Scalable multi-class sampling via filtered sliced optimal transport

We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We demonstrate the effectiveness of our framework on various sampling applications like stippling, object placement, and Monte-Carlo integration. We a derive multi-class error bound for perceptual rendering error which can be minimized using our optimization. We provide source code at https://github.com/iribis/filtered-sliced-optimal-transport.Comment: 15 pages, 17 figures, ACM Trans. Graph., Vol. 41, No. 6, Article 261. Publication date: December 202

ИНТЕЛЛЕКТУАЛЬНЫЙ числовым программным ДЛЯ MIMD-компьютер

For most scientific and engineering problems simulated on computers the solving of problems of the computational mathematics with approximately given initial data constitutes an intermediate or a final stage. Basic problems of the computational mathematics include the investigating and solving of linear algebraic systems, evaluating of eigenvalues and eigenvectors of matrices, the solving of systems of non-linear equations, numerical integration of initial- value problems for systems of ordinary differential equations.Для більшості наукових та інженерних задач моделювання на ЕОМ рішення задач обчислювальної математики з наближено заданими вихідними даними складає проміжний або остаточний етап. Основні проблеми обчислювальної математики відносяться дослідження і рішення лінійних алгебраїчних систем оцінки власних значень і власних векторів матриць, рішення систем нелінійних рівнянь, чисельного інтегрування початково задач для систем звичайних диференціальних рівнянь.Для большинства научных и инженерных задач моделирования на ЭВМ решение задач вычислительной математики с приближенно заданным исходным данным составляет промежуточный или окончательный этап. Основные проблемы вычислительной математики относятся исследования и решения линейных алгебраических систем оценки собственных значений и собственных векторов матриц, решение систем нелинейных уравнений, численного интегрирования начально задач для систем обыкновенных дифференциальных уравнений

Digital halftoning and the physical reconstruction function

Originally presented as author's thesis (Ph. D.--Massachusetts Institute of Technology), 1986.Bibliography: p. 397-405."This work has been supported by the Digital Equipement Corporation."by Robert A. Ulichney

Coherent EUV lithography with table-top laser

2012 Fall.Includes bibliographical references.This dissertation describes alternative techniques of optical lithography in the extreme ultraviolet (EUV) region of the electromagnetic spectrum. The pursuit of the Moore's law forces the semiconductor industry to transfer to shorter wavelengths of illumination in projection lithography. The EUV light is perhaps the most viable candidate for the next generation integrated circuits printing. However, the EUV lithography encounters many challenges associated with the very nature of the light it is using. Many novel techniques and materials are being applied at the same time in the lithography process. As such the process itself is far from being reliable. Thus the solutions are being sought among the alternative methods of printing in the nano-scale that would aid to temporarily overpass the resolution gap. This thesis contains a description of several alternative techniques of nanofabrication with the EUV light. For each method the analytical description is provided that is further corroborated with numerical model simulations. Furthermore every technique presented here is verified experimentally. The proposed techniques are discussed in terms of their applicability as a self consistent nanofabrication process. The illumination source for all the techniques presented is the capillary discharge laser (CDL) that was engineered at Colorado State University; it is characterized in the chapter 2 of this dissertation. The CDL is an unbeatable table-top source of high average power illumination with the degree of coherence that is sufficient for coherent nano-scale printing. A separate chapter is dedicated to the description of the fabrication protocol of a diffractive optical element (the mask) used in the EUV nanopatterning techniques. This particular chapter is intended to serve as a potential reference manual for the EUV masks fabrication. The coherent EUV nanofabrication techniques described in the chapters 4-6 are: the holographic projection lithography, generalized Talbot imaging (GTI), and de-magnified generalized Talbot imaging. A separate chapter is devoted to the defect tolerance property of the GTI technique

Electropermanent magnetic connectors and actuators : devices and their application in programmable matter

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 199-206).Programmable matter is a digital material having computation, sensing, and actuation capabilities as continuous properties active over its whole extent. To make programmable matter economical to fabricate, we want to use electromagnetic direct drive, rather than clockwork, to actuate the particles. Previous attempts to fabricate small scale (below one centimeter) robotic systems with electromagnetic direct-drive have typically run into problems with insufficient force or torque, excessive power consumption and heat generation (for magnetic-drive systems), or high-voltage requirements, humidity sensitivity, and air breakdown. (for electrostatic-drive systems) The electropermanent magnet is a solid-state device whose external magnetic flux can be stably switched on and off by a discrete electrical pulse. Electropermanent magnets can provide low-power connection and actuation for programmable matter and other small-scale robotic systems. The first chapter covers the electropermanent magnet, its physics, scaling, fabrication, and our experimental device performance data. The second introduces the idea of electropermanent actuators, covers their fundamental limits and scaling, and shows prototype devices and performance measurements. The third chapter describes the smart pebbles system, which consists of 12-mm cubes that can form shapes by stochastic self-assembly and self-disassembly. The fourth chapter describes the millibot, a continuous chain of programmable matter which forms shapes by folding.by Ara Nerses Knaian.Ph.D