The hypertoric intersection cohomology ring

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset.Comment: Significant revisions in Section 5, with several corrected proof

Poisson-de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.Comment: 25 page

Equivariant log concavity and representation stability

We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra $\mathfrak{sl}_n$, we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree

A semi-small decomposition of the Chow ring of a matroid

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result of [AHK18]. We also show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring of M

Genome-wide analysis of poly(A) site selection in schizosaccharomyces pombe,

Polyadenylation of pre-mRNAs, a critical step in eukaryotic gene expression, is mediated by cis elements collectively called the polyadenylation signal. Genome-wide analysis of such polyadenylation signals was missing in fission yeast, even though it is an important model organism. We demonstrate that the canonical AATAAA motif is the most frequent and functional polyadenylation signal in Schizosaccharomyces pombe. Using analysis of RNA-Seq data sets from cells grown under various physiological conditions, we identify 3′ UTRs for nearly 90% of the yeast genes. Heterogeneity of cleavage sites is common, as is alternative polyadenylation within and between conditions. We validated the computationally identified sequence elements likely to promote polyadenylation by functional assays, including qRT-PCR and 3′RACE analysis. The biological importance of the AATAAA motif is underlined by functional analysis of the genes containing it. Furthermore, it has been shown that convergent genes require trans elements, like cohesin for efficient transcription termination. Here we show that convergent genes lacking cohesin (on chromosome 2) are generally associated with longer overlapping mRNA transcripts. Our bioinformatic and experimental genome-wide results are summarized and can be accessed and customized in a user-friendly database Pomb(A)

Topological Order in Projected Wave Functions and Effective Theories of Quantum Antiferromagnets

We study the topological order in RVB state derived from Gutzwiller projection of BCS-like mean field state. We propose to construct the topological excitation on the projected RVB state through Gutzwiller projection of mean field state with inserted $Z_{2}$ flux tube. We prove that all projected RVB states derived from bipartite effective theories, no matter the gauge structure in the mean field ansatz, are positive definite in the sense of the Marshall sign rule, which provides a universal origin for the absence of topological order in such RVB state.Comment: 5 pages, 1 figure

Noninvasive vagus nerve stimulation alters neural response and physiological autonomic tone to noxious thermal challenge.

The mechanisms by which noninvasive vagal nerve stimulation (nVNS) affect central and peripheral neural circuits that subserve pain and autonomic physiology are not clear, and thus remain an area of intense investigation. Effects of nVNS vs sham stimulation on subject responses to five noxious thermal stimuli (applied to left lower extremity), were measured in 30 healthy subjects (n = 15 sham and n = 15 nVNS), with fMRI and physiological galvanic skin response (GSR). With repeated noxious thermal stimuli a group × time analysis showed a significantly (p < .001) decreased response with nVNS in bilateral primary and secondary somatosensory cortices (SI and SII), left dorsoposterior insular cortex, bilateral paracentral lobule, bilateral medial dorsal thalamus, right anterior cingulate cortex, and right orbitofrontal cortex. A group × time × GSR analysis showed a significantly decreased response in the nVNS group (p < .0005) bilaterally in SI, lower and mid medullary brainstem, and inferior occipital cortex. Finally, nVNS treatment showed decreased activity in pronociceptive brainstem nuclei (e.g. the reticular nucleus and rostral ventromedial medulla) and key autonomic integration nuclei (e.g. the rostroventrolateral medulla, nucleus ambiguous, and dorsal motor nucleus of the vagus nerve). In aggregate, noninvasive vagal nerve stimulation reduced the physiological response to noxious thermal stimuli and impacted neural circuits important for pain processing and autonomic output

Fetuin-A and albumin alter cytotoxic effects of calcium phosphate nanoparticles on human vascular smooth muscle cells

Calcification is a detrimental process in vascular ageing and in diseases such as atherosclerosis and arthritis. In particular, small calcium phosphate (CaP) crystal deposits are associated with inflammation and atherosclerotic plaque de-stabilisation. We previously reported that CaP particles caused human vascular smooth muscle cell (VSMC) death and that serum reduced the toxic effects of the particles. Here, we found that the serum proteins fetuin-A and albumin (≥1 µM) reduced intracellular Ca2+ elevations and cell death in VSMCs in response to CaP particles. In addition, CaP particles functionalised with fetuin-A, but not albumin, were less toxic than naked CaP particles. Electron microscopic studies revealed that CaP particles were internalised in different ways; via macropinocytosis, membrane invagination or plasma membrane damage, which occurred within 10 minutes of exposure to particles. However, cell death did not occur until approximately 30 minutes, suggesting that plasma membrane repair and survival mechanisms were activated. In the presence of fetuin-A, CaP particle-induced damage was inhibited and CaP/plasma membrane interactions and particle uptake were delayed. Fetuin-A also reduced dissolution of CaP particles under acidic conditions, which may contribute to its cytoprotective effects after CaP particle exposure to VSMCs. These studies are particularly relevant to the calcification observed in blood vessels in patients with kidney disease, where circulating levels of fetuin-A and albumin are low, and in pathological situations where CaP crystal formation outweighs calcification-inhibitory mechanisms