Northeastern University, Department of Mathematics
Organizers: Adam Ding, Ken Duffy, Paul Hand, Eugene Tang, He Wang
*For remote/hybrid meetings, Zoom/Teams link will be sent by email. Contact He Wang at he.wang@northeastern.edu
The seminar features talks in Applied and Interdisciplinary Mathematics (AIM) by our own faculty as well as faculty from other departments at Northeastern and other Universities. For additional information or to be added to the mailing list, please contact He Wang.
Upcoming Talks
| Date: Tuesday, November 5th, 2024 Time: 12:00 pm-1:00 pm Location: EXP-610A Speaker: Mathieu Beau (University of Massachusetts, Boston) Title: A Stochastic Approach to Time-of-Arrival in Quantum Mechanics and its Applications to Free-Falling Systems Abstract: The concept of time in quantum mechanics presents unique challenges, particularly concerning the measurement of time-of-arrival (TOA), which lacks a formal mathematical treatment within the standard quantum theory. In this presentation, we propose a stochastic approach to TOA, employing the Born rule and probabilistic techniques to rigorously derive TOA distributions for both Gaussian and non-Gaussian quantum systems. We begin by addressing the underlying mathematical problem of time in quantum mechanics, focusing on why time cannot be treated as an observable within the conventional framework. We then introduce an experimental protocol for measuring TOA and present a mathematical formulation of TOA using a random variable. A general formula for the TOA distribution is derived, first in the Gaussian case and then extended to more complex non-Gaussian systems. As a case study, we apply this approach to a free-falling quantum particle, demonstrating how quantum corrections introduce a measurable delay in comparison to classical free-fall times. Furthermore, we demonstrate the existence of a novel uncertainty relation between TOA and position measurements, underscoring their mutual exclusiveness. Finally, we explore the broader mathematical implications of these results and extensions to more abstract systems such as spin systems and open quantum systems Bio: Mathieu Beau is a research associate at the University of Massachusetts Boston and a mathematics teacher at the International School of Boston. He earned his Ph.D. in Theoretical and Mathematical Physics from the University of Marseille, France, in 2010. He held postdoctoral positions at the Dublin Institute for Advanced Studies and the University of Massachusetts Boston before transitioning to high school teaching in 2017. While teaching at the high school level, Mathieu Beau has continued to publish articles in international journals on quantum physics and mathematical physics. |
| Date: Tuesday, November 19th, 2024 Time: 3 pm-4 pm Location: EXP-401A Conference Room Speaker: Charles Wiame (MIT) Title: Stochastic Geometry for Wireless Networks: A Tutorial and Overview of Current Trends Abstract: Stochastic Geometry (SG) is a branch of spatial statistics with applications across diverse fields such as communication networks, image processing, material science, and astronomy. In wireless networks, SG uses point processes to model network nodes (such as mobile phones and base stations). These processes capture the randomness in the relative positions of users and base stations in large-scale networks. Using powerful theorems, analytical expressions can be derived to describe the statistical distribution of network performance, taking into account this spatial randomness. The first part of the seminar will introduce the fundamental theorems of SG, a taxonomy of point processes, and key performance metrics. Some results will be illustrated through examples relying on the Poisson point process, the canonical model in SG. The second part of the talk will explore applications and current research topics in SG. These topics will include THz networks, integrated communication and sensing, and non-terrestrial networks. Biography: Charles Wiame earned his M.Sc. degree in electrical engineering from UCLouvain, Belgium, in 2017. As a Ph.D. student under the guidance of Prof. L. Vandendorpe and Prof. C. Oestges at UCLouvain, he successfully obtained his Ph.D. degree in 2023. His doctoral research focused on exploring the trade-offs between coverage and electromagnetic field (EMF) exposure in wireless systems, approached from a stochastic geometry perspective. Simultaneously, Charles served as a teaching assistant and lecturer at both the bachelor and master levels. In 2022, he was visiting researcher in the lab of Prof. Emil Björnson at the Kungliga Tekniska Högskolan (KTH), Stockholm, Sweden, where he studied cell-free massive Multiple Input Multiple Output (MIMO) systems. After receiving a postdoctoral research fellowship from the Belgian American Education Foundation (BAEF), Charles joined the Research Laboratory of Electronics (RLE) at the Massachusetts Institute of Technology (MIT). He currently works in the Reliable Communications and Network Coding (NCRC) group, led by Prof. Muriel Médard. His ongoing research projects are dedicated to improvements in the GRAND decoder for wireless systems. In 2024, Charles was a co-recipient of the Ellersick Best Paper Award at the IEEE Military Communications Conference. |
Past Talks
| Date: Tuesday, April 9, 2024 Time: 10:30am Location: 509/511 Lake Hall Speaker: Ying Zhang (Northeastern University) Title: Understanding the Biased Distribution in Traction Forces in Cooperative Cell Motility Abstract: Streams of migratory Dictyostelium cells are initiated by the formation of tandem pairs of cells connected head to tail to which other cells and subsequently adhere. Interestingly, when cells migrating in tandem pairs the dynamics of the traction forces exhibit two distinct patterns with a significant bias in their occurrences. In about 80% of the time each cell in the migrating tandem pairs generates a contractile traction force dipole, maintaining the traction force signature of the single cell case. In about 20% of the time the two cells fuse into a single contractile traction force dipole. Although previous experimental works suggested linking the pair mechanically, it remains unclear what are the contributing factors that lead to this bias. In this work, we develop a model to explain the emergence of the biased distribution traction forces mechanistically. As the mechanism at the cell-cell junction with the environment in Dictyostelium cells is unknown, we will use both a simplified and a 2D model to reveal the mechanical coupling at the cell-cell junction that gives rise to this bias. Bio: Ying Zhang received the Ph.D. degree in Mathematics from Boston University in May 2020 and is currently a postdoc researcher in the Department of Mathematics at Northeastern University. Ying is interested in modeling, numerical analysis, and simulation of microscopic cellular processes, immune receptor signaling pathways, and applications of immersed boundary methods in red blood cell motion. Her research interests include mathematical biology, PDEs/ODEs, stochastic processes, and numerical solutions to partial differential equations. |
| Date: Tuesday, April 16, 2024 Time: 10:30am Location: 509/511 Lake Hall Speaker: Jiewei Feng (Northeastern University) Title: Fluid Limit of a Distributed Ledger Model with Random Delay Abstract: Blockchain and other decentralized databases, known as distributed ledgers, are designed to store information online where all trusted network members can update the data with transparency. The dynamics of ledger’s development can be mathematically represented by a directed acyclic graph (DAG). In this paper, we study a DAG model which considers batch arrivals and random delay of attachment. We analyze the asymptotic behavior of this model by letting the arrival rate go to infinity and the inter arrival time go to zero. We establish that the number of leaves in the DAG and various random variables characterizing the vertices in the DAG can be approximated by its fluid limit, represented as delayed partial differential equations. Furthermore, we establish the stable state of this fluid limit and validate our findings through simulations. Bio: Jiewei Feng received the Ph.D. degree in Mathematics from Northeastern University, Boston, USA, in 2023. In Spring 2024, he started his current position as a postdoc in the Department of Electrical and Computer Engineering at Northeastern University. His research interests are in stochastic systems, random growth models and communication systems. |
| Date: Tuesday, April 2, 2024 Time: 10:30am Location: 509/511 Lake Hall Speaker: Jie Xu (Northeastern University) Title: Uncertainty Quantification for Parabolic PDEs with Random Domain Abstract: The numerical solution of linear parabolic partial differential equations with random coefficients and domains becomes highly intractable with well-known statistical methods such as Monte Carlo even for a relatively small number of stochastic dimensions. In this talk we analyze the linear parabolic partial differential equation with stochastic domain deformations. In particular, we concentrate on the problem of numerically approximating the statistical moments of a given Quantity of Interest (QoI). The geometry is assumed to be described by a random field. The parabolic problem is remapped to a fixed deterministic domain with random coefficients, and it is shown that the solution admits a complex analytic extension on a well-defined region embedded in the complex hyperplane. This is a non-trivial result since the map from the geometry to the solution is non-linear. The stochastic moments of the QoI are computed by employing a stochastic collocation method in conjunction with an isotropic Smolyak sparse grid. The complex analytic extension of the solution leads to sub-exponential convergence rates as a function to the number of collocation interpolation knots. Numerical experiments confirm the theoretical error estimates. For the numerical examples, this approach is over 10^10 times more efficient than Monte Carlo, making it well suited for handling moderately high dimensional intractable stochastic geometrical problems. This is a joint work with Julio Castrillón-Candás at Boston University. Bio: Jie Xu received the Ph.D. degree in Mathematics from Boston University in May 2022 and is currently a Zelevinsky Postdoctoral Fellow in the Department of Mathematics at Northeastern University. Jie’s research is concentrating on the area of PDE-related problems, especially the application of PDE into Riemannian geometry. |
| Date: Thursday, March 28, 2024 (Note: unusual day and time. Calendar) Time: 1:30-2:30 pm Location: 509/511 Lake Hall Speaker: Vijay Subramanian (University of Michigan) Title: Wireless Video Streaming with Delayed Client-Feedback: A Constrained Decentralized Team View Abstract: We study the optimal control of multiple video streams over a wireless downlink from a base-transceiver-station (BTS)/access point to N end-devices (EDs). The BTS sends video packets to each ED under a joint transmission energy constraint, the EDs choose when to play out the received packets, and the collective goal is to provide a high Quality-of-Experience (QoE) to the clients/end-users. All EDs send feedback about their states and actions to the BTS which reaches it after a fixed deterministic delay. We analyze this team problem with delayed feedback as a cooperative Multi-Agent Constrained Partially Observable Markov Decision Process (MA-C-POMDP). A core result that we will discuss is a recently established strong duality result for MAC-POMDPs. Using this new result the original video-streaming problem is decomposed into N independent unconstrained transmitter-receiver (two-agent) problems—all sharing a Lagrange multiplier (that also needs to be optimized for optimal control). Thereafter, the common information (CI) approach and the formalism of approximate information states (AISs) are used to guide the design of a neural-network based architecture for learning-based multi-agent control in a single un- constrained transmitter-receiver problem. Finally, simulations on a single transmitter-receiver pair with a stylized QoE model are performed to highlight the advantage of delay-aware two-agent coordination over the transmitter choosing both transmission and play-out actions (perceiving the delayed state of the receiver as its current state). This is joint work with Nouman Khan (University of Michigan, Ann Arbor), and Ujwal Dinesha, Subrahmanyam Arunachalam, Dheeraj Narasimha, and Srinivas Shakkottai at TAMU. It is based on two recent papers, one presented at IEEE CDC 2023 and the other accepted at IEEE INFOCOM 2024. Bio: Vijay Subramanian received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, Champaign, IL, USA, in 1999. He worked at Motorola Inc., and at the Hamilton Institute, Maynooth, Ireland, for many years, and also in the EECS Department, Northwestern University, Evanston, IL, USA. In Fall 2014, he started in his current position as an Associate Professor with the EECS Department at the University of Michigan, Ann Arbor. For the academic year 2022-2023, he was an Adjunct Research Associate Professor in CSL and ECE at UIUC, and he continues to hold this position in academic year 2023-2024 as well. His research interests are in stochastic analysis, random graphs, multi-agent systems, and game theory (mechanism and information design) with applications to social, economic and technological networks. |
| Date: Friday, March 22, 2024 (Note: unusual day and time) Time: 2:30-3:30 pm Location: 509/511 Lake Hall Speaker: Sean Meyn (University of Florida) Title: Quasi-Stochastic Approximation: Algorithm Design Principles with Applications to Machine Learning and Optimization. Abstract: Many machine learning and optimization algorithms solve hidden root-finding problems through the magic of stochastic approximation (SA). Unfortunately, these algorithms are slow to converge: the optimal convergence rate for the mean squared error (MSE) is of order O(n⁻¹) at iteration n. Far faster convergence rates are possible by reconsidering the design of exploration signals used in these algorithms. In this lecture the focus is on quasi-stochastic approximation (QSA), in which a multi-dimensional clock process defines exploration. It is found that algorithms can be designed to achieve a MSE convergence rate approaching O(n⁻⁴). Although the framework is entirely deterministic, this new theory leans heavily on concepts from the theory of Markov processes. Most critical is Poisson’s equation to transform the QSA equations into a mean flow with additive “noise” with attractive properties. Existence of solutions to Poisson’s equation is based on Baker’s Theorem from number theory—to the best of our knowledge, this is the first time this theorem has been applied to any topic in engineering! The theory is illustrated with applications to gradient free optimization. Joint research with Caio Lauand, current graduate student at UF. References [1] C. Kalil Lauand and S. Meyn. Approaching quartic convergence rates for quasi-stochastic approximation with application to gradient-free optimization. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 15743–15756. Curran Associates, Inc., 2022. [2] C. K. Lauand and S. Meyn. Quasi-stochastic approximation: Design principles with applications to extremum seeking control. IEEE Control Systems Magazine, 43(5):111–136, Oct 2023. [3] C. K. Lauand and S. Meyn. The curse of memory in stochastic approximation. In Proc. IEEE Conference on Decision and Control, pages 7803–7809, 2023. Extended version. arXiv 2309.02944, 2023 Abstract: Bio: Dr. Sean Meyn received the B.A. degree in mathematics from the University of California, Los Angeles (UCLA), in 1982 and the Ph.D. degree in electrical engineering from McGill University, Canada, in 1987 (with Prof. P. Caines, McGill University). He is now Professor and Robert C. Pittman Eminent Scholar Chair in the Department of Electrical and Computer Engineering at the University of Florida and is director of the Laboratory for Cognition & Control. His academic research interests include theory and applications of decision and control, stochastic processes, and optimization. He has received many awards for his research on these topics. Current funding comes from NSF, ARO and Google research. He is a fellow of the IEEE, holds an Inria International Chair, is a IEEE CSS Distinguished Lecturer, and holds an Inria International Chair for collaborations with colleagues in Paris, France. He has held visiting positions at universities all over the world, including the Indian Institute of Science, Bangalore during 1997-1998 where he was a Fulbright Research Scholar, and sabbatical stays at MIT, Berkeley, Stanford, United Technologies Research Center (UTRC), and Inria Paris. His award-winning 1993 monograph with Richard Tweedie, Markov Chains and Stochastic Stability, has been cited thousands of times in journals from a range of fields. The latest version is published in the Cambridge Mathematical Library. This is a foundation for current research in reinforcement learning. For the past ten years his applied research has focused on engineering, markets, and policy in energy systems. He regularly engages in industry, government, and academic panels on these topics, and hosts an annual workshop at the University of Florida. |
| Date: Wednesday, December 6, 2023 Time: 1:30-2:30 pm Location: 509/511 Lake Hall Speaker: Aditya Gopalan ( UIUC) Title: On an Asymptotic Criterion for Blockchain Design Abstract: The salient feature of blockchains is the use of a stochastic growth process to generalize the notion of consensus in the classical Byzantine Generals Problem. In this talk, we introduce the Asynchronous Composition Model to study a sequence of random graphs growing according to blockchain dynamics. The term “asynchronous” refers to the fact that our updates take the form $X_t =X_{t-1} \cup f( X_{t – \xi_t})$, where $\xi_t$ is random, and $f$ randomly adds a single vertex to the graph. We discuss the limiting behavior of asynchronous composition as time goes to infinity. Our main focus is the one-endedness of the limit random graph, which is a precise statement of the notion that the limit graph “only grows to infinity in one direction.” One-endedness is a key property for ensuring the consensus dynamics in a blockchain. In particular, we establish one-endedness for the Nakamoto rule, the canonical choice in protocols like Bitcoin, and the $f_2$ rule from the Iota protocol, the most non-trivial rule used in a widely adopted blockchain protocol. Bio of the speaker: Aditya Gopalan is a PhD student in the Industrial and Enterprise Systems Engineering Department at the University of Illinois Urbana-Champaign. He is advised by Partha Dey. He is broadly interested in applied probability, with a current methodological focus on point process dynamics, stochastic growth processes, and stochastic recursive sequences with random delays. Some applications of his interest include blockchains, opinion dynamics, first-passage percolation, and queueing. Aditya received his bachelor’s degree from MIT in 2018. This talk is jointly hosted with Northeastern Mathematics Graduate Students Seminar |
| Date: Tuesday, November 28, 2023 Time: 3-4 pm Location: ISEC Room 432 (Northeastern University Interdisciplinary Science and Engineering Complex) Speaker: Thierry Mora (École Normale Supérieure in Paris) Title: Propagating waves of immune-virus coevolution Abstract: Fast-evolving viruses and immune systems play an evolutionary game of cat and mouse. Viruses thrive upon escaping the hosts’ immunity, while the hosts’ immune systems collectively track the virus. I will show how a theory of this process predicts the emergence of solitary propagating waves in antigenic space, and suggests new insights into the evolution of mutability and virulence. I will also discuss some data analysis of virus and antibody repertoires of HIV patients supporting in-host immune-viral co-evolution. Bio of the speaker: Thierry Mora got his PhD from the University of Paris-Saclay on the statistical physics of random optimization problems. During his postdoc in Princeton he got closer to questions related to biology. Since 2010 he has been a permanent researcher at the Ecole normale supérieure in Paris, where he works on a variety of topics from biophysics to neuroscience, collective behaviour, and immunology, applying tools from physics and statistical inference to biological data, and where he teaches as an attached Professor. He is presently a visiting scientist at the University of Chicago. This talk is jointly hosted with faculty from the Center for Theoretical Biological Physics and the Department of Bioengineering. |
| Date: 3-4 pm, Tuesday, April 18, 2023 in 511 Lake and by Teams (Hybrid) Speaker: Kaifeng Bu (Harvard University) Title: Magic from a quantum convolutional approach Abstract: Stabilizer states and Clifford unitaries have played important roles in quantum information and computation, such as quantum error correcting code and measurement-based quantum computation. In this work, I will introduce a convolutional framework to study stabilizer states and channels based on qudits. Moreover, we establish a quantum central limit theorem, based on iterating the convolution of a quantum state, and show this converges to a stabilizer state. This talk is based on the joint work with Weichen Gu, and Arthur Jaffe (arXiv:2302.07841, 2302.08423). |
| Date: 3-4 pm, Thursday, March 30, 2023 in 105 Shillman and by Zoom ( Note unusual day, time, and location) Speaker: Stuart Brorson (Northeastern University) Title: Anomaly Detection using Linear Algebra Abstract: Detecting anomalous events in time series is an important new application for computers. For example, if a problematic squeak or a rumble emitted by an industrial motor could be caught and repaired early, potentially millions of dollars of repair costs may be avoided. I will outline a simple anomaly detection algorithm which uses the Fourier Transform and methods drawn from Linear Algebra. I will demonstrate the algorithm running on a Beaglebone single-board computer and some inexpensive electronics. This talk will be accessible to undergrads and anybody interested in applications of applied math. |