise multipliers of Calderón- Lozanovskii spaces. Math. Nachr. 286, 876–907 (2013)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)Kuo, W.-C., Labuschagne, C.C.A., Watson, B.A.: Conditional expectations on Riesz spaces. J. Math. Anal. Appl. 303, 509–521 (2005)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1979)Maharam, D.: The representation of abstract integrals. Trans. Am. Math. Soc. 75, 154–184 (1953)Maharam, D.: On kernel representation of linear operators. Trans. Am. Math. Soc. 79, 229–255 (1955)Maligranda, L., Persson, L.E.: Generalized duality of some Banach function spaces. Indag. Math. 51, 323–338 (1989)Neugebauer, C.J.: Weighted norm inequalities for averaging operators of monotone functions. Publ. Mat. 35, 429–447 (1991)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Rota, G.C.: On the representation of averaging operators. Rend. Sem. Mat. Univ. Padova. 30, 52–64 (1960)Sánchez Pérez, E.A.: Factorization theorems for multiplication operators on Banach function spaces. Integr. Equ. Oper. Theory 80(1), 117–135 (2014)Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28(4), 579–591 (1984)Schep, A.R.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010

Integrated information increases with fitness in the evolution of animats

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.Comment: 27 pages, 8 figures, one supplementary figure. Three supplementary video files available on request. Version commensurate with published text in PLoS Comput. Bio

Development of the Pulmonary Vein and the Systemic Venous Sinus: An Interactive 3D Overview

Knowledge of the normal formation of the heart is crucial for the understanding of cardiac pathologies and congenital malformations. The understanding of early cardiac development, however, is complicated because it is inseparably associated with other developmental processes such as embryonic folding, formation of the coelomic cavity, and vascular development. Because of this, it is necessary to integrate morphological and experimental analyses. Morphological insights, however, are limited by the difficulty in communication of complex 3D-processes. Most controversies, in consequence, result from differences in interpretation, rather than observation. An example of such a continuing debate is the development of the pulmonary vein and the systemic venous sinus, or “sinus venosus”. To facilitate understanding, we present a 3D study of the developing venous pole in the chicken embryo, showing our results in a novel interactive fashion, which permits the reader to form an independent opinion. We clarify how the pulmonary vein separates from a greater vascular plexus within the splanchnic mesoderm. The systemic venous sinus, in contrast, develops at the junction between the splanchnic and somatic mesoderm. We discuss our model with respect to normal formation of the heart, congenital cardiac malformations, and the phylogeny of the venous tributaries

The epidemiology of mumps in Italy

In Italy, although vaccination has been recommended for a number of years, vaccination coverage for mumps is still sub-optimal. The objective of the present study was to evaluate the seroprevalence of mumps antibodies in the Italian population, stratified by age, gender and geographical area. The proportion of individuals positive for mumps antibodies remained stable in the age classes 0-11 months and 1 year (25.4% and 30.8%, respectively) and showed a continuous increase after the second year of life. The percentage of susceptible individuals was higher than 20% in persons 2-14 years of age and exceeded 10% in persons 15-39 years of age. No statistically significant differences were observed by gender or geographical area. Comparison between these results and the data obtained from a 1996 survey showed a statistically significant increase in seroprevalence in the age class 2-4 years. No changes were observed in the other age-groups. The results of this study confirm that the efforts made in recent years to improve vaccination coverage within the second year of life should be strengthened. \ua9 2008 Elsevier Ltd. All rights reserved

Genome-wide evolutionary dynamics of influenza B viruses on a global scale

The global-scale epidemiology and genome-wide evolutionary dynamics of influenza B remain poorly understood compared with influenza A viruses. We compiled a spatio-temporally comprehensive dataset of influenza B viruses, comprising over 2,500 genomes sampled worldwide between 1987 and 2015, including 382 newly-sequenced genomes that fill substantial gaps in previous molecular surveillance studies. Our contributed data increase the number of available influenza B virus genomes in Europe, Africa and Central Asia, improving the global context to study influenza B viruses. We reveal Yamagata-lineage diversity results from co-circulation of two antigenically-distinct groups that also segregate genetically across the entire genome, without evidence of intra-lineage reassortment. In contrast, Victoria-lineage diversity stems from geographic segregation of different genetic clades, with variability in the degree of geographic spread among clades. Differences between the lineages are reflected in their antigenic dynamics, as Yamagata-lineage viruses show alternating dominance between antigenic groups, while Victoria-lineage viruses show antigenic drift of a single lineage. Structural mapping of amino acid substitutions on trunk branches of influenza B gene phylogenies further supports these antigenic differences and highlights two potential mechanisms of adaptation for polymerase activity. Our study provides new insights into the epidemiological and molecular processes shaping influenza B virus evolution globally

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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