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Terahertz (THz) tomography is a rather novel technique for nondestructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from…
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for…
A neural network mechanism that can compensate for poor optical quality was recently discovered in a biological context. We propose that this mechanism can and should be adopted for astronomical purposes. This would shift emphasis away from…
Driven by human ingenuity and creativity, the discovery of super-resolution techniques, which circumvent the classical diffraction limit of light, represent a leap in optical microscopy. However, the vast space encompassing all possible…
Active optics is defined as the control of the shape and the alignment of the components of an optical system at low temporal frequencies. For modern large telescopes with flexible monolithic or segmented primary mirrors and also flexible…
An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multi-photonic quantum systems. The proposals…
A concept of the ground-based optical astronomical observations efficiency is considered in this paper. We believe that a telescope efficiency can be increased by properly allocating observation tasks with respect to the current environment…
Combinational creativity, a form of creativity involving the blending of familiar ideas, is pivotal in design innovation. While most research focuses on how combinational creativity in design is achieved through blending elements, this…
In this paper, we address the inverse problem of fast, stable, and high-quality wavefront reconstruction from pyramid wavefront sensor data for Adaptive Optics systems on Extremely Large Telescopes. For solving the indicated problem we…
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…
Whilst there are perhaps only a few scientific methods, there seem to be almost as many artistic methods as there are artists. Artistic processes appear to inhabit the highest order of open-endedness. To begin to understand some of the…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…
Ich m\"ochte in diesem Bericht algorithmische Methoden vorstellen, die im wesentlichen in diesem Jahrzehnt Einzug in die Computeralgebra gefunden haben. Die haupts\"achlichen Ideen gehen auf Stanley \cite{Sta} und Zeilberger…
Computational methods for electromagnetic and light scattering can be used for the calculation of optical forces and torques. Since typical particles that are optically trapped or manipulated are on the order of the wavelength in size,…
We propose a novel algorithm to estimate the channel covariance matrix of a desired user in multiuser massive MIMO systems. The algorithm uses only knowledge of the array response and rough knowledge of the angular support of the incoming…
Machine-learning excels in many areas with well-defined goals. However, a clear goal is usually not available in art forms, such as photography. The success of a photograph is measured by its aesthetic value, a very subjective concept. This…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…
High throughput optical system is defined to possess the features of both large field of view (FOV) and high resolution. However, it is full of challenge to design such a telescope with the two conflicting specifications at the same time.…