83 research outputs found
p̲ -reduced Multicomponent KP Hierarchy and Classical W -algebras W(glN,p̲)
For each partition p̲ of an integer N≥ 2 , consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p̲-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction of the generators of the corresponding classical W-algebra W(glN,p̲), and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows
Multiple sums and integrals as neutral BKP tau functions
We consider multiple sums and multi-integrals as tau functions of the BKP
hierarchy using neutral fermions as the simplest tool for deriving these. The
sums are over projective Schur functions for strict partitions
. We consider two types of such sums: weighted sums of over
strict partitions and sums over products . In this
way we obtain discrete analogues of the beta-ensembles ().
Continuous versions are represented as multiple integrals. Such sums and
integrals are of interest in a number of problems in mathematics and physics.Comment: 16 page
Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies
We propose a method for computing any Gelfand-Dickey tau function living in
Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant
associated to a certain class of symbols. Also truncated block Toeplitz
determinants associated to the same symbols are shown to be tau function for
rational reductions of KP. Connection with Riemann-Hilbert problems is
investigated both from the point of view of integrable systems and block
Toeplitz operator theory. Examples of applications to algebro-geometric
solutions are given.Comment: 35 pages. Typos corrected, some changes in the introductio
Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets
We show that the quantum field theoretical formulation of the -function
theory has a geometrical interpretation within the classical transformation
theory of conjugate nets. In particular, we prove that i) the partial charge
transformations preserving the neutral sector are Laplace transformations, ii)
the basic vertex operators are Levy and adjoint Levy transformations and iii)
the diagonal soliton vertex operators generate fundamental transformations. We
also show that the bilinear identity for the multicomponent
Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a
bilinear identity for the multidimensional quadrilateral lattice equations.Comment: 28 pages, 3 Postscript figure
Extremal projectors for contragredient Lie (super)symmetries (short review)
A brief review of the extremal projectors for contragredient Lie
(super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie
superalgebras, infinite-dimensional affine Kac-Moody algebras and
superalgebras, as well as their quantum -analogs) is given. Some
bibliographic comments on the applications of extremal projectors are
presented.Comment: 21 pages, LaTeX; typos corrected, references adde
Metabolic analysis of the interaction between plants and herbivores
Insect herbivores by necessity have to deal with a large arsenal of plant defence metabolites. The levels of defence compounds may be increased by insect damage. These induced plant responses may also affect the metabolism and performance of successive insect herbivores. As the chemical nature of induced responses is largely unknown, global metabolomic analyses are a valuable tool to gain more insight into the metabolites possibly involved in such interactions. This study analyzed the interaction between feral cabbage (Brassica oleracea) and small cabbage white caterpillars (Pieris rapae) and how previous attacks to the plant affect the caterpillar metabolism. Because plants may be induced by shoot and root herbivory, we compared shoot and root induction by treating the plants on either plant part with jasmonic acid. Extracts of the plants and the caterpillars were chemically analysed using Ultra Performance Liquid Chromatography/Time of Flight Mass Spectrometry (UPLCT/MS). The study revealed that the levels of three structurally related coumaroylquinic acids were elevated in plants treated on the shoot. The levels of these compounds in plants and caterpillars were highly correlated: these compounds were defined as the ‘metabolic interface’. The role of these metabolites could only be discovered using simultaneous analysis of the plant and caterpillar metabolomes. We conclude that a metabolomics approach is useful in discovering unexpected bioactive compounds involved in ecological interactions between plants and their herbivores and higher trophic levels.
A new extended q-deformed KP hierarchy
A method is proposed in this paper to construct a new extended q-deformed KP
(-KP) hiearchy and its Lax representation. This new extended -KP
hierarchy contains two types of q-deformed KP equation with self-consistent
sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey
hierarchy with self-consistent sources and the constrained q-deformed KP
hierarchy, which include two types of q-deformed KdV equation with sources and
two types of q-deformed Boussinesq equation with sources. All of these results
reduce to the classical ones when goes to 1. This provides a general way to
construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with
sources and their Lax representations.Comment: 17 pages, no figur
Ionic Motion in Polypyrrole−Cellulose Composites: Trap Release Mechanism during Potentiostatic Reduction
Impact of infection on proteome-wide glycosylation revealed by distinct signatures for bacterial and viral pathogens
Mechanisms of infection and pathogenesis have predominantly been studied based on differential gene or protein expression. Less is known about posttranslational modifications, which are essential for protein functional diversity. We applied an innovative glycoproteomics method to study the systemic proteome-wide glycosylation in response to infection. The protein site-specific glycosylation was characterized in plasma derived from well-defined controls and patients. We found 3862 unique features, of which we identified 463 distinct intact glycopeptides, that could be mapped to more than 30 different proteins. Statistical analyses were used to derive a glycopeptide signature that enabled significant differentiation between patients with a bacterial or viral infection. Furthermore, supported by a machine learning algorithm, we demonstrated the ability to identify the causative pathogens based on the distinctive host blood plasma glycopeptide signatures. These results illustrate that glycoproteomics holds enormous potential as an innovative approach to improve the interpretation of relevant biological changes in response to infection
Genomic investigations of unexplained acute hepatitis in children
Since its first identification in Scotland, over 1,000 cases of unexplained paediatric hepatitis in children have been reported worldwide, including 278 cases in the UK1. Here we report an investigation of 38 cases, 66 age-matched immunocompetent controls and 21 immunocompromised comparator participants, using a combination of genomic, transcriptomic, proteomic and immunohistochemical methods. We detected high levels of adeno-associated virus 2 (AAV2) DNA in the liver, blood, plasma or stool from 27 of 28 cases. We found low levels of adenovirus (HAdV) and human herpesvirus 6B (HHV-6B) in 23 of 31 and 16 of 23, respectively, of the cases tested. By contrast, AAV2 was infrequently detected and at low titre in the blood or the liver from control children with HAdV, even when profoundly immunosuppressed. AAV2, HAdV and HHV-6 phylogeny excluded the emergence of novel strains in cases. Histological analyses of explanted livers showed enrichment for T cells and B lineage cells. Proteomic comparison of liver tissue from cases and healthy controls identified increased expression of HLA class 2, immunoglobulin variable regions and complement proteins. HAdV and AAV2 proteins were not detected in the livers. Instead, we identified AAV2 DNA complexes reflecting both HAdV-mediated and HHV-6B-mediated replication. We hypothesize that high levels of abnormal AAV2 replication products aided by HAdV and, in severe cases, HHV-6B may have triggered immune-mediated hepatic disease in genetically and immunologically predisposed children
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