Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization

Hensel’s symbolic lifting is a highly effective method for the solution of a general or structured (e.g. Toeplitz or Hankel) linear system of equations with integer or rational coefficients of bounded length. It can handle ill conditioned inputs, for which numerical methods become costly. Lifting amounts to recursive multiplications by vectors of the input coefficient matrices and its precomputed inverse modulo a fixed integer s. Such multiplications only involve small numbers of data movements and arithmetic operations with bounded precision. The known methods for precomputation of the inverse are more costly, however; in particular they involve more data movements. As our remedy for this bottleneck stage we create an auxiliary matrix sharing its inverse modulo s with the input matrix, and we readily compute this inverse by applying numerical iterative refinement, which is a numerical counterpart of lifting. In the case of general unstructured as well as Toeplitz, Hankel, and other popular structured inputs our hybrid algorithms involve a small number of data movements and optimal number of Boolean (that is bitwise) operations (up to a logarithmic factor). We extend the algorithms to nearly optimal computation of polynomial greatest common divisors (gcds), least common multiples (lcms) and Padé approximations, as well as the Berlekamp-Massey reconstruction of linear recurrences. We also cover Newton’s lifting for matrix inversion, specialize it to the case of structured input, and combine it with Hensel’s to enhance the overall efficiency. Our initialization techniques work for Newton’s lifting as well. Furthermore we extend all our lifting algorithms to allow their initialization modulo powers of two, thus implementing them in the binary base.     

A family of variational principles for linear micromorphic elasticity

Via He’s semi-inverse method, a family of generalized variational principles of micromorphic elasticity is established directly from the field equations and boundary conditions. This paper aims at providing a more complete theoretical basis for the finite element applications and other direct variational methods such as Ritz’s, Trefftz’s and Kantorovitch’s methods.     

The Dirichlet problem for a 3D elliptic equation with two singular coefficients

In the present work, we investigate the Dirichlet problem for a three-dimensional (3D) elliptic equation with two singular coefficients. We find four fundamental solutions of the equation, containing hypergeometric functions of Appell. Then using an “a-b-c” method, the uniqueness for the solution of the Dirichlet problem is proved. Applying a method of Green’s function, we are able to find the solution of the problem in an explicit form. Moreover, decomposition formulas, formulas of differentiation and some adjacent relations for Appell’s hypergeometric functions were used in order to find the explicit solution for the formulated problem.     

The effect of nonhuman’s external regulation on children’s responses to detect children with developmental problems (DP) associated with the natural development of self-regulation during learning tasks

The present study sought to examine the effect of the nonhuman’s external regulation on children’s responses during learning tasks to detect children with developmental problems (DP) associated with the natural development process of self-regulation. The material was an isolated, computer-based learning system that acts as a standalone learning environment and used by 100 preschool children, which were randomly selected from ten preschools without revising their medical files. Participants were classified by the system itself during learning progression in three essential groups based on Aginian’s zone of children regulation (ZCR), which is “the equilibrium point in the self-regulation’s development process that controls the child to be either a self-Vygotskyian’s learner, self-Piagetian’s learner, or self-Aginian’s learner during learning tasks” ( Agina, Kommers, & Steehouder, 2011d). The results showed that the preschool children can spontaneously do diagnostic tests during learning tasks and the nonhuman external regulator was able to analysis children’s responses that, in turn, used for detecting those children with DP. This result was practically confirmed by revising all children’s medical files that matched the final judgment of the nonhuman external regulator. However, the results confirmed that the natural development of self-regulation was fluctuated among three paradoxical views (Vygotskyian vs. Piagetian vs. Aginian).     

Symmetric cryptographic solution to Yao’s millionaires’ problem and an evaluation of secure multiparty computations

Secure multiparty computation has become a central research focus in the international cryptographic community and in the future likely will represent an integral part of computing science. Protocols for Yao’s millionaires’ problem provide the building blocks for many secure multiparty computation protocols, which makes their efficiency critical. Unfortunately, all known protocols for Yao’s millionaires’ problem employ public key cryptography and thus are inefficient. This article constructs a new efficient solution to Yao’s millionaires’ problem based on symmetric cryptography. We first develop an efficient protocol for set-inclusion problems, which has independent interest for secure multiparty computations. The privacy-preserving property of the solution is demonstrated by a well-accepted simulation paradigm. To compare the security levels of different solutions, we propose a new security paradigm that quantitatively captures the security levels of different solutions and can determine which secure multiparty computation solution is preferable. This article thus provides an important supplement to the simulation paradigm. Together with the simulation paradigm, it offers a complete security evaluation benchmark for multiparty computations.     

Three-dimensional quantum simulation of multigate nanowire field effect transistors

Detailed numerical methods for the three-dimensional quantum simulation of the multigate nanowire field effect transistors in the ballistic transport regime are presented in this work. The device has been modeled based on the effective mass theory and the non-equilibrium Green’s function formalism, and its simulation consists of solutions of the three-dimensional Poisson’s equation, two-dimensional Schrödinger equations on the cross-sectional planes, and one-dimensional transport equation. Details on numerical techniques for each of the simulation steps are described, with a special attention to the solution of the most CPU demanding two-dimensional Schrödinger equation.     

Élie Cartan’s geometrical vision or how to avoid expression swell

The aim of the paper is to demonstrate the superiority of Cartan’s method over direct methods based on differential elimination for handling otherwise intractable equivalence problems. In this sense, using our implementation of Cartan’s method, we establish two new equivalence results. We establish when a system of second order ODEs is equivalent to flat system (second derivations are zero), and when a system of holomorphic PDEs with two independent variables and one dependent variable is flat. We consider the problem of finding transformation that brings a given equation to the target one. We shall see that this problem becomes algebraic when the symmetry pseudogroup of the target equation is zerodimensional. We avoid the swelling of the expressions, by using non-commutative derivations adapted to the problem.     

The effect of nonhuman’s external regulation on young children’s self-regulation to regulate their own process of learning

The present study sought to examine the effect of nonhuman’s external regulation on children’s self-regulation to regulate their own process of learning and to what extent did children succeed in terms of application when they talk and think while act alone with nonhuman’s external regulator. The Aginian’s methodology (, , ,  and ) that used an isolated, computer-based learning system and acts as a standalone learning environment with special set of tasks was used by hundred healthy preschool children. The results showed that young children were able to regulate their own process of learning and engage with their full free-will without the need of their real teacher’s regulation. The conclusion provided evidence that the verbalization of thinking aloud should occur spontaneously by nature, the nonhuman’s external regulation has a positive effect on young children’s development when they act with their full free-will, and has a positive effect on their behavior either.     

Control of a bicycle using virtual holonomic constraints

The paper studies the problem of making Getz’s bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method. Specifically, a VHC is enforced making the roll angle of the bicycle become a function of the bicycle’s position along the curve. It is shown that the VHC can be automatically generated as a periodic solution of a scalar periodic differential equation, which we call virtual constraint generator. Finally, it is shown that if the curve is sufficiently long as compared to the height of the bicycle’s center of mass and its wheel base, then the enforcement of a suitable VHC makes the bicycle traverse the curve with a steady-state speed profile which is periodic and independent of initial conditions. An outcome of this work is a proof that the constrained dynamics of a Lagrangian control system subject to a VHC are generally not Lagrangian.     

Online advertising on popular children’s websites: Structural features and privacy issues

This study examined advertisements placed on popular children’s websites. A total of 117 commercial children’s websites, 933 unique ads and 813 advertising websites were included in the sample. Results show that a majority of children’s websites carried advertisements, a third of which were Google ads. Less than half (47%) of the children’s websites and about a quarter (24%) of the advertising websites complied with COPPA when they collected personal information from children. Implications for children’s online safety are discussed.     

The effect of nonhuman’s external regulation on detecting the natural development process of young children’s self-regulation during learning tasks

The present study explored the effect of nonhuman’s external regulation on children’s natural development of self-regulation and the effect of each natural developed class on children’s spontaneous thinking aloud and satisfaction. The Aginian’s methodology (Agina et al., 2011a) that relied on special computer agents for the external regulation, measuring self-regulation and children’s satisfaction, and producing the final results in points was used with 40 preschool children, which were divided into classes based on their natural development of self-regulation during learning tasks. The results showed that children who followed Piagetian’s view were outperforming children who followed Vygotskyian’s view and Aginian’s view, which is a new psychological view generated by computer indicates that the child either followed unknown class of self-regulation’s natural development or the child holds an ambiguous psychological problem. The results also showed that the relationship between children’s spontaneous thinking aloud and children’s self-regulation is a reverse. The supplemental analysis showed that computer, as a nonhuman external regulator, can identify those children who hold psychological problems and can integrate the net signed of self-regulation of each child at each task through embedding the mathematics integration where the computer becomes fully conscious with all the occurrences of children’s behavioral regulation.     

The effect of the nonhuman external regulator’s answer-until-correct (AUC) versus knowledge-of-result (KR) task feedback on children’s behavioral regulation during learning tasks

The present study was conducted to shed a new light on the nonhuman’s external regulation effect on children’s behavioral regulation through investigating the effect of the computer’s task feedback answer-until-correct (AUC) versus knowledge-of-result (KR) with 40 preschool children (boys/girls) divided into AUC-Condition versus KR-Condition. The Aginian’s methodology (Agina, Kommers, & Steehouder, 2010) with the latest updates (Agina, Kommers, & Steehouder, 2011) was used, which involves an isolated, computer-based learning system with three different computer’s agents for measuring self-regulation as a function of the task level selection, self-regulation as a function of task precision, and special agent for evaluating children’s satisfaction. It was hypothesized that AUC-Condition will outperform KR-Condition in verbalization intensity, manifested self-regulation, and the degree of satisfaction. Despite the results were not confirmed the hypothesis, the results generated by the game were consistent with the statistical results in which this consistency increases, to a great extent, the reliability of the Aginian’s measurements. However, both results were not confirmed Vygotsky’s view or Piaget’s view of self-regulation development as both concluded that thinking aloud and self-regulation have a reverse relationship and, therefore, thinking aloud, per se, can be used to explore the problems the children may not agree to talk about.     

Animated solid model of the lung constructed from unsynchronized MR sequential images

This work discusses a 4D lung reconstruction method from unsynchronized MR sequential images. The lung, differently from the heart, does not have its own muscles, turning impossible to see its real movements. The visualization of the lung in motion is an actual topic of research in medicine. CT (Computerized Tomography) can obtain spatio-temporal images of the heart by synchronizing with electrocardiographic waves. The FOV of the heart is small when compared to the lung’s FOV. The lung’s movement is not periodic and is susceptible to variations in the degree of respiration. Compared to CT, MR (Magnetic Resonance) imaging involves longer acquisition times and it is not possible to obtain instantaneous 3D images of the lung. For each slice, only one temporal sequence of 2D images can be obtained. However, methods using MR are preferable because they do not involve radiation. In this paper, based on unsynchronized MR images of the lung an animated B-Rep solid model of the lung is created. The 3D animation represents the lung’s motion associated to one selected sequence of MR images. The proposed method can be divided in two parts. First, the lung’s silhouettes moving in time are extracted by detecting the presence of a respiratory pattern on 2D spatio-temporal MR images. This approach enables us to determine the lung’s silhouette for every frame, even on frames with obscure edges. The sequence of extracted lung’s silhouettes are unsynchronized sagittal and coronal silhouettes. Using our algorithm it is possible to reconstruct a 3D lung starting from a silhouette of any type (coronal or sagittal) selected from any instant in time. A wire-frame model of the lung is created by composing coronal and sagittal planar silhouettes representing cross-sections. The silhouette composition is severely underconstrained. Many wire-frame models can be created from the observed sequences of silhouettes in time. Finally, a B-Rep solid model is created using a meshing algorithm. Using the B-Rep solid model the volume in time for the right and left lungs were calculated. It was possible to recognize several characteristics of the 3D real right and left lungs in the shaded model.     

Conditional copulas, association measures and their applications

One way to model a dependence structure is through the copula function which is a mean to capture the dependence structure in the joint distribution of variables. Association measures such as Kendall’s tau or Spearman’s rho can be expressed as functionals of the copula. The dependence structure between two variables can be highly influenced by a covariate, and it is of real interest to know how this dependence structure changes with the value taken by the covariate. This motivates the need for introducing conditional copulas, and the associated conditional Kendall’s tau and Spearman’s rho association measures. After the introduction and motivation of these concepts, two nonparametric estimators for a conditional copula are proposed and discussed. Then nonparametric estimates for the conditional association measures are derived. A key issue is that these measures are now looked at as functions in the covariate. The performances of all estimators are investigated via a simulation study which also includes a data-driven algorithm for choosing the smoothing parameters. The usefulness of the methods is illustrated on two real data examples.     

A comparison of regression methods for remote tracking of Parkinson’s disease progression

Remote patient tracking has recently gained increased attention, due to its lower cost and non-invasive nature. In this paper, the performance of Support Vector Machines (SVM), Least Square Support Vector Machines (LS-SVM), Multilayer Perceptron Neural Network (MLPNN), and General Regression Neural Network (GRNN) regression methods is studied in application to remote tracking of Parkinson’s disease progression. Results indicate that the LS-SVM provides the best performance among the other three, and its performance is superior to that of the latest proposed regression method published in the literature.     

Approximate analytic solution of the Dirichlet problems for Laplace’s equation in planar domains by a perturbation method

In this paper, we propose a regular perturbation method to obtain approximate analytic solutions of exterior and interior Dirichlet problems for Laplace’s equation in planar domains. This method, starting from a geometrical perturbation of these planar domains, reduces our problems to a family of classical Dirichlet problems for Laplace’s equation in a circle. Numerical examples are given and comparisons are made with the solutions obtained by other approximation methods.     

Morley’s theorem revisited: Origami construction and automated proof

Morley’s theorem states that for any triangle, the intersections of its adjacent angle trisectors form an equilateral triangle. The construction of Morley’s triangle by the straightedge and compass method is impossible because of the well-known impossibility result for angle trisection. However, by origami, the construction of an angle trisector is possible, and hence that of Morley’s triangle. In this paper we present a computational origami construction of Morley’s triangle and an automated correctness proof of the generalized Morley’s theorem.During the computational origami construction, geometrical constraints in symbolic representation are generated and accumulated. Those constraints are then transformed into algebraic forms, i.e. a set of polynomials, which in turn are used to prove the correctness of the construction. The automated proof is based on the Gröbner bases method. The timings of the experiments of the Gröbner bases computations for our proofs are given. They vary greatly depending on the origami construction methods, the algorithms for the Gröbner bases computation, and variable orderings.     

Interactive genetic algorithms with individual’s fuzzy fitness

Interactive genetic algorithms are effective methods to solve an optimization problem with implicit or fuzzy indices, and have been successfully applied to many real-world optimization problems in recent years. In traditional interactive genetic algorithms, many researchers adopt an accurate number to express an individual’s fitness assigned by a user. But it is difficult for this expression to reasonably reflect a user’s fuzzy and gradual cognitive to an individual. We present an interactive genetic algorithm with an individual’s fuzzy fitness in this paper. Firstly, we adopt a fuzzy number described with a Gaussian membership function to express an individual’s fitness. Then, in order to compare different individuals, we generate a fitness interval based on α-cut set, and obtain the probability of individual dominance by use of the probability of interval dominance. Finally, we determine the superior individual in tournament selection with size two based on the probability of individual dominance, and perform the subsequent evolutions. We apply the proposed algorithm to a fashion evolutionary design system, a typical optimization problem with an implicit index, and compare it with two interactive genetic algorithms, i.e., an interactive genetic algorithm with an individual’s accurate fitness and an interactive genetic algorithm with an individual’s interval fitness. The experimental results show that the proposed algorithm is advantageous in alleviating user fatigue and looking for user’s satisfactory individuals.     

“Who vs. Whom AND Where Should We Go Through?”: A reflection towards clarifying the effect of media and entertainment on children’s development for future research

Despite the massive body of research on the effect of media and entertainment on children’s development, especially through computer that clearly stands as the most interactive and appealing medium not only between children but also among people, the research, up to date, still lacks a true understanding of the powerful effect of the communication between children, generally all users, and the content of the entertainment. Thus, the present reflection paper was conducted towards clarifying the directions of the future research concerning the effect of media and entertainment on young children’s development based on the literature’s theoretical critiques. However, the present paper only paid attention to the most effective studies in the literature given the fact that many and many studies are just repeating what already available in the literature. The conclusion came up with two main directions of the future research on children’s development, (1) media as a quasi-human’s external regulator and (2) entertainment as a context of the learning process. Both directions yielded a new phase of learning (Self-Arousal Learning (SAL)) that the future research has to take it into account and consideration. The main topics of the SAL were stated as guidance for the main two directions of the future research.