Local trace formulae and scaling asymptotics in Toeplitz quantization

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szeg\"o kernel along the diagonal

Stage progression and neurological symptoms in Trypanosoma brucei rhodesiense sleeping sickness: role of the CNS inflammatory response

Background: Human African trypanosomiasis progresses from an early (hemolymphatic) stage, through CNS invasion to the late (meningoencephalitic) stage. In experimental infections disease progression is associated with neuroinflammatory responses and neurological symptoms, but this concept requires evaluation in African trypanosomiasis patients, where correct diagnosis of the disease stage is of critical therapeutic importance. Methodology/Principal Findings: This was a retrospective study on a cohort of 115 T.b.rhodesiense HAT patients recruited in Eastern Uganda. Paired plasma and CSF samples allowed the measurement of peripheral and CNS immunoglobulin and of CSF cytokine synthesis. Cytokine and immunoglobulin expression were evaluated in relation to disease duration, stage progression and neurological symptoms. Neurological symptoms were not related to stage progression (with the exception of moderate coma). Increases in CNS immunoglobulin, IL-10 and TNF-α synthesis were associated with stage progression and were mirrored by a reduction in TGF-β levels in the CSF. There were no significant associations between CNS immunoglobulin and cytokine production and neurological signs of disease with the exception of moderate coma cases. Within the study group we identified diagnostically early stage cases with no CSF pleocytosis but intrathecal immunoglobulin synthesis and diagnostically late stage cases with marginal CSF pleocytosis and no detectable trypanosomes in the CSF. Conclusions: Our results demonstrate that there is not a direct linkage between stage progression, neurological signs of infection and neuroinflammatory responses in rhodesiense HAT. Neurological signs are observed in both early and late stages, and while intrathecal immunoglobulin synthesis is associated with neurological signs, these are also observed in cases lacking a CNS inflammatory response. While there is an increase in inflammatory cytokine production with stage progression, this is paralleled by increases in CSF IL-10. As stage diagnostics, the CSF immunoglobulins and cytokines studied do not have sufficient sensitivity to be of clinical value

Central Nervous System Parasitosis and Neuroinflammation Ameliorated by Systemic IL-10 Administration in Trypanosoma brucei-Infected Mice

Peer reviewedPublisher PD

Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

Bundle Theory of Improper Spin Transformations

{\it We first give a geometrical description of the action of the parity operator ($\hat{P}$) on non relativistic spin ${{1}\over{2}}$ Pauli spinors in terms of bundle theory. The relevant bundle, $SU(2)\odot \Z_2\to O(3)$, is a non trivial extension of the universal covering group $SU(2)\to SO(3)$. $\hat{P}$ is the non relativistic limit of the corresponding Dirac matrix operator ${\cal P}=i\gamma_0$ and obeys $\hat{P}^2=-1$. Then, from the direct product of O(3) by $\Z_2$, naturally induced by the structure of the galilean group, we identify, in its double cover, the time reversal operator ($\hat{T}$) acting on spinors, and its product with $\hat{P}$. Both, $\hat{P}$ and $\hat{T}$, generate the group $\Z_4 \times \Z_2$. As in the case of parity, $\hat{T}$ is the non relativistic limit of the corresponding Dirac matrix operator ${\cal T}=\gamma^3 \gamma^1$, and obeys $\hat{T}^2=-1$.}Comment: 8 pages, Plaintex; titled changed, minor text modifications, one reference complete

Creativity in savant artists with autism

Background: Individuals with autism spectrum disorder (ASD) often display impairments in creativity, yet savant artists with ASD can produce highly novel and original artistic outputs. To date, there have been no systematic attempts to explore creativity in savant artists with ASD. Methods: Nine savant artists with ASD were compared with nine talented artists, nine non-artistically talented individuals with ASD, and nine individuals with moderate learning difficulties (MLD), on tasks in and out of their domain of expertise. This was to ascertain whether the performance of the savant artists was related to their artistic ability, their diagnosis of ASD or their level of intellectual functioning. Results: On a drawing task (the Torrance Test of Creative Thinking; Torrance, 1974), the responses of the art students were more creative (scoring higher on measures of fluency, originality, elaboration and flexibility) than the savant, ASD and MLD groups. However, the savants did produce more elaborative responses than the ASD and MLD groups. On a non-drawing construction task (figural synthesis; Finke & Slayton, 1988), the savants produced more original outputs than the ASD and MLD groups (scoring similarly to the art students). No group differences were found regarding fluency on this task. Conclusions: On standardised creativity tasks, savant artists with ASD display high levels of elaboration (on drawing tasks) and originality (on non-drawing construction tasks), relative to groups with ASD or MLD. High elaboration and originality may result from a local processing bias, coupled with artistic talent, in this group

Predicting gene essentiality in Caenorhabditis elegans by feature engineering and machine-learning

Defining genes that are essential for life has major implications for understanding critical biological processes and mechanisms. Although essential genes have been identified and characterised experimentally using functional genomic tools, it is challenging to predict with confidence such genes from molecular and phenomic data sets using computational methods. Using extensive data sets available for the model organism Caenorhabditis elegans, we constructed here a machine-learning (ML)-based workflow for the prediction of essential genes on a genome-wide scale. We identified strong predictors for such genes and showed that trained ML models consistently achieve highly-accurate classifications. Complementary analyses revealed an association between essential genes and chromosomal location. Our findings reveal that essential genes in C. elegans tend to be located in or near the centre of autosomal chromosomes; are positively correlated with low single nucleotide polymorphim (SNP) densities and epigenetic markers in promoter regions; are involved in protein and nucleotide processing; are transcribed in most cells; are enriched in reproductive tissues or are targets for small RNAs bound to the argonaut CSR-1. Based on these results, we hypothesise an interplay between epigenetic markers and small RNA pathways in the germline, with transcription-based memory; this hypothesis warrants testing. From a technical perspective, further work is needed to evaluate whether the present ML-based approach will be applicable to other metazoans (including Drosophila melanogaster) for which comprehensive data set (i.e. genomic, transcriptomic, proteomic, variomic, epigenetic and phenomic) are available