Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis of the one-parameter scaling of the conductance distribution. From the collected numerical data for quasi one dimensional systems up to the system size 24 x 24 x infinity we found the critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu < 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.Comment: 4 pages, 2 figure

Modeling the variability of the BL Lacertae object PKS 2155-304

The bright X-ray selected BL Lacertae object PKS 2155-304 has been the target of two intense multiwavelength campaigns, in November 1991 and in May 1994. Although the spectral energy distributions at both epochs were quite similar, the source exhibited two very distinct variability patterns that cannot be easily reconciled with homogeneous, one-zone jet models. During the first epoch the variability was almost achromatic in amplitude, with a time lag between X-rays and UV of $\approx 3$ h, while during the second epoch the variability amplitude increased as a function of wavelength, with the EUV flare peaking $\approx 1$ day after the X-ray flare. We model the source using a time-dependent inhomogeneous accelerating jet model. e reproduce the general characteristics of the different variability signatures by assuming that plasma disturbances with different physical properties propagate downstream in an underlying jet characterized by the same set of physical parameters at both epochs. A time delay of $\approx$ 1 day between the hardening of the UV spectral index and the UV flux, present at both epochs, is modeled with stochastic fluctuations in the particle acceleration manifested through small variations of the maximum energy of the injected electrons. We predict that similar time delays will be present in future observations, even in the absence of strong variability events. We stress the importance of observations at neighboring frequencies as a diagnostic tool for the structure of the quiescent jet in blazars, especially in the seemingly dull case when strong variability is absent.Comment: 8 pages, 5 figures. Accepted in ApJ Letter

Comparison of laser speckle contrast imaging with laser Doppler for assessing microvascular function

Objective: To compare the inter-day reproducibility of post-occlusive reactive hyperaemia (PORH) and sympathetic vasomotor reflexes assessed by single-point laser Doppler flowmetry (SP-LDF), integrating-probe LDF (IP-LDF) and laser speckle contrast imaging (LSCI), and the spatial variability of PORH assessed by IP-LDF and LSCI. We also evaluated the relationship between IP-LDF and LSCI perfusion values across a broad range of skin blood flows. Methods: Eighteen healthy adults (50% male, age 27 ± 4 years) participated in this study. Using SP-LDF, IP-LDF and LSCI, an index of skin blood flow was measured on the forearm during PORH (1-, 5- and 10-min occlusions) and on the finger pad during inspiratory gasp and cold pressor tests. These tests were repeated 3-7 days later. Data were converted to cutaneous vascular conductance (CVC; laser Doppler flow/mean arterial pressure) and expressed as absolute and relative changes from pre-stimulus CVC (ΔCVCABS and ΔCVCREL, respectively), as well as normalised to peak CVC for the PORH tests. Reproducibility was expressed as within-subjects coefficients of variation (CV, in %) and intraclass correlation coefficients. Results: The reproducibility of PORH on the forearm was poorer when assessed with SP-LDF and IP-LDF compared to LSCI (e.g., CV for 5-min PORH ΔCVCABS = 35, 27 and 19%, respectively), with no superior method of data expression. In contrast, the reproducibility of the inspiratory gasp and cold pressor test responses on the finger pad were better with SP-LDF and IP-LDF compared to LSCI (e.g., CV for inspiratory gasp ΔCVCREL = 13, 7 and 19%, respectively). The spatial variability of PORH responses was poorer with IP-LDF compared to LSCI (e.g., CV ranging 11-35% versus 3-16%, respectively). The association between simultaneous LSCI and IP-LDF perfusion values was non-linear. Conclusion: The reproducibility of cutaneous PORH was better when assessed with LSCI compared to SP-LDF and IP-LDF; probably due to measuring larger skin areas (lower inter-site variability). However, when measuring sympathetic vasomotor reflexes on the finger pad, reproducibility was better with SP-LDF and IP-LDF, perhaps due to the high sensitivity of LSCI to changes in skin blood flow at low levels

Relativistic and slowing down: the flow in the hotspots of powerful radio galaxies and quasars

Pairs of radio emitting jets with lengths up to several hundred kiloparsecs emanate from the central region (the `core') of radio loud active galaxies. In the most powerful of them, these jets terminate in the `hotspots', compact high brightness regions, where the jet flow collides with the intergalactic medium (IGM). Although it has long been established that in their inner ($\sim$parsec) regions these jet flows are relativistic, it is still not clear if they remain so at their largest (hundreds of kiloparsec) scales. We argue that the X-ray, optical and radio data of the hotspots, despite their at-first-sight disparate properties, can be unified in a scheme involving a relativistic flow upstream of the hotspot that decelerates to the sub-relativistic speed of its inferred advance through the IGM and viewed at different angles to its direction of motion. This scheme, besides providing an account of the hotspot spectral properties with jet orientation, it also suggests that the large-scale jets remain relativistic all the way to the hotspots.Comment: to appear in ApJ

A mean-field games laboratory for generative modeling

In this paper, we demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. There is a pervasive sense in the generative modeling community that the various flow and diffusion-based generative models have some common foundational structure and interrelationships. We establish connections between MFGs and major classes of flow and diffusion-based generative models including continuous-time normalizing flows, score-based models, and Wasserstein gradient flows. We derive these three classes of generative models through different choices of particle dynamics and cost functions. Furthermore, we study the mathematical structure and properties of each generative model by studying their associated MFG's optimality condition, which is a set of coupled forward-backward nonlinear partial differential equations (PDEs). The theory of MFGs, therefore, enables the study of generative models through the theory of nonlinear PDEs. Through this perspective, we investigate the well-posedness and structure of normalizing flows, unravel the mathematical structure of score-based generative modeling, and derive a mean-field game formulation of the Wasserstein gradient flow. From an algorithmic perspective, the optimality conditions of MFGs also allow us to introduce HJB regularizers for enhanced training of a broad class of generative models. In particular, we propose and demonstrate an Hamilton-Jacobi-Bellman regularized SGM with improved performance over standard SGMs. We present this framework as an MFG laboratory which serves as a platform for revealing new avenues of experimentation and invention of generative models. This laboratory will give rise to a multitude of well-posed generative modeling formulations and will provide a consistent theoretical framework upon which numerical and algorithmic tools may be developed.Comment: 38 pages, 10 figures. Version 4 includes derivation of the score probability flo

Aging and aerobic fitness affect the contribution of noradrenergic sympathetic nerves to the rapid cutaneous vasodilator response to local heating

Sedentary aging results in a diminished rapid cutaneous vasodilator response to local heating. We investigated whether this diminished response was due to altered contributions of noradrenergic sympathetic nerves; assessing 1) the age-related decline and, 2) the effect of aerobic fitness. We measured skin blood flow (SkBF)(laser-Doppler flowmetry) in young (24±1 yr) and older (64±1 yr) endurance-trained and sedentary men (n=7 per group) at baseline and during 35 min of local skin heating to 42 °C at three forearm sites: 1) untreated; 2) bretylium tosylate (BT), preventing neurotransmitter release from noradrenergic sympathetic nerves; and 3) yohimbine and propranolol (YP), antagonising α- and β-adrenergic receptors. SkBF was converted to cutaneous vascular conductance (CVC) (SkBF/mean arterial pressure) and normalized to maximal CVC (%CVCmax) achieved by skin heating to 44 °C. Pharmacological agents were administered using microdialysis. In the young trained, the rapid vasodilator response was reduced at the BT and YP sites (P0.05) but treatment with BT did (P>0.05). Neither BT nor YP treatments affected the rapid vasodilator response in the older sedentary group (P>0.05). These data suggest that the age-related reduction in the rapid vasodilator response is due to an impairment of sympathetic-dependent mechanisms, which can be partly attenuated with habitual aerobic exercise. Rapid vasodilation involves noradrenergic neurotransmitters in young trained men, and non-adrenergic sympathetic cotransmitters (e.g., neuropeptide Y) in young sedentary and older trained men, possibly as a compensatory mechanism. Finally, in older sedentary men, the rapid vasodilation appears not to involve the sympathetic system