Shadows and traces in bicategories

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the Lefschetz theorem, one needs "noncommutative" traces, such as the Hattori-Stallings trace for modules over noncommutative rings. In this paper we study a generalization of the symmetric monoidal trace which applies to noncommutative situations; its context is a bicategory equipped with an extra structure called a "shadow." In particular, we prove its functoriality and 2-functoriality, which are essential to its applications in fixed-point theory. Throughout we make use of an appropriate "cylindrical" type of string diagram, which we justify formally in an appendix.Comment: 46 pages; v2: reorganized and shortened, added proof for cylindrical string diagrams; v3: final version, to appear in JHR

Pulsar Results with the Fermi Large Area Telescope

The launch of the Fermi Gamma-ray Space Telescope has heralded a new era in the study of gamma-ray pulsars. The population of confirmed gamma-ray pulsars has gone from 6-7 to more than 60, and the superb sensitivity of the Large Area Telescope (LAT) on Fermi has allowed the detailed study of their spectra and light curves. Twenty-four of these pulsars were discovered in blind searches of the gamma-ray data, and twenty-one of these are, at present, radio quiet, despite deep radio follow-up observations. In addition, millisecond pulsars have been confirmed as a class of gamma-ray emitters, both individually and collectively in globular clusters. Recently, radio searches in the direction of LAT sources with no likely counterparts have been highly productive, leading to the discovery of a large number of new millisecond pulsars. Taken together, these discoveries promise a great improvement in the understanding of the gamma-ray emission properties and Galactic population of pulsars. We summarize some of the results stemming from these newly-detected pulsars and their timing and multi-wavelength follow-up observations.Comment: 21 pages, 9 figures, to appear in Proceedings of ICREA Workshop on The High-Energy Emission from Pulsars and their Systems, Sant Cugat, Spain, 2010 April 12-16 (Springer

Correlation between K+-Na+ diffusion coefficient and flexural strength of chemically tempered aluminosilicate glass

The correlation between K+-Na+ diffusion coefficient and mechanical properties of chemically tempered and hybridly tempered (thermally plus chemically tempered) aluminosilicate glass is investigated. First, the profile of the potassium ion concentration is experimentally measured, and the diffusion coefficient is calculated according to the Boltzmann-Matano approach. Second, the flexural strength and the Weibull modulus are determined using a method combining experimental (coaxial double ring) and finite element analysis. The results indicate that the flexural strength decreases with the diffusion coefficient of the air side for both types of glass samples, while there is no significant relationship between the diffusion coefficient and the Weibull modulus. The diffusion coefficient on the air side shows a higher value than that on the tin side. With the same diffusion coefficient, the flexural strength of chemically tempered glasses is found to be higher than that of hybridly tempered glasses. The effect of the diffusion coefficient on the modulus of rupture (MOR) for the hybridly tempered glass is more remarkable. These results would be useful for designing the glass strength and guiding the strengthening process by chemical or hybrid tempering

Different mechanisms of cis-9,trans-11- and trans-10,cis-12- conjugated linoleic acid affecting lipid metabolism in 3T3-L1 cells

Conjugated linoleic acid (CLA) has been shown to reduce body fat mass in various experimental animals. It is valuable to identify its influence on enzymes involved in energy expenditure, apoptosis, fatty acid oxidation and lipolysis. We investigated isomer-specific effects of high dose, long treatment of CLA (75.4 Μmol/L, 8 days) on protein and gene expression of these enzymes in cultured 3T3-L1 cells. Proteomics identified significant up- or down-regulation of 52 proteins by either CLA isomer. Protein and gene expression of uncoupling protein (UCP) 1, UCP3, perilipin and peroxisome proliferator-activated receptor (PPAR) α increased whereas UCP2 reduced for both CLA isomers. And eight-day treatment of trans-10,. cis-12 CLA, but not cis-9,. trans-11 CLA, significantly up-regulated protein and mRNA levels of PKA (P<05), CPT-1 and TNF-α (P<01). Compared to protein expression, both isomers did not significantly influence the mRNA expression of HSL, ATGL, ACO and leptin. In conclusion, high-dose, long treatment of cis-9,. trans-11 CLA did not promote apoptosis, fatty acid oxidation and lipolysis in adipocytes, but may induce an increase in energy expenditure. trans-10,. cis-12 CLA exhibited greater influence on lipid metabolism, stimulated adipocyte energy expenditure, apoptosis and fatty acid oxidation, but its effect on lipolysis was not obvious. © 2010 Elsevier Inc.postprin

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Spectral Line-by-Line Pulse Shaping of an On-Chip Microresonator Frequency Comb

We report, for the first time to the best of our knowledge, spectral phase characterization and line-by-line pulse shaping of an optical frequency comb generated by nonlinear wave mixing in a microring resonator. Through programmable pulse shaping the comb is compressed into a train of near-transform-limited pulses of \approx 300 fs duration (intensity full width half maximum) at 595 GHz repetition rate. An additional, simple example of optical arbitrary waveform generation is presented. The ability to characterize and then stably compress the frequency comb provides new data on the stability of the spectral phase and suggests that random relative frequency shifts due to uncorrelated variations of frequency dependent phase are at or below the 100 microHertz level.Comment: 18 pages, 4 figure

Metal-insulator transition in vanadium dioxide nanobeams: probing sub-domain properties of strongly correlated materials

Many strongly correlated electronic materials, including high-temperature superconductors, colossal magnetoresistance and metal-insulator-transition (MIT) materials, are inhomogeneous on a microscopic scale as a result of domain structure or compositional variations. An important potential advantage of nanoscale samples is that they exhibit the homogeneous properties, which can differ greatly from those of the bulk. We demonstrate this principle using vanadium dioxide, which has domain structure associated with its dramatic MIT at 68 degrees C. Our studies of single-domain vanadium dioxide nanobeams reveal new aspects of this famous MIT, including supercooling of the metallic phase by 50 degrees C; an activation energy in the insulating phase consistent with the optical gap; and a connection between the transition and the equilibrium carrier density in the insulating phase. Our devices also provide a nanomechanical method of determining the transition temperature, enable measurements on individual metal-insulator interphase walls, and allow general investigations of a phase transition in quasi-one-dimensional geometry.Comment: 9 pages, 3 figures, original submitted in June 200

Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.Comment: 13 pages, 5 figure

Abelian Gauge Fluxes and Local Models in F-Theory

We analyze the Abelian gauge fluxes in local F-theory models with G_S=SU(6) and SO(10). For the case of G_S=SO(10), there is a no-go theorem which states that for an exotic-free spectrum, there are no solutions for U(1)^2 gauge fluxes. We explicitly construct the U(1)^2 gauge fluxes with an exotic-free bulk spectrum for the case of G_S=SU(6). We also analyze the conditions for the curves supporting the given field content and discuss non-minimal spectra of the MSSM with doublet-triplet splitting.Comment: 43 pages, 15 tables; typos corrected, reference adde

On Global Flipped SU(5) GUTs in F-theory

We construct an SU(4) spectral divisor and its factorization of types (3,1) and (2,2) based on the construction proposed in [1]. We calculate the chiral spectra of flipped SU(5) GUTs by using the spectral divisor construction. The results agree with those from the analysis of semi-local spectral covers. Our computations provide an example for the validity of the spectral divisor construction and suggest that the standard heterotic formulae are applicable to the case of F-theory on an elliptically fibered Calabi-Yau fourfold with no heterotic dual.Comment: 45 pages, 12 tables, 1 figure; typos corrected, footnotes added, and a reference adde