Proof: otra vuelta de tuerca

En marzo de 2006 han coincidido en nuestras pantallas los estrenos de un largometraje y de una serie televisiva donde las Matemáticas tienen un papel estelar. Se trata de La verdad oculta (singular traducción del título original Proof) y de la serie Numb3rs. En ambos casos hay un alto nivel de producción, con directores y actores famosos, y con una puesta en escena y un montaje cuidados; pero divergen en su enfoque de las matemáticas en relación con el bienestar humano.

Homenaje a Reuleaux

En 2005, centenario de la muerte de Franz Reuleaux, parece un momento adecuado para recordar a tan singular personaje. Franz Reuleaux (1829-1905) es un nombre engañoso pues el apellido Reuleaux induce a pensar en un perfume de París o en alguien indiscutiblemente francés. En realidad fue un inteligente ingeniero mecánico alemán. Profesor y especialista en cinemática, supo combinar durante toda su vida su interés docente con sus ideas investigadoras para diseñar y describir máquinas. Su maravillosa colección llegó a tener hasta 800 mecanismos que usó para enseñar, para sugerir nuevos avances técnicos (y para enriquecer el pabellón alemán en la Expo de Filadelfia de su época).

Los orígenes del método de mínimos cuadrados

En los actuales manuales de estadística se suele plantear el método de mínimos cuadrados como una importante y singular técnica relacionado con el problema del ajuste, consiste no tener la ecuación de una curva que como algo determinado criterio, se acerca acuérdate de lo mejor posible los puntos observados de una distribución bidimensional.

Tennyson and youth

This paper will examine the prominence of Alfred Tennyson's work in several textual accounts of youth penned between 1892 and the present day, by writers including T. S. Eliot, Virgina Woolf, Joseph Conrad, James Joyce, Kingsley Amis, J. M. Coetzee, William Faulkner and Andrew Motion. The young Woolf broke in her new pens by copying out Tennyson's 'Tithonus'; Eliot had a taste for Tennyson's 'martial and sanguinary poetry; as a young man. Kingsley Amis was singular among his contemporaries precisely because he admired the work of a poet considered outdated, and a reference for Modernist verse over that of Tennyson is seen as a sign of sophistication (however ironically presented) in the writings of people as diverse as Auden, Motion and Coetzee. [From the Author]

Why do we struggle when we try to learn a language as adults?

Whereas the acquisition of a first language is successful for normally developing individuals, native-like attainment in a language learnt as adults is not guaranteed. As far as grammar is concerned, the area that typically shows up as more problematic is that of Morphology, and more specifically, that part of Morphology related to the specific ways languages have to indicate notions like temporal location (e.g. English –-ed for past tense She walked) or person agreement (e.g. English –s for the third person singular She sings). Language students and teachers are familiar with exclamations like “Oh, after so many years I still have problems with the past tenses in Spanish!” or “I cannot cope with the masculine/feminine thing in French!” In this talk I will present two different accounts that are currently debated in the field of Second Language Acquisition about why it is not enough to memorize those “blessed endings” for us to master their use in our speech production. I will also introduce the latest study I have conducted in collaboration with colleagues, with the aim of evaluating the explanatory power of the hypotheses debated in current literature. [From the Author]

Individual crisis episodes and cultural transition: finding the macrocosm in the microcosm

According to dialogical self theory (Hermans, 2001), individual identities reflect cultural and subcultural values, and appropriate voices and discourses from the social environment. Bronfenbrenner’s (1979) systemic theory of human development similarly postulates that individual and social development occur in a symbiotic and interdependent fashion. It would therefore be predicted that individual changes in identity reflect macrocosmic changes in cultural values and social structures. The current study investigated narratives of crisis transitions within adults aged 25-40, by way of interviews with 22 participants. An intensive qualitative analysis showed that the narratives of crisis could indeed be viewed as individual manifestations of contemporary cultural changes. National statistics and academic research have documented in the UK substantial cultural shifts over the last twenty years including the lessening popularity of marriage, the rise of freelance and portfolio careers and the growth of accepted alternative gender roles. In individual crises, changes made over the course of the episode were invariably in the same direction as these social changes; towards flexible work patterns, non-marital relationships and redefined gender identities. Before the crisis, participants described their identity as bound into an established discourse of conventionality, a traditional sense of masculinity or feminitity and a singular career role, while after the crisis alternative and fluid identities are explored, and identity is less defined by role and institution. These findings show that changes in the social macrocosm can be found in the individual microcosm, and therefore support dialogical self theory.

The interprofessional practitioner: changing professional identity in social work

Twenty years ago the first joint training programme in learning disability nursing and social work was established as a collaborative project to develop practitioners able to work holistically with people with learning disabilities. Since then a number of programmes have continued this work and more recently the approach has developed in the mental health specialism. These programmes have changed the nature of singular social work education and created a new region of knowledge (Bernstein, 2000) for those who have experienced them. What began as a radical experiment in interprofessional education has been sustained by a strong commitment to the belief that the practitioners who qualify from such programmes are well equipped to support people with learning disabilities in changing and multi-professional services. As with much interprofessional education, however, there is an ongoing need to build an evidence base linking such education with successful outcomes in practice. This paper presents and explores the outcomes of a doctoral research study aimed at evaluating the impact of joint training in learning disability nursing and social work on the professional identity, skills and working practices of practitioners who undertook it. The research was undertaken with almost fifty jointly trained practitioners and involved a national survey followed by semi-structured interviews. The results suggest that practitioners who experience the dual socialisation inherent in this type of training found both gains and losses in the process. They appear to emerge, however, with a confidence, resilience and breadth of knowledge which were part of the early vision for this transformative approach to professional training. Bernstein B. (2000). Pedagogy, Symbolic Control and Identity. Theory, Research, Critique. Revised Edition. Lanham: Rowman and Littlefield (USA).

Application of regularization methods to damage detection in large scale plane frame structures using incomplete noisy modal data

This paper presents an approach for detecting local damage in large scale frame structures by utilizing regularization methods for ill-posed problems. A direct relationship between the change in stiffness caused by local damage and the measured modal data for the damaged structure is developed, based on the perturbation method for structural dynamic systems. Thus, the measured incomplete modal data can be directly adopted in damage identification without requiring model reduction techniques, and common regularization methods could be effectively employed to solve the developed equations. Damage indicators are appropriately chosen to reflect both the location and severity of local damage in individual components of frame structures such as in brace members and at beam-column joints. The Truncated Singular Value Decomposition solution incorporating the Generalized Cross Validation method is introduced to evaluate the damage indicators for the cases when realistic errors exist in modal data measurements. Results for a 16-story building model structure show that structural damage can be correctly identified at detailed level using only limited information on the measured noisy modal data for the damaged structure.

Una mirada científico-teórica al quehacer de la Propaganda Indirecta en el medio radiofónico

A partir del triunfo de la Revolución Cubana las acciones de propaganda indirecta devinieron ejercicio profesional dentro de la gama de acciones de los medios de comunicación masivos, asociados a la construcción y afianzamiento de la ideología socialista imperante en nuestro país y al mismo tiempo, aferrados a los preceptos de la comunicación política.Este factor ha influido en que esta tipología comunicativa en la emisora Radio Vitral de Sancti Spíritus constituya un quehacer imprescindible en los mensajes, lo cual se convirtió en punto de partida para, mediante una metodología de corte cualitativo y con los merecidos referentes teóricos, realizar un diagnóstico de cada una de las particularidades, dígase categoría, subcategorías e indicadores de la propaganda indirecta en este medio de comunicación del centro de Cuba, lo cual sirvió de soporte para la validación teórico metodológica de este instrumento evaluador.Asimismo, con los resultados analizados en el diagnóstico de la propaganda indirecta se determinó que se carecía, a diferencia de la creación directa, de herramientas para evaluar la eficacia de los mensajes comunicativos, acordes con las características propias del sistema radiofónico, lo cual devino motivo para proponer una herramienta científica y teórico metodológica que permita evaluar el quehacer propagandístico indirecto en el medio radiofónico, que des las miradas de las mediaciones sociales y la recepción activa garantice su aplicación en cada una de las emisoras cubanas.

Application-Specific Instruction Set Processor for SoC implementation of Modern Signal Processing Algorithms

A novel application-specific instruction set processor (ASIP) for use in the construction of modern signal processing systems is presented. This is a flexible device that can be used in the construction of array processor systems for the real-time implementation of functions such as singular-value decomposition (SVD) and QR decomposition (QRD), as well as other important matrix computations. It uses a coordinate rotation digital computer (CORDIC) module to perform arithmetic operations and several approaches are adopted to achieve high performance including pipelining of the micro-rotations, the use of parallel instructions and a dual-bus architecture. In addition, a novel method for scale factor correction is presented which only needs to be applied once at the end of the computation. This also reduces computation time and enhances performance. Methods are described which allow this processor to be used in reduced dimension (i.e., folded) array processor structures that allow tradeoffs between hardware and performance. The net result is a flexible matrix computational processing element (PE) whose functionality can be changed under program control for use in a wider range of scenarios than previous work. Details are presented of the results of a design study, which considers the application of this decomposition PE architecture in a combined SVD/QRD system and demonstrates that a combination of high performance and efficient silicon implementation are achievable. © 2005 IEEE.

CORDIC based application-specific instruction set processor for QRD/SVD

An application specific programmable processor (ASIP) suitable for the real-time implementation of matrix computations such as Singular Value and QR Decomposition is presented. The processor incorporates facilities for the issue of parallel instructions and a dual-bus architecture that are designed to achieve high performance. Internally, it uses a CORDIC module to perform arithmetic operations, with pipelining of the internal recursive loop exploited to multiplex the two independent micro-rotations onto a single piece of hardware. The net result is a flexible processing element whose functionality can be changed under program control, which combines high performance with efficient silicon implementation. This is illustrated through the results of a detailed silicon design study and the applications of the techniques to a combined SVD/QRD system.

Cultural policy models and cultural facilities models: from national to local models. Analysis of Barcelona’s case

The development of cultural policy analysis by social science has been produced a theorization about cultural policy models from sociology and political science. This analysis shows the influence of the national model of cultural policy on the forms of governance and management of cultural facilities. However, in this paper we will defend that currently the local model of cultural policy decisively influences the model of cultural institutions. This is explained by the growing importance of culture in local development strategies. In order to demonstrate this we will analyze the case of the Barcelona Model of local development and cultural policy, that is characterized for the level of local government leadership, multilevel governance, the use of culture in urban planning processes and a tendency to use public-private partnership in public management. This Model influences the genesis and development of the cultural facilities and it produces a singular and relatively successful model.

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.