Multiple testing, uncertainty and realistic pictures

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report 2011-004. Link to the abstract at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd

Segmentation of Time Series: Parameter Dependence of Blake-Zisserman and Mumford-Shah Functionals and the Transition from Discrete to Continuous

The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in continuous time are the Mumford-Shah functionals. Time series which minimise these functionals are proper estimates or representations of the signals behind recorded data. We focus on consistent behaviour of the functionals and the estimates, as parameters vary or as the sampling rate increases. For each time continuous time series $f\in L^2 (\lbrack 0,1\rbrack)$ we take conditional expectations w.r.t. to $\sigma$-algebras generated by finer and finer partitions of the time domain into intervals, and thereby construct a sequence $(f_n)_{n\in\N}$ of discrete time series. As $n$ increases this amounts to sampling the continuous time series with more and more accuracy. Our main result is consistent behaviour of segmentations w.r.t. to variation of parameters and increasing sampling rate

Consistencies and rates of convergence of jump-penalized least squares estimators

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our results cover other metrics like Skorokhod metric on the space of c\`{a}dl\`{a}g functions and uniform metrics on $C([0,1])$. We will show that these estimators are in an adaptive sense rate optimal over certain classes of "approximation spaces." Special cases are the class of functions of bounded variation (piecewise) H\"{o}lder continuous functions of order $0<\alpha\le1$ and the class of step functions with a finite but arbitrary number of jumps. In the latter setting, we will also deduce the rates known from change-point analysis for detecting the jumps. Finally, the issue of fully automatic selection of the smoothing parameter is addressed.Comment: Published in at http://dx.doi.org/10.1214/07-AOS558 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust nonparametric detection of objects in noisy images

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd

Проектирование цеха для производства транспортировочных крышек

Объектом исследования является технология печати и установка для 3Dпечати. Предметом проектирования – транспортировочные крышки. Целью работы является исследование и расчёт физических характеристик напечатанных деталей. В процессе работы проведен аналитический обзор. Также изучены основные виды технологий печати, принципы их работы и создания 3D моделей с помощью 3D принтера.The object of research is printing technology and installation for 3D printing. The subject of design is transportation covers. The aim of the work is to study and calculate the physical characteristics of printed parts. In the process, an analytical review was carried out. The main types of printing technologies, the principles of their work and the creation of 3D models with using a 3D printer

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis