Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Steady state evoked potential (SSEP) responses in the primary and secondary somatosensory cortices of anesthetized cats: Nonlinearity characterized by harmonic and intermodulation frequencies

When presented with an oscillatory sensory input at a particular frequency, F [Hz], neural systems respond with the corresponding frequency, f [Hz], and its multiples. When the input includes two frequencies (F1 and F2) and they are nonlinearly integrated in the system, responses at intermodulation frequencies (i.e., n1*f1+n2*f2 [Hz], where n1 and n2 are non-zero integers) emerge. Utilizing these properties, the steady state evoked potential (SSEP) paradigm allows us to characterize linear and nonlinear neural computation performed in cortical neurocircuitry. Here, we analyzed the steady state evoked local field potentials (LFPs) recorded from the primary (S1) and secondary (S2) somatosensory cortex of anesthetized cats (maintained with alfaxalone) while we presented slow (F1 = 23Hz) and fast (F2 = 200Hz) somatosensory vibration to the contralateral paw pads and digits. Over 9 experimental sessions, we recorded LFPs from N = 1620 and N = 1008 bipolar-referenced sites in S1 and S2 using electrode arrays. Power spectral analyses revealed strong responses at 1) the fundamental (f1, f2), 2) its harmonic, 3) the intermodulation frequencies, and 4) broadband frequencies (50-150Hz). To compare the computational architecture in S1 and S2, we employed simple computational modeling. Our modeling results necessitate nonlinear computation to explain SSEP in S2 more than S1. Combined with our current analysis of LFPs, our paradigm offers a rare opportunity to constrain the computational architecture of hierarchical organization of S1 and S2 and to reveal how a large-scale SSEP can emerge from local neural population activities.

Steady state evoked potential (SSEP) responses in the primary and secondary somatosensory cortices of anesthetized cats: nonlinearity characterized by harmonic and intermodulation frequencies

When presented with an oscillatory sensory input at a particular frequency, F [Hz], neural systems respond with the corresponding frequency, f [Hz], and its multiples. When the input includes two frequencies (F1 and F2) and they are nonlinearly integrated in the system, responses at intermodulation frequencies (i.e., n1*f1+n2*f2 [Hz], where n1 and n2 are non-zero integers) emerge. Utilizing these properties, the steady state evoked potential (SSEP) paradigm allows us to characterize linear and nonlinear neural computation performed in cortical neurocircuitry. Here, we analyzed the steady state evoked local field potentials (LFPs) recorded from the primary (S1) and secondary (S2) somatosensory cortex of anesthetized (ketamine-xylazine) cats while we presented slow (F1=23Hz) and fast (F2=200Hz) somatosensory vibration to the contralateral paw pads and digits. Over 9 experimental sessions, we recorded LFPs from N=1620 and N=1008 bipolar-referenced sites in S1 and S2 using electrode arrays. Power spectral analyses revealed strong responses at 1) the fundamental (f1, f2), 2) its harmonic, 3) the intermodulation frequencies, and 4) broadband frequencies (50-150Hz). To compare the computational architecture in S1 and S2, we employed simple computational modeling. Our modeling results necessitate nonlinear computation to explain SSEP in S2 more than S1. Combined with our current analysis of LFPs, our paradigm offers a rare opportunity to constrain the computational architecture of hierarchical organization of S1 and S2 and to reveal how a large-scale SSEP can emerge from local neural population activities.

Symbolic Computation Using Cellular Automata-Based Hyperdimensional Computing

This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells, and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking, What is the automobile of air?

Adaptive Zooming Method for the Simulation of Quasi-Brittle Materials

A method to simulate concrete structures (quasi-brittle material) with localized nonlinearities is presented. Based on Guyan’s condensation, it consists in replacing the elastic zones of the structure by their equivalent rigidities (super-elements). The nonlinear computation is then performed only on the zones of interest (ie, damaged). As new damaged zones may appear, the proposed method monitors the evolution of the system and re-integrates previously condensed areas if necessary. This method, applied on different tests cases, allows a substantial computation economy.