Generic Kernel Research Articles

Second-Moment/Order Approximations by Kernel Smoothers with Application to Volatility Estimation

Second-Moment/Order Approximations by Kernel Smoothers with Application to Volatility Estimation

Rectified Euler [formula omitted]-means and beyond

Euler k-means (EulerK) first maps data onto the unit hyper-sphere surface of equi-dimensional space via a complex mapping which induces the robust Euler kernel and next employs the popular k-means. Consequently, besides enjoying the virtues of k-means such as simplicity and scalability to large data sets, EulerK is also robust to noises and outliers. Although so, the centroids captured by EulerK deviate from the unit hyper-sphere surface and thus in strict distributional sense, actually are outliers. This weird phenomenon also occurs in some generic kernel clustering methods. Intuitively, using such outlier-like centroids should not be quite reasonable but it is still seldom attended. To eliminate the deviation, we propose two Rectified Euler k-means methods, i.e., REK1 and REK2, which retain the merits of EulerK while acquiring real centroids residing on the mapped space to better characterize the data structures. Specifically, REK1 rectifies EulerK by imposing the constraint on the centroids while REK2 views each centroid as the mapped image from a pre-image in the original space and optimizes these pre-images in Euler kernel induced space. Undoubtedly, our proposed REKs can methodologically be extended to solve problems of such a category. Finally, the experiments validate the effectiveness of REK1 and REK2.

Ensemble Model for Diagnostic Classification of Alzheimer's Disease Based on Brain Anatomical Magnetic Resonance Imaging.

Alzheimer's is one of the fast-growing diseases among people worldwide leading to brain atrophy. Neuroimaging reveals extensive information about the brain's anatomy and enables the identification of diagnostic features. Artificial intelligence (AI) in neuroimaging has the potential to significantly enhance the treatment process for Alzheimer's disease (AD). The objective of this study is two-fold: (1) to compare existing Machine Learning (ML) algorithms for the classification of AD. (2) To propose an effective ensemble-based model for the same and to perform its comparative analysis. In this study, data from the Alzheimer's Diseases Neuroimaging Initiative (ADNI), an online repository, is utilized for experimentation consisting of 2125 neuroimages of Alzheimer's disease (n = 975), mild cognitive impairment (n = 538) and cognitive normal (n = 612). For classification, the framework incorporates a Decision Tree (DT), Random Forest (RF), Naïve Bayes (NB), and K-Nearest Neighbor (K-NN) followed by some variations of Support Vector Machine (SVM), such as SVM (RBF kernel), SVM (Polynomial Kernel), and SVM (Sigmoid kernel), as well as Gradient Boost (GB), Extreme Gradient Boosting (XGB) and Multi-layer Perceptron Neural Network (MLP-NN). Afterwards, an Ensemble Based Generic Kernel is presented where Master-Slave architecture is combined to attain better performance. The proposed model is an ensemble of Extreme Gradient Boosting, Decision Tree and SVM_Polynomial kernel (XGB + DT + SVM). At last, the proposed method is evaluated using cross-validation using statistical techniques along with other ML models. The presented ensemble model (XGB + DT + SVM) outperformed existing state-of-the-art algorithms with an accuracy of 89.77%. The efficiency of all the models was optimized using Grid-based tuning, and the results obtained after such process showed significant improvement. XGB + DT + SVM with optimized parameters outperformed all other models with an efficiency of 95.75%. The implication of the proposed ensemble-based learning approach clearly shows the best results compared to other ML models. This experimental comparative analysis improved understanding of the above-defined methods and enhanced their scope and significance in the early detection of Alzheimer's disease.

Delay Effects on Amplitude Death, Oscillation Death, and Renewed Limit Cycle Behavior in Cyclically Coupled Oscillators

The effects of a distributed `weak generic kernel' delay on cyclically coupled limit cycle and chaotic oscillators are considered. For coupled Van der Pol oscillators (and in fact, other oscillators as well) the delay can produce transitions from amplitude death(AD) or oscillation death (OD) to Hopf bifurcation-induced periodic behavior, with the delayed limit cycle shrinking or growing as the delay is varied towards or away from the bifurcation point respectively. The transition from AD to OD is mediated here via a pitchfork bifurcation, as seen earlier for other couplings as well. Also, the cyclically coupled undelayed van der Pol system here is already in a state of AD/OD, and introducing the delay allows both oscillations and AD/OD as the delay parameter is varied. This is in contrast to other limit cycle systems, where diffusive coupling alone does not result in the onset of AD/OD.\\ For systems where the individual oscillators are chaotic, such as a Sprott oscillator system or a coupled van der Pol-Rayleigh system with parametric forcing, the delay may produce AD/OD (as in the Sprott case), with the AD to OD transition now occurring via a transcritical bifurcation instead. However, this may not be possible, and the delay might just vary the attractor shape. In either of these situations however, increased delay strength tends to cause the system to have simpler behavior, streamlining the shape of the attractor, or shrinking it in cases with oscillations.

Amplitude death, oscillation death, and periodic regimes in dynamically coupled Landau–Stuart oscillators with and without distributed delay

The effects of a distributed ’weak generic kernel’ delay on dynamically coupled Landau–Stuart limit cycle oscillators are considered. The system is closed via the ’linear chain trick’ and the linear stability analysis of the system and conditions for Hopf bifurcations that initiate oscillations are investigated. After reformulation, the effect of the weak generic kernel delay turns out to be mathematically similar to the linear augmentation scheme considered earlier for coupled oscillator systems. For our coupled Landau–Stuart oscillators the distributed delay produces transitions from amplitude death (AD) or oscillation death (OD) to periodic behavior via Hopf Bifurcations, with the delayed limit cycle shrinking or growing as the delay is varied towards or away from the bifurcation point respectively. The transition from AD to OD occurs here via a supercritical pitchfork bifurcation, as also seen previously for some other couplings. In addition, the dynamically coupled Landau–Stuart system has a secondary limit cycle emerging within the OD parameter regime, in contrast to other couplings and systems studied earlier.The various transitions among AD, OD and periodic domains that we observe are more intricate than the simple AD states, and the rough boundaries of the parameter regimes where they occur, predicted by linear stability analysis and experimentally verified in earlier work on dynamically coupled systems. Also, although our delayed system mathematically resembles linear augmentation schemes used earlier, the numerical searches here reveal more complex transitions among various dynamical regimes than the direct AD and OD found in those studies.

A geometric q‐character formula for snake modules

Let $\mathscr{C}$ be the category of finite dimensional modules over the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of a simple complex Lie algebra ${\mathfrak{g}}$. Let $\mathscr{C}^-$ be the subcategory introduced by Hernandez and Leclerc. We prove the geometric $q$-character formula conjectured by Hernandez and Leclerc in types $\mathbb{A}$ and $\mathbb{B}$ for a class of simple modules called snake modules introduced by Mukhin and Young. Moreover, we give a combinatorial formula for the $F$-polynomial of the generic kernel associated to the snake module. As an application, we show that snake modules correspond to cluster monomials with square free denominators and we show that snake modules are real modules. We also show that the cluster algebras of the category $\mathscr{C}_1$ are factorial for Dynkin types $\mathbb{A,D,E}$.

Plug-and-Play ISTA Converges With Kernel Denoisers

Plug-and-play (PnP) method is a recent paradigm for image regularization, where the proximal operator (associated with some given regularizer) in an iterative algorithm is replaced with a powerful denoiser. Algorithmically, this involves repeated inversion (of the forward model) and denoising until convergence. Remarkably, PnP regularization produces promising results for several restoration applications. However, a fundamental question in this regard is the theoretical convergence of the PnP iterations, since the algorithm is not strictly derived from an optimization framework. This question has been investigated in recent works, but there are still many unresolved problems. For example, it is not known if convergence can be guaranteed if we use generic kernel denoisers (e.g. nonlocal means) within the ISTA framework (PnP-ISTA). We prove that, under reasonable assumptions, fixed-point convergence of PnP-ISTA is indeed guaranteed for linear inverse problems such as deblurring, inpainting and superresolution (the assumptions are verifiable for inpainting). We compare our theoretical findings with existing results, validate them numerically, and explain their practical relevance.

Хонгодоры: проблемы происхождения этнонима и формирования бурятского племени

The article is devoted to the consideration of the ethnonym origins and the formation of the Buryat tribe “Khongodor”. The study of this topic is one of the current problems, the resolution of which can clarify some unknown aspects of the ethnogenesis and ethnic history of the Buryats, as well as the origin of its separate local component. This article presents a new version, according to which the emergence of the ethnonym of the Buryat tribe was associated with ethnopolitical processes that took place in the early Buryat community. And this ethnopolitical community was dominated by Bulagats. This was indicated by the etymological analysis of the ethnonym “Khongodor” and the names of the main genera. These names indicate the dependent position of the bearers of these names on the leading Association. It explains the formation of the generic kernel Khongodors presented by these two groups. Its ethnic basis is based on the Oirat component, known in the Buryat tradition as “Segenut” or “Olet”. This ethnic element is also characterized by the presence of a Turkic admixture. This proves the Mongol origin of the Khongodor core. It was part of the early inhabitants of the Western Baikal region and did not represent a tribal formation during the period of Bulagat domination. Changes in the ethnic history of the Khongodors occur in the second half of the 17th century. This aspect is connected with the external factors – the military and political influence of the Russian state and the migration of Mongolian groups to the territory of Buryatia. All this had an impact on the internal structure of the Buryat community. The study proves that due to the Russian influence, which caused a violation of established ties within the Buryat community, conditions for the formation of an ethnolocal Khongodor association arose. From the Khongodors and Mongol groups (Khotogouts, Torgouts, Zungars), the Russian authorities organized an administrative formation that gave rise to the tribal formation. In the process of living together on the same administrative territory, they become aware of unity and form a common genealogical relationship. They take a common name and form a tribe. All this happened in the 18–19th centuries.

Representability of cohomological functors over extension fields

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor H:D^{b}_{\mathrm{Coh}}(X)\to \underline{\mathrm{mod}}_{L} to the case where L is a field extension of the base field k of the variety X , with trdeg _k L\leq 1 or L purely transcendental of degree 2. This result can be applied to investigate the behavior of an exact functor F:D^{b}_{\mathrm{Coh}}(X)\to D^{b}_{\mathrm{Coh}}(Y) with X and Y smooth projective varieties and dim Y\leq 1 or Y a rational surface. We show that for any such F there exists a "generic kernel" A in D^{b}_{\mathrm{Coh}}(X\times Y) , such that F is isomorphic to the Fourier–Mukai transform with kernel A after composing both with the pullback to the generic point of Y .

A unified complexity analysis of interior point methods for semidefinite problems based on trigonometric kernel functions

In this paper, we present an interior-point algorithm for semidefinite optimization (SDO) problems based on a new generic trigonometric kernel function, which is constructed by introducing some new conditions on the kernel function. Based on these conditions, we propose a new trigonometric kernel function and present some properties of this function. We present some complexity results for the generic kernel function and prove that, a large-update primal–dual interior-point method for solving SDO problems with this new kernel function enjoys as worst case iteration complexity bound which matches the currently best known complexity bound for large update methods. Moreover, some numerical results show that the new proposed kernel function has better results than the other trigonometric kernel functions.

Modules of constant Jordan type, pullbacks of bundles and generic kernel filtrations

Let kE denote the group algebra of an elementary abelian p-group of rank r over an algebraically closed field of characteristic p. We investigate the functors Fi from kE-modules of constant Jordan type to vector bundles on Pr−1(k), constructed by Benson and Pevtsova. For a kE-module M of constant Jordan type, we show that restricting the sheaf Fi(M) to a dimension s−1 linear subvariety of Pr−1(k) is equivalent to restricting M along a corresponding rank s shifted subgroup of kE and then applying Fi.In the case r=2, we examine the generic kernel filtration of M in order to show that Fi(M) may be computed on certain subquotients of M whose Loewy lengths are bounded in terms of i. More precise information is obtained by applying similar techniques to the nth power generic kernel filtration of M. The latter approach also allows us to generalise our results to higher ranks r.

Kernel Methods for Ill-Posed Range-Based Localization Problems

A kernel regression technique for the ill-posed range-based localization problem is proposed. We introduce a generic kernel design method which relies on a probabilistic modeling of the respective physical environment in terms of a class of stochastic differential equations. The combination of dynamic modeling with physical and stochastic interpretability leads to a unique solution in a Reproducing Kernel Hilbert Space and thus eliminates the need for a time-discrete representation of the localization solution. By design of the problem formulation, an extended Kalman filter naturally evolves as an iterative optimization method. As a practical example, we tackle an ill-posed localization problem that stems from a preinstalled sensor network of unknown geometry, providing nonsynchronous range information to a moving beacon. To obtain a unique solution for the beacon positions and the network geometry, we apply the proposed kernel regression technique and kernel design method. The proposed approach eventually leads to a least squares optimization problem that can be interpreted as a maximum a posteriori estimation problem. While the methodology is not restricted to localization problems only, its validity is shown by a demonstrator which is comprised of a mobile robot and a network of multiple nonmoving beacons that provide time-of-arrival measurements of ultra wide band signals.

Subpixel Registration With Gradient Correlation

We address the problem of subpixel registration of images assumed to be related by a pure translation. We present a method which extends gradient correlation to achieve subpixel accuracy. Our scheme is based on modeling the dominant singular vectors of the 2-D gradient correlation matrix with a generic kernel which we derive by studying the structure of gradient correlation assuming natural image statistics. Our kernel has a parametric form which offers flexibility in modeling the functions obtained from various types of image data. We estimate the kernel parameters, including the unknown subpixel shifts, using the Levenberg-Marquardt algorithm. Experiments with LANDSAT and MRI data show that our scheme outperforms recently proposed state-of-the-art phase correlation methods.

Multi-agent based simulations using fast multipole method: application to large scale simulations of flocking dynamical systems

This article introduces a novel approach to increase the performances of multi-agent based simulations. We focus on a particular kind of multi-agent based simulation where a collection of interacting autonomous situated entities evolve in a situated environment. Our approach combines the fast multipole method coming from computational physics with agent-based microscopic simulations. The aim is to speed up the execution of a multi-agent based simulation while controlling the precision of the associated approximation. This approach may be considered as the first step of a larger effort aiming at designing a generic kernel to support efficient large-scale multi-agent based simulations. This approach is illustrated in this paper by the simulation of large scale flocking dynamical systems.

An operational calculus framework to characterize droplet size populations from turbulent breakup by a small number of parameters

A systematic operational calculus framework that characterizes droplet/bubble size distributions resulting from turbulent breakup of an immiscible fluid into a carrier one is presented. The proposed formulation is derived from dynamical arguments; a finite-difference formulation of the integro-differential continuous coagulation and fragmentation equation is shown to exhibit the same structure as a discrete sequence of Mellin convolutions between the probability distribution of the evolving dispersed phase and a generic kernel. This kernel may have its physical correspondence with the probability distribution resulting from a single breakup event, e.g. a liquid ligament breakup in a ligament-mediated spray formation. The number of convolution steps in the sequence can be reduced to a single parameter. As an illustration, this procedure is applied to the exponential and the gamma distributions, obtaining as a result the Fréchet distribution earlier used by Rosin and Rammler (1934 Kolloid-Zeitschrift 67 16–26), and by Nukiyama and Tanasawa (1939 Trans. Soc. Mech. Eng. Japan 5 62–7). Thus, the framework introduced in this work provides a physical foundation for the success of the Fréchet distribution in accurately fitting experimentally measured droplet size distributions in sprays and emulsions.

Wavefront solutions in diffusive Nicholson’s blowflies equation with nonlocal delay

This paper is concerned with the diffusive Nicholson’s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain ℝ. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.

A modeling framework to describe the transmission of bluetongue virus within and between farms in Great Britain.

BackgroundRecently much attention has been given to developing national-scale micro-simulation models for livestock diseases that can be used to predict spread and assess the impact of control measures. The focus of these models has been on directly transmitted infections with little attention given to vector-borne diseases such as bluetongue, a viral disease of ruminants transmitted by Culicoides biting midges. Yet BT has emerged over the past decade as one of the most important diseases of livestock.Methodology/Principal FindingsWe developed a stochastic, spatially-explicit, farm-level model to describe the spread of bluetongue virus (BTV) within and between farms. Transmission between farms was modeled by a generic kernel, which includes both animal and vector movements. Once a farm acquired infection, the within-farm dynamics were simulated based on the number of cattle and sheep kept on the farm and on local temperatures. Parameter estimates were derived from the published literature and using data from the outbreak of bluetongue in northern Europe in 2006. The model was validated using data on the spread of BTV in Great Britain during 2007. The sensitivity of model predictions to the shape of the transmission kernel was assessed.Conclusions/SignificanceThe model is able to replicate the dynamics of BTV in Great Britain. Although uncertainty remains over the precise shape of the transmission kernel and certain aspects of the vector, the modeling approach we develop constitutes an ideal framework in which to incorporate these aspects as more and better data become available. Moreover, the model provides a tool with which to examine scenarios for the spread and control of BTV in Great Britain.

Development of a lightweight CAE middleware for CAE data exchange

Computer-aided engineering (CAE) analysis is considered essential for product development because it decreases the simulation time, reduces the prototyping costs, and enhances the reusability of product parts. The reuse of quality-assured CAE data has been continually increasing in order to shorten the product development cycle and to improve the product quality. However, less attention has been paid to systematic research on the interoperability of CAE data because of the diversity of CAE data and because the structure of CAE data is more complex than that of CAD data. In this paper, we suggest a CAE data exchange method for the effective sharing of geometric and analysis data. The method relies on heterogeneous CAE systems, a virtual reality system, and our developed lightweight CAE middleware for CAE data exchange. We also designed a generic CAE kernel, which is a critical part of the CAE middleware. The kernel offers a way of storing analysis data from various CAE systems, and, with the aid of a script command, enabling the data to be translated for a different system. The reuse of CAE data is enhanced by the fact that the CAE middleware can be linked with a virtual reality system or a product data management system.

Alternative kernel functions for Smoothed Particle Hydrodynamics in cylindrical symmetry

In this paper we present an alternative generic kernel function for use in Smoothed Particle Hydrodynamics (SPH) based methods. The alternative kernel has been implemented in a standard Cartesian description, and the results for the Sod shock tube problem is presented both with the alternative kernel and the traditional B-spline kernel. Kernels for cylindrically symmetric systems are developed based on fundamental interpolation theory for the cylindrical symmetry. A set of modified equations of motions are further derived through the use of Lagrangian formalism. Previous results have shown that the use of the traditional B-spline kernel function as a generic kernel implies that the cylindrically symmetric solution must be solved by table interpolation. By introducing an alternative generic kernel function, we derive simple analytical solution also for cylindrically symmetric systems. When compared to the B-spline function, the computational efficiency has been increased and the results improved. The results show good agreement with the analytical solution both for the Noh infinite shock problem and the Sedov point source explosion.

SU-FF-J-68: Motion-Compensation in IMRT Employing Probability Distribution of Target Location: Phantom Tests and Computer Simulation

Purpose: To investigate potential utility of the probability density function (PDF) of target location in managing the detrimental effect of target motion on the delivered dose distribution. Method and Materials: Recent advances in 4-D imaging allowed for a more detailed and precise observation and description of internal organ motion due to respiration. Realistic average target trajectories and corresponding PDF were obtained from the analysis of 4D-CT data. It was assumed that these motion patterns were stable and reproducible during treatment delivery. Dose calculation and treatment plan optimization were performed with a modified “motion kernel”, obtained by superimposing pencil beam doses delivered to different instances of anatomy (phases of motion), or, in the first approximation, through convolution of the generic pencil beam kernel with the PDF of target location. With this approach, sample motion-compensated plans were optimized and delivered in fractions to a movable phantom, which reproduced preset motion patterns in two dimensions. Dose measurements were performed with diagnostic film for the linac rates of 100, 300 and 500 MU/minute. Robustness of treatment plans with respect to delivery errors and variations in target motion, as well as interplay with the MLC leaf movement, was further investigated in a computer simulation. Results: While optimized fluence patterns showed deviation of as much as 50% between standard and motion-compensated plans (for 2-cm peak-to-peak amplitude of target motion), the doses delivered in a single fraction deviated by less than 15% point-by-point, and were within 3% of prescription after 30 fractions (reduced approximately as the inverse square root of the number of fractions). Conclusion: Phantom tests showed that the use of motion kernel for treatment planning allowed maintaining the conformality of dose distribution delivered over multiple fractions, without expanding planning margins beyond the CTV. Supported in part by the NCI grant 5P01-CA21239-25, AAPM Summer Undergraduate Fellowship.