Spectral fluctuations of Schr\"odinger operators generated by critical points of the potential

Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.\medskip keywords : Semi-classical analysis; Schr\"odinger operators; Equilibriums in classical mechanics.Comment: 18 pages, Final versio

First cohomology for finite groups of Lie type: simple modules with small dominant weights

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\mathbb{F}_p$. Given $r \geq 1$, set $q=p^r$, and let $G(\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\mathbb{F}_q),L(\lambda))$ where $L(\lambda)$ is the simple $G$-module of highest weight $\lambda$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $\lambda$ is less than or equal to a fundamental dominant weight. In particular, in the cases we consider, we show that the first cohomology group has dimension at most one. Our calculations significantly extend, and provide new proofs for, earlier results of Cline, Parshall, Scott, and Jones, who considered the special case when $\lambda$ is a minimal nonzero dominant weight.Comment: 24 pages, 5 figures, 6 tables. Typos corrected and some proofs streamlined over previous versio

Differential expression and co-expression gene networks reveal candidate biomarkers of boar taint in non-castrated pigs

Abstract Boar taint (BT) is an offensive odour or taste observed in pork from a proportion of non-castrated male pigs. Surgical castration is effective in avoiding BT, but animal welfare issues have created an incentive for alternatives such as genomic selection. In order to find candidate biomarkers, gene expression profiles were analysed from tissues of non-castrated pigs grouped by their genetic merit of BT. Differential expression analysis revealed substantial changes with log-transformed fold changes of liver and testis from −3.39 to 2.96 and −7.51 to 3.53, respectively. Co-expression network analysis revealed one module with a correlation of −0.27 in liver and three modules with correlations of 0.31, −0.44 and −0.49 in testis. Differential expression and co-expression analysis revealed candidate biomarkers with varying biological functions: phase I (COQ3, COX6C, CYP2J2, CYP2B6, ACOX2) and phase II metabolism (GSTO1, GSR, FMO3) of skatole and androstenone in liver to steroidgenesis (HSD17B7, HSD17B8, CYP27A1), regulation of steroidgenesis (STARD10, CYB5R3) and GnRH signalling (MAPK3, MAP2K2, MAP3K2) in testis. Overrepresented pathways included “Ribosome”, “Protein export” and “Oxidative phosphorylation” in liver and “Steroid hormone biosynthesis” and “Gap junction” in testis. Future work should evaluate the biomarkers in large populations to ensure their usefulness in genomic selection programs

Interferon regulatory factor 4 sustains CD8+ T cell expansion and effector differentiation

Upon infection, CD8(+) T cells undergo a stepwise process of early activation, expansion, and differentiation into effector cells. How these phases are transcriptionally regulated is incompletely defined. Here, we report that interferon regulatory factor 4 (IRF4), dispensable for early CD8(+) T cell activation, was vital for sustaining the expansion and effector differentiation of CD8(+) T cells. Mechanistically, IRF4 promoted the expression and function of Blimp1 and T-bet, two transcription factors required for CD8(+) T cell effector differentiation, and simultaneously repressed genes that mediate cell cycle arrest and apoptosis. Selective ablation of Irf4 in peripheral CD8(+) T cells impaired antiviral CD8(+) T cell responses, viral clearance, and CD8(+) T cell-mediated host recovery from influenza infection. IRF4 expression was regulated by T cell receptor (TCR) signaling strength via mammalian target of rapamycin (mTOR). Our data reveal that IRF4 translates differential strength of TCR signaling into different quantitative and qualitative CD8(+) T cell respons

Robot Task Commander with Extensible Programming Environment

A system for developing distributed robot application-level software includes a robot having an associated control module which controls motion of the robot in response to a commanded task, and a robot task commander (RTC) in networked communication with the control module over a network transport layer (NTL). The RTC includes a script engine(s) and a GUI, with a processor and a centralized library of library blocks constructed from an interpretive computer programming code and having input and output connections. The GUI provides access to a Visual Programming Language (VPL) environment and a text editor. In executing a method, the VPL is opened, a task for the robot is built from the code library blocks, and data is assigned to input and output connections identifying input and output data for each block. A task sequence(s) is sent to the control module(s) over the NTL to command execution of the task

Interplay between tolerance mechanisms to copper and acid stress in Escherichia coli

Copper (Cu) is a key antibacterial component of the host innate immune system and almost all bacterial species possess systems that defend against the toxic effects of excess Cu. The Cu tolerance system in Gram-negative bacteria is composed minimally of a Cu sensor (CueR) and a Cu export pump (CopA). The cueR and copA genes are encoded on the chromosome typically as a divergent but contiguous operon. In Escherichia coli, cueR and copA are separated by two additional genes, ybaS and ybaT, which confer glutamine (Gln)-dependent acid tolerance and contribute to the glutamate (Glu)-dependent acid resistance system in this organism. Here we show that Cu strongly inhibits growth of a ∆copA mutant strain in acidic cultures. We further demonstrate that Cu stress impairs the pathway for Glu biosynthesis via glutamate synthase, leading to decreased intracellular levels of Glu. Addition of exogenous Glu rescues the ∆copA mutant from Cu stress in acidic conditions. Gln is also protective but this relies on the activities of YbaS and YbaT. Notably, expression of both enzymes is up-regulated during Cu stress. These results demonstrate a link between Cu stress, acid stress, and Glu/Gln metabolism, establish a role for YbaS and YbaT in Cu tolerance, and suggest that subtle changes in core metabolic pathways may contribute to overcoming host-imposed copper toxicity