Surfaces are really beautiful, and we could spend years, some people spend all their life, studying surfaces, but once again, we only have time for a few key concepts that will help us to understand, for example, active surfaces, how to do segmentation of volumes in three dimensional images. so its going to be a much shorter video than the previous one, and we're going to be discussing Surfaces instead of curves. I just want to spend a few minutes explaining some of the concepts that we learn about curves on the plane, but now surfaces in 3D. Each module is independent, so you can follow your interests. There are optional MATLAB exercises learners will have access to MATLAB Online for the course duration. This course consists of 7 basic modules and 2 bonus (non-graded) modules. Finally, we will end with image processing techniques used in medicine. You will learn the basic algorithms used for adjusting images, explore JPEG and MPEG standards for encoding and compressing video images, and go on to learn about image segmentation, noise removal and filtering. The course starts by looking at how the human visual system works and then teaches you about the engineering, mathematics, and computer science that makes digital images work. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space. In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. Effective geometry, complexity, and universality. Holographic complexity equals bulk action? Phys. Computational complexity and black hole horizons. Curvatures of left invariant metrics on lie groups. Circuit complexity in fermionic field theory. Toward a definition of complexity for quantum field theory states. Circuit complexity in quantum field theory. Sectional curvatures distribution of complexity geometry. ![]() Complexity growth in integrable and chaotic models. Quantum complexity of time evolution with chaotic Hamiltonians. Quantum complexity and negative curvature. in Quantum Computation and Quantum Information Ch. A relation between volume, mean curvature, and diameter. ![]() Quantum control via geometry: an explicit example. Optimal control, geometry, and quantum computing. A geometric approach to quantum circuit lower bounds. This method thus realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity. This technique gives results that are tighter than all known lower bounds in the literature, as well as establishing lower bounds for a much broader class of complexity geometry metrics than has hitherto been bounded. For a broad class of models, the typical complexity is shown to be exponentially large in the number of qubits. Here I apply the Bishop–Gromov bound to Nielsen’s complexity geometry to prove lower bounds on the quantum complexity of a typical unitary. The Bishop–Gromov bound-a cousin of the focusing lemmas used to prove the Penrose–Hawking black hole singularity theorems-is a differential geometry result that gives an upper bound on the rate of growth of the volume of geodesic balls in terms of the Ricci curvature. More recently, it was proposed by Nielsen that the tools of differential geometry, when applied to the unitary group, might be used to bound the complexity of quantum operations. ![]() Differential geometry has long found applications in physics in general relativity and related areas.
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