We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study r-resiliently k-colorable graphs, which are those k-colorable graphs that remain k-colorable even after the addition of any r new edges. We prove lower...

B-SPLINE MODELING AND ESTIMATOR PERFORMANCE Stephen R. Titus, Alfred O. Hero III, Je rey A. Fessler Department of EECS University of Michigan Ann Arbor, MI 48109 [email protected] ABSTRACT We give estimation error bounds and specify optimal estimators for continuous, closed boundary curves in an NMR image. The boundary is parameterized using periodic B-Splines. A Cramer-Rao lower bound on ...

Abstract. We calculate the boundary correlation function of fixed-to-free boundary condition changing operators in the square-lattice Ising model. The correlation function is expressed in four different ways using 2×2 block Toeplitz determinants. We show that these can be transformed into a scalar Toeplitz determinant when the size of the matrix is even. To know the asymptotic behavior of the c...

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric Lévy processes in R. We show that, if D ⊂ R is an open set which is κ-fat at a boundary point Q ∈ ∂D, then there is exactly one Martin boundary point associated with Q and this Martin boundary point is minimal. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40;...

Given a rectangular boundary partitioned into rectangles, the MLC-R problem is to find a Minimum EdgeLength Corridor that visits at least one point from the boundary of every rectangle and from the rectangular boundary. We present the first polynomial time constant ratio approximation algorithm for the MLC-R problem, which has been shown to be NP-hard [5].

Let T ⊂ R be a strictly convex domain bounded by a smooth hypersurface X = ∂T . In this paper we find lower bounds on the number of billiard trajectories in T , which have a prescribed initial point A ∈ X , a prescribed final point B ∈ X and make a prescribed number n of reflections at the boundary X . We apply a topological approach based on calculation of cohomology rings of certain configura...

The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP). In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,R). Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can i...

1-Nearest Neighbor with the Dynamic TimeWarping (DTW) distance is one of the most effective classifiers on time series domain. Since the global constraint has been introduced in speech community, many global constraint models have been proposed including Sakoe-Chiba (S-C) band, Itakura Parallelogram, and Ratanamahatana-Keogh (R-K) band. The R-K band is a general global constraint model that can...

We give an example of an autonomous functional F (u) = R f (u; Du)dx ((open subset of IR 2 , u : ! IR 2 in the Sobolev space W 1;1) which is sequentially weakly lower semicontinuous in W 1;p for every p 1 but does not agree with the relaxation of the same functional restricted to smooth functions when p < 2. A Lavrentiev phenomenon occurs for a related boundary problem.

We consider the system ⎧ ⎪ ⎨ ⎪ ⎩ −Δ p u = λf (v) in Ω −Δ q v = μg(u) in Ω u = v = 0 on ∂Ω (I) where Δ p u = div(|∇u| p−2 ∇u), Δ q v = div(|∇v| q−2 ∇v), p, q > 1, Ω is the open unit ball in R N , N ≥ 2 and ∂Ω is its boundary. We establish upper and lower estimates for possible positive solutions of system(I).