Set Of Basis Vectors Research Articles

WavDepressionNet: Automatic Depression Level Prediction Via Raw Speech Signals

Physiological reports have confirmed that there are differences in speech signals between depressed and healthy individuals. Therefore, as an application in the field of affective computing, automatic depression level prediction through speech signals has received the attention of researchers, which often estimate the depression severity of individuals by the Fourier or Mel spectrograms of speech signals. However, some studies on speech emotion recognition suggest that directly modeling the raw speech signal is more helpful for extracting emotion-related information. Inspired by this fact, we develop a WavDepressionNet to model raw speech signals for the improvement of prediction accuracy. In our method, a representation block is proposed to find a set of basis vectors to construct the optimal transformation space and generate the transformation result (named Depression Feature Map, DFM) of speech signal for facilitating the perception of depression cues. We further propose an assessment block, which cannot only use the designed spatiotemporal self-calibration mechanism to calibrate the DFM and highlight the useful elements, but also aggregates the calibrated DFM across various temporal ranges with the dilated convolution. Experimental results on the AVEC 2013 and AVEC 2014 depression databases demonstrate the effectiveness of our approach over previous works.

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. We have implemented CSP in a C++ open-source library CSPlib1 using the Kokkos2 parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS. Program summaryProgram Title: CSPlibCPC Library link to program files:https://doi.org/10.17632/p9gb7z54sp.1Developer's repository link:https://github.com/sandialabs/csplibLicensing provisions: BSD 2-clauseProgramming language: C++Nature of problem: Dynamical systems can involve coupled processes with a wide range of time scales. The computational singular perturbation (CSP) method offers a reformulation of these systems which enables the use of dynamically-based diagnostic tools to better comprehend the dynamics by decoupling fast and slow processes. CSPlib is an open-source software library for analyzing general ordinary differential equation (ODE) and differential algebraic equation (DAE) systems, with specialized implementations for detailed chemical kinetic ODE/DAE systems. It relies on CSP for the analysis of these systems. CSPlib has been used in gas kinetic and heterogeneous catalytic kinetic models.Solution method: CSP analysis seeks a set of basis vectors to linearly decompose the right-hand side (RHS) of a dynamical system in a manner that decouples fast and slow processes. The CSP basis vectors are often well approximated with the right eigenvectors of the RHS Jacobian. And the left basis vectors are found by the inversion of the matrix, whose columns are the CSP basis vectors. Accordingly, the right and left CSP basis vectors are orthonormal. CSP defines mode amplitudes as the projections of the left basis vectors on the RHS; the time scales as the reciprocals of the RHS Jacobian eigenvalue magnitudes; and the CSP pointers, which are the element-wise multiplication of the transpose of the right CSP basis vectors with the left CSP basis vectors. For kinetic models that can be cast as the product of a generalized stoichiometric matrix and a rate of progress vector, CSP defines the participation index, which represents the contribution of a chemical reaction to each mode. Further, it defines the slow and fast importance indices, which describe the contribution of a chemical reaction to the slow and fast dynamics of a state variable, respectively. These indices are useful in diagnostic studies of dynamical systems and the construction of simplified models.Additional comments including restrictions and unusual features: CSPlib is a portable library that carries out many CSP analyses in parallel and can be used in modern high-performance platforms.

Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases

This paper formulates, analyzes and demonstrates numerically a method for the explicit partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order models (FOMs). The method builds on the partitioned scheme developed in Peterson et al. (2019), which starts from a well-posed formulation of the coupled interface problem and uses its dual Schur complement to obtain an approximation of the interface flux. Explicit time integration of this problem decouples its subdomain equations and enables their independent solution on each subdomain. Extension of this partitioned scheme to coupled ROM–ROM or ROM–FOM problems requires formulations with non-singular Schur complements. To obtain these problems, we project a well-posed coupled FOM–FOM problem onto a composite reduced basis comprising separate sets of basis vectors for the interface and interior variables, and use the interface reduced basis as a Lagrange multiplier. Our analysis confirms that the resulting coupled ROM–ROM and ROM–FOM problems have provably non-singular Schur complements, independent of the mesh size and the reduced basis size. In the ROM–FOM case, analysis shows that one can also use the interface FOM space as a Lagrange multiplier. We illustrate the theoretical and computational properties of the partitioned scheme through reproductive and predictive tests for a model advection–diffusion transmission problem.

The World of Fourier Series

The idea of Fourier analysis is to express general functions as sums of other choices of basic functions such as sines and cosines. One can interpret it as decomposing a vector into a set of basis vectors in the context of linear algebra. This paper will discuss differential equations and specifically focusing on approximating solutions using Fourier analysis. In modern times, Fourier analysis is not only used in the field of signal processing. As an important subfield of mathematical analysis, Fourier analysis has been broadly applied to various engineering fields, such as image processing, vibration analysis, acoustics, etc.

Characterization of infrasonic wind noise using the Discrete Orthonormal Stockwell Transform

The Discrete Orthonormal Stockwell Transform (DOST) (Stockwell, 2007) projects a finite-length, periodically sampled signal onto a set of orthonormal basis vectors that are localized in time and scale such that all basis functions at each scale are represented by a finite number of Discrete Fourier Transform (DFT) basis functions. It is based on the Stockwell Transform (Stockwell et al., 1996), sometimes referred to as the S-transform, which is applicable to continuously defined waveforms. Furthermore, the DFT basis functions corresponding to each DOST scale are non-overlapping. The shorter DOST scales correspond to higher-frequency DFT basis functions and greater bandwidths than the longer DOST scales. Thus, the DOST is a type of time-frequency transform and is suitable for non-stationary time-series analysis. Additionally, the DOST of an N-point record can be calculated efficiently in order N log N operations (Wang and Orchard, 2009). Several applications of the S-transform and the DOST have been documented including beamforming with array data (Collar and Frazier, 2022; Frazier, 2022). In this presentation, the DOST used is to examine the statistics of data measured with infrasound sensors as a function of the DOST scales, adaptively characterize the amplitude distributions of the DOST coefficients at each scale and perform near-optimal detection of transient signals. Results corresponding to infrasound data recorded under various conditions are presented.

ProMask: Probability mask representation for skeleton detection

Detecting object skeletons in natural images presents challenges due to varied object scales and complex backgrounds. The skeleton is a highly compressing shape representation, which can bring some essential advantages but cause difficulties in detection. This skeleton line occupies a small part of the image and is overly sensitive to spatial position. Inspired by these issues, we propose the ProMask, which is a novel skeleton detection model. The ProMask includes the probability mask representation and vector router. This skeleton probability mask describes the gradual formation process of skeleton points, which can achieve high detection performance and robustness. Moreover, the vector router module possesses two sets of orthogonal basis vectors in a two-dimensional space, which can dynamically adjust the predicted skeleton position. Experiments show that our approach realizes better performance, efficiency, and robustness than state-of-the-art methods. We consider that our proposed skeleton probability representation will serve as a standard configuration for future skeleton detection, since it is reasonable, simple, and very effective.

Reference-frame-independent quantum key distribution based on passive light source monitoring

In quantum key distribution (QKD), the users need to share the same reference frame. If their reference frames are inconsistent, the QKD system will not function properly. The most widely used method today is the active real-time calibration of both communication reference frames by using classical communication. In order to get rid of the real-time calibration operation of the reference frames, a QKD protocol independent of reference frame is proposed, called reference-frame-independent QKD (RFI-QKD). The RFI-QKD protocol is immune to the effects of slowly changing reference frame drift, requiring that only one set of bases should be aligned by Alice and Bob, and the remaining two sets of bases can slowly change in the channel. In the real QKD system, a set of basis vectors can always be found to maintain a stable alignment. However, some assumptions are made for the sources in most reported researches, i.e. with a trusted and fixed photon-number distribution (PND), which usually cannot be satisfied in practical implementations. Those unreasonable assumptions will inevitably compromise the security of practical QKD systems. To solve the problem, in this work, we present a passive light source monitoring (PLSM) scheme for RFI-QKD, which is accomplished by a passive monitoring module consisting of a beam splitter and two detectors on the source side. Through the PLSM module, we can have four monitoring events by using two local detectors and then precisely estimate the bounds of source distributions. Specifically, we take the three-intensity decoy-state-based RFI-QKD for example for illustraing the events. Compared with the original RFI-QKD, our PLSM method can passively monitor the PND and has many advantages, with light source fluctuations, finite-size effects and reference frame deflection angles taken into account.

Projection-Based Multiple Notch Filtering

A method for multi-frequency notch filtering is described. The approach is based on quadratic programming, which leads to projecting the signal vector onto the orthogonal complement of the subspace spanned by a set of sinusoidal basis vectors, each corresponding to a notch frequency. The projection matrix uses a weighted inner product whose weights are samples of a standard spectral analysis window. An overlap-add method suitable for block processing is also described. The projection-based notch filter (PNF) is compared with linear-phase FIR and IIR multiple notch filters and is found to have improved amplitude and phase distortion.

The Discriminative Discrete Basis Problem: Definitions, Algorithms, Benchmarking, and Application to Brain's Functional Dynamics

In this paper, considering two Boolean matrices, we tackle the problem of finding a set of Boolean basis vectors that capture the latent components most discriminative of one matrix from another. We refer to this problem as the discriminative discrete basis problem (DDBP). Depending on the symmetry/asymmetry of the problem about the two input matrices, different classes of the DDBP are defined. We present an ensemble of new algorithms, called the discriminative-associative (DASSO) algorithms, to find solutions for these classes of the DDBP. Furthermore, we design a comprehensive, simulation-based benchmarking framework for evaluating the performance of such algorithmic solutions to the DDBP over a wide range of variables, including the effects of disturbances, noise, the geometric features of the latent components within each matrix, and the relationships among these components across the contrasted matrices. As an example application, we demonstrate the utility of the DASSO algorithms in studying the dynamics of the brain function by identifying the cortical activities that discriminate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">motor</i> from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-motor</i> tasks using recordings obtained via electroencephalography (EEG). The results highlight the location of such discriminating activities in the cortex and the time of their occurrence, which can lead to the design of efficient and accurate brain computer interfaces (BCIs). To the best of our knowledge, this is the first time the DDBP is recognized, defined, and addressed through the development of algorithmic solutions. The DASSO algorithms can be utilized in a variety of data mining and feature selection applications, in which finding discriminating structures across two datasets is of interest.

A Preserving Precision Mixed Finite Element Dimensionality Reduction Method for Unsaturated Flow Problem

The unsaturated flow problem is of important applied background and its mixed finite element (MFE) method can be used to simultaneously calculate both water content and flux in soil, which is the most ideal calculation method. Nonetheless, it includes many unknowns. Thereby, herein we will employ the proper orthogonal decomposition (POD) to lower the dimension of unknown solution coefficient vectors in the MFE method for the unsaturated flow problem. Thus, we first examine the MFE method for the unsaturated flow problem and the existence and convergence of the classical MFE solutions. We then take advantage of the initial L MFE solution coefficient vectors to generate a set of POD basis vectors and utilize the most POD basis vectors to create the preserving precision MFE reduced-dimension (PPMFERD) format. Under the circumstances, the PPMFERD format has the same basis functions as the classical MFE format so that it can maintain the same accuracy as the classical MFE format, but it only includes a few unknowns, so it greatly lightens the calculating load, retards the accumulation of computing errors, saves CPU runtime, and improves the accuracy of the real-time calculation in the computational process. Next, we employ the analysis of matrices to demonstrate the existence and convergence of the PPMFERD solutions such that the theoretical analysis becomes very simple and elegant. Finally, we take advantage of some numerical simulations to check on the correctness of the PPMFERD method. It shows that the PPMFERD method is effective and feasible for simulating both water content and flux in unsaturated flow soil.

A POD-RBF-FD scheme for simulating chemotaxis models on surfaces

The main aim of this paper is to develop a new framework of a meshless approximation for solving numerically three nonlinear partial differential equations in biology, i.e., the chemotaxis models defined on the smooth, closed manifolds embedded in R3. The radial basis function-generated finite difference scheme is considered to deal with the spatial variables, which depends only on the location of nodes and the value of normal vector at each point per spherical cap. The robust artificial hyperviscosity formulation is derived for each model, which has been used for preventing the spurious growth modes in the numerical solution. An implicit–explicit time discretization is employed to deal with the time variable. The resulting fully discrete scheme is solved via the biconjugate gradient stabilized method with a zero-fill incomplete lower upper preconditioner per time step, where a positivity-preserving filter is used to prevent the negative sign of the cell density variable. Besides, to reduce the used central processor unit (CPU) time, the proper orthogonal decomposition is considered for constructing a set of new orthogonal basis vectors based on the singular value decomposition. The developed numerical method is called a proper orthogonal decomposition-radial basis function-generated finite difference (POD-RBF-FD) scheme. Finally, the ability of the proposed method is investigated by simulation results showing the blowing-up, pattern formulation (perforated stripe) and aggregations of bacteria on some surfaces.

Lossy compression of statistical data using quantum annealer

We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3–3.5 times better compression performance than the algorithm based on neural-network autoencoder. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.

Potential distribution of polar optical phonons and their electron–phonon coupling properties of a wurtizite GaN-based trianglar quantum dot

Polar optical phonon modes of a wurtzite nitride trianglar quantum dot (QD) are deduced and analyzed by using the dielectric continuum model. Based on a method of nonseparable variables, the Laplace equation of electristatic potential of the structure is solved, and the exact and analytical phonon states of exact confined (EC) modes are derived. It is found that the frequency of EC modes in the nitride trianglar QD systems can take both the longitudinal optical phonons in [Formula: see text]-direction [Formula: see text] and the longitudinal optical phonons in [Formula: see text]-plane [Formula: see text], which is obviously different from the cases of EC modes in wurtzite GaN quantum wells and quantum wires due to their different confined dimensions. The polarization eigenvectors and their orthogonality relations for the EC phonon modes are derived, which could form a set of orthogonal and completed basis vectors. By using the orthogonality relations of polarization eigenvector and field quantization method, the free phonon field of EC modes and the corresponding Fröhlich electron–phonon interaction Hamiltonian are obtained. Numerical calculations on a wurtztie GaN trianglar QD are performed. The spatial distributions of phonon potentials of EC phonons both in [Formula: see text]-plane and in [Formula: see text]-direction as well as the electron–phonon coupling strength are plotted and discussed. It is observed that the potential of these EC phonon modes is strictly confined within the trianglar QD ranges. The dependence of symmetries and electron–phonon coupling strength on the quantum numbers [Formula: see text] and [Formula: see text] in [Formula: see text]-plane, and the quantum number [Formula: see text] in [Formula: see text]-direction are analyzed in detail. The relationship of the total number of peaks and troughs with these quantum numbers are also discussed and induced.

Contravariant tensor algebra for anisotropic hyperelasticity

Analysis of tensors in oblique Cartesian coordinate systems always requires the definition of a set of orthogonal covariant basis vectors called the Reciprocal basis. This increases the complexity of the analysis and hence makes the method cumbersome. In this work a novel method is presented to effectively carry out the various transformations of tensors to and between oblique coordinate system/s without the need to create the covariant reciprocal basis. This will simplify the procedure of transformations involving problems where tensors are required to be defined in the oblique coordinate system. This work also demonstrates how the analysis of contravariant tensors can be applied to hyperelasticity. Continuum material and damage models can integrate this approach to model anisotropy and non linearity using a much simpler approach. The accuracy of the models was illustrated by matching the predictions to experimental results. A finite element analysis of material and damage model based on contravariant tensors was also carried out on a simple geometry with a re-entrant corner.

Predicting supersonic jet mode-switching using non-negative matrix factorization

Imperfectly expanded supersonic jets contain a shock-cell structure in the jet plume which plays a role in generating screech tones along with other jet noise sources. Depending on the Mach number of the jet, two types of jet motion or “jet modes”—a toroidal mode and flapping mode may occur, resulting in the generation of different screech tones that are not harmonics of each other. At a given jet condition, these jet modes (and the corresponding screech tones) can switch between each other based on environmental conditions in a seemingly non-deterministic manner. Understanding when mode-switching occurs at a fine time resolution can provide better understanding of the sensitivity of the jet structure dynamics. This work presents the preliminary results of a novel method that predicts when a particular screech tone is active using non-negative matrix factorization. Using this technique, spectrograms of jet noise are decomposed into a set of basis vectors corresponding to the screech tones present in the jet, and a set of activation functions that indicate when each screech basis is dominant. An activation function comparison technique is then used to identify activations corresponding to mode-switching.

Hybrid Precoding and Combining for Millimeter Wave/Sub-THz MIMO-OFDM Systems With Beam Squint Effects

In this paper, we consider the problem of hybrid precoding and combining for wideband millimeter wave (mmWave) and sub-terahertz (THz) MIMO-OFDM systems with beam squint effects. In the presence of the beam squint effect, the conventional spatially sparse precoding-based hybrid precoding method which approximates the optimal precoder/combiner with a set of array response vectors suffers severe performance degradation. To address this difficulty, we propose a new set of basis vectors to approximate the optimal precoder/combiner. Each new basis vector is devised to form a radiation pattern with a wide beam to cover the squinted beam directions caused by different frequencies. Simulation results show that the proposed method can effectively alleviate the beam squint effect and achieve a substantial performance improvement over the existing state-of-the-art hybrid precoding method.

Probabilistic Load Forecasting via Neural Basis Expansion Model Based Prediction Intervals

To narrow the width of prediction interval while guaranteeing coverage for probabilistic short term load forecasting, we propose a deep-learning forecasting model based on neural basis expansion analysis (N-BEATS). It takes load data as input, and feed the load sequence into three stacks. Each stack projects the load sequence on a set of basis vectors. Both the basis vectors and the corresponding coefficients are learned by the neural networks. A novel doubly residual stacking strategy is adopted, which decomposes forecasting task into three sub-problems, i.e., pattern characterization tasks corresponding to the stacks, under the assumption that load series can generally be represented by three patterns in subspaces with lower dimensions respectively. It removes redundant information in each stack, which guides the stack to concentrate on learning of one pattern. We further apply conformal quantile regression, which uses the residuals in a held-out validation, to calibrate constructed prediction interval for better theoretical coverage guarantee. Experiments based on load dataset provided by UT Dallas demonstrate improved performance of the proposed model in capturing the characteristics of load and providing narrow prediction intervals with nearly nominal coverage.

A generative-discriminative framework that integrates imaging, genetic, and diagnosis into coupled low dimensional space

We propose a novel optimization framework that integrates imaging and genetics data for simultaneous biomarker identification and disease classification. The generative component of our model uses a dictionary learning framework to project the imaging and genetic data into a shared low dimensional space. We have coupled both the data modalities by tying the linear projection coefficients to the same latent space. The discriminative component of our model uses logistic regression on the projection vectors for disease diagnosis. This prediction task implicitly guides our framework to find interpretable biomarkers that are substantially different between a healthy and disease population. We exploit the interconnectedness of different brain regions by incorporating a graph regularization penalty into the joint objective function. We also use a group sparsity penalty to find a representative set of genetic basis vectors that span a low dimensional space where subjects are easily separable between patients and controls. We have evaluated our model on a population study of schizophrenia that includes two task fMRI paradigms and single nucleotide polymorphism (SNP) data. Using ten-fold cross validation, we compare our generative-discriminative framework with canonical correlation analysis (CCA) of imaging and genetics data, parallel independent component analysis (pICA) of imaging and genetics data, random forest (RF) classification, and a linear support vector machine (SVM). We also quantify the reproducibility of the imaging and genetics biomarkers via subsampling. Our framework achieves higher class prediction accuracy and identifies robust biomarkers. Moreover, the implicated brain regions and genetic variants underlie the well documented deficits in schizophrenia.

An improved hybrid FE-SEA model using modal analysis for the mid-frequency vibro-acoustic problems

Based on the hybrid finite element (FE)-statistical energy analysis (SEA) method, an improved hybrid model with less time-consuming is proposed for the mid-frequency vibro-acoustic problems. Mode shapes are used to reduce the order of the deterministic acoustic component modeled by the finite element method in this paper. The governing equation of the residual response, which is derived to correct the modal truncation error, can be reduced by constructing a set of basis vectors. The model order reduction (MOR) equation of the acoustic component is formulated through a combination of the truncated mode shapes equation and the reduced residual response equation. The dimension of the overall equation of motion is efficiently decreased. The statistical structural component is modeled by SEA, and the responses of a mid-frequency vibro-acoustic system can be solved after introducing the diffuse field reciprocity relationship. Based on the efficient correction of the modal truncation error, the proposed hybrid MOR-SEA method promotes the reduction of order using mode shapes in mid-frequency vibro-acoustic systems. Compared with the traditional hybrid FE-SEA method, the present method has an evident advantage in computational efficiency, as shown in two numerical examples.

Molecular function recognition by supervised projection pursuit machine learning

Identifying mechanisms that control molecular function is a significant challenge in pharmaceutical science and molecular engineering. Here, we present a novel projection pursuit recurrent neural network to identify functional mechanisms in the context of iterative supervised machine learning for discovery-based design optimization. Molecular function recognition is achieved by pairing experiments that categorize systems with digital twin molecular dynamics simulations to generate working hypotheses. Feature extraction decomposes emergent properties of a system into a complete set of basis vectors. Feature selection requires signal-to-noise, statistical significance, and clustering quality to concurrently surpass acceptance levels. Formulated as a multivariate description of differences and similarities between systems, the data-driven working hypothesis is refined by analyzing new systems prioritized by a discovery-likelihood. Utility and generality are demonstrated on several benchmarks, including the elucidation of antibiotic resistance in TEM-52 beta-lactamase. The software is freely available, enabling turnkey analysis of massive data streams found in computational biology and material science.