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

Random geometric complexes

We study the expected topological properties of Cech and Vietoris-Rips complexes built on i.i.d. random points in R^d. We find higher dimensional analogues of known results for connectivity and component counts for random geometric graphs. However, higher homology H_k is not monotone when k > 0. In particular for every k > 0 we exhibit two thresholds, one where homology passes from vanishing to nonvanishing, and another where it passes back to vanishing. We give asymptotic formulas for the expectation of the Betti numbers in the sparser regimes, and bounds in the denser regimes. The main technical contribution of the article is in the application of discrete Morse theory in geometric probability.Comment: 26 pages, 3 figures, final revisions, to appear in Discrete & Computational Geometr

FAS-dependent cell death in α-synuclein transgenic oligodendrocyte models of multiple system atrophy

Multiple system atrophy is a parkinsonian neurodegenerative disorder. It is cytopathologically characterized by accumulation of the protein p25α in cell bodies of oligodendrocytes followed by accumulation of aggregated α-synuclein in so-called glial cytoplasmic inclusions. p25α is a stimulator of α-synuclein aggregation, and coexpression of α-synuclein and p25α in the oligodendroglial OLN-t40-AS cell line causes α-synuclein aggregate-dependent toxicity. In this study, we investigated whether the FAS system is involved in α-synuclein aggregate dependent degeneration in oligodendrocytes and may play a role in multiple system atrophy. Using rat oligodendroglial OLN-t40-AS cells we demonstrate that the cytotoxicity caused by coexpressing α-synuclein and p25α relies on stimulation of the death domain receptor FAS and caspase-8 activation. Using primary oligodendrocytes derived from PLP-α-synuclein transgenic mice we demonstrate that they exist in a sensitized state expressing pro-apoptotic FAS receptor, which makes them sensitive to FAS ligand-mediated apoptosis. Immunoblot analysis shows an increase in FAS in brain extracts from multiple system atrophy cases. Immunohistochemical analysis demonstrated enhanced FAS expression in multiple system atrophy brains notably in oligodendrocytes harboring the earliest stages of glial cytoplasmic inclusion formation. Oligodendroglial FAS expression is an early hallmark of oligodendroglial pathology in multiple system atrophy that mechanistically may be coupled to α-synuclein dependent degeneration and thus represent a potential target for protective intervention

EuCARD Newsletter Issue 2

European Coordination for Accelerator Research and Development (EuCARD) Newsletter Issue 2: July - September 2009 * A word from the Governing Board Chairman * Amassing the neutrino community * Start by probing the crab cavities * Breaking news for Proton "Surfatrons" * For EuCARD members: Interim reportin

Analysing multiparticle quantum states

The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions concerning systematic errors of quantum devices, the reconstruction of quantum states, and the analysis of correlations and complexity in multiparticle density matrices.Comment: 20 pages, 4 figures, prepared for proceedings of the "Quantum [Un]speakables II" conference (Vienna, 2014

Personal values, social capital, and higher education student career decidedness: a new 'protean'-informed model

This study investigates the role of personal values as motivational antecedents for understanding HE student career decidedness among university business school (UBS) students. We propose a new ‘protean’ informed HE student career decidedness model for theorizing how both personal values and social capital mediators (student social capital; personal, social and enterprise skills; access to resources) help in the student-centric and self-directed processes of career decision-making. A mixed methods study combines a (stage 1) survey of 308 UBS students from five (UK) university business schools, with results from (stage 2) four student focus groups, and (stage 3) two staff-student interactive seminars. From an employability perspective, arguably, the ultimate responsibility for becoming a ‘protean graduate’ rests with each UBS student, whilst the obligation of HE staff is to effectively facilitate and nurture all possible personal growth and skills development opportunities

ORBIT PRECISION ANALYSIS OF SMALL MAN-MADE SPACE OBJECTS IN LEO BASED ON RADAR TRACKING MEASUREMENTS

Abstract: The German Space Operations Center (GSOC

TOM40 Mediates Mitochondrial Dysfunction Induced by α-Synuclein Accumulation in Parkinson's Disease.

Alpha-synuclein (α-Syn) accumulation/aggregation and mitochondrial dysfunction play prominent roles in the pathology of Parkinson's disease. We have previously shown that postmortem human dopaminergic neurons from PD brains accumulate high levels of mitochondrial DNA (mtDNA) deletions. We now addressed the question, whether alterations in a component of the mitochondrial import machinery -TOM40- might contribute to the mitochondrial dysfunction and damage in PD. For this purpose, we studied levels of TOM40, mtDNA deletions, oxidative damage, energy production, and complexes of the respiratory chain in brain homogenates as well as in single neurons, using laser-capture-microdissection in transgenic mice overexpressing human wildtype α-Syn. Additionally, we used lentivirus-mediated stereotactic delivery of a component of this import machinery into mouse brain as a novel therapeutic strategy. We report here that TOM40 is significantly reduced in the brain of PD patients and in α-Syn transgenic mice. TOM40 deficits were associated with increased mtDNA deletions and oxidative DNA damage, and with decreased energy production and altered levels of complex I proteins in α-Syn transgenic mice. Lentiviral-mediated overexpression of Tom40 in α-Syn-transgenic mice brains ameliorated energy deficits as well as oxidative burden. Our results suggest that alterations in the mitochondrial protein transport machinery might contribute to mitochondrial impairment in α-Synucleinopathies