In particular, it achieves nearly linear time for DP-SCO in low-dimension settings. We will start with a primer week to learn the very basics of continuous optimization (July 26 - July 30), followed by two weeks of talks by the speakers on more advanced . Gary L. Miller Carnegie Mellon University Verified email at cs.cmu.edu. Abstract. } 4(JR!$AkRf[(t Bw!hz#0 )l`/8p.7p|O~ My research focuses on the design of efficient algorithms based on graph theory, convex optimization, and high dimensional geometry (CV). with Yair Carmon, Aaron Sidford and Kevin Tian He received his PhD from the Electrical Engineering and Computer Science Department at the Massachusetts Institute of Technology, where he was advised by Jonathan Kelner. << Here is a slightly more formal third-person biography, and here is a recent-ish CV. Publications and Preprints. Applying this technique, we prove that any deterministic SFM algorithm . Allen Liu. Multicalibrated Partitions for Importance Weights Parikshit Gopalan, Omer Reingold, Vatsal Sharan, Udi Wieder ALT, 2022 arXiv . Improved Lower Bounds for Submodular Function Minimization. Associate Professor of . Aaron Sidford is an assistant professor in the department of Management Science and Engineering and the department of Computer Science at Stanford University. Prof. Erik Demaine TAs: Timothy Kaler, Aaron Sidford [Home] [Assignments] [Open Problems] [Accessibility] sample frame from lecture videos Data structures play a central role in modern computer science. Janardhan Kulkarni, Yang P. Liu, Ashwin Sah, Mehtaab Sawhney, Jakub Tarnawski, Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao, FOCS 2021 With Jack Murtagh, Omer Reingold, and Salil P. Vadhan. ", "General variance reduction framework for solving saddle-point problems & Improved runtimes for matrix games. With Bill Fefferman, Soumik Ghosh, Umesh Vazirani, and Zixin Zhou (2022). O! Lower bounds for finding stationary points II: first-order methods. aaron sidford cvnatural fibrin removalnatural fibrin removal Summer 2022: I am currently a research scientist intern at DeepMind in London. % Prior to that, I received an MPhil in Scientific Computing at the University of Cambridge on a Churchill Scholarship where I was advised by Sergio Bacallado. In Symposium on Discrete Algorithms (SODA 2018) (arXiv), Variance Reduced Value Iteration and Faster Algorithms for Solving Markov Decision Processes, Efficient (n/) Spectral Sketches for the Laplacian and its Pseudoinverse, Stability of the Lanczos Method for Matrix Function Approximation. University, where . Before Stanford, I worked with John Lafferty at the University of Chicago. Alcatel One Touch Flip Phone - New Product Recommendations, Promotions I maintain a mailing list for my graduate students and the broader Stanford community that it is interested in the work of my research group. My research was supported by the National Defense Science and Engineering Graduate (NDSEG) Fellowship from 2018-2021, and by a Google PhD Fellowship from 2022-2023. Thesis, 2016. pdf. Information about your use of this site is shared with Google. Source: www.ebay.ie Enrichment of Network Diagrams for Potential Surfaces. Sequential Matrix Completion. Neural Information Processing Systems (NeurIPS, Oral), 2020, Coordinate Methods for Matrix Games In each setting we provide faster exact and approximate algorithms. /Producer (Apache FOP Version 1.0) Aaron Sidford is an Assistant Professor in the departments of Management Science and Engineering and Computer Science at Stanford University. I am broadly interested in optimization problems, sometimes in the intersection with machine learning theory and graph applications. Faster energy maximization for faster maximum flow. I am fortunate to be advised by Aaron Sidford. Email / " Geometric median in nearly linear time ." In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, USA, June 18-21, 2016, Pp. arXiv | conference pdf (alphabetical authorship), Jonathan Kelner, Annie Marsden, Vatsal Sharan, Aaron Sidford, Gregory Valiant, Honglin Yuan, Big-Step-Little-Step: Gradient Methods for Objectives with Multiple Scales. February 16, 2022 aaron sidford cv on alcatel kaios flip phone manual. Aaron Sidford - Home - Author DO Series small tool to obtain upper bounds of such algebraic algorithms. Our method improves upon the convergence rate of previous state-of-the-art linear programming . I have the great privilege and good fortune of advising the following PhD students: I have also had the great privilege and good fortune of advising the following PhD students who have now graduated: Kirankumar Shiragur (co-advised with Moses Charikar) - PhD 2022, AmirMahdi Ahmadinejad (co-advised with Amin Saberi) - PhD 2020, Yair Carmon (co-advised with John Duchi) - PhD 2020. In International Conference on Machine Learning (ICML 2016). Yu Gao, Yang P. Liu, Richard Peng, Faster Divergence Maximization for Faster Maximum Flow, FOCS 2020 Jan van den Brand, Yin Tat Lee, Yang P. Liu, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang: Minimum Cost Flows, MDPs, and 1 -Regression in Nearly Linear Time for Dense Instances. Optimization Algorithms: I used variants of these notes to accompany the courses Introduction to Optimization Theory and Optimization . Outdated CV [as of Dec'19] Students I am very lucky to advise the following Ph.D. students: Siddartha Devic (co-advised with Aleksandra Korolova . Google Scholar Digital Library; Russell Lyons and Yuval Peres. [PDF] Faster Algorithms for Computing the Stationary Distribution with Arun Jambulapati, Aaron Sidford and Kevin Tian Before attending Stanford, I graduated from MIT in May 2018. My research interests lie broadly in optimization, the theory of computation, and the design and analysis of algorithms. with Vidya Muthukumar and Aaron Sidford with Yair Carmon, Arun Jambulapati and Aaron Sidford "FV %H"Hr ![EE1PL* rP+PPT/j5&uVhWt :G+MvY c0 L& 9cX& Given an independence oracle, we provide an exact O (nr log rT-ind) time algorithm. Discrete Mathematics and Algorithms: An Introduction to Combinatorial Optimization: I used these notes to accompany the course Discrete Mathematics and Algorithms. Publications | Jakub Pachocki - Harvard University Management Science & Engineering July 8, 2022. Jonathan A. Kelner, Yin Tat Lee, Lorenzo Orecchia, and Aaron Sidford; Computing maximum flows with augmenting electrical flows. I received a B.S. with Yang P. Liu and Aaron Sidford. aaron sidford cv Yujia Jin. In Symposium on Theory of Computing (STOC 2020) (arXiv), Constant Girth Approximation for Directed Graphs in Subquadratic Time, With Shiri Chechik, Yang P. Liu, and Omer Rotem, Leverage Score Sampling for Faster Accelerated Regression and ERM, With Naman Agarwal, Sham Kakade, Rahul Kidambi, Yin Tat Lee, and Praneeth Netrapalli, In International Conference on Algorithmic Learning Theory (ALT 2020) (arXiv), Near-optimal Approximate Discrete and Continuous Submodular Function Minimization, In Symposium on Discrete Algorithms (SODA 2020) (arXiv), Fast and Space Efficient Spectral Sparsification in Dynamic Streams, With Michael Kapralov, Aida Mousavifar, Cameron Musco, Christopher Musco, Navid Nouri, and Jakab Tardos, In Conference on Neural Information Processing Systems (NeurIPS 2019), Complexity of Highly Parallel Non-Smooth Convex Optimization, With Sbastien Bubeck, Qijia Jiang, Yin Tat Lee, and Yuanzhi Li, Principal Component Projection and Regression in Nearly Linear Time through Asymmetric SVRG, A Direct (1/) Iteration Parallel Algorithm for Optimal Transport, In Conference on Neural Information Processing Systems (NeurIPS 2019) (arXiv), A General Framework for Efficient Symmetric Property Estimation, With Moses Charikar and Kirankumar Shiragur, Parallel Reachability in Almost Linear Work and Square Root Depth, In Symposium on Foundations of Computer Science (FOCS 2019) (arXiv), With Deeparnab Chakrabarty, Yin Tat Lee, Sahil Singla, and Sam Chiu-wai Wong, Deterministic Approximation of Random Walks in Small Space, With Jack Murtagh, Omer Reingold, and Salil P. Vadhan, In International Workshop on Randomization and Computation (RANDOM 2019), A Rank-1 Sketch for Matrix Multiplicative Weights, With Yair Carmon, John C. Duchi, and Kevin Tian, In Conference on Learning Theory (COLT 2019) (arXiv), Near-optimal method for highly smooth convex optimization, Efficient profile maximum likelihood for universal symmetric property estimation, In Symposium on Theory of Computing (STOC 2019) (arXiv), Memory-sample tradeoffs for linear regression with small error, Perron-Frobenius Theory in Nearly Linear Time: Positive Eigenvectors, M-matrices, Graph Kernels, and Other Applications, With AmirMahdi Ahmadinejad, Arun Jambulapati, and Amin Saberi, In Symposium on Discrete Algorithms (SODA 2019) (arXiv), Exploiting Numerical Sparsity for Efficient Learning: Faster Eigenvector Computation and Regression, In Conference on Neural Information Processing Systems (NeurIPS 2018) (arXiv), Near-Optimal Time and Sample Complexities for Solving Discounted Markov Decision Process with a Generative Model, With Mengdi Wang, Xian Wu, Lin F. Yang, and Yinyu Ye, Coordinate Methods for Accelerating Regression and Faster Approximate Maximum Flow, In Symposium on Foundations of Computer Science (FOCS 2018), Solving Directed Laplacian Systems in Nearly-Linear Time through Sparse LU Factorizations, With Michael B. Cohen, Jonathan A. Kelner, Rasmus Kyng, John Peebles, Richard Peng, and Anup B. Rao, In Symposium on Foundations of Computer Science (FOCS 2018) (arXiv), Efficient Convex Optimization with Membership Oracles, In Conference on Learning Theory (COLT 2018) (arXiv), Accelerating Stochastic Gradient Descent for Least Squares Regression, With Prateek Jain, Sham M. Kakade, Rahul Kidambi, and Praneeth Netrapalli, Approximating Cycles in Directed Graphs: Fast Algorithms for Girth and Roundtrip Spanners. [pdf] [talk] 2015 Doctoral Dissertation Award - Association for Computing Machinery University of Cambridge MPhil. Kirankumar Shiragur | Data Science Optimization Algorithms: I used variants of these notes to accompany the courses Introduction to Optimization Theory and Optimization Algorithms which I created. Some I am still actively improving and all of them I am happy to continue polishing. 2022 - Learning and Games Program, Simons Institute, Sept. 2021 - Young Researcher Workshop, Cornell ORIE, Sept. 2021 - ACO Student Seminar, Georgia Tech, Dec. 2019 - NeurIPS Spotlight presentation. ", "About how and why coordinate (variance-reduced) methods are a good idea for exploiting (numerical) sparsity of data. [pdf] [poster] Aleksander Mdry; Generalized preconditioning and network flow problems Microsoft Research Faculty Fellowship 2020: Researchers in academia at Lower Bounds for Finding Stationary Points II: First-Order Methods Simple MAP inference via low-rank relaxations. 22nd Max Planck Advanced Course on the Foundations of Computer Science Intranet Web Portal. Slides from my talk at ITCS. with Hilal Asi, Yair Carmon, Arun Jambulapati and Aaron Sidford Aaron Sidford, Gregory Valiant, Honglin Yuan COLT, 2022 arXiv | pdf. Prior to coming to Stanford, in 2018 I received my Bachelor's degree in Applied Math at Fudan I am a fifth-and-final-year PhD student in the Department of Management Science and Engineering at Stanford in ", "A low-bias low-cost estimator of subproblem solution suffices for acceleration! CV; Theory Group; Data Science; CSE 535: Theory of Optimization and Continuous Algorithms. Cameron Musco, Praneeth Netrapalli, Aaron Sidford, Shashanka Ubaru, David P. Woodruff Innovations in Theoretical Computer Science (ITCS) 2018. He received his PhD from the Electrical Engineering and Computer Science Department at the Massachusetts Institute of Technology, where he was advised by Jonathan Kelner. We present an accelerated gradient method for nonconvex optimization problems with Lipschitz continuous first and second . with Yair Carmon, Aaron Sidford and Kevin Tian Aaron Sidford - Google Scholar Yair Carmon, Arun Jambulapati, Yujia Jin, Yin Tat Lee, Daogao Liu, Aaron Sidford, and Kevin Tian. With Michael Kapralov, Yin Tat Lee, Cameron Musco, and Christopher Musco. riba architectural drawing numbering system; fort wayne police department gun permit; how long does chambord last unopened; wayne county news wv obituaries MI #~__ Q$.R$sg%f,a6GTLEQ!/B)EogEA?l kJ^- \?l{ P&d\EAt{6~/fJq2bFn6g0O"yD|TyED0Ok-\~[`|4P,w\A8vD$+)%@P4 0L ` ,\@2R 4f Allen Liu - GitHub Pages I am a fourth year PhD student at Stanford co-advised by Moses Charikar and Aaron Sidford. Oral Presentation for Misspecification in Prediction Problems and Robustness via Improper Learning. with Sepehr Assadi, Arun Jambulapati, Aaron Sidford and Kevin Tian Honorable Mention for the 2015 ACM Doctoral Dissertation Award went to Aaron Sidford of the Massachusetts Institute of Technology, and Siavash Mirarab of the University of Texas at Austin. Research interests : Data streams, machine learning, numerical linear algebra, sketching, and sparse recovery.. Advanced Data Structures (6.851) - Massachusetts Institute of Technology Neural Information Processing Systems (NeurIPS, Oral), 2019, A Near-Optimal Method for Minimizing the Maximum of N Convex Loss Functions Given a linear program with n variables, m > n constraints, and bit complexity L, our algorithm runs in (sqrt(n) L) iterations each consisting of solving (1) linear systems and additional nearly linear time computation. However, many advances have come from a continuous viewpoint. Aaron Sidford - All Publications %PDF-1.4 We establish lower bounds on the complexity of finding $$-stationary points of smooth, non-convex high-dimensional functions using first-order methods. Instructor: Aaron Sidford Winter 2018 Time: Tuesdays and Thursdays, 10:30 AM - 11:50 AM Room: Education Building, Room 128 Here is the course syllabus. stream The Journal of Physical Chemsitry, 2015. pdf, Annie Marsden. STOC 2023. with Aaron Sidford Aaron Sidford | Management Science and Engineering Aaron Sidford's 143 research works with 2,861 citations and 1,915 reads, including: Singular Value Approximation and Reducing Directed to Undirected Graph Sparsification what is a blind trust for lottery winnings; ithaca college park school scholarships; If you have been admitted to Stanford, please reach out to discuss the possibility of rotating or working together. rl1 ", "Team-convex-optimization for solving discounted and average-reward MDPs! Conference Publications 2023 The Complexity of Infinite-Horizon General-Sum Stochastic Games With Yujia Jin, Vidya Muthukumar, Aaron Sidford To appear in Innovations in Theoretical Computer Science (ITCS 2023) (arXiv) 2022 Optimal and Adaptive Monteiro-Svaiter Acceleration With Yair Carmon, MS&E213 / CS 269O - Introduction to Optimization Theory Conference of Learning Theory (COLT), 2021, Towards Tight Bounds on the Sample Complexity of Average-reward MDPs [pdf] Semantic parsing on Freebase from question-answer pairs. Faster Matroid Intersection Princeton University Goethe University in Frankfurt, Germany. Improves the stochas-tic convex optimization problem in parallel and DP setting. Yujia Jin. The paper, Efficient Convex Optimization Requires Superlinear Memory, was co-authored with Stanford professor Gregory Valiant as well as current Stanford student Annie Marsden and alumnus Vatsal Sharan. Many of these algorithms are iterative and solve a sequence of smaller subproblems, whose solution can be maintained via the aforementioned dynamic algorithms. I am particularly interested in work at the intersection of continuous optimization, graph theory, numerical linear algebra, and data structures. Efficient accelerated coordinate descent methods and faster algorithms for solving linear systems. Prof. Sidford's paper was chosen from more than 150 accepted papers at the conference. Navajo Math Circles Instructor. Selected for oral presentation. We prove that deterministic first-order methods, even applied to arbitrarily smooth functions, cannot achieve convergence rates in $$ better than $^{-8/5}$, which is within $^{-1/15}\\log\\frac{1}$ of the best known rate for such . aaron sidford cv Fall'22 8803 - Dynamic Algebraic Algorithms, small tool to obtain upper bounds of such algebraic algorithms. Main Menu. The authors of most papers are ordered alphabetically. Google Scholar; Probability on trees and . in Chemistry at the University of Chicago. The Complexity of Infinite-Horizon General-Sum Stochastic Games, With Yujia Jin, Vidya Muthukumar, Aaron Sidford, To appear in Innovations in Theoretical Computer Science (ITCS 2023) (arXiv), Optimal and Adaptive Monteiro-Svaiter Acceleration, With Yair Carmon, Danielle Hausler, Arun Jambulapati, and Yujia Jin, To appear in Advances in Neural Information Processing Systems (NeurIPS 2022) (arXiv), On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood, With Moses Charikar, Zhihao Jiang, and Kirankumar Shiragur, Improved Lower Bounds for Submodular Function Minimization, With Deeparnab Chakrabarty, Andrei Graur, and Haotian Jiang, In Symposium on Foundations of Computer Science (FOCS 2022) (arXiv), RECAPP: Crafting a More Efficient Catalyst for Convex Optimization, With Yair Carmon, Arun Jambulapati, and Yujia Jin, International Conference on Machine Learning (ICML 2022) (arXiv), Efficient Convex Optimization Requires Superlinear Memory, With Annie Marsden, Vatsal Sharan, and Gregory Valiant, Conference on Learning Theory (COLT 2022), Sharper Rates for Separable Minimax and Finite Sum Optimization via Primal-Dual Extragradient Method, Conference on Learning Theory (COLT 2022) (arXiv), Big-Step-Little-Step: Efficient Gradient Methods for Objectives with Multiple Scales, With Jonathan A. Kelner, Annie Marsden, Vatsal Sharan, Gregory Valiant, and Honglin Yuan, Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching, With Arun Jambulapati, Yujia Jin, and Kevin Tian, International Colloquium on Automata, Languages and Programming (ICALP 2022) (arXiv), Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary, With Aaron Bernstein, Jan van den Brand, Maximilian Probst, Danupon Nanongkai, Thatchaphol Saranurak, and He Sun, Faster Maxflow via Improved Dynamic Spectral Vertex Sparsifiers, With Jan van den Brand, Yu Gao, Arun Jambulapati, Yin Tat Lee, Yang P. Liu, and Richard Peng, In Symposium on Theory of Computing (STOC 2022) (arXiv), Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space, With Sepehr Assadi, Arun Jambulapati, Yujia Jin, and Kevin Tian, In Symposium on Discrete Algorithms (SODA 2022) (arXiv), Algorithmic trade-offs for girth approximation in undirected graphs, With Avi Kadria, Liam Roditty, Virginia Vassilevska Williams, and Uri Zwick, In Symposium on Discrete Algorithms (SODA 2022), Computing Lewis Weights to High Precision, With Maryam Fazel, Yin Tat Lee, and Swati Padmanabhan, With Hilal Asi, Yair Carmon, Arun Jambulapati, and Yujia Jin, In Advances in Neural Information Processing Systems (NeurIPS 2021) (arXiv), Thinking Inside the Ball: Near-Optimal Minimization of the Maximal Loss, In Conference on Learning Theory (COLT 2021) (arXiv), The Bethe and Sinkhorn Permanents of Low Rank Matrices and Implications for Profile Maximum Likelihood, With Nima Anari, Moses Charikar, and Kirankumar Shiragur, Towards Tight Bounds on the Sample Complexity of Average-reward MDPs, In International Conference on Machine Learning (ICML 2021) (arXiv), Minimum cost flows, MDPs, and 1-regression in nearly linear time for dense instances, With Jan van den Brand, Yin Tat Lee, Yang P. Liu, Thatchaphol Saranurak, and Zhao Song, Di Wang, In Symposium on Theory of Computing (STOC 2021) (arXiv), Ultrasparse Ultrasparsifiers and Faster Laplacian System Solvers, In Symposium on Discrete Algorithms (SODA 2021) (arXiv), Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration, In Innovations in Theoretical Computer Science (ITCS 2021) (arXiv), Acceleration with a Ball Optimization Oracle, With Yair Carmon, Arun Jambulapati, Qijia Jiang, Yujia Jin, Yin Tat Lee, and Kevin Tian, In Conference on Neural Information Processing Systems (NeurIPS 2020), Instance Based Approximations to Profile Maximum Likelihood, In Conference on Neural Information Processing Systems (NeurIPS 2020) (arXiv), Large-Scale Methods for Distributionally Robust Optimization, With Daniel Levy*, Yair Carmon*, and John C. Duch (* denotes equal contribution), High-precision Estimation of Random Walks in Small Space, With AmirMahdi Ahmadinejad, Jonathan A. Kelner, Jack Murtagh, John Peebles, and Salil P. Vadhan, In Symposium on Foundations of Computer Science (FOCS 2020) (arXiv), Bipartite Matching in Nearly-linear Time on Moderately Dense Graphs, With Jan van den Brand, Yin Tat Lee, Danupon Nanongkai, Richard Peng, Thatchaphol Saranurak, Zhao Song, and Di Wang, In Symposium on Foundations of Computer Science (FOCS 2020), With Yair Carmon, Yujia Jin, and Kevin Tian, Unit Capacity Maxflow in Almost $O(m^{4/3})$ Time, Invited to the special issue (arXiv before merge)), Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity, In International Conference on Artificial Intelligence and Statistics (AISTATS 2020) (arXiv), Efficiently Solving MDPs with Stochastic Mirror Descent, In International Conference on Machine Learning (ICML 2020) (arXiv), Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond, With Oliver Hinder and Nimit Sharad Sohoni, In Conference on Learning Theory (COLT 2020) (arXiv), Solving Tall Dense Linear Programs in Nearly Linear Time, With Jan van den Brand, Yin Tat Lee, and Zhao Song, In Symposium on Theory of Computing (STOC 2020). ", "Streaming matching (and optimal transport) in \(\tilde{O}(1/\epsilon)\) passes and \(O(n)\) space. /Length 11 0 R 2016. Try again later. [i14] Yair Carmon, Arun Jambulapati, Yujia Jin, Yin Tat Lee, Daogao Liu, Aaron Sidford, Kevin Tian: ReSQueing Parallel and Private Stochastic Convex Optimization. I am an assistant professor in the department of Management Science and Engineering and the department of Computer Science at Stanford University. IEEE, 147-156. I am generally interested in algorithms and learning theory, particularly developing algorithms for machine learning with provable guarantees. aaron sidford cvis sea bass a bony fish to eat. AISTATS, 2021. Student Intranet. Faculty Spotlight: Aaron Sidford - Management Science and Engineering ReSQueing Parallel and Private Stochastic Convex Optimization. One research focus are dynamic algorithms (i.e. Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, Sushant Sachdeva, Online Edge Coloring via Tree Recurrences and Correlation Decay, STOC 2022 [pdf] [talk] [poster] Roy Frostig - Stanford University We are excited to have Professor Sidford join the Management Science & Engineering faculty starting Fall 2016. With Cameron Musco, Praneeth Netrapalli, Aaron Sidford, Shashanka Ubaru, and David P. Woodruff. [pdf] I am broadly interested in mathematics and theoretical computer science. We organize regular talks and if you are interested and are Stanford affiliated, feel free to reach out (from a Stanford email). This site uses cookies from Google to deliver its services and to analyze traffic. MS&E welcomes new faculty member, Aaron Sidford ! with Yair Carmon, Arun Jambulapati, Qijia Jiang, Yin Tat Lee, Aaron Sidford and Kevin Tian We provide a generic technique for constructing families of submodular functions to obtain lower bounds for submodular function minimization (SFM). In Symposium on Foundations of Computer Science (FOCS 2020) Invited to the special issue ( arXiv) Deeparnab Chakrabarty, Andrei Graur, Haotian Jiang, Aaron Sidford. Assistant Professor of Management Science and Engineering and of Computer Science. I am a senior researcher in the Algorithms group at Microsoft Research Redmond.