Analyzing Fragmentation of Simple Fluids with Percolation Theory

We show that the size distributions of fragments created by high energy nuclear collisions are remarkably well reproduced within the framework of a parameter free percolation model. We discuss two possible scenarios to explain this agreement and suggest that percolation could be an universal mechanism to explain the fragmentation of simple fluids.Comment: 12 pages, 11 figure

Partial energies fluctuations and negative heat capacities

We proceed to a critical examination of the method used in nuclear fragmentation to exhibit signals of negative heat capacity. We show that this method leads to unsatisfactory results when applied to a simple and well controlled model. Discrepancies are due to incomplete evaluation of potential energies.Comment: Modified figures 3 and

Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems

Recently, a new finite-sample system identification algorithm, called Sign-Perturbed Sums (SPS), was introduced in [2]. SPS constructs finite-sample confidence regions that are centered around the least squares estimate, and are guaranteed to contain the true system parameters with a user-chosen exact probability for any finite number of data points. The main assumption of SPS is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. Although it is easy to determine if a particular parameter belongs to the confidence region, it is not easy to describe the boundary of the region, and hence to compactly represent the exact confidence region. In this paper we show that an ellipsoidal outer-approximation of the SPS confidence region can be found by solving a convex optimization problem, and we illustrate the properties of the SPS region and the ellipsoidal outer-approximation in simulation examples

NON-ASYMPTOTIC QUALITY ASSESSMENT OF THE LEAST SQUARES ESTIMATE

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Asymptotic properties of SPS confidence regions

Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example

A Little Big Bang scenario of fragmentation

We suggest a multifragmentation scenario in which fragments are produced at an early, high temperature and high density, stage of the reaction. In this scenario, self-bound clusters of particles in the hot and dense fluid are the precursors of the observed fragments. This solves a number of recurrent problems concerning the kinetic energies and the temperature of the fragments, encountered with the standard low density fragmentation picture. The possibility to recover the initial thermodynamic parameters from the inspection of the asymptotic fragment size and kinetic energy distributions is discussed

Changes in mobility and socioeconomic conditions during the COVID-19 outbreak

Since the outbreak of the 2019 novel coronavirus (COVID-19) pandemic, governments have been implementing containment measures aimed at mitigating the spread of the virus, including restrictions to human mobility. The ability to adapt to the pandemic and respond to containment measures can be bound by socioeconomic conditions, which are heterogeneous in large urban areas of low-income and middle-income countries. In this paper, we analyse mobility changes following the implementation of containment measures in Bogotá, Colombia. We characterise the mobility network before and during the pandemic and analyse its evolution and changes between January and July 2020. We observe a general reduction in mobility trends, but the overall connectivity between different areas of the city remains after the lockdown, reflecting the resilience of the mobility network. Then, we estimate a gravity model to assess the effect of socioeconomic conditions on mobility flows. We find that the responses to lockdown policies depend on the socioeconomic conditions of the population. Before the pandemic, the population with better socioeconomic conditions shows higher mobility flows. Since the lockdown, mobility presents a general decrease, but the population with worse socioeconomic conditions shows lower reductions in mobility flows. We conclude by deriving policy implications.Fil: Dueñas, Marco. Universidad de Bogota Jorge Tadeo Lozano; ColombiaFil: Campi, Mercedes Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Interdisciplinario de Economía Política de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Instituto Interdisciplinario de Economía Política de Buenos Aires; ArgentinaFil: Olmos, Luis E.. University of California; Estados Unidos. Universidad de Medellin; Colombi

Zipf's law in Multifragmentation

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition

A "Little Big Bang" Scenario of Multifragmentation

We suggest a multifragmentation scenario in which fragments are produced at an early, high temperature and high density, stage of the reaction. In this scenario, self-bound clusters of particles in the hot and dense fluid are the precursors of the observed fragments. This solves a number of recurrent problems concerning the kinetic energies and the temperature of the fragments, encountered with the standard low density fragmentation picture. The possibility to recover the initial thermodynamic parameters from the inspection of the asymptotic fragment size and kinetic energy distributions is discussed.Comment: 15 pages, 12 figure

Finite-sample system identification: An overview and a new correlation method

Finite-sample system identification algorithms can be used to build guaranteed confidence regions for unknown model parameters under mild statistical assumptions. It has been shown that in many circumstances these rigorously built regions are comparable in size and shape to those that could be built by resorting to the asymptotic theory. The latter sets are, however, not guaranteed for finite samples and can sometimes lead to misleading results. The general principles behind finite-sample methods make them virtually applicable to a large variety of even nonlinear systems. While these principles are simple enough, a rigorous treatment of the attendant technical issues makes the corresponding theory complex and not easy to access. This is believed to be one of the reasons why these methods have not yet received widespread acceptance by the identification community and this letter is meant to provide an easy access point to finite-sample system identification by presenting the fundamental ideas underlying these methods in a simplified manner. We then review three (classes of) methods that have been proposed so far-1) Leave-out Sign-dominant Correlation Regions (LSCR); 2) Sign-Perturbed Sums (SPS); 3) Perturbed Dataset Methods (PDMs). By identifying some difficulties inherent in these methods, we also propose in this letter a new sign-perturbation method based on correlation which overcome some of these difficulties