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 $n$-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 $m$-vector $k$-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 $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. In this way we obtain discrete analogues of the beta-ensembles ($\beta=1,2,4$). 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 $\tau$-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