Largest Non-Unique Subgraphs

The reduction number r(G) of a graph G is the maximum integer m≤|E(G)| such that the graphs G−E, E⊆E(G),|E|≤m, are mutually non-isomorphic, i.e., each graph is unique as a subgraph of G. We prove that and show by probabilistic methods that r(G) can come close to this bound for large orders. By direct construction, we exhibit graphs with large reduction number, although somewhat smaller than the upper bound. We also discuss similarities to a parameter introduced by Erdős and Rényi capturing the degree of asymmetry of a graph, and we consider graphs with few circuits in some detail. Supported by a grant from the Danish Natural Science Research Council.     

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.     

Impact of particle shape on refractive-index dependence of scattering in resonance domain

The impact of particle shape on how scattering, in particular the asymmetry parameter g, depends on the refractive index m is studied. Light scattering simulations for spheres and 16 different spheroids with varying refractive indices and sizes are carried out using an exact T-matrix method to establish how m affects scattering for different shapes. In addition to single shapes, shape distributions of spheroids are used to mimic scattering properties of ensembles of irregularly shaped particles. The results show that Δg resulting from Δm are both size and shape dependent, and spheroids are not universally less or more sensitive to m than the corresponding spheres are. While shape distributions of spheroids show much weaker and much more consistent m-dependence of g than the spheres of the same size, an integration over a size distribution (SD) largely eliminates these differences. Thus, the use of spheres for estimating Δg resulting from Δm for a collection of nonspherical particles appears to be safe except for very narrow SDs. The actual g-values tend to be, however, considerably and consistently in error.     

Consistent estimation of location region

Asymmetric multivariate probability distributions can be difficult to characterize in terms of their location. The works of Doksum (1975, Scand. J. Statist., 2, 11–22) and Blough (1985, Ann. Inst. Statist. Math., 37, 545–555) provide the construction of a location region for a given distribution. Any point in this closed, convex region will serve as a location parameter. It is the purpose of this paper to obtain a consistent estimator of the location region. Consistency is defined in terms of an appropriate pseudometric.     

The asymptotic distribution of magnitude trimmed sums for distributions in the Feller class

LetX, X ₁,X ₂,... be i.i.d. with common distribution functionF. Rather than study limit behavior of the sum,S _n =X ₁++X _n , under constant normalizations, we consider the sum with ther _n summands largest in magnitude removed from the sumS _n , wherer _n andr _n n ^–10. This is known as an intermediate magnitude trimmed sum. LetF be such that lim inf_t lim inf _t EX ² I(|X|t/)t ² P((|X|>t)>0. The collection of suchF is known as the Feller class, a large class of distributions which includes all domains of attraction (in particular the stable laws). Pruitt(¹³) showed that asymptotic normality always holds for the trimmed sums ifF is in the Feller class and ifF is symmetric. Here, for anyF in the Feller class, we obtain complete results including the form of the possible limit laws and their convergence criteria, thus generalizing Pruitt's result to the asymmetric setting.This paper forms a portion of the author's Ph.D. dissertation under the supervision of Daniel C. Weiner.     

Copper catalyzed enantioselective allylic substitution by MeMgX

Methyl Grignard undergoes highly regio (>90/10) and enantioselective (ee 91-96%) copper catalyzed allylic substitution on cinnamyl-type chlorides. CuBr (3%) and 3.3% of a chiral phosphoramidite ligand are sufficient for a complete reaction. The synthesis of a precursor of (+)-Naproxen is described. The reaction can be extended to alkyl substituted allylic chlorides (ee 72%).     

非对称量子点中电子的激发能量和跃迁谱线频率

研究了非对称量子点中与声子强耦合的电子的性质.采用线性组合算符和幺正变换方法研究非对称量子点中与声子强耦合的电子的第一内部激发态能量、激发能量和第一内部激发态到基态的跃迁谱线频率随量子点的横向和纵向有效受限长度,电子-声子耦合强度的变化关系。数值计算结果表明：非对称量子点中与声子强耦合的电子的第一内部激发态能量、激发能量和第一内部激发态到基态的跃迁谱线频率随量子点的横向和纵向有效受限长度的减小而迅速增大,表现出奇特的量子尺寸效应。非对称量子点中与声子强耦合的电子的第一内部激发态能量随电子-声子耦合强度的增加而减小。非对称量子点中与声子强耦合的电子的激发能量和第一内部激发态到基态的跃迁谱线频率随电子-声子耦合强度的增加而增大。     

Kinetic Asymmetry and Directionality of Nonequilibrium Molecular Systems

Scientists have long been fascinated by the biomolecular machines in living systems that process energy and information to sustain life. The first synthetic molecular rotor capable of performing repeated 360° rotations due to a combination of photo- and thermally activated processes was reported in 1999. The progress in designing different molecular machines in the intervening years has been remarkable, with several outstanding examples appearing in the last few years. Despite the synthetic accomplishments, there remains confusion regarding the fundamental design principles by which the motions of molecules can be controlled, with significant intellectual tension between mechanical and chemical ways of thinking about and describing molecular machines. A thermodynamically consistent analysis of the kinetics of several molecular rotors and pumps shows that while light driven rotors operate by a power-stroke mechanism, kinetic asymmetry—the relative heights of energy barriers—is the sole determinant of the directionality of catalysis driven machines. Power-strokes—the relative depths of energy wells—play no role whatsoever in determining the sign of the directionality. These results, elaborated using trajectory thermodynamics and the nonequilibrium pump equality, show that kinetic asymmetry governs the response of many non-equilibrium chemical phenomena.     

Magnetotransport in fractal network with loop sub-structures: Anisotropic effect and delocalization

We make an in-depth analysis of electronic transport and localization properties of non-interacting electrons in a Sierpinski gasket (SPG) fractal lattice in presence of magnetic field within a tight-binding framework. Unlike conventional symmetric systems, asymmetric SPG triangle leads to more conducting behavior, and thus delocalization of energy states, which we examine by calculating magnetic flux driven circular current and inverse participation ratio. The spectral peculiarity, that is the gapped nature of energy spectrum in fractal lattices, is clearly reflected from the variation of current with electron filling, yielding possibilities of getting filling dependent switching action. The effect of temperature is also discussed. Our analysis can be utilized to study magnetotransport properties in any other fractal lattices having loop sub-structures.     

An order of asymmetry in copulas,and implications for risk management

We study symmetry properties of bivariate copulas. For this, we introduce an order of asymmetry, as well as measures of asymmetry which are monotone in that order. In an empirical study, we illustrate that asymmetric dependence structures do indeed occur in financial market data and discuss its relevance for financial risk management.