On optimal recovery of a holomorphic function in the unit ball of Cn

Some problems of optimal recovery in the Hardy and Bergman spaces in the unit ball ofC ⁿ are solved. In particular, some variants of the Schwartz Lemma follow.Communicated by Charles A. Micchelli.     

A description of the segment [1,T], where T is the meeting number of a set-lattice

To 80^th birthday of Paul Erds     

Correlation inequalities and a conjecture for permanents

This paper presents conditions on nonnegative real valued functionsf ₁,f ₂,...,f _m andg ₁,g ₂,...g _m implying an inequality of the type

A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution

Given a multivariate compactly supported distribution, we derive here a necessary and sufficient condition for the global linear independence of its integer translates. This condition is based on the location of the zeros of =the Fourier-Laplace transform of. The utility of the condition is demonstrated by several examples and applications, showing, in particular, that previous results on box splines and exponential box splines can be derived from this condition by a simple combinatorial argument.Communicated by Carl de Boor.     

Direct and inverse theorems for Bernstein polynomials in the space of riemann integrable functions

Equivalence theorems concerning the convergence of the Bernstein polynomialsB _n f are well known for continuous functionsf in the sup-norm. The purpose of this paper is to extend these results for functionsf, Riemann integrable on [0, 1], We have therefore to consider the seminorm

A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

A generalized expression is given for the similarity of spectra, based on the normalized integral of a weighted crosscorrelation function. It is shown that various similarity and dissimilarity criteria previously described in literature can be written as special cases of this general expression. A new similarity criterion, based on this generalized expression, is introduced. The benefits of this criterion are that it properly recognizes shifted but otherwise similar details in spectra and that the resulting similarity measure is normalized. Moreover, the criterion can easily be adapted to specific properties of spectra resulting from various analytical methods. The new criterion is applied to the classification of a series of crystal structures of cephalosporin complexes, based on comparison of their calculated powder diffraction patterns. The results are compared with those obtained using previously described criteria. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 273–289, 2001     

Cross-Entropy Learning for Aortic Pathology Classification of Artificial Multi-Sensor Impedance Cardiography Signals

An aortic dissection, a particular aortic pathology, occurs when blood pushes through a tear between the layers of the aorta and forms a so-called false lumen. Aortic dissection has a low incidence compared to other diseases, but a relatively high mortality that increases with disease progression. An early identification and treatment increases patients’ chances of survival. State-of-the-art medical imaging techniques have several disadvantages; therefore, we propose the detection of aortic dissections through their signatures in impedance cardiography signals. These signatures arise due to pathological blood flow characteristics and a blood conductivity that strongly depends on the flow field, i.e., the proposed method is, in principle, applicable to any aortic pathology that changes the blood flow characteristics. For the signal classification, we trained a convolutional neural network (CNN) with artificial impedance cardiography data based on a simulation model for a healthy virtual patient and a virtual patient with an aortic dissection. The network architecture was tailored to a multi-sensor, multi-channel time-series classification with a categorical cross-entropy loss function as the training objective. The trained network typically yielded a specificity of (93.9±0.1)% and a sensitivity of (97.5±0.1)%. A study of the accuracy as a function of the size of an aortic dissection yielded better results for a small false lumen with larger noise, which emphasizes the question of the feasibility of detecting aortic dissections in an early state.     

神经网络方法用于分辨3种化学物质

神经网络方法用于分辨３种化学物质冯伟,胡上序（浙江大学化工系,杭州,３１００２７）关键词模式分类,神经网络,模拟退火,遗传算法,传感器阵列传感器阵列技术是利用传感器阵列所提供的交叉敏和模式识别及微机处理技术,来提高传感器的选择性和传感器的测量精度［１...     

双因素不完全配对模型和分离聚类法

双因素分离聚类法是一种有广泛应用背景的处理双因素不完全配对模型的数理统计方法．在大样本下,该方法能有效地把影响试验结果的两个因素分离开来,并按事先确定的准则对每个因素的各水平聚类．     

Second-order expansion for the expected regret risk in classification of one-parametric distributions

The plug-in rule is used for the classification of random observations into one of two regular one-parametric distributions. The maximum likelihood estimates of unknown parameters obtained from the stratified training sample are used. The second-order asymptotic expansion in terms of the inverses of the training sample sizes is derived for the expected regret risk. The closed-form expressions of the expansion coefficients are applicable for the performance evaluation of the proposed classification rule. Klaipėda University, H. Manto 84, 5808 Klaipėda; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp. 220–230, April–June, 1999.