Poincar-Cartan intregral invariant and canonical trasformation for singular Lagrangians: an addendum

The results of a previous work, concerning a method for performing the canonical formalism for constrained systems, are extended when the canonical transformation proposed in that paper is explicitly time dependent.

Reconstructing images from their most singular fractal manifold

Real-world images are complex objects, difficult to describe but at the same time possessing a high degree of redundancy. A very recent study [1] on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature. One particular fractal component, related to the most singular (sharpest) transitions in the image, seems to be highly informative about the whole scene. In this paper we will show how to decompose the image into their fractal components.We will see that the most singular component is related to (but not coincident with) the edges of the objects present in the scenes. We will propose a new, simple method to reconstruct the image with information contained in that most informative component.We will see that the quality of the reconstruction is strongly dependent on the capability to extract the relevant edges in the determination of the most singular set.We will discuss the results from the perspective of coding, proposing this method as a starting point for future developments.

Coisotropic regularization of singular Lagrangians

We present an alternative approach to the usual treatments of singular Lagrangians. It is based on a Hamiltonian regularization scheme inspired on the coisotropic embedding of presymplectic systems. A Lagrangian regularization of a singular Lagrangian is a regular Lagrangian defined on an extended velocity phase space that reproduces the original theory when restricted to the initial configuration space. A Lagrangian regularization does not always exists, but a family of singular Lagrangians is studied for which such a regularization can be described explicitly. These regularizations turn out to be essentially unique and provide an alternative setting to quantize the corresponding physical systems. These ideas can be applied both in classical mechanics and field theories. Several examples are discussed in detail. 1995 American Institute of Physics.

Bump time-frequency toolbox: a toolbox for time-frequency oscillatory bursts extraction in electrophysiological signals

Background: oscillatory activity, which can be separated in background and oscillatory burst pattern activities, is supposed to be representative of local synchronies of neural assemblies. Oscillatory burst events should consequently play a specific functional role, distinct from background EEG activity – especially for cognitive tasks (e.g. working memory tasks), binding mechanisms and perceptual dynamics (e.g. visual binding), or in clinical contexts (e.g. effects of brain disorders). However extracting oscillatory events in single trials, with a reliable and consistent method, is not a simple task. Results: in this work we propose a user-friendly stand-alone toolbox, which models in a reasonable time a bump time-frequency model from the wavelet representations of a set of signals. The software is provided with a Matlab toolbox which can compute wavelet representations before calling automatically the stand-alone application. Conclusion: The tool is publicly available as a freeware at the address: http:// www.bsp.brain.riken.jp/bumptoolbox/toolbox_home.html

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Fachada solar como pieza singular de arquitectura sostenible

Articulo sobre la importancia de las energias renovables y su integración arquitectónica en el camino hacia una arquitectura sostenible. Descripción y evaluación del proyecto Fachada Solar SCHOTT Iberica.

El maltrato singular cualificado por razon de género. Debate acerca de su constitucionalidad

En la presente aportación se analiza la prosperabilidad de las cuestiones de inconstitucionalidad que en la fecha de publicación del artículo penden ante el Tribunal Constit ucional en referencia al art. 153.1 CP. Con la aprobación de la Ley Orgánica de medidas de protecció integral contra la violencia de género se incluyó en el referido precepto del texto punitivo un tipo cualificado de maltrato singular u ocasional cuando el sujeto pasivo sea esposa o ex-esposa, pareja o ex-pareja, aun sin convivencia, del maltratador, entre otros supuestos agravados. La inclusión de un delito en que tanto el sexo del sujeto pasivo como el del activo se hallan más o menos explicitados ha enerado el planteamiento de un rosario de cuestiones de inconstitucionalidad por parte de distintos órganos jurisdiccionales que están pendientes de resolución ante el Tribunal Constitucional. Dichas cuestiones plantean la posible inconstitucionalidad del art. 153.1 CP sobre la base de su posible contradicción con los arts. 10, 14 y 24.2 CP. En este trabajo se pretende salvar la constitucionalidad del precepto, sobre la base de los postulados del principio de conservación de las normas, con ayuda de una exégesis restrictiva del tipo.

Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex

Short-term synaptic depression (STD) is a form of synaptic plasticity that has a large impact on network computations. Experimental results suggest that STD is modulated by cortical activity, decreasing with activity in the network and increasing during silent states. Here, we explored different activity-modulation protocols in a biophysical network model for which the model displayed less STD when the network was active than when it was silent, in agreement with experimental results. Furthermore, we studied how trains of synaptic potentials had lesser decay during periods of activity (UP states) than during silent periods (DOWN states), providing new experimental predictions. We next tackled the inverse question of what is the impact of modifying STD parameters on the emergent activity of the network, a question difficult to answer experimentally. We found that synaptic depression of cortical connections had a critical role to determine the regime of rhythmic cortical activity. While low STD resulted in an emergent rhythmic activity with short UP states and long DOWN states, increasing STD resulted in longer and more frequent UP states interleaved with short silent periods. A still higher synaptic depression set the network into a non-oscillatory firing regime where DOWN states no longer occurred. The speed of propagation of UP states along the network was not found to be modulated by STD during the oscillatory regime; it remained relatively stable over a range of values of STD. Overall, we found that the mutual interactions between synaptic depression and ongoing network activity are critical to determine the mechanisms that modulate cortical emergent patterns.

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context.

Theta EEG oscillatory activity and auditory change detection

The mismatch negativity is an electrophysiological marker of auditory change detection in the event-related brain potential and has been proposed to reflect an automatic comparison process between an incoming stimulus and the representation of prior items in a sequence. There is evidence for two main functional subcomponents comprising the MMN, generated by temporal and frontal brain areas, respectively. Using data obtained in an MMN paradigm, we performed time-frequency analysis to reveal the changes in oscillatory neural activity in the theta band. The results suggest that the frontal component of the MMN is brought about by an increase in theta power for the deviant trials and, possibly, by an additional contribution of theta phase alignment. By contrast, the temporal component of the MMN, best seen in recordings from mastoid electrodes, is generated by phase resetting of theta rhythm with no concomitant power modulation. Thus, frontal and temporal MMN components do not only differ with regard to their functional significance but also appear to be generated by distinct neurophysiological mechanisms.

Les dunes litorals, un paisatge singular en regressió

Escrit que vol donar a conèixer el medi dunar litoral amb l’objectiu de recomanar la seva protecció urgent

Global eriodicity and complete integrability of discrete dynamical systems

Vegeu el resum a l'inici del document del fitxer adjunt

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.