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- ItemThe Contrasting Character of Early and Late Transition Metal Fluorides as Hydrogen Bond Acceptors(Washington, DC : ACS Publications, 2015) Smith, Dan A.; Beweries, Torsten; Blasius, Clemens; Jasim, Naseralla; Nazir, Ruqia; Nazir, Sadia; Robertson, Craig C.; Whitwood, Adrian C.; Hunter, Christopher A.; Brammer, Lee; Perutz, Robin N.The association constants and enthalpies for the binding of hydrogen bond donors to group 10 transition metal complexes featuring a single fluoride ligand (trans-[Ni(F)(2-C5NF4)(PR3)2], R = Et 1a, Cy 1b, trans-[Pd(F)(4-C5NF4)(PCy3)2] 2, trans-[Pt(F){2-C5NF2H(CF3)}(PCy3)2] 3 and of group 4 difluorides (Cp2MF2, M = Ti 4a, Zr 5a, Hf 6a; Cp*2MF2, M = Ti 4b, Zr 5b, Hf 6b) are reported. These measurements allow placement of these fluoride ligands on the scales of organic H-bond acceptor strength. The H-bond acceptor capability β (Hunter scale) for the group 10 metal fluorides is far greater (1a 12.1, 1b 9.7, 2 11.6, 3 11.0) than that for group 4 metal fluorides (4a 5.8, 5a 4.7, 6a 4.7, 4b 6.9, 5b 5.6, 6b 5.4), demonstrating that the group 10 fluorides are comparable to the strongest organic H-bond acceptors, such as Me3NO, whereas group 4 fluorides fall in the same range as N-bases aniline through pyridine. Additionally, the measurement of the binding enthalpy of 4-fluorophenol to 1a in carbon tetrachloride (−23.5 ± 0.3 kJ mol–1) interlocks our study with Laurence’s scale of H-bond basicity of organic molecules. The much greater polarity of group 10 metal fluorides than that of the group 4 metal fluorides is consistent with the importance of pπ–dπ bonding in the latter. The polarity of the group 10 metal fluorides indicates their potential as building blocks for hydrogen-bonded assemblies. The synthesis of trans-[Ni(F){2-C5NF3(NH2)}(PEt3)2], which exhibits an extended chain structure assembled by hydrogen bonds between the amine and metal-fluoride groups, confirms this hypothesis.
- ItemMomentum space entanglement from the Wilsonian effective action(Woodbury, NY : Inst., 2022) Martins Costa, Matheus H.; van den Brink, Jeroen; Nogueira, Flavio S.; Krein, Gastão I.The entanglement between momentum modes of a quantum field theory at different scales is not as well studied as its counterpart in real space, despite the natural connection with the Wilsonian idea of integrating out the high-momentum degrees of freedom. Here, we push such a connection further by developing a novel method to calculate the Rényi and entanglement entropies between slow and fast modes, which is based on the Wilsonian effective action at a given scale. This procedure is applied to the perturbative regime of some scalar theories, comparing the lowest-order results with those from the literature and interpreting them in terms of Feynman diagrams. This method is easily generalized to higher-order or nonperturbative calculations. It has the advantage of avoiding matrix diagonalizations of other techniques.
- ItemThe complexity of gene expression dynamics revealed by permutation entropy(London : BioMed Central Ltd., 2010) Sun, Xiaoliang; Zou, Yong; Nikiforova, Victoria; Kurths, Jürgen; Walther, DirkBackground: High complexity is considered a hallmark of living systems. Here we investigate the complexity of temporal gene expression patterns using the concept of Permutation Entropy (PE) first introduced in dynamical systems theory. The analysis of gene expression data has so far focused primarily on the identification of differentially expressed genes, or on the elucidation of pathway and regulatory relationships. We aim to study gene expression time series data from the viewpoint of complexity.Results: Applying the PE complexity metric to abiotic stress response time series data in Arabidopsis thaliana, genes involved in stress response and signaling were found to be associated with the highest complexity not only under stress, but surprisingly, also under reference, non-stress conditions. Genes with house-keeping functions exhibited lower PE complexity. Compared to reference conditions, the PE of temporal gene expression patterns generally increased upon stress exposure. High-complexity genes were found to have longer upstream intergenic regions and more cis-regulatory motifs in their promoter regions indicative of a more complex regulatory apparatus needed to orchestrate their expression, and to be associated with higher correlation network connectivity degree. Arabidopsis genes also present in other plant species were observed to exhibit decreased PE complexity compared to Arabidopsis specific genes.Conclusions: We show that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.
- ItemCan One Series of Self-Organized Nanoripples Guide Another Series of Self-Organized Nanoripples during Ion Bombardment: From the Perspective of Power Spectral Density Entropy?(Basel : MDPI, 2023) Li, Hengbo; Li, Jinyu; Yang, Gaoyuan; Liu, Ying; Frost, Frank; Hong, YilinIon bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of nanoripples is an outstanding issue to be overcome, similar to other self-organization methods. In this study, the IB-induced nanoripples on bilayer systems with enhanced quality are revisited from the perspective of guided self-organization. First, power spectral density (PSD) entropy is introduced to evaluate the degree of ordering of the irradiated nanoripples, which is calculated based on the PSD curve of an atomic force microscopy image (i.e., the Fourier transform of the surface height. The PSD entropy can characterize the degree of ordering of nanoripples). The lower the PSD entropy of the nanoripples is, the higher the degree of ordering of the nanoripples. Second, to deepen the understanding of the enhanced quality of nanoripples on bilayer systems, the temporal evolution of the nanoripples on the photoresist (PR)/antireflection coating (ARC) and Au/ARC bilayer systems are compared with those of single PR and ARC layers. Finally, we demonstrate that a series of intrinsic IB-induced nanoripples on the top layer may act as a kind of self-organized template to guide the development of another series of latent IB-induced nanoripples on the underlying layer, aiming at improving the ripple ordering. The template with a self-organized nanostructure may alleviate the critical requirement for periodic templates with a small period of ~100 nm. The work may also provide inspiration for guided self-organization in other fields.
- ItemA new color image encryption scheme using CML and a fractional-order chaotic system(San Francisco, CA : Public Library of Science (PLoS), 2015) Wu, X.; Li, Y.; Kurths, J.
- ItemThermal effects in gravitational Hartree systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Aki, Gonca L.; Dolbeault, Jean; Sparber, ChristofWe consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass $M>0$, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T^*>0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature T_c in (0, T^*) above which mixed states appear.
- ItemThe sharp interface limit of the Van der Waals-Cahn-Hilliard phase model for fixed and time dependent domains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Dreyer, Wolfgang; Kraus, ChristianeWe study the equilibria of liquid--vapor phase transitions of a single substance at constant temperature and relate the sharp interface model of classical thermodynamics to a phase field model that determines the equilibria by the stationary van der Waals--Cahn--Hilliard theory. For two reasons we reconsider this old problem. 1. Equilibria in a two phase system can be established either under fixed total volume of the system or under fixed external pressure. The latter case implies that the domain of the two--phase system varies. However, in the mathematical literature rigorous sharp interface limits of phase transitions are usually considered under fixed volume. This brings the necessity to extend the existing tools for rigorous sharp interface limits to changing domains since in nature most processes involving phase transitions run at constant pressure. 2. Thermodynamics provides for a single substance two jump conditions at the sharp interface, viz. the continuity of the specific Gibbs free energies of the adjacent phases and the discontinuity of the corresponding pressures, which is balanced by the mean curvature. The existing estimates for rigorous sharp interface limits show only the first condition ...
- ItemLarge deviations for the capacity in dynamic spatial relay networks(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hirsch, Christian; Jahnel, BenediktWe derive a large deviation principle for the space-time evolution of users in a relay network that are unable to connect due to capacity constraints. The users are distributed according to a Poisson point process with increasing intensity in a bounded domain, whereas the relays are positioned deterministically with given limiting density. The preceding work on capacity for relay networks by the authors describes the highly simplified setting where users can only enter but not leave the system. In the present manuscript we study the more realistic situation where users leave the system after a random transmission time. For this we extend the point process techniques developed in the preceding work thereby showing that they are not limited to settings with strong monotonicity properties.
- ItemSpace-time large deviations in capacity-constrained relay networks(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hirsch, Christian; Jahnel, Benedikt; Patterson, RobertWe consider a single-cell network of random transmitters and fixed relays in a bounded domain of Euclidean space. The transmitters arrive over time and select one relay according to a spatially inhomogeneous preference kernel. Once a transmitter is connected to a relay, the connection remains and the relay is occupied. If an occupied relay is selected by another transmitters with later arrival time, this transmitter becomes frustrated. We derive a large deviation principle for the space-time evolution of frustrated transmitters in the high-density regime.
- ItemTrends in recurrence analysis of dynamical systems(Les Ulis : EDP Sciences, 2023) Marwan, Norbert; Kraemer, K. HaukeThe last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research.