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-$m$ 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 $m$ 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