yang liu math

satisfying are modified Dirac delta functions. The infinity norm is often used as a model in analysis and geometry, not for continuous scenarios, but for the discrete or singular scenarios. Before attending Stanford, I graduated from MIT in May 2018. Placement Criteria for Entry-Level Mathematics Courses at UGA; Advanced Placement Credit; Transfer Credit; Slideshow. Currently, I am a postdoctoral fellow in the Geometry and Mathematical Physics group, at SISSA, Trieste. Click here to learn more about giving. Email: [name]@stanford.edu Moreover, we parametrize the Grassmannian in an elementary linear algebra approach, and give a characterization on the image of the (ab solute value) co- sine transform on the space of distributions on the Grassman nian , by computing the coefficients in the Legendre series expansion o f distributions. In this paper, the  p -singular values of random matrices with  Gaussian entries defined in terms of the  l p -p -norm for  p> 1, as is studied. Research Interests . Create a free website or blog at WordPress.com. 2018 AMC-ICPC World Finals 11th place We know that , for any , can be expressed as an integral on by spreading a measure on it, which is. About Me. Our mission is to preserve, expand, and disseminate mathematical knowledge. I received my Ph.D. in 2015 from the Ohio State University, Columbus under the supervision of Henri Moscovici. Enter your SISSA password Office: E2-341A. 2014, 2015 International Math Olympiad gold medal and first-place team, Department of Mathematics Follow. We appreciate your financial support. Yang Liu's interests include logic, decision theory, foundations of probability, philosophy of ai. Also, we show  some numerical experiential results, which verify the theoretical  results. eliminates the feasibility of sifting out the maximal modulus. But in the complex case the double integral on the torus. … But it is unknown yet what exactly the function is, because the invariance yields that , but this doesn’t produce an appropriate function in the general expression for the complex infinity norm. Based on the results in probabilistic estimates on the largest q-singular value, we also give probabilistic estimates on the smallest q-singular value for pre-Gaussian random matrices. I am fascinated by the question of how much we are able to uncover in a weakly supervised setting (e.g., noisy supervision, low-quality/biased training inputs, etc). In this paper, we study the ranges of (absolute value) cosine trans- forms for which we give a proof for an extended surjectivity t heorem by mak- ing applications of the Fredholm’s theorem in integral equa tions, and show a Hermitian characterization theorem for complex Minkowsk i metrics on . 2015, 2017 Putnam N2 (top 25 out of over 4000 students) I am interested in theoretical computer science at large, especially algorithm design. I also am interested in geometric functional analysis and combinatorics (CV). ), Written Qualifying Examination Study Guide, Past Mathematics Department Award Winners, Placement Criteria for Entry-Level Mathematics Courses at UGA. In this paper, we study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the q-quasinorm with 0 < q ≤ 1. March 17, 2016 by Louis Y. Liu Leave a comment. Dissertation/Thesis Title: Non-Convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements. In this paper, the p -singular values of random matrices with Gaussian entries defined in terms of the l p -p -norm for p> 1, as is studied. In this paper, we study the decay of the smallest singular value of submatrices that consist of bounded column vectors. March 12, 2016 by Louis Y. Liu Leave a comment. These results  provide probabilistic description or picture on the behaviors  of the largest  p -singular values of random matrices in probability for  p> 1. March 17, 2016 by Louis Y. Liu Leave a comment. In the numeral or computational aspect, we conduct some numerical experiments for many sets of points and analyze the smallest distance for some extremal configurations. My research is supported by the National Defense Science and Engineering Graduate (NDSEG) Fellowship. A problem is what function would satisfy, if one parametrizes by the Hopf coordinates, One can show that the function is actually some function independent of and by the invariance of the complex norm under action, so it can be denoted as . Main menu . ©University of Georgia, Athens, GA 30602(706)‑542‑3000, Non-Convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements, Academic Professionals, Lecturers, Instructors, MATH 1113: Testing and Homework Information, Upper Division Mathematics Course Offerings 2014-2015, Upper Division Mathematics Course Offerings 2015-2016, Faculty Teaching Schedule/Final Exam Schedules, Ways to satisfy the experiential learning requirement, Master of Applied Mathematical Sciences (M.A.M.S. Every dollar given has a direct impact upon our students and faculty. Yang Liu, SISSA. Office: 380-T In September 2018, I started a PhD at Stanford University in mathematics, and am advised by Aaron Sidford. In September 2018, I started a PhD at Stanford University in mathematics, and am advised by Aaron Sidford. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices. Trieste, Italy; About me. The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices, On the Decay of the Smallest Singular Value of Submatrices of Rectangular Matrices, On the Range of Cosine Transform of Distributions for Torus-invariant Complex Minkowski Spaces, THE PROBABILISTIC ESTIMATES ON THE LARGEST AND SMALLEST q-SINGULAR VALUES OF RANDOM MATRICES. YANG LIU'S MATH BLOG. In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value , when the number of rows of the matrices becomes very large. [name] = yangpliu. Stanford University Math Colloquium Schedule; Number Theory/Arithmetic Geometry; SMARTS ; Topology ; Placement. If one looks back the case of real infinity norm, the way of expressing the infinity norm is by making use of the absolute values on sum and difference smartly to sift out the maximum from two number. Yang Liu's Math Page Welcome to the Department of Mathematics. Dr. Yang Liu, an Assistant Professor of Mathematics, received his Ph.D. in Mathematics from the University of Georgia in the U.S. and previously his M.S. This is the academic homepage of Yang Liu (I publish under Yang P. Liu). March 15, 2016 by Louis Y. Liu Leave a comment. I am interested in theoretical computer science at large, especially algorithm design. Photo: Research. Your gift is important to us and helps support critical opportunities for students and faculty alike, including lectures, travel support, and any number of educational events that augment the classroom experience. One might also be able to put a measure on for the complex norm , , which can be written in real norm as . Mainly, using analytical techniques, we show the probabilist ic estimate,  precisely, the decay, on the upper tail probability of the larges t strictly  convex singular values, when the number of rows of the mat rices becomes  very large and the lower tail probability of theirs as well. Before attending Stanford, I graduated from MIT in May 2018. Yang Liu. Yang Liu is a philosopher at University of Cambridge. We find that that the smallest singular value of submatrices is related to the minimal distance of points to the lines connecting other two points in a bounded point set. Password *. Liuzhou, China. Enter your FULLNAME: Name Surname. Pursue a degree in the fields of Finanical, Pure, Applied, … This is the academic homepage of Yang Liu (I publish under Yang P. Liu). I’m an Assistant Professor at the Computer Science and Engineering department at UC Santa Cruz.I am interested in learning without ground truth supervision. Using a technique from integral geometry and from the perspective of combinatorial geometry, we show the decay rate of the minimal distance for the sets of points if the number of the points that are on the boundary of the convex hull of any subset is not too large, relative to the cardinality of the set.

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