Consider two n-point configurations X and Y in R with the same distance distribution and distinct distances. We begin with proposing an algorithm that tries to find a bijection ψ : X → Y such that X and Y are congruent under ψ, or determines that no such bijection exists. Next, we discuss extending this algorithm to the case where X and Y have small multiplicities of recurring distances, then t...

Let fX(x) be an intractable probability density. If f(x, y) is a joint density whose x-marginal is fX(x), then f(x, y) can be used to build a data augmentation (DA) algorithm that simulates a Markov chain whose invariant density is fX(x). The move from the current state of the chain, Xn = x, to the new state, Xn+1, involves two simulation steps: Draw Y ∼ fY |X(·|x), call the result y, and then ...

Given two time series X and Y , their mutual information, I (X,Y) = I (Y,X) , is the average number of bits of X that can be predicted by measuring Y and vice versa. In the analysis of observational data, calculation of mutual information occurs in three contexts: identification of nonlinear correlation, determination of an optimal sampling interval, particularly when embedding data, and in the...

Consider points (x 1 ; y 1) and (x 2 ; y 2) in < 2. We say (x 1 ; y 1) is dominated by (x 2 ; y 2) if x 1 < x 2 and y 1 < y 2. If (x 1 ; y 1) is dominated by (x 2 ; y 2), then we write (x 1 ; y 1) < D (x 2 ; y 2). For any nite subset P < 2 , the partially ordered set (P; D) is called the dominance poset. In this paper we present two distributed algorithms to compute the maximal points of a domi...

In this paper, a very efficient method, called single matrix block analyzer (SMBA), has been developed to determine relative permeability and capillary pressure curves from spontaneous imbibition (SI) data. SMBA mimics realistically the SI tests by appropriate boundary conditions modeling. In the proposed method, a cuboid with an identical core plug height is considered. The equal dimensions of...

Let K〈x, y〉 be the free associative algebra of rank 2 over an algebraically closed constructive field of any characteristic. We present an algorithm which decides whether or not two elements in K〈x, y〉 are equivalent under an automorphism of K〈x, y〉. A modification of our algorithm solves the problem whether or not an element in K〈x, y〉 is a semiinvariant of a nontrivial automorphism. In partic...

Abbreviated title: Interior-point algorithm for the LCP Abstract. The linear complementarity problem (LCP) can be viewed as the problem of minimizing x T y subject to y = M x + q and x; y 0. We are interested in nding a point with x T y < for a given > 0: The algorithm proceeds by iteratively reducing the potential function f (x; y) = ln x T y ? X ln x j y j ; where, for example, = 2n. The dire...

We present a modification of Simon’s Algorithm 2 that in some cases is able to fit experimentally obtained data to appropriately chosen trial functions with high probability. Modulo constants pertaining to the reliability and probability of success of the algorithm, the algorithm runs using only O(polylog(|Y |)) queries to the quantum database and O(polylog(|X |, |Y |)) elementary quantum gates...

Many manifold learning algorithms aim to create embeddings with low or no distortion (isometric). If the data has intrinsic dimension d, it is often impossible to obtain an isometric embedding in d dimensions, but possible in s > d dimensions. Yet, most geometry preserving algorithms cannot do the latter. This paper proposes an embedding algorithm to overcome this. The algorithm accepts as inpu...

A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish...