### Speaker: Laurent Demanet, Professor in the Department of Mathematics, Imaging and Computing Group, MIT

**1930s analysis for 2010s signal processing: recent progress on the superresolution question**

4:15pm to 5:30pm

The ability to access signal features below the diffraction limit of an imaging system is a delicate and nonlinear phenomenon called superresolution. The main theoretical question in this area is still mostly open: it concerns the precise balance of noise, bandwidth, and signal structure that enables super-resolved recovery. When structure is understood as sparsity on a grid, we show that there is a precise scaling law that extends Shannon-Nyquist theory, and which governs the asymptotic performance of a class of simple "subspace-based" algorithms. This law is universal in the minimax sense that no statistical estimator can outperform it significantly. Compressed sensing, by contrast, is in many cases suboptimal for the same task. Joint work with Nam Nguyen.

8:30am to 4:30pm

This year, Bay Area Scientific Computing Day will be at Stanford University on Saturday, December 13, 2014.

An annual one-day meeting focused on fostering interactions and collaborations between researchers in the fields of scientific computing and computational science and engineering from the San Francisco Bay Area, BASCD provides junior researchers a venue to present their work to the local community and an opportunity for the Bay Area scientific and computational science and engineering communities at large to interchange views on today’s multidisciplinary computational challenges and state-of-the-art developments.

If you are interested in speaking at the event, please send an abstract and the title of your presentation to Michael Minion: mlminion@stanford.edu by November 20.

Register if you will attend

Before Friday, December 5th at http://bascd2014.rsvpify.com/

Schedule

Schedule is available here: https://icme.stanford.edu/system/files/file-insertions/Agenda_3.pdf

Location, Maps, and Parking

BASCD will take place on the Stanford campus in the Jen-Hsun Huang Engineering Center in the Science and Engineering Quad.

3rd floor, room 300 (the Mackenzie Board Room)

Information about visiting the Stanford campus: http://visit.stanford.edu/

Information on visitor parking: http://transportation.stanford.edu/parking_info/VisitorParking.shtml (parking is generally free of charge on Saturday; check posted signs)

4:00pm to 5:00pm

Speakers: Michael Minion and Margot Gerritsen

ICME will be celebrating our annual holiday party on Friday, December 5th at 2:00p.m. Join us in the ICME main lobby for an afternoon of food, drinks, and good conversation.

4:15pm to 5:30pm

**Communication-avoiding Krylov subspace methods in finite precision**

Communication-avoiding (s-step) Krylov subspace methods can achieve an O(s) reduction in data movement over classical Krylov subspace methods for a fixed number of iterations, allowing the potential for significant speedups on modern computers. However, although the s-step variants are equivalent to the classical variants in exact arithmetic, empirical observations demonstrate that they can behave quite differently in finite precision. Increased roundoff errors can manifest as a loss of accuracy and/or deterioration of convergence rate relative to the classical method, reducing the potential performance benefits of the s-step approach.

We present our work in developing efficient techniques for mitigating the loss of convergence and accuracy in s-step Krylov methods without sacrificing performance gains, including residual replacement, reorthogonalization, and preconditioning. We also summarize our recent work, which extends the bounds on accuracy for the finite precision classical Lanczos method given by Paige [Lin. Alg. Appl., 34:235--258, 1980] to the s-step Lanczos method. Our results indicate that if one can guarantee that the condition numbers of the precomputed Krylov bases

are not too large in any iteration, then the finite precision behavior of the s-step Lanczos method will be similar to that of the classical method. We conclude with some ideas about how these new bounds can be applied to improve the finite precision behavior of the s-step Lanczos method while still achieving an asymptotic reduction in communication.

4:15pm to 5:30pm

12:15pm to 1:15pm

Jack Poulson is a Simon’s Math+X Assistant Professor in the Department of Mathematics at Stanford University. His research tends to focus on distributed-memory algorithms and software for modern numerical algorithms, with concentrations on direct linear algebra and optimization and algebra on/with structured matrices.

4:00pm to 5:00pm

Speaker: Margot Gerritsen

4:15pm to 5:30pm

**Ceres Solver**

Ceres Solver (http://ceres-solver.org) is an open source C++ library for modeling and solving nonlinear least squares problems. It is used at Google to estimate the pose of Street View cars, aircraft, and satellites; to build 3D models for PhotoTours; stitch panoramic images on your cellphone, and more. Outside Google, its uses include movie special effects, computer vision, computer graphics, robot navigation, and semi-conductor physics.

I will describe the architecture of Ceres Solver, what goes into engineering a high performance and portable optimization library, and some of the lessons learned from observing people use it over the past four years.

Thursday, November 20, 2014 - 8:00am to Friday, November 21, 2014 - 12:00pm

Antony Jameson, Professor of Aeronautics and Astronautics at Stanford, will be celebrating his 80th birthday this year. In honor of his 80th birthday, the Boeing Company will be hosting a Symposium from November 20-21, 2014 with a Dinner & Social on the evening on November 20th. Support and additional sponsorship will be provided by the Institute for Computational and Mathematical Engineering.

Please click here for additional information as well register for the events.

4:15pm to 5:30pm

12:15pm to 1:15pm

George Papanicolaou is a Professor in the Department of Mathematics at Stanford University. In the past, George Papanicolaou has been interested in waves and diffusion in inhomogeneous or random media and in the mathematical analysis of multi-scale phenomena that arise in their study. Applications come from electromagnetic wave propagation in the atmosphere, underwater sound, waves in the lithosphere, diffusion in porous media, etc. He has studied both linear and nonlinear waves and diffusion, in both direct and inverse problems. He is now working on assessing multiple scattering effects in imaging and communication systems, including time reversal arrays. Another recent interest is financial mathematics, the use of asymptotics for stochastic equations in analyzing complex models of financial markets and in data analysis.

Emmanuel Candes is a Professor of Statistics and Mathematics at Stanford University. His research interests include compressive sensing, mathematical signal processing, computational harmonic analysis, multiscale analysis, scientific computing, statistical estimation and detection, high-dimensional statistics; applications to the imaging sciences and inverse problems. Other topics of recent interest include theoretical computer science, mathematical optimization, and information theory.

4:15pm to 5:15pm

Eileen Martin

Optimizing memory traffic in pf3D laster-plasma simulations

4:00pm to 5:00pm

Speaker: Margot Gerritsen

Here are the PDFs from this TGIF:

Tips for Talks

4:15pm to 5:30pm

The capabilities in Mathematica 10 and other Wolfram technologies that are applicable for teaching and research on campus.

4:15pm to 5:30pm

**Operationalizing Financial Covenants**

We study the interplay between financial covenants and the operational decisions of a firm that obtains financing through a secured (asset-based) lending contract. While it is widely held that covenants serve to protect lenders, the specific ways in which a borrowing firm can adapt its operations in response have not been studied. We characterize the product market conditions, involving demand distribution, growth potential, profit margin, and product depreciation rate, under which covenants are necessary, and argue that these are routinely met in practice. Furthermore, we show that covenants are not substitutable by other contractual terms, such as interest rates and loan limits, and provide operational insights for their optimal design. We discuss when covenants ensure that system-optimal decisions are taken in equilibrium, and show that operational flexibility can impact their effectiveness in a surprising, non-monotonic way.

12:15pm to 1:15pm

Michael Minion is a Consulting Professor in the Institute for Computational and Mathematical Engineering. Michael's research interests are in scientific computing with an emphasis on novel algorithms for problems in fluid dynamics.

4:15pm to 5:15pm

Akshay Mittal

An efficient non-intrusive uncertainty propagation method for stochastic multi-physics models.

Multi-physics systems are mathematically represented as coupled partial differential equation (PDE) systems, which are naturally suited for module-based (partitioned) numerical solution methods. While modularization is well established for solving deterministic PDE systems, several challenges arise in extending the framework to uncertainty propagation i.e. solving stochastic PDE systems. Monte-Carlo-based methods are blind to the module-based structure of the solver and in general, they require millions of expensive PDE solves to yield accurate statistics. Moreover, although standard (traditional) implementations of spectral methods can be modularized, they can easily succumb to the curse of dimension (COD), since the coupled nature of the model dictates that each module should handle the global (combined) stochastic space for uncertainty propagation.

Therefore, we present a reduced non-intrusive spectral projection (NISP) method for uncertainty propagation which addresses the COD and facilitates a reuse of deterministic solver modules. Our method is a modification of the standard NISP method with the intermediate construction of reduced dimensional (and order) approximations of the input data entering each respective module. Assuming a generalized polynomial chaos (gPC) approximation of the raw input data, the construction methods are based on straightforward linear algebraic computations, the costs of which are negligible in comparison to repeated module calls. We implement the reduced NISP method on some benchmark problems and demonstrate its performance gains over the standard NISP method.

Han Wang

Benevolent vs malicious high frequency trading

Recent publications such as "Flash Boys" by Micheal Lewis has stirred up controversy regarding low latency algorithmic trading. However, recent attention has focused solely on a single subtype of algorithm, latency based front running. This talk will discuss the general types of high frequency trading algorithms and their contributions or detraction to a free and efficient market.

Thursday, November 6, 2014 - 9:00am to Saturday, November 8, 2014 - 11:00am

ICME hosts the first-ever Xtend event this autumn!

This will be a unique opportunity for alumni, students, faculty, and industry partners to network, discuss current trends in our fields, and attend several workshops and short courses.

- Industry networking and recruiting
- Demo of our new HIVE: https://icme.stanford.edu/computer-resources/hive
- Lectures from faculty and industry
- Short courses
- Group dinner
- Industry-Alumni mixer

Thursday, November 6, 2014

- 9:00- 11:00am: Industry Networking
- 11:00- 5:00pm: Meetings with Industry Partners (Note: student registration will take place in early October)
- 12:00-2:00pm: Box lunches available for Industry Partners
- 5:00- 6:30pm: Happy Hour @ ICME- HIVE Demonstrations, Networking, and Welcome
- casual dinners may be organized

Friday, November 7, 2014: Huang Engineering Center, Mackenzie Room

- 9:00am: Breakfast/Registration
- 9:15- 9:30am: Welcome and Introduction
- 9:30- 10:30am: Big Math in Academia: ICME Faculty Panel with Stephen Boyd, Ramesh Johari, and Jack Poulson
- 10:45- 11:45am: Big Math in Industry: Industry Panel with Esteban Arcaute, @Walmart Labs; Brad Betts, Blackrock; Anand Saminathan, Infosys; and Lori Sherer, Bain
- 12:00- 1:00pm: Lunch
- 1:00- 1:45pm: Keynote Speaker- Persis S. Drell, Dean of the Stanford School of Engineering
- 2:00- 5:00pm: Short Courses

- Reza Zadeh teaching "Intro to distributed computing, using the high-speed cluster programming framework, Spark"
- Paul Constantine teaching "Essential Concepts in Uncertainty Quantification"
- Dave Deriso teaching "Data Visualization"

- 5:00- 8:30pm: ICME Happy Hour and Dinner
- 6:00- 7:00pm: "Blues by 5" Performance

Saturday, November 8

- 9:30- 11:00am: Farewell brunch for ICME/SCCM/ FinMath alumni

As always, ICME appreciates the financial generosity of our Alumni which supports our ongoing teaching and research mission.

We look forward to welcoming you back to the Farm!

Questions? Contact us at icme-contact@stanford.edu or 650-724-3313.

Xtend Keynote by **Persis S. Drell, Dean of the Stanford School of Engineering**

Persis S. Drell is the Frederick Emmons Terman Dean of the Stanford School of Engineering, the James and Anna Marie Spilker Professor in the School of Engineering and a professor of Materials Science and Engineering and Physics at Stanford University. She received her B.A. in mathematics and physics from Wellesley College in 1977. She received her Ph.D. in atomic physics from the University of California, Berkeley, in 1983. She then switched to high-energy experimental physics and worked as a postdoctoral scientist with Lawrence Berkeley National Laboratory. She joined the faculty of the Physics Department at Cornell University in 1988. In 2000, she became head of the Cornell high-energy group; in 2001, she was named deputy director of Cornell's Laboratory of Nuclear Studies. In 2002, Dr. Drell accepted a position as Professor and Associate Director, Research Division at SLAC. She was the Deputy Project Manager for the Fermi Gamma Ray Space Telescope 2004-2005. In 2007 she was named Director at SLAC. She stepped down from the SLAC Directorship in 2012. Her current research activities are in Particle Astrophysics and Free Electron Laser science.

Dr. Drell has been the recipient of a Guggenheim Fellowship; a National Science Foundation Presidential Young Investigator Award; she is a fellow of the American Physical Society; a member of the American Academy of Arts and Sciences; and a member of the National Academy of Sciences. In 2012 she was the recipient of the 2012 Helmholtz International Fellow Award for outstanding scientific achievement.

4:15pm to 5:30pm

12:15pm to 1:15pm

Anders Petersson is a Consulting Professor in the Institute for Computational and Mathematical Engineering. His research interests lie in area of grid generation and numerical solution of partial differential equations. Anders earned his Ph.D. in Numerical Analysis from the Royal Institute of Technology in 1991. He joined the Lawrence Livermore Laboratory in 1999.

4:15pm to 5:15pm

Matthew Zahr

Acceleration of PDE-Constrained Optimization Problems using Progressively-Constructed Reduced-Order Models

Optimization problems constrained by nonlinear Partial Differential Equations (PDE) arise in many engineering fields and contexts including inverse modeling, control, and shape optimization. An inherent difficulty in solving PDE-constrained optimization problems is that the solution of the PDE is required at many parameter configurations. For practical problems defined by a complicated geometry and complex physics, each PDE solution will require significant computational resources, rendering the optimization problem prohibitively expensive.

In this talk, I will present a methodology for accelerating the solution of PDE-constrained optimization problems using projection-based Reduced-Order Models (ROM). The key feature of the proposed approach is construction of the ROM occurs incrementally during the optimization process. The proposed methodology will be applied to a variety of PDE-constrained optimization problems, including aerodynamic shape optimization, structural topology optimization, and nozzle design.

Ryan Lewis

Introduction to applied topology and some recent work.

We will give a brief overview of the emerging field of applied topology, in particular, and ordinary persistent homology. We will focus on definitions and examples, and the basic algorithms. Time permitting we will mention some work on deriving correct parallel algorithms, there implementations, and experimental results. For those interested in Numerical Linear Algebra, the theory of persistence generalizes standard numerical linear algebra to the module setting.

4:00pm to 5:00pm

Speaker: Margot Gerritsen

4:15pm to 5:30pm

As High-Performance Computing systems approach Exascale the feature sizes of their circuits will shrink, while their overall size will grow, all at a fixed power budget. As transistors are packed more tightly and hold less charge, they are expected to grow more vulnerable to a range of faults that corrupt the computations of the logic circuits built from them. These faults manifest themselves as errors in hardware computations, which can propagate to cause applications to crash, or worse---to silently return incorrect results. While it is possible to make hardware more reliable in a way that is transparent to application software, such techniques are expensive, requiring all computations to be repeated multiple times, or circuits

to be built from more reliable transistors. This motivates the development of algorithms that are naturally resilient to hardware errors.

This talk will survey work on algorithmic resilience techniques for linear algebra computations. It will cover techniques for basic operations such as matrix multiplication and factorization, as well as iterative linear solvers. Finally,Greg Bronevetsky will point out the wide range of algorithms for which no checkers are known, and various open research opportunities in the field of resilient algorithms, resilience-aware

programming models, and approximate computing in general.

4:15pm to 5:30pm

12:15pm to 1:15pm

Adrian Lew is an Associate Professor in Mechanical Engineering at Stanford University. Prof. Lew's interests lie in the broad area of computational solid mechanics. He is concerned with the fundamental design and mathematical analysis of material models and numerical algorithms.

4:15pm to 5:15pm

Madeleine Udell

Generalized Low Rank Models

Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. In this talk, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features.

Sven Schmit

Learning Multifractal Structure in Large Networks

Using random graphs to model networks has a rich history. In this talk, we analyze and improve the multifractal network generators (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. We leverage this theory to propose a new method of moments algorithm for fitting MFNG to large networks. Empirically, this new approach effectively simulates properties of several social and information networks. In terms of matching subgraph counts, our method outperforms similar algorithms used with the Stochastic Kronecker Graph model. Furthermore, we present a fast approximation algorithm to generate graph instances following the multifractal structure. Combined, our method of moments and fast sampling scheme provide the first scalable framework for effectively modeling large networks with MFNG.

4:00pm to 5:00pm

Speakers: Michael Minion

4:15pm to 5:30pm

4:15pm to 5:30pm

**Inventing the Future of Money**

Throughout history technology has played a transformational role in how people relate to and use money. We are living in another time of great transformation as money moves from atoms to bits. But many other factors beyond technology will separate the winners from the losers. James Patterson, head of Capital One Labs, the experimental product and technology arm of Capital One, will share his experiences on reimagining the future of money.

12:15pm to 1:15pm

Mykel Kochenderfer is an Assistant Professor in the Department of Aeronautics and Astronautics at Stanford University. Prior to joining the faculty, he was a member of the technical staff at Lincoln Laboratory for seven years where he worked on aircraft collision avoidance for manned and unmanned aircraft. He holds a Ph.D. from the University of Edinburgh and B.S. and M.S. degrees from Stanford. He has worked for Microsoft Research, the Honda Research Institute, and Rockwell Scientific. He is a third generation pilot.

4:15pm to 5:15pm

Austin Benson

A Framework for Practical Parallel Fast Matrix Multiplication

In this work, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and Strassen's fast algorithm on modest problem sizes and shapes. Furthermore, we show that the best choice of fast algorithm depends not only on the size of the matrices but also the shape. We develop a code generation tool to automatically implement multiple sequential and shared-memory parallel variants of each fast algorithm, and this allows us to rapidly benchmark over 20 fast algorithms. We will discuss practical implementation issues for these algorithms on shared-memory machines that can direct further research on making fast algorithms practical.

Anil Damle

Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix

Given a set of Kohn-Sham orbitals from an insulating system, we present a direct method to construct a localized basis for the associated subspace. We construct the basis via the use of a set of selected columns of the density matrix (SCDM) coupled with an optional orthogonalization procedure. Our method is simple, robust, does not depend on any adjustable parameters, and may be used in any code for electronic structure calculations. We demonstrate the benefits of such a localized basis by using the SCDM to efficiently perform Hartree-Fock exchange energy calculations with near linear scaling.

4:00pm to 5:00pm

Speaker: Jennifer Schwartz from the Center for Teaching and Learning

4:15pm to 5:30pm

**Design Optimization and the Consider-Then-Choose Behavioral Model**

Recent research in engineering design and operations adopts discrete choice models to maximize profits (or revenues). Conventional discrete choice models are mainly predictive, instead of descriptive, in that they only intend to predict choices rather than describe the processes underlying choice. The consider-then-choose model describes a two-stage decision-making process in which consumers first eliminate a large number of product alternatives with heuristic screening rules, then perform careful tradeoff evaluation over the remaining alternatives.

Consideration, also called choice set formation, is an empirically validated choice behavior that has been shown to greatly improve model quality. From the perspective of firm strategy, modeling consideration introduces discontinuous choice probabilities to optimal design problems, as changes in product features or prices can change individuals' choice sets. We introduce consider-then-choose models, review research suggesting their importance for use in design, and compare several treatments of the discontinuous optimal design problem. We use a stylized new vehicle portfolio design example throughout.

4:15pm to 5:30pm

We will see how mathematical tools from the optimal stochastic control theory allow to compute the indifference utility or the super-hedging price of a claim in an incomplete market. In particular, we will focus on the impact of portfolio contraints, such as short sell prohibition, in multidimensional local volatility models. In the one dimensional case, we will observe that super-hedging a claim simply boils down to the replication of a proper ‘facelift’ transform of the claim. We will also provide alternatives to very costly super-hedging prices, by computing quantile hedging prices in a dynamically consistent manner.

9:00am to 4:00pm

Brought to you by NVIDIA and ICME (a NVIDA CUDA Center of Excellence), each year we get together in the Huang Engineering Center for a morning full of

tech talks and an afternoon with GPU computing labs.

This year we have an amazing list of Stanford & SLAC faculty and researchers talking about how GPUs computing is an enabler to new frontiers in Machine Learning, Computer Vision, Astronomy, Medicine.

**What is the event: ** Tech Talks & Hands on GPU Labs in GPU Computing, Machine Learning and Computer Vision

**Who is it for:** Undergraduate, graduate students, postdocs, researchers, and professors.

Tech Talks – 9AM to Noon

Research Symposium where you will hear from fellow researchers on tools, research discoveries, best practices and trends using GPU computing for computational research.

- Keynote: Bill Dally, Chief Scientist and Senior Vice President of NVIDIA Research
- GPU Tech Talks – Presented by Stanford Faculty and Researchers

GPU Computing Hands-on Labs – 1PM to 4PM

GPU Computing workshop with hands-on exercises in GPU Computing where you will learn how to program GPUs via the use of libraries, OpenACC compiler directives, and CUDA programming.

- Track 1 – Intro to GPU Computing Lab
- OR
- Track 2 – Machine Learning & Computer Vision Lab

https://www.eventbrite.com/e/stanford-nvidia-tech-talks-hands-on-labs-ti...

Bill Dally is chief scientist at NVIDIA and senior vice president of NVIDIA Research, the company’s world-class research organization, which is chartered with developing the strategic technologies that will help drive the company’s future growth and success. Dally first joined NVIDIA in 2009 after spending 12 years at Stanford University, where he was chairman of the computer science department and the Willard R. and Inez Kerr Bell Professor of Engineering. Dally and his Stanford team developed the system architecture, network architecture, signaling, routing and synchronization technology that is found in most large parallel computers today. He is a member of the National Academy of Engineering, a Fellow of the American Academy of Arts & Sciences, a Fellow of the IEEE and the ACM. He received the 2010 Eckert-Mauchly Award, considered the highest prize in computer architecture, as well as the 2004 IEEE Computer Society Seymour Cray Computer Engineering Award and the 2000 ACM Maurice Wilkes Award.

*Coffee & Lunch will be provided. **Please bring a laptop for remote access to GPU Cluster – no gpu required in your laptop.*

12:15pm to 1:15pm

Margot Gerritsen and Marco Thiele on Numerical Methods for Reservoir Modeling

Nicola Castelleto is a Postdoctoral Research Fellow in the Department ol Energy Resources Engineering. His research interests concern the physics of fluid flow and deformation in porous media.

Hamdi Tchelepi is a Professor in the Department of Energy Resources Engineering. He is interested in modeling flow and transport in natural porous media. Application areas include reservoir simulation and subsurface CO2 sequestration.

Margot Gerritsen, Professor in the Department of Energy Resources Engineering and the Director of the Institute for Computational and Mathematical Engineering. She is interested in computer simulation and mathematical analysis of engineering processes.

Marco Thiele is a Consulting Associate Professor in the Department of Energy Resources Engineering. In the summer of 2014, Marco Thiele embarked on a new project in thermal EOR for heavy oil along with Margot Gerritsen and Tony Kovscek.

4:15pm to 5:15pm

Brian Jo

Direct volume rendering for deformable models

We present a system for interactive direct volume rendering of voxel grid data under deformations defined on an underlying tetrahedral mesh. The need for such a system often arises in medical simulation, where the voxel grid may contain radiodensities from a CT scan, and a finite element model deforms an underlying tetrahedral mesh. The fundamental idea of our algorithm is to first map rays in the deformed space of the object to the undeformed space before casting them through the voxel grid. This preliminary step allows us to avoid having to either resample the voxel data each time step or update any kind of underlying acceleration structure. We also introduce a spatial acceleration structure tailored for tetrahedral meshes that uses a combination of octrees and variance-based binary search partitions (BSPs), as well as a texture encoding scheme to upload this structure to a shader.

Christopher Fougner

Scaling Convex Optimization with GPUs

Convex optimization is prevalent in fields such as machine learning, finance, automatic control, and signal processing. To cope with large data sets and real-time processing requirements, it is necessary to use computing architectures and algorithms that scale. By harnessing the power of GPUs, in conjunction with operator splitting methods, we have been able to solve convex optimization problems orders of magnitude faster than traditional solvers. In this presentation we discuss why GPU architectures are ideally suited to convex optimization. Our main contributions are a first of its kind open source CUDA based solver for general convex optimization problems, as well as improved heuristics for choosing parameters in operator splitting methods. Link: foges.github.io/pogs

4:00pm to 5:00pm

Speakers: Graduate Students and Faculty

4:15pm to 5:30pm

It is well known that in K-user constant single-antenna interference channels K/2 degrees of freedom (DoF) can be achieved for almost all channel matrices. It is also known that almost all channel matrices admit K/2 DoF, but explicit conditions available guaranteeing K/2 DoF are satisfied only on a set of Lebesgue measure zero. We close this gap by identifying explicit conditions for K/2 DoF, which are satisfied for Lebesgue almost all channel matrices. We also provide a construction of corresponding asymptotically DoF-optimal input distributions. The main technical tool used is a recent breakthrough result by Hochman in fractal geometry. We conclude by discussing connections between interference alignment and additive combinatorics.

**NOTE: This seminar will be held with the Information Systems Laboratory (ISL) Colloquium**

4:15pm to 5:30pm

We show that liquidity risk is priced in the cross section of returns on credit default swaps (CDSs). Liquidity risk is defined as covariation between CDS returns and a liquidity factor that captures innovations to CDS market liquidity. Market-wide CDS illiquidity is measured by aggregating deviations of credit index levels from their no-arbitrage values implied by the index constituents’ CDS spreads, and the liquidity factor is the return on a diversified portfolio of index arbitrage strategies. Liquidity risk increases CDS spreads and the expected excess returns earned by sellers of credit protection. Our benchmark model implies that liquidity risk accounts for approximately 20% of CDS spreads, on average.

12:15pm to 1:15pm

Lexing Ying is a Professor in the Department of Mathematics and Institute for Computational and Mathematical Engineering at Stanford University. Professor Ying's research focuses on developing fast and accurate numerical algorithms for problems in acoustics and electromagnetics, computational seismology, computational material sciences, and transport theory.

Ramesh Johari is an Associate Professor at Stanford University and the Cisco Faculty Scholar in the School of Engineering, with a full-time appointment in the Department of Management Science and Engineering (MS&E), and courtesy appointments in the Departments of Computer Science (CS) and Electrical Engineering (EE). Professor Johari is interested in the design and management of large-scale complex networks, such as the Internet. Using tools from operations research, engineering, and economics, he has developed models to analyze efficient market mechanisms for resource allocation in networks.

4:15pm to 5:15pm

Victor Minder

A numerical method for solving Maxwell's equations in free-space using an approzimate IVP Green's function

Two popular classes of methods for solving wave equations such as the free-space Maxwell's equations are finite-difference time-domain (FDTD) schemes and pseudo-spectral schemes. The former typically suffer from restrictive CFL conditions on the size of the time-step for stability but are easily parallelizable, whereas the latter do not face stability restrictions but require a change of basis (i.e., fft) at each step that limits parallelizability. We introduce a scheme for Maxwell's equations in free-space that uses a regularized approximation to the initial-value problem Green's function to allow for little restriction on the time step for stability while maintaining parallelization potential.

Yuekai Sun

A one-shot approach to distributed sparse regression

We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The main idea is to estimate the regression coefficients by averaging corrected lasso estimates. We show the approach recovers the convergence rate of the lasso as long as the number of machines does not grow too quickly.

4:00pm to 5:00pm

Speaker: Helen Doyle from VPGE

4:15pm to 5:30pm

**Mathematical Programming Methods for Large-scale Structural Topology Optimization**

Structural topology optimization is a relatively new but rapidly expanding field because of its interesting theoretical implications in mathematics, mechanics, and computer science, and its important practical applications in the manufacturing and aerospace industries.

Topology optimization determines the optimal distribution of material in a prescribed design domain. The domain is often discretized by finite elements, with the variables representing the density of each element. A common example is maximizing the stiffness of the structure while satisfying a volume constraint and equilibrium equations [2].

While a variety of large-scale nonlinear solvers could be applied, structural topology optimization problems are usually solved by sequential convex approximation methods such as the Method of Moving Asymptotes (MMA) [1]. This method was specially designed for use within optimal design and is now extensively used in commercial optimal design software as well as academic research codes. However, it is a first-order method with slow convergence rates.

A large set of test problems has now been gathered, along with extensive results for different solvers. Performance profiles compare the special-purpose first-order methods with some general-purpose solvers such as FMINCON, IPOPT, and SNOPT, confirming that the use of second-order information leads to better designs more efficiently than the classical structural optimization solvers.

Given the performance profiles, a sequential quadratic programming method SQP+ has been developed based on the algorithm explained in [3].Two phases, an inequality and an equality phase, are combined to produce faster convergence. Both phases use second-order information and problem-specific characteristics to improve the efficiency of the solver.

[1] K. Svanberg.* The method of moving asymptotes: A new method for structural optimization.* International J. for Numerical Methods in Engineering, 24:2, 359-373, 1987.

[2] M.P. Bendsoe and O. Sigmund. *Topology Optimization: Theory, Methods and Applications*, Springer, 2003.

[3] J.L. Morales, J. Nocedal, and Y. Wu.* A sequential quadratic programming algorithm with an additional equality constrained phase*, J. of Numerical Analysis, 32:2, 553-579, 2010.

4:15pm to 5:30pm

The US Mortgage Market, at $10 trillion in size, represents one of the largest components in The Fixed Income Market. Since the financial crisis, US government corporation (Ginnie Mae) and Government-Sponsored Enterprises (Fannie Mae and Freddie Mac) continue to support much of the US mortgage lending, while private lending channels contract dramatically. As a result, Agency Mortgage Backed Security (MBS) market share increased to over 90% of the total mortgage market. There have been many policy changes and several proposals aiming to wind down GSEs, though the financial industry assigns little odds to any concrete steps in the near future.

One way to re-privatize US mortgage market is through risk transfer deals (STACR and CAS). The newly devised quarterly deals package part of the credit risk of GSE mortgage loans into tranches with various grading profiles. In addition to transferring away the credit risk from GSE to private market, these deals also enable market pricing of the fair guarantee cost of GSE-backed mortgage loans. Morgan Stanley is an active participant in Agency risk transfer deals, having led or co-managed 4 out of 5 so far and is hired to lead future deals.

4:15pm to 5:30pm

4:15pm to 5:15pm

Ernest Ryu

Monte Carlo and Convex Optimization: Importance sampling and Stochastic Optimization

Importance sampling is one of the most widely used variance reduction technique used to speed up Monte Carlo simulations. Roughly speaking, the idea is to sample from an alternative importance distribution that over-weights the important region. However, the basic idea of importance sampling does not specify how to choose this importance distribution, and a poor choice will even worsen the estimate. In this talk, we will introduce an adaptive importance sampling based on stochastic optimization. The method will adaptively improve the importance distribution while simultaneously accumulating the Monte Carlo estimate. We will provide theoretical bounds on the method’s performance and discuss in what sense the method is optimal.

Jason Lee

Exact Statistical Inference after Model Selection

We develop a framework for statistical inference after model selection, via lasso or marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response y, conditional on the model being selected (``condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix X. Furthermore, the computational cost of the algorithm is negligible compared to the cost of lasso. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit, non-negative least squares, and marginal screening+Lasso. This is joint work with Dennis Sun, Yuekai Sun, and Jonathan Taylor.

4:00pm to 5:00pm

Speakers: Graduate Student Panel