How Damage Diversification Can Reduce Systemic Risk

We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses resulting from defaulting neighbors, which may lead to large failure cascades. Classical risk diversification strategies usually neglect network effects and therefore suggest that risk can be reduced if possible losses (i.e., exposures) are split among many neighbors (exposure diversification, ED). But from a complex networks perspective diversification implies higher connectivity of the system as a whole which can also lead to increasing failure risk of a node. To cope with this, we propose a different strategy (damage diversification, DD), i.e. the diversification of losses that are imposed on neighboring nodes as opposed to losses incurred by the node itself. Here, we quantify the potential of DD to reduce systemic risk in comparison to ED. For this, we develop a branching process approximation that we generalize to weighted networks with (almost) arbitrary degree and weight distributions. This allows us to identify systemically relevant nodes in a network even if their directed weights differ strongly. On the macro level, we provide an analytical expression for the average cascade size, to quantify systemic risk. Furthermore, on the meso level we calculate failure probabilities of nodes conditional on their system relevance

Statistical mechanics of the international trade network

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e. quasi-static process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills fluctuation-response theorem, which states that the average relative change in import (export) between two countries is a sum of relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.Comment: 6 pages, 2 figure

Revised metallicity classes for low-mass stars: dwarfs (dM), subdwarfs (sdM), extreme subdwarfs (esdM), and ultra subdwarfs (usdM)

The current classification system of M stars on the main sequence distinguishes three metallicity classes (dwarfs - dM, subdwarfs - sdM, and extreme subdwarfs - esdM). The spectroscopic definition of these classes is based on the relative strength of prominent CaH and TiO molecular absorption bands near 7000A, as quantified by three spectroscopic indices (CaH2, CaH3, and TiO5). We re-examine this classification system in light of our ongoing spectroscopic survey of stars with proper motion \mu > 0.45 "/yr, which has increased the census of spectroscopically identified metal-poor M stars to over 400 objects. Kinematic separation of disk dwarfs and halo subdwarfs suggest deficiencies in the current classification system. Observations of common proper motion doubles indicates that the current dM/sdM and sdM/esdM boundaries in the [TiO5,CaH2+CaH3] index plane do not follow iso-metallicity contours, leaving some binaries inappropriately classified as dM+sdM or sdM+esdM. We propose a revision of the classification system based on an empirical calibration of the TiO/CaH ratio for stars of near solar metallicity. We introduce the parameter \zeta_{TiO/CaH} which quantifies the weakening of the TiO bandstrength due to metallicity effect, with values ranging from \zeta_{TiO/CaH}=1 for stars of near-solar metallicity to \zeta_{TiO/CaH}~0 for the most metal-poor (and TiO depleted) subdwarfs. We redefine the metallicity classes based on the value of the parameter \zeta_{TiO/CaH}; and refine the scheme by introducing an additional class of ultra subdwarfs (usdM). We introduce sequences of sdM, esdM, and usdM stars to be used as formal classification standards.Comment: 15 pages, accepted for publication in the Astrophysical Journa

Building a comprehensive mentoring academy for schools of health.

Formal mentoring programs are increasingly recognized as critical for faculty career development. We describe a mentoring academy (MA) developed for faculty across tracks (i.e., researchers, clinicians, educators) within a "school of health" encompassing schools of medicine and nursing. The program is anchored dually in a clinical and translational science center and a school of health. The structure includes the involvement of departmental and center mentoring directors to achieve widespread uptake and oversight. A fundamental resource provided by the MA includes providing workshops to enhance mentoring skills. Initiatives for junior faculty emphasize establishing and maintaining strong mentoring relationships and implementing individual development plans (IDPs) for career planning. We present self-report data on competency improvement from mentor workshops and data on resources and barriers identified by junior faculty (n = 222) in their IDPs. Mentors reported statistically significantly improved mentoring competency after workshop participation. Junior faculty most frequently identified mentors (61%) and collaborators (23%) as resources for goal attainment. Top barriers included insufficient time and time-management issues (57%), funding limitations (18%), work-life balance issues (18%), including inadequate time for self-care and career development activities. Our MA can serve as a model and roadmap for providing resources to faculty across traditional tracks within medical schools

Conductivity in a symmetry broken phase: Spinless fermions with 1/d1/d corrections

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.Comment: 23 pages, 19 figures included with psfig, Revtex; Physical Review B15, in press (October/November 1996) depending on the printer/screen driver, it might be necessary to comment out figures 3,4,5,10,11,12,19 and have them printed separatel

Active Brownian particles with velocity-alignment and active fluctuations

We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed as independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account for example for thermal fluctuations. We derive a macroscopic description of the active Brownian particle gas with velocity-alignment interaction. Hereby, we start from the individual based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here in particular on the different impact of active and passive fluctuations on the onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuation lead to an earlier breakdown of collective motion and to emergence of a new bistable regime in the mean-field case.Comment: 5 figures, 22 pages, submitted to New Journal of Physic

A k-shell decomposition method for weighted networks

We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptible-infectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.Comment: 17 pages, 6 figure

Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling

The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the critical point. It is shown that the critical spacing distribution is size independent and has a Poisson-like decay at large spacings as distinct from the Gaussian asymptotic form obtained by the random-matrix theory.Comment: 7 pages REVTeX, 2 uuencoded, gzipped figures; J. Phys. Condensed Matter, in prin