Number Of Discontinuity Points Research Articles

Detection of Structure Characteristics and Its Discontinuity Based Field Programmable Gate Array Processor in Cancer Cell by Wavelet Transform

Digital clinical histopathology is one of the crucial techniques for precise cancer cell diagnosing in modern medicine. The Synovial Sarcoma (SS) cancer cell patterns seem to be a spindle shaped cell (SSC) structure and it is very difficult to identify the exact oval shaped cell structure through pathologist’s eye perception. Meanwhile, there is necessitating for monitoring and securing the successful and effective image data processing in the the huge network data which is also a complex one. A field programmable Gate Array (FPGA) was regarded as a necessary one for this. In this work, based on FPGA a Cancer Cell classification is made for the regulation and execution. Hence, mathematically the SSC regularity structures and its discontinuities are measured by the holder exponent (HE) function. In this research work, HE values have been determined by Wavelet Transform Modulus Maxima (WTMM) and Wavelet Leader (WL) methods with basis function of Haar wavelet based on FPGA Processor. The quantitative parameters such as Mean of Asymptotic Discontinuity (MAD), Mean of Removable Discontinuity (MRD) and Number of Discontinuity Points (NDPs) have been considered to determine the prediction of discontinuity detection between WTMM and WL methods. With the help of receiver operating characteristics (ROC) curve, the significant difference of discontinuity detection performance between both the methods has been analyzed. From the experimental results, it is clear that the WL method is more practically feasible and it gives satisfactory performance, in terms of sensitivity and specificity percentage values, which are 80.56% and 59.46%, respectively in the blue color components of the SNR 20 dB noise image.

A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture

Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n>1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.

LIDAR 자료의 분산함수의 불연속점 수의 추정

Ruppert 등 (1997)이 연구한 LIDAR 자료의 회귀함수의 비모수적 추정에 의한 잔차들은 분산함수가 불연속점을 한두 개 가지고 있음을 추측하게 한다. Kang과 Huh (2006)는 분산함수의 불연속점의 위치와 점프크기의 비모수적 추론을 잔차들의 Nadar-aya-Watson 추정량으로 연구하였다. 한편, Huh (2016) 등은 국소다항추정량의 장점을 이용하기 위하여 분산함수의 로그변환이나 잔차의 로그변환을 통하여 분산함수 대신 로그분산함수의 불연속점의 위치와 점프크기의 비모수적 추론을 제시하였다. 그들의 연구에서 점프크기추정량의 점근분포를 이용하여 불연속점이 있는지 없는지에 대한 검정법들이 제시되었다. 이러한 방법을 바탕으로 분산함수 혹은 로그분산함수의 불연속점의 수를 추정하는 알고리듬을 소개하고, 모의실험과 함께 LIDAR 자료에서 분산함수의 불연속점의 수를 추정해 보고자 한다.

Global dynamics of a nonlinear state-dependent feedback control ecological model with a multiple-hump discrete map

An ecological model with nonlinear state-dependent feedback control is proposed and studied. The Poincaré map defined in the phase set integrates the properties of continuous, discrete and impulsive dynamical systems. The map has complex behavior including single hump and multiple-hump functions and multiple discontinuous points. The properties of various cases of the Poincaré map are systematically studied including monotonicity, continuity and the existence of a fixed point and a transcritical bifurcation, which correspond to the existence and global stability of the order-1 periodic solutions or limit cycles of the proposed model. Moreover, the conditions under which the discontinuity occurs and the number of discontinuous points are discussed, which can result in the coexistence of multiple order-1 periodic solutions and complex dynamics. Furthermore, some sufficient conditions for the global stability of the fixed point (order-1 limit cycle) have been provided even when there are multiple peaks and valleys or multiple discontinuous points for the Poincaré map.

On an optimal flow in a class of nilpotent convex problems

A comprehensive analysis of optimal synthesis is carried out for a class of nilpotent convex problems with multidimensional control. It is shown that the synthesis of optimal trajectories forms a nonsmooth half-flow (which is reasonably called optimal) in the state space. An optimal solution starting at some point of the state space is the trajectory of this point under the action of the optimal flow. The existence of an optimal flow entails many important corollaries. For example, applying the Cantor–Bendixson theorem, one can prove that an optimal control in nilpotent convex problems may have at most a countable number of discontinuity points.

On the time-optimal problem for three- and four-dimensional control systems

The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications.