Importance of the heavier singlet neutrinos in leptogenesis

We argue that fast interactions of the lightest singlet neutrino N1 would project part of a preexisting lepton asymmetry L{p} onto a direction that is protected from N1 washout effects, thus preventing it from being erased. In particular, we consider an asymmetry generated in N2 decays, assuming that N1 interactions are fast enough to bring N1 into full thermal equilibrium. If N1 decays occur at T > or = 10{9} GeV, that is, before the muon Yukawa interactions enter into thermal equilibrium, then generically part of L{p} survives. In this case some of the constraints implied by the standard N1 leptogenesis scenario hold only if L{p} approximately 0. For T < or = 10{9} GeV, L{p} is generally erased, unless special alignment or orthogonality conditions in flavor space are realized.     

Design and optimization for variable rate selective excitation using an analytic RF scaling function

At higher B(0) fields, specific absorption rate (SAR) deposition increases. Due to maximum SAR limitation, slice coverage decreases and/or scan time increases. Conventional selective RF pulses are played out in conjunction with a time independent field gradient. Variable rate selective excitation (VERSE) is a technique that modifies the original RF and gradient waveforms such that slice profile is unchanged. The drawback is that the slice profile for off-resonance spins is distorted. A new VERSE algorithm based on modeling the scaled waveforms as a Fermi function is introduced. It ensures that system related constraints of maximum gradient amplitude and slew rate are not exceeded. The algorithm can be used to preserve the original RF pulse duration while minimizing SAR and peak b1 or to minimize the RF pulse duration. The design is general and can be applied to any symmetrical or asymmetrical RF waveform. The algorithm is demonstrated by using it to (a) minimize the SAR of a linear phase RF pulse, (b) minimize SAR of a hyperbolic secant RF pulse, and (c) minimize the duration of a linear phase RF pulse. Images with a T1-FLAIR (T1 FLuid Attenuated Inversion Recovery) sequence using a conventional and VERSE adiabatic inversion RF pulse are presented. Comparison of images and scan parameters for different anatomies and coils shows increased scan coverage and decreased SAR with the VERSE inversion RF pulse, while image quality is preserved.     

Graphical balanced allocations and the (1 + β)‐choice process

Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well‐known that the gap between the load of the most loaded bin and the average is , for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to independent of m. Consider a constrained setting where not all pairs of bins can be sampled. We are given a graph where each node corresponds to a bin. The process sequentially samples an edge from the graph and places a ball in the lesser loaded of its endpoints. We show the gap is at most where σ is the edge expansion of the graph. Our results extend naturally to the hypergraph version of this question. Our technique involves a tight analysis of what we call the “‐choice” process for some parameter : each ball goes to a random bin with probability and the lesser loaded of two random bins with probability β. For this process we show that the gap is , irrespective of m. Moreover the gap stays at in the weighted case for a large class of weight distributions. No non‐trivial bounds were previously known in the weighted case, even for the 2‐choice case. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 760–775, 2015     

On Trees and Characters

A new family of trees, defined in term of Young diagrams, is introduced. Values of central characters of the symmetric group are represented as a weighted enumeration of such trees. The proof involves a new decomposition theorem for representations corresponding to general shapes.     

Sensing clouds: A distributed cooperative target tracking with tiny binary noisy sensors

This paper suggests a novel algorithm for mobile object tracking using wireless sensor networks (WSNs). The paper assumes a future model of WSNs, where a large number of low to medium range inexpensive and noisy sensors are distributed randomly over an area. The distributed algorithm is based on short range communication between neighboring sensors, and is designed to work with very basic low cost binary sensors, that can report only a sensing, not sensing value.Neighboring sensors that sense the object form a cloud around the object which is dynamically updated as the object moves. To save energy on reporting a subset of the cloud, the cloud core, is elected. A trade-off between the accuracy and the core size (namely transmission power) is presented, as well as an extensive simulation study. Our algorithm works well with false negative sensing and up to 10% false positive sensing.     

The trace of spatial brownian motion is capacity-equivalent to the unit square

Summary. We show that with probability 1, the trace B[0, 1] of Brownian motion in space, has positive capacity with respect to exactly the same kernels as the unit square. More precisely, the energy of occupation measure on B[0, 1] in the kernel f(∣x−y∣), is bounded above and below by constant multiples of the energy of Lebesgue measure on the unit square. (The constants are random, but do not depend on the kernel.) As an application, we give almost-sure asymptotics for the probability that an α-stable process approaches within ɛ of B[0, 1], conditional on B[0, 1]. The upper bound on energy is based on a strong law for the approximate self-intersections of the Brownian path. We also prove analogous capacity estimates for planar Brownian motion and for the zero-set of one-dimensional Brownian motion. Received: 8 February 1995 / In revised form: 27 July 1995     

Diffraction by a discontinuity in curvature including the effect ofthe creeping wave

The existing geometrical theory of diffraction (GTD) solution for the diffraction by a discontinuity in curvature on a perfectly conducting cylindrical surface is uniformly extended in the region where the surface diffraction of the creeping wave launched by the discontinuity is involved     

Monte Carlo study of chiral structure: The Gross-Neveu model

The two-dimensional Gross-Neveu model is studied by Monte Carlo integration of Fermi fields. A clear transition is seen from a strong-coupling, massive, chiral symmetric phase to the weak-coupling chiral broken phase found in the continuum model. The weak-coupling behaviour of the dynamically generated scale agrees well with asymptotic freedom results.     

Realistic split fermion models

The standard model flavor structure can be explained in theories where the fermions are localized on different points in a compact extra dimension. We explain how models with two bulk scalars compactified on an orbifold can produce such separations in a natural way. We show that, generically, models of Gaussian overlaps are unnatural since they require very large Yukawa couplings between the fermions and the bulk scalars. We present a two-scalar model that accounts naturally for the quark flavor parameters and in particular yields order one CP violating phase.