Search results for: reproducing%20kernel

Authors: Wei Zhang, Su-Yan Tang, Yi-Fan Zhu, Wei-Ping Wang

Abstract:

Support vector regression (SVR) has been regarded as a state-of-the-art method for approximation and regression. The importance of kernel function, which is so-called admissible support vector kernel (SV kernel) in SVR, has motivated many studies on its composition. The Gaussian kernel (RBF) is regarded as a “best" choice of SV kernel used by non-expert in SVR, whereas there is no evidence, except for its superior performance on some practical applications, to prove the statement. Its well-known that reproducing kernel (R.K) is also a SV kernel which possesses many important properties, e.g. positive definiteness, reproducing property and composing complex R.K by simpler ones. However, there are a limited number of R.Ks with explicit forms and consequently few quantitative comparison studies in practice. In this paper, two R.Ks, i.e. SV kernels, composed by the sum and product of a translation invariant kernel in a Sobolev space are proposed. An exploratory study on the performance of SVR based general R.K is presented through a systematic comparison to that of RBF using multiple criteria and synthetic problems. The results show that the R.K is an equivalent or even better SV kernel than RBF for the problems with more input variables (more than 5, especially more than 10) and higher nonlinearity.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, support vector regression.

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

Abstract:

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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Authors: Shiping Zhou, Minggen Cui

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This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

Abstract:

Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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Authors: Wei Zhang, Yao-Yu Li, Yi-Fan Zhu, Qun Li, Wei-Ping Wang

Abstract:

It-s known that incorporating prior knowledge into support vector regression (SVR) can help to improve the approximation performance. Most of researches are concerned with the incorporation of knowledge in the form of numerical relationships. Little work, however, has been done to incorporate the prior knowledge on the structural relationships among the variables (referred as to Structural Prior Knowledge, SPK). This paper explores the incorporation of SPK in SVR by constructing appropriate admissible support vector kernel (SV kernel) based on the properties of reproducing kernel (R.K). Three-levels specifications of SPK are studied with the corresponding sub-levels of prior knowledge that can be considered for the method. These include Hierarchical SPK (HSPK), Interactional SPK (ISPK) consisting of independence, global and local interaction, Functional SPK (FSPK) composed of exterior-FSPK and interior-FSPK. A convenient tool for describing the SPK, namely Description Matrix of SPK is introduced. Subsequently, a new SVR, namely Motivated Support Vector Regression (MSVR) whose structure is motivated in part by SPK, is proposed. Synthetic examples show that it is possible to incorporate a wide variety of SPK and helpful to improve the approximation performance in complex cases. The benefits of MSVR are finally shown on a real-life military application, Air-toground battle simulation, which shows great potential for MSVR to the complex military applications.

Keywords: admissible support vector kernel, reproducing kernel, structural prior knowledge, motivated support vector regression

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Authors: Wei Zhang, Yao-Yu Li, Yi-Fan Zhu, Qun Li, Wei-Ping Wang

Abstract:

It-s known that incorporating prior knowledge into support vector regression (SVR) can help to improve the approximation performance. Most of researches are concerned with the incorporation of knowledge in form of numerical relationships. Little work, however, has been done to incorporate the prior knowledge on the structural relationships among the variables (referred as to Structural Prior Knowledge, SPK). This paper explores the incorporation of SPK in SVR by constructing appropriate admissible support vector kernel (SV kernel) based on the properties of reproducing kernel (R.K). Three-levels specifications of SPK are studies with the corresponding sub-levels of prior knowledge that can be considered for the method. These include Hierarchical SPK (HSPK), Interactional SPK (ISPK) consisting of independence, global and local interaction, Functional SPK (FSPK) composed of exterior-FSPK and interior-FSPK. A convenient tool for describing the SPK, namely Description Matrix of SPK is introduced. Subsequently, a new SVR, namely Motivated Support Vector Regression (MSVR) whose structure is motivated in part by SPK, is proposed. Synthetic examples show that it is possible to incorporate a wide variety of SPK and helpful to improve the approximation performance in complex cases. The benefits of MSVR are finally shown on a real-life military application, Air-toground battle simulation, which shows great potential for MSVR to the complex military applications.

Keywords: admissible support vector kernel, reproducing kernel, structural prior knowledge, motivated support vector regression

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Hiroto Nakashima, Toshihiro Morita, Koichiro Ohgushi

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Laser Profiler (LP) data from aerial laser surveys have been increasingly used as topographical inputs to numerical simulations of flooding and inundation in river basins. LP data has great potential for reproducing topography, but its effective usage has not yet been fully established. In this study, flooding and inundation are simulated numerically using LP data for the Jobaru River basin of Japan’s Saga Plain. The analysis shows that the topography is reproduced satisfactorily in the computational domain with urban and agricultural areas requiring different grid sizes. A 2-D numerical simulation shows that flood flow behavior changes as grid size is varied.

Keywords: LP data, numerical simulation, topological analysis, mesh size.

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Authors: Giovanni Aloisio, Lucio T. De Paolis, Luciana Provenzano, Lucio Colizzi, Gianluca Pantile

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One of the essential requirements in order to have a realistic surgical simulator is real-time interaction by means of a haptic interface is. In fact, reproducing haptic sensations increases the realism of the simulation. However, the interaction need to be performed in real-time, since a delay between the user action and the system reaction reduces the user immersion. In this paper, we present a prototype of the coronary stent implant simulator developed in the HERMES Project; this system allows real-time interactions with a artery by means of a specific haptic device; thus the user can interactively navigate in a reconstructed artery and force feedback is produced when contact occurs between the artery walls and the medical instruments

Keywords: Collision Detection, Haptic Interface, Real-Time Interaction, Surgical Simulator.

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: KLMS, online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS.

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Authors: Josip Vasilj, Petar Sarajcev, Damir Jakus

Abstract:

One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

Keywords: Wind power, Uncertainty, Stochastic process, Monte Carlo simulation.

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Authors: Mayank Kumar, D B Mahesh Kumar, Ashwin S Kumar, N K Srinath

Abstract:

In this era of technology, fueled by the pervasive usage of the internet, security is a prime concern. The number of new attacks by the so-called “bots", which are automated programs, is increasing at an alarming rate. They are most likely to attack online registration systems. Technology, called “CAPTCHA" (Completely Automated Public Turing test to tell Computers and Humans Apart) do exist, which can differentiate between automated programs and humans and prevent replay attacks. Traditionally CAPTCHA-s have been implemented with the challenge involved in recognizing textual images and reproducing the same. We propose an approach where the visual challenge has to be read out from which randomly selected keywords are used to verify the correctness of spoken text and in turn detect the presence of human. This is supplemented with a speaker recognition system which can identify the speaker also. Thus, this framework fulfills both the objectives – it can determine whether the user is a human or not and if it is a human, it can verify its identity.

Keywords: CAPTCHA, automatic speech recognition, keyword spotting.

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

Abstract:

Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle based method, hyper-elasticity, analysis of stability.

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Authors: C. De Lazzari, E. Del Prete, I. Genuini, F. Fedele

Abstract:

Cardiovascular human simulator can be a useful tool in understanding complex physiopathological process in cardiocirculatory system. It can also be a useful tool in order to investigate the effects of different drugs on hemodynamic parameters. The aim of this work is to test the potentiality of our cardiovascular numerical simulator CARDIOSIM© in reproducing flow/pressure coronary waveforms in presence of two different drugs: Amlodipine (AMLO) and Adenosine (ADO). In particular a time-varying intramyocardial compression, assumed to be proportional to the left ventricular pressure, was related to the venous coronary compliances in order to study its effects on the coronary blood flow and the flow/pressure loop. Considering that coronary circulation dynamics is strongly interrelated with the mechanics of the left ventricular contraction, relaxation, and filling, the numerical model allowed to analyze the effects induced by the left ventricular pressure on the coronary flow.

Keywords: Cardiovascular system, Coronary blood flow, Hemodynamic, Numerical simulation.

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

Abstract:

Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: Synthetic gene network, network identification, nonlinear modeling, optimization.

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Authors: Sung-Chul Hwang, Di Ren, Sang-Moon Yoon, Jong-Chun Park, Abbas Khayyer, Hitoshi Gotoh

Abstract:

This paper presents a fully Lagrangian coupled Fluid-Structure Interaction (FSI) solver for simulations of fluid-structure interactions, which is based on the Moving Particle Semi-implicit (MPS) method to solve the governing equations corresponding to incompressible flows as well as elastic structures. The developed solver is verified by reproducing the high velocity impact loads of deformable thin wedges with three different materials such as mild steel, aluminium and tin during water entry. The present simulation results for aluminium are compared with analytical solution derived from the hydrodynamic Wagner model and linear Wan’s theory. And also, the impact pressure and strain on the water entry wedge with three different materials, such as mild steel, aluminium and tin, are simulated and the effects of hydro-elasticity are discussed.

Keywords: Fluid-structure interaction (FSI), Moving Particle Semi-implicit (MPS) method, Elastic structure, Incompressible fluid Wedge slamming impact.

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Authors: Zarita Zainuddin, Mohammed Mahmod Shuaib, Ibtesam M. Abu-Sulyman

Abstract:

The social force model which belongs to the microscopic pedestrian studies has been considered as the supremacy by many researchers and due to the main feature of reproducing the self-organized phenomena resulted from pedestrian dynamic. The Preferred Force which is a measurement of pedestrian-s motivation to adapt his actual velocity to his desired velocity is an essential term on which the model was set up. This Force has gone through stages of development: first of all, Helbing and Molnar (1995) have modeled the original force for the normal situation. Second, Helbing and his co-workers (2000) have incorporated the panic situation into this force by incorporating the panic parameter to account for the panic situations. Third, Lakoba and Kaup (2005) have provided the pedestrians some kind of intelligence by incorporating aspects of the decision-making capability. In this paper, the authors analyze the most important incorporations into the model regarding the preferred force. They make comparisons between the different factors of these incorporations. Furthermore, to enhance the decision-making ability of the pedestrians, they introduce additional features such as the familiarity factor to the preferred force to let it appear more representative of what actually happens in reality.

Keywords: Pedestrian movement, social force model, preferredforce, familiarity.

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Authors: Sze Wai Veera Fung, Peter W. Ferretto

Abstract:

Similar to most ethnic groups in China, men of the Dong minority hold the primary position in policymaking, moral authority, social values, and the control of the property. As the spatial embodiment of the patriarchal ideals, the house plays a significant role in producing and reproducing the distinctive gender status within the Dong society. Nevertheless, Dong women do not see their home as a cage of confinement, nor do they see themselves as a victim of oppression. For these women with reference to their productive identity, a house is a dwelling place with manifold meanings, including a proof of identity, an economic instrument, and a public resource operating on the community level. This paper examines the role of the house as a central site for identity construction and maintenance for the southern dialect Dong minority women in Hunan, China. Drawing on recent interviews with the Dong women, this study argues that women as productive individuals have a strong influence on the form of their house and the immediate environment, regardless of the male-dominated social construct of the Dong society. The aim of this study is not to produce a definitive relationship between women, house, and identity. Rather, it seeks to offer an alternative lens into the complexity and diversity of gender dynamics operating in and beyond the boundary of the house in the context of contemporary rural China.

Keywords: Conception of home, Dong minority, house, rural China, woman’s identity.

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Authors: M. Ramezanifard, J. Dargahi, S. Najarian, N. Narayanan

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One of the major disadvantages of the minimally invasive surgery (MIS) is the lack of tactile feedback to the surgeon. In order to identify and avoid any damage to the grasped complex tissue by endoscopic graspers, it is important to measure the local softness of tissue during MIS. One way to display the measured softness to the surgeon is a graphical method. In this paper, a new tactile sensor has been reported. The tactile sensor consists of an array of four softness sensors, which are integrated into the jaws of a modified commercial endoscopic grasper. Each individual softness sensor consists of two piezoelectric polymer Polyvinylidene Fluoride (PVDF) films, which are positioned below a rigid and a compliant cylinder. The compliant cylinder is fabricated using a micro molding technique. The combination of output voltages from PVDF films is used to determine the softness of the grasped object. The theoretical analysis of the sensor is also presented. A method has been developed with the aim of reproducing the tactile softness to the surgeon by using a graphical method. In this approach, the proposed system, including the interfacing and the data acquisition card, receives signals from the array of softness sensors. After the signals are processed, the tactile information is displayed by means of a color coding method. It is shown that the degrees of softness of the grasped objects/tissues can be visually differentiated and displayed on a monitor.

Keywords: Minimally invasive surgery, Robotic surgery, Sensor, Softness, Tactile.

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Authors: M. Raciti Castelli, A. Fedrigo, E. Benini

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A multiple-option analytical model for the evaluation of the energy performance and distribution of aerodynamic forces acting on a vertical-axis Darrieus wind turbine depending on both rotor architecture and operating conditions is presented. For this purpose, a numerical algorithm, capable of generating the desired rotor conformation depending on design geometric parameters, is coupled to a Single/Double-Disk Multiple-Streamtube Blade Element – Momentum code. Both single and double-disk configurations are analyzed and model predictions are compared to literature experimental data in order to test the capability of the code for predicting rotor performance. Effective airfoil characteristics based on local blade Reynolds number are obtained through interpolation of literature low-Reynolds airfoil databases. Some corrections are introduced inside the original model with the aim of simulating also the effects of blade dynamic stall, rotor streamtube expansion and blade finite aspect ratio, for which a new empirical relationship to better fit the experimental data is proposed. In order to predict also open field rotor operation, a freestream wind shear profile is implemented, reproducing the effect of atmospheric boundary layer.

Keywords: Wind turbine, BE-M, dynamic stall, streamtube expansion, airfoil finite aspect ratio

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Authors: Cleto J. Sauer Jr

Abstract:

Introduction: Brazil’s new national curriculum guidelines (NCG) for medical education were published in 2014, presenting active learning methodologies as a cornerstone. Simulation was initially applied for aviation pilots’ training and is currently applied in health sciences. The high-fidelity simulator replicates human body anatomy in detail, also reproducing physiological functions and its use is increasing in medical schools. Realistic Simulation (RS) has pedagogical aspects that are aligned with Brazil’s NCG teaching concepts. The main objective of this study is to carry on a narrative review on RS’s aspects that are aligned with Brazil’s new NCG teaching concepts. Methodology: A narrative review was conducted, with search in three databases (PubMed, Embase and BVS) of studies published between 2010 and 2020. Results: After systematized search, 49 studies were selected and divided into four thematic groups. RS is aligned with new Brazilian medical curriculum as it is an active learning methodology, providing greater patient safety, uniform teaching, and student's emotional skills enhancement. RS is based on reflective learning, a teaching concept developed for adult’s education. Conclusion: RS is a methodology aligned with NCG teaching concepts and has potential to assist in the implementation of new Brazilian medical school’s curriculum. It is an immersive and interactive methodology, which provides reflective learning in a safe environment for students and patients.

Keywords: Curriculum, high-fidelity simulator, medical education, realistic simulation.

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