Computing the channel capacity of a communication system affected by uncertain transition probabilities

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPM). However, for large-scale problems, IPM are not practical. Here, we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski (2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure

Concept of an Agent-stress Model of a Tissue

This paper stands for a concept of coupling between agent modeling and stress analysis valid for a tissue. The stress analysis of evolving tissue is underestimated in previous studies. The experimental observations and numerical simulations of stress development in a single cell and in particular, in a growing tissue are still rare in the literature. We use a tensegrity model for a single cell that serves for stress evaluation in a growing tissue. We propose to couple the mechanical modeling with the agent one using a staggered scheme for two exemplary scenarios. The first example is devoted to scratching of the epithelium, and the second one to the pins and slits. We observe the systems sensitivities with respect to the selected groups of design parameters. The groups of parameters have been associated with clusters of cells. We have found that the sensitivities may be used for comparing the complex structures of the tissue

Advances in Modeling of Scanning Charged-Particle-Microscopy Images

Modeling artificial scanning electron microscope (SEM) and scanning ion microscope images has recently become important. This is because of the need to provide repeatable images with a priori determined parameters. Modeled artificial images are highly useful in the evaluation of new imaging and metrological techniques, like image-sharpness calculation, or drift-corrected image composition (DCIC). Originally, the NIST-developed artificial image generator was designed only to produce the SEM images of gold-on-carbon resolution sample for image-sharpness evaluation. Since then, the new improved version of the software was written in C++ programming language and is in the Public Domain. The current version of the software can generate arbitrary samples, any drift function, and many other features. This work describes scanning in charged-particle microscopes, which is applied both in the artificial image generator and the DCIC technique. As an example, the performance of the DCIC technique is demonstrated.Comment: 9 pages, 6 figure

Nieliniowość, asymetria i zależność od warunków początkowych mechanizmu transmisji monetarnej ery Alana Greenspana

The thesis deals with the problems of nonlinearity and state-dependency of the monetary transmission model and asymmetric impulse responses in the Greenspan era. The main aim of the thesis is to verify whether the standard assumption of linearity and state-independency of the monetary transmission model holds in practice when a small three-equation model of monetary transmission is confronted with a broad set of data. The issue of asymmetric monetary transmission is of utmost importance from the perspective of strategic dilemmas regarding optimal scheduling of monetary policy actions. The literature overview leaves very little doubt that there are many theoretical and empirical reasons to believe that monetary transmission exhibits significant sign, size and state asymmetries no matter whether we make some general considerations or whether we focus solely on the Greenspan era. The econometric analysis performed here, based on the STAR framework, delivers statistically significant sign and size asymmetries, but the obtained patterns are not robust among the estimated models. On the other hand, the adopted framework is successful at identifying sources of state-dependency of the estimated equations and state asymmetry of monetary transmission. Variables from all but one of the defined groups are found to deliver significant patterns of state asymmetry and, at the same time, the obtained patterns of state asymmetries are explicable from the theoretical point of view. We find the results to be useful from the perspective of conducting the monetary policy in practice.Praca podejmuje problematykę nieliniowości i zależności od warunków początkowych mechanizmu transmisji monetarnej oraz asymetrycznych odpowiedzi na impuls w erze Alana Greenspana. Głównym celem pracy jest weryfikacja, czy standardowe założenia liniowości i niezależności od warunków początkowych mechanizmu transmisji monetarnej są spełnione, gdy mały trzyrównaniowy model mechanizmu transmisji monetarnej zostaje skonfrontowany z szerokim zbiorem rzeczywistych danych. Zagadnienie asymetrycznej transmisji monetarnej jest szczególnie istotne z perspektywy strategicznych dylematów dotyczących optymalnego rozłożenia w czasie działań władz monetarnych. Przegląd literatury dostarcza wielu – zarówno teoretycznych, jak i empirycznych – przesłanek asymetrii transmisji monetarnej. Ekonometryczna analiza przeprowadzona w niniejszej pracy bazuje na metodyce modelowania modeli wygładzone przejścia klasy STAR. Wskazuje ona na występowanie istotnych asymetrii znaku i wielkości, ale otrzymane wzorce asymetrii są wrażliwe na wybór estymowanego modelu. Z drugiej strony zastosowana metodyka modelowania skutecznie identyfikuje źródła zależności od warunków początkowych estymowanych równań oraz asymetrii stanu transmisji monetarnej. Zmienne z wszystkich oprócz jednej ze zdefiniowanych grup stanowią istotne źródło asymetrii stanu, a oszacowane wzorce asymetrii stanu znajdują wytłumaczenie w teorii ekonomii. Otrzymane rezultaty mogą być przydatne z perspektywy praktyki prowadzenia polityki pieniężnej

Scanning Electron Microscope-based Metrological Electron Microscope System and New Prototype Scanning Electron Microscope Magnification Standard

A metrological electron microscope has been developed at the National Institute of Standards and Technology (NIST) traceable to national standards of length, and a new prototype magnification standard meeting the current needs of the scanning electron microscope (SEM) user community has been fabricated. This metrology instrument is designed to certify standards for the calibration of the magnification of the SEM and for the certification of artifacts for linewidth measurement done in the SEM. The artifacts will be useful for various applications in which the SEM is currently being used. The SEM-based metrology system is now operational at the Institute, and its design criteria and the progress on the characterization of the instrument are presented. The design and criteria for the new lithographically produced SEM low accelerating voltage magnification standard to be calibrated on this system are also discussed

Multi-stage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty set (Revision of CentER Discussion Paper 2014-056)

In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multi period robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period decisions based on the revealed uncertain parameters. At the same time, the problem’s computational complexity stays at the same level as for the static robust problem. This holds also in the non-fixed recourse situation. In the fixed recourse situation our approach can be combined with linear decision rules for the continuous decision variables. We provide theoretical results how to split the uncertainty set by identifying sets of uncertain parameter scenarios to be divided for an improvement in the worst-case objective value. Based on this theory, we propose several splitting heuristics. Numerical examples entailing a capital budgeting and a lot sizing problem illustrate the advantages of the proposed approach