This thesis treats the implementational and some theoretical aspects of the Q-Morph algorithm for 2D domains. The main application areas are within FE methods. Q-Morph uses an advancing front method for generating unstructured, almost all-quadrilateral meshes containing at most one triangle, and few irregular nodes. The main algorithm is described in [16], while the post-processing methods are ...

Using the framework provided by Clifford algebras, we consider a noncommutative quotient-difference algorithm for obtaining the elements of a continued fraction corresponding to a given vector-valued power series. We demonstrate that these elements are ratios of vectors, which may be calculated with the aid of a cross rule using only vector operations. For vector-valued meromorphic functions we...

We describe a new paradigm for implementing inference in belief networks, which consists of two steps: (1) compiling a belief network into an arithmetic expression called a Query DAG (Q-DAG); and (2) answering queries using a simple evaluation algorithm. Each node of a Q-DAG represents a numeric operation, a number, or a symbol for evidence. Each leaf node of a Q-DAG represents the answer to a ...

Root extraction is a classical problem in computers algebra. It plays an essential role in cryptosystems based on elliptic curves. In 2006, Barreto and Voloch proposed an algorithm to compute rth roots in Fqm for certain choices of m and q. If r || q − 1 and (m, r) = 1, they proved that the complexity of their method is Õ(r(logm + log log q)m log q). In this paper, we extend the Barreto-Voloch ...

The software Q-system is designed to study the parallelism resource of numerical algorithms. By use Q-system, we can calculate any algorithm. Also, for set algorithms solving a given algorithmic problem, find an algorithm with best resource. theoretical basis concept Q-determinant where Q operations used by Any has and be represented in form Q-determinant. Such representation universal descript...

We study the quantum summation (QS) algorithm of Brassard, HHyer, Mosca and Tapp, see 1], which approximates the arithmetic mean of a Boolean function deened on N elements. We present sharp error bounds of the QS algorithm in the worst-average setting with the average performance measured in the Lq norm, q 2 1; 1]. We prove that the QS algorithm with M quantum queries, M < N, has the worst-aver...

This article presents an algorithm that combines a FAST-based algorithm (Flexible Adaptable-Size Topology), called ARM, and Q-learning algorithm. The ARM is a self organizing architecture. Dynamically adjusting the size of sensitivity regions of each neuron and adaptively pruning one of the redundant neurons, the ARM can preserve resources (available neurons) to accommodate more categories. The...

Q-learning is a one of the well-known Reinforcement Learning algorithms that has been widely used in various problems. The main contribution of this work is how to speed up the learning in a single agent environment (e.g. the robot). In this work, an attempt to optimize the traditional Q-learning algorithm has been done via using the Repeated Update Q-learning (RUQL) algorithm (the recent state...

This work describes a novel algorithm that integrates an adaptive resonance method (ARM), i.e. an ART-based algorithm with a self-organized design, and a Q-learning algorithm. By dynamically adjusting the size of sensitivity regions of each neuron and adaptively eliminating one of the redundant neurons, ARM can preserve resources, i.e. available neurons, to accommodate additional categories. As...

We present a new algorithm, the COLD PRISM, for computing matrix elements in molecular orbital calculations. Whereas traditional approaches form these from two-electron repulsion integrals ~ERIs! which, in turn, are formed from shell-pair data, we introduce several alternative paths that do not involve ERIs as intermediates. Tensor multiplication can be used as the basic arithmetic operation on...