Asymptotic entropic uncertainty relations

We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar measure on the unitary group. We provide lower bounds on the average Shannon entropy of probability distributions related to both measurements. The bounds are stronger than these obtained with use of the entropic uncertainty relation by Maassen and Uffink, and they are optimal up to additive constants. We also analyze the case of a large number of measurements and obtain strong entropic uncertainty relations which hold with high probability with respect to the random choice of bases. The lower bounds we obtain are optimal up to additive constants and allow us to establish the conjecture by Wehner and Winter on the asymptotic behavior of constants in entropic uncertainty relations as the dimension tends to infinity. As a tool we develop estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the Haar measure, which are of an independent interest.Comment: 23 pages, 1 figur

Habitat - idea, sztuka, filozofia

Publikacja recenzowana / Peer-reviewed publicationZE WSTĘPU: Architektura a habitat. Wyzwaniem na dziś nie jest chyba tylko kształt architektonicznych ikon, ale to jak w najbliższej przyszłości projektanci, architekci i urbaniści mają sobie radzić z problemami demograficznymi, socjalnymi i ekonomicznymi. Zapewne habitat będzie się zmieniał i przybierał coraz to inne formy, które zharmonizowane zostaną jako proekologiczny organizm współgrający z wszystkimi samowystarczającymi systemami. Znaczącą jednak funkcję pełnić będzie zawsze sztuka budowania miejsc i nieodłączną w tym znaczeniu formą i funkcją. Łącząc piękno, piękno życia i przeżywania, piękno naturalne i stworzone przez człowieka, będziemy mieli zawsze moralny obowiązek ochrony i pomnażania tego piękna. Ta wielka kompozycja o nieograniczonej liczbie możliwości i wariantów będzie udziałem Nowego Człowieka solidarnie budującego i przeżywającego Nową Postać Świata

Sztuka tworzenia miejsc

Publikacja recenzowana / Peer-reviewed publicatio

Inspiracje twórcze a dzieło stworzone

Praca recenzowana / peer-reviewed pape

3D GRAY-LEVEL HISTOMORPHOMETRY OF TRABECULAR BONE - A METHODOLOGICAL REVIEW

The goal of standard histomorphometry is to provide methods of qualitative description of tissue structure based on image data. Typical measurements include geometric areas, perimeters, length, angle of orientation, form factors, center of gravity coordinates etc. There are well-established procedures for deriving the aforementioned quantities from binary images. However, segmentation of in vivo images of trabecular bone poses a problem which has not been solved yet. Recent years have brought significant developments within an emerging field of “gray-level histomorphometry”. The general goal of gray-level histomorphometry is to provide procedures for measuring geometric areas, perimeters, length, angle of orientation, form factors, center of gravity coordinates etc. without the need for image segmentation. Although the field is not very mature yet, the collected results suggest that this approach opens new perspectives which should not be overlooked by the scientific community. In the present review we summarize the state-of-the-art within the 3D gray-level histomorphometry.</p

The potential of multi-slice computed tomography based quantification of the structural anisotropy of vertebral trabecular bone

In the present paper we addressed the problem of whether the information about the structural anisotropy of trabecular bone can be retrieved from low-quality data, captured with clinical multi-raw spiral CT scanners. Two measures of quantifying structural anisotropy were tested – the current standard mean intercept length (MIL) and the gray-level structure tensor (GST). Thirty two vertebral bodies were μCT and CT scanned. The reference values of structural anisotropy were measured in μCT images and compared with the measures of structural anisotropy determined from low-quality CT data. MIL-based measures of structural anisotropy cannot be reliably determined from CT data. The assessment of the GST is significantly better than that of MIL, but the accuracy is not, in general, satisfactory. Based on the results of experiments with artificial data and the analysis of the real images, it can be concluded that a possible reason of the poor performance is anisotropic resolution of clinical CT scanners

APPLICATION OF IMAGE ANALYSIS METHODS FOR ISOCENTER QUALITY ASSURANCE IN RADIOTHERAPY

One of the major procedures for testing the geometrical accuracy of devices used in radiotherapy treatments is the test of the geometrical position of the radiation isocenter. The importance of the test reflects the fact that geometrical position of the radiation isocenter generally affects the tumor targeting. At present the geometric accuracy is assessed with the Winston-Lutz test which checks the position of an image of a ball marker with the respect to the center of the radiation field as projected on a detector plane. Obviously, determination of coordinates of a single marker is not sufficient to fully account for a complicated geometry of a therapeutic device. The purpose of the study was to design a new image analysis tool to better determine the isocenter. The proposed automated procedure for determining isocenter position uses projection data acquired for a special cube phantom. The projection images of a phantom are acquired for various angles of rotation of the gantry. A procedure is proposed to extract some geometric characteristics of a therapeutic device from the projection images

APPLICATION OF IMAGE ANALYSIS METHODS FOR ISOCENTER QUALITY ASSURANCE IN RADIOTHERAPY

One of the major procedures for testing the geometrical accuracy of devices used in radiotherapy treatments is the test of the geometrical position of the radiation isocenter. The importance of the test reflects the fact that geometrical position of the radiation isocenter generally affects the tumor targeting. At present the geometric accuracy is assessed with the Winston-Lutz test which checks the position of an image of a ball marker with the respect to the center of the radiation field as projected on a detector plane. Obviously, determination of coordinates of a single marker is not sufficient to fully account for a complicated geometry of a therapeutic device. The purpose of the study was to design a new image analysis tool to better determine the isocenter. The proposed automated procedure for determining isocenter position uses projection data acquired for a special cube phantom. The projection images of a phantom are acquired for various angles of rotation of the gantry. A procedure is proposed to extract some geometric characteristics of a therapeutic device from the projection images