3,331 research outputs found
Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems
We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low‐frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed
Comment on "Finite size scaling in Neural Networks"
We use a binary search tree and the simplex algorithm to measure the fraction
of patterns that can be stored by an Ising perceptron. The algorithm is much
faster than exhaustive search and allows us to obtain accurate statistics up to
a system size of N=42. The results show that the finite size scaling ansatz
Nadler and Fink suggest in [1] cannot be applied to estimate accurately the
storage capacity from small systems.
[1] W.Nadler and W.Fink: Phys.Rev.Lett. 78, 555 (1997)Comment: LaTeX with 1 postscript figure, using REVTe
Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators
This paper presents a diffusion based probabilistic interpretation of
spectral clustering and dimensionality reduction algorithms that use the
eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency
matrix of all points, we define a diffusion distance between any two data
points and show that the low dimensional representation of the data by the
first few eigenvectors of the corresponding Markov matrix is optimal under a
certain mean squared error criterion. Furthermore, assuming that data points
are random samples from a density p(\x) = e^{-U(\x)} we identify these
eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck
operator in a potential 2U(\x) with reflecting boundary conditions. Finally,
applying known results regarding the eigenvalues and eigenfunctions of the
continuous Fokker-Planck operator, we provide a mathematical justification for
the success of spectral clustering and dimensional reduction algorithms based
on these first few eigenvectors. This analysis elucidates, in terms of the
characteristics of diffusion processes, many empirical findings regarding
spectral clustering algorithms.Comment: submitted to NIPS 200
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A simulation approach to the investigation of the statistical properties of the rebalancing policy of portfolio adjustment.
Kinetic distance and kinetic maps from molecular dynamics simulation
Characterizing macromolecular kinetics from molecular dynamics (MD)
simulations requires a distance metric that can distinguish
slowly-interconverting states. Here we build upon diffusion map theory and
define a kinetic distance for irreducible Markov processes that quantifies how
slowly molecular conformations interconvert. The kinetic distance can be
computed given a model that approximates the eigenvalues and eigenvectors
(reaction coordinates) of the MD Markov operator. Here we employ the
time-lagged independent component analysis (TICA). The TICA components can be
scaled to provide a kinetic map in which the Euclidean distance corresponds to
the kinetic distance. As a result, the question of how many TICA dimensions
should be kept in a dimensionality reduction approach becomes obsolete, and one
parameter less needs to be specified in the kinetic model construction. We
demonstrate the approach using TICA and Markov state model (MSM) analyses for
illustrative models, protein conformation dynamics in bovine pancreatic trypsin
inhibitor and protein-inhibitor association in trypsin and benzamidine
Connecting up strategy: are senior strategy directors a missing link?
With companies being exhorted to become more strategically agile and internally connected, this article examines the role of the Senior Strategy Director, the executive tasked specifically with internal strategy. In particular, it explores what they do, what specific capabilities they deploy to enable effective contribution to the company, and in what ways they facilitate the connectedness of strategy. An analysis of multiple interviews over time with Senior Strategy Directors of large companies shows the vital and challenging role these executives play in both shaping, connecting up, and executing strategy. This article identifies the particular capabilities necessary for Senior Strategy Directors to perform their role and shows how it all depends upon their skilful deployment. These findings have significant implications for understanding unfolding micro-processes of strategy in large organizations, for assumptions about the skills and capabilities necessary to be an effective Senior Strategy Director, and for business schools in terms of the content and style of strategy courses they provide
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