Kernel Coefficients Research Articles

Chaotic Encryption of ECG Signals with a Random Kernel Approach

Security of biometric data is very important in the healthcare domain. Due to uniqueness of electrocardiogram (ECG) is very high even in identical twins, so it can be used as biometric signature.This paper introduces a simple efficient ECG encryption technique based on random kernel approach. As ECG signals contain sensitive confidential information with details for patient identification, it needs to be encrypted before transmission through public network to avoid the data being breached and hacked. The security of the proposed system will depend on random kernel coefficients, substitution process and length of kernel filter. Simulation results show that the proposed system is capable of encrypting ECG signals for secure communication efficiently.

Super heat kernel and one-loop divergence of super Yang–Mills theory in conformal supergravity

Abstract We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.

Super heat kernel of general second order operators in N=1 superspace and one-loop divergence of dilaton-coupled SYM theory

We shall develop a general technique to obtain the super heat kernel coefficients of an arbitrary second order operator in $N=1$ superspace. We focus on the space of conformal supergravity here but the method presented is equally applicable for other types of superspace. The first three coefficients which determine the one-loop divergence of the corresponding quantum theory will be calculated. As an application we shall present the one-loop logarithmic divergence of super Yang-Mills theory coupled to a string dilaton $S$. This is the first superfield calculation for SYM with a non-trivial gauge kinetic function, which generalize the previous result with a constant coupling strength. We also demonstrate that the method presented can be extended to the case of third order operators, with the restriction that its third order part is composed of only spinor derivatives.

RPSOVF Prediction Model for Speech Signal Series Based on UPSO

In this paper, we propose a nonlinear prediction model of speech signal series with an explicit structure. In order to overcome some intrinsic shortcomings, such as traps at the local minimum, improper selection of parameters, and slow convergence rate, which are always caused by improper parameters generated by, typically, the low performance of least mean square (LMS) in updating kernel coefficients of the Volterra model, a uniform searching particle swarm optimization (UPSO) algorithm to optimize the kernel coefficients of the Volterra model is proposed. The second-order Volterra filter (SOVF) speech prediction model based on UPSO is established by using English phonemes, words, and phrases. In order to reduce the complexity of the model, given a user-designed tolerance of errors, we extract the reduced parameter of SOVF (RPSOVF) for acceleration. The experimental results show that in the tasks of single-frame and multiframe speech signals, both UPSO-SOVF and UPSO-RPSOVF are better than LMS-SOVF and PSO-SOVF in terms of root mean square error (RMSE) and mean absolute deviation (MAD). UPSO-SOVF and UPSO-RPSOVF can better reflect trends and regularity of speech signals, which can fully meet the requirements of speech signal prediction. The proposed model presents a nonlinear analysis and valuable model structure for speech signal series, and can be further employed in speech signal reconstruction or compression coding.

On the evaluation of density of ionic liquids: towards a comparative study

Superior physicochemical properties of ionic liquids (ILs) including dissolution potential for a large number of compounds, recyclability, suitable thermal stability, tuneability characteristics and trivial volatility make them attention-grabbing in electrochemistry and chemical industries. Owing to this fact, the accurate knowledge of ILs properties is demanded for the thermodynamic calculations involved in such processes. Amongst such properties, density is crucially significant in separation processes including CO2 absorption, extractive distillation and liquid–liquid extraction; thereby, creating and/or seeking a robust technique for density prediction is of great importance. In the present study, a new and combined version of least-square support vector machine as a powerful machine learning theory, and group contribution technique (GC-LSSVM) was extended for estimating the ILs density. It is worthwhile mentioning that genetic algorithm (GA) is applied to find the best values of kernel and regularization coefficients involved in GC-LSSVM. A widespread database was collected from the reliable open sources including 918 data points relevant to the 747 classes of ILs in relation with 47 substructures, pressure and temperature. The data was randomly separated into two subsets of test and train using a computer program. After the model was developed, graphical techniques and parametric statistics were executed to show the supremacy of the suggested GC-LSSVM in this study. The model findings were also compared to the available empirical and theoretical models in literature. Hence, the developed tool in this study gives the best match with target data and the least deviations from the actual ones with mean square error (MSE) of 0.0004 and coefficients of determination (R2) of 0.9925. The residual error analysis and outliers detection demonstrated the highest accuracy of GC-LSSVM model, and the validity of the employed database for density modeling, respectively. It can be concluded that the recommended tool in this study is a new combinatorial model which is employed for the first time in computation of ILs density.

An Fpga Implementation of SAR Polar Format Algorithm

In order to improve the imaging processing efficiency of two-dimensional interpolated synthetic aperture radar (SAR) polar format algorithm (PFA), the SINC interpolation based on block RAM group approach was proposed in this paper. Sampling floating point coordinates were converted to the fixed point, with the integer part of the coordinate being the address. And the echo data and the remaining fractional part were written into the block RAM group. And then we completed the addressing of the echo data and interpolation kernel coefficient in a clock. Echo data were weighted and the interpolation result was obtained. The parallel structure was easy to implement and pipeline output the result to be interpolated. Interpolation points can be down compatible, and it doesn’ t increase resource utilization. Based on the SINC interpolation polar format algorithm, the measured data are processed by FPGA, experimental SA R data of 8 KB × 16 KB points can be processed with 1. 78 s when the system operating frequency is 200 MHz, which verifies the validity of the scheme.

A Quantitative Intelligent Diagnosis Method for Early Weak Faults of Aviation High-speed Bearings

An intelligent diagnosis method based on support vector machine (SVM) is proposed to quantitatively diagnose early weak faults of high-speed aero-engine’s bearings. In order to achieve a better performance in contrast with conventional kernel function, a mixed kernel function is constructed and particle swarm optimization (PSO) is used to optimize kernel coefficients and other parameters. Experimental raw data is preprocessed by sparse decomposition and reconstruction method to remove noise in original signals, which can provide effective and reliable samples for SVM. In order to verify the validity of the proposed method, experiments on different fault types with different defect sizes of high-speed bearings working at 30000rpm are carried out. The results show that the accuracy of the proposed method is greatly improved compared with traditional SVM. The proposed method can not only distinguish different types of failure but also distinguish different degrees of the same fault pattern, which achieves a quantitative intelligent diagnosis of early weak faults in aviation’s high-speed bearings.

Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

The holographic Weyl anomaly for GJMS operators (or conformal powers of the Laplacian) are obtained in four and six dimensions. In the context of AdS/CFT correspondence, free conformal scalars with higher-derivative kinetic operators are induced by an ordinary second-derivative massive bulk scalar. At one-loop quantum level, the duality dictionary for partition functions entails an equality between the functional determinants of the corresponding kinetic operators and, in particular, it provides a holographic route to their Weyl anomalies. The heat kernel of a single bulk massive scalar field encodes the Weyl anomaly (type-A and type-B) coefficients for the whole tower of GJMS operators whenever they exist, as in the case of Einstein manifolds where they factorize into product of Laplacians.While a holographic derivation of the type-A Weyl anomaly was already worked out some years back, in this note we compute holographically (for the first time to the best of our knowledge) the type-B Weyl anomaly for the whole family of GJMS operators in four and six dimensions. There are two key ingredients that enable this novel holographic derivation that would be quite a daunting task otherwise: (i) a simple prescription for obtaining the holographic Weyl anomaly for higher-curvature gravities, previously found by the authors, that allows to read off directly the anomaly coefficients from the bulk action; and (ii) an implied WKB-exactness, after resummation, of the heat kernel for the massive scalar on a Poincaré-Einstein bulk metric with an Einstein metric on its conformal infinity.The holographically computed Weyl anomaly coefficients are explicitly verified on the boundary by exploiting the factorization of GJMS operators on Einstein manifolds and working out the relevant heat kernel coefficient.

MCK-ELM: multiple composite kernel extreme learning machine for hyperspectral images

Multiple kernel (MK) learning (MKL) methods have a significant impact on improving the classification performance. Besides that, composite kernel (CK) methods have high capability on the analysis of hyperspectral images due to making use of the contextual information. In this work, it is aimed to aggregate both CKs and MKs autonomously without the need of kernel coefficient adjustment manually. Convex combination of predefined kernel functions is implemented by using multiple kernel extreme learning machine. Thus, complex optimization processes of standard MKL are disposed of and the facility of multi-class classification is profited. Different types of kernel functions are placed into MKs in order to realize hybrid kernel scenario. The proposed methodology is performed over Pavia University, Indian Pines, and Salinas hyperspectral scenes that have ground-truth information. Multiple composite kernels are constructed using Gaussian, polynomial, and logarithmic kernel functions with various parameters, and then the obtained results are presented comparatively along with the state-of-the-art standard machine learning, MKL, and CK methods.

Unsupervised nonlinear feature selection algorithm via kernel function

Feature selection is one of the important methods of data preprocessing, but the general feature selection algorithm has the following shortcomings: (1) Noise and outliers cannot be ruled out so that the algorithm does not work well. (2) They only consider the linear relationship between data without considering the nonlinear relationship between data. For this reason, an unsupervised nonlinear feature selection algorithm via kernel function is proposed in this paper. First, each data feature is mapped to a kernel space by a kernel function. In this way, nonlinear feature selection can be performed. Secondly, the low-rank processing of the kernel coefficient matrix is used to eliminate the interference of noise samples. Finally, the feature selection is performed through a sparse regularization factor in the kernel space. Experimental results show that our algorithm has better results than contrast algorithms.

Boundary stabilization of a class of reaction–advection–diffusion systems via a gradient-based optimization approach

In this paper, the boundary stabilization problem of a class of unstable reaction–advection–diffusion (RAD) systems described by a scalar parabolic partial differential equation (PDE) is considered. Different the previous research, we present a new gradient-based optimization framework for designing the optimal feedback kernel for stabilizing the unstable PDE system. Our new method does not require solving non-standard Riccati-type or Klein–Gorden-type PDEs. Instead, the feedback kernel is parameterized as a second-order polynomial whose coefficients are decision variables to be tuned via gradient-based dynamic optimization, where the gradients of the system cost functional (which penalizes both kernel and output magnitude) with respect to the decision parameters are computed by solving a so-called “costate” PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that the optimized kernel yields closed-loop stability. Finally, three numerical examples are illustrated to verify the effectiveness of the proposed approach.

Virial coefficients expressed by heat kernel coefficients

In this paper, we generally expressed the virial expansion of ideal quantum gases by the heat kernel coefficients for the corresponding Laplace type operator. As examples, we give the virial coefficients for quantum gases in d-dimensional confined space and spheres, respectively. Our results show that, the relative correction from the boundary to the second virial coefficient is independent of the dimension and it always enhances the quantum exchange interaction. In d-dimensional spheres, however, the influence of the curvature enhances the quantum exchange interaction in two dimensions, but weakens it in higher dimensions (d>3).

Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

In this work we present a parallel implementation of numerical algorithm solving the Cauchy problem for equation of advection of coagulating particles. This equation describes time-evolution of the concentration f(x, v, t) of particles of size v at the point x at the time-moment t. Our numerical algorithm is based on use of total variation diminishing (TVD) scheme and perfectly matching layers (PML) for approximation of advection operator along spatial coordinate x and utilization of the fast numerical method for evaluation of coagulation integrals exploiting low-rank decomposition of coagulation kernel coefficients and fast FFT-based implementation of convolution operation along particle size coordinate v. In our work we exploit one-dimensional domain decomposition approach along spatial coordinate x because it allows to avoid use of parallel FFT implementations which are very expensive in terms of data exchanges and have poor parallel scalability. Moreover, locality of finite-difference operator from TVD-scheme along x coordinate allows to obtain good scalability even for computing clusters with slow network interconnect due to modest volumes of data necessary for synchronization exchanges between times integration steps.

Bose–Einstein condensation temperature of finite systems

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

General heat kernel coefficients for massless free spin-3/2 Rarita–Schwinger field

We review the general heat kernel method for the Dirac spinor field as an elementary example in any arbitrary background. We, then compute the first three Seeley–DeWitt coefficients for the massless free spin-3/2 Rarita–Schwinger field without imposing any limitations on the background geometry.

Volterra Kernel Estimation of White Light LEDs in the Time Domain.

In this paper, we present a time domain method for extracting coefficients of nonlinear Volterra-series kernels for white light-emitting diodes (LED) used both for illumination and visible light communications. We show that this method may have several advantages over the thus far more popular frequency domain method. We successfully apply the measured kernel coefficients up to the 3rd order for the modeling of nonlinear distortion impact on advanced modulation formats: pulse amplitude modulation, carrierless amplitude phase and orthogonal frequency division multiplexing. The impact of blue filtering on dynamic nonlinearity is also presented.

Blind Image Deblurring Using Row–Column Sparse Representations

Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recover the deblurred image. The problem is of strong practical relevance since many imaging devices such as cellphone cameras, must rely on deblurring algorithms to yield satisfactory image quality. Despite significant research effort, handling large motions remains an open problem. In this paper, we develop a new method called Blind Image Deblurring using Row-Column Sparsity (BD-RCS) to address this issue. Specifically, we model the outer product of kernel and image coefficients in certain transformation domains as a rank-one matrix, and recover it by solving a rank minimization problem. Our central contribution then includes solving {\em two new} optimization problems involving row and column sparsity to automatically determine blur kernel and image support sequentially. The kernel and image can then be recovered through a singular value decomposition (SVD). Experimental results on linear motion deblurring demonstrate that BD-RCS can yield better results than state of the art, particularly when the blur is caused by large motion. This is confirmed both visually and through quantitative measures.

Kernel density estimation and its application

Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram. Unlike the histogram, the kernel technique produces smooth estimate of the pdf, uses all sample points' locations and more convincingly suggest multimodality. In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. Two concepts play fundamental role in kernel estimation: kernel function shape and coefficient of smoothness, of which the latter is crucial to the method. Several real-life examples, both for univariate and bivariate applications, are shown.

A digital arbitrary size kernel convolution smart image sensor based on in-pixel pulse width processors

PurposeThe purpose of this study is to propose a pulse width based, in-pixel, arbitrary size kernel convolution processor. When image sensors are used in machine vision tasks, large amount of data need to be transferred to the output and fed to a processor. Basic and low-level image processing functions such as kernel convolution is used extensively in the early stages of most machine vision tasks. These low-level functions are usually computationally extensive and if the computation is performed inside every pixel, the burden on the external processor will be greatly reduced.Design/methodology/approachIn the proposed architecture, digital pulse width processing is used to perform kernel convolution on the image sensor data. With this approach, while the photocurrent fluctuations are expressed with changes in the pulse width of an output signal, the small processor incorporated in each pixel receives the output signal of the corresponding pixel and its neighbors and produces a binary coded output result for that specific pixel. The process is commenced in parallel among all pixels of the image sensor.FindingsIt is shown that using the proposed architecture, not only kernel convolution can be performed in the digital domain inside smart image sensors but also arbitrary kernel coefficients are obtainable simply by adjusting the sampling frequency at different phases of the processing.Originality/valueAlthough in-pixel digital kernel convolution has been previously reported however with the presented approach no in-pixel analog to binary coded digital converter is required. Furthermore, arbitrary kernel coefficients and scaling can be deployed in the processing. The given architecture is a suitable choice for smart image sensors which are to be used in high-speed machine vision tasks.

Renormalization group flow, entropy and eigenvalues

The irreversibility of the renormalization group flow is conjectured to be closely related to the concept of entropy. In this paper, the variation of eigenvalues of the Laplacian in the Polyakov action under the renormalization group flow will be studied. Based on the one-loop approximation to the effective field theory, we will use the heat kernel method and zeta function regularization. In even dimensions, the variation of eigenvalues is given by the top heat kernel coefficient, and the conformal anomaly is relevant. In odd dimensions, we will conjecture a formula for the variation of eigenvalues through the holographic renormalization in the setting of geometric AdS/CFT correspondence.