On codimension two flats in Fermat-type arrangements

In the present note we study certain arrangements of codimension $2$ flats in projective spaces, we call them "Fermat arrangements". We describe algebraic properties of their defining ideals. In particular, we show that they provide counterexamples to an expected containment relation between ordinary and symbolic powers of homogeneous ideals.Comment: 9 page

Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

An Antimicrobial Peptidomimetic Induces Mucorales Cell Death through Mitochondria-Mediated Apoptosis

The incidence of mucormycosis has dramatically increased in immunocompromised patients. Moreover, the array of cellular targets whose inhibition results in fungal cell death is rather limited. Mitochondria have been mechanistically identified as central regulators of detoxification and virulence in fungi. Our group has previously designed and developed a proteolytically-resistant peptidomimetic motif D(KLAKLAK)2 with pleiotropic action ranging from targeted (i.e., ligand-directed) activity against cancer and obesity to non-targeted activity against antibiotic resistant gram-negative rods. Here we evaluated whether this non-targeted peptidomimetic motif is active against Mucorales. We show that D(KLAKLAK)2 has marked fungicidal action, inhibits germination, and reduces hyphal viability. We have also observed cellular changes characteristic of apoptosis in D(KLAKLAK)2-treated Mucorales cells. Moreover, the fungicidal activity was directly correlated with vacuolar injury, mitochondrial swelling and mitochondrial membrane depolarization, intracellular reactive oxygen species accumulation (ROS), and increased caspase-like enzymatic activity. Finally, these apoptotic features were prevented by the addition of the ROS scavenger N-acetyl-cysteine indicating mechanistic pathway specificity. Together, these findings indicate that D(KLAKLAK)2 makes Mucorales exquisitely susceptible via mitochondrial injury-induced apoptosis. This prototype may serve as a candidate drug for the development of translational applications against mucormycosis and perhaps other fungal infections

First Principle Local Density Approximation Description of the Electronic Properties of Ferroelectric Sodium Nitrite

The electronic structure of the ferroelectric crystal, NaNO$_2$, is studied by means of first-principles, local density calculations. Our ab-initio, non-relativistic calculations employed a local density functional approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). Following the Bagayoko, Zhao, Williams, method, as enhanced by Ekuma, and Franklin (BZW-EF), we solved self-consistently both the Kohn-Sham equation and the equation giving the ground state charge density in terms of the wave functions of the occupied states. We found an indirect band gap of 2.83 eV, from W to R. Our calculated direct gaps are 2.90, 2.98, 3.02, 3.22, and 3.51 eV at R, W, X, {\Gamma}, and T, respectively. The band structure and density of states show high localization, typical of a molecular solid. The partial density of states shows that the valence bands are formed only by complex anionic states. These results are in excellent agreement with experiment. So are the calculated densities of states. Our calculated electron effective masses of 1.18, 0.63, and 0.73 mo in the {\Gamma}-X, {\Gamma}-R, and {\Gamma}-W directions, respectively, show the highly anisotropic nature of this material.Comment: 13 Pages, 4 Figures, and 2 Table

Potential role of monkey inferior parietal neurons coding action semantic equivalences as precursors of parts of speech

The anterior portion of the inferior parietal cortex possesses comprehensive representations of actions embedded in behavioural contexts. Mirror neurons, which respond to both self-executed and observed actions, exist in this brain region in addition to those originally found in the premotor cortex. We found that parietal mirror neurons responded differentially to identical actions embedded in different contexts. Another type of parietal mirror neuron represents an inverse and complementary property of responding equally to dissimilar actions made by itself and others for an identical purpose. Here, we propose a hypothesis that these sets of inferior parietal neurons constitute a neural basis for encoding the semantic equivalence of various actions across different agents and contexts. The neurons have mirror neuron properties, and they encoded generalization of agents, differentiation of outcomes, and categorization of actions that led to common functions. By integrating the activities of these mirror neurons with various codings, we further suggest that in the ancestral primates' brains, these various representations of meaningful action led to the gradual establishment of equivalence relations among the different types of actions, by sharing common action semantics. Such differential codings of the components of actions might represent precursors to the parts of protolanguage, such as gestural communication, which are shared among various members of a society. Finally, we suggest that the inferior parietal cortex serves as an interface between this action semantics system and other higher semantic systems, through common structures of action representation that mimic language syntax

The plight of the sense-making ape

This is a selective review of the published literature on object-choice tasks, where participants use directional cues to find hidden objects. This literature comprises the efforts of researchers to make sense of the sense-making capacities of our nearest living relatives. This chapter is written to highlight some nonsensical conclusions that frequently emerge from this research. The data suggest that when apes are given approximately the same sense-making opportunities as we provide our children, then they will easily make sense of our social signals. The ubiquity of nonsensical contemporary scientific claims to the effect that humans are essentially--or inherently--more capable than other great apes in the understanding of simple directional cues is, itself, a testament to the power of preconceived ideas on human perception

Nna1 Mediates Purkinje Cell Dendritic Development via Lysyl Oxidase Propeptide and NF-κB Signaling

SummaryThe molecular pathways controlling cerebellar Purkinje cell dendrite formation and maturation are poorly understood. The Purkinje cell degeneration (pcd) mutant mouse is characterized by mutations in Nna1, a gene discovered in an axonal regenerative context, but whose actual function in development and disease is unknown. We found abnormal development of Purkinje cell dendrites in postnatal pcdSid mice and linked this deficit to a deletion mutation in exon 7 of Nna1. With single cell gene profiling and virus-based gene transfer, we analyzed a molecular pathway downstream to Nna1 underlying abnormal Purkinje cell dendritogenesis in pcdSid mice. We discovered that mutant Nna1 dramatically increases intranuclear localization of lysyl oxidase propeptide, which interferes with NF-κB RelA signaling and microtubule-associated protein regulation of microtubule stability, leading to underdevelopment of Purkinje cell dendrites. These findings provide insight into Nna1's role in neuronal development and why its absence renders Purkinje cells more vulnerable