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991.
Chih-Chun Hou Theodore E. Simos Ioannis Th. Famelis 《Mathematical Methods in the Applied Sciences》2020,43(6):3369-3374
We investigate the approximate solution of pantograph type functional differential equations using neural networks. The methodology is based on the ideas of Lagaris et al, and itis applied to various problems with a proportional delay term subject to initial or boundary conditions. The proposed methodology proves to be very efficient. 相似文献
992.
Ioannis Andreadis 《Applied mathematics and computation》2010,217(6):2883-2890
In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of a family of additive dynamic noise Mandelbrot maps from the Julia set of the Mandelbrot map as a function of the noise level. Additionally, using the above tools, we support the invariance of the Julia set of a noise-perturbed Mandelbrot map under different noise realizations. 相似文献
993.
Carmeline J. Dsilva Ronen Talmon Ronald R. Coifman Ioannis G. Kevrekidis 《Applied and Computational Harmonic Analysis》2018,44(3):759-773
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One such challenge is the existence of “repeated eigendirections,” which obscures the detection of the true dimensionality of the underlying manifold and arises when several embedding coordinates parametrize the same direction in the intrinsic geometry of the data set. We propose an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections. We construct a more parsimonious embedding using only the eigenvectors corresponding to unique eigendirections, and we show that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance. We first demonstrate the utility and flexibility of our approach on synthetic data sets. We then apply our algorithm to data collected from a stochastic model of cellular chemotaxis, where our approach for factoring out repeated eigendirections allows us to detect changes in dynamical behavior and the underlying intrinsic system dimensionality directly from data. 相似文献
994.
We consider rationally parameterized plane curves, where the polynomials in the parameterization have fixed supports and generic
coefficients. We apply sparse (or toric) elimination theory in order to determine the vertex representation of the implicit
equation’s Newton polygon. In particular, we consider mixed subdivisions of the input Newton polygons and regular triangulations
of point sets defined by Cayley’s trick. We consider polynomial and rational parameterizations, where the latter may have
the same or different denominators; the implicit polygon is shown to have, respectively, up to four, five, or six vertices. 相似文献
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We present an efficient method for the partitioning of rectangular domains into equi-area sub-domains of minimum total perimeter. For a variety of applications in parallel computation, this corresponds to a load-balanced distribution of tasks that minimize interprocessor communication. Our method is based on utilizing, to the maximum extent possible, a set of optimal shapes for sub-domains. We prove that for a large class of these problems, we can construct solutions whose relative distance from a computable lower bound converges to zero as the problem size tends to infinity. PERIX-GA, a genetic algorithm employing this approach, has successfully solved to optimality million-variable instances of the perimeter-minimization problem and for a one-billion-variable problem has generated a solution within 0.32% of the lower bound. We report on the results of an implementation on a CM-5 supercomputer and make comparisons with other existing codes.This research was partially funded by Air Force Office of Scientific Research grant F496-20-94-1-0036 and National Science Foundation grants CDA-9024618 and CCR-9306807. 相似文献
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