On the Distortion of a Copula and its Margins

This article examines the notion of distortion of copulas, a natural extension of distortion within the univariate framework. We study three approaches to this extension: (1) distortion of the margins alone while keeping the original copula structure, (2) distortion of the margins while simultaneously altering the copula structure, and (3) synchronized distortion of the copula and its margins. When applying distortion within the multivariate framework, it is important to preserve the properties of a copula function. For the first two approaches, this is a rather straightforward result, however for the third approach, the proof has been exquisitely constructed in Morillas (2005). These three approaches of multivariate distortion unify the different types of multivariate distortion that have scarcely scattered in the literature. Our contribution in this paper is to further consider this unifying framework: we give numerous examples to illustrate and we examine their properties particularly with some aspects of ordering multivariate risks. The extension of multivariate distortion can be practically implemented in risk management where there is a need to perform aggregation and attribution of portfolios of correlated risks. Furthermore, ancillary to the results discussed in this article, we are able to generalize the formula developed by Genest and Rivest (2001) for computing the distribution of the probability integral transformation of a random vector and extend it to the case within the distortion framework.Multivariate distortion; Ordering of risks; Probability integral transformation

Origin and evolution of ferroelectricity in the layered rare-earth-titanate, R2R_2Ti2_2O7_{7}, Lichtenberg phases

We report a systematic first-principles study based on density functional theory (DFT) of the structural and ferroelectric properties of the $R_2$Ti$_2$O$_{7}$ perovskite-related oxides with $R=$ La, Ce, Pr, and Nd. We show that, in all cases, the ferroelectric distortion to the ground-state polar $P2_1$ structure from its parent centrosymmetric $P2_1/m$ phase is driven by a single polar soft mode consisting of rotations and tilts of the TiO$_6$ octahedra combined with displacements of the $R$ ions. A secondary centrosymmetric distortion, which is stable in the parent structure, contributes substantially to the energy lowering of the ground state. We evaluate the trends in structure and polarization across the series as a function of $R$ and reconcile discrepancies in reported values of polarization in the literature. Our results confirm that the family of $R_2$Ti$_2$O$_{7}$ materials belong to the class of proper geometric ferroelectrics.Comment: 15 pages, 12 figures, 7 table

Failure-recovery model with competition between failures in complex networks: a dynamical approach

Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdand\v{z}i\'c $et\;al.$ [Nature Physics 10, 34 (2014)] proposed a model to study systems in which active nodes fail and recover spontaneously in a complex network and found that in the steady state the density of active nodes can exhibit an abrupt transition and hysteresis depending on the values of the parameters. Here we investigate a model of recovery-failure from a dynamical point of view. Using an effective degree approach we find that the systems can exhibit a temporal sharp decrease in the fraction of active nodes. Moreover we show that, depending on the values of the parameters, the fraction of active nodes has an oscillatory regime which we explain as a competition between different failure processes. We also find that in the non-oscillatory regime, the critical fraction of active nodes presents a discontinuous drop which can be related to a "targeted" k-core percolation process. Finally, using mean field equations we analyze the space of parameters at which hysteresis and oscillatory regimes can be found

Social distancing strategies against disease spreading

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, $i.e$, the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.Comment: to be published in "Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade", Word Scientific Pres

Use of the STAR PROCESS for Children with Sensory Processing Challenges

Background: This study examined the effectiveness of the STAR PROCESS, an intensive, short-term intervention that combines principles of sensory integration, relationship-based therapy, and parental-therapist collaboration for children with sensory processing challenges. Method: A nonconcurrent multiple baseline, repeated measures design was used. Four boys, aged 5 years 0 months to 7 years 9 months, participated in this study. The mean length of intervention was 22 sessions delivered 3 to 5 times per week. A behavioral coding system was used to measure change in four areas: play level, positive affect, joint attention, and novel use of equipment. The theory of change reflects the use of multisensory experiences in combination with parent participation to impact outcomes. Results: Improvement was noted in play level in all of the participants. Multisensory experiences and parent participation were associated with these changes in two participants. Discussion: The study results suggest a feasible methodology to study occupational therapy interventions. The behavioral coding system was sensitive to change. Play abilities changed in all four children. Preliminary support was provided for the theory of change combining multisensory experiences with parent participation. Conclusion: A targeted treatment approach that emphasizes parents as play partners in a multisensory environment shows promise in remediating these deficits

Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies

The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August---which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80\% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015