Binomial Ideals and Congruences on Nn

Producción CientíficaA congruence on Nn is an equivalence relation on Nn that is compatible with the additive structure. If k is a field, and I is a binomial ideal in k[X1,…,Xn] (that is, an ideal generated by polynomials with at most two terms), then I induces a congruence on Nn by declaring u and v to be equivalent if there is a linear combination with nonzero coefficients of Xu and Xv that belongs to I. While every congruence on Nn arises this way, this is not a one-to-one correspondence, as many binomial ideals may induce the same congruence. Nevertheless, the link between a binomial ideal and its corresponding congruence is strong, and one may think of congruences as the underlying combinatorial structures of binomial ideals. In the current literature, the theories of binomial ideals and congruences on Nn are developed separately. The aim of this survey paper is to provide a detailed parallel exposition, that provides algebraic intuition for the combinatorial analysis of congruences. For the elaboration of this survey paper, we followed mainly (Kahle and Miller Algebra Number Theory 8(6):1297–1364, 2014) with an eye on Eisenbud and Sturmfels (Duke Math J 84(1):1–45, 1996) and Ojeda and Piedra Sánchez (J Symbolic Comput 30(4):383–400, 2000).National Science Foundation (grant DMS-1500832)Ministerio de Economía, Industria y Competitividad (project MTM2015-65764-C3-1)Junta de Extremadura (grupo de investigación FQM-024

Complexity Measures from Interaction Structures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex

Dental pulp exposure, periapical inflammation and suppurative osteomyelitis of the jaws in juvenile Baltic grey seals (<i>Halichoerus grypus grypus</i>) from the late 19th century

<div><p>The systematic analysis of museum collections can provide important insights into the dental and skeletal pathology of wild mammals. Here we present a previously unreported type of dental defect and related skull pathology in five juvenile Baltic grey seals that had been collected in the course of a seal culling program along the Danish coast in 1889 and 1890. All five skulls exhibited openings into the pulp cavities at the crown tips of all (four animals) or two (one animal) canines as well as several incisors and (in one animal) also some anterior premolars. The affected teeth showed wide pulp cavities and thin dentin. Pulp exposure had caused infection, inflammation, and finally necrosis of the pulp. As was evidenced by the extensive radiolucency around the roots of the affected teeth, the inflammation had extended from the pulp into the periapical space, leading to apical periodontitis with extensive bone resorption. Further spreading of the inflammation into the surrounding bone regions had then caused suppurative osteomyelitis of the jaws. The postcanine teeth of the pathological individuals typically had dentin of normal thickness and, except for one specimen, did not exhibit pulp exposure. The condition may have been caused by a late onset of secondary and tertiary dentin formation that led to pulp exposure in anterior teeth exposed to intense wear. Future investigations could address a possible genetic causation of the condition in the studied grey seals.</p></div

Quantifying structure in networks

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure

The WNK-SPAK/OSR1 pathway: master regulator of cation-chloride cotransporters

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordThe WNK-SPAK/OSR1 kinase complex is composed of the kinases WNK (with no lysine) and SPAK (SPS1-related proline/alanine-rich kinase) or the SPAK homolog OSR1 (oxidative stress-responsive kinase 1). The WNK family senses changes in intracellular Cl(-) concentration, extracellular osmolarity, and cell volume and transduces this information to sodium (Na(+)), potassium (K(+)), and chloride (Cl(-)) cotransporters [collectively referred to as CCCs (cation-chloride cotransporters)] and ion channels to maintain cellular and organismal homeostasis and affect cellular morphology and behavior. Several genes encoding proteins in this pathway are mutated in human disease, and the cotransporters are targets of commonly used drugs. WNKs stimulate the kinases SPAK and OSR1, which directly phosphorylate and stimulate Cl(-)-importing, Na(+)-driven CCCs or inhibit the Cl(-)-extruding, K(+)-driven CCCs. These coordinated and reciprocal actions on the CCCs are triggered by an interaction between RFXV/I motifs within the WNKs and CCCs and a conserved carboxyl-terminal docking domain in SPAK and OSR1. This interaction site represents a potentially druggable node that could be more effective than targeting the cotransporters directly. In the kidney, WNK-SPAK/OSR1 inhibition decreases epithelial NaCl reabsorption and K(+) secretion to lower blood pressure while maintaining serum K(+). In neurons, WNK-SPAK/OSR1 inhibition could facilitate Cl(-) extrusion and promote γ-aminobutyric acidergic (GABAergic) inhibition. Such drugs could have efficacy as K(+)-sparing blood pressure-lowering agents in essential hypertension, nonaddictive analgesics in neuropathic pain, and promoters of GABAergic inhibition in diseases associated with neuronal hyperactivity, such as epilepsy, spasticity, neuropathic pain, schizophrenia, and autism.D.R.A. research in this area is supported by the Medical Research Council and the Wellcome Trust [grant number 091415] and the pharmaceutical companies supporting the Division of Signal Transduction Therapy Unit (AstraZeneca, Boehringer-Ingelheim, GlaxoSmithKline, Merck KGaA, Janssen Pharmaceutica and Pfizer). K.T.K. is supported by the Manton Center for Orphan Diseases at Children's Hospital Boston at Harvard Medical School, and the Harvard/MIT Joint Research Grants Program in Basic Neuroscience

WNK Kinase Signaling in Ion Homeostasis and Human Disease

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.WNK kinases, along with their upstream regulators (CUL3/KLHL3) and downstream targets (the SPAK/OSR1 kinases and the cation-Cl- cotransporters [CCCs]), comprise a signaling cascade essential for ion homeostasis in the kidney and nervous system. Recent work has furthered our understanding of the WNKs in epithelial transport, cell volume homeostasis, and GABA signaling, and uncovered novel roles for this pathway in immune cell function and cell proliferation.This work was supported by a NIHNRCDP grant (K.T.K.), Simons Foundation grant #400947 (K.T.K.), March of Dimes Basil O’Connor Award (K.T.K.), and NIH grant DK93501 to E.D

Analysis workflow to assess de novo genetic variants from human whole-exome sequencing

Here, we present a protocol to analyz