Quantum immanants, double Young-Capelli bitableaux and Schur shifted symmetric functions

We propose a new method for a unified study of some of the main features of the theory of the center $\boldsymbol{\zeta}(n)$ of the enveloping algebra U(gl(n)) and of the algebra $\Lambda^*(n)$ of shifted symmetric polynomials, that allows the whole theory to be developed, in a transparent and concise way, from the representation-theoretic point of view, that is entirely in the center of U(gl(n)). Our methodological innovation is the systematic use of the superalgebraic method of virtual variables for gl(n), which is, in turn, an extension of Capelli's method of ``variabili ausiliarie''. The passage $n \rightarrow \infty$ for the algebras $\boldsymbol{\zeta}(n)$ and $\Lambda^*(n)$ is here obtained both as direct and inverse limit in the category of filtered algebras. The present approach leads to proofs that are almost direct consequences of the definitions and constructions: they often reduce to a few lines computation

An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

Blind protein structure prediction using accelerated free-energy simulations.

We report a key proof of principle of a new acceleration method [Modeling Employing Limited Data (MELD)] for predicting protein structures by molecular dynamics simulation. It shows that such Boltzmann-satisfying techniques are now sufficiently fast and accurate to predict native protein structures in a limited test within the Critical Assessment of Structure Prediction (CASP) community-wide blind competition

Calcium dynamics and circadian rhythms in suprachiasmatic nucleus neurons

The hypothalamic suprachiasmatic nucleus (SCN) has a pivotal role in the mammalian circadian clock. SCN neurons generate circadian rhythms in action potential firing frequencies and neurotransmitter release, and the core oscillation is thought to be driven by "clock gene" transcription-translation feedback loops. Cytosolic Ca2+ mobilization followed by stimulation of various receptors has been shown to reset the gene transcription cycles in SCN neurons, whereas contribution of steady-state cytosolic Ca2+ levels to the rhythm generation is unclear. Recently, circadian rhythms in cytosolic Ca2+ levels have been demonstrated in cultured SCN neurons. The circadian Ca2+ rhythms are driven by the release of Ca2+ from ryanodine-sensitive internal stores and resistant to the blockade of action potentials. These results raise the possibility that gene translation/transcription loops may interact with autonomous Ca2+ oscillations in the production of circadian rhythms in SCN neurons

Il controllo delle zanzare malarigene dai pipistrellai alle bat-box

The control of the malarial mosquitoes using Bat-Bo

Five-dimensional gauge theories and the local B-model

We propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi–Yau geometries related to the circle compactification of five-dimensional N=1 super Yang–Mills theory with simple gauge group. In the simply laced case, we construct Picard–Fuchs operators from the Dubrovin connection on the Frobenius manifolds associated with the extended affine Weyl groups of type ADE. In general, we propose a purely algebraic construction of Picard–Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg–Witten curve, encompassing non-simply laced cases as well. We offer several precision tests of our proposal for simply laced cases by comparing with the gauge theory prepotentials obtained from the K-theoretic blow-up equations, finding perfect agreement. Whenever there is more than one candidate Seiberg-Witten curve for non-simply laced gauge groups in the literature, we employ our framework to verify which one agrees with the K-theoretic blow-up equations

Crepant resolutions and open strings II

We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of threefold type A-singularities. In this paper we enlarge the body of evidence in favor of our open CRCs, along two different strands. In one direction, we consider non-hard Lefschetz targets and verify the disk CRC for local weighted projective planes. In the other, we complete the proof of the quantized (all-genus) open CRC for hard Lefschetz toric Calabi-Yau three dimensional representations by a detailed study of the G-Hilb resolution of [C3/G] for G=Z2×Z2. Our results have implications for closed-string CRCs of Coates-Iritani-Tseng, Iritani, and Ruan for this class of examples