Re: Sl Arora Physics Class 11 Pdf Download
Emmanuelle Riker
Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widelyused class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS'S by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS'S is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS'S with very simple initial distributions, thus suggesting that QDS'S are intrinsically more complicated than Markov chains.
N2 - Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widelyused class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS'S by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS'S is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS'S with very simple initial distributions, thus suggesting that QDS'S are intrinsically more complicated than Markov chains.
AB - Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widelyused class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS'S by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS'S is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS'S with very simple initial distributions, thus suggesting that QDS'S are intrinsically more complicated than Markov chains.
This multidisciplinary junior-level course is designed to provide a thorough introduction to modern constructive logic, its roots in philosophy, its numerous applications in computer science, and its mathematical properties. Some of the topics to be covered are intuitionistic logic, inductive definitions, functional programming, type theory, realizability, connections between classical and constructive logic, decidable classes. This course counts as a Fundamentals course in the Computer Science major.
Computational photography is the convergence of computer graphics, computer vision and imaging. Its role is to overcome the limitations of the traditional camera, by combining imaging and computation to enable new and enhanced ways of capturing, representing, and interacting with the physical world. This advanced undergraduate course provides a comprehensive overview of the state of the art in computational photography. At the start of the course, we will study modern image processing pipelines, including those encountered on mobile phone and DSLR cameras, and advanced image and video editing algorithms. Then we will proceed to learn about the physical and computational aspects of tasks such as 3D scanning, coded photography, lightfield imaging, time-of-flight imaging, VR/AR displays, and computational light transport. Near the end of the course, we will discuss active research topics, such as creating cameras that capture video at the speed of light, cameras that look around walls, or cameras that can see through tissue. The course has a strong hands-on component, in the form of seven homework assignments and a final project. In the homework assignments, students will have the opportunity to implement many of the techniques covered in the class, by both acquiring their own images of indoor and outdoor scenes and developing the computational tools needed to extract information from them. For their final projects, students will have the choice to use modern sensors provided by the instructors (lightfield cameras, time-of-flight cameras, depth sensors, structured light systems, etc.).
The goal of this course is to acquaint students with the code required to turn ideas into games. This includes both runtime systems -- e.g., AI, sound, physics, rendering, and networking -- and the asset pipelines and creative tools that make it possible to author content that uses these systems. In the first part of the course, students will implement small games that focus on specific runtime systems, along with appropriate asset editors or exporters. In the second part, students will work in groups to build a larger, polished, open-ended game project. Students who have completed the course will have the skills required to extend -- or build from scratch -- a modern computer game. Students wishing to take this class should be familiar with the C++ language and have a basic understanding of the OpenGL API. If you meet these requirements but have not taken 15-462 (the formal prerequisite), please contact the instructor.
Physically-based simulation is a core topic in computer graphics, where it is used to create the natural motions necessary for realistic training simulations, movies, video games, and other interactive applications. With the advent of affordable and accessible 3D Printing technologies, physics-based methods are also being adopted to enable the design and fabrication of physical objects. This course will cover a broad range of techniques -- from particle systems to rigid bodies to finite elements -- and applications to animation and digital fabrication. A hands-on approach will be taken, with an emphasis on developing fun, interactive computer programs.
This course is an introduction to physics-based rendering at the advanced undergraduate and introductory graduate level. During the course, we will cover fundamentals of light transport, including topics such as the rendering and radiative transfer equation, light transport operators, path integral formulations, and approximations such as diffusion and single scattering. Additionally, we will discuss state-of-the-art models for illumination, surface and volumetric scattering, and sensors. Finally, we will use these theoretical foundations to develop Monte Carlo algorithms and sampling techniques for efficiently simulating physically-accurate images. Towards the end of the course, we will look at advanced topics such as rendering wave optics, neural rendering, and differentiable rendering.
Data science is the study and practice of how we can extract insight and knowledge from large amounts of data. This course provides a practical introduction to the "full stack" of data science analysis, including data collection and processing, data visualization and presentation, statistical model building using machine learning, and big data techniques for scaling these methods. Topics covered include: collecting and processing data using relational methods, time series approaches, graph and network models, free text analysis, and spatial geographic methods; analyzing the data using a variety of statistical and machine learning methods include linear and non-linear regression and classification, unsupervised learning and anomaly detection, plus advanced machine learning methods like kernel approaches, boosting, or deep learning; visualizing and presenting data, particularly focusing the case of high-dimensional data; and applying these methods to big data settings, where multiple machines and distributed computation are needed to fully leverage the data.Students will complete weekly programming homework that emphasize practical understanding of the methods described in the course. In addition, students will develop a tutorial on an advanced topic, and will complete a group project that applies these data science techniques to a practical application chosen by the team; these two longer assignments will be done in lieu of a midterm or final.
Faculty Support: Ryan Boudreau (Internal Medicine)
Human Physiology B.S.
Minor in International Studies
Connor works in the Boudreau lab investigating both cancer and cardiovascular disease. He characterized the location of the protein Sorbs2 in smooth muscle and uncovered a novel role of the protein in muscle cell transition to a proliferative state. Furthermore, he is investigating microproteins Mitoregulin and NC672 and their role in cancer cell response to drug treatment. This work has incorporated his knowledge from his human physiology classes and increased his passion for medicine. He has presented this research at an OUR Research Festival, as well as the American Physiology Summit and American Heart Association.
Margaret plans to continue to medical school as a physician scientist. Until then, she fills her time outside of class in lab and volunteering with the Free Medical Clinic, serving as the President for Medicus, an active member of the Minority Association of Premedical Students, and the public relations of Women in STEM Ambassadors.
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