13,695 research outputs found
Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series
The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067
Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large
We study the holographic hydrodynamics in the Einstein-Gauss-Bonnet(EGB)
gravity in the framework of the large expansion. We find that the large
EGB equations can be interpreted as the hydrodynamic equations describing the
conformal fluid. These fluid equations are truncated at the second order of the
derivative expansion, similar to the Einstein gravity at large . From the
analysis of the fluid flows, we find that the fluid equations can be taken as a
variant of the compressible version of the non-relativistic Navier-Stokes
equations. Particularly, in the limit of small Mach number, these equations
could be cast into the form of the incompressible Navier-Stokes equations with
redefined Reynolds number and Mach number. By using numerical simulation, we
find that the EGB holographic turbulence shares similar qualitative feature as
the turbulence from the Einstein gravity, despite the presence of two extra
terms in the equations of motion. We analyze the effect of the GB term on the
holographic turbulence in detail.Comment: 30 pages, 11 figure
3-Chloro-N′-(3-ethÂoxy-2-hyÂdroxyÂbenzylÂidene)benzohydrazide monohydrate
In the title compound, C16H15ClN2O3·H2O, the water molÂecule is linked to the Schiff base molÂecule via an O—H⋯O hydrogen bond. In the Schiff base molÂecule, an intramolecular O—H⋯N hydrogen bond occurs and the dihedral angle between the two benzene rings is 20.5 (5)°. In the crystal, the Schiff base and water molÂecules are linked by interÂmolecular N—H⋯O and O—H⋯O hydrogen bonds, forming layers in the ab plane
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