151,819 research outputs found
Accurate estimates of dynamical statistics using memory
Many chemical reactions and molecular processes occur on timescales that are
significantly longer than those accessible by direct simulation. One successful
approach to estimating dynamical statistics for such processes is to use many
short time series observations of the system to construct a Markov state model
(MSM), which approximates the dynamics of the system as memoryless transitions
between a set of discrete states. The dynamical Galerkin approximation (DGA)
generalizes MSMs for the problem of calculating dynamical statistics, such as
committors and mean first passage times, by replacing the set of discrete
states with a projection onto a basis. Because the projected dynamics are
generally not memoryless, the Markov approximation can result in significant
systematic error. Inspired by quasi-Markov state models, which employ the
generalized master equation to encode memory resulting from the projection, we
reformulate DGA to account for memory and analyze its performance on two
systems: a two-dimensional triple well and helix-to-helix transitions of the
AIB peptide. We demonstrate that our method is robust to the choice of
basis and can decrease the time series length required to obtain accurate
kinetics by an order of magnitude.Comment: 17 pages, 14 figure
General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
We consider discrete self-adjoint Dirac systems determined by the potentials
(sequences) such that the matrices are positive definite and
-unitary, where is a diagonal matrix and has entries
and entries () on the main diagonal. We construct
systems with rational Weyl functions and explicitly solve inverse problem to
recover systems from the contractive rational Weyl functions. Moreover, we
study the stability of this procedure. The matrices (in the potentials)
are so called Halmos extensions of the Verblunsky-type coefficients .
We show that in the case of the contractive rational Weyl functions the
coefficients tend to zero and the matrices tend to the indentity
matrix .Comment: This paper is a generalization and further development of the topics
discussed in arXiv:math/0703369, arXiv:1206.2915, arXiv:1508.07954,
arXiv:1510.0079
All Mutually Unbiased Product Bases in Dimension Six
All mutually unbiased bases in dimension six consisting of product states
only are constructed. Several continuous families of pairs and two triples of
mutually unbiased product bases are found to exist but no quadruple. The
exhaustive classification leads to a proof that a complete set of seven
mutually unbiased bases, if it exists, cannot contain a triple of mutually
unbiased product bases.Comment: 32 pages, 3 figures, identical to published versio
RDF Querying
Reactive Web systems, Web services, and Web-based publish/
subscribe systems communicate events as XML messages, and in
many cases require composite event detection: it is not sufficient to react
to single event messages, but events have to be considered in relation to
other events that are received over time.
Emphasizing language design and formal semantics, we describe the
rule-based query language XChangeEQ for detecting composite events.
XChangeEQ is designed to completely cover and integrate the four complementary
querying dimensions: event data, event composition, temporal
relationships, and event accumulation. Semantics are provided as
model and fixpoint theories; while this is an established approach for rule
languages, it has not been applied for event queries before
Orbit based procedure for doublets of scalar fields and the emergence of triple kinks and other defects
In this work we offer an approach to enlarge the number of exactly solvable
models with two real scalar fields in (1+1)D. We build some new two-field
models, and obtain their exact orbits and exact or numerical field
configurations. It is noteworthy that a model presenting triple-kinks and
double-flat-top lumps is among those new models
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