On Markov State Models for Metastable Processes

We consider Markov processes on large state spaces and want to find low-dimensional structure-preserving approximations of the process in the sense that the longest timescales of the dynamics of the original process are reproduced well. Recent years have seen the advance of so-called Markov state models (MSM) for processes on very large state spaces exhibiting metastable dynamics. It has been demonstrated that MSMs are especially useful for modelling the interesting slow dynamics of biomolecules (cf. Noe et al, PNAS(106) 2009) and materials. From the mathematical perspective, MSMs result from Galerkin projection of the transfer operator underlying the original process onto some low-dimensional subspace which leads to an approximation of the dominant eigenvalues of the transfer operators and thus of the longest timescales of the original dynamics. Until now, most articles on MSMs have been based on full subdivisions of state space, i.e., Galerkin projections onto subspaces spanned by indicator functions. We show how to generalize MSMs to alternative low-dimensional subspaces with superior approximation properties, and how to analyse the approximation quality (dominant eigenvalues, propagation of functions) of the resulting MSMs. To this end, we give an overview of the construction of MSMs, the associated stochastics and functional-analysis background, and its algorithmic consequences. Furthermore, we illustrate the mathematical construction with numerical examples

Estimating the eigenvalue error of Markov State Models

We consider a continuous-time, ergodic Markov process on a large continuous or discrete state space. The process is assumed to exhibit a number of metastable sets. Markov state models (MSM) are designed to represent the effective dynamics of such a process by a Markov chain that jumps between the metastable sets with the transition rates of the original process. MSM are used for a number of applications, including molecular dynamics (cf. Noe et al, PNAS(106) 2009)[1], since more than a decade. The rigorous and fully general (no zero temperature limit or comparable restrictions) analysis of their approximation quality, however, has only been started recently. Our first article on this topics (Sarich et al, MMS(8) 2010)[2] introduces an error bound for the difference in propagation of probability densities between the MSM and the original process on long time scales. Herein we provide upper bounds for the error in the eigenvalues between the MSM and the original process which means that we analyse how well the longest timescales in the original process are approximated by the MSM. Our findings are illustrated by numerical experiments

Political will, work values, and objective career success: A novel approach – The Trait-Reputation-Identity Model

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordIndividual-level political will in organizations and careers is recognized by many scholars as an important yet under-investigated construct. Only recently has a scale directly assessing political will been developed, and its validation process has just begun (Kapoutsis, Papalexandris, Treadway, & Bentley, 2017). We used the Trait-Reputation-Identity Model (McAbee & Connelly, 2016) and a triadic multisource design to explore and elucidate the nomological network of political will, including its link to objective career success. We found supporting empirical evidence for the construct (power striving) and criterion validity (hierarchical position and income) of the self-serving political will scale. However, our findings did not support the multi-rater convergence and the interpretation of the benevolent political will scale as representing an altruistic political motive. Hence, we suggest the development and validation of new items that directly relate to benevolence toward others at work. We further encourage researchers to develop and validate an additional scale assessing altruistic political will above and beyond self-serving and benevolent political will. We discuss additional implications, limitations, and directions for future research

Political Skill Moderates the Success of Psychopaths at the Workplace

On one hand, psychopaths tend to be callous, emotionally deficient, aggressive, self promoting, impulsive, and pursuant of unmitigated agency regardless of the extent to which it comes at the expense of others. On the other hand, by all accounts, psychopaths tend to be charming, seductive, self-confident, composed, risk-seeking, and adept at impression management (Babiak & Hare, 2006; Paulhus & Williams, 2002). Therefore, the purpose of this study was to reconcile these contrasting positions by examining whether (non-violent) psychopaths truly can be “successful” in the workplace. Drawing on socioanalytic theory (Hogan, 1983), we hypothesized that psychopaths in possession of political skill would be better able to package, conceal, and/or restrain their desires to get ahead in such a way as to be perceived as less counterproductive and more adaptive. Results provided support for these hypotheses. Implications for theory, practice, and future research are provided in light of a number of notable strengths and limitations

Modularity revisited: A novel dynamics-based concept for decomposing complex networks

Finding modules (or clusters) in large, complex networks is a challenging task, in particular if one is not interested in a full decomposition of the whole network into modules. We consider modular networks that also contain nodes that do not belong to one of modules but to several or to none at all. A new method for analyzing such networks is presented. It is based on spectral analysis of random walks on modular networks. In contrast to other spectral clustering approaches, we use different transition rules of the random walk. This leads to much more prominent gaps in the spectrum of the adapted random walk and allows for easy identification of the network's modular structure, and also identifying the nodes belonging to these modules. We also give a characterization of that set of nodes that do not belong to any module, which we call transition region. Finally, by analyzing the transition region, we describe an algorithm that identifies so called hub-nodes inside the transition region that are important connections between modules or between a module and the rest of the network. The resulting algorithms scale linearly with network size (if the network connectivity is sparse) and thus can also be applied to very large networks

Ein nichtlineares anisotropes Materialmodell auf der Basis der Hencky-Dehnung und der logarithmischen Rate zur Beschreibung duktiler Schädigung

Ein nichtlineares, dreidimensionales und anisotropes Sehddigungsmodell wird vorgestellt. Basis des Modells ist der Rahmen für finite Elastoplastizität von Xiao, Bruhns & Meyers. Von entscheidender Bedeutung für die Modellierung ist eine doppelte Interpretation des Schädigungsparameters. Für die thermodgnamischen Betrachtungen wird der Schädigungsparameter als eine interne Zustandsuariable betrachtet. Zur Modellierung der schädigungsinduzierten Anisotropie wird er als ein sich mit der  Deformation entwickelnder Struktur- oder Materialtensor interpretiert. Schädigungsmodellierung reduziert sich damit auf die Formulierung von Euolutionsgleichungen, die Festlegung von Versagenskriterien und die Bestimmung von Materialkonstanten

The role of interpersonal influence in counterbalancing psychopathic personality trait facets at work

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordThe purpose of this study was to examine the relations of two facets of psychopathic personality (i.e., self-centered impulsivity and fearless dominance) with interpersonally directed counterproductive work behavior (CWB-I) and contextual performance (CP). Consistent with research on psychopathy, our hypothesis suggested that self-centered impulsivity (i.e., behavioral impulsivity characterized by disregard for rules and responsibilities) would be positively related to CWB-I and negatively related to CP. Using socioanalytic theory, we further suggested that fearless dominance (i.e., an egotistical personal style characterized by self-promotion and prioritization of one’s own needs before those of others) would be negatively associated with interpersonal performance (i.e., high CWB-I and low CP) only when individuals indicated low levels of interpersonal influence (i.e., a dimension of political skill reflecting an ability to adapt one’s behavior in subtle, sophisticated, and situationally effective ways). Results provided strong support for the differential relations of the psychopathic personality dimensions with the criteria of interest. Implications for theory, practice, and future research are provided in light of a number of notable strengths and limitations

Quantitative spectroscopy of single molecule interaction times

Funding Information: Deutsche Forschungsgemeinschaft (421152132 (subproject C03)), EXC 2046 (MATH+Incubator project IN-B2).Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets.Publisher PDFPeer reviewe

Covalency effects on the magnetism of EuRh2P2

In experiments, the ternary Eu pnictide EuRh2P2 shows an unusual coexistence of a non-integral Eu valence of about 2.2 and a rather high Neel temperature of 50 K. In this paper, we present a model which explains the non-integral Eu valence via covalent bonding of the Eu 4f-orbitals to P2 molecular orbitals. In contrast to intermediate valence models where the hybridization with delocalized conduction band electrons is known to suppress magnetic ordering temperatures to at most a few Kelvin, covalent hybridization to the localized P2 orbitals avoids this suppression. Using perturbation theory we calculate the valence, the high temperature susceptibility, the Eu single-ion anisotropy and the superexchange couplings of nearest and next-nearest neighbouring Eu ions. The model predicts a tetragonal anisotropy of the Curie constants. We suggest an experimental investigation of this anisotropy using single crystals. From experimental values of the valence and the two Curie constants, the three free parameters of our model can be determined.Comment: 9 pages, 5 figures, submitted to J. Phys.: Condens. Matte

Algebraic totality, towards completeness

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\mathcal{B}}^n\to{\mathcal{B}}$ for every n by an algebraic method