Related papers: A numerical algorithm for zero counting II: Random…

This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.

We describe a technique for attributing parts of a written text to a set of unknown authors. Nothing is assumed to be known a priori about the writing styles of potential authors. We use multiple independent clusterings of an input text to…

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a…

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

This paper has been withdrawn by the authors, due the copyright policy of the journal it has been submited to.

In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.

Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…

Integer counting processes increment of an integer value at transitions between states of an underlying Markov process. The generator of a counting process, which depends on a parameter conjugate to the increments, defines a complex…

The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…

In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…

We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erd\"os and H. Fried) of the so called Szeg\"o's power series. This characterization is then applied to readily…

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…

The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…

This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.

In this paper, we extend our earlier result (see [Y-2008]) on the distribution of normalized zero-sets of random entire functions to random entire functions with small random perturbation.

We introduce an optimization technique to discriminate signal and background in any phenomeno- logical study based on the cut and count-based method. The core ideas behind this technique are the introduction of a ranking scheme that can…

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

The present paper shows meta-programming turn programming, which is rich enough to express arbitrary arithmetic computations. We demonstrate a type system that implements Peano arithmetics, slightly generalized to negative numbers. Certain…