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Convexity and Minimum Distance Energy
"... We look at the problem of reducing the minimum distance energy of polygonal knots as an isoperimetric problem. Building on techniques used to show that a regular ngon maximizes area for a given perimeter, we have been able to prove that convex figures minimize the minimum distance energy for all po ..."
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Cited by 1 (0 self)
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We look at the problem of reducing the minimum distance energy of polygonal knots as an isoperimetric problem. Building on techniques used to show that a regular ngon maximizes area for a given perimeter, we have been able to prove that convex figures minimize the minimum distance energy for all
Contractions in the 2Wasserstein Length Space and Thermalization of Granular Media
, 2004
"... An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flowthrough model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical ..."
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Cited by 115 (32 self)
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the dynamical problem as the gradient flow of a convex energy on an infinitedimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even nonconvexity) — if uniformly controlled — will quantify contractivity (limit expansivity
Mapping the Energy Landscape of NonConvex Optimization Problems
"... Abstract. An energy landscape map (ELM) characterizes and visualizes an energy function with a tree structure, in which each leaf node represents a local minimum and each nonleaf node represents the barrier between adjacent energy basins. We demonstrate the utility of ELMs in analyzing nonconvex ..."
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Abstract. An energy landscape map (ELM) characterizes and visualizes an energy function with a tree structure, in which each leaf node represents a local minimum and each nonleaf node represents the barrier between adjacent energy basins. We demonstrate the utility of ELMs in analyzing nonconvex
Optimal Routing, Link Scheduling and Power Control in Multihop Wireless Networks
, 2003
"... In this paper, we study the problem of joint routing, link scheduling and power control to support high data rates for broadband wireless multihop networks. We first address the problem of finding an optimal link scheduling and power control policy that minimizes the total average transmission powe ..."
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Cited by 194 (0 self)
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the optimal policy, we find the sensitivity of the minimal total average power with respect to the average data rate for each link. Since the minimal total average power is a convex function of the required minimum average data rates, shortest path algorithms with the link weights set to the link
MAP Estimation, Linear Programming and Belief Propagation with Convex Free Energies
, 2007
"... Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with maxproduct belief propagation (BP) and its variants. In particular, it is known that using BP on a singlecycle graph or tree reweighted BP on an arbitrary ..."
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Cited by 74 (4 self)
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graph will give the MAP solution if the beliefs have no ties. In this paper we extend the setting under which BP can be used to provably extract the MAP. We define Convex BP as BP algorithms based on a convex free energy approximation and show that this class includes ordinary BP with singlecycle, tree
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
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Cited by 99 (25 self)
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Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness
Optimal Weights for Convex Functionals in Medical Image Segmentation
"... Abstract. Energy functional minimization is a popular technique for medical image segmentation. The segmentation must be initialized, weights for competing terms of an energy functional must be tuned, and the functional minimized. There is a substantial amount of guesswork involved. We reduce this g ..."
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Cited by 7 (4 self)
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this guesswork by analytically determining the optimal weights and minimizing a convex energy functional independent of the initialization. We demonstrate improved results over state of the art on a set of 470 clinical examples. 1
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
, 2004
"... In this paper, we develop a robust uncertainty principle for finite signals in C N which states that for nearly all choices T, Ω ⊂ {0,..., N − 1} such that T  + Ω  ≍ (log N) −1/2 · N, there is no signal f supported on T whose discrete Fourier transform ˆ f is supported on Ω. In fact, we can mak ..."
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Cited by 181 (17 self)
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make the above uncertainty principle quantitative in the sense that if f is supported on T, then only a small percentage of the energy (less than half, say) of ˆ f is concentrated on Ω. As an application of this robust uncertainty principle (QRUP), we consider the problem of decomposing a signal into a
Energyefficient scheduling of packet transmissions over wireless networks
 in Proc. INFOCOM Conf
"... Abstract—The paper develops algorithms for minimizing the energy required to transmit packets in a wireless environment. It is motivated by the following observation: In many channel coding schemes it is possible to significantly lower the transmission energy by transmitting packets over a long peri ..."
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Cited by 132 (2 self)
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period of time. Based on this observation, we show that for a variety of scenarios the offline energyefficient transmission scheduling problem reduces to a convex optimization problem. Unlike for the special case of a single transmitterreceiver pair studied in [5], the problem does not, in general
Results 11  20
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1,382