Kato square root problem with unbounded leading coefficients

We prove the Kato conjecture for elliptic operators, $L=-\nabla\cdot\left((\mathbf A+\mathbf D)\nabla\ \right)$, with $\mathbf A$ a complex measurable bounded coercive matrix and $\mathbf D$ a measurable real-valued skew-symmetric matrix in $\mathbb{R}^n$ with entries in $BMO(\mathbb{R}^n)$;\, i.e., the domain of $\sqrt{L}\,$ is the Sobolev space $\dot H^1(\mathbb{R}^n)$ in any dimension, with the estimate $\|\sqrt{L}\, f\|_2\lesssim \| \nabla f\|_2$

Characterization of the prohormone complement in cattle using genomic libraries and cleavage prediction approaches

<p>Abstract</p> <p>Background</p> <p>Neuropeptides are cell to cell signalling molecules that regulate many critical biological processes including development, growth and reproduction. These peptides result from the complex processing of prohormone proteins, making their characterization both challenging and resource demanding. In fact, only 42 neuropeptide genes have been empirically confirmed in cattle. Neuropeptide research using high-throughput technologies such as microarray and mass spectrometry require accurate annotation of prohormone genes and products. However, the annotation and associated prediction efforts, when based solely on sequence homology to species with known neuropeptides, can be problematic.</p> <p>Results</p> <p>Complementary bioinformatic resources were integrated in the first survey of the cattle neuropeptide complement. Functional neuropeptide characterization was based on gene expression profiles from microarray experiments. Once a gene is identified, knowledge of the enzymatic processing allows determination of the final products. Prohormone cleavage sites were predicted using several complementary cleavage prediction models and validated against known cleavage sites in cattle and other species. Our bioinformatics approach identified 92 cattle prohormone genes, with 84 of these supported by expressed sequence tags. Notable findings included an absence of evidence for a cattle relaxin 1 gene and evidence for a cattle galanin-like peptide pseudogene. The prohormone processing predictions are likely accurate as the mammalian proprotein convertase enzymes, except for proprotein convertase subtilisin/kexin type 9, were also identified. Microarray analysis revealed the differential expression of 21 prohormone genes in the liver associated with nutritional status and 8 prohormone genes in the placentome of embryos generated using different reproductive techniques. The neuropeptide cleavage prediction models had an exceptional performance, correctly predicting cleavage in more than 86% of the prohormone sequence positions.</p> <p>Conclusion</p> <p>A substantial increase in the number of cattle prohormone genes identified and insights into the expression profiles of neuropeptide genes were obtained from the integration of bioinformatics tools and database resources and gene expression information. Approximately 20 prohormones with no empirical evidence were detected and the prohormone cleavage sites were predicted with high accuracy. Most prohormones were supported by expressed sequence tag data and many were differentially expressed across nutritional and reproductive conditions. The complete set of cattle prohormone sequences identified and the cleavage prediction approaches are available at <url>http://neuroproteomics.scs.uiuc.edu/neuropred.html</url>.</p

Cerebellum Transcriptome of Mice Bred for High Voluntary Activity Offers Insights into Locomotor Control and Reward-Dependent Behaviors.

The role of the cerebellum in motivation and addictive behaviors is less understood than that in control and coordination of movements. High running can be a self-rewarding behavior exhibiting addictive properties. Changes in the cerebellum transcriptional networks of mice from a line selectively bred for High voluntary running (H) were profiled relative to an unselected Control (C) line. The environmental modulation of these changes was assessed both in activity environments corresponding to 7 days of Free (F) access to running wheel and to Blocked (B) access on day 7. Overall, 457 genes exhibited a significant (FDR-adjusted P-value &lt; 0.05) genotype-by-environment interaction effect, indicating that activity genotype differences in gene expression depend on environmental access to running. Among these genes, network analysis highlighted 6 genes (Nrgn, Drd2, Rxrg, Gda, Adora2a, and Rab40b) connected by their products that displayed opposite expression patterns in the activity genotype contrast within the B and F environments. The comparison of network expression topologies suggests that selection for high voluntary running is linked to a predominant dysregulation of hub genes in the F environment that enables running whereas a dysregulation of ancillary genes is favored in the B environment that blocks running. Genes associated with locomotor regulation, signaling pathways, reward-processing, goal-focused, and reward-dependent behaviors exhibited significant genotype-by-environment interaction (e.g. Pak6, Adora2a, Drd2, and Arhgap8). Neuropeptide genes including Adcyap1, Cck, Sst, Vgf, Npy, Nts, Penk, and Tac2 and related receptor genes also exhibited significant genotype-by-environment interaction. The majority of the 183 differentially expressed genes between activity genotypes (e.g. Drd1) were under-expressed in C relative to H genotypes and were also under-expressed in B relative to F environments. Our findings indicate that the high voluntary running mouse line studied is a helpful model for understanding the molecular mechanisms in the cerebellum that influence locomotor control and reward-dependent behaviors

Meta-analysis of genome-wide expression patterns associated with behavioral maturation in honey bees

<p>Abstract</p> <p>Background</p> <p>The information from multiple microarray experiments can be integrated in an objective manner <it>via </it>meta-analysis. However, multiple meta-analysis approaches are available and their relative strengths have not been directly compared using experimental data in the context of different gene expression scenarios and studies with different degrees of relationship. This study investigates the complementary advantages of meta-analysis approaches to integrate information across studies, and further mine the transcriptome for genes that are associated with complex processes such as behavioral maturation in honey bees. Behavioral maturation and division of labor in honey bees are related to changes in the expression of hundreds of genes in the brain. The information from various microarray studies comparing the expression of genes at different maturation stages in honey bee brains was integrated using complementary meta-analysis approaches.</p> <p>Results</p> <p>Comparison of lists of genes with significant differential expression across studies failed to identify genes with consistent patterns of expression that were below the selected significance threshold, or identified genes with significant yet inconsistent patterns. The meta-analytical framework supported the identification of genes with consistent overall expression patterns and eliminated genes that exhibited contradictory expression patterns across studies. Sample-level meta-analysis of normalized gene-expression can detect more differentially expressed genes than the study-level meta-analysis of estimates for genes that were well described by similar model parameter estimates across studies and had small variation across studies. Furthermore, study-level meta-analysis was well suited for genes that exhibit consistent patterns across studies, genes that had substantial variation across studies, and genes that did not conform to the assumptions of the sample-level meta-analysis. Meta-analyses confirmed previously reported genes and helped identify genes (e.g. <it>Tomosyn</it>, <it>Chitinase 5, Adar, Innexin 2, Transferrin 1</it>, <it>Sick</it>, <it>Oatp26F</it>) and Gene Ontology categories (e.g. purine nucleotide binding) not previously associated with maturation in honey bees.</p> <p>Conclusion</p> <p>This study demonstrated that a combination of meta-analytical approaches best addresses the highly dimensional nature of genome-wide microarray studies. As expected, the integration of gene expression information from microarray studies using meta-analysis enhanced the characterization of the transcriptome of complex biological processes.</p

Semiparametric approach to characterize unique gene expression trajectories across time

BACKGROUND: A semiparametric approach was used to identify groups of cDNAs and genes with distinct expression profiles across time and overcome the limitations of clustering to identify groups. The semiparametric approach allows the generalization of mixtures of distributions while making no specific parametric assumptions about the distribution of the hidden heterogeneity of the cDNAs. The semiparametric approach was applied to study gene expression in the brains of Apis mellifera ligustica honey bees raised in two colonies (A. m. mellifera and ligustica) with consistent patterns across five maturation ages. RESULTS: The semiparametric approach provided unambiguous criteria to detect groups of genes, trajectories and probability of gene membership to groups. The semiparametric results were cross-validated in both colony data sets. Gene Ontology analysis enhanced by genome annotation helped to confirm the semiparametric results and revealed that most genes with similar or related neurobiological function were assigned to the same group or groups with similar trajectories. Ten groups of genes were identified and nine groups had highly similar trajectories in both data sets. Differences in the trajectory of the reminder group were consistent with reports of accelerated maturation in ligustica colonies compared to mellifera colonies. CONCLUSION: The combination of microarray technology, genomic information and semiparametric analysis provided insights into the genomic plasticity and gene networks linked to behavioral maturation in the honey bee

NeuroPred: a tool to predict cleavage sites in neuropeptide precursors and provide the masses of the resulting peptides

NeuroPred is a web application designed to predict cleavage sites at basic amino acid locations in neuropeptide precursor sequences. The user can study one amino acid sequence or multiple sequences simultaneously, selecting from several prediction models and optional, user-defined functions. Logistic regression models are trained on experimentally verified or published cleavage data from mollusks, mammals and insects, and amino acid motifs reported to be associated with cleavage. Confidence interval limits of the probabilities of cleavage indicate the precision of the predictions; these predictions are transformed into cleavage or non-cleavage events according to user-defined thresholds. In addition to the precursor sequence, NeuroPred accepts user-specified cleavage information, providing model accuracy statistics based on observed and predicted cleavages. Neuropred also computes the mass of the predicted peptides, including user-selectable post-translational modifications. The resulting mass list aids the discovery and confirmation of new neuropeptides using mass spectrometry techniques. The NeuroPred application, manual, reference manuscripts and training sequences are available at

The Evolution of Contractual Terms in Sovereign Bonds

In reaction to defaults on sovereign debt contracts, issuers and creditors have strengthened the terms in sovereign debt contracts that enable creditors to enforce their debts judicially and that enable sovereigns to restructure their debts. These apparently contradictory approaches reflect attempts to solve an incomplete contracting problem in which debtors need to be forced to repay debts in good states of the world; debtors need to be granted partial relief from debt payments in bad states; debtors may attempt to exploit divisions among creditors in order to opportunistically reduce their debt burden; debtors may engage in excessively risky activities using creditors\u27 money; and debtors and creditors may attempt to externalize costs on the taxpayers of other coun­tries. We support this argument with a statistical study of the development of sovereign bond terms from 1960 to the present

Voluntary Wheel Running Reverses Age-Induced Changes in Hippocampal Gene Expression

Normal aging alters expression of numerous genes within the brain. Some of these transcription changes likely contribute to age-associated cognitive decline, reduced neural plasticity, and the higher incidence of neuropathology. Identifying factors that modulate brain aging is crucial for improving quality of life. One promising intervention to counteract negative effects of aging is aerobic exercise. Aged subjects that exercise show enhanced cognitive performance and increased hippocampal neurogenesis and synaptic plasticity. Currently, the mechanisms behind the anti-aging effects of exercise are not understood. The present study conducted a microarray on whole hippocampal samples from adult (3.5-month-old) and aged (18-month-old) male BALB/c mice that were individually housed with or without running wheels for 8 weeks. Results showed that aging altered genes related to chromatin remodeling, cell growth, immune activity, and synapse organization compared to adult mice. Exercise was found to modulate many of the genes altered by aging, but in the opposite direction. For example, wheel running increased expression of genes related to cell growth and attenuated expression of genes involved in immune function and chromatin remodeling. Collectively, findings show that even late-onset exercise may attenuate age-related changes in gene expression and identifies possible pathways through which exercise may exert its beneficial effects

Gene Network Dysregulation in the Trigeminal Ganglia and Nucleus Accumbens of a Model of Chronic Migraine-Associated Hyperalgesia

The pharmacological agent nitroglycerin (NTG) elicits hyperalgesia and allodynia in mice. This model has been used to study the neurological disorder of trigeminovascular pain or migraine, a debilitating form of hyperalgesia. The present study validates hyperalgesia in an established mouse model of chronic migraine triggered by NTG and advances the understanding of the associated molecular mechanisms. The RNA-seq profiles of two nervous system regions associated with pain, the trigeminal ganglia (TG) and the nucleus accumbens (NAc), were compared in mice receiving chronic NTG treatment relative to control (CON) mice. Among the 109 genes that exhibited an NTG treatment-by-region interaction, solute carrier family 32 (GABA vesicular transporter) member 1 (Slc32a1) and preproenkephalin (Penk) exhibited reversal of expression patterns between the NTG and CON groups. Erb-b2 receptor tyrosine kinase 4 (Erbb4) and solute carrier family 1 (glial high affinity glutamate transporter) member 2 (Slc1a2) exhibited consistent differential expression between treatments across regions albeit at different magnitude. Period circadian clock 1 (Per1) was among the 165 genes that exhibited significant NTG treatment effect. Biological processes disrupted by NTG in a region-specific manner included adaptive and innate immune responses; whereas glutamatergic and dopaminergic synapses and rhythmic process were disrupted in both regions. Regulatory network reconstruction highlighted the widespread role of several transcription factors (including Snrnp70, Smad1, Pax6, Cebpa, and Smpx) among the NTG-disrupted target genes. These results advance the understanding of the molecular mechanisms of hyperalgesia that can be applied to therapies to ameliorate chronic pain and migraine