4,499 research outputs found
Variational cross-validation of slow dynamical modes in molecular kinetics
Markov state models (MSMs) are a widely used method for approximating the
eigenspectrum of the molecular dynamics propagator, yielding insight into the
long-timescale statistical kinetics and slow dynamical modes of biomolecular
systems. However, the lack of a unified theoretical framework for choosing
between alternative models has hampered progress, especially for non-experts
applying these methods to novel biological systems. Here, we consider
cross-validation with a new objective function for estimators of these slow
dynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures
the ability of a rank- projection operator to capture the slow subspace of
the system. It is shown that a variational theorem bounds the GMRQ from above
by the sum of the first eigenvalues of the system's propagator, but that
this bound can be violated when the requisite matrix elements are estimated
subject to statistical uncertainty. This overfitting can be detected and
avoided through cross-validation. These result make it possible to construct
Markov state models for protein dynamics in a way that appropriately captures
the tradeoff between systematic and statistical errors
Possible ferro-spin nematic order in NiGa2S4
We explore the possibility that the spin-1 triangular lattice magnet NiGa2 S4
may have a ferro-nematic ground state with no frozen magnetic moment but a
uniform quadrupole moment. Such a state may be stabilized by biquadratic spin
interactions. We describe the physical properties of this state and suggest
experiments to help verify this proposal. We also contrast this state with a
`non-collinear' nematic state proposed earlier by Tsunetsugu and Arikawa for
NiGa2S4
Techniques to identify physical sources of aerodynamically generated sound
Title: Techniques to identify physical sources of aerodynamically generated sound
Presenter: Vishal T Vijay
Abstract:
Aerodynamic noise is a problem that has been haunting researchers for decades. As the
proximity of society to aerodynamic machinery increases, it becomes even more imperative that
methods to reduce aerodynamic noise are developed. In an attempt to better understand the
mechanism of aerodynamic sound generation, a method is developed to isolate the sources of
sound from its effects.
The approach is to design a filter designed using the dispersion relation to remove the
propagation effects from the flow. The dispersion relation is well defined in the frequency-wavenumber
domain and hence the flow parameter, pressure, is transformed through successive
Fourier transforms in time and space into this domain. The method was verified on analytical
solutions of single-frequency point sources, monopole, dipole, and quadrupole. The approach
was then applied to CFD solutions of these point sources obtained using the flow solver FDL3DI.
The results are promising in that the filtering algorithm removes the propagation effects of
the sound sources. Although much lesser in magnitude, some noise inevitably remains after the
filtering procedure due to several limitations including finiteness of data, sampling frequency,
etc. Different approaches were considered to implement the filtering algorithm to mitigate the
errors with varying degree of success
Encoding Multi-Resolution Brain Networks Using Unsupervised Deep Learning
The main goal of this study is to extract a set of brain networks in multiple
time-resolutions to analyze the connectivity patterns among the anatomic
regions for a given cognitive task. We suggest a deep architecture which learns
the natural groupings of the connectivity patterns of human brain in multiple
time-resolutions. The suggested architecture is tested on task data set of
Human Connectome Project (HCP) where we extract multi-resolution networks, each
of which corresponds to a cognitive task. At the first level of this
architecture, we decompose the fMRI signal into multiple sub-bands using
wavelet decompositions. At the second level, for each sub-band, we estimate a
brain network extracted from short time windows of the fMRI signal. At the
third level, we feed the adjacency matrices of each mesh network at each
time-resolution into an unsupervised deep learning algorithm, namely, a Stacked
De- noising Auto-Encoder (SDAE). The outputs of the SDAE provide a compact
connectivity representation for each time window at each sub-band of the fMRI
signal. We concatenate the learned representations of all sub-bands at each
window and cluster them by a hierarchical algorithm to find the natural
groupings among the windows. We observe that each cluster represents a
cognitive task with a performance of 93% Rand Index and 71% Adjusted Rand
Index. We visualize the mean values and the precisions of the networks at each
component of the cluster mixture. The mean brain networks at cluster centers
show the variations among cognitive tasks and the precision of each cluster
shows the within cluster variability of networks, across the subjects.Comment: 6 pages, 3 figures, submitted to The 17th annual IEEE International
Conference on BioInformatics and BioEngineerin
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