Covariance function of vector self-similar process

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

On the reheating stage after inflation

We point out that inflaton decay products acquire plasma masses during the reheating phase following inflation. The plasma masses may render inflaton decay kinematicaly forbidden, causing the temperature to remain frozen for a period at a plateau value. We show that the final reheating temperature may be uniquely determined by the inflaton mass, and may not depend on its coupling. Our findings have important implications for the thermal production of dangerous relics during reheating (e.g., gravitinos), for extracting bounds on particle physics models of inflation from Cosmic Microwave Background anisotropy data, for the production of massive dark matter candidates during reheating, and for models of baryogenesis or leptogensis where massive particles are produced during reheating.Comment: 8 pages, 2 figures. Submitted for publication in Phys. Rev.

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure

Shell Neurons of the Master Circadian Clock Coordinate the Phase of Tissue Clocks Throughout the Brain and Body

Background: Daily rhythms in mammals are programmed by a master clock in the suprachiasmatic nucleus (SCN). The SCN contains two main compartments (shell and core), but the role of each region in system-level coordination remains ill defined. Herein, we use a functional assay to investigate how downstream tissues interpret region-specific outputs by using in vivo exposure to long day photoperiods to temporally dissociate the SCN. We then analyze resulting changes in the rhythms of clocks located throughout the brain and body to examine whether they maintain phase synchrony with the SCN shell or core. Results: Nearly all of the 17 tissues examined in the brain and body maintain phase synchrony with the SCN shell, but not the SCN core, which indicates that downstream oscillators are set by cues controlled specifically by the SCN shell. Interestingly, we also found that SCN dissociation diminished the amplitude of rhythms in core clock gene and protein expression in brain tissues by 50–75 %, which suggests that light-driven changes in the functional organization of the SCN markedly influence the strength of rhythms in downstream tissues. Conclusions: Overall, our results reveal that body clocks receive time-of-day cues specifically from the SCN shell, which may be an adaptive design principle that serves to maintain system-level phase relationships in a changing environment. Further, we demonstrate that lighting conditions alter the amplitude of the molecular clock in downstream tissues, which uncovers a new form of plasticity that may contribute to seasonal changes in physiology and behavior

Beam envelope calculations in general linear coupled lattices

The envelope equations and Twiss parameters (beta and alpha) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for b which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems. (C) 2015 AIP Publishing LLC.open1

A retinoscopic survey of 333 horses and ponies in the UK

Introduction: Ophthalmic examination in the horse is generally limited to crude assessment of vision and screening for ocular lesions. The refractive state of equine eyes and the potential impact on vision and performance requires further investigation. Objective: To assess the refractive state of a large, mixed breed sample of horses and ponies in the United Kingdom (UK). Procedure: The refractive state of both eyes of 333 horses and ponies was determined by streak retinoscopy and the effect of age, height, gender, breed and management regime on the refractive state assessed. Results: The majority of eyes tested were emmetropic (83.63%), with 68.5% of horses having refractive errors of ≤ -0.50D or ≥ +0.50D. Refractive errors of greater than 1.50D (in either direction) were found in 2.7% of the eyes tested. Ametropic eyes included hyperopia (54%) and myopia (46%). Anisometropia was found in 30.3% of horses and ponies. Breed of horse/pony was the only factor that affected refractive state (in the left eye only, p<0.05) with 2 Thoroughbred crosses having a tendency towards myopia and Warmbloods / Shires towards hyperopia. Discussion / Conclusion: The retinoscopic survey found emmetropia to be the predominant refractive state of the equine eye with no evidence of an overall trend towards myopia or hyperopia. However, individual and breed related differences were found. Such factors should be considered in the selection of horses for sport and leisure, and when evaluating their performance potential. More comprehensive visual testing would be valuable in identifying underlying causes of behavioural problems

Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix

In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that the many-particle eigenvalues and eigenstates of the many-body density matrix $\rho_B$ of a block of $B$ sites cut out from an infinite chain of noninteracting spinless fermions can all be constructed out of the one-particle eigenvalues and one-particle eigenstates respectively. In this paper we developed a statistical-mechanical analogy between the density matrix eigenstates and the many-body states of a system of noninteracting fermions. Each density matrix eigenstate corresponds to a particular set of occupation of single-particle pseudo-energy levels, and the density matrix eigenstate with the largest weight, having the structure of a Fermi sea ground state, unambiguously defines a pseudo-Fermi level. We then outlined the main ideas behind an operator-based truncation of the density matrix eigenstates, where single-particle pseudo-energy levels far away from the pseudo-Fermi level are removed as degrees of freedom. We report numerical evidence for scaling behaviours in the single-particle pseudo-energy spectrum for different block sizes $B$ and different filling fractions \nbar. With the aid of these scaling relations, which tells us that the block size $B$ plays the role of an inverse temperature in the statistical-mechanical description of the density matrix eigenstates and eigenvalues, we looked into the performance of our operator-based truncation scheme in minimizing the discarded density matrix weight and the error in calculating the dispersion relation for elementary excitations. This performance was compared against that of the traditional density matrix-based truncation scheme, as well as against a operator-based plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb, graphicx and mathrsfs package

Towards a complete theory of thermal leptogenesis in the SM and MSSM

We perform a thorough study of thermal leptogenesis adding finite temperature effects, RGE corrections, scatterings involving gauge bosons and by properly avoiding overcounting on-shell processes. Assuming hierarchical right-handed neutrinos with arbitrary abundancy, successful leptogenesis can be achieved if left-handed neutrinos are lighter than 0.15 eV and right-handed neutrinos heavier than 2 10^7 GeV (SM case, 3sigma C.L.). MSSM results are similar. Furthermore, we study how reheating after inflation affects thermal leptogenesis. Assuming that the inflaton reheats SM particles but not directly right-handed neutrinos, we derive the lower bound on the reheating temperature to be T_RH > 2 10^9 GeV. This bound conflicts with the cosmological gravitino bound present in supersymmetric theories. We study some scenarios that avoid this conflict: `soft leptogenesis', leptogenesis in presence of a large right-handed (s)neutrino abundancy or of a sneutrino condensate.Comment: 56 pages, many figures (17) and appendices (20 pages). v2: ref.s added, final version. Results available at http://www.cern.ch/astrumia/Leptogenesis.htm