Operator interpretation of resonances generated by some operator matrices

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.Comment: LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, August 18-22, 199

Semiseparable integral operators and explicit solution of an inverse problem for the skew-self-adjoint Dirac-type system

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form $\phi(\lambda)\exp\{-2i\lambda D\}$, where $\phi$ is a strictly proper rational matrix function and $D=D^* \geq 0$ is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case

Increased CCL2, CCL3, CCL5, and IL-1β cytokine concentration in piriform cortex, hippocampus, and neocortex after pilocarpine-induced seizures

BACKGROUND: Cytokines and chemokines play an important role in the neuroinflammatory response to an initial precipitating injury such as status epilepticus (SE). These signaling molecules participate in recruitment of immune cells, including brain macrophages (microglia), as well as neuroplastic changes, deterioration of damaged tissue, and epileptogenesis. This study describes the temporal and brain region pattern expression of numerous cytokines, including chemokines, after pilocarpine-induced seizures and discusses them in the larger context of their potential involvement in the changes that precede the development of epilepsy. FINDINGS: Adult rats received pilocarpine to induce SE and 90 min after seizure onset were treated with diazepam to mitigate seizures. Rats were subsequently deeply anesthetized and brain regions (hippocampus, piriform cortex, neocortex, and cerebellum) were freshly dissected at 2, 6, and 24 h or 5 days after seizures. Using methodology identical to our previous studies, simultaneous assay of multiple cytokines (CCL2, CCL3, CCL5, interleukin IL-1β, tumor necrosis factor (TNF-α)), and vascular endothelial growth factor (VEGF) was performed and compared to control rats. These proteins were selected based on existing evidence implicating them in the epileptogenic progression. A robust increase in CCL2 and CCL3 concentrations in the hippocampus, piriform cortex, and neocortex was observed at all time-points. The concentrations peaked with a ~200-fold increase 24 h after seizures and were two orders of magnitude greater than the significant increases observed for CCL5 and IL-1β in the same brain structures. TNF-α levels were altered in the piriform cortex and neocortex (24 h) and in the hippocampus (5 days) after SE. CONCLUSIONS: Pilocarpine-induced status epilepticus causes a rapid increase of multiple cytokines in limbic and neocortical regions. Understanding the precise spatial and temporal pattern of cytokines and chemokine changes could provide more viable therapeutic targets to reduce, reverse, or prevent the development of epilepsy following a precipitating injury

Transcriptome Analysis of the Hippocampal CA1 Pyramidal Cell Region after Kainic Acid-Induced Status Epilepticus in Juvenile Rats

Molecular mechanisms involved in epileptogenesis in the developing brain remain poorly understood. The gene array approach could reveal some of the factors involved by allowing the identification of a broad scale of genes altered by seizures. In this study we used microarray analysis to reveal the gene expression profile of the laser microdissected hippocampal CA1 subregion one week after kainic acid (KA)-induced status epilepticus (SE) in 21-day-old rats, which are developmentally roughly comparable to juvenile children. The gene expression analysis with the Chipster software generated a total of 1592 differently expressed genes in the CA1 subregion of KA-treated rats compared to control rats. The KEGG database revealed that the identified genes were involved in pathways such as oxidative phosporylation (26 genes changed), and long-term potentiation (LTP; 18 genes changed). Also genes involved in Ca2+ homeostasis, gliosis, inflammation, and GABAergic transmission were altered. To validate the microarray results we further examined the protein expression for a subset of selected genes, glial fibrillary protein (GFAP), apolipoprotein E (apo E), cannabinoid type 1 receptor (CB1), Purkinje cell protein 4 (PEP-19), and interleukin 8 receptor (CXCR1), with immunohistochemistry, which confirmed the transcriptome results. Our results showed that SE resulted in no obvious CA1 neuronal loss, and alterations in the expression pattern of several genes during the early epileptogenic phase were comparable to previous gene expression studies of the adult hippocampus of both experimental epileptic animals and patients with temporal lobe epilepsy (TLE). However, some changes seem to occur after SE specifically in the juvenile rat hippocampus. Insight of the SE-induced alterations in gene expression and their related pathways could give us hints for the development of new target-specific antiepileptic drugs that interfere with the progression of the disease in the juvenile age group

What’s new with numbers? Sociological approaches to the study of quantification

Calculation and quantification have been critical features of modern societies, closely linked to science, markets, and administration. In the past thirty years, the pace, purpose, and scope of quantification have greatly expanded, and there has been a corresponding increase in scholarship on quantification. We offer an assessment of the widely dispersed literature on quantification across four domains where quantification and quantification scholarship have particularly flourished: administration, democratic rule, economics, and personal life. In doing so, we seek to stimulate more cross-disciplinary debate and exchange. We caution against unifying accounts of quantification and highlight the importance of tracking quantification across different sites in order to appreciate its essential ambiguity and conduct more systematic investigations of interactions between different quantification regimes

Lack of Galanin 3 Receptor Aggravates Murine Autoimmune Arthritis

Neurogenic inflammation mediated by peptidergic sensory nerves has a crucial impact on the pathogenesis of various joint diseases. Galanin is a regulatory sensory neuropeptide, which has been shown to attenuate neurogenic inflammation, modulate neutrophil activation, and be involved in the development of adjuvant arthritis, but our current understanding about its targets and physiological importance is incomplete. Among the receptors of galanin (GAL1-3), GAL3 has been found to be the most abundantly expressed in the vasculature and on the surface of some immune cells. However, since there are minimal in vivo data on the role of GAL3 in joint diseases, we analyzed its involvement in different inflammatory mechanisms of the K/BxN serum transfer-model of autoimmune arthritis employing GAL 3 gene-deficient mice. After arthritis induction, GAL3 knockouts demonstrated increased clinical disease severity and earlier hindlimb edema than wild types. Vascular hyperpermeability determined by in vivo fluorescence imaging was also elevated compared to the wild-type controls. However, neutrophil accumulation detected by in vivo luminescence imaging or arthritic mechanical hyperalgesia was not altered by the lack of the GAL3 receptor. Our findings suggest that GAL3 has anti-inflammatory properties in joints by inhibiting vascular hyperpermeability and consequent edema formation