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

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

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

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

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 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

A hop-count based positioning algorithm for wireless ad-hoc networks

We propose a range-free localization algorithm for a wireless ad-hoc network utilizing the hop-count metric’s ability to indicate proximity to anchors (i.e., nodes with known positions). In traditional sense, hop-count generally means the number of intermediate routers a datagram has to go through between its source and the destination node. We analytically show that hop-count could be used to indicate proximity relative to an anchor node. Our proposed algorithm is computationally feasible for resource constrained wireless ad-hoc nodes, and gives reasonable accuracy. We perform both real experiments and simulations to evaluate the algorithm’s performance. Experimental results show that our algorithm outperforms similar proximity based algorithms utilizing received signal strength and expected transmission count. We also analyze the impact of various parameters like the number of anchor nodes, placements of anchor nodes and varying transmission powers of the nodes on the hop-count based localization algorithm’s performance through simulation

Transdiagnostic phenomena of psychopathology in the context of the RDoC: protocol of a multimodal cross-sectional study

In the past, affective and cognitive processes related to psychopathology have been examined within the boundaries of phenotype-based diagnostic labels, which has led to inconsistent findings regarding their underlying operating principles. Investigating these processes dimensionally in healthy individuals and by means of multiple modalities may provide additional insights into the psychological and neuronal mechanisms at their core. The transdiagnostic phenomena Neuroticism and Rumination are known to be closely linked. However, the exact nature of their relationship remains to be elucidated. The same applies to the associations between Hedonic Capacity, Negativity Bias and different Emotion Regulation strategies. This multimodal cross-sectional study examines the relationship of the transdiagnostic phenomena Neuroticism and Rumination as well as Hedonic Capacity, the Negativity Bias and Emotion Regulation from a RDoC (Research Domain Criteria) perspective. A total of 120 currently healthy subjects (past 12 months) will complete several questionnaires regarding personality, emotion regulation, hedonic capacity, and psychopathologies as well as functional magnetic resonance imaging (fMRI) during cognitive and emotional processing, to obtain data on the circuit, behavioral and self-report level. This study aims to contribute to the understanding of the relationship between cognitive and affective processes associated with psychopathologies as well as their neuronal correlates. Ultimately, a grounded understanding of these processes could guide improvement of diagnostic labels and treatments. Limitations include the cross-sectional design and the limited variability in psychopathology scores due to the restriction of the sample to currently healthy subjects

Enhancing preschoolers' executive functions through embedding cognitive activities in shared book reading

Given evidence that early executive functioning sets the stage for a broad range of subsequent outcomes, researchers have sought to identify ways to foster these cognitive capacities. An increasingly common approach involves computerized ‘brain training’ programs, yet there are questions about whether these are well suited for fostering the early development of executive functions (EFs). The current series of studies sought to design, develop, and provide evidence for the efficacy of embedding cognitive activities in a commonplace activity – shared reading of a children’s book. The book, Quincey Quokka’s Quest, required children to control their thinking and behaviour to help the story’s main character through a series of obstacles. The first study investigated effects of reading with embedded cognitive activities in individual and group contexts on young children’s executive functions (EFs). The second study compared reading with embedded cognitive activities against a more-active control condition (dialogic reading) that similarly engaged children in the reading process yet lacked clear engagement of EFs. The third study sought to investigate whether the effect of reading the story with embedded EF activities changed across differing doses of the intervention and whether effects persisted 2 months post-intervention. Findings provide converging evidence of intervention effects on working memory and shifting in as little as 3 weeks (compared to more traditional reading) and maintenance of these gains 2 months later. This suggests the efficacy of embedding cognitive activities in the context of everyday activities, thereby extending the range of users and contexts in which this approach can be used