The largest eigenvalue of rank one deformation of large Wigner matrices

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue of some non necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one used by A. Soshnikov in the investigations of classical real or complex Wigner Ensembles. It is based on the computation of moments of traces of high powers of the random matrices under consideration

The International Urban Energy Balance Comparison Project: Initial Results from Phase 2.

Many urban land surface schemes have been developed, incorporating different assumptions about the features of, and processes occurring at, the surface. Here, the first results from Phase 2 of an international comparison are presented. Evaluation is based on analysis of the last 12 months of a 15 month dataset. In general, the schemes have best overall capability to model net all-wave radiation. The models that perform well for one flux do not necessarily perform well for other fluxes. Generally there is better performance for net all wave radiation than sensible heat flux. The degree of complexity included in the models is outlined, and impacts on model performance are discussed in terms of the data made available to modellers at four successive stages

Origin-Destination (O-D) Trip Table Estimation Using Traffic Movement Counts from Vehicle Tracking System at Intersection

A new video-based vehicle tracking system is proposed to provide accurate information on directional traffic counts at intersections. The extracted counts are fed to estimate an origin- destination trip table which is necessary information for traffic impact study and transportation planning. The system utilizes a fisheye lens to expand the area covered by a single camera and uses a particle filtering method to track an individual vehicle. The filter is designed to handle environmental changes and multiple motion dynamics. Experimental results show its strong ability on tracking in various conditions. The paper shows how to use the tracking outputs in obtaining accurate origin-destination (O-D) table

Chaos synchronization in generalized Lorenz systems and an application to image encryption

Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our intuition. Synchronization in chaotic dynamical systems, of which the Lorenz system is a quintessential example, is even more surprising because the very defining features of chaos include sensitive dependence on initial conditions. It is worth pursuing, then, the question of whether high-dimensional extensions of such a system also exhibit synchronization. This study investigates synchronization in a set of high-dimensional generalizations of the Lorenz system obtained from the inclusion of additional Fourier modes. Numerical evidence supports that these systems exhibit self-synchronization. An example application of this phenomenon to image encryption is also provided. Numerical experiments also suggest that there is much more to synchronization in these generalized Lorenz systems than self-synchronization; while setting the dimension of the driver system higher than that of the receiver system does not result in perfect synchrony, the smaller the dimensional difference between the two, the more closely the receiver system tends to follow the driver, leading to self-synchronization when their dimensions are equal. © 2021 The Author

Visual Traffic Movement Counts at Intersection for Origin-Destination (O-D) Trip Table Estimation

Origin-destination (O-D) trip table is necessary information for transportation planning and traffic impact study. However, current O-D estimations rely on estimated directional traffic counts at intersections, which obviously diminish reliability in the table. A video-based vehicle tracking system that utilizes wide view-angle lenses has been studied [26] to provide accurate direction traffic counts. The system expands the area covered by a single camera and uses a particle filtering method to handle environmental changes as well as geometric distortion caused by those lenses. This paper shows tracking capability of the system and also shows how to incorporate the directional traffic counts in the O-D estimation

Exponential torsion growth for random 3-manifolds

We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth

Random walks and random fixed-point free involutions

A bijection is given between fixed point free involutions of $\{1,2,...,2N\}$ with maximum decreasing subsequence size $2p$ and two classes of vicious (non-intersecting) random walker configurations confined to the half line lattice points $l \ge 1$. In one class of walker configurations the maximum displacement of the right most walker is $p$. Because the scaled distribution of the maximum decreasing subsequence size is known to be in the soft edge GOE (random real symmetric matrices) universality class, the same holds true for the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page

Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure

Distinct mechanisms of Drosophila CRYPTOCHROME-mediated light-evoked membrane depolarization and in vivo clock resetting.

Drosophila CRYPTOCHROME (dCRY) mediates electrophysiological depolarization and circadian clock resetting in response to blue or ultraviolet (UV) light. These light-evoked biological responses operate at different timescales and possibly through different mechanisms. Whether electron transfer down a conserved chain of tryptophan residues underlies biological responses following dCRY light activation has been controversial. To examine these issues in in vivo and in ex vivo whole-brain preparations, we generated transgenic flies expressing tryptophan mutant dCRYs in the conserved electron transfer chain and then measured neuronal electrophysiological phototransduction and behavioral responses to light. Electrophysiological-evoked potential analysis shows that dCRY mediates UV and blue-light-evoked depolarizations that are long lasting, persisting for nearly a minute. Surprisingly, dCRY appears to mediate red-light-evoked depolarization in wild-type flies, absent in both cry-null flies, and following acute treatment with the flavin-specific inhibitor diphenyleneiodonium in wild-type flies. This suggests a previously unsuspected functional signaling role for a neutral semiquinone flavin state (FADH•) for dCRY. The W420 tryptophan residue located closest to the FAD-dCRY interaction site is critical for blue- and UV-light-evoked electrophysiological responses, while other tryptophan residues within electron transfer distance to W420 do not appear to be required for light-evoked electrophysiological responses. Mutation of the dCRY tryptophan residue W342, more distant from the FAD interaction site, mimics the cry-null behavioral light response to constant light exposure. These data indicate that light-evoked dCRY electrical depolarization and clock resetting are mediated by distinct mechanisms

Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh–Bénard convection

The classic Lorenz equations were originally derived from the two-dimensional Rayleigh–Bénard convection system considering an idealized case with the lowest order of harmonics. Although the low-order Lorenz equations have traditionally served as a minimal model for chaotic and intermittent atmospheric motions, even the dynamics of the two-dimensional Rayleigh–Bénard convection system is not fully represented by the Lorenz equations, and such differences have yet to be clearly identified in a systematic manner. In this paper, the convection problem is revisited through an investigation of various dynamical behaviors exhibited by a two-dimensional direct numerical simulation (DNS) and the generalized expansion of the Lorenz equations (GELE) derived by considering additional higher-order harmonics in the spectral expansions of periodic solutions. Notably, GELE allows us to understand how nonlinear interactions among high-order modes alter the dynamical features of the Lorenz equations including fixed points, chaotic attractors, and periodic solutions. It is verified that numerical solutions of the DNS can be recovered from the solutions of GELE when we consider the system with sufficiently high-order harmonics. At the lowest order, the classic Lorenz equations are recovered from GELE. Unlike in the Lorenz equations, we observe limit tori, which are the multi-dimensional analog of limit cycles, in the solutions of the DNS and GELE at high orders. Initial condition dependency in the DNS and Lorenz equations is also discussed. The Lorenz equations are a simplified nonlinear dynamical system derived from the two-dimensional Rayleigh–Bénard (RB) convection problem. They have been one of the best-known examples in chaos theory due to the peculiar bifurcation and chaos behaviors. They are often regarded as the minimal chaotic model for describing the convection system and, by extension, weather. Such an interpretation is sometimes challenged due to the simplifying restriction of considering only a few harmonics in the derivation. This study loosens this restriction by considering additional high-order harmonics and derives a system we call the generalized expansion of the Lorenz equations (GELE). GELE allows us to study how solutions transition from the classic Lorenz equations to high-order systems comparable to a two-dimensional direct numerical simulation (DNS). This study also proposes mathematical formulations for a direct comparison between the Lorenz equations, GELE, and two-dimensional DNS as the system’s order increases. This work advances our understanding of the convection system by bridging the gap between the classic model of Lorenz and a more realistic convection syste