Entrevista al profesor Alan Bishop

En este artículo, se presentan las ideas del profesor Alan Bishop sobre la Etnomatemática, sus objetivos, su metodología, la relación entre Etnomatemática y Educación Matemática y la enseñanza de las matemáticas en aulas multiculturales. Esta entrevista fue realizada el miércoles, 29 de noviembre de 2006 en el Seminario de formación avanzada: tres fases básicas en un estudio de investigación doctoral en educación. Universidad Distrital Francisco José de Caldas. Bogotá, Colombia.

Estudio sobre diferencias de género en el aula de matemáticas

Este proyecto indagó sobre las relaciones de género entre las y los profesores y las y los estudiantes en el aula de matemáticas, y cómo éstas influyen en el desempeño académico de ellos y ellas. Esta investigación se realizó en dos instituciones mixtas de la ciudad de San Juan de Pasto, y la información fue recolectada por medio de entrevistas y observaciones dentro del aula de clase, las cuales se analizaron desde un punto de vista cualitativo y cuantitativo. Finalmente, se espera que esta investigación contribuya a crear conciencia sobre esta problemática y a mejorar las relaciones en el salón de clase de matemáticas entre docentes y estudiantes, tomando en cuenta las diferencias de género.

El problema isoperimétrico en la arquitectura, literatura, música…, en la naturaleza

Siempre me ha interesado la historia de las matemáticas cuando la resolución de problemas ha sido su columna vertebral. Ahora que estamos en el 2000, tenemos muy presente aquella famosa lista de 23 problemas dados por Hilbert hace 100 años.

Números trascendentes: desarrollo histórico

Sabemos que los números trascendentes son aquellos que no son raíces de ecuaciones algebraicas con coeficientes racionales. Su origen, el origen de la trascendencia, se remonta a los griegos con la aparición de problemas como la duplicación del cubo, trisección del ángulo y cuadratura del círculo irresolubles con regla y compás. Entre 1844 fecha en la que nace el primer número trascendente y 1900 fecha en la que Hilbert plantea el llamado séptimo problema de Hilbert cuya solución, obtenida en 1934 por Gelfand y Scheider, a partir de los trabajos de Polya en 1914 y Siegel en 1929, abren las puertas de una nueva era para esta teoría. En este intervalo de tiempo se produjeron numerosos eventos importantes que vamos a tratar de desarrollar.

Model-based pilot and data power adaptation in psam with periodic delayed feedback

We consider the optimum design of pilot-symbol-assisted modulation (PSAM) schemes with feedback. The received signal is periodically fed back to the transmitter through a noiseless delayed link and the time-varying channel is modeled as a Gauss-Markov process. We optimize a lower bound on the channel capacity which incorporates the PSAM parameters and Kalman-based channel estimation and prediction. The parameters available for the capacity optimization are the data power adaptation strategy, pilot spacing and pilot power ratio, subject to an average power constraint. Compared to the optimized open-loop PSAM (i.e., the case where no feedback is provided from the receiver), our results show that even in the presence of feedback delay, the optimized power adaptation provides higher information rates at low signal-to-noise ratios (SNR) in medium-rate fading channels. However, in fast fading channels, even the presence of modest feedback delay dissipates the advantages of power adaptation.

Jung’s cultural writing: spiral essays and performing symbols (in literature)

Performance is a key ingredient of Jung’s writings on culture and of the function of the Jungian symbol in literature. This paper will compare and contrast Jung’s performance of cultural analysis and healing in his essays with the way his notion of the symbol works in literature to knit the individual psyche into the collective. It will explore Jung’s unique essay form of the spiral as a literary innovation, and look at the way a Jungian reading of literary reveals a significant contribution to cultural studies. [From the Author]

Antimony revisited

Antimony,symbol Sb,one of the earliest elements to be recognised, demonstrates that there is much intriguing chemistry to be found in the nether regions of the Periodic Table. Ametalloid with a strong affinity for sulfur, antimony is pharmacologically active and hasbeen used in medicines, but is also a poison.

Communication system model for information rate evaluation of differential detection over time-varying channels

A communication system model for mutual information performance analysis of multiple-symbol differential M-phase shift keying over time-correlated, time-varying flat-fading communication channels is developed. This model is a finite-state Markov (FSM) equivalent channel representing the cascade of the differential encoder, FSM channel model and differential decoder. A state-space approach is used to model channel phase time correlations. The equivalent model falls in a class that facilitates the use of the forward backward algorithm, enabling the important information theoretic results to be evaluated. Using such a model, one is able to calculate mutual information for differential detection over time-varying fading channels with an essentially finite time set of correlations, including the Clarke fading channel. Using the equivalent channel, it is proved and corroborated by simulations that multiple-symbol differential detection preserves the channel information capacity when the observation interval approaches infinity.

Mutual information performance of differential MPSK detection over time-varying channels

This paper provides mutual information performance analysis of multiple-symbol differential WSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals

Diversity of functional groups in the vegetation sandy seashore of the Grande, Anclitas and Caguamas Cays (Jardines de la Reina Archipelago, Cuba)

Sandy shores are known to be extreme ecosystems where the vegetation has evolved many morphological and physiological adaptations for its survival. With the aim of identify possible relationships between the vegetation´s functional diversity with abiotic factors and its corresponding quantification, we collected data on the abundance and richness of the sandy coast vegetation complex in Grande, Anclitas and Caguamas keys. Its flora is largely characterized by the dominance of hemicryptophytes and chamaephytes plants with nanophyllous leaves and displaying dispersal syndromes such as zoochory and anemochory. However, the functional groups´ richness, in the present study, varies from one key to another. Functional diversity is similar between the wet and dry seasons, and its spatial variation is influenced by the interplay of the set of abiotic factors herein studied.

Entanglement distribution with global control in a star-shaped multi-splitter

Distributed quantum information processing (QIP) is a promising way to bypass problems due to unwanted interactions between elements. However, this strategy presupposes the engineering of protocols for remote processors. In many of them, pairwise entanglement is a key resource. We study a model which distributes entanglement among elements of a delocalized network without local control. The model is efficient both in finite- and infinite-dimensional Hilbert spaces. We suggest a setup of electromechanical systems to implement our proposal.

REporting and calibration of post-bomb C-14 data

The definitive paper by Stuiver and Polach (1977) established the conventions for reporting of 14C data for chronological and geophysical studies based on the radioactive decay of 14C in the sample since the year of sample death or formation. Several ways of reporting 14C activity levels relative to a standard were also established, but no specific instructions were given for reporting nuclear weapons testing (post-bomb) 14C levels in samples. Because the use of post-bomb 14C is becoming more prevalent in forensics, biology, and geosciences, a convention needs to be adopted. We advocate the use of fraction modern with a new symbol F14C to prevent confusion with the previously used Fm, which may or may not have been fractionation corrected. We also discuss the calibration of post-bomb 14C samples and the available datasets and compilations, but do not give a recommendation for a particular dataset.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel

An entangled two-mode coherent state is studied within the framework of 2 x 2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.

Quantum teleportation via mixed two-mode squeezed states in the coherent-state representation

Quantum teleportation for continuous variables is generally described in phase space by using the Wigner functions. We study quantum teleportation via a mixed two-mode squeezed state in Hilbert-Schmidt space by using the coherent-state representation and operators. This shows directly how the teleported state is related to the original state.