Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Nonlinear Analysis of Irregular Variables

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been developed for analyzing irregular stellar light or radial velocity variations, and we describe what useful physical and astronomical information can be gained from their use.Comment: 31 pages, to appear as a chapter in `Nonlinear Stellar Pulsation' in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselo

Stimuli Responsive Silylene: Electromerism Induced Reversible Switching Between Mono‐ and Bis‐Silylene

Electromerism is a very well-known phenomenon in transition metal chemistry. In main group chemistry, this concept has only started getting attention recently. We report stimuli responsive low-valent silicon compounds exhibiting electromerism. A mixed-valent silaiminyl-silylene 1, [LSi−Si(NDipp)L] (L=PhC(N$^t$Bu)$_2$), was synthesized in a single step from amidinate-chlorosilylene. Compound 1 has two interconnected Si atoms in formally +I and +III oxidation states. Upon treatment with Lewis acidic Cu$^I$X (X=mesityl, Cl, Br, I), electron redistribution occurs resulting in the formation of [{LSi(NDipp)Si(L)}−CuX], in which both silicon atoms are in the +II formal oxidation state. Removal of the copper center from [{LSi(NDipp)Si(L)}−CuX] by using a Lewis basic carbene led to reformation of the precursor [LSi−Si(NDipp)L]. Thus, the process is fully reversible. This showcases the first example of Lewis acid/base-induced reversible electromerism in silicon chemistry

The prediction of future from the past: an old problem from a modern perspective

The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability results to be hindered rather by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, regardless the regular or chaotic nature of the system, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.Comment: 9 pages, 4 figure

A case of behavioural diversification in male floral function – the evolution of thigmonastic pollen presentation

The authors gratefully acknowledge funding provided by an Else-Neumann-Stipendium (http://www.fu-berlin.de/sites/promovieren/drs/nachwuchs/nachwuchs/nafoeg.html), Deutscher Akademischer Austausch Dienst (DAAD) and botconsult GmbH at different stages of data acquisition. We thank Tobias Grass, Joana Bergmann and Franziska Weber (Freie Universität Berlin) for help with data collection in the field and in the greenhouse. Nicole Schmandt, Federico Luebert, Juliana Chacón and Dietmar Quant (Universität Bonn) provided help in the molecular laboratory and the edition of the molecular dataset. We furthermore thank Markus Ackermann (Koblenz) for providing photographs, Philipp Klein (Berlin) for editing the video and Katy Jones (Berlin) for helpful comments on an earlier version of the manuscript. Rafael Acuña has been supported by the ALECOSTA scholarship program. Coverage of the article processing charge by the German Research Foundation via the Open Access Publication Fund of the Freie Universität Berlin is gratefully acknowledged.Peer reviewedPublisher PD

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT (IAAFT), which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be re-investigated taken into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.Comment: 14 pages, 15 figures, submitted to Physical Review

A QM/MM approach for the study of monolayer-protected gold clusters

We report the development and implementation of hybrid methods that combine quantum mechanics (QM) with molecular mechanics (MM) to theoretically characterize thiolated gold clusters. We use, as training systems, structures such as Au25(SCH2-R)18 and Au38(SCH2-R)24, which can be readily compared with recent crystallographic data. We envision that such an approach will lead to an accurate description of key structural and electronic signatures at a fraction of the cost of a full quantum chemical treatment. As an example, we demonstrate that calculations of the 1H and 13C NMR shielding constants with our proposed QM/MM model maintain the qualitative features of a full DFT calculation, with an order-of-magnitude increase in computational efficiency.Comment: Journal of Materials Science, 201

Distributed Multipoles from a Robust Basis-Space Implementation of the Iterated Stockholder Atoms Procedure

The recently developed iterated stockholder atoms (ISA) approach of Lillestolen and Wheatley (<i>Chem. Commun.</i> <b>2008</b>, 5909) offers a powerful method for defining atoms in a molecule. However, the real-space algorithm is known to converge very slowly, if at all. Here, we present a robust, basis-space algorithm of the ISA method and demonstrate its applicability on a variety of systems. We show that this algorithm exhibits rapid convergence (taking around 10–80 iterations) with the number of iterations needed being unrelated to the system size or basis set used. Further, we show that the multipole moments calculated using this basis-space ISA method are as good as, or better than, those obtained from Stone’s distributed multipole analysis (<i>J. Chem. Theory Comput.</i> <b>2005</b>, <i>1</i>, 1128), exhibiting better convergence properties and resulting in better behaved penetration energies. This can have significant consequences in the development of intermolecular interaction models