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USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 568 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
 Proc. Japan Acad. Ser. A 65
, 1989
"... This paper treats degenerate parabolic equations of second order (1.1) u t + F{Vu, V 2 w) = 0 ..."
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Cited by 370 (16 self)
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This paper treats degenerate parabolic equations of second order (1.1) u t + F{Vu, V 2 w) = 0
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3393 (12 self)
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SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 427 (36 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Motion of level sets by mean curvature
 II, Trans. Amer. Math. Soc
"... We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γ o a unique generalized motion by mean curvature, existing for all time. We investigate the various ..."
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Cited by 435 (6 self)
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We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γ o a unique generalized motion by mean curvature, existing for all time. We investigate the various
NP IS AS EASY AS DETECTING UNIQUE SOLUTIONS
, 1986
"... For every known NPcomplete problem, the number of solutions of its instances varies over a large range, from zero to exponentially many. It is therefore natural to ask if the inherent intractability of NPcomplete problems is caused by this wide variation. We give a negative answer to this questi ..."
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Cited by 233 (1 self)
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is the question as to whether there exist NPproblems whose instances have solutions that are unique but are hard to find. Our result can be interpreted as strengthening the belief that such problems exist.
Viceroy: A Scalable and Dynamic Emulation of the Butterfly
, 2002
"... We propose a family of constantdegree routing networks of logarithmic diameter, with the additional property that the addition or removal of a node to the network requires no global coordination, only a constant number of linkage changes in expectation, and a logarithmic number with high probabilit ..."
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Cited by 343 (16 self)
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probability. Our randomized construction improves upon existing solutions, such as balanced search trees, by ensuring that the congestion of the network is always within a logarithmic factor of the optimum with high probability. Our construction derives from recent advances in the study of peertopeer lookup
The Stable Paths Problem and Interdomain Routing
 IEEE/ACM Transactions on Networking
, 2002
"... Abstract—Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem sinc ..."
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Cited by 262 (11 self)
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local optimum. We study the stable paths problem using a derived structure called a dispute wheel, representing conflicting routing policies at various nodes. We show that if no dispute wheel can be constructed, then there exists a unique solution for the stable paths problem. We define the simple path
An analysis of the optimum node density for ad hoc mobile networks
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS
, 2001
"... An ad hoc mobile network is a collection of nodes, each of which communicates over wireless channels and is capable of movement. Wireless nodes have the unique capability of transmission at different power levels. As the transmission power is varied, a tradeoff exists between the number of hops from ..."
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Cited by 203 (0 self)
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An ad hoc mobile network is a collection of nodes, each of which communicates over wireless channels and is capable of movement. Wireless nodes have the unique capability of transmission at different power levels. As the transmission power is varied, a tradeoff exists between the number of hops
Results 1  10
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