Tue, 18 Feb 2025
14:00
14:00
C4
Temporal graph reproduction with RWIG
Piet Van Mieghem
(Delft University of Technology)
Abstract
Our Random Walkers Induced temporal Graphs (RWIG) model generates temporal graph sequences based on M independent, random walkers that traverse an underlying graph as a function of time. Co-location of walkers at a given node and time defines an individual-level contact. RWIG is shown to be a realistic model for temporal human contact graphs.
A key idea is that a random walk on a Markov graph executes the Markov process. Each of the M walkers traverses the same set of nodes (= states in the Markov graph), but with own transition probabilities (in discrete time) or rates (in continuous time). Hence, the Markov transition probability matrix Pj reflects the policy of motion of walker wj. RWIG is analytically feasible: we derive closed form solutions for the probability distribution of contact graphs.
Usually, human mobility networks are inferred through measurements of timeseries of contacts between individuals. We also discuss this “inverse RWIG problem”, which aims to determine the parameters in RWIG (i.e. the set of probability transfer matrices P1, P2, ..., PM and the initial probability state vectors s1[0], ...,sM[0] of walkers w1,w2, ...,wM in discrete time), given a timeseries of contact graphs.
This talk is based on the article:
Almasan, A.-D., Shvydun, S., Scholtes, I. and P. Van Mieghem, 2025, "Generating Temporal Contact Graphs Using Random Walkers", IEEE Transactions on Network Science and Engineering, to appear.
Want a quick flavour of who we are and what we do?
Our YouTube shorts are, unsurprisingly, short films featuring Oxford Mathematicians talking about, among other things, their research, their toys and their toothpaste. And there are also clips from our popular public lectures to whet the appetite for the full thing.
Tue, 11 Feb 2025
16:00
16:00
Derivative moments of CUE characteristic polynomials and the Riemann zeta function
Nick Simm
(University of Sussex)
Abstract
I will discuss recent work on the derivative of the characteristic polynomial from the Circular Unitary Ensemble. The main focus is on the calculation of moments with values of the spectral parameter z inside the unit disc. We investigate three asymptotic regimes depending on the distance of z to the unit circle, as the size of the matrices tends to infinity. I will also discuss some corresponding results for the derivative of the Riemann zeta function. This is joint work with Fei Wei (Sussex).
Mon, 24 Feb 2025
16:30
16:30
L4
Stability of positive radial steady states for the parabolic Henon-Lane-Emden system
Paschalis Karageorgis
(Trinity College Dublin)
Abstract
When it comes to the nonlinear heat equation u_t - \Delta u = u^p, a sharp condition for the stability of positive radial steady states was derived in the classical paper by Gui, Ni and Wang. In this talk, I will present some recent joint work with Daniel Devine that focuses on a more general system of reaction-diffusion equations (which is also also known as the parabolic Henon-Lane-Emden system). We obtain a sharp condition that determines the stability of positive radial steady states, and we also study the separation property of these solutions along with their asymptotic behaviour at infinity.
Wednesday 12th March.
It would be great to have as many teams as possible racing in this idyllic 4-leg relay around Oxford, encompassing the River Thames and Christ Church Meadow and beginning and ending at Iffley Road track where Roger Bannister ran the first ever sub-4-minute mile. Each leg is approximately 7km in length. Further details can be found on the Facebook event page.