Scaling Green-Kubo relation and application to three aging systems

The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function $\langle v(t+\tau) v(t) \rangle$ asymptotically exhibits a certain scaling behavior and the diffusion is anomalous $\langle x^2(t) \rangle \simeq 2 D_\nu t^{\nu}$. We show how both the anomalous diffusion coefficient $D_\nu$ and exponent $\nu$ can be extracted from this scaling form. Our scaling Green-Kubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale invariant dynamics. This includes stationary systems with slowly decaying power law correlations as well as aging systems, whose properties depend on the the age of the system. Even for systems that are stationary in the long time limit, we find that the long time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity $D_{\nu}$ is not unique and we determine its values for a stationary respectively nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: Free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells and the L\'evy walk with numerous applications, in particular blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.Comment: 16 pages, 6 figures, 1 tabl

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.Comment: 5 pages, 3 figure

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

Machine Learning Clifford Invariants of ADE Coxeter Elements

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for A8, D8 and E8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results

Experimental Impacts into Strength-Layered Targets: Crater Morphology and Morphometry

Impact cratering is a fundamental physical process that has dominated the evolution and modification of nearly every planetary surface in the Solar System. Impact craters serve as a means to probe the subsurface structure of a planetary body and provide hints about target surface properties. By examining small craters on the lunar maria and comparing these to experimental impacts in the laboratory, Oberbeck and Quaide first suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter increases for a given regolith thickness. This quantitative relationship is commonly used to estimate regolith thicknesses on the lunar surface and has also been explored via numerical and experimental studies. Here we report on a series of experimental impact craters formed in targets com-posed of a thin layer of loose sand on top of a stronger substrate at the Experimental Impact Laboratory at NASA Johnson Space Center

Experimental Impacts into Strength-Layered Targets: Ejecta Kinematics

AImpact cratering has dominated the evolution and modification of planetary surfaces through-out the history of the solar system. Impact craters can serve as probes to understanding the details of a planetary subsurface; for example, Oberbeck and Quaide, suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter in-creases for a given regolith thickness. The final shape of the impact crater is a result of the subsurface flow-field initiated as the projectile transfers its energy and momentum to the target surface at the moment of impact. Therefore, when a regolith layer is present over a stronger substrate, such as is the case on the lunar surface, the substrate modifies the flow-field and thereby the excavation flow of the crater, which is reflected in the morphology of the final crater. Here we report on a series of experimental impacts into targets composed of a thin layer of loose sand on top of a stronger substrate. We use the Ejection-Velocity Measurement System developed to examine the ejecta kinematics during the formation of these craters

Easing into Reality: Experimental Impacts into Slopes and Layers

Impact cratering is the dominant geo-logic process affecting the surfaces of solid bodies throughout our solar system. Because large impacts are (luckily) rare on Earth, the process is studied through experiments, observations of existing structures, numerical modeling, and theory, most of which make the simplifying assumptions that the target is homogeneous, with no substantial topography. Craters do not always form on level targets com-posed of homogeneous loose material. Rather (Fig. 1), they often form on sloped surfaces and in layered tar-gets, both of which significantly influence the excavation and ejecta deposition processes. Such craters are common on the Moon and asteroids. We are investigating crater formation in two separate suites of experiments using sloped and layered targets (Fig. 2) at the Experimental Impact Laboratory at NASA Johnson Space Center. An experiment was also performed in a flat, homogenous target to serve as a reference

EFFECTS OF MANAGEMENT PRACTICES ON GRASSLAND BIRDS: LESSER PRAIRIE-CHICKEN

Information on the habitat requirements and effects of habitat management on grassland birds were summarized from information in more than 4,000 published and unpublished papers. A range map is provided to indicate the breeding distribution of Lesser Prairie-Chicken in the United States and southern Canada. Although birds frequently are observed outside the breeding range indicated, the maps are intended to show areas where managers might concentrate their attention. It may be ineffectual to manage habitat at a site for a species that rarely occurs in an area. The species account begins with a brief capsule statement, which provides the fundamental components or keys to management for the species. A section on breeding range outlines the current breeding distribution of the species in North America. The suitable habitat section describes the breeding habitat and occasionally microhabitat characteristics of the species, especially those habitats that occur in the Great Plains. Details on habitat and microhabitat requirements often provide clues to how a species will respond to a particular management practice. A table near the end of the account complements the section on suitable habitat, and lists the specific habitat characteristics for the species by individual studies. A special section on prey habitat is included for those predatory species that have more specific prey requirements. The area requirements section provides details on territory and home range sizes, minimum area requirements, and the effects of patch size, edges, and other landscape and habitat features on abundance and productivity. It may be futile to manage a small block of suitable habitat for a species that has minimum area requirements that are larger than the area being managed. The Brown-headed Cowbird (Molothrus ater) is an obligate brood parasite of many grassland birds. The section on cowbird brood parasitism summarizes rates of cowbird parasitism, host responses to parasitism, and factors that influence parasitism, such as nest concealment and host density. The impact of management depends, in part, upon a species’ nesting phenology and biology. The section on breeding-season phenology and site fidelity includes details on spring arrival and fall departure for migratory populations in the Great Plains, peak breeding periods, the tendency to renest after nest failure or success, and the propensity to return to a previous breeding site. The duration and timing of breeding varies among regions and years. Species’ response to management summarizes the current knowledge and major findings in the literature on the effects of different management practices on the species. The section on management recommendations complements the previous section and summarizes specific recommendations for habitat management provided in the literature. If management recommendations differ in different portions of the species’ breeding range, recommendations are given separately by region. The literature cited contains references to published and unpublished literature on the management effects and habitat requirements of the species. This section is not meant to be a complete bibliography; a searchable, annotated bibliography of published and unpublished papers dealing with habitat needs of grassland birds and their responses to habitat management is posted at the Web site mentioned below

Elucidating glycosaminoglycan–protein–protein interactions using carbohydrate microarray and computational approaches

Glycosaminoglycan polysaccharides play critical roles in many cellular processes, ranging from viral invasion and angiogenesis to spinal cord injury. Their diverse biological activities are derived from an ability to regulate a remarkable number of proteins. However, few methods exist for the rapid identification of glycosaminoglycan–protein interactions and for studying the potential of glycosaminoglycans to assemble multimeric protein complexes. Here, we report a multidisciplinary approach that combines new carbohydrate microarray and computational modeling methodologies to elucidate glycosaminoglycan–protein interactions. The approach was validated through the study of known protein partners for heparan and chondroitin sulfate, including fibroblast growth factor 2 (FGF2) and its receptor FGFR1, the malarial protein VAR2CSA, and tumor necrosis factor-α (TNF-α). We also applied the approach to identify previously undescribed interactions between a specific sulfated epitope on chondroitin sulfate, CS-E, and the neurotrophins, a critical family of growth factors involved in the development, maintenance, and survival of the vertebrate nervous system. Our studies show for the first time that CS is capable of assembling multimeric signaling complexes and modulating neurotrophin signaling pathways. In addition, we identify a contiguous CS-E-binding site by computational modeling that suggests a potential mechanism to explain how CS may promote neurotrophin-tyrosine receptor kinase (Trk) complex formation and neurotrophin signaling. Together, our combined microarray and computational modeling methodologies provide a general, facile means to identify new glycosaminoglycan–protein–protein interactions, as well as a molecular-level understanding of those complexes

Three-Dimensional High-Resolution Black-Blood Magnetic Resonance Imaging for Detection of Arteritic Anterior Ischemic Optic Neuropathy in Patients With Giant Cell Arteritis

Objectives: Arteritic anterior ischemic optic neuropathy (A-AION) caused by inflammatory occlusion of the posterior ciliary arteries is the most common reason for irreversible vision loss in patients with giant cell arteritis. Atypical clinical presentation and negative funduscopy can delay systemic high-dose corticosteroid therapy to prevent impending permanent blindness and involvement of the contralateral eye. The purpose of this study was to assess the diagnostic accuracy of 3-dimensional (3D) high-resolution T1-weighted black-blood magnetic resonance imaging (T1-BB-MRI) for the detection of posterior ciliary artery involvement in patients with giant cell arteritis and funduscopic A-AION. Materials and Methods: After institutional review board approval and informed consent, 27 patients with suspected giant cell arteritis and vision disturbances were included in this monocentric prospective cohort study. Giant cell arteritis was diagnosed in 18 patients according to the diagnostic reference standard (6 men, 73.8 [69.0-78.0] years);14 of those were positive for A-AION. Precontrast and postcontrast 3D T1-BB-MRI was performed in all 27 patients. Two radiologists separately assessed image quality and local fat suppression (4-point scale), visual contrast enhancement (3-point scale), and diagnostic confidence (5-point scale) regarding arteritic posterior ciliary artery involvement. Magnetic resonance imaging findings were assessed in comparison to funduscopy. Statistical analysis included accuracy parameters and interrater agreement. Results: Sensitivity of 3D T1-BB-MRI was 92.9% (95% confidence interval, 66.1%-99.8%) and specificity was 92.3% (95% confidence interval, 64.0%-99.8%) for detection of A-AION-positive patients. Image quality and local fat suppression were assessed with 3.2 +/- 0.8 (median 3) and 3.8 +/- 0.5 (median 4). Visual contrast enhancement with 2.3 +/- 0.8 (median 3) and diagnostic confidence was rated at 4.7 +/- 0.5 (median 5). Interrater agreement was high (kappa = 0.85, P < 0.001). Three-dimensional T1-BB-MRI displayed bilateral findings in 50% of the cases, whereas only unilateral A-AION was detected in funduscopy as a possible indication for the contralateral eye at risk. Conclusions: Three-dimensional T1-BB-MRI allows accurate detection of arteritic posterior ciliary artery involvement in patients with A-AION. Further, 3D T1-BB-MRI seems to display arteritic involvement of the posterior ciliary arteries earlier than funduscopy and might, therefore, display "vision-at-risk" in patients with visual impairment and suspected giant cell arteritis but unremarkable funduscopy