BIRD, BCAM's Institutional Repository DataThe BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://bird.bcamath.org:802019-09-16T01:12:24Z2019-09-16T01:12:24ZSingle-trajectory spectral analysis of scaled Brownian motionSposini V.Metzler R.Oshanin G.http://hdl.handle.net/20.500.11824/10102019-09-09T01:00:12Z2019-06-01T00:00:00ZSingle-trajectory spectral analysis of scaled Brownian motion
Sposini V.; Metzler R.; Oshanin G.
A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, $T\to \infty $. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit $T\to \infty $ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion. We demonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent. We also compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing single-trajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
2019-06-01T00:00:00ZCrowd-Centric Counting via Unsupervised LearningMorselli F.Bartoletti S.Mazuelas S.Win M.Conti A.http://hdl.handle.net/20.500.11824/10092019-09-09T01:00:13Z2019-07-11T00:00:00ZCrowd-Centric Counting via Unsupervised Learning
Morselli F.; Bartoletti S.; Mazuelas S.; Win M.; Conti A.
Counting targets (people or things) within a moni-tored area is an important task in emerging wireless applications,including those for smart environments, safety, and security.Conventional device-free radio-based systems for counting targetsrely on localization and data association (i.e., individual-centric information) to infer the number of targets present in an area(i.e., crowd-centric information). However, many applications(e.g., affluence analytics) require only crowd-centric rather than individual-centric information. Moreover, individual-centric approaches may be inadequate due to the complexity of data association. This paper proposes a new technique for crowd-centric counting of device-free targets based on unsupervised learning, where the number of targets is inferred directly from a low-dimensional representation of the received waveforms. The proposed technique is validated via experimentation using an ultra-wideband sensor radar in an indoor environment.
2019-07-11T00:00:00ZVariational Formulations for Explicit Runge-Kutta MethodsMuñoz-Matute J.Pardo D.Calo V. M.Alberdi E.http://hdl.handle.net/20.500.11824/10082019-09-09T01:00:09Z2019-08-01T00:00:00ZVariational Formulations for Explicit Runge-Kutta Methods
Muñoz-Matute J.; Pardo D.; Calo V. M.; Alberdi E.
Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that
implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary di fferential equations employing speci fic
inexact quadrature rules. In this work, we prove that the explicit Runge-Kutta methods can be expressed as discontinuous-in-time Petrov-Galerkin methods for the linear di ffusion equation. We systematically build trial
and test functions that, after exact integration in time, lead to one, two, and general stage explicit Runge-Kutta methods. This approach enables us to reproduce the existing time-domain (goal-oriented) adaptive algorithms
using explicit methods in time.
2019-08-01T00:00:00ZA mathematical analysis of edas with distance-based exponential modelsUnanue I.Merino M.Lozano J.A.http://hdl.handle.net/20.500.11824/10072019-09-09T01:00:14Z2019-07-01T00:00:00ZA mathematical analysis of edas with distance-based exponential models
Unanue I.; Merino M.; Lozano J.A.
Estimation of Distribution Algorithms have been successfully used for solving many combinatorial optimization problems. One type of problems in which Estimation of Distribution Algorithms have presented strong competitive results are permutation-based combinatorial optimization problems. In this case, the algorithms use probabilistic models specifically designed for codifying probability distributions over permutation spaces. One class of these probability models is distance-based exponential models, and one example of this class is the Mallows model. In spite of the practical success, the theoretical analysis of Estimation of Distribution Algorithms for permutation-based combinatorial optimization problems has not been extensively developed. With this motivation, this paper presents a first mathematical analysis of the convergence behavior of Estimation of Distribution Algorithms based on the Mallows model by using an infinite population to associate a dynamical system to the algorithm. Several scenarios, with different fitness functions and initial probability distributions of increasing complexity, are analyzed obtaining unexpected results in some cases.
2019-07-01T00:00:00Z