Planar spin glasses

Imperial Users onl

Validity and Failure of the Boltzmann Weight

The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on $d$-dimensional lattices ($d=1,2,$ and 3), through molecular dynamics. The interactions between rotators decay with the distance $r_{ij}$ like~$1/r_{ij}^{\alpha}$ ($\alpha \geq 0$), where $\alpha\to\infty$ and $\alpha=0$ respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas $q$-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to $q$-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on $d$ and $\alpha$ through the ratio $\alpha/d$.Comment: 10 pages, 6 figures. To appear in EP

Arterial blood pressure monitoring (ABPM)

Arterial Blood Pressure Monitoring (ABPM) is a metodology appropriate to analyse the variations of arterial blood pressure during 24 or more hours, with indirect and programable measurements. Advantages, limitations, indications and utility of this metodology are discussed in this review.Monitorização Ambulatorial da Pressão Arterial (MAPA) é uma técnica que permite a observação das variações tensionais durante 24 ou mais horas, através de medidas programadas e indiretas da pressão arterial. Vantagens, limitações, indicações e utilidades sobre esta metodologia são discutidas nesta revisão

Robust Self-Calibration and Mapping for Long Term Autonomy

Robust long term autonomy represents one of the most important targets for advancing robotic applications in the next 10 to 15 years, particularly because of the the advances in the socalled Classical Age of Simultaneous Localization and Mapping (SLAM) which place us in the age of Robust-Perception. Creating algorithms which allow robots to operate for years, unsupervised, in any environment is key step in the direction of true autonomy. This thesis presents a suite of algorithms to help enable robust long term autonomy, specifically robustness to a robot&rsquo;s calibration parameters (internal knowledge the robot must possess in order operate) and to the environment the robot is situated in. Starting from the fundamentals of SLAM, the now de facto formulation is presented as a segue into self-calibration - the task of estimating calibration parameters such as the camera position on the robot. The following extensions are then developed: (i) an approach to treat slowly varying quantities, such as the position of a sensor drifting over years of operation, (ii) an algorithm which allows a robot to learn what movements it needs to perform in order to know its calibration parameters - using a reinforcement learning framework for self-calibration and (iii) all the insight from previous research is used to create a real-time self-calibration system which is capable of dealing with drift, unobservable parameters - for example when the robot is constrained to planar movement - and an information theoretic based segment selection mechanism which only choses &ldquo;informative&rdquo; segments of the trajectory in order to reduce computation time. However robustness is not only in regards to internal parameters such as a robot&rsquo;s sensor position - the environment the robot operates in is dynamic - dealing with that environment is the final contribution, where an online probabilistic approximate joint feature persistence model is presented to determine which parts of the world are changing.</p

q-Gaussians in the porous-medium equation: stability and time evolution

The stability of $q$-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, \pderiv{P(x,t)}{t} = D \pderiv{^2 [P(x,t)]^{2-q}}{x^2}, the \emph{porous-medium equation}, is investigated through both numerical and analytical approaches. It is shown that an \emph{initial} $q$-Gaussian, characterized by an index $q_i$, approaches the \emph{final}, asymptotic solution, characterized by an index $q$, in such a way that the relaxation rule for the kurtosis evolves in time according to a $q$-exponential, with a \emph{relaxation} index $q_{\rm rel} \equiv q_{\rm rel}(q)$. In some cases, particularly when one attempts to transform an infinite-variance distribution ($q_i \ge 5/3$) into a finite-variance one ($q<5/3$), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.Comment: 20 pages, 6 figure