Random walks on dynamic graphs: Mixing times, hitting times, and return probabilities

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion properties which allows us to capture the progress the random walk makes through t-step probabilities. We apply our framework to dynamically changing graphs, where the set of vertices is fixed while the set of edges changes in each round. For random walks on dynamic connected graphs for which the stationary distribution does not change over time, we show that their behaviour is in a certain sense similar to static graphs. For example, we show that the mixing and hitting times of any sequence of d-regular connected graphs is O(n^2), generalising a well-known result for static graphs. We also provide refined bounds depending on the isoperimetric dimension of the graph, matching again known results for static graphs. Finally, we investigate properties of random walks on dynamic graphs that are not always connected: we relate their convergence to stationarity to the spectral properties of an average of transition matrices and provide some examples that demonstrate strong discrepancies between static and dynamic graphs

Laserprobe 40Ar/39Ar dating of strain fringes: Mid-Cretaceous synconvergent orogen-parallel extension in the interior of the Sevier orogen:

[1] UV and CO2 laser-probe 40Ar/39Ar in situ analyses of phlogopite and muscovite in fibrous strain fringes from greenschist-facies metamorphic rocks document mica growth ages at temperatures lower than their closure temperatures, and therefore directly date deformation. The new dates resolve the age of the earliest ductile fabric recorded in the Raft River–Albion–Grouse Creek metamorphic core complex of Utah and Idaho. Phlogopite was dated in quartz-calcite-phlogopite strain fringes around pyrite in Pennsylvanian-Permian rocks from the Grouse Creek Mountains (Utah) using both the UV and CO2 laser probe; muscovite was dated in quartz-muscovite strain fringes around pyrite in deformed Jurassic sills from the Black Pine Mountains (Idaho) using the CO2 laser probe. Phlogopite 40Ar/39Ar ages for individual strain fringes (Grouse Creek Mountains) range from 92 Ma to 110 Ma, with the most reliable ages ranging from 101 Ma to 110 Ma (mean age, 105.0 ± 5.8 Ma). Muscovite 40Ar/39Ar ages for individual strain fringes (Black Pine Mountains) range from 97 Ma to 112 Ma (mean age, 104.7 ± 5.8 Ma). Strain fringes are associated with a subhorizontal foliation and a generally N-trending elongation lineation exhibiting components of top-to-the-north simple shear and coaxial strain accommodating N-S extension and subvertical shortening. Midcrustal northward flow at 105 (±6) Ma within the interior of the Sevier orogen, coeval with east-directed shortening in the foreland and with plate convergence, records orogen-parallel synconvergent extension. We favor gravitational relaxation of structural culminations resulting from focused crustal shortening as a driving mechanism for orogen-parallel flow

Transition from accelerated to decelerated regimes in JT and CGHS cosmologies

In this work we discuss the possibility of positive-acceleration regimes, and their transition to decelerated regimes, in two-dimensional (2D) cosmological models. We use general relativity and the thermodynamics in a 2D space-time, where the gas is seen as the sources of the gravitational field. An early-Universe model is analyzed where the state equation of van der Waals is used, replacing the usual barotropic equation. We show that this substitution permits the simulation of a period of inflation, followed by a negative-acceleration era. The dynamical behavior of the system follows from the solution of the Jackiw-Teitelboim equations (JT equations) and the energy-momentum conservation laws. In a second stage we focus the Callan-Giddings-Harvey-Strominger model (CGHS model); here the transition from the inflationary period to the decelerated period is also present between the solutions, although this result depend strongly on the initial conditions used for the dilaton field. The temporal evolution of the cosmic scale function, its acceleration, the energy density and the hydrostatic pressure are the physical quantities obtained in through the analysis.Comment: To appear in Europhysics Letter

Effects of a resistance training intervention on the strength-deficit of elite young soccer players

The aim of this study was to examine the effects of a traditional resistance training scheme on the relative strength (RS), relative peak-force (RPF), strength deficit (SDef), and vertical jump and sprint abilities in elite young soccer players. Thirty-five under-20 soccer players from two professional clubs were assessed before and after a 4-week competitive period. One team performed 12 sessions of a structured resistance training program and the other maintained their regular soccer-specific training and competitive routines. The resistance training program consisted of performing half-squat and jump squat exercises at distinct percentages of the one-repetition maximum. Both teams performed pre- and post-measurements in the following order: (1) countermovement jump (CMJ), (2) 20-m sprint, and (3) half-squat one-repetition maximum to determine the RS, RPF, and SDef. A two-way analysis of variance was used to test for group x time interaction among variables. Effect sizes (ES) and 95% confidence intervals (CI) were also calculated. Group x time interactions were demonstrated for RS ([ES [95%CI] = 1.21 [0.57; 1.85], P = 0.001), RPF (ES [95%CI] = 1.18 [0.52; 1.80], P = 0.001), SDef (ES [95%CI] = 0.86 [0.01; 1.71], P = 0.04), and CMJ (ES [95%CI] = 0.64 [0.28; 0.99], P = 0.001); whereas a non-significant interaction was observed for 20-m sprint performance (ES [95%CI] = 0.02 [-0.32; 0.36], P = 0.85). Traditional strength-power oriented training resulted in improved maximum strength performance and CMJ ability but, paradoxically, increased the SDef. As a consequence, stronger athletes are not necessarily able to use greater percentages of their peak-force against relatively lighter loads

CORRELATIONS BETWEEN HEAD ROTATIONAL KINEMATICS AND BRAIN TISSUE STRAIN FOR LOW AND HIGH LEVEL FOOTBALL HELMET IMPACTS

This study examined the correlation between head angular velocity and acceleration with brain strain for low and high level impacts. Impacts at 2.4m/s (low) and 11m/s (high) were delivered to a American football helmeted Hybrid III headform using a centric/non-centric protocol. A finite element model calculated strain from headform accelerations. The lowlevel impact data were obtained from a previous subset eliciting angular responses occurring at 20g, therefore linear acceleration relationships were not examined. High correlations (r=>0.8) existed for non-centric conditions between strain with angular acceleration and velocity, while centric conditions had moderate relationships (r=0.50.68). This research demonstrates that kinematic-strain relationships are dependent on the impact event, and that a single variable may not represent strain under all conditi

Gully Formation at the Haughton Impact Structure (Arctic Canada) Through the Melting of Snow and Ground Ice, with Implications for Gully Formation on Mars

The formation of gullies on Mars has been the topic of active debate and scientific study since their first discovery by Malin and Edgett in 2000. Several mechanisms have been proposed to account for gully formation on Mars, from dry mass movement processes, release of water or brine from subsurface aquifers, and the melting of near-surface ground ice or snowpacks. In their global documentation of martian gullies, report that gullies are confined to ~2783S and ~2872N latitudes and span all longitudes. Gullies on Mars have been documented on impact crater walls and central uplifts, isolated massifs, and on canyon walls, with crater walls being the most common situation. In order to better understand gully formation on Mars, we have been conducting field studies in the Canadian High Arctic over the past several summers, most recently in summer 2018 and 2019 under the auspices of the Canadian Space Agency-funded Icy Mars Analogue Program. It is notable that the majority of previous studies in the Arctic and Antarctica, including our recent work on Devon Island, have focused on gullies formed on slopes generated by regular endogenic geological processes and in regular bedrock. How-ever, as noted above, meteorite impact craters are the most dominant setting for gullies on Mars. Impact craters provide an environment with diverse lithologies including impact-generated and impact-modified rocks and slope angle, and thus greatly variable hill slope processes could occur within a localized area. Here, we investigate the formation of gullies within the Haughton impact structure and compare them to gullies formed in unimpacted target rock in the nearby Thomas Lee Inle

Imperfect Information, Heterogeneous Demand Shocks, and Inflation Dynamics

Using sector-level survey data for the universe of Japanese firms, we establish the positive co-movement in the firm’s expectations about aggregate and sector-specific demand shocks. We show that a simple model with imperfect information on the current aggregate and sector-specific components of demand explains the positive co-movement of expectations in the data. The model predicts that an increase in the relative volatility of sector-specific demand shocks compared to aggregate demand shocks reduces the sensitivity of inflation to changes in aggregate demand. We test and corroborate the theoretical prediction on Japanese data and find that the observed decrease in the relative volatility of sector-specific demand has played a significant role for the decline in the sensitivity of inflation to movements in aggregate demand from mid-1980s to mid-2000s

Imperfect information, shock heterogeneity, and inflation dynamics

We establish novel empirical regularities on firms' expectations about aggregate and idiosyncratic components of sectoral demand using industry-level survey data for the universe of Japanese rfims. Expectations of the idiosyncratic component of demand differ across sectors, and they positively co-move with expectations about the aggregate component of demand. To study the implications for in ation, we develop a model with firms that form expectations based on the inference of distinct shocks from a common signal. We show that the sensitivity of in ation to changes in demand decreases with the volatility of idiosyncratic component of demand that proxies the degree of shock heterogeneity. We apply principal component analysis on Japanese sectoral-level data to estimate the degree of shock heterogeneity, and we establish that the observed increase in shock heterogeneity plays a significant role for the reduced sensitivity of in ation to movements in real activity since the late 1990s