On The Weak-Coupling Limit for Bosons and Fermions

In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time $t$, agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows in spirit the companion work [\rcite{BCEP}], where the authors investigated the weak-coupling limit for particles obeying the Maxwell-Boltzmann statistics: here, they proved a (much stronger) convergence result towards the solution of the Boltzmann equation

Fractal properties of quantum spacetime

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of \k-Minkowski, the latter being relevant in the context of quantum gravity.Comment: 4 pages, 2 figures; some minor corrections; reference adde

Designing optimal low-thrust gravity-assist trajectories using space-pruning and a multi-objective approach

A multi-objective problem is addressed consisting of finding optimal low-thrust gravity-assist trajectories for interplanetary and orbital transfers. For this, recently developed pruning techniques for incremental search space reduction - which will be extended for the current situation - in combination with subdivision techniques for the approximation of the entire solution set, the so-called Pareto set, are used. Subdivision techniques are particularly promising for the numerical treatment of these multi-objective design problems since they are characterized (amongst others) by highly disconnected feasible domains, which can easily be handled by these set oriented methods. The complexity of the novel pruning techniques is analysed, and finally the usefulness of the novel approach is demonstrated by showing some numerical results for two realistic cases

General static spherically symmetric solutions in Horava gravity

We derive general static spherically symmetric solutions in the Horava theory of gravity with nonzero shift field. These represent "hedgehog" versions of black holes with radial "hair" arising from the shift field. For the case of the standard de Witt kinetic term (lambda =1) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point lambda = 1/3.Comment: References adde

Free monadic Tarski and MMI3-algebras

MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued £ukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI3-algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.Fil: Entizne, Rosana V.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Monteiro, Luiz F.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Savini, Sonia M.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Viglizzo, Ignacio Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentin

Neurological modeling of what experts vs. non-experts find interesting

The P3 and related ERP's have a long history of use to identify stimulus events in subjects as part of oddball-style experiments. In this work we describe the ongoing development of oddball style experiments which attempt to capture what a subject finds of interest or curious, when presented with a set of visual stimuli i.e. images. This joint work between Dublin City University (DCU) and the European Space Agency's Advanced Concepts Team (ESA ACT) is motivated by the challenges of autonomous space exploration where the time lag for sending data back to earth for analysis and then communicating an action or decision back to the spacecraft means that decision-making is slow. Also, when extraterrestrial sensors capture data, the determination of what data to send back to earth is driven by an expertly devised rule set, that is scientists need to determine apriori what will be of interest. This cannot adapt to novel or unexpected data that a scientist may find curious. Our work is attempting to determine if it is possible to capture what a scientist (subject) finds of interest (curious) in a stream of image data through EEG measurement. One of the our challenges is to determine the difference between an expert and a lay subject response to stimulus. To investigate the theorized difference, we use a set of lifelog images as our dataset. Lifelog images are first person images taken by a small wearable camera which continuously records images whilst it is worn. We have devised two key experiments for use with this data and two classes of subjects. Our subjects are a person who has worn the personal camera, from which our collection of lifelog images is taken and who becomes our expert, and the remaining subjects are people who have no association with the captured images. Our first experiment is a traditional oddball experiment where the oddballs are people having coffee, and can be thought of as a directed information seeking task. The second experiment is to present a stream of lifelog images to the subjects and record which images cause a stimulus response. Once the data from these experiments has been captured our task is to compare the responses between the expert and lay subject groups, to determine if there are any commonalities between these groups or any distinct differences. If the latter outcome is the case the objective is then to investigate methods for capturing properties of images which cause an expert to be interested in a presented image. Further novelty is added to our work by the fact we are using entry-level off-the-shelf EEG devices, consisting of 4 nodes with a sampling rate of 255Hz