Persistent currents of noninteracting electrons

We thoroughly study the persistent current of noninteracting electrons in one, two, and three dimensional thin rings. We find that the results for noninteracting electrons are more relevant for individual mesoscopic rings than hitherto appreciated. The current is averaged over all configurations of the disorder, whose amount is varied from zero up to the diffusive limit, keeping the product of the Fermi wave number and the ring's circumference constant. Results are given as functions of disorder and aspect ratios of the ring. The magnitude of the disorder-averaged current may be larger than the root-mean-square fluctuations of the current from sample to sample even when the mean free path is smaller, but not too small, than the circumference of the ring. Then a measurement of the persistent current of a typical sample will be dominated by the magnitude of the disorder averaged current.Comment: 10 pages, 4 figure

Chaotic Phenomenon in Nonlinear Gyrotropic Medium

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself a model of nonlinear coupled oscillators. This article is devoted to the study of the Kuhn's nonlinear model. In the first paragraph of the paper we study classical dynamics in case of weak as well as strong nonlinearity. In case of week nonlinearity we have obtained the analytical solutions, which are in good agreement with the numerical solutions. In case of strong nonlinearity we have determined the values of those parameters for which chaos is formed in the system under study. The second paragraph of the paper refers to the question of the Kuhn's model integrability. It is shown, that at the certain values of the interaction potential this model is exactly integrable and under certain conditions it is reduced to so-called universal Hamiltonian. The third paragraph of the paper is devoted to quantum-mechanical consideration. It shows the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium. The last forth paragraph of the paper is devoted to generalization of the Kuhn's model for infinite chain of interacting oscillators

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Restoration of energy homeostasis by SIRT6 extends healthy lifespan

Aging leads to a gradual decline in physical activity and disrupted energy homeostasis. The NAD+-dependent SIRT6 deacylase regulates aging and metabolism through mechanisms that largely remain unknown. Here, we show that SIRT6 overexpression leads to a reduction in frailty and lifespan extension in both male and female B6 mice. A combination of physiological assays, in vivo multi-omics analyses and 13C lactate tracing identified an age-dependent decline in glucose homeostasis and hepatic glucose output in wild type mice. In contrast, aged SIRT6-transgenic mice preserve hepatic glucose output and glucose homeostasis through an improvement in the utilization of two major gluconeogenic precursors, lactate and glycerol. To mediate these changes, mechanistically, SIRT6 increases hepatic gluconeogenic gene expression, de novo NAD+ synthesis, and systemically enhances glycerol release from adipose tissue. These findings show that SIRT6 optimizes energy homeostasis in old age to delay frailty and preserve healthy aging

The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Big-Bang Nucleosynthesis and Hadronic Decay of Long-Lived Massive Particles

We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called X. If the lifetime of X is longer than \sim 0.1 sec, its decay may cause non-thermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. Using the result, we derive constraints on the primordial abundance of X. Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of X; The evolution of the hadronic shower is studied taking account of the details of the energy-loss processes of the nuclei in the thermal bath; We have used the most recent observational constraints on the primordial abundances of the light elements; In order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transfered energies. We will see that the non-thermal productions of D, He3, He4 and Li6 provide stringent upper bounds on the primordial abundance of late-decaying particle, in particular when the hadronic branching ratio of X is sizable. We apply our results to the gravitino problem, and obtain upper bound on the reheating temperature after inflation.Comment: 94 pages, 49 figures, to appear in Phys. Rev. D. This is a full length paper of the preprint astro-ph/040249

A study of the centrally produced pi0pi0pi0 channel in pp interactions at 450 GeV/c

The reaction pp -> pf (pi0pi0pi0) ps has been studied at 450 GeV/c. The pi0pi0pi0 effective mass spectrum shows clear eta(547) and pi2(1670) signals. Branching ratios for the eta(547) and pi_2(1670) are given as well as upper limits for the decays of the omega(782), a1(1260) and a2(1320) into 3pi0.Comment: 10 pages, Latex, 4 Figure

Three-body halos. V. Computations of continuum spectra for Borromean nuclei

We solve the coordinate space Faddeev equations in the continuum. We employ hyperspherical coordinates and provide analytical expressions allowing easy computation of the effective potentials at distances much larger than the ranges of the interactions where only s-waves in the different Jacobi coordinates couple. Realistic computations are carried out for the Borromean halo nuclei 6He (n+n+\alpha) for J\pi = 0+-, 1+-, 2+- and 11Li (n+n+9Li) for (1/2)+-, (3/2)+-, (5/2)+-. Ground state properties, strength functions, Coulomb dissociation cross sections, phase shifts, complex S-matrix poles are computed and compared to available experimental data. We find enhancements of the strength functions at low energies and a number of low-lying S-matrix poles.Comment: 35 pages, 14 figure

Candidate Genes for Expansion and Transformation of Hematopoietic Stem Cells by NUP98-HOX Fusion Genes

BACKGROUND: Hox genes are implicated in hematopoietic stem cell (HSC) regulation as well as in leukemia development through translocation with the nucleoporin gene NUP98. Interestingly, an engineered NUP98-HOXA10 (NA10) fusion can induce a several hundred-fold expansion of HSCs in vitro and NA10 and the AML-associated fusion gene NUP98-HOXD13 (ND13) have a virtually indistinguishable ability to transform myeloid progenitor cells in vitro and to induce leukemia in collaboration with MEIS1 in vivo. METHODOLOGY/PRINCIPAL FINDINGS: These findings provided a potentially powerful approach to identify key pathways mediating Hox-induced expansion and transformation of HSCs by identifying gene expression changes commonly induced by ND13 and NA10 but not by a NUP98-Hox fusion with a non-DNA binding homedomain mutation (N51S). The gene expression repertoire of purified murine bone marrow Sca-1+Lin- cells transduced with retroviral vectors encoding for these genes was established using the Affymetrix GeneChip MOE430A. Approximately seventy genes were differentially expressed in ND13 and NA10 cells that were significantly changed by both compared to the ND13(N51S) mutant. Intriguingly, several of these potential Hox target genes have been implicated in HSC expansion and self-renewal, including the tyrosine kinase receptor Flt3, the prion protein, Prnp, hepatic leukemia factor, Hlf and Jagged-2, Jag2. Consistent with these results, FLT3, HLF and JAG2 expression correlated with HOX A cluster gene expression in human leukemia samples. CONCLUSIONS: In conclusion this study has identified several novel Hox downstream target genes and provides important new leads to key regulators of the expansion and transformation of hematopoietic stem cells by Hox