The Experts below are selected from a list of 15690 Experts worldwide ranked by ideXlab platform
Ralph E. White - One of the best experts on this subject based on the ideXlab platform.
-
Cubic Spline regression for the open circuit potential curves of a lithium ion battery
Journal of The Electrochemical Society, 2005Co-Authors: Qingzhi Guo, Ralph E. WhiteAbstract:A Cubic Spline regression model was used to fit the experimental open-circuit potential (OCP) curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predictable by a third-order polynomial. The locations of the data points used to separate regression intervals were optimized. Compared to a polynomial model with the same number of fitting parameters, the Cubic Spline regression model is more accurate. The Cubic Spline regression model presented here can be used conveniently to fit complicated profiles such as the OCP curves of lithium-ion battery electrodes. © 2004 The Electrochemical Society. All rights reserved.
-
Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery
Journal of The Electrochemical Society, 2005Co-Authors: Qingzhi Guo, Ralph E. WhiteAbstract:A Cubic Spline regression model was used to fit the experimental open-circuit potential (OCP) curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predictable by a third-order polynomial. The locations of the data points used to separate regression intervals were optimized. Compared to a polynomial model with the same number of fitting parameters, the Cubic Spline regression model is more accurate. The Cubic Spline regression model presented here can be used conveniently to fit complicated profiles such as the OCP curves of lithium-ion battery electrodes.
Qingzhi Guo - One of the best experts on this subject based on the ideXlab platform.
-
Cubic Spline regression for the open circuit potential curves of a lithium ion battery
Journal of The Electrochemical Society, 2005Co-Authors: Qingzhi Guo, Ralph E. WhiteAbstract:A Cubic Spline regression model was used to fit the experimental open-circuit potential (OCP) curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predictable by a third-order polynomial. The locations of the data points used to separate regression intervals were optimized. Compared to a polynomial model with the same number of fitting parameters, the Cubic Spline regression model is more accurate. The Cubic Spline regression model presented here can be used conveniently to fit complicated profiles such as the OCP curves of lithium-ion battery electrodes. © 2004 The Electrochemical Society. All rights reserved.
-
Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery
Journal of The Electrochemical Society, 2005Co-Authors: Qingzhi Guo, Ralph E. WhiteAbstract:A Cubic Spline regression model was used to fit the experimental open-circuit potential (OCP) curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predictable by a third-order polynomial. The locations of the data points used to separate regression intervals were optimized. Compared to a polynomial model with the same number of fitting parameters, the Cubic Spline regression model is more accurate. The Cubic Spline regression model presented here can be used conveniently to fit complicated profiles such as the OCP curves of lithium-ion battery electrodes.
Aurelio Uncini - One of the best experts on this subject based on the ideXlab platform.
-
learning activation functions from data using Cubic Spline interpolation
Neural Advances in Processing Nonlinear Dynamic Signals, 2020Co-Authors: Simone Scardapane, Danilo Comminiello, Michele Scarpiniti, Aurelio UnciniAbstract:Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on Cubic Spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Preliminary experimental results validate the proposal.
-
learning activation functions from data using Cubic Spline interpolation
arXiv: Machine Learning, 2016Co-Authors: Simone Scardapane, Danilo Comminiello, Michele Scarpiniti, Aurelio UnciniAbstract:Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on Cubic Spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.
-
hammerstein uniform Cubic Spline adaptive filters learning and convergence properties
Signal Processing, 2014Co-Authors: Michele Scarpiniti, Danilo Comminiello, Raffaele Parisi, Aurelio UnciniAbstract:In this paper a novel class of nonlinear Hammerstein adaptive filters, consisting of a flexible memory-less function followed by a linear combiner, is presented. The nonlinear function involved in the adaptation process is based on a uniform Cubic Spline function that can be properly modified during learning. The Spline control points are adaptively changed by using gradient-based techniques. This new kind of adaptive function is then applied to the input of a linear adaptive filter and it is used for the identification of Hammerstein-type nonlinear systems. In addition, we derive a simple form of the adaptation algorithm, an upper bound on the choice of the step-size and a lower bound on the excess mean square error in a theoretical manner. Some experimental results are also presented to demonstrate the effectiveness of the proposed method in the identification of high-order nonlinear systems.
Lianggee Chen - One of the best experts on this subject based on the ideXlab platform.
-
Cubic Spline interpolation with overlapped window and data reuse for on line hilbert huang transform biomedical microprocessor
International Conference of the IEEE Engineering in Medicine and Biology Society, 2011Co-Authors: Naifu Chang, Chengyi Chiang, Tungchien Chen, Lianggee ChenAbstract:On-chip implementation of Hilbert-Huang transform (HHT) has great impact to analyze the non-linear and non-stationary biomedical signals on wearable or implantable sensors for the real-time applications. Cubic Spline interpolation (CSI) consumes the most computation in HHT, and is the key component for the HHT processor. In tradition, CSI in HHT is usually performed after the collection of a large window of signals, and the long latency violates the realtime requirement of the applications. In this work, we propose to keep processing the incoming signals on-line with small and overlapped data windows without sacrificing the interpolation accuracy. 58% multiplication and 73% division of CSI are saved after the data reuse between the data windows.
-
design and implementation of Cubic Spline interpolation for spike sorting microsystems
International Conference on Acoustics Speech and Signal Processing, 2011Co-Authors: Tungchien Chen, Yunyu Chen, Lianggee ChenAbstract:Accurate spike sorting is important for neuroscientific and neuroprosthetic applications. The sorting of spikes depends on the features extracted from the neural waveforms, and a better sorting performance usually comes with a higher sampling rate (SR). However for long duration experiments on free-moving subjects, the miniaturized and wireless neural recording ICs are the current trend. The compromise on sorting accuracy is usually made for the low power consumption with a lower SR. In this paper, the VLSI architecture of Cubic Spline interpolation is proposed to improve the power-accuracy tradeoff for the spike sorting microsystems. The window-based interpolation schedule, event-triggered processing, and two-step interpolation scheme are applied to save the memory and computation. 0.04 µW/channel is finally achieved after the implementation in 90nm process.
-
accuracy and power tradeoff in spike sorting microsystems with Cubic Spline interpolation
International Symposium on Circuits and Systems, 2010Co-Authors: Yunyu Chen, Tungchien Chen, Lianggee ChenAbstract:Accurate spike sorting is an important issue for neuroscientific and neuroprosthetic applications. The sorting of spikes depends on the features extracted from the neural waveforms, and a better sorting performance usually comes with a higher sampling rate (SR). However the long duration experiment on free-moving subjects is the current trend. For low power considerations, the compromise on sorting accuracy is made for the miniaturized and wireless neural recording ICs with a lower SR. In this paper, we introduce the Cubic Spline interpolation to strike the power and accuracy tradeoff on the recording microsystems for the off-site and on-chip spike sorter. According to the simulation results, the recorder operated with the SR of 12.5k sample per second (sps) outperforms the system with 25ksps SR on both accuracy and power if the interpolation is appropriately performed before the spike sorting.
A K B Chand - One of the best experts on this subject based on the ideXlab platform.
-
a new class of rational Cubic Spline fractal interpolation function and its constrained aspects
Applied Mathematics and Computation, 2019Co-Authors: S K Katiyar, A K B Chand, Saravana G KumarAbstract:Abstract This paper pertains to the area of shape preservation and sets a theoretical foundation for the applications of preserving constrained nature of a given constraining data in fractal interpolation functions (FIFs) techniques. We construct a new class of rational Cubic Spline FIFs (RCSFIFs) with a preassigned quadratic denominator with two shape parameters, which includes classical rational Cubic interpolant [Appl. Math. Comp., 216 (2010), pp. 2036–2049] as special case and improves the sufficient conditions for positivity. Convergence analysis of RCSFIF to the original function in C 1 is studied. In order to meet the needs of practical design or overcome the drawback of the tension effect in the proposed RCSFIFs, we improve our method by introducing a new tension parameter wi and construct a new class of rational Cubic Spline FIFs with three shape parameters. The scaling factors and shape parameters have a predictable adjusting role on the shape of curves. The elements of the rational iterated function system in each subinterval are identified befittingly so that the graph of the resulting C 1 -rational Cubic Spline FIF constrained (i) within a prescribed rectangle (ii) above a prescribed straight line (iii) between two piecewise straight lines. These parameters include, in particular, conditions on the positivity of the C 1 -rational Cubic Spline FIF. Several numerical examples are presented to ascertain the correctness and usability of developed scheme and to suggest how these schemes outperform their classical counterparts.
-
Positive blending Hermite rational Cubic Spline fractal interpolation surfaces
Calcolo, 2015Co-Authors: A K B Chand, N. VijenderAbstract:Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational Cubic Spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational Cubic Spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational Cubic Spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational Cubic Spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS.
-
preserving convexity through rational Cubic Spline fractal interpolation function
Journal of Computational and Applied Mathematics, 2014Co-Authors: P Viswanathan, A K B Chand, Ravi P AgarwalAbstract:We propose a new type of C^1-rational Cubic Spline Fractal Interpolation Function (FIF) for convexity preserving univariate interpolation. The associated Iterated Function System (IFS) involves rational functions of the form P"n(x)Q"n(x), where P"n(x) are Cubic polynomials determined through the Hermite interpolation conditions of the FIF and Q"n(x) are preassigned quadratic polynomials with two shape parameters. The rational Cubic Spline FIF converges to the original function @F as rapidly as the rth power of the mesh norm approaches to zero, provided @F^(^r^) is continuous for r=1 or 2 and certain mild conditions on the scaling factors are imposed. Furthermore, suitable values for the rational IFS parameters are identified so that the property of convexity carries from the data set to the rational Cubic FIFs. In contrast to the classical non-recursive convexity preserving interpolation schemes, the present fractal scheme is well suited for the approximation of a convex function @F whose derivative is continuous but has varying irregularity.
-
Cubic hermite and Cubic Spline fractal interpolation functions
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics, 2012Co-Authors: A K B Chand, P ViswanathanAbstract:Despite that the Spline theory is a well studied topic, its relationship with the fractal theory is novel. Fractal approach offers a single specification for a large class of interpolants of which the classical Spline is a particular member, and hence possesses considerable flexibility in the choice of an interpolant. The explicit construction of a C1-Cubic Hermite fractal interpolation function (FIF) is introduced in the present work. If slopes at knot points are not known, then they are calculated through solution of a suitable linear system of equations so as to have C2 global smoothness for the resulting Cubic FIF. Thus, the present method generalizes the classical C1-Cubic Hermite and C2-Cubic Spline interpolants simultaneously, and offers a new approach to the development of Cubic Spline FIF in contrast to the construction through moments by Chand and Kapoor [SIAM J. Numer. Anal., 44(2), (2006), pp. 655-676]. It is shown that, for appropriate values of vertical scaling factors involved in the defini...
-
Cubic hermite and Cubic Spline fractal interpolation functions
Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics, 2012Co-Authors: A K B Chand, P ViswanathanAbstract:Despite that the Spline theory is a well studied topic, its relationship with the fractal theory is novel. Fractal approach offers a single specification for a large class of interpolants of which the classical Spline is a particular member, and hence possesses considerable flexibility in the choice of an interpolant. The explicit construction of a C1-Cubic Hermite fractal interpolation function (FIF) is introduced in the present work. If slopes at knot points are not known, then they are calculated through solution of a suitable linear system of equations so as to have C2 global smoothness for the resulting Cubic FIF. Thus, the present method generalizes the classical C1-Cubic Hermite and C2-Cubic Spline interpolants simultaneously, and offers a new approach to the development of Cubic Spline FIF in contrast to the construction through moments by Chand and Kapoor [SIAM J. Numer. Anal., 44(2), (2006), pp. 655-676]. It is shown that, for appropriate values of vertical scaling factors involved in the definition, developed C1-Cubic Hermite FIF converges uniformly to the data generating function Φ ∈ C4 at least as rapidly as fourth power of the mesh norm approaches zero.