On reliable computation by noisy random Boolean formulas

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.

Use of the Maple System in Math Tuition at Universities

The following article explores the application of educational technologies at a University level and their contribution in enhancing the educational effectiveness. It discusses the capabilities of computer algebra systems, such as Maple. It is integrated in the math tuition of the Technical University (TU) in Varna and is used by its students during laboratory exercises.

DNA Simulation of Genetic Algorithms: Fitness Computation

* This work has been partially supported by Spanish Project TIC2003-9319-c03-03 “Neural Networks and Networks of Evolutionary Processors”.

Generalization by Computation Through Memory

Usually, generalization is considered as a function of learning from a set of examples. In present work on the basis of recent neural network assembly memory model (NNAMM), a biologically plausible 'grandmother' model for vision, where each separate memory unit itself can generalize, has been proposed. For such a generalization by computation through memory, analytical formulae and numerical procedure are found to calculate exactly the perfectly learned memory unit's generalization ability. The model's memory has complex hierarchical structure, can be learned from one example by a one-step process, and may be considered as a semi-representational one. A simple binary neural network for bell-shaped tuning is described.

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

Practical, Computation Efficient High-Order Neural Network for Rotation and Shift Invariant Pattern Recognition

In this paper, a modification for the high-order neural network (HONN) is presented. Third order networks are considered for achieving translation, rotation and scale invariant pattern recognition. They require however much storage and computation power for the task. The proposed modified HONN takes into account a priori knowledge of the binary patterns that have to be learned, achieving significant gain in computation time and memory requirements. This modification enables the efficient computation of HONNs for image fields of greater that 100 × 100 pixels without any loss of pattern information.

Experimental Support of Argument-based Syntactic Computation

Linguistic theory, cognitive, information, and mathematical modeling are all useful while we attempt to achieve a better understanding of the Language Faculty (LF). This cross-disciplinary approach will eventually lead to the identification of the key principles applicable in the systems of Natural Language Processing. The present work concentrates on the syntax-semantics interface. We start from recursive definitions and application of optimization principles, and gradually develop a formal model of syntactic operations. The result – a Fibonacci- like syntactic tree – is in fact an argument-based variant of the natural language syntax. This representation (argument-centered model, ACM) is derived by a recursive calculus that generates a mode which connects arguments and expresses relations between them. The reiterative operation assigns primary role to entities as the key components of syntactic structure. We provide experimental evidence in support of the argument-based model. We also show that mental computation of syntax is influenced by the inter-conceptual relations between the images of entities in a semantic space.

Computation of some Differential Operators in Toric Coordinates

Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.

JSONYA/FN: Functional Computation in JSON

Functional programming has a lot to offer to the developers of global Internet-centric applications, but is often applicable only to a small part of the system or requires major architectural changes. The data model used for functional computation is often simply considered a consequence of the chosen programming style, although inappropriate choice of such model can make integration with imperative parts much harder. In this paper we do the opposite: we start from a data model based on JSON and then derive the functional approach from it. We outline the identified principles and present Jsonya/fn — a low-level functional language that is defined in and operates with the selected data model. We use several Jsonya/fn implementations and the architecture of a recently developed application to show that our approach can improve interoperability and can achieve additional reuse of representations and operations at relatively low cost. ACM Computing Classification System (1998): D.3.2, D.3.4.

Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

The Methodology of the Subsistence Minimum Calculation for Developing Countries and its Computation on the Georgian Example

This article shows the social importance of subsistence minimum in Georgia. The methodology of its calculation is also shown. We propose ways of improving the calculation of subsistence minimum in Georgia and how to extend it for other developing countries. The weights of food and non-food expenditures in the subsistence minimum baskets are essential in these calculations. Daily consumption value of the minimum food basket has been calculated too. The average consumer expenditures on food supply and the other expenditures to the share are considered in dynamics. Our methodology of the subsistence minimum calculation is applied for the case of Georgia. However, it can be used for similar purposes based on data from other developing countries, where social stability is achieved, and social inequalities are to be actualized. ACM Computing Classification System (1998): H.5.3, J.1, J.4, G.3.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^