8,188 research outputs found
Data-driven Efficient Solvers and Predictions of Conformational Transitions for Langevin Dynamics on Manifold in High Dimensions
We work on dynamic problems with collected data that
distributed on a manifold . Through the
diffusion map, we first learn the reaction coordinates where is a manifold isometrically embedded into an
Euclidean space for . The reaction coordinates
enable us to obtain an efficient approximation for the dynamics described by a
Fokker-Planck equation on the manifold . By using the reaction
coordinates, we propose an implementable, unconditionally stable, data-driven
upwind scheme which automatically incorporates the manifold structure of
. Furthermore, we provide a weighted convergence analysis of
the upwind scheme to the Fokker-Planck equation. The proposed upwind scheme
leads to a Markov chain with transition probability between the nearest
neighbor points. We can benefit from such property to directly conduct
manifold-related computations such as finding the optimal coarse-grained
network and the minimal energy path that represents chemical reactions or
conformational changes. To establish the Fokker-Planck equation, we need to
acquire information about the equilibrium potential of the physical system on
. Hence, we apply a Gaussian Process regression algorithm to
generate equilibrium potential for a new physical system with new parameters.
Combining with the proposed upwind scheme, we can calculate the trajectory of
the Fokker-Planck equation on based on the generated equilibrium
potential. Finally, we develop an algorithm to pullback the trajectory to the
original high dimensional space as a generative data for the new physical
system.Comment: 59 pages, 16 figure
Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation
We consider detecting the evolutionary oscillatory pattern of a signal when
it is contaminated by non-stationary noises with complexly time-varying data
generating mechanism. A high-dimensional dense progressive periodogram test is
proposed to accurately detect all oscillatory frequencies. A further
phase-adjusted local change point detection algorithm is applied in the
frequency domain to detect the locations at which the oscillatory pattern
changes. Our method is shown to be able to detect all oscillatory frequencies
and the corresponding change points within an accurate range with a prescribed
probability asymptotically. This study is motivated by oscillatory frequency
estimation and change point detection problems encountered in physiological
time series analysis. An application to spindle detection and estimation in
sleep EEG data is used to illustrate the usefulness of the proposed
methodology. A Gaussian approximation scheme and an overlapping-block
multiplier bootstrap methodology for sums of complex-valued high dimensional
non-stationary time series without variance lower bounds are established, which
could be of independent interest
[1,1′-Bis(dicyclohexylphosphino)cobaltocenium-κ2 P,P′]chlorido(η5-cyclopentadienyl)ruthenium(II) hexafluoridophosphate
In the title structure, [CoRu(C5H5)(C17H26P)2Cl]PF6, the RuII atom is bonded to a cyclopentadienyl ring, a Cl atom and two P atoms of the chelating 1,1′-bis(dicyclohexylphosphino)cobaltocenium (di-cypc) ligand, leading to a three-legged piano-stool coordination. Part of the PF6
− counter-anion is disordered over two positions, with a site-occupancy ratio of 0.898 (7):0.102 (7). The components are linked by C—H⋯F and C—H⋯Cl hydrogen bonds
Coalescence of Carbon Atoms on Cu (111) Surface: Emergence of a Stable Bridging-Metal Structure Motif
By combining first principles transition state location and molecular
dynamics simulation, we unambiguously identify a carbon atom approaching
induced bridging metal structure formation on Cu (111) surface, which strongly
modify the carbon atom coalescence dynamics. The emergence of this new
structural motif turns out to be a result of the subtle balance between Cu-C
and Cu-Cu interactions. Based on this picture, a simple theoretical model is
proposed, which describes a variety of surface chemistries very well
Building quantum neural networks based on swap test
Artificial neural network, consisting of many neurons in different layers, is
an important method to simulate humain brain. Usually, one neuron has two
operations: one is linear, the other is nonlinear. The linear operation is
inner product and the nonlinear operation is represented by an activation
function. In this work, we introduce a kind of quantum neuron whose inputs and
outputs are quantum states. The inner product and activation operator of the
quantum neurons can be realized by quantum circuits. Based on the quantum
neuron, we propose a model of quantum neural network in which the weights
between neurons are all quantum states. We also construct a quantum circuit to
realize this quantum neural network model. A learning algorithm is proposed
meanwhile. We show the validity of learning algorithm theoretically and
demonstrate the potential of the quantum neural network numerically.Comment: 10 pages, 13 figure
Single-walled carbon nanotube bundle under hydrostatic pressure studied by the first-principles calculations
The structural, electronic, optical and vibrational properties of the
collapsed (10,10) single-walled carbon nanotube bundle under hydrostatic
pressure have been studied by the first-principles calculations. Some features
are observed in the present study: First, a collapsed structure is found, which
is distinct from both of the herringbone and parallel structures obtained
previously. Secondly, a pseudo-gap induced by the collapse appears along the
symmetry axis \textit{X}. Thirdly, the relative orientation between
the collapsed tubes has an important effect on their electronic, optical and
vibrational properties, which provides an efficient experimental method to
distinguish unambiguously three different collapsed structures.Comment: 14 pages, 6 figure
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