Constructions of Coupling Processes for L\'evy Processes

We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by reflection.Comment: 16 page

Detecting independence of random vectors: generalized distance covariance and Gaussian covariance

Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Sz\'{e}kely, Rizzo and Bakirov can be embedded into a more general framework based on symmetric L\'{e}vy measures and the corresponding real-valued continuous negative definite functions. The L\'{e}vy measures replace the weight functions used in the original definition of distance covariance. All essential properties of distance covariance are preserved in this new framework. From a practical point of view this allows less restrictive moment conditions on the underlying random variables and one can use other distance functions than Euclidean distance, e.g. Minkowski distance. Most importantly, it serves as the basic building block for distance multivariance, a quantity to measure and estimate dependence of multiple random vectors, which is introduced in a follow-up paper [Distance Multivariance: New dependence measures for random vectors (submitted). Revised version of arXiv: 1711.07775v1] to the present article.Comment: Published at https://doi.org/10.15559/18-VMSTA116 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

Real-Time Description of the Electronic Dynamics for a Molecule close to a Plasmonic Nanoparticle

The optical properties of molecules close to plasmonic nanostructures greatly differ from their isolated molecule counterparts. To theoretically investigate such systems in a Quantum Chemistry perspective, one has to take into account that the plasmonic nanostructure (e.g., a metal nanoparticle - NP) is often too large to be treated atomistically. Therefore, a multiscale description, where the molecule is treated by an ab initio approach and the metal NP by a lower level description, is needed. Here we present an extension of one such multiscale model [Corni, S.; Tomasi, J. {\it J. Chem. Phys.} {\bf 2001}, {\it 114}, 3739] originally inspired by the Polarizable Continuum Model, to a real-time description of the electronic dynamics of the molecule and of the NP. In particular, we adopt a Time-Dependent Configuration Interaction (TD CI) approach for the molecule, the metal NP is described as a continuous dielectric of complex shape characterized by a Drude-Lorentz dielectric function and the molecule- NP electromagnetic coupling is treated by an equation-of-motion (EOM) extension of the quasi-static Boundary Element Method (BEM). The model includes the effects of both the mutual molecule- NP time-dependent polarization and the modification of the probing electromagnetic field due to the plasmonic resonances of the NP. Finally, such an approach is applied to the investigation of the light absorption of a model chromophore, LiCN, in the presence of a metal NP of complex shape.Comment: This is the final peer-reviewed manuscript accepted for publication of an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Link to the original article: http://pubs.acs.org/doi/abs/10.1021/acs.jpcc.6b1108

Gender gap in the ERASMUS mobility program

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subject areas. Namely, for almost all participating countries, female students are over-represented in the ERASMUS program when compared to the entire population of tertiary students. The same tendency is observed across different subject areas. We also found a gender asymmetry in the geographical distribution of hosting institutions, with a bias of male students in Scandinavian countries. However, a detailed analysis reveals that this latter asymmetry is rather driven by subject and consistent with the distribution of gender ratios among subject areas

Clout, Activists and Budget: The Road to Presidency

Political campaigns involve, in the simplest case, two competing campaign groups which try to obtain a majority of votes. We propose a novel mathematical framework to study political campaign dynamics on social networks whose constituents are either political activists or persuadable individuals. Activists are convinced and do not change their opinion and they are able to move around in the social network to motivate persuadable individuals to vote according to their opinion. We describe the influence of the complex interplay between the number of activists, political clout, budgets, and campaign costs on the campaign result. We also identify situations where the choice of one campaign group to send a certain number of activists already pre-determines their victory. Moreover, we show that a candidate's advantage in terms of political clout can overcome a substantial budget disadvantage or a lower number of activists, as illustrated by the US presidential election 2016.Comment: 23 pages, 10 figure

Electrostatic fluctuations in cavities within polar liquids and thermodynamics of polar solvation

We present the results of numerical simulations of fluctuations of the electrostatic potential and electric field inside cavities created in the fluid of dipolar hard spheres. We found that the thermodynamics of polar solvation dramatically changes its regime when the cavity size becomes about 4-5 times larger than the size of the liquid particle. The range of small cavities can be reasonably understood within the framework of current solvation models. On the contrary, the regime of large cavities is characterized by a significant softening of the cavity interface resulting in a decay of the fluctuation variances with the cavity size much faster than anticipated by both the continuum electrostatics and microscopic theories. For instance, the variance of potential decays with the cavity size $R_0$ approximately as $1/R_0^{4-6}$ instead of the $1/R_0$ scaling expected from standard electrostatics. Our results suggest that cores of non-polar molecular assemblies in polar liquids lose solvation strength much faster than is traditionally anticipated.Comment: 10 pp, 10 fig

Modeling the Emission Processes in Blazars

Blazars are the most violent steady/recurrent sources of high-energy gamma-ray emission in the known Universe. They are prominent emitters of electromagnetic radiation throughout the entire electromagnetic spectrum. The observable radiation most likely originates in a relativistic jet oriented at a small angle with respect to the line of sight. This review starts out with a general overview of the phenomenology of blazars, including results from a recent multiwavelength observing campaign on 3C279. Subsequently, issues of modeling broadband spectra will be discussed. Spectral information alone is not sufficient to distinguish between competing models and to constrain essential parameters, in particular related to the primary particle acceleration and radiation mechanisms in the jet. Short-term spectral variability information may help to break such model degeneracies, which will require snap-shot spectral information on intraday time scales, which may soon be achievable for many blazars even in the gamma-ray regime with the upcoming GLAST mission and current advances in Atmospheric Cherenkov Telescope technology. In addition to pure leptonic and hadronic models of gamma-ray emission from blazars, leptonic/hadronic hybrid models are reviewed, and the recently developed hadronic synchrotron mirror model for TeV gamma-ray flares which are not accompanied by simultaneous X-ray flares (``orphan TeV flares'') is revisited.Comment: Invited Review at "The Multimessenger Approach to Gamma-Ray Sources", Barcelona, Spain, July 2006; submitted to Astrophysics and Space Science. 10 pages, including 6 eps figures. Uses Springer's ApSS macro