TY - GEN
AB - This is a study of the universality of spectral statistics for large random matrices. Considered are N×N symmetric, Hermitian, or quaternion self-dual random matrices with independent identically distributed entries (Wigner matrices), where the probability distribution of each matrix element is given by a measure v with zero expectation and with subexponential decay. The main result is that the correlation functions of the local eigenvalue statistics in the bulk of the spectrum coincide with those of the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble (GUE), and the Gaussian Symplectic Ensemble (GSE), respectively, in the limit as N → ∞. This approach is based on a study of the Dyson Brownian motion via a related new dynamics, the local relaxation flow. As a main input, it is established that the density of the eigenvalues converges to the Wigner semicircle law, and this holds even down to the smallest possible scale. Moreover, it is shown that the eigenvectors are completely delocalized. These results hold even without the condition that the matrix elements are identically distributed: only independence is used. In fact, for the matrix elements of the Green function strong estimates are given that imply that the local statistics of any two ensembles in the bulk are identical if the first four moments of the matrix elements match. Universality at the spectral edges requires matching only two moments. A Wigner-type estimate is also proved, and it is shown that the eigenvalues repel each other on arbitrarily small scales.
AU - László Erdös
ID - 2765
IS - 3
T2 - Russian Mathematical Surveys
TI - Universality of Wigner random matrices: A survey of recent results
VL - 66
ER -
TY - JOUR
AB - We consider Hermitian and symmetric random band matrices H in d ≥ dimensions. The matrix elements Hxy, indexed by x,y ∈ Λ ⊂ ℤd are independent and their variances satisfy σ2xy:= E{pipe}Hxy{pipe}2 = W-d f((x-y)/W for some probability density f. We assume that the law of each matrix element Hxy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales ≪ Wd/3. We also show that the localization length of the eigenvectors of H is larger than a factor Wd/6 times the band width W. All results are uniform in the size {pipe}Λ{pipe} of the matrix. This extends our recent result (Erdo{double acute}s and Knowles in Commun. Math. Phys., 2011) to general band matrices. As another consequence of our proof we show that, for a larger class of random matrices satisfying Σx σ2xy for all y, the largest eigenvalue of H is bounded with high probability by 2+M-2/3+e{open} for any e{open} > 0, where M:= 1/(maxx,y σ2xy).
AU - László Erdös
AU - Knowles, Antti
ID - 2766
IS - 7
JF - Annales Henri Poincare
TI - Quantum diffusion and delocalization for band matrices with general distribution
VL - 12
ER -
TY - JOUR
AB - Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point. Through extensive experiments and computer simulations, we were able to identify and characterize the processes ultimately responsible for sustaining turbulence. In contrast to the classical Landau-Ruelle-Takens view that turbulence arises from an increase in the temporal complexity of fluid motion, here, spatial proliferation of chaotic domains is the decisive process and intrinsic to the nature of fluid turbulence.
AU - Avila, Kerstin
AU - Moxey, David
AU - de Lózar, Alberto
AU - Avila, Marc
AU - Barkley, Dwight
AU - Björn Hof
ID - 2799
IS - 6039
JF - Science
TI - The onset of turbulence in pipe flow
VL - 333
ER -
TY - JOUR
AB - In shear flows, turbulence first occurs in the form of localized structures (puffs/spots) surrounded by laminar fluid. We here investigate such spatially intermittent flows in a pipe experiment showing that turbulent puffs have a well-defined interaction distance, which sets their minimum spacing as well as the maximum observable turbulent fraction. Two methodologies are employed. Starting from a laminar flow, puffs are first created by locally injecting a jet of fluid through the pipe wall. When the perturbation is applied periodically at low frequencies, as expected, a regular sequence of puffs is observed where the puff spacing is given by the ratio of the mean flow speed to the perturbation frequency. At large frequencies however puffs are found to interact and annihilate each other. Varying the perturbation frequency, an interaction distance is determined which sets the highest possible turbulence fraction. This enables us to establish an upper bound for the friction factor in the transitional regime, which provides a well-defined link between the Blasius and the Hagen-Poiseuille friction laws. In the second set of experiments, the Reynolds number is reduced suddenly from fully turbulent to the intermittent regime. The resulting flow reorganizes itself to a sequence of constant size puffs which, unlike in Couette and Taylor–Couette flow are randomly spaced. The minimum distance between the turbulent patches is identical to the puff interaction length. The puff interaction length is found to be in agreement with the wavelength of regular stripe and spiral patterns in plane Couette and Taylor–Couette flow.
AU - Samanta, Devranjan
AU - de Lózar, Alberto
AU - Björn Hof
ID - 2800
JF - Journal of Fluid Mechanics
TI - Experimental investigation of laminar turbulent intermittency in pipe flow
VL - 681
ER -
TY - CONF
AB - Turbulent puffs in pipe flow are characterized by a sharp laminar-turbulent interface at the trailing edge and a more diffused leading interface. It is known that these laminar-turbulent interfaces propagate at a speed that is approximately equal to the flow rate. Our results from direct numerical simulation show that, locally, the interface velocity relative to the fluid (i) counteracts the advection due to the laminar velocity profile so that the puff can preserve its characteristic overall shape, (ii) is very small in magnitude, but involves a large interface area so that the global propagation velocity relative to the mean flow can be large and (iii) is determined by both inertial and viscous effects. The analysis provides some new insights into the mechanisms that sustain or expand localized turbulence and might be relevant for the design of new control strategies.
AU - Holzner, Markus
AU - Avila, Marc
AU - de Lózar, Alberto
AU - Björn Hof
ID - 2801
IS - 5
TI - A Lagrangian approach to the interface velocity of turbulent puffs in pipe flow
VL - 318
ER -
TY - JOUR
AB - Despite their relatively simple appearance, roots are incredibly complex organs that are highly adapted to differing environments. Many aspects of root development are co-ordinated by subtle spatial differences in the concentrations of the phytohormones auxin and cytokinin. Events from the formation of a root during embryogenesis to the determination of the network of lateral roots are controlled by interactions between these hormones. Recently, interactions have been defined where auxin signaling promotes the expression of cytokinin signaling inhibitors, cytokinin signaling promotes the expression of auxin signaling inhibitors and finally where cytokinin signaling regulates the complex network of auxin transport proteins to position zones of high auxin signaling. We are witnessing a period of discovery in which we are beginning to understand how these hormonal pathways communicate to regulate root formation.
AU - Bishopp, Anthony
AU - Eva Benková
AU - Helariutta, Ykä
ID - 2871
IS - 1
JF - Current Opinion in Plant Biology
TI - Sending mixed messages: Auxin-cytokinin crosstalk in roots
VL - 14
ER -
TY - JOUR
AB - The apical hook develops in the upper part of the hypocotyl when seeds buried in the soil germinate, and serves to protect cotyledons and the shoot apical meristem from possible damage caused by pushing through the soil. The curvature is formed through differential cell growth that occurs at the two opposite sides of the hypocotyl, and it is established by a gradient of auxin activity and refined by the coordinated action of auxin and ethylene. Here we show that gibberellins (GAs) promote hook development through the transcriptional regulation of several genes of the ethylene and auxin pathways in Arabidopsis. The level of GA activity determines the speed of hook formation and the extent of the curvature during the formation phase independently of ethylene, probably by modulating auxin transport and response through HLS1, PIN3, and PIN7. Moreover, GAs cooperate with ethylene in preventing hook opening, in part through the induction of ethylene production mediated by ACS5/ETO2 and ACS8.
AU - Gallego-Bartolomé, Javier
AU - Arana, María V
AU - Vandenbussche, Filip
AU - Žádníková, Petra
AU - Minguet, Eugenio G
AU - Guardiola, Vicente
AU - Van Der Straeten, Dominique
AU - Eva Benková
AU - Alabadí, David
AU - Blázquez, Miguel A
ID - 2874
IS - 4
JF - Plant Journal
TI - Hierarchy of hormone action controlling apical hook development in Arabidopsis
VL - 67
ER -
TY - JOUR
AU - Tiago Paixao
AU - Azevedo, Ricardo B
ID - 2897
IS - 7
JF - PLoS Computational Biology
TI - Redundancy and the Evolution of Cis Regulatory Element Multiplicity
VL - 6
ER -
TY - JOUR
AB - Sex allocation theory has been remarkably successful at explaining the prevalence of even sex ratios in natural populations and at identifying specific conditions that can result in biased sex ratios. Much of this theory focuses on parental sex determination (SD) strategies. Here, we consider instead the evolutionary causes and consequences of mixed offspring SD strategies, in which the genotype of an individual determines not its sex, but the probability of developing one of multiple sexes. We find that alleles specifying mixed offspring SD strategies can generally outcompete alleles that specify pure strategies, but generate constraints that may prevent a population from reaching an even sex ratio. We use our model to analyze sex ratios in natural populations of Tetrahymena thermophila, a ciliate with seven sexes determined by mixed SD alleles. We show that probabilistic SD is sufficient to account for the occurrence of skewed sex ratios in natural populations of T. thermophila, provided that their effective population sizes are small. Our results highlight the importance of genetic drift in sex ratio evolution and suggest that mixed offspring SD strategies should be more common than currently thought.
AU - Tiago Paixao
AU - Phadke, Sujal S
AU - Azevedo, Ricardo B
AU - Zufall, Rebecca A
ID - 2898
IS - 7
JF - Evolution; International Journal of Organic Evolution
TI - Sex ratio evolution under probabilistic sex determination
VL - 65
ER -
TY - CHAP
AU - Vicente, Sara
AU - Vladimir Kolmogorov
AU - Rother, Carsten
ED - Blake, Andrew
ED - Kohli, Pushmeet
ED - Rother, Carsten
ID - 2922
T2 - Markov Random Fields for Vision and Image Processing
TI - Graph-cut Based Image Segmentation with Connectivity Priors
ER -