Online workshop: Optimal transport, topological data analysis and applications to shape and machine learning

Dear all,

We wanted to bring to your attention an upcoming workshop — July 27 to
July 31 — on applied topology, optimal transport and machine learning.
These are rapidly-developing verticals with budding interactions that
some of you might find interesting. The workshop will be entirely
online, and hosted through MBI-Ohio State. More information on events,
schedule and how to register can be found here:

https://mbi.osu.edu/events/optimal-transport-topological-data-analysis-and-applications-shape-and-machine-learning

Hope to see you there.

Jose Perea
Facundo Memoli
Tom Needham
Nicolas Garcia-Trillos

TDA at JSM

 ( https://ww2.amstat.org/meetings/jsm/2020/onlineprogram/ActivityDetails.cfm?SessionID=219282 )

Time: Thursday, August, 6th, 2020, 10:00 AM – 11:50 AM Eastern Daylight Time (EDT)

Place: Virtual Joint Statistical Meeting 2020 (https://ww2.amstat.org/meetings/jsm/2020/index.cfm).

Organizer(s): Chul Moon, chulm@smu.edu, Southern Methodist University

Chair(s): Hengrui Luo, luo.619@osu.edu, The Ohio State University

10:05 AM         Solution manifold and Its Statistical Applications

Speaker. Yen-Chi Chen, University of Washington

Abstract. A solution manifold is the collection of points in a d-dimensional space satisfying a system of s equations with s<d. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families, constrained mixture models, partial identifications, and nonparametric set estimation. We analyze solution manifolds both theoretically and algorithmically. In terms of theory, we derive five useful results: the smoothness theorem, the stability theorem (which implies the consistency of a plug-in estimator), the convergence of a gradient flow, the local center manifold theorem and the convergence of the gradient descent algorithm. To numerically approximate a solution manifold, we propose a Monte Carlo gradient descent algorithm. In the case of likelihood inference, we design a manifold constraint maximization procedure to find the maximum likelihood estimator on the manifold. We also develop a method to approximate a posterior distribution defined on a solution manifold.

10:25 AM         Persistent Topological Descriptors for Functional Brain Network

Speaker. Hyunnam Ryu, University of Georgia; Nicole Lazar, University of Georgia

Abstract. We compare the topological features of functional brain networks. In general, functional brain networks are dealt with in an elementwise manner based on the connectivity matrix as part of network data analysis. This tends to ignore the higher-order topology of the network, which can have significant implications. In recent studies, researchers have been interested in topological data analysis. Persistent homology is known to be useful for studying dynamic topological invariants hidden in complex data obtained from topological space. Analysis using persistent homology not only captures topological features that could be overlooked in the network data analysis but also addresses threshold selection problems commonly found in network data analysis.

We use persistent homology to compare the topological features of brain networks. We construct a brain network from the fMRI time series BOLD signal and calculate the persistent homology through the weighted brain network. Also, we compare the summarized topological features of different subject groups by calculating the persistence landscape.

10:45 AM         Uncovering the Holes in the Universe with Topological Data Analysis

Speaker. Jessi Cisewski-Kehe, Yale University

Abstract. The large-scale structure (LSS) of the Universe is a spatially complex web of matter that is difficult to analyze without losing potentially important information, but can help to constrain the underlying cosmological model that describes the Universe. Topological Data Analysis (TDA) is especially suitable for such weblike data and we have used this framework to visualize, define, and do inference on known (i.e., voids) and new (i.e., filament loops) cosmological structures. 

During this talk, I will discuss how TDA can be used to uncover cosmological structures.  The features on a persistence diagram represent homology group generators (connected components, loops, voids, etc.), which are not uniquely defined back in the dataset. However, having a way to visualize the generators in the dataset can be useful to better understand the data and to possibly determine the physical meaning of the structure. This led to a new procedure called “Significant Cosmic Holes in Universe” (SCHU) for defining representations of homology group generators in a cosmological survey, such as the Sloan Digital Sky Survey galaxy survey.  Cosmological voids correspond to the second homology group generators, and we also define a new class of voids based on the first homology group generators, which we call filament loops.

Persistence diagrams can also be used in hypothesis tests in order to make statistical comparisons between complicated spatial structures such as LSS.  I will present some developments using a two-sample hypothesis testing framework to distinguish LSS under different cosmological assumptions (e.g., cold dark matter vs. warm dark matter).

11:05 AM         Confidence Band for Persistent Homology

Speaker. Jisu Kim, INRIA

Abstract. Topological Data Analysis generally refers to utilizing topological features from data. For this talk, I will focus on persistent homology, which quantifies the salient topological features of data. I will present how the confidence band can be computed for determining the significance of the topological features in the persistent homology, based on the bootstrap procedure. First, I will present how the confidence band can be computed for the persistent homology of KDEs (kernel density estimators) computed on a grid. In practice, however, calculating the persistent homology of KDEs on d-dimensional Euclidean spaces requires to approximate the ambient space to a grid, which could be computationally inefficient when the dimension of the ambient space is high or topological features are in different scales. Hence, I will consider the persistent homology of KDE filtrations on Rips complexes as an alternative. I will describe how to construct an asymptotic confidence set for the persistent homology based on the bootstrap procedure. Unlike existing procedures, this method does not heavily rely on grid-approximations, scales to higher dimensions, and is adaptive to heterogeneous topological features.

11:25 AM         Discussant: Chul Moon, Southern Methodist University

11:45 AM         Floor Discussion and Follow-ups

Everyone is welcomed to register for Joint Statistical Meeting (JSM) to join our virtual session!

Young Topologists Meeting, KTH, Stockholm

We are pleased to announce that next year’s Young Topologists Meeting will take place between 12-16 July 2021 in Stockholm, jointly organized by the KTH Royal Institute of Technology and Stockholm University.

The intention of the conference is to create a setting in which young researchers in topology can meet each other and share their work. The program will consist of short talks given by the participants and three lecture series by invited speakers. This meeting serves as a replacement for the YTM 2020, which had to be cancelled because of the ongoing COVID-19 pandemic. In particular the invited speakers are the same ones that were invited for this year’s edition: Kathryn Hess (EPFL), Thomas Nikolaus (WWU Münster) and Karen Vogtmann (Cornell University and University of Warwick).

More information will be available soon on the conference website https://sites.google.com/view/ytm2021. We plan to open the registration mid-December.

If you have any questions, please do not hesitate to contact the organizers at youngtopologistsmeeting@gmail.com.

We look forward to seeing you in Stockholm!

Kind regards,
The organizers

Thomas Blom
Tobias Grøsfjeld
Louis Hainaut
Alvin Jin
Erik Lindell
Robin Stoll
Francesca Tombari

Fields Institute: TDA Workshop and Clay Lectures online

As part of the Fields thematic program on Toric Topology and Polyhedral Products there will be two sets of Clay Lectures by 

Gunnar Carlsson on 15 and 17 June 

Shmuel Weinberger on 16 and 18 June 

and an associated Workshop on Topological Data Analysis from 15-18 June. 

All events are online. For more information and to register, please go to 

http://www.fields.utoronto.ca/activities/19-20/toric-TDA

Registration is free and all are welcome. 

Best regards from the organizers: 

Peter Bubenik 
Vidit Nanda 
Don Stanley 
Stephen Theriault 

CfP Topology in Real-World Machine Learning and Data Analysis

Kathryn Hess, Frédéric Chazal and Umberto Lupo are curating an Article Collection published in Frontiers in Artificial Intelligence and entitled “Topology in Real-World Machine Learning and Data Analysis” (webpage). Its core mission is to promote the use of topological ideas and techniques as mainstream tools in data science.
We welcome contribution(s) to our Article Collection. Papers can be original research, reviews, or perspectives, among other article types. Deadlines are as follows:

  • 17 August 2020 – Abstracts (soft deadline);
  • 14 December 2020 – Manuscripts.

Upon publications, papers will be free to read for everyone.
There are processing charges associated to publishing with Frontiers in AI, but waivers can be applied for if your institution or grant does not cover Open Access fees.
Please get in touch if you would like to learn more about scope, deadlines, and publishing fees. Alternatively, you can sign up for participation directly from the Collection’s webpage.
Best wishes,Umberto, Kathryn, Frédéric

Probabilistic and Topological methods for Biological Data (June 11, 2020)

Dr. Veronica Ciocanel and Dr. Wasiur KhudaBuksh are organising a virtual mini-symposium on “Probabilistic and Topological Methods for Biological Data” as part of the SIAM conference on Mathematics of Data Science 2020. More information below. 

Time: June 11, 2020 1-3pm EST (topology session) and 3-5pm EST (probability session)

Registration: Registration is free (and would take less than 30 seconds), but limited to 300 people. Link here:

wasiur.github.io/MDS2020/mds2020.html

Speakers in the topology session:
1. Francis Motta, Florida Atlantic University
2. Marilyn Vazquez, the Ohio State University
3. Veronica Ciocanel, the Ohio State University
4. Manuchehr Aminian, Colorado State University

Speakers in the probability session:
1. Wasiur KhudaBukhsh, the Ohio State University 
2. Arindam Fadikar, Argonne National Lab
3. Pragya Sur, Harvard University
4. Yuekai Sun, University of Michigan

The talks will cover many different application areas ranging from microscopic cell biology to macroscopic epidemiology using tools from topology and probability theory.

Please register as soon as possible. 

SIAM Mini-Symposium on Topological Image Analysis

Aras Asaad writes:

I’m organizing a virtual mini-symposium titled ‘Topological Image Analysis’, which is part of  SIAM2020 conference of Mathematics of Data Science.

To sign up for our online mini-symposium: Click at this site to get ZOOM details and a short description about this event: https://docs.google.com/forms/d/e/1FAIpQLSef7aJKpIKktF-mto1m1RAvd-ULJxIK2-uXsfqNCT3mu48M-Q/viewform

See attached, the flyer of the symposium for Date, Time, program schedule and speaker info’s.
Titles and Abstract of Talks can be found here:Session One: https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=68044 Session Two: https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=68045

Subset of ATMCS talks hosted online by AATRN

Unfortunately, the ATMCS (Algebraic Topology: Methods, Computation, and Science) conference will not be happening in 2020. However, a subset of early-career ATMCS talks will be hosted in an online summer seminar series by AATRN (Applied Algebraic Topology Research Network). These talks were contributed and accepted for ATMCS, but this is not going to be ATMCS itself.

For a list of these ATMCS talks hosted by AATRN, please see our webpage:
https://tgda.osu.edu/atmcs2020/atmcs-2020-talks-hosted-by-the-aatn/
The majority of the talks will be on Mondays at 11am-12pm Eastern Times, starting Monday, May 25. We will have two speakers per week, with each speaker giving a 20 minute talk. The first speakers (on Monday, May 25) are Vincent Divol and Théo Lacombe, on Studying the space of Persistence Diagrams using Optimal Partial Transport.

If you want to attend these talks, then please become an AATRN member by clicking on the “members” tab at https://topology.ima.umn.edu/. We will send out one announcement email to all AATRN members per talk, including information for how to join the talk on Zoom. You will receive an email with the Zoom details for our first May 25 talk either later today, or within a day after you first join the network. If you have any difficulties joining or obtaining the Zoom details (or for example want the Zoom details for the first talk before becoming an AATRN member), then please send an email to aatrn.director@gmail.com.

Best,
Henry Adams and Sara Kalisnik, AATRN
Ulrich Bauer and Claudia Landi, ATMCS

TDA Postdoc at the Dioscuri Center, Warsaw

https://www.impan.pl/wydarzenia/konkursy/2020/postdoctoral-position-dioscuri.pdf

The Dioscuri Center is a new research center for Topological Data Analysis, to start in July 2020 and led by Dr Pawel Dlotko.

The Dioscuri Center is seeking a postdoctoral researcher for a fixed-term 24-month position to work on developing mathematically rigorous geometry and topology based shape descriptors to solve important applied problems.

Application deadline: June 30, 2020

TDA Postdoc at Oxford

https://www.maths.ox.ac.uk/node/36016

We invite applications for a Postdoctoral Research Associate in Topological Data Analysis to work with Professors Heather Harrington and Ulrike Tillmann here at the Mathematical Institute, University of Oxford. The position is fixed-term for 30 months (2.5 years), and the successful candidate will become a member of the Centre for Topological Data Analysis at Oxford.

The postholder will be responsible for conducting research in applied topology, including topological data analysis, as well as techniques within computational topology aimed at bridging levels of organisation within molecular biology. You will be expected to contribute ideas for new research projects, write up the results of your research for publication, and provide guidance to junior members of the research group including project students, PhD students, and/or project volunteers.

Applicants will be expected to have, or be close to completing, a PhD in computational mathematics, topology or applied algebra. You will possess sufficient specialist knowledge to work within the research interests of the Centre for Topological Data Analysis, alongside the ability to manage your own research and administrative activities. Previous experience of computational mathematics and/or computer programming is desirable.

https://my.corehr.com/pls/uoxrecruit/erq_jobspec_details_form.jobspec?p_id=146092

Applicants will be selected for interview based on their ability to satisfy the selection criteria as outlined in the job description document below. You will be required to upload a letter setting out how you meet the selection criteria, a curriculum vitae including full list of publications, a statement of research interests and the contact details of two referees as part of your online application (NOTE: Applicants are responsible for contacting their referees and making sure that their letters are received by the closing date).

Only applications received before 12.00 noon on Wednesday 17 June 2020 can be considered. Interviews are anticipated to take place week commencing Monday 29 June 2020.