Effects of math anxiety on student success in higher education

This study examines whether math anxiety and negative attitudes toward mathematics have an effect on university students" academic achievement in a methodological course forming part of their degree. A total of 193 students were presented with a math anxiety test and some questions about their enjoyment, self-confidence and motivation regarding mathematics, and their responses were assessed in relation to the grades they had obtained during continuous assessment on a course entitled"Research Design". Results showed that low performance on the course was related to math anxiety and negative attitudes toward mathematics. We suggest that these factors may affect students" performance and should therefore be taken into account in attempts to improve students" learning processes in methodological courses of this kind.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

Computer-aided system for morphometric mandibular index computation (Using dental panoramic radiographs)

Objective: We propose and validate a computer aided system to measure three different mandibular indexes: cortical width, panoramic mandibular index and, mandibular alveolar bone resorption index. Study Design: Repeatability and reproducibility of the measurements are analyzed and compared to the manual estimation of the same indexes. Results: The proposed computerized system exhibits superior repeatability and reproducibility rates compared to standard manual methods. Moreover, the time required to perform the measurements using the proposed method is negligible compared to perform the measurements manually. Conclusions: We have proposed a very user friendly computerized method to measure three different morphometric mandibular indexes. From the results we can conclude that the system provides a practical manner to perform these measurements. It does not require an expert examiner and does not take more than 16 seconds per analysis. Thus, it may be suitable to diagnose osteoporosis using dental panoramic radiographs.

Implementation of the Rijndael-AES algorithm on a Sage-Math worksheet

La principal motivació d'aquest treball ha estat implementar l'algoritme Rijndael-AES en un full Sage-math, paquet de software matemàtic de lliure distribució i en actual desenvolupament, aprofitant les seves eines i funcionalitats integrades.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Computer-aided system for morphometric mandibular index computation (Using dental panoramic radiographs)

Objective: We propose and validate a computer aided system to measure three different mandibular indexes: cortical width, panoramic mandibular index and, mandibular alveolar bone resorption index. Study Design: Repeatability and reproducibility of the measurements are analyzed and compared to the manual estimation of the same indexes. Results: The proposed computerized system exhibits superior repeatability and reproducibility rates compared to standard manual methods. Moreover, the time required to perform the measurements using the proposed method is negligible compared to perform the measurements manually. Conclusions: We have proposed a very user friendly computerized method to measure three different morphometric mandibular indexes. From the results we can conclude that the system provides a practical manner to perform these measurements. It does not require an expert examiner and does not take more than 16 seconds per analysis. Thus, it may be suitable to diagnose osteoporosis using dental panoramic radiographs

On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

Abnormal Error Monitoring in Math-Anxious Individuals: Evidence from Error-Related Brain Potentials.

This study used event-related brain potentials to investigate whether math anxiety is related to abnormal error monitoring processing. Seventeen high math-anxious (HMA) and seventeen low math-anxious (LMA) individuals were presented with a numerical and a classical Stroop task. Groups did not differ in terms of trait or state anxiety. We found enhanced error-related negativity (ERN) in the HMA group when subjects committed an error on the numerical Stroop task, but not on the classical Stroop task. Groups did not differ in terms of the correct-related negativity component (CRN), the error positivity component (Pe), classical behavioral measures or post-error measures. The amplitude of the ERN was negatively related to participants" math anxiety scores, showing a more negative amplitude as the score increased. Moreover, using standardized low resolution electromagnetic tomography (sLORETA) we found greater activation of the insula in errors on a numerical task as compared to errors in a nonnumerical task only for the HMA group. The results were interpreted according to the motivational significance theory of the ERN.

Reactive Recruitment of Attentional Control in Math Anxiety: An ERP Study of Numeric Conflict Monitoring and Adaptation

This study uses event-related brain potentials (ERPs) to investigate the electrophysiological correlates of numeric conflict monitoring in math-anxious individuals, by analyzing whether math anxiety is related to abnormal processing in early conflict detection (as shown by the N450 component) and/or in a later, response-related stage of processing (as shown by the conflict sustained potential; Conflict-SP). Conflict adaptation effects were also studied by analyzing the effect of the previous trial"s congruence in current interference. To this end, 17 low math-anxious (LMA)and 17 high math-anxious (HMA) individuals were presented with a numerical Stroop task. Groups were extreme in math anxiety but did not differ in trait or state anxiety or in simple math ability. The interference effect of the current trial (incongruent-congruent) and the interference effect preceded by congruence and by incongruity were analyzed both for behavioral measures and for ERPs. A greater interference effect was found for response times in the HMA group than in the LMA one. Regarding ERPs, the LMA group showed a greater N450 component for the interference effect preceded by congruence than when preceded by incongruity, while the HMA group showed greater Conflict-SP amplitude for the interference effect preceded by congruence than when preceded by incongruity. Our study showed that the electrophysiological correlates of numeric interference in HMA individuals comprise the absence of a conflict adaptation effect in the first stage of conflict processing (N450) and an abnormal subsequent up-regulation of cognitive control in order to overcome the conflict (Conflict-SP). More concretely, our study shows that math anxiety is related to a reactive and compensatory recruitment of control resources that is implemented only when previously exposed to a stimuli presenting conflicting information

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

Anàlisi del sistema operatiu RTLinux e implementació d'un entorn de desenvolupament de tasques en temps real (aplicat al control de processos)

El projecte "Anàlisi del sistema operatiu RTLinux i implementació d'un entorn de desenvolupament de tasques en temps real" analitza la possibilitat de crear un entorn de desenvolupament de tasques en temps real per poder crear sistemes de control complex, tot això mitjançant codi lliure. Inicialment es fa un aprenentatge sobre el concepte de temps real, després s'elegeix el sistema operatiu en temps real RTLinux per a crear l'entorn de desenvolupament utilitzant el llenguatge de programació Tcl/Tk. Es creen un conjunt d'aplicacions (pel control computacional) per estudiar la viabilitat de la construcció de l'entorn desitjat per facilitar la tasca de l'usuari final. Aquest projecte obre multitud de possibles camins a continuar: comunicació remota, implementació de planificadors, estudi de controladors, etc.

Càlcul distribuït en BOINC per el trencament de l'algorisme RC5

Aquest projecte té com a objectiu participar en el desafiament d'RSA Laboratories corresponent a trencar el criptosistema RC5-32-12-9 proposat. Per realitzar-ho s'ha triat realitzar un atac per força bruta, mitjançant el càlcul distribuït i, més concretament, utilitzant la Public Resource Computing. La plataforma escollida és la Berkeley Open Infrastructure for Network Computing (BOINC), coneguda per la seva utilització en grans projectes com ara SETI@home. En aquest projecte es posa en funcionament la infraestructura i es desenvolupen les aplicacions necessàries per iniciar els càlculs que haurien de permetre el trencament del criptosistema.

Análisis de rendimiento de aplicaciones paralelas de memoria compartida: problema N-body

Este trabajo analiza el rendimiento de cuatro nodos de cómputo multiprocesador de memoria compartida para resolver el problema N-body. Se paraleliza el algoritmo serie, y se codifica usando el lenguaje C extendido con OpenMP. El resultado son dos variantes que obedecen a dos criterios de optimización diferentes: minimizar los requisitos de memoria y minimizar el volumen de cómputo. Posteriormente, se realiza un proceso de análisis de las prestaciones del programa sobre los nodos de cómputo. Se modela el rendimiento de las variantes secuenciales y paralelas de la aplicación, y de los nodos de cómputo; se instrumentan y ejecutan los programas para obtener resultados en forma de varias métricas; finalmente se muestran e interpretan los resultados, proporcionando claves que explican ineficiencias y cuellos de botella en el rendimiento y posibles líneas de mejora. La experiencia de este estudio concreto ha permitido esbozar una incipiente metodología de análisis de rendimiento, identificación de problemas y sintonización de algoritmos a nodos de cómputo multiprocesador de memoria compartida.

Optimització i implementació en Simulink de l'adquisició d'un senyal GPS amb blocs FFT

Aquest projecte es tracta de la optimització i la implementació de l’etapa d’adquisició d’un receptor GPS. També inclou una revisió breu del sistema GPS i els seus principis de funcionament. El procés d’adquisició s’ha estudiat amb detall i programat en els entorns de treball Matlab i Simulink. El fet d’implementar aquesta etapa en dos entorns diferents ha estat molt útil tant de cara a l’aprenentatge com també per la comprovació dels resultats obtinguts. El principal objectiu del treball és el disseny d’un model Simulink que es capaç d’adquirir una senyal capturada amb hardware real. En realitat, s’han fet dues implementacions: una que utilitza blocs propis de Simulink i l’altra que utilitza blocs de la llibreria Xilinx. D’aquesta manera, posteriorment, es facilitaria la transició del model a la FPGA utilitzant l’entorn ISE de Xilinx. La implementació de l’etapa d’adquisició es basa en el mètode de cerca de fase de codi en paral·lel, el qual empra la operació correlació creuada mitjançant la transformada ràpida de Fourier (FFT). Per aquest procés es necessari realitzar dues transformades (per a la senyal entrant i el codi de referència) i una antitransformada de Fourier (per al resultat de la correlació). Per tal d’optimitzar el disseny s’utilitza un bloc FFT, ja que tres blocs consumeixen gran part dels recursos d’una FPGA. En lloc de replicar el bloc FFT, en el model el bloc és compartit en el temps gràcies a l’ús de buffers i commutadors, com a resultat la quantitat de recursos requerits per una implementació en una FPGA es podria reduir considerablement.