**WINTER 2018 SCHEDULE**

**This seminar is held on Mondays at 4:30-5:20 PM in Building 300, Room 300**(unless otherwise noted).

**January 8: NO SEMINAR**

**January 15: NO SEMINAR (HOLIDAY)**

**January 22: Eileen Martin, ICME PhD student**

Title: Subsurface imaging from random vibrations recorded by fiber optic networks

Abstract: By recording controlled vibration sources on a seismic sensor array, we can estimate images of the speed of sound in the subsurface. Such experiments are expensive to conduct and logistically difficult in populated areas, so time-lapse experiments showing changes in the underlying material model are rarely done. I combine two methods to make continuous subsurface monitoring significantly cheaper: estimating wave equation Green's functions from random vibration recordings in the area of interest, and measuring vibrations as meter-scale strain rate profiles along fiber optic cables (which may already exist in urban areas or can easily be installed along infrastructure).

These methods can make continuous high-resolution subsurface imaging a possibility where it was previously impossible, but there are several computational and mathematical challenges I will address: (i) algorithms must be modified for real-time analysis of streaming data from many sensors, (ii) the theory for Green's function estimation must be altered to account for new sensors measuring tensor strain rates as opposed to particle velocity vectors or pressure scalars, and (iii) existing Green's function estimation theory assumes independent, uncorrelated vibration sources (which is far from the reality of urban and infrastructure noise sources). These issues will be shown in the context of two data sets: a buried fiber array near a road in Alaska for monitoring permafrost thaw, and a fiber network in existing telecom conduits under the Stanford campus for earthquake hazard analysis. The fundamental issues behind working with noisy, streaming data for imaging and inverse problems are common to a wide range of science and engineering problems.

**January 29: Zeyu Zheng, Management Science & Engineering, Stanford**

Title: Top-Down Statistical Modeling

Abstract: In this talk, we will argue that data-driven service systems engineering should take a statistical perspective that is guided by the decisions and performance measures that are critical from a managerial perspective. We further take the view that the statistical models will often be used as inputs to simulations that will be used to drive either capacity decisions or real-time decisions (such as dynamic staffing levels). We start by discussing Poisson arrival modeling in the context of systems in which time-of-day effects play a significant role. We will discuss several new statistical tools that we have developed that significantly improve the quality of the performance predictions made by the simulation models. In the second part of our talk, we show that in dealing with high-intensity arrival streams (such as in the call center context), the key statistical features of the arrivals that must be captured for good performance prediction lie at much longer time scales than the inter-arrival times that are the usual focus of conventional statistical analysis for such problems. This observation is consistent with the extensive limit theory available for many-server systems. Our “top-down” approach focuses on data collected at these longer time scales, and on building statistical models that capture the key data features at this scale. In particular, we will discuss the use of Poisson auto-regressive processes as a basic tool in such “top-down” modeling, and on the statistical framework we are creating to build effective simulation-based decision tools based on real-world data.

**February 5: Cindy Orozco, ICME PhD student**

Title: Tensor Networks: Developing An Algebra

Abstract: What if a function with exponential number of values can be defined using only a linear number of parameters? In statistical physics, many particle interaction problems can be represented as basic tensor operations, in such a way that the total storage is not exponential but linear in the number of particles. This compression framework, called Tensor Networks, also provides a graphical representation of the operations, making simpler the tracking of tensor subscripts. Nevertheless in this context there is not a trivial strategy to reuse the compressed form of functions to derive new ones. In this talk, we will construct an algebra of some basic structures, called Tensor Rings, such that we can preserve the compressed form once we apply a nice function. Assuming that most of the audience is not familiar with this framework, we will give a brief introduction to Tensor Network language and we will present the practical steps needed to make such definition computationally feasible.

**February 12:**

**Katerina Velcheva, Department of Mathematics**

Title: Mean Field Learning Models

Abstract: We will discuss a model economy with infinitely many agents, each with a different knowledge about producing a given good. Agents choose how to divide their time between producing goods and interacting with others in search of new knowledge. These choices jointly determine the economy’s production level and its rate of learning and real growth. Each agent aims to maximize a given value function that depends on his productivity at any given time. This optimization gives rise to a backward in time Hamilton-Jacobi-Bellman equation. The evolution of knowledge over time is determined by a forward Kolmogorov equation for the distribution function of knowledge. An equilibrium solution of the model is a pair of functions, solving the HJB and the Kolmogorov equations. We will look at traveling wave solutions of the system and we will discuss their importance. We will write explicit traveling wave solutions for a simplified version of the model. We will also talk about more general existence and uniqueness results for traveling wave solutions.

**February 19: NO SEMINAR (HOLIDAY)**

**February 26:**TBA

**March 5:**TBA

**March 12:**TBA