3D performance capture for facial animation

This work describes how a photogrammetry based 3D capture system can be used as an input device for animation. The 3D Dynamic Capture System is used to capture the motion of a human face, which is extracted from a sequence of 3D models captured at TV frame rate. Initially the positions of a set of landmarks on the face are extracted. These landmarks are then used to provide motion data in two different ways. First, a high level description of the movements is extracted, and these can be used as input to a procedural animation package (i.e. CreaToon). Second the landmarks can be used as registration points for a conformation process where the model to be animated is modified to match the captured model. This approach gives a new sequence of models, which have the structure of the drawn model but the movement of the captured sequence

Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6

An analytic proof is given of the necessity of the Borland-Dennis conditions for 3-representability of a one particle density matrix with rank 6. This may shed some light on Klyachko's recent use of Schubert calculus to find general conditions for N-representability

Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev. E(an error in proof of theorem 1 was corrected, typos corrected

Individual and collective stock dynamics: intra-day seasonalities

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, early hours of trading are dominated by idiosyncratic or sector specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure

Point-Contact Conductances from Density Correlations

We formulate and prove an exact relation which expresses the moments of the two-point conductance for an open disordered electron system in terms of certain density correlators of the corresponding closed system. As an application of the relation, we demonstrate that the typical two-point conductance for the Chalker-Coddington model at criticality transforms like a two-point function in conformal field theory.Comment: 4 pages, 2 figure

Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics

We obtain within Fokker-Planck dynamics an explicit generalization of Einstein's relation between drag, diffusion and equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We then provide a complete characterization of when the equilibrium distribution becomes a Boltzmann/J"uttner distribution, and when it satisfies the more general Tsallis distribution. We apply this analysis to recent calculations of drag and diffusion of a charm quark in a thermal plasma, and show that only a Tsallis distribution describes the equilibrium distribution well. We also provide a practical recipe applicable to highly relativistic plasmas, for determining both diffusion coefficients so that a specific equilibrium distribution will arise for a given drag coefficient.Comment: 4 pages including 2 figure

Goodness-of-Fit tests with Dependent Observations

We revisit the Kolmogorov-Smirnov and Cram\'er-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not distribution-free but rather depend on all the lagged bivariate copulas. These objects, that we call "self-copulas", encode all the non-linear temporal dependences. We introduce a specific, log-normal model for these self-copulas, for which a number of analytical results are derived. An application to financial time series is provided. As is well known, the dependence is to be long-ranged in this case, a finding that we confirm using self-copulas. As a consequence, the acceptance rates for GoF tests are substantially higher than if the returns were iid random variables.Comment: 26 page