CMSA

Topological and geometrical aspects of spinors in insulating crystals
2022-07-14 09:00 - 10:00 (America/New_York)
Abstract: Introducing internal degrees of freedom in the description of crystalline insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses. Here, we present a semiclassical approach to transport and accumulation of general spinor degrees of freedom in adiabatically driven, weakly inhomogeneous crystals of dimensions one, two and three under external electromagnetic fields. Our approach shows that spatio-temporal modulations of the system induce a spinor current and density that is related to geometrical and topological objects — the spinor-Chern fluxes and numbers — defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates.
The results are available here: https://arxiv.org/abs/2203.14902
Bio: Ioannis Petrides is a postdoctoral fellow at the School of Engineering and Applied Sciences at Harvard University. He received his Ph.D. from the Institute for Theoretical Physics at ETH Zurich. His research focuses on the topological and geometrical aspects of condensed matter systems.

Infants’ sensory-motor cortices undergo microstructural tissue growth coupled with myelination
2022-07-21 09:00 - 10:00
Abstract: The establishment of neural circuitry during early infancy is critical for developing visual, auditory, and motor functions. However, how cortical tissue develops postnatally is largely unknown. By combining T1 relaxation time from quantitative MRI and mean diffusivity (MD) from diffusion MRI, we tracked cortical tissue development in infants across three timepoints (newborn, 3 months, and 6 months). Lower T1 and MD indicate higher microstructural tissue density and more developed cortex. Our data reveal three main findings: First, primary sensory-motor areas (V1: visual, A1: auditory, S1: somatosensory, M1: motor) have lower T1 and MD at birth than higher-level cortical areas. However, all primary areas show significant reductions in T1 and MD in the first six months of life, illustrating profound tissue growth after birth. Second, significant reductions in T1 and MD from newborns to 6-month-olds occur in all visual areas of the ventral and dorsal visual streams. Strikingly, this development was heterogenous across the visual hierarchies: Earlier areas are more developed with denser tissue at birth than higher-order areas, but higher-order areas had faster rates of development. Finally, analysis of transcriptomic gene data that compares gene expression in postnatal vs. prenatal tissue samples showed strong postnatal expression of genes associated with myelination, synaptic signaling, and dendritic processes. Our results indicate that these cellular processes may contribute to profound postnatal tissue growth in sensory cortices observed in our in-vivo measurements. We propose a novel principle of postnatal maturation of sensory systems: development of cortical tissue proceeds in a hierarchical manner, enabling the lower-level areas to develop first to provide scaffolding for higher-order areas, which begin to develop more rapidly following birth to perform complex computations for vision and audition.
This work is published here: https://www.nature.com/articles/s42003-021-02706-w

Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data
2022-07-28 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Interdisciplinary Science Seminar
Speaker: Sumit Sinha, Harvard University
Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)
Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.
Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”. I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.

Recent Advances on Maximum Flows and Minimum-Cost Flows
2022-08-10 09:00 - 10:00 | Virtual
Interdisciplinary Science Seminar

Speaker: Yang P. Liu

Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.
Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning
2022-08-11 09:00 - 10:00 | Hybrid
Interdisciplinary Science Seminar
Speaker: Yue M. Lu, Harvard University
Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning
Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.
Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007. He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

Scalable Dynamic Graph Algorithms
2022-08-18 10:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Interdisciplinary Science Seminar
Speaker: Quanquan Liu, Northwestern University
Title: Scalable Dynamic Graph Algorithms
Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.
Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.
Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).
