Kernel Distribution Research Articles

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System.

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.

Effect of a distributed delay on relative stability of diffusely coupled systems, with application to synchronized equilibria

We perform a linear stability analysis of synchronized equilibria in networks of diffusely coupled oscillators, affected by distributed delays in the coupling and we characterize the structure of the emanating solutions in the bifurcations, under the assumption that the delay kernels are equal to each other. The motivation comes from the fact that valuable quantitative and qualitative information about the occurrence and type of synchronous or partially synchronous solutions can be obtained from this inear analysis. We analyze stability of synchronized equilibria as a function of the parameters of a so-called shifted gamma-distributed delay, which allows to represent or approximate a large class of distributed delay kernels. We also present an asymptotic analysis method, which is particularly suitable for studying the effect of a distribution of delays on stability. We apply the methods to networks of coupled Lorenz systems, where we highlight that stability is favored by a distributed delay compared with a discrete delay with the same average value. Among others, we show that if the coupling is diffusive, the synchronized equilibria become asymptotically stable for large values of the coupling gain, i.e. the systems locally asymptotically synchronize at an equilibrium, independently of the network topology. Received. . .

On spectral distribution of kernel matrices related to radial basis functions

This paper focuses on spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional linear algebra problem to a classical problem on infinite-dimensional linear integral operator, the paper shows how the spectral distribution of a kernel matrix relates to the smoothness of the underlying kernel function. The asymptotic behaviour of the eigenvalues of a infinite-dimensional kernel operator are studied from a perspective of low rank approximation--approximating an integral operator in terms of Fourier series or Chebyshev series truncations. Further, we study how the spectral distribution of interpolation matrices of an infinite smooth kernel with flat limit depends on the geometric property of the underlying interpolation points. In particularly, the paper discusses the analytic eigenvalue distribution of Gaussian kernels, which has important application on stably computing of Gaussian radial basis functions.

Fighting their last stand? A global analysis of the distribution and conservation status of gymnosperms

AbstractAimGymnosperms are often described as a marginal and threatened group, members of which tend to be out‐competed by angiosperms and which therefore preferentially persist at higher latitudes and elevations. The aim of our synthesis was to test these statements by investigating the global latitudinal and elevational distribution of gymnosperms, as well as their conservation status, using all extant gymnosperm groups (cycads, gnetophytes, ginkgophytes and conifers).LocationWorldwide.MethodsWe developed a database of 1014 species of gymnosperms containing latitudinal and elevational distribution data, as well as their global conservation status, as described in the literature. The 1014 species comprised 305 cycads, 101 gnetophytes, the only living representative of ginkgophytes, and 607 conifers. Generalized additive models, frequency histograms, kernel density estimations and distribution maps based on Takhtajan's floristic regions were used.ResultsAlthough the diversity of gymnosperms decreases at equatorial latitudes, approximately 50% of the extant species occur primarily between the tropics. More than 43% of gymnosperms can occur at very low elevations (≤ 200 m a.s.l.). Gymnosperms, considering all species together as well as their main taxonomic groups separately, do not exhibit a latitudinal diversity gradient as commonly observed for many other taxa. Gymnosperms, and especially conifers, are on average less threatened at higher and equatorial latitudes.Main conclusionsGymnosperms display an unusual latitudinal diversity gradient, which we suggest cannot fully be accounted for by angiosperm dominance and competitive superiority. We hypothesize that other factors explain their present distribution, such as the development of centres of endemism in several regions and the adaptation of certain taxa to cold and arid climates.

Dynamics of Neural Systems with Discrete and Distributed Time Delays

In real-world systems, interactions between elements do not happen instantaneously, due to the time required for a signal to propagate, reaction times of individual elements, and so forth. Moreover, time delays are normally nonconstant and may vary with time. This means that it is vital to introduce time delays in any realistic model of neural networks. In order to analyze the fundamental properties of neural networks with time-delayed connections, we consider a system of two coupled two-dimensional nonlinear delay differential equations. This model represents a neural network, where one subsystem receives a delayed input from another subsystem. An exciting feature of the model under consideration is the combination of both discrete and distributed delays, where distributed time delays represent the neural feedback between the two subsystems, and the discrete delays describe the neural interaction within each of the two subsystems. Stability properties are investigated for different commonly used distribution kernels, and the results are compared to the corresponding results on stability for networks with no distributed delays. It is shown how approximations of the boundary of the stability region of a trivial equilibrium can be obtained analytically for the cases of delta, uniform, and weak gamma delay distributions. Numerical techniques are used to investigate stability properties of the fully nonlinear system, and they fully confirm all analytical findings.

Optimized connected cruise control with time delay

In this paper, we optimize the connectivity structure for connected cruise control (CCC) using linear quadratic regulation (LQR) while taking into account driver reaction time delay. We consider that a CCC-equipped vehicle receives position and velocity signals through wireless vehicle-to-vehicle (V2V) communication from multiple vehicles ahead and minimize a cost function defined by headway and velocity errors and the acceleration of the CCC vehicle over an infinite horizon. The resulting optimal feedback contains distributed delay. We show that the feedback gains and the distribution kernels can be obtained recursively as signals from vehicles farther ahead become available. Moreover, the gains exhibit exponential decay as the number of cars between the source and the CCC vehicle increases. The performance of the developed CCC controller is verified by numerical simulations.

Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays

This paper analyzes the stability and bifurcation criteria of cyclic genetic regulatory networks with mixed time delays (discrete and Gamma-type distributed delays). It is of more realistic biological background to use Gamma-type distributed delay kernels to describe the delays in the process between genes. The key aim of our research is to reveal more about the dynamic functions played by biochemical parameters and different mechanisms of discrete and distributed time delays. The existence of positive equilibria in this kind of genetic network is verified. With the mathematical tools of subharmonic function and complex theory, exact conditions of biochemical parameters for stability and bifurcations in cyclic genetic regulatory networks with both positive and negative gains are deduced, respectively. Finally, several simulation examples are adopted to deepen our analysis.

Symbolic Calculus and Boundedness of Multi-parameter and Multi-linear Pseudo-differential Operators

Abstract Since the work of Hörmander on linear pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, harmonic analysis, theory of several complex variables and other branches of modern analysis (e.g., they are used to construct parametrices and establish the regularity of solutions to PDEs such as the ∂̅ problem, etc.). The work of Coifman and Meyer on multi-linear Fourier multipliers and pseudo-differential operators has stimulated further such applications. In [2], the authors developed a fairly satisfactory theory of symbolic calculus for multi-linear pseudo-differential operators. Motivated by this work [2] and Lp estimates of [34, 35] on multi-parameter and multi-linear Fourier multipliers and of [12] on multi-parameter and multi-linear pseudo-differential operators, we study and carry out the theory of symbolic calculus for multi-parameter and multi-linear pseudo-differential operators. Our results include the symbol estimates of the adjoints, asymptotic behavior, kernel estimates and boundedness properties and extend those in [2] to the multi-parameter and multi-linear setting. The estimates of the distributional kernel of associated multi-parameter and multilinear pseudo-differential operators can be found useful in establishing the boundedness of such multi-parameter and multi-linear pseudo-differential operators.

Recovery with Unbounded Diffusion Processes

We analyze the problem of recovering the pricing kernel and real probability distribution from observed option prices, when the state variable is an unbounded diffusion process. We derive necessary and sufficient conditions for recovery. In the general case, these conditions depend on the properties of the diffusion process, but not on the pricing kernel. We also show that the same conditions determine whether recovery works in practice, when the continuous problem is approximated on a bounded or discrete domain without further specification of boundary conditions. Altogether, our results suggest that recovery is possible for many interesting diffusion processes on unbounded domains.

Sources of China’s Economic Growth: An Empirical Analysis Based on the BML Index with Green Growth Accounting

This study develops a biennial Malmquist–Luenberger productivity index that is used to measure the sources of economic growth by utilizing data envelopment analysis and the directional distance function. Taking restrictions on resources and the environment into account based on the green growth accounting framework; we split economic growth into seven components: technical efficiency change, technological change, labor effect, capital effect, energy effect, output structure effect and environmental regulation effect. Further, we apply the Silverman test and Li-Fan-Ullah nonparametric test in combination with kernel distribution to test for the counterfactual contributions at the provincial level in China from 1998 to 2012. The empirical results show that: (1) technological progress and TFP make positive contributions to economic growth in China, while technical efficiency drags it down; (2) the effect of output structure and CO2 emissions with environmental regulation restrain economic growth in some provinces; and (3) overall, physical capital accumulation is the most important driving force for economic take-off, irrespective of whether the government adopts environmental regulations.

A refinement of theabcconjecture

Based on recent work, by the first and third authors, on the distribution of the squarefree kernel of an integer, we present precise refinements of the famous abc conjecture. These rest on the sole heuristic assumption that, whenever a and b are coprime, then the kernels of a, b and c = a + b are statistically independent.

Gaussian bounds, strong ellipticity and uniqueness criteria

Let h be a quadratic form with domain W 1 , 2 ( R d ) given by h ( φ ) = ∑ i , j = 1 d ( ∂ i φ , c i j ∂ j φ ) , where c i j = c j i are real-valued, locally bounded, measurable functions and C = ( c i j ) ⩾ 0 . If C is strongly elliptic, that is, if there exist λ , μ > 0 such that λ I ⩾ C ⩾ μ I > 0 , then h is closable, the closure determines a positive self-adjoint operator H on L 2 ( R d ) which generates a submarkovian semigroup S with a positive distributional kernel K and the kernel satisfies Gaussian upper and lower bounds. Moreover, S is conservative, that is, S t 1 = 1 for all t > 0 . Our aim is to examine converse statements. First, we establish that C is strongly elliptic if and only if h is closable, the semigroup S is conservative and K satisfies Gaussian bounds. Secondly, we prove that if the coefficients are such that a Tikhonov growth condition is satisfied, then S is conservative. Thus, in this case, strong ellipticity of C is equivalent to closability of h together with Gaussian bounds on K. Finally, we consider coefficients c i j ∈ W loc 1 , ∞ ( R d ) . It follows that h is closable and a growth condition of the Täcklind type is sufficient to establish the equivalence of strong ellipticity of C and Gaussian bounds on K.

Kernel Distribution Consistency Based Local Domain Adaptation Learning

Kernel Distribution Consistency Based Local Domain Adaptation Learning

Intertwining operators and the restriction of representations of rank-one orthogonal groups

We give a complete classification of intertwining operators (breaking symmetry operators) between spherical principal series representations of O(n+1,1) and O(n,1) together with explicit formulae of the distribution kernels. Further we use this to determine the breaking symmetry operators between their irreducible composition factors.

Large and moderate deviation principles for kernel distribution estimator

In this paper we prove large and moderate deviations principles for the kernel estimator of a distribution function introduced by Nadaraya [1964. Some new estimates for distribution functions. Theory Probab. Appl. 9, 497500]. We provide results both for the pointwise and the uniform deviations.

Minimizing the Discrepancy Between Source and Target Domains by Learning Adapting Components

Predicting the response variables of the target dataset is one of the main problems in machine learning. Predictive models are desired to perform satisfactorily in a broad range of target domains. However, that may not be plausible if there is a mismatch between the source and target domain distributions. The goal of domain adaptation algorithms is to solve this issue and deploy a model across different target domains. We propose a method based on kernel distribution embedding and Hilbert-Schmidt independence criterion (HSIC) to address this problem. The proposed method embeds both source and target data into a new feature space with two properties: 1) the distributions of the source and the target datasets are as close as possible in the new feature space, and 2) the important structural information of the data is preserved. The embedded data can be in lower dimensional space while preserving the aforementioned properties and therefore the method can be considered as a dimensionality reduction method as well. Our proposed method has a closed-form solution and the experimental results show that it works well in practice.

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

Fourier methods for smooth distribution function estimation

The limit behavior of the optimal bandwidth sequence for the kernel distribution function estimator is analyzed, in its greatest generality, by using Fourier transform methods. We show a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical estimator.

Learning a mixture model for clustering with the completed likelihood minimum message length criterion

Mixture model based clustering (also simply called model-based clustering hereinafter) consists of fitting a mixture model to data and identifying each cluster with one of its components. This paper tackles the model selection and parameter estimation problems in model-based clustering so as to improve the clustering performance on the data sets whose true kernel distribution functions are not in the family of assumed ones, as well as with inherently overlapped clusters. Being tailored to clustering applications, an effective model selection criterion is first proposed. Unlike most criteria that measure the goodness-of-fit of the model only to generate data, the proposed one also evaluates whether the candidate model provides a reasonable partition for the observed data, which enforces a model with well-separated components. Accordingly, an improved method for the estimation of mixture parameters is derived, which aims to suppress the spurious estimates by the standard expectation maximization (EM) algorithm and enforce well-supported components in the mixture model. Finally, the estimation of mixture parameters and the model selection is integrated in a single algorithm which favors a compact mixture model with both the well-supported and well-separated components. Extensive experiments on synthetic and real-world data sets are carried out to show the effectiveness of the proposed approach to the mixture model based clustering.

Amplitude and phase dynamics in oscillators with distributed-delay coupling

This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.