Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which, for any given m m symmetric matrix ^ Y , either connrms that ^ Y 2 ? or returns a cut, i.e., a symmetric matrix A...

We derandomize G. Valiant’s [J. ACM 62 (2015) Art. 13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant’s randomized algorithm, but the precise constants we save over quadratic scaling are more modest. Our main technical tool for derandomization is ...

A standard isosurface extraction algorithm for a 3D image is the Marching Cubes algorithm [4]. The image is assumed to be defined on a regular lattice of size N0×N1×N2 with integer points (x, y, z) where 0 ≤ x < N0, 0 ≤ y < N1, and 0 ≤ z < N2. The image values themselves are F (x, y, z). An isosurface is of the form F (x, y, z) = c for some specified level value c where x, y, and z are treated ...

The Normalized Edit Distance (NED) between two strings X and Y is defined as the minimum quotient between the sum of weights of the edit operations required to transform X into Y and the length of the editing path corresponding to these operations. An algorithm for computing the NED has recently been introduced by Marzal and Vidal that exhibits O(mn2) computing complexity, where m and n are the...

Let X and Y be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group G. Assuming that Y is dconnected and dimX ≤ 2d, for some d ≥ 1, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps |X| → |Y |; the existence of such a map can be decided even for dimX ≤ 2d+1. For fix...

1 Derivation of Mean-field Updating Equations In the following we present a detailed derivation of the mean-field inference algorithm which is explained in Sec. 4 in [2] (i.e., Inference of RTDF). Here, we use the same notation as in [2]. The Kullback-Leibler divergence betweenQ(y,h;μ,ν) and P (y,h|y, I) is defined as KL(Q||P ) = ∑ yt,ht Q(y,h;μ,ν) ln Q(y,h;μ,ν) P (yt,ht|y<t, It) = −H(Q)− ∑ yt,...

By using the brute force algorithm, the application of the two-dimensional two-sample Kolmogorov–Smirnov test can be prohibitively computationally expensive. Thus a fast algorithm for computing the two-sample Kolmogorov–Smirnov test statistic is proposed to alleviate this problem. The newly proposed algorithm is O(n) times more efficient than the brute force algorithm, where n is the sum of the...

1 : x||y String x is concatenated with string y. 2 : λ(C) Distribution of a given instance or random variable C. 3 : D(X, Y) Statistical distance between the distributions of the two random variables X and Y. 6 : = Stat Statistical indistinguishability between two Random Variables: see Definition 8. 7 : = Comp Computational indistinguishability between two Random Variables: see Definition 9. 8 ...

ion: [x] P1 P2 : : : Pm = t1t2 : : : tm Q1 Q2 : : : Qm; where, for 1 i m and m 1, ti = y and Qi = [x] Pi, if x 2 FV (Pi); and ti = n and Qi = Pi, if x 62 FV (Pi). Reduction: t1t2 : : : tm P1 P2 : : : Pm Pm+1 ! Q1 Q2 : : : Qm; where, for 1 i m and m 1, Qi = Pi, if ti = n; and Qi = Pi Pm+1, if ti = y. Figure 4: Abstraction and reduction schemas for m-place yes-no combinators. call J. The abstract...

Let be a nite alphabet and let be a homomorphism i e a mapping satisfying xy x y for all x y Let a and let i n be integers We give the rst e cient algorithm for computing the ith letter of n a Our algorithm runs in time polynomial in the size of the input i e polynomial in logn log i and the description size of Our algorithm can be easily modi ed to give the distribution of letters in the pre x...