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The Decoupling Theorem
(2010)arXivIf a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing ...Working Paper -
Fermi-Liquid Behavior of the Normal Phase of a Strongly Interacting Gas of Cold Atoms
(2010)arXivWe measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.Working Paper -
Metric spaces with unique tangents
(2010)arXivWe are interested in studying doubling metric spaces with the property that at some of the points the metric tangent is unique. In such a setting, Finsler-Carnot-Caratheodory geometries and Carnot groups appear as models for the tangents. The results are based on an analogue for metric spaces of Preiss's phenomenon: tangents of tangents are tangents.Working Paper -
Entropy stable schemes for initial-boundary-value conservation laws
(2010)SAM Research ReportWe consider initial boundary value problems for systems of conservation laws and design entropy stable finite difference schemes to approximate them. The schemes are shown to be entropy stable for a large class of systems that are equipped with a symmetric splitting, derived from the entropy formulation. Numerical examples for the Euler equations of gas dynamics are presented to illustrate the robust performance of the proposed method.Report -
Analytical Framework for Streaming over TCP
(2010)TIK ReportStreaming over TCP is practical and widely used in commercial multimedia applications such as YouTube. Evaluations show commercial multimedia applications are suffering from providing good Quality of Experience [1]. Given the dynamic of Internet and the variability of TCP throughput, we propose an analytical framework for TCP streaming to trade the probability of discontinual playout against delay and buffer size. Guided by our proposed ...Report -
Tree approximation with anisotropic decompositions
(2010)SAM Research ReportIn recent years anisotropic transforms like the shearlet or curvelet transform have received a considerable amount of interest due to their ability to efficiently capture anisotropic features in terms of nonlinear N -term approximation. In this paper we study tree-approximation properties of such transforms where the N -term approximant has to satisfy the additional constraint that the set of kept indices possesses a tree structure. The ...Report -
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Reconstruction of a polygon from angles without prior knowledge of the size
(2010)Technical reportWe consider a simple agent exploring a polygon by moving from vertex to vertex along the boundary. At every vertex, the agent observes all angles between pairs of edges of the visibility graph, i.e. the angle between all pairs of visible vertices. The goal of the agent is to reconstruct the shape of the polygon, or equivalently its visibility graph. A polynomial time algorithm exists if the agent knows the total number of vertices a priori. ...Report