Canonical solution of a system of long-range interacting rotators on a lattice

The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees' Comments it has been transferred to Phys. Rev. E, because of supposed no general interest. Divided into sections, corrections in (5) and (20), reference 5 updated. 8 pages 1 figur

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pres

Invariant measures of the 2D Euler and Vlasov equations

We discuss invariant measures of partial differential equations such as the 2D Euler or Vlasov equations. For the 2D Euler equations, starting from the Liouville theorem, valid for N-dimensional approximations of the dynamics, we define the microcanonical measure as a limit measure where N goes to infinity. When only the energy and enstrophy invariants are taken into account, we give an explicit computation to prove the following result: the microcanonical measure is actually a Young measure corresponding to the maximization of a mean-field entropy. We explain why this result remains true for more general microcanonical measures, when all the dynamical invariants are taken into account. We give an explicit proof that these microcanonical measures are invariant measures for the dynamics of the 2D Euler equations. We describe a more general set of invariant measures, and discuss briefly their stability and their consequence for the ergodicity of the 2D Euler equations. The extension of these results to the Vlasov equations is also discussed, together with a proof of the uniqueness of statistical equilibria, for Vlasov equations with repulsive convex potentials. Even if we consider, in this paper, invariant measures only for Hamiltonian equations, with no fluxes of conserved quantities, we think this work is an important step towards the description of non-equilibrium invariant measures with fluxes.Comment: 40 page

The interplay between shell effects and electron correlations in quantum dots

We use the Path Integral Monte Carlo method to investigate the interplay between shell effects and electron correlations in single quantum dots with up to 12 electrons. By use of an energy estimator based on the hypervirial theorem of Hirschfelder we study the energy contributions of different interaction terms in detail. We discuss under which conditions the total spin of the electrons is given by Hund's rule, and the temperature dependence of the crystallization effects.Comment: 6 pages, 4 figure

Lyapunov exponent of many-particle systems: testing the stochastic approach

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the interaction, which can be calculated as suitable thermal averages. We have verified that there is a satisfactory quantitative agreement between theory and simulations in the disordered phases of the XY models, either with attractive or repulsive interactions. Part of the success of the theory is due to the possibility of predicting the shape of the required correlation functions, because this permits the calculation of correlation times as thermal averages.Comment: 11 pages including 6 figure

Canonical Solution of Classical Magnetic Models with Long-Range Couplings

We study the canonical solution of a family of classical $n-vector$ spin models on a generic $d$-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power $\alpha$, with $\alpha<d$. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables. The properties of a class of functions related to the modified Bessel functions had to be investigated. For given $n$, and for any $\alpha$, $d$ and lattice geometry, the solution is equivalent to that of the $\alpha=0$ model, where the dimensionality $d$ and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic

Combined inhibition of Aurora-A and ATR kinase results in regression of MYCN-amplified neuroblastoma

Amplification of MYCN is the driving oncogene in a subset of high-risk neuroblastoma. The MYCN protein and the Aurora-A kinase form a complex during S phase that stabilizes MYCN. Here we show that MYCN activates Aurora-A on chromatin, which phosphorylates histone H3 at serine 10 in S phase, promotes the deposition of histone H3.3 and suppresses R-loop formation. Inhibition of Aurora-A induces transcription-replication conflicts and activates the Ataxia telangiectasia and Rad3 related (ATR) kinase, which limits double-strand break accumulation upon Aurora-A inhibition. Combined inhibition of Aurora-A and ATR induces rampant tumor-specific apoptosis and tumor regression in mouse models of neuroblastoma, leading to permanent eradication in a subset of mice. The therapeutic efficacy is due to both tumor cell-intrinsic and immune cell-mediated mechanisms. We propose that targeting the ability of Aurora-A to resolve transcription-replication conflicts is an effective therapy for MYCN-driven neuroblastoma (141 words)

Technology Innovation Enabling Falls Risk Assessment in a Community Setting

Approximately one in three people over the age of 65 will fall each year, resulting in significant financial, physical, and emotional cost on the individual, their family, and society. Currently, falls are managed using on-body sensors and alarm pendants to notify others when a falls event occurs. However these technologies do not prevent a fall from occurring. There is now a growing focus on falls risk assessment and preventative interventions. Falls risk is currently assessed in a clinical setting by expert physiotherapists, geriatricians, or occupational therapists following the occurrence of an injurious fall. As the population ages, this reactive model of care will become increasingly unsatisfactory, and a proactive community-based prevention strategy will be required. Recent advances in technology can support this new model of care by enabling community-based practitioners to perform tests that previously required expensive technology or expert interpretation. Gait and balance impairment is one of the most common risk factors for falls. This paper reviews the current technical and non-technical gait and balance assessments, discusses how low-cost technology can be applied to objectively administer and interpret these tests in the community, and reports on recent research where body-worn sensors have been utilized. It also discusses the barriers to adoption in the community and proposes ethnographic research as a method to investigate solutions to these barriers