Spectral Geometry Processing with Manifold Harmonics

Music visualizations are nowadays included with virtually any media player. They usually rely on harmonic analysis of each sound channel, which automatically generate parameters for procedural image generation. However, only few music visualizations make use of 3d shapes. This paper proposes to use spectral mesh processing techniques, here manifold harmonics, to produce 3d stereo music visualization. The images are generated from 3d models by deforming an initial shape, mapping the sound frequencies to the mesh harmonics. A symmetry criterion is introduced to enhance the stereo effects on the deformed shape. A concise representation of the frequency mapping is proposed to allow for an animated gallery interface with genetic reproduction. Such galleries let the user quickly navigate between visual effects. Rendering such animated galleries in real time is a challenging task, since it requires computing and rendering the deformed shapes at a very high rate. This paper introduces a direct GPU implementation of manifold harmonics filters, which allows the displaying of the animated galleries.

BACKGROUNDMajor depressive disorder (MDD) tends to have a high incidence and high suicide risk. Electroconvulsive therapy (ECT) is currently a relatively effective treatment for MDD. However, the mechanism of efficacy of ECT is still unclear.AIMTo investigate the changes in the amplitude of low-frequency fluctuations in specific frequency bands in patients with MDD after ECT.METHODSTwenty-two MDD patients and fifteen healthy controls (HCs) were recruited to this study. MDD patients received 8 ECT sessions with bitemporal placement. Resting-state functional magnetic resonance imaging was adopted to examine regional cerebellar blood flow in both the MDD patients and HCs. The MDD patients were scanned twice (before the first ECT session and after the eighth ECT session) to acquire data. Then, the amplitude of low-frequency fluctuations (ALFF) was computed to characterize the intrinsic neural oscillations in different bands (typical frequency, slow-5, and slow-4 bands).RESULTSCompared to before ECT (pre-ECT), we found that MDD patients after the eighth ECT (post-ECT) session had a higher ALFF in the typical band in the right middle frontal gyrus, posterior cingulate, right supramarginal gyrus, left superior frontal gyrus, and left angular gyrus. There was a lower ALFF in the right superior temporal gyrus. Compared to pre-ECT values, the ALFF in the slow-5 band was significantly increased in the right limbic lobe, cerebellum posterior lobe, right middle orbitofrontal gyrus, and frontal lobe in post-ECT patients, whereas the ALFF in the slow-5 band in the left sublobar region, right angular gyrus, and right frontal lobe was lower. In contrast, significantly higher ALFF in the slow-4 band was observed in the frontal lobe, superior frontal gyrus, parietal lobe, right inferior parietal lobule, and left angular gyrus.CONCLUSIONOur results suggest that the abnormal ALFF in pre- and post-ECT MDD patients may be associated with specific frequency bands.

Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of machine learning to recover physical models from experiments and increase the accuracy of physical simulations, purely data-driven models have limited generalization and interpretability. To overcome these limitations, we propose a framework that combines symbolic regression (SR) and discrete exterior calculus (DEC) for the automated discovery of physical models starting from experimental data. Since these models consist of mathematical expressions, they are interpretable and amenable to analysis, and the use of a natural, general-purpose discrete mathematical language for physics favors generalization with limited input data. Importantly, DEC provides building blocks for the discrete analog of field theories, which are beyond the state-of-the-art applications of SR to physical problems. Further, we show that DEC allows to implement a strongly-typed SR procedure that guarantees the mathematical consistency of the recovered models and reduces the search space of symbolic expressions. Finally, we prove the effectiveness of our methodology by re-discovering three models of continuum physics from synthetic experimental data: Poisson equation, the Euler’s elastica and the equations of linear elasticity. Thanks to their general-purpose nature, the methods developed in this paper may be applied to diverse contexts of physical modeling.

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

This paper discusses computation of time-harmonic wave problems using a mixed formulation and the controllability method introduced by Roland Glowinski. As an example, a scattering problem (in an exterior domain) is considered, and the continuous problem is first formulated in terms of differential forms. Based on the continuous formulation, we write the discrete problem and the controllability algorithm for methods based on both the finite element exterior calculus (FEEC) and the discrete exterior calculus (DEC). As the discrete exterior calculus method provides us with a diagonal “mass matrix”, time-stepping in the DEC approach is remarkably more efficient than in the FEEC approach. For the computations in this paper, we choose the lowest order Whitney elements (a.k.a. Raviart–Thomas elements) for the FEEC approach, and in the DEC discretization we use different diagonal approximations for the Hodge star. Especially, in the DEC approach, a “harmonic Hodge” approximation is used, the derivation of which is based on the time-harmonicity of the problem. Different type of grids are used to study the sensitivity of the solution to the quality of the grid. Putting an effort on meshes regular enough, the computed DEC-solution is as accurate as the FEEC-solution, but reached in the fraction of the time. Both methods seem to be able to keep the solution accuracy rather well in computations with a high wave number (corresponding to a high frequency and a small wave length).

In order to improve the accuracy of the brain state classification, the time-frequency-spatial filter algorithm is put forward. In this algorithm, the signal features are extracted in terms of time, frequency and space. The parameters of the spatial pattern filter are not fixed, but variable with time. Specific frequency bands are also optimized simultaneously in this algorithm. So it can perfect the BCI pattern. It is applied to BCI datasets to illustrate the performance and validity of the algorithm. And the results indicate the algorithm can improve the accuracy of classification. The method will facilitate to classify EEG signals with small training sets.

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore provides an interesting test case with direct connection and applicability to atmospheric remote-sensing measurements at NIR wavelengths. We find that the correction for inhomogeneous waves systematically increases the single-scattering albedo throughout the NIR spectrum for both randomly-oriented, column-like hexagonal crystals and ice crystals shaped like Gaussian random spheres. The largest increase in the single-scattering albedo is 0.042 for hexagonal crystals and 0.044 for Gaussian random spheres, both at λ=2.725 µm. Although the effects on the 4 × 4 scattering-matrix elements are generally small, the largest differences are seen at 2.0 µm and 3.969 µm wavelengths where the correction for inhomogeneous waves affects mostly the backscattering hemisphere of the depolarization-connected P22/P11, P33/P11, and P44/P11. We evaluated the correction for inhomogeneous waves through comparisons against the discrete exterior calculus (DEC) method. We computed scattering by hexagonal ice crystals using the DEC, a traditional ray-optics code (SIRIS3), and a ray-optics code with inhomogeneous waves (SIRIS4). Comparisons of the scattering-matrix elements from SIRIS3 and SIRIS4 against those from the DEC suggest that consideration of the inhomogeneous waves brings the ray-optics solution generally closer to the exact result and, therefore, should be taken into account in scattering by absorbing particles large compared to the wavelength of incident light.

ObjectiveDexmedetomidine (DEX) has been widely used as a sedative, acting as an α2-adrenergic agonist on autoreceptors, presynaptic receptors and postsynaptic receptors without risk of respiratory depression. Although consciousness impairment is closely related to disturbances of brain function in different frequency bands, the time-varying DEX effects on cortical activity in specific frequency bands has not yet been studied.MethodsWe used electroencephalography (EEG) to analyse differences in cerebral cortex activity between the awake and sedated states, using electromagnetic tomography (standardized low resolution electromagnetic tomography (sLORETA)) to localize multiple channel scalp recordings of cerebral electric activity to specific brain regions.ResultsThe results revealed increased activity in the cuneus at delta-band frequencies, and in the posterior cingulate cortex at theta frequencies, during awake and sedated states induced by DEX at specific frequency bands. Differences in standardized low resolution cingulate gyrus were found in beta1 frequencies (13–18 Hz), and in the cuneus at gamma frequencies.ConclusionCerebral cortical activity was significantly altered in various brain areas during DEX sedation, including parts of the default mode network and common midline core in different frequency ranges. These alterations may elucidate the mechanisms underlying DEX sedation.

The increasing interest in Electro-encephalogram (EEG)-based stress prediction is driven by the global prevalence of stress. However, current studies predominantly rely on machine learning and deep learning techniques, utilizing extensive EEG data from 8 to 32 channels for stress prediction. In contrast, our research proposes an innovative approach that predicts stress using only 2 EEG channels and focuses on a specific frequency band (beta). The dataset used in this work is collected and pre-processed in a novel approach which is discussed in depth. Moreover, we have transformed the entire system into a TFLite model to enhance portability. Our experimental results, conducted on 10 subjects, demonstrate that our proposed technique achieves a remarkable prediction accuracy of 74%. Notably, this performance is comparable to other models that employ up to 128-channel data and consider multiple frequency bands. Our work lays the foundation for future advancements, with the ultimate goal of developing a portable EEG-based headband featuring only 2 channels. This would enable stress prediction, and the results could be easily accessed through either a mobile or web interface. By streamlining the EEG data acquisition and focusing on a specific frequency band, our approach not only achieves impressive prediction accuracy but also paves the way for the development of more user-friendly and accessible stress prediction technologies. This has the potential to significantly impact stress management and well-being on a global scale.

A resonant acoustic wave detector combined with Fabry–Pérot interference (FPI) and piezoelectric (PE) effects based on a polyvinylidene fluoride (PVDF) piezoelectric film was proposed to enhance the ability of the sensor to detect acoustic signals in a specific frequency band. The deformation of circular thin films was indicated by the interference and piezoelectric effects simultaneously, and the noise level was decreased by the real-time convolution of the two-way parallel signal. This study reveals that, at the film’s resonance frequency, the minimum detection limits for the FPI and piezoelectric impacts on acoustic waves are 3.39 μPa/Hz1/2 and 20.8 μPa/Hz1/2, respectively. The convolution result shows that the background noise was reduced by 98.81% concerning the piezoelectric signal, and by 85.21% concerning the FPI signal. The convolution’s signal-to-noise ratio (SNR) was several times greater than the other two signals at 10 mPa. Therefore, this resonance sensor, which the FPI and the piezoelectric effect synergistically enhance, can be applied to scenarios of acoustic wave detection in a specific frequency band and with ultrahigh sensitivity requirements.

The physical models and numerical methodologies of Computational Fluid Dynamics (CFD) are historically linked to the concept of continuous medium and to analysis where continuity, derivation and integration are defined as limits at a point. The first consequence is the need to extend these notions in a multidimensional space by establishing a global inertial frame of reference in order to project the variables there. In recent decades, the emergence of methodologies based on differential geometry or exterior calculus has changed the point of view by starting with the creation of entangled polygonal and polyhedral structures where the variables are located. Mimetic methods and Discrete Exterior Calculus, notably, have intrinsic conservation properties which make them very efficient for solving fluid dynamics equations. The natural extension of this discrete vision relates to the derivation of the equations of mechanics by abandoning the notion of continuous medium. The Galilean frame of reference is replaced by a local frame of reference composed of an oriented segment where the acceleration of the material medium or of a particle is defined. The extension to a higher dimensional space is carried from cause to effect, from one local structure to another. The conservation of acceleration over a segment and the Helmholtz–Hodge decomposition are two essential principles adopted for the derivation of a discrete law of motion. As the fields covered by CFD are increasingly broad, it is natural to return to the deeper meaning of physical phenomena to try a new research or new path which would preserve the properties of current formulations.

This paper introduces a new computational method to solve differential equations on subdivision surfaces. Our approach adapts the numerical framework of Discrete Exterior Calculus (DEC) from the polygonal to the subdivision setting by exploiting the refin-ability of subdivision basis functions. The resulting Subdivision Exterior Calculus (SEC) provides significant improvements in accuracy compared to existing polygonal techniques, while offering exact finite-dimensional analogs of continuum structural identities such as Stokes' theorem and Helmholtz-Hodge decomposition. We demonstrate the versatility and efficiency of SEC on common geometry processing tasks including parameterization, geodesic distance computation, and vector field design.

Automatic recognition of epileptic EEG patterns via Extreme Learning Machine and multiresolution feature extraction

An audio broadcast receiving apparatus and an audio broadcast receiving method implemented by the audio broadcast receiving apparatus are disclosed. A tuner simultaneously receives a radio wave in a specific frequency band of the analog audio broadcast and a radio wave of the digital audio broadcast transmitted in parallel with the analog audio broadcast in the specific frequency band. A demodulator retrieves the intended audio information by demodulating the signal received by the tuner. An analog receiving signal bandpass filter selectively passes the receiving signal corresponding to the analog audio broadcast radio wave. An analog receiving signal amplifier outputs an output signal representing an amplified receiving signal that has passed the analog receiving signal bandpass filter to the demodulator, and the gain of the amplifier is controlled in accordance with the level of the same output signal. A digital receiving signal bandpass filter selectively passes the receiving signal corresponding to the digital audio broadcast radio wave. A digital receiving signal amplifier amplifies the receiving signal that has passed through the digital receiving signal bandpass filter with a gain controlled in accordance with the level of the same output signal and outputs the amplified signal to the demodulator.