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 $\|\sqrt{L}\, f\|_2\lesssim \| \nabla f\|_2$

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 < 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

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

Striatal transcriptome of a mouse model of ADHD reveals a pattern of synaptic remodeling

Despite the prevalence and high heritability of Attention-Deficit/Hyperactivity Disorder (ADHD), genetic etiology remains elusive. Clinical evidence points in part to reduced function of the striatum, but which specific genes are differentially expressed and how they sculpt striatal physiology to predispose ADHD are not well understood. As an exploratory tool, a polygenic mouse model of ADHD was recently developed through selective breeding for high home cage activity. Relative to the Control line, the High-Active line displays hyperactivity and motor impulsivity which are ameliorated with amphetamine. This study compared gene expression in the striatum between Control and High-Active mice to develop a coherent hypothesis for how genes might affect striatal physiology and predispose ADHD-like symptoms. To this end, striatal transcriptomes of High-Active and Control mice were analyzed after mice were treated with saline or amphetamines. The pseudogene Gm6180 for n-cofilin (Cfl1) displayed 20-fold higher expression in High-Active mice corresponding with reduced Cfl1 expression suggesting synaptic actin dysregulation. Latrophilin 3 (Lphn3), which is associated with ADHD in human populations and is involved in synapse structure, and its ligand fibronectin leucine rich transmembrane protein 3 (Flrt3), were downregulated in High-Active mice. Multiple genes were altered in High-Active mice in a manner predicted to downregulate the canonical Wnt pathway. A smaller and different set of genes including glyoxalase (Glo1) were differentially regulated in High-Active as compared to Control in response to amphetamine. Together, results suggest genes involved in excitatory synapse regulation and maintenance are downregulated in ADHD-like mice. Consistent with the molecular prediction, stereological analysis of the striatum from a separate set of mice processed for imunohistochemical detection of synaptophysin revealed approximately a 46% reduction in synaptophysin immunoreactivity in High-Active relative to Control. Results provide a new set of molecular targets related to synapse maintenance for the next generation of ADHD medicines

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

The Songbird Neurogenomics (SoNG) Initiative: Community-based tools and strategies for study of brain gene function and evolution

BACKGROUND: Songbirds hold great promise for biomedical, environmental and evolutionary research. A complete draft sequence of the zebra finch genome is imminent, yet a need remains for application of genomic resources within a research community traditionally focused on ethology and neurobiological methods. In response, we developed a core set of genomic tools and a novel collaborative strategy to probe gene expression in diverse songbird species and natural contexts. RESULTS: We end-sequenced cDNAs from zebra finch brain and incorporated additional sequences from community sources into a database of 86,784 high quality reads. These assembled into 31,658 non-redundant contigs and singletons, which we annotated via BLAST search of chicken and human databases. The results are publicly available in the ESTIMA:Songbird database. We produced a spotted cDNA microarray with 20,160 addresses representing 17,214 non-redundant products of an estimated 11,500–15,000 genes, validating it by analysis of immediate-early gene (zenk) gene activation following song exposure and by demonstrating effective cross hybridization to genomic DNAs of other songbird species in the Passerida Parvorder. Our assembly was also used in the design of the "Lund-zfa" Affymetrix array representing ~22,000 non-redundant sequences. When the two arrays were hybridized to cDNAs from the same set of male and female zebra finch brain samples, both arrays detected a common set of regulated transcripts with a Pearson correlation coefficient of 0.895. To stimulate use of these resources by the songbird research community and to maintain consistent technical standards, we devised a "Community Collaboration" mechanism whereby individual birdsong researchers develop experiments and provide tissues, but a single individual in the community is responsible for all RNA extractions, labelling and microarray hybridizations. CONCLUSION: Immediately, these results set the foundation for a coordinated set of 25 planned experiments by 16 research groups probing fundamental links between genome, brain, evolution and behavior in songbirds. Energetic application of genomic resources to research using songbirds should help illuminate how complex neural and behavioral traits emerge and evolve

Highlights from the Pierre Auger Observatory

The Pierre Auger Observatory is the world's largest cosmic ray observatory. Our current exposure reaches nearly 40,000 km$^2$ str and provides us with an unprecedented quality data set. The performance and stability of the detectors and their enhancements are described. Data analyses have led to a number of major breakthroughs. Among these we discuss the energy spectrum and the searches for large-scale anisotropies. We present analyses of our X$_{max}$ data and show how it can be interpreted in terms of mass composition. We also describe some new analyses that extract mass sensitive parameters from the 100% duty cycle SD data. A coherent interpretation of all these recent results opens new directions. The consequences regarding the cosmic ray composition and the properties of UHECR sources are briefly discussed.Comment: 9 pages, 12 figures, talk given at the 33rd International Cosmic Ray Conference, Rio de Janeiro 201

Ultrahigh-energy neutrino follow-up of Gravitational Wave events GW150914 and GW151226 with the Pierre Auger Observatory

On September 14, 2015 the Advanced LIGO detectors observed their first gravitational-wave (GW) transient GW150914. This was followed by a second GW event observed on December 26, 2015. Both events were inferred to have arisen from the merger of black holes in binary systems. Such a system may emit neutrinos if there are magnetic fields and disk debris remaining from the formation of the two black holes. With the surface detector array of the Pierre Auger Observatory we can search for neutrinos with energy above 100 PeV from point-like sources across the sky with equatorial declination from about -65 deg. to +60 deg., and in particular from a fraction of the 90% confidence-level (CL) inferred positions in the sky of GW150914 and GW151226. A targeted search for highly-inclined extensive air showers, produced either by interactions of downward-going neutrinos of all flavors in the atmosphere or by the decays of tau leptons originating from tau-neutrino interactions in the Earth's crust (Earth-skimming neutrinos), yielded no candidates in the Auger data collected within $\pm 500$ s around or 1 day after the coordinated universal time (UTC) of GW150914 and GW151226, as well as in the same search periods relative to the UTC time of the GW candidate event LVT151012. From the non-observation we constrain the amount of energy radiated in ultrahigh-energy neutrinos from such remarkable events.Comment: Published version. Added journal reference and DOI. Added Report Numbe