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

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 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.

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

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

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

Switching the stereochemical outcome of 6-endo-trig cyclizations; Synthesis of 2,6-Cis-6-substituted 4-oxopipecolic acids

A base-mediated 6-endo-trig cyclization of readily accessible enone-derived α-amino acids has been developed for the direct synthesis of novel 2,6-cis-6- substituted-4-oxo-L-pipecolic acids. A range of aliphatic and aryl side chains were tolerated by this mild procedure to give the target compounds in good overall yields. Molecular modeling of the 6-endo-trig cyclization allowed some insight as to how these compounds were formed, with the enolate intermediate generated via an equilibrium process, followed by irreversible tautomerization/neutralization providing the driving force for product formation. Stereoselective reduction and deprotection of the resulting 2,6-cis-6-substituted 4-oxo-L-pipecolic acids to the corresponding 4-hydroxy-L-pipecolic acids was also performed

Improved catalytic activity of ruthenium–arene complexes in the reduction of NAD+

A series of neutral Ru-II half-sandwich complexes of the type [(eta(6)-arene)Ru(N,N')Cl] where the arene is para-cymene (p-cym), hexamethylbenzene (hmb), biphenyl (bip), or benzene (bn) and N,N' is N-(2-aminoethyl) -4-(trifluoromethyl)benzenesulfonamide (TfEn), N-(2-aminoethyl)-4-toluenesulfonamide (TsEn), or N-(2-aminoethyl)-methylenesulfonamide (MsEn) were synthesized and characterized. X-ray crystal structures of [(p-cym)Ru(MsEn)Cl] (1), [(hmb)Ru(TsEn)Cl] (5), [(hmb)Ru(TfEn)Cl] (6), [(bip)Ru(MsEn)Cl] (7), and [(bip)Ru(TsEn)Cl] (8) have been determined. The complexes can regioselectively catalyze the transfer hydrogenation of NAD(+) to give 1,4-NADH in the presence of formate. The turnover frequencies (TOF) when the arene is varied decrease in the order bn > bip > p-cym > hmb for complexes with the same N,N' chelating ligand. The TOF decreased with variation in the N,N' chelating ligand in the order TfEn > TsEn > MsEn for a given arene. [(bn)Ru(TfEn)Cl] (12) was the most active, with a TOP of 10.4 h(-1). The effects of NAD(+) and formate concentration on the reaction rates were determined for [(p-cym)Ru(TsEn)Cl] (2). Isotope studies implicated the formation of [(arene)Ru(N,N')(H)] as the rate-limiting step. The coordination of formate and subsequent CO2 elimination to generate the hydride were modeled computationally by density functional theory (DFT). CO2 elimination occurs via a two-step process with the coordinated formate first twisting to present its hydrogen toward the metal center. The computed barriers for CO2 release for arene = benzene follow the order MsEn > TsEn > TfEn, and for the Ms En system the barrier followed bn < hmb, both consistent with the observed rates. The effect of methanol on transfer hydrogenation rates in aqueous solution was investigated. A study of pH dependence of the reaction in D2O gave the optimum pH* as 7.2 with a TOF of 1.58 h(-1) for 2. The series of compounds reported here show an improvement in the catalytic activity by an order of magnitude compared to the ethylenediamine analogues

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure