Single-Trial Decoding of Bistable Perception Based on Sparse Nonnegative Tensor Decomposition

The study of the neuronal correlates of the spontaneous alternation in perception elicited by bistable visual stimuli is promising for understanding the mechanism of neural information processing and the neural basis of visual perception and perceptual decision-making. In this paper, we develop a sparse nonnegative tensor factorization-(NTF)-based method to extract features from the local field potential (LFP), collected from the middle temporal (MT) visual cortex in a macaque monkey, for decoding its bistable structure-from-motion (SFM) perception. We apply the feature extraction approach to the multichannel time-frequency representation of the intracortical LFP data. The advantages of the sparse NTF-based feature extraction approach lies in its capability to yield components common across the space, time, and frequency domains yet discriminative across different conditions without prior knowledge of the discriminating frequency bands and temporal windows for a specific subject. We employ the support vector machines (SVMs) classifier based on the features of the NTF components for single-trial decoding the reported perception. Our results suggest that although other bands also have certain discriminability, the gamma band feature carries the most discriminative information for bistable perception, and that imposing the sparseness constraints on the nonnegative tensor factorization improves extraction of this feature

Parametric Forcing of Confined and Stratified Flows

abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.Dissertation/ThesisSupplemental Materials Description Filezip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description FileDoctoral Dissertation Mathematics 201

Nelinearne pojave u energetskoj elektronici

A new class of phenomena has recently been discovered in nonlinear dynamics. New concepts and terms have entered the vocabulary to replace time functions and frequency spectra in describing their behavior, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. The main objective of the paper is to summarize the state of the art in the advanced theory of nonlinear dynamical systems and illustrate its application in power electronics by three examples.Nedavno je otkrivena nova vrsta pojava na području dinamike nelinearnih sustava. Novi pojmovi i nazivi zamijenili su vremenske funkcije i frekvencijske spektre u opisivanju njihovog ponašanja. U rječnik su uvedeni nazivi kao što su: kaos, bifurkacija, fraktal, Lyapunov koeficijent, period udvostručavanja, Poincaréov dijagram, nepoznati atractor, itd. Osnovni cilj članka je dati pregled sadašnjeg stanja napredne teorije nelinearnih dinamičkih sustava. S tri primjera ilustrirana je njezina primjenu u energetskoj elektronici

Analysis of Square-Root Kalman Filters for Angles-Only Orbital Navigation and the Effects of Sensor Accuracy on State Observability

Angles-only navigation is simple, robust, and well proven in many applications. However, it is sometimes ill-conditioned for orbital rendezvous and proximity operations because, without a direct range measurement, the distance to approaching satellites must be estimated by firing thrusters and observing the change in the target\u27s bearing. Nevertheless, the simplicity of angles-only navigation gives it great appeal. The viability of this technique for relative navigation is examined by building a high-fidelity simulation and evaluating the sensitivity of the system to sensor errors. The relative performances of square-root filtering methods, including Potter, Carlson, and UD factorization filters, are compared to the conventional and Joseph formulations. Filter performance is evaluated during closed-loop station keeping operations in simulation