The cohomological excess of certain moduli spaces of curves of genus g

ABSTRACT. The open set M6kg ⊂ Mg parametrizes stable curves of genus g having at most k rational components. By the work of Looijenga, one expects that the cohomological excess of M6kg is at most g − 1 + k. In this paper we show that when k = 0, the conjectured upper bound is sharp by showing that there is a constructible sheaf on H60g (the hyperelliptic locus) which has non-vanishing cohomology in degree 3g − 2. 1

A semiclassical theory of quantum noise in open chaotic systems

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica

Studies of structural, magnetic, electrical and photoconducting properties of Bi1−x_{1-x}Cax_{x}MnO3_{3} epitaxial thin films

The dynamics of the charge ordered (CO) state under non-equilibrium conditions created by strong dc-electric field (~106 V/cm) and photo-illumination with short (~ 6 ns) laser pulses is investigated in Bi1-xCaxMnO3 (x > 0.5) epitaxial films. A pulsed laser deposition method was used to synthesize films on (100) LaAlO3 (LAO) and (100) SrTiO3 (STO) substrates. The crystallographic structure, temperature dependence of electrical resistivity and magnetization of the samples of different composition prepared under different oxygen partial pressure (pO2) and deposition temperature (TD) are studied. For the x = 0.6 sample grown on LAO, a clear signature of charge ordering at ~275 K is seen in the magnetization and at ~ 260 K in the resistivity data. The same sample grown on STO revealed a complex behavior, which entails charge ordering at ~300 K, a Neel order at ~150 K and finally a weak ferromagnetic phase below 50 K. A strong correlation between charge ordering temperature (TCO) and the c-axis lattice parameter (c) of the type (dTCO/dc ~-350 K/A) imerges from measurements on films deposited under different growth conditions. Since the out of plane lattice parameter (c) increases with in plane compressive strain, this effect directly show a compressive strain induced suppression of the TCO. The current (I)- voltage (V) characteristics of the samples at T < TCO show hysteresis due to a compound effect of Joule heating and collapse of the CO state. Transient changes in conductivity of lifetime ranging from nano to microseconds are seen at T < TCO on illumination with pulsed UV (355 nm) radiation. These observations are explained on the basis of the topological and electronic changes in the charge ordered phase.Comment: 19 figures, 34 page

Complementarity of perturbations driving insulator-to-metal transition in a charge ordered manganite

Modulation of charge carrier dynamics and hence electrical conductivity of solids by photoexcitation has been a rich field of research with numerous applications. Similarly, electric and magnetic field assisted enhancement of conductivity are of fundamental importance and technological use. Hole doped manganites of the type (A$_{1-x}$B$_{x})$MnO$_{3}$, where A and B are rare and alkaline earth metals respectively have the distinction of showing all three effects. Here we establish the complementarity of the electric, magnetic and photon fields in driving an insulator-metal transition in epitaxial thin films of La$_{0.175}$Pr$_{0.45}$Ca$_{0.375}$MnO$_{3}$ whose electrical ground state is insulating. Both pulsed and CW lasers cause a giant photon flux dependent enhancement of conductivity. It is further observed that electric and magnetic fields trigger the persistent enhancement of conductivity whose magnitude can be accentuated by application of these fields in parallel.Comment: 17 pages 6 figure

Transverse energy distributions and J/ψJ/\psi production in Pb+Pb collisions

We have analyzed the latest NA50 data on transverse energy distributions and $J/\psi$ suppression in Pb+Pb collisions. The transverse energy distribution was analysed in the geometric model of AA collisions. In the geometric model, fluctuations in the number of NN collisions at fixed impact parameter are taken into account. Analysis suggests that in Pb+Pb collisions, individual NN collisions produces less $$, than in other AA collisions. The nucleons are more transparent in Pb+Pb collisions. The transverse energy dependence of the $J/\psi$ suppression was obtained following the model of Blaizot et al, where charmonium suppression is assumed to be 100% effective above a threshold density. With fluctuations in number of NN collisions taken into account, good fit to the data is obtained, with a single parameter, the threshold density.Comment: Revised version with better E_T fit. 4 pages, 2 figure

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

J/ψJ/\psi production in Au+Au collisions at RHIC and the nuclear absorption

It is shown that a QCD based nuclear absorption model, with few parameters fixed to reproduce experimental $J/\psi$ yield in 200 GeV pp/pA and 450 GeV pA collisions can explain the preliminary PHENIX data on the centrality dependence of $J/\psi$ suppression in Cu+Cu collisions at RHIC energy, $\sqrt{s_{NN}}$=200 GeV. However, the model does not give satisfactory description to the preliminary PHENIX data on the centrality dependence of $J/\psi$ suppression in Au+Au collisions. The analysis suggest that in Au+Au collisions, $J/\psi$ are suppressed in a medium unlike the medium produced in SPS energy nuclear collisions or in RHIC energy Cu+Cu collisions.Comment: Revised version, published in Phys. Rev. C 74(2006)044907. PHENIX preliminary data on the centrality dependence of nuclear modification factor for $J/\psi$ in Cu+Cu and in Au+Au are analysed. 6 pages, 5 figure

Dual composition of odd-dimensional models

A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are considered. Specially the recently advocated topologically massive gravity is analysed in some details.Comment: minor modification