21. Sets of Invariant Measures and Cesaro StabilitySergey Kryzhevich, 2017, original scientific article Abstract: We take a space X of dynamical systems that could be: homeomorphisms or continuous maps of a compact metric space K or diffeomorphisms of a smooth manifold or actions of an amenable group. We demonstrate that a typical dynamical system of X is a continuity point for the set of probability invariant measures considered as a function of a map, let Y be the set of all such continuity points. As a corollary we prove that for typical dynamical systems average values of continuous functions calculated along trajectories do not drastically change if the system is perturbed.
Keywords: ergodic theory, invariant measures, shadowing, stability, tolerance stability, topological dynamics
Published in RUNG: 02.10.2017; Views: 3637; Downloads: 0
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22. Weak forms of shadowing in topological dynamicsSergey Kryzhevich, Danila Cherkashin, 2017, original scientific article Abstract: We consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomorphisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing) implies possibility to calculate minimal points of the dynamical system.
We prove that for the non-wandering case multishadowing is equivalent to density of minimal points. Moreover, it is equivalent to existence of a family of $\varepsilon$-networks ($\varepsilon > 0$) whose iterations are also $\varepsilon$-networks. Relations between multishadowing and some ergodic and topological properties of dynamical systems are discussed.
Keywords: Topological dynamics, minimal points, invariant measure, shadowing, chain recurrence, $\varepsilon$-networks, syndetic sets
Published in RUNG: 27.07.2017; Views: 4190; Downloads: 0
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23. Heart rate variability and nonlinear dynamic analysis in patients with stress-induced cardiomyopathyGoran Krstačić, Gianfranco Parati, Dragan Gamberger, Paolo Castiglioni, Antonija Krstačić, Robert Steiner, 2012, original scientific article Abstract: Complexity-based analyses may quantify abnormalities in heart rate variability (HRV). The aim of this study was to investigate the clinical and prognostic significances of dynamic HRV changes in patients with stress-induced cardiomyopathy Takotsubo syndrome (TS) by means of linear and nonlinear analysis. Patients with TS were included in study after complete noninvasive and invasive cardiovascular diagnostic evaluation and compared to an age and gender matched control group of healthy subjects. Series of R–R interval and of ST–T interval values were obtained from 24-h ECG recordings after digital sampling. HRV analysis was performed by ‘range rescaled analysis’ to determine the Hurst exponent, by detrended fluctuation analysis to quantify fractal longrange correlation properties, and by approximate entropy to assess time-series predictability. Short- and long-term fractal-scaling exponents were significantly higher in patients with TS in acute phases, opposite to lower approximate entropy and Hurst exponent, but all variables normalized in a few weeks. Dynamic HRV analysis allows assessing changes in complexity features of HRV in TS patients during the acute stage, and to monitor recovery after treatment, thus complementing traditional ECG and clinically analysis.
Keywords: Heart rate variability, Nonlinear dynamics, Chaos theory, Stress-induced cardiomyopathy, Takotsubo syndrome
Published in RUNG: 13.07.2017; Views: 5036; Downloads: 0
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24. Self-amplified photo-induced gap quenching in a correlated electron materialMathias Stefan, Eich Steffen, Jurij Urbančič, 2016, original scientific article Abstract: Capturing the dynamic electronic band structure of a correlated material presents a powerful capability for uncovering the complex couplings between the electronic and structural degrees of freedom. When combined with ultrafast laser excitation, new phases of matter can result, since far-from-equilibrium excited states are instantaneously populated. Here, we elucidate a general relation between ultrafast non-equilibrium electron dynamics and the size of the characteristic energy gap in a correlated electron material. We show that carrier multiplication via impact ionization can be one of the most important processes in a gapped material, and that the speed of carrier multiplication critically depends on the size of the energy gap. In the case of the charge-density wave material 1T-TiSe 2 , our data indicate that carrier multiplication and gap dynamics mutually amplify each other, which explains—on a microscopic level—the extremely fast response of this material to ultrafast optical excitation.
Self-amplified photo-induced gap quenching in a correlated electron material. Available from: https://www.researchgate.net/publication/308804379_Self-amplified_photo-induced_gap_quenching_in_a_correlated_electron_material [accessed Apr 20, 2017].
Keywords: high harmonic generation, charge-density wave material, 1T-TiSe2, non-equilibrium electron dynamics, ultrafast surface science
Published in RUNG: 20.04.2017; Views: 5472; Downloads: 0
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25. Distance-based configurational entropy of proteins from molecular dynamics simulationsFederico Fogolari, Alessandra Corazza, Sara Fortuna, Miguel Angel Soler, Bryan VanSchouwen, Giorgia Brancolini, Stefano Corni, Giuseppe Melacini, Gennaro Esposito, 2015, original scientific article Abstract: Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes.
In particular:
reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;
the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;
backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);
the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface.
This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.
Keywords: entropy, protein, molecular dynamics, simulations, MD
Published in RUNG: 12.10.2016; Views: 4232; Downloads: 221
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26. Accurate estimation of the entropy of rotation-translation probability distributionsFederico Fogolari, Cedrix Jurgal Dongmo Foumthuim, Sara Fortuna, Miguel Angel Soler, Alessandra Corazza, Gennaro Esposito, 2016, original scientific article Abstract: The estimation of rotational and translational entropies in the context of ligand binding has been the subject of long-time investigations. The high dimensionality (six) of the problem and the limited amount of sampling often prevent the required resolution to provide accurate estimates by the histogram method. Recently, the nearest-neighbor distance method has been applied to the problem, but the solutions provided either address rotation and translation separately, therefore lacking correlations, or use a heuristic approach. Here we address rotational–translational entropy estimation in the context of nearest-neighbor-based entropy estimation, solve the problem numerically, and provide an exact and an approximate method to estimate the full rotational–translational entropy.
Keywords: entropy, probability distribution, molecular dynamics, nearest-neighbor
Published in RUNG: 11.10.2016; Views: 4367; Downloads: 0
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27. Molecular dynamics simulations and docking enable to explore the biophysical factors controlling the yields of engineered nanobodiesMiguel Soler, Ario De Marco, Sara Fortuna, 2016, original scientific article Abstract: Nanobodies (VHHs) have proved to be valuable substitutes of conventional antibodies for molecular
recognition. Their small size represents a precious advantage for rational mutagenesis based on
modelling. Here we address the problem of predicting how Camelidae nanobody sequences can tolerate
mutations by developing a simulation protocol based on all-atom molecular dynamics and wholemolecule
docking. The method was tested on two sets of nanobodies characterized experimentally
for their biophysical features. One set contained point mutations introduced to humanize a wild type
sequence, in the second the CDRs were swapped between single-domain frameworks with Camelidae
and human hallmarks. The method resulted in accurate scoring approaches to predict experimental
yields and enabled to identify the structural modifications induced by mutations. This work is a
promising tool for the in silico development of single-domain antibodies and opens the opportunity to
customize single functional domains of larger macromolecules
Keywords: nanobodies, molecular dynamics, modeling, antibody solubility
Published in RUNG: 11.10.2016; Views: 4664; Downloads: 244
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