Klaus M. Frahm’s research while affiliated with French National Centre for Scientific Research and other places

We analyze the Google matrix of directed networks of Wikipedia articles related to eight recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm, we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the eight editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish five poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as five poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter-edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the eight cultures with respect to the selected society concepts and religions.

We analyze the Google matrix of directed networks of Wikipedia articles related to 8 recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the 8 editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish 5 poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as 5 poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the 8 cultures with respect to the selected society concepts and religions.

We analyze the Google matrix of directed networks of Wikipedia articles related to 8 recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the 8 editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish 5 poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as 5 poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the 8 cultures with respect to the selected society concepts and religions.

Myocardial fibrosis is a major pathologic disorder associated with a multitude of cardiovascular diseases (CVD). The pathogenesis is complex and encompasses multiple molecular pathways. Integration of fibrosis-associated genes into the global MetaCore network of protein-protein interactions (PPI) offers opportunities to identify PPI with functional and therapeutic significance. Here, we report the generation of a fibrosis-focused PPI network and identification of fibroblast-specific arbitrators driving reparative and reactive myocardial fibrosis. In TGF-β-mediated fibroblast activation, developed network analysis predicts new regulatory mechanisms for fibrosis-associated genes. We introduce an efficient Erdös barrage approach to suppress activation of a number of fibrosis-associated nodes in order to reverse fibrotic cascades. In the network model each protein node is characterized by an Ising up or down spin corresponding to activated or repairing state acting on other nodes being initially in a neutral state. An asynchronous Monte Carlo process describes fibrosis progression determined by a dominant action of linked proteins. Our results suggest that the constructed Ising Network Fibrosis Interaction model offers network insights into fibrosis mechanisms and can complement future experimental efforts to counteract cardiac fibrosis.

Myocardial fibrosis is a major pathologic disorder associated with a multitude of cardiovascular diseases (CVD). The pathogenesis is complex and encompasses multiple molecular pathways. Integration of fibrosis-associated genes into the global MetaCore network of protein-protein interactions (PPI) offers opportunities to identify PPI with functional and therapeutic significance. Here, we report the generation of a fibrosis-focused PPI network and identification of fibroblast-specific PPI driving reparative and reactive myocardial fibrosis. In TGFb-mediated fibroblast activation, PPI hubs predict new regulatory mechanisms for fibrosis-associated genes. We introduce an efficient Erdös barrage approach to suppress activation of a number of fibrosis-associated nodes in order to reverse fibrotic cascades. Our results suggest that PPI prediction model can offer network insights into fibrosis mechanisms and can complement future experimental efforts to counteract cardiac fibrosis.

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows us to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erdös numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to target B. We argue that such an algorithm provides unique hints for motion control in chaotic flows.

We consider a system of linear oscillators, or quantum states, described by random matrix theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values, and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Owing to universal features of random matrix theory we argue that the obtained results describe the generic properties of its nonlinear perturbation.

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erd\"os numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to the target B. We argue that such an algorithm provides new hints for motion control in chaotic flows.

We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Due to universal features of Random Matrix Theory we argue that the obtained results describe the generic properties of its nonlinear perturbation.