Experimental research on impacts of dimensionality on clustering algorithms

Experiments are carried out on datasets with different dimensions selected from UCI datasets by using two classical clustering algorithms. The results of the experiments indicate that when the dimensionality of the real dataset is less than or equal to 30, the clustering algorithms based on distance are effective. For high-dimensional datasets - dimensionality is greater than 30, the clustering algorithms are of weaknesses, even if we use dimension reduction methods, such as Principal Component Analysis (PCA). ©2010 IEEE

Excitation Dependent Phosphorous Property and New Model of the Structured Green Luminescence in ZnO

published_or_final_versio

Plasma biomarkers inclusive of α-synuclein/amyloid-beta40 ratio strongly correlate with Mini-Mental State Examination score in Parkinson’s disease and predict cognitive impairment

Plasma biomarkers for Parkinson’s disease (PD) diagnosis that carry predictive value for cognitive impairment are valuable. We explored the relationship of Mini-Mental State Examination (MMSE) score with plasma biomarkers in PD patients and compared results to vascular dementia (VaD) and normal controls. The predictive accuracy of an individual biomarker on cognitive impairment was evaluated using area under the receiver operating characteristic curve (AUROC), and multivariate logistic regression was applied to evaluate predictive accuracy of biomarkers on cognitive impairment; 178 subjects (41 PD, 31 VaD and 106 normal controls) were included. In multiple linear regression analysis of PD patients, α-synuclein, anti-α-synuclein, α-synuclein/Aβ40 and anti-α-synuclein/Aβ40 were highly predictive of MMSE score in both full model and parsimonious model (R2 = 0.838 and 0.835, respectively) compared to non-significant results in VaD group (R2 = 0.149) and in normal controls (R2 = 0.056). Α-synuclein and anti-α-synuclein/Aβ40 were positively associated with MMSE score, and anti-α-synuclein, α-synuclein/Aβ40 were negatively associated with the MMSE score among PD patients (all Ps < 0.005). In the AUROC analysis, anti-α-synuclein (AUROC = 0.788) and anti-α-synuclein/Aβ40 (AUROC = 0.749) were significant individual predictors of cognitive impairment. In multivariate logistic regression, full model of combined biomarkers showed high accuracy in predicting cognitive impairment (AUROC = 0.890; 95%CI 0.796–0.984) for PD versus controls, as was parsimonious model (AUROC = 0.866; 95%CI 0.764–0.968). In conclusion, simple combination of biomarkers inclusive of α-synuclein/Aβ40 strongly correlates with MMSE score in PD patients versus controls and is highly predictive of cognitive impairment

Simulation of water entry of a two-dimension finite wedge with flow detachment

A two-dimensional finite wedge entering water obliquely at a prescribed speed is considered through the velocity potential theory for the incompressible liquid. The gravity is also included. The problem is solved by using the boundary element method in the time domain. The method of the stretched coordinate system is adopted at the initial stage. A condition is imposed at the intersection of the free surface and the body surface after flow detachment to allow the liquid to leave the body surface smoothly. A new methodology is developed to treat free jet with free surface on both sides. The auxiliary function method is used to calculate the pressure on the body surface. Detailed results for the free surface shape and pressure distribution are provided, and the effect of physical parameters on water entry is discussed

Solving random boundary heat model using the finite difference method under mean square convergence

"This is the peer reviewed version of the following article: Cortés, J. C., Romero, J. V., Roselló, M. D., Sohaly, MA. Solving random boundary heat model using the finite difference method under mean square convergence. Comp and Math Methods. 2019; 1:e1026. https://doi.org/10.1002/cmm4.1026 , which has been published in final form at https://doi.org/10.1002/cmm4.1026. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] This contribution is devoted to construct numerical approximations to the solution of the one-dimensional boundary value problem for the heat model with uncertainty in the diffusion coefficient. Approximations are constructed via random numerical schemes. This approach permits discussing the effect of the random diffusion coefficient, which is assumed a random variable. We establish results about the consistency and stability of the random difference scheme using mean square convergence. Finally, an illustrative example is presented.Spanish Ministerio de Economía y Competitividad. Grant Number: MTM2017-89664-PCortés, J.; Romero, J.; Roselló, M.; Sohaly, M. (2019). Solving random boundary heat model using the finite difference method under mean square convergence. Computational and Mathematical Methods. 1(3):1-15. https://doi.org/10.1002/cmm4.1026S11513Han, X., & Kloeden, P. E. (2017). Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling. doi:10.1007/978-981-10-6265-0Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Logan, J. D. (2004). Partial Differential Equations on Bounded Domains. Undergraduate Texts in Mathematics, 121-171. doi:10.1007/978-1-4419-8879-9_4Cannon, J. R. (1964). A Cauchy problem for the heat equation. Annali di Matematica Pura ed Applicata, 66(1), 155-165. doi:10.1007/bf02412441LinPPY.On The Numerical Solution of The Heat Equation in Unbounded Domains[PhD thesis].New York NY:New York University;1993.Li, J.-R., & Greengard, L. (2007). On the numerical solution of the heat equation I: Fast solvers in free space. Journal of Computational Physics, 226(2), 1891-1901. doi:10.1016/j.jcp.2007.06.021Han, H., & Huang, Z. (2002). Exact and approximating boundary conditions for the parabolic problems on unbounded domains. Computers & Mathematics with Applications, 44(5-6), 655-666. doi:10.1016/s0898-1221(02)00180-3Han, H., & Huang, Z. (2002). A class of artificial boundary conditions for heat equation in unbounded domains. Computers & Mathematics with Applications, 43(6-7), 889-900. doi:10.1016/s0898-1221(01)00329-7Strikwerda, J. C. (2004). Finite Difference Schemes and Partial Differential Equations, Second Edition. doi:10.1137/1.9780898717938Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. doi:10.1007/978-3-662-12616-5Øksendal, B. (2003). Stochastic Differential Equations. Universitext. doi:10.1007/978-3-642-14394-6Holden, H., Øksendal, B., Ubøe, J., & Zhang, T. (2010). Stochastic Partial Differential Equations. doi:10.1007/978-0-387-89488-1El-Tawil, M. A., & Sohaly, M. A. (2012). Mean square convergent three points finite difference scheme for random partial differential equations. Journal of the Egyptian Mathematical Society, 20(3), 188-204. doi:10.1016/j.joems.2012.08.017Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Sohaly, M. A. (2018). Solving the random Cauchy one-dimensional advection–diffusion equation: Numerical analysis and computing. Journal of Computational and Applied Mathematics, 330, 920-936. doi:10.1016/j.cam.2017.02.001Cortés, J. C., Jódar, L., Villafuerte, L., & Villanueva, R. J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48. doi:10.1016/j.matcom.2007.01.020Cortés, J. C., Jódar, L., & Villafuerte, L. (2009). Random linear-quadratic mathematical models: Computing explicit solutions and applications. Mathematics and Computers in Simulation, 79(7), 2076-2090. doi:10.1016/j.matcom.2008.11.008Henderson, D., & Plaschko, P. (2006). Stochastic Differential Equations in Science and Engineering. doi:10.1142/580

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

Electronic Origin of High Temperature Superconductivity in Single-Layer FeSe Superconductor

The latest discovery of high temperature superconductivity signature in single-layer FeSe is significant because it is possible to break the superconducting critical temperature ceiling (maximum Tc~55 K) that has been stagnant since the discovery of Fe-based superconductivity in 2008. It also blows the superconductivity community by surprise because such a high Tc is unexpected in FeSe system with the bulk FeSe exhibiting a Tc at only 8 K at ambient pressure which can be enhanced to 38 K under high pressure. The Tc is still unusually high even considering the newly-discovered intercalated FeSe system A_xFe_{2-y}Se_2 (A=K, Cs, Rb and Tl) with a Tc at 32 K at ambient pressure and possible Tc near 48 K under high pressure. Particularly interesting is that such a high temperature superconductivity occurs in a single-layer FeSe system that is considered as a key building block of the Fe-based superconductors. Understanding the origin of high temperature superconductivity in such a strictly two-dimensional FeSe system is crucial to understanding the superconductivity mechanism in Fe-based superconductors in particular, and providing key insights on how to achieve high temperature superconductivity in general. Here we report distinct electronic structure associated with the single-layer FeSe superconductor. Its Fermi surface topology is different from other Fe-based superconductors; it consists only of electron pockets near the zone corner without indication of any Fermi surface around the zone center. Our observation of large and nearly isotropic superconducting gap in this strictly two-dimensional system rules out existence of node in the superconducting gap. These results have provided an unambiguous case that such a unique electronic structure is favorable for realizing high temperature superconductivity

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Quantum Transduction of Telecommunications-band Single Photons from a Quantum Dot by Frequency Upconversion

The ability to transduce non-classical states of light from one wavelength to another is a requirement for integrating disparate quantum systems that take advantage of telecommunications-band photons for optical fiber transmission of quantum information and near-visible, stationary systems for manipulation and storage. In addition, transducing a single-photon source at 1.3 {\mu}m to visible wavelengths for detection would be integral to linear optical quantum computation due to the challenges of detection in the near-infrared. Recently, transduction at single-photon power levels has been accomplished through frequency upconversion, but it has yet to be demonstrated for a true single-photon source. Here, we transduce the triggered single-photon emission of a semiconductor quantum dot at 1.3 {\mu}m to 710 nm with a total detection (internal conversion) efficiency of 21% (75%). We demonstrate that the 710 nm signal maintains the quantum character of the 1.3 {\mu}m signal, yielding a photon anti-bunched second-order intensity correlation, g^(2)(t), that shows the optical field is composed of single photons with g^(2)(0) = 0.165 < 0.5.Comment: 7 pages, 4 figure