Shape Outlier Detection and Visualization for Functional Data: the Outliergram

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that exhibit atypically high or low values at some points or across the whole interval, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article we exploit the relation between two depths for functional data to help visualizing curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and asses the performance of the algorithm on a simulation study. We apply them to the detection of outliers in a children growth dataset in which the girls sample is contaminated with boys curves and viceversa.Comment: 27 pages, 5 figure

The impact of immigration on the wage structure : Spain 1995-2002

In this paper we estimate the impact of inward migration flows on the Spanish wage structure over the period 1995-2002 by constructing counterfactual wage distributions that provide the wages that would have been observed had individual and job characteristics remain constant over time. Hence, we compute the impact of immigration on the wage distribution from (i) the estimated wage gaps between similar immigrants and native workers and (ii) the changes in the composition of employment associated to the arrival of new immigrants. Overall, we find that (i) the effects of immigration on wage changes are small and only noticeable when job characteristics are included as determinants of wages, and (ii) the correlation between the incidence of immigration in each decile of the wage distribution and the change in native wages not explained by changes in their individual and job characteristics is positive. These results suggest that other factors, besides immigration, should be identified as the key determinants of the wage moderation observed since the early nineties in Spain

On the error term of the logarithm of the lcm of quadratic sequences

We study the logarithm of the least common multiple of the sequence of integers given by 12 + 1, 2 2 + 1, . . . , n2 + 1. Using a result of Homma [4] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by CillerueloPostprint (updated version

The effect of immigration on the employment opportunities of native-born workers : some evidence for Spain

Spain is one of the European countries where immigration flows during the last decade have increased noticeably. The Spanish labor market institutions and the Spanish immigration policy exhibit some peculiarities which may be relevant when analyzing the impact of immigration. This paper provides a first approximation to the labor market effects of immigrants in Spain during the second half of the 1990s, the period in which immigration flows to Spain have accelerated. By using alternative datasets, we estimate both the impact of legal and total immigration flows on the employment rates of native workers, accounting for the possible occupationa l and geographical mobility of immigrants and native-born workers. Using different samples and estimation procedures, we have not found a significant negative effect of immigration on the employment rates of native workers. The corresponding estimated elasticity is low, around -0.1, when considering only legal immigrants, and is not significant when considering both legal and illegal immigrants

Memory and long-range correlations in chess games

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations; rescaled range analysis and detrented fluctuation analysis. We found that long-range memory is related to the level of the players. When the database is filtered according to player levels we found differences in the persistence of the different subsets. For high level players, correlations are stronger at long time scales; whereas in intermediate and low level players they reach the maximum value at shorter time scales. This can be interpreted as a signature of the different strategies used by players with different levels of expertise. These results are robust against the assignation rules and the method employed in the analysis of the time series.Comment: 12 pages, 5 figures. Published in Physica

Engineering a QoS Provider Mechanism for Edge Computing with Deep Reinforcement Learning

With the development of new system solutions that integrate traditional cloud computing with the edge/fog computing paradigm, dynamic optimization of service execution has become a challenge due to the edge computing resources being more distributed and dynamic. How to optimize the execution to provide Quality of Service (QoS) in edge computing depends on both the system architecture and the resource allocation algorithms in place. We design and develop a QoS provider mechanism, as an integral component of a fog-to-cloud system, to work in dynamic scenarios by using deep reinforcement learning. We choose reinforcement learning since it is particularly well suited for solving problems in dynamic and adaptive environments where the decision process needs to be frequently updated. We specifically use a Deep Q-learning algorithm that optimizes QoS by identifying and blocking devices that potentially cause service disruption due to dynamicity. We compare the reinforcement learning based solution with state-of-the-art heuristics that use telemetry data, and analyze pros and cons

A study of memory effects in a chess database

A series of recent works studying a database of chronologically sorted chess games --containing 1.4 million games played by humans between 1998 and 2007-- have shown that the popularity distribution of chess game-lines follows a Zipf's law, and that time series inferred from the sequences of those game-lines exhibit long-range memory effects. The presence of Zipf's law together with long-range memory effects was observed in several systems, however, the simultaneous emergence of these two phenomena were always studied separately up to now. In this work, by making use of a variant of the Yule-Simon preferential growth model, introduced by Cattuto et al., we provide an explanation for the simultaneous emergence of Zipf's law and long-range correlations memory effects in a chess database. We find that Cattuto's Model (CM) is able to reproduce both, Zipf's law and the long-range correlations, including size-dependent scaling of the Hurst exponent for the corresponding time series. CM allows an explanation for the simultaneous emergence of these two phenomena via a preferential growth dynamics, including a memory kernel, in the popularity distribution of chess game-lines. This mechanism results in an aging process in the chess game-line choice as the database grows. Moreover, we find burstiness in the activity of subsets of the most active players, although the aggregated activity of the pool of players displays inter-event times without burstiness. We show that CM is not able to produce time series with bursty behavior providing evidence that burstiness is not required for the explanation of the long-range correlation effects in the chess database.Comment: 18 pages, 7 figure

Visualizing the Doppler Effect

The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes as close to reality as we want. However, when we are trying to explain some complex physical processes, it is better to simplify the problem under study using simplified pictures of the total process by eliminating some elements that make it difficult to understand this process. In this work we focus our attention on the Doppler effect which requires the space-time visualization that is very difficult to obtain using the traditional teaching resources. We have designed digital simulations as a complement of the theoretical explanation in order to help students understand this phenomenon.Comment: 16 pages, 8 figure

A fractional porous medium equation

We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $\frac{\partial u}{\partial t} + (-\Delta)^{1/2} (|u|^{m-1}u)=0$ in $\mathbb{R}^N$, with $m>m_*=(N-1)/N$, $N\ge1$ and $f\in L^1(\mathbb{R}^N)$. An $L^1$-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all $x\in\mathbb{R}^N$, $t>0$