Recursion relations for Double Ramification Hierarchies

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in [Bur15] using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the Hamiltonians, the one associated to the first descendant of the unit of a cohomological field theory. Moreover, we introduce analogues of the topological recursion relations and the divisor equation both for the hamiltonian densities and for the string solution of the double ramification hierarchy. This machinery is very efficient and we apply it to various computations for the trivial and Hodge cohomological field theories, and for the $r$-spin Witten's classes. Moreover we prove the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for the Gromov-Witten theory of the complex projective line (extended Toda hierarchy).Comment: Revised version, to be published in Communications in Mathematical Physics, 27 page

Mean-field expansion for spin models with medium-range interactions

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as $R^{-3}, R$ being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.Comment: 49 pages, 8 figure

Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity. We choose radiative boundary conditions at the vertical boundaries in which the heat flux is propor- tional to the fourth power of the temperature. We compare the results with the corresponding cases in which fixed temperature boundary conditions are applied. The most notable result is that the formation of a fully convective state in which the density is nearly constant as a function of height and the heat is transported to the upper and lower boundaries by overturning motions is robust and persists even in cases with radiative boundary conditions. Interestingly, in the convective regime, although the diffusive transport is negligible the mean stratification does not relax to an adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter

Deformed W_N algebras from elliptic sl(N) algebras

We extend to the sl(N) case the results that we previously obtained on the construction of W_{q,p} algebras from the elliptic algebra A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining q-deformations of the W_N algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N algebras depending on the parity of h, characterizing the exchange structures at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page

Universal construction of W_{p,q} algebras

We present a direct construction of abstract generators for q-deformed W_N algebras. This procedure hinges upon a twisted trace formula for the elliptic algebra A_{q,p}(sl(N)_c) generalizing the previously known formulae for quantum groups.Comment: packages amsfonts, amssym

Optimal Diversity in Investments with Recombinant Innovation

The notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation is addressed. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next diversity is optimized by trading off the benefits of recombinant innovation and returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. Threshold values of returns to scale and recombination probability define regions where either specialization or diversity is the best choice. In the time domain, when the investment time horizon is beyond a threshold value, a diversified investment becomes the best choice. This threshold will be larger the higher the returns to scale.

Technical quality assessment of an optoelectronic system for movement analysis

The Optoelectronic Systems (OS) are largely used in gait analysis to evaluate the motor performances of healthy subjects and patients. The accuracy of marker trajectories reconstruction depends on several aspects: the number of cameras, the dimension and position of the calibration volume, and the chosen calibration procedure. In this paper we propose a methodology to evaluate the eects of the mentioned sources of error on the reconstruction of marker trajectories. The novel contribution of the present work consists in the dimension of the tested calibration volumes, which is comparable with the ones normally used in gait analysis; in addition, to simulate trajectories during clinical gait analysis, we provide non-default paths for markers as inputs. Several calibration procedures are implemented and the same trial is processed with each calibration le, also considering dierent cameras congurations. The RMSEs between the measured trajectories and the optimal ones are calculated for each comparison. To investigate the signicant dierences between the computed indices, an ANOVA analysis is implemented. The RMSE is sensible to the variations of the considered calibration volume and the camera congurations and it is always inferior to 43 mm

Extension of the C star rotation curve of the Milky Way to 24 kpc

Demers and Battinelli published, in 2007 the rotation curve of the Milky Way based on the radial velocity of carbon stars outside the Solar circle. Since then we have established a new list of candidates for spectroscopy. The goal of this paper is to determine the rotation curve of the galaxy, as far as possible from the galactic center, using N type carbon stars. The stars were selected from their dereddened 2MASS colours, then the spectra were obtained with the Dominion Astrophysical Observatory and Asiago 1.8 meter telescopes. This publication adds radial velocities and Galactrocentric distances of 36 carbon stars, from which 20 are new confirmed. The new results for stars up to 25 kpc from the galactic center, suggest that the rotation curve shows a slight decline beyond the Solar circle.Comment: 13 pages, 3 figures, 1 table; accepted for publication in Astrophysic