Bath Numerical Analysis seminar - upcoming

Fridays at 12.15 at Wolfson 4W 1.7. All talks will be broadcast on Zoom.

Link to Zoom meeting

Everyone is welcome at these talks.

Date Speaker Title
3 Oct 2025 Xinle Tian (University of Bath)
Large multi-response linear regression estimation based on low-rank pre-smoothing

Pre-smoothing is a technique aimed at increasing the signal-to-noise ratio in data to improve subsequent estimation and model selection in regression problems. Motivated by the many scientific applications in which multi-response regression problems arise, particularly when the number of responses is large, we propose here to extend pre-smoothing methods to the multiple outcome setting. Specifically, we introduce and study a simple technique for pre-smoothing based on low-rank approximation. We establish theoretical results on the performance of the proposed methodology, which show that in the large-response setting, the proposed technique outperforms ordinary least squares estimation with the mean squared error criterion, whilst being computationally more efficient than alternative approaches such as reduced rank regression. We quantify our estimator’s benefit empirically in a number of simulated experiments. We also demonstrate our proposed low-rank pre-smoothing technique on real data arising from the environmental and biological sciences.
3 Oct 2025 James Martin (University of Bath)
Percolation and localisation: Sub-leading eigenvalues of the nonbacktracking matrix

Network percolation is a well-studied random process that investigates the long-range connectivity properties of a network. The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties. Indeed, the inverse of its leading eigenvalue is often used as an estimate for the percolation threshold. However, for many networks where nonbacktracking centrality is localised on a few nodes, such as networks with a core-periphery structure, this spectral approach badly underestimates the threshold. We study networks that exhibit this localisation effect by looking beyond the leading eigenvalue and searching deeper into the spectrum of the nonbacktracking matrix. We identify that, when localisation is present, the threshold often more closely aligns with the inverse of one of the sub-leading real eigenvalues: the largest real eigenvalue with a “delocalised” corresponding eigenvector. We discuss some intuition behind this observation and present experimental results on large scale real-world networks that showcase the usefulness of our approach.
10 Oct 2025 Caitlin O'Hara (University of Bath)
TBC
10 Oct 2025 Viraj Patel (University of Bath)
Intraventricular flow reconstruction and graph-based representations

Ultrasound imaging is a widely used technique for assessing cardiovascular health and diagnosing various heart conditions. There is good data to suggest that blood flow is sensitive to disease and may provide valuable insights into the efficiency of cardiac pumping and overall circulation. As a result, the blood velocity field within the heart chambers may be a critical parameter in evaluating cardiac function, so accurate measurements could potentially lead to new diagnostic or prognostic metrics for heart failure. However, accurately measuring blood velocity using ultrasound remains challenging due to inherent limitations like noise and the complex nature of blood flow dynamics, in conjunction with flaws in current velocimetry techniques. The left ventricle is particularly important as its primary function is to provide sufficient cardiac output to maintain blood flow to other organ systems in the body. As the left ventricle fills up with blood, the difference between the inlet width and the ventricle width causes a vortex to form, called the left ventricular vortex (LVV). The literature suggests that the vortex formation time and the geometry of the LVV are connected to heart failure and diastolic function. The deviations of expected dynamics of the LVV has been attributed to structural and functional deformities in the heart walls and myocardium (left ventricular muscle). Much of the work in this field have relied on simulations and experiments with models of the left ventricle, while this work has used data collected from a real heart under controlled conditions. Thus far, I have developed an ellipse-fit method to quantify the size and orientation of the LVV in real-time. I aim to extend this work to find unique representations of intraventricular flow fields that can discern different flow conditions. In this talk, I will present an idea that uses Gabriel graphs to form a latent representation of flow fields in the heart.
17 Oct 2025 Thomas Coxon (Loughborough University)
From 1/√n to 1/n: Accelerating SDE Simulation with Cubature Formulae (part 1)

Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but its error decays only as 1/√n, requiring huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian driving paths with “cubature formulae”, deterministic weighted sets of paths that match Brownian “signature moments” up to some degree D. They prove that cubature formulae exist for arbitrary D, but explicit constructions are difficult and have only reached D=7, too small for practical use. We present an algorithm that efficiently and automatically constructs cubature formulae of arbitrary degree, reproducing D=7 in seconds and reaching D=17 within hours on modest hardware. In simulations across multiple SDEs, our cubature formulae achieve an error roughly of order 1/n, orders of magnitude smaller than Monte Carlo with the same number of paths.
17 Oct 2025 Peter Koepernik (University of Oxford)
From 1/√n to 1/n: Accelerating SDE Simulation with Cubature Formulae (part 2)

Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but its error decays only as 1/√n, requiring huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian driving paths with “cubature formulae”, deterministic weighted sets of paths that match Brownian “signature moments” up to some degree D. They prove that cubature formulae exist for arbitrary D, but explicit constructions are difficult and have only reached D=7, too small for practical use. We present an algorithm that efficiently and automatically constructs cubature formulae of arbitrary degree, reproducing D=7 in seconds and reaching D=17 within hours on modest hardware. In simulations across multiple SDEs, our cubature formulae achieve an error roughly of order 1/n, orders of magnitude smaller than Monte Carlo with the same number of paths.
24 Oct 2025 Cangxiong Chen (University of Bath)
TBC
24 Oct 2025 Ahmed Rashwan (University of Bath)
TBC
31 Oct 2025 Sam Power (University of Bristol)
TBC
7 Nov 2025 Robert Johnson (University of Bath)
TBC
7 Nov 2025 Joanna Ni (University of Bath)
TBC
14 Nov 2025 Zhengang Zhong (University of Warwick)
TBC
21 Nov 2025 Alain Zemkoho (University of Southampton)
TBC
28 Nov 2025 David Wörgötter (TU Wien)
TBC
5 Dec 2025

MMath students
Year-Long Projects
12 Dec 2025 Sean Holman (University of Manchester)
TBC
Subscribe to seminar calendar

You can subscribe to the NA calendar directly from your calendar client, including Outlook, Apple’s iCalendar or Google calendar. The web address of the calendar is this ICS link which you will need to copy.

To subscribe to a calendar in Outlook:

  1. In Calendar view, select “Add Calendar” (large green +)
  2. Select “From Internet”
  3. Copy paste the ICS link, click OK, and click Yes to subscribe.

To subscribe to a calendar in iCalendar, please follow these instructions. Copy paste the ICS link in “web address”.

To subscribe to a calendar in Google Calendar:

  1. Go to link.
  2. On the left side go to "Other Calendars" and click on the dropdown.
  3. Choose "Add by URL".
  4. Copy paste the ICS link in the URL of the calendar.
  5. Click on "Add Calendar" and wait for Google to import your events. This creates a calendar with a somewhat unreadable name.
  6. To give a readable name to the calendar, click on the three vertical dots sign next to the newly created calendar and select Settings.
  7. Choose a name for the calendar, eg. Numerical Analysis @ Bath, and click back button on top left.

How to get to Bath See here for instructions how to get to Bath. Please email James Foster (jmf68@bath.ac.uk) if you intend to come by car and require a parking permit for Bath University Campus for the day.
Tips for giving talks

Tips for new students on giving talks

Since the audience of the NA seminar contains both PhD students and staff with quite wide interests and backgrounds, the following are some guidelines/hints to make sure people don't give you evil looks at lunch afterwards.

Before too much time passes in your talk, ideally the audience should know the answers to the following 4 questions:

  • What is the problem you're considering?
  • Why do you find this interesting?
  • What has been done before on this problem/what's the background?
  • What is your approach/what are you going to talk about?

There are lots of different ways to communicate this information. One way, if you're doing a slide show, could be for the first 4 slides to cover these 4 questions; although in this case you may want to revisit these points later on in the talk (e.g. to give more detail).

Remember:

  • "vertebrate style" (structure hidden inside - like the skeleton of a vertebrate) = good for detective stories, bad for maths talks.
  • "crustacean style" (structure visible from outside - like the skeleton of a crustacean) = bad for detective stories, good for maths talks.