73 research outputs found
The construction of Frobenius manifolds from KP tau-functions
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates
are determined by the system of Darboux-Egoroff equations. This system of
partial differential equations appears as a specific subset of the
-component KP hierarchy. KP representation theory and the related Sato
infinite Grassmannian are used to construct solutions of this Darboux-Egoroff
system and the related Frobenius manifolds. Finally we show that for these
solutions Dubrovin's isomonodromy tau-function can be expressed in the KP
tau-function.Comment: 29 pages, latex2e, no figure
Geometric B\"acklund--Darboux transformations for the KP hierarchy
We shown that, if you have two planes in the Segal-Wilson Grassmannian that
have an intersection of finite codimension, then the corresponding solutions of
the KP hierarchy are linked by B\"acklund-Darboux transformations (BDT). The
pseudodifferential operator that performs this transformation is shown to be
built up in a geometric way from elementary BDT's and is given here in a closed
form. The geometric description of elementary DBT's requires that one has a
geometric interpretation of the dual wavefunctions involved. This is done here
with the help of a suitable algebraic characterization of the wavefunction. The
BDT's also induce transformations of the tau-function associated to a plane in
the Grassmannian. For the Gelfand-Dickey hierarchies we derive a geometric
characterization of the BDT'ss that preserves these subsystems of the KP
hierarchy. This generalizes the classical Darboux-transformations. we also
determine an explicit expression for the squared eigenfunction potentials. Next
a connection is laid between the KP hierarchy and the 1-Toda lattice hierarchy.
It is shown that infinite flags in the Grassmannian yield solutions of the
latter hierarchy. these flags can be constructed by means of BDT's, starting
from some plane. Other applications of these BDT's are a geometric way to
characterize Wronskian solutions of the -vector -constrained KP hierarchy
and the construction of a vast collection of orthogonal polynomials, playing a
role in matrix models.Comment: 44 pages Latex2
WDVV Equations, Darboux-Egoroff Metric and the Dressing Method
Dressing technique is used to construct commuting Lax operators which provide
an integrable (canonical) structure behind
Witten--Dijkgraaf--Verlinde--Verlinde equations. The commuting flows are
related to the isomonodromic flows. Examples of the canonical integrable
structure are given in two- and three-dimensional cases. The three-dimensional
example is associated with the rational Landau-Ginzburg potentials.Comment: Contribution to the conference "Workshop on Integrable Theories,
Solitons and Duality", Unesp2002, LaTeX file w. JHEP style fil
Irreducible Highest Weight Representations Of The Simple n-Lie Algebra
A. Dzhumadil'daev classified all irreducible finite dimensional
representations of the simple n-Lie algebra. Using a slightly different
approach, we obtain in this paper a complete classification of all irreducible,
highest weight modules, including the infinite-dimensional ones. As a corollary
we find all primitive ideals of the universal enveloping algebra of this simple
n-Lie algebra.Comment: 24 pages, 24 figures, mistake in proposition 2.1 correcte
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
Integrated management of atrial fibrillation in primary care:results of the ALL-IN cluster randomized trial
Aims To evaluate whether integrated care for atrial. fibrillation (AF) can be safely orchestrated in primary care. Methods and results The ALL-IN trial was a cluster randomized, open-label, pragmatic non-inferiority trial performed in primary care practices in the Netherlands. We randomized 26 practices: 15 to the integrated care intervention and 11 to usual care. The integrated care intervention consisted of (i) quarterly AF check-ups by trained nurses in primary care, also focusing on possibly interfering comorbidities, (ii) monitoring of anticoagulation therapy in primary care, and finally (iii) easy-access availability of consultations from cardiologists and anticoagulation clinics. The primary endpoint was all-cause mortality during 2 years of follow-up. In the intervention arm, 527 out of 941 eligible AF patients aged >65 years provided informed consent to undergo the intervention. These 527 patients were compared with 713 AF patients in the control arm receiving usual care. Median age was 77 (interquartile range 72-83) years. The all-cause mortality rate was 3.5 per 100 patient-years in the intervention arm vs. 6.7 per 100 patient-years in the control arm [adjusted hazard ratio (HR) 0.55; 95% confidence interval (CI) 0.37-0.82]. For non cardiovascular mortality, the adjusted HR was 0.47 (95% CI 0.27-0.82). For other adverse events, no statistically significant differences were observed. Conclusion In this cluster randomized trial, integrated care for elderly AF patients in primary care showed a 45% reduction in all-cause mortality when compared with usual care
Variational Lie algebroids and homological evolutionary vector fields
We define Lie algebroids over infinite jet spaces and establish their
equivalent representation through homological evolutionary vector fields.Comment: Int. Workshop "Nonlinear Physics: Theory and Experiment VI"
(Gallipoli, Italy; June-July 2010). Published v3 = v2 minus typos, to appear
in: Theoret. and Mathem. Phys. (2011) Vol.167:3 (168:1), 18 page
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.
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
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