Singular values of some modular functions

We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.Comment: 19 pages,corrected typo

Generation of Relativistic Electron Bunches with Arbitrary Current Distribution via Transverse-to-Longitudinal Phase Space Exchange

We propose a general method for tailoring the current distribution of relativistic electron bunches. The technique relies on a recently proposed method to exchange the longitudinal phase space emittance with one of the transverse emittances. The method consists of transversely shaping the bunch and then converting its transverse profile into a current profile via a transverse-to-longitudinal phase-space-exchange beamline. We show that it is possible to tailor the current profile to follow, in principle, any desired distributions. We demonstrate, via computer simulations, the application of the method to generate trains of microbunches with tunable spacing and linearly-ramped current profiles. We also briefly explore potential applications of the technique.Comment: 13 pages, 17 figure

Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the k-space Berry phase of occupied Bloch states. The theory is able to account for both dc and magneto-optical Hall conductivities with no adjustable parameters.Comment: 4 pages, 6 figures, author list correcte

Interacting Constituents in Cosmology

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure $\times$ energy-density equations of state $p(\rho)$. The usual approach in Cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the Statistical Mechanics of real fluids, is proposed to include them. A toy-model is presented which shows how such interaction terms can engender significant cosmological effects.Comment: 24 pages, 6 figures. It includes results presented in "Cosmic Acceleration from Elementary Interactions" [arXiv:gr-qc/0512135]. Citations added in v.

A Real-Time Capable Software-Defined Receiver Using GPU for Adaptive Anti-Jam GPS Sensors

Due to their weak received signal power, Global Positioning System (GPS) signals are vulnerable to radio frequency interference. Adaptive beam and null steering of the gain pattern of a GPS antenna array can significantly increase the resistance of GPS sensors to signal interference and jamming. Since adaptive array processing requires intensive computational power, beamsteering GPS receivers were usually implemented using hardware such as field-programmable gate arrays (FPGAs). However, a software implementation using general-purpose processors is much more desirable because of its flexibility and cost effectiveness. This paper presents a GPS software-defined radio (SDR) with adaptive beamsteering capability for anti-jam applications. The GPS SDR design is based on an optimized desktop parallel processing architecture using a quad-core Central Processing Unit (CPU) coupled with a new generation Graphics Processing Unit (GPU) having massively parallel processors. This GPS SDR demonstrates sufficient computational capability to support a four-element antenna array and future GPS L5 signal processing in real time. After providing the details of our design and optimization schemes for future GPU-based GPS SDR developments, the jamming resistance of our GPS SDR under synthetic wideband jamming is presented. Since the GPS SDR uses commercial-off-the-shelf hardware and processors, it can be easily adopted in civil GPS applications requiring anti-jam capabilities

Seroepidemiologic studies of hantavirus infection among wild rodents in California.

A total of 4,626 mammals were serologically tested for antibodies to Sin Nombre virus. All nonrodent species were antibody negative. Among wild rodents, antibody prevalence was 8.5% in murids, 1.4% in heteromyids, and < 0.1% in sciurids. Of 1,921 Peromyscus maniculatus (deer mice), 226 (11.8%) were antibody positive, including one collected in 1975. The highest antibody prevalence (71.4% of 35) was found among P. maniculatus on Santa Cruz Island, off the southern California coast. Prevalence of antibodies among deer mice trapped near sites of human cases (26.8% of 164) was significantly higher than that of mice from other sites (odds ratio = 4.5; 95% confidence interval = 1.7, 11.6). Antibody prevalence increased with rising elevation (> 1,200 meters) and correlated with a spatial cluster of hantavirus pulmonary syndrome cases in the Sierra Nevada

A Pomeron Approach to Hadron-Nucleus and Nucleus-Nucleus "Soft" Interactions at High Energy

We formulate a generalization of the Glauber formalism for hadron-nucleus and nucleus-nucleus collisions based on the Pomeron approach to high energy interactions. Our treatment is based on two physical assumptions (i.e. two small parameters) : (i) that only sufficiently small distances contribute to the Pomeron structure; and (ii) the triple Pomeron vertex $G_{3P}/g_{P-N} \ll 1$ (where $g_{P-N}$ is the Pomeron-nucleon vertex) is small. A systematic method is developed for calculating the total, elastic and diffractive dissociation cross sections as well as the survival probability of large rapidity gap processes and inclusive observables, both for hadron - nucleus and nucleus-nucleus collisions. Our approach suggests saturation of the density of the produced hadrons in nucleus-nucleus collisions, the value of the saturation density turns out to be large and depends on the number of nucleons in the lightest nucleus.Comment: 54 pages, 63 figure

Capture Hi-C identifies the chromatin interactome of colorectal cancer risk loci.

Multiple regulatory elements distant from their targets on the linear genome can influence the expression of a single gene through chromatin looping. Chromosome conformation capture implemented in Hi-C allows for genome-wide agnostic characterization of chromatin contacts. However, detection of functional enhancer-promoter interactions is precluded by its effective resolution that is determined by both restriction fragmentation and sensitivity of the experiment. Here we develop a capture Hi-C (cHi-C) approach to allow an agnostic characterization of these physical interactions on a genome-wide scale. Single-nucleotide polymorphisms associated with complex diseases often reside within regulatory elements and exert effects through long-range regulation of gene expression. Applying this cHi-C approach to 14 colorectal cancer risk loci allows us to identify key long-range chromatin interactions in cis and trans involving these loci