On Sampling of stationary increment processes

Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi by at most \epsilon, with a given probability, asymptotically as \epsilon \downarrow0. The canonical application is to discretization errors in computer simulation of stochastic processes.Comment: Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On overload in a storage model, with a self-similar and infinitely divisible input

Let {X(t)}_{t\ge0} be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H>0. Pick constants \gamma >H and c>0. Let \nu be the L\'evy measure on R^{[0,\infty)} of X, and suppose that R(u)\equiv\nu({y\inR^{[0,\infty)}:supt\ge 0y(t)/(1+ct^{\gamma})>u}) is suitably ``heavy tailed'' as u\to\infty (e.g., subexponential with positive decrease). For the ``storage process'' Y(t)\equiv sup_{s\ge t}(X(s)-X(t)-c(s-t)^{\gamma}), we show that P{sup_{s\in[0,t(u)]}Y(s)>u}\sim P{Y(\hat t(u))>u} as u\to\infty, when 0\le \hat t(u)\le t(u) do not grow too fast with u [e.g., t(u)=o(u^{1/\gamma})]

Effort and catch estimates for northern and central California marine recreational fisheries, 1981-1986

Nearly 200 species of finfish are taken by the marine recreational fishery along the northern and central California coast. This data report provides estimates of total effort, total catch, and fishery demographics for the years 1981 through 1986 for that fishery. Catch estimate data are presented by number and weight of species, by disposition of the fish caught (e.g. kept or thrown back), by type of access and fishing gear used, and by geographic zone. (311pp.

The Apparent Madness of Crowds: Irrational collective behavior emerging from interactions among rational agents

Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as the extreme instance of financial bubbles and crashes, imply that markets (at least occasionally) do display irrational behavior. In this paper, we briefly outline our recent work demonstrating that a market with interacting agents having bounded rationality can display price fluctuations that are {\em quantitatively} similar to those seen in real markets.Comment: 4 pages, 1 figure, to appear in Proceedings of International Workshop on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II), Feb 14-17, 200

Hodge theory on Cheeger spaces

We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary operators and the notion of mezzoperversity, which intermediates between the standard lower and upper middle perversities in intersection theory, as interpreted in this de Rham setting, and show that the de Rham operator with these boundary conditions is Fredholm and has compact resolvent. We also prove an isomorphism between the resulting Hodge and L2 de Rham cohomology groups, and that these are independent of the choice of iterated edge metric. On spaces which admit ideal boundary conditions of this type which are also self-dual, which we call ‘Cheeger spaces’, we show that these Hodge/de Rham cohomology groups satisfy Poincare' Duality

Comparison of Hamstring and Quadriceps Muscle Activity in Men and Women Performing a Body Weight Squat

Multiple studies support the idea that women use a more quadriceps dominant activation pattern at the knee during stabilizing movements which may predispose them to a greater risk of ACL injury. A body weight squat is a common exercise used to strengthen knee musculature in attempt to minimize the risk of ACL injury. However, it is not clear whether this exercise activates the knee musculature in a manner that would not exacerbate the quadriceps dominance often observed in women. PURPOSE: To determine if women are more quadriceps dominant than men when performing a two-legged body weight squat. METHODS: Seven male and seven female Division III collegiate athletes (20.5±1.0 yrs, 176.2± 12.6 cm, and 79.7± 16.6 kg) provided informed consent and participated in this study. Surface EMG collected at 1000 Hz was used to measure the muscle activity of the vastus lateralis (VL) and the biceps femoris (BF), and normalized to the respective maximum voluntary isometric contraction (MVIC) for each muscle. Participants performed eight repetitions of a two-legged body weight squat at a cadence of 54 bpm. RMS EMG was computed across a 200 ms window and analyzed for the middle six repetitions at 15°, 45° and 60° of knee flexion during the movement. Hamstrings and quadriceps activity for the concentric phase of movement were evaluated separately, with two 2x3 (gender x joint position) mixed model ANOVAs. RESULTS: No interaction was observed between gender and joint position for either quadriceps (F(1,11) = 0.64, p = 0.54) or hamstring activity (F(1,11) = 1.24, p = .31). As knee flexion decreased, both quadriceps and hamstrings activity significantly decreased. Quadriceps activity, decreased from 41.7± 24.9%MVIC at 60° to 37.6± 21.7% at 45° to 34.2± 22.7% at 15° (F(1,11) = 5.74, p = 0.01). Likewise, hamstring activity decreased from 26.7± 28.9%MVIC at 60° to 20.6± 20.6% at 45° and to 18.2± 19.1% at 15° (F(1,11) = 3.92, p = 0.04). CONCLUSION: Gender-specific muscular imbalances do not occur during the performance of a bodyweight squat suggesting that such an exercise is appropriate as a part of strength training program designed to reduce ACL risk in women. However, knee angle is a relevant factor to consider when examining muscular characteristics of dynamic movements and injury mechanisms

On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau)$ and relaxation times $P(\mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau)$, $P(\mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~fran

A note on a gauge-gravity relation and functional determinants

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.Comment: 6 pages, io