Supporting the reuse of effective CSCL learning designs through social structure representations

Distance and blended collaborative learning settings are usually characterized by different social structures defined in terms of groups' number, dimension, and composition; these structures are variable and can change within the same activity. This variability poses additional complexity to instructional designers, when they are trying to develop successful experiences from existing designs. This complexity is greatly associated with the fact that learning designs do not render explicit how social structures influenced the decisions of the original designer, and thus whether the social structures of the new setting could preclude the effectiveness of the reused design. This article proposes the usage of new representations (social structure representations, SSRs) able to support unskilled designers in reusing existing learning designs, through the explicit characterization of the social structures and constraints embedded either by the original designers or the reusing teachers, according to well-known principles of good collaborative learning practice. The article also describes an evaluation process that involved university professors, as well as the main findings derived from it. This process supported the initial assumptions about the effectiveness of SSRs, with significant evidence from both qualitative and qualitative data.

Optimum pilot overhead in wireless communication: a unified treatment of continuous and block-fading channels

The optimization of the pilot overhead in wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. It is also shown that the widely-usedblock fading model is a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency. Furthermore, it is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with thenormalized Doppler frequency multiplied by the number of transmit antennas.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

Ignoring information in binary choice with continuous variables: When is less 'more'?

When can a single variable be more accurate in binary choice than multiple sources of information? We derive analytically the probability that a single variable (SV) will correctly predict one of two choices when both criterion and predictor are continuous variables. We further provide analogous derivations for multiple regression (MR) and equal weighting (EW) and specify the conditions under which the models differ in expected predictive ability. Key factors include variability in cue validities, intercorrelation between predictors, and the ratio of predictors to observations in MR. Theory and simulations are used to illustrate the differential effects of these factors. Results directly address why and when one-reason decision making can be more effective than analyses that use more information. We thus provide analytical backing to intriguing empirical results that, to date, have lacked theoretical justification. There are predictable conditions for which one should expect less to be more.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Continuous phase shift of sinusoidal signals using injection locked oscillators

This work presents an alternative to generate continuous phase shift of sinusoidal signals based on the use of super harmonic injection locked oscillators (ILO). The proposed circuit is a second harmonic ILO with varactor diodes as tuning elements. In the locking state, by changing the varactor bias, a phase shift instead of a frequency shift is observed at the oscillator output. By combining two of these circuits, relative phases up to 90 could be achieved. Two prototypes of the circuit have been implemented and tested, a hybrid version working in the range of 200-300 MHz and a multichip module (MCM) version covering the 900¿1000 MHz band.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Continuous-time random-walk model for financial distributions

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollardeutsche mark future exchange, finding good agreement between theory and the observed data.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Optimization of analytical methods for the assessment of the quality of fats and oils used in continuous deep fat frying

La aplicabilidad, repetibilidad y capacidad de diferentes métodos de análisis para discriminar muestras de aceites con diferentes grados de oxidación fueron evaluadas mediante aceites recogidos en procesos de fritura en continuo en varias empresas españolas. El objetivo de este trabajo fue encontrar métodos complementarios a la determinación del índice de acidez para el control de calidad rutinario de los aceites de fritura empleados en estas empresas. La optimización de la determinación de la constante dieléctrica conllevó una clara mejora de la variabilidad. No obstante, excepto en el caso del índice del ATB, el resto de métodos ensayados mostraron una menor variabilidad. La determinación del índice del ATB fue descartada ya que su sensibilidad fue insuficiente para discriminar entre aceites con diferente grado de oxidación. Los diferentes parámetros de alteración determinados en los aceites de fritura mostraron correlaciones significativas entre el índice de acidez y varios parámetros de oxidación diferentes, como la constante dieléctrica, el índice de p-anisidina, la absorción al ultravioleta y el contenido en polímeros de los triacilgliceroles. El índice de acidez solo evalúa la alteración hidrolítica, por lo que estos parámetros aportan información complementaria al evaluar la alteración termooxidativa.