Tue 06 Aug 10:00: Numerically Solving Diffusion Control and Queueing Control Problems Based on Neural Networks SSDW02 - Stochastic reflection
Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we develop and illustrate a simulation-based computational method that relies heavily on deep neural network technology. Furthermore, we develop and implement disrete-review polices that effectively solve the pre-limit queueing control problems. To show that nearly optimal solutions are obtainable using those methods, we present computational results for a variety of queueing network examples that have appeared previously in the literature. This talk is based on joint works with Michael Harrison from Stanford university, and Baris Ata from the University of Chicago.
SSDW02 - Stochastic reflection
- Speaker: Nian Si (University of Chicago)
- Tuesday 06 August 2024, 10:00-11:00
- Venue: External.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 11 Jun 14:50: Fluctuations and Structure at Active Interfaces ADIW04 - Anti-Diffusion in Multiphase and Active Flows
The simplest class of active soft matter may be modelled at the particle level by a system of self-propelled Brownian particles (ABPs) and at the hydrodynamic level by the (active) model B+ for the dynamics of a conserved scalar order parameter field. Studies revealed surprising collective behavior, notably phase separation in systems of purely repulsive particles, known as motility induced phase separation (MIPS) [1]. Even for these systems fundamental questions, such as the surface tension [2] and the scaling of interfacial fluctuations [3] were addressed only recently. Early work based on computer simulations of phase separated ABPs in two dimensions (2D) reported an interfacial roughness compatible with equilibrium Edwards-Wilkinson behaviour [4,5] in contrast with results from non-linear field theory that predict the existence of a MIPS universality class (qKPZ) away from the critical region [3]. One suggestion is that the system of ABPs undergoes bubbly phase separation [6,3] for which no theoretical predictions are available. Here we consider phase separation of ABPs on a 2D lattice and perform simulations using rejection-free Kinetic Monte Carlo (KMC) methods [7] to access long length and time scales, over a wide range of parameters: at fixed activity system sizes L = 10 to 6500 (in lattice units) and at fixed L activities from near-critical to deep in the phase separated system (persistence length lp = 50 to 230). We found different regimes: lp/L>1, where w(t) saturates with L, and lp/L MIPS . Finally, near the critical point the auto-correlation function exhibits a fat tail. Clearly, further work is needed (and is underway) to understand the rich behaviour of active interfaces. References
E. Cates and J. Tailleur, Motility-Induced Phase Separation, Annu. Rev. Condens. Matter Phys., 6, 219 (2015). Fausti, E. Tjhung, M. E. Cates, and C. Nardini, Capillary Interfacial Tension in Active Phase Separation, Phys. Rev. Lett., 127, 068001; Erratum Phys. Rev. Lett. 128, 219901 (2021) Besse, G. Fausti, M. E. Cates, B. Delamotte, and C. Nardini, Interface Roughening in Nonequilibrium Phase-Separated Systems, Phys. Rev. Lett., 130, 187102 (2023). Bialké, J. T. Siebert, H. Löwen, and T. Speck, Negative interfacial tension in phase-separated active Brownian particles, Phys. Rev. Lett., 115, 098301 (2015). Patch, D. M. Sussman, D. Yllanes, and M. C. Marchetti, Curvature-dependent tension and tangential flows at the interface of motility-induced phases, Soft Matter, 14, 7435–7445 (2018). Tjhung, C. Nardini, and M. E. Cates, Cluster phases and bubbly phase separation in active fluids: Reversal of the ostwald process, Phys. Rev. X 8 , 031080 (2018). Neta, M. Tasinkevych, M. M. Telo da Gama, C. S. Dias, Wetting of a solid surface by active matter, Soft Matter, 17, 2468-2478 (2021). Surfaces and Interfaces of Soft Active Matter, J. M. Cordeiro, MSc Thesis, University of Lisbon, 2023
ADIW04 - Anti-Diffusion in Multiphase and Active Flows
- Speaker: Margarida Telo da Gama (Universidade de Lisboa)
- Tuesday 11 June 2024, 14:50-15:20
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 15:30: Continuous-time weakly self-avoiding walk on Z has strictly monotone escape speed SSDW01 - Self-interacting processes
Weakly self-avoiding walk is a model of simple random walk paths that penalizes self-intersections. On Z, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS —Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance.
SSDW01 - Self-interacting processes
- Speaker: Yucheng Liu (University of British Columbia)
- Tuesday 09 July 2024, 15:30-16:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 11:45: An Invariance Principle for a Random Walk Among Moving Traps SSDW01 - Self-interacting processes
We consider a random walk among a Poisson cloud of moving traps on Z^d, where the walk is killed at a rate proportional to the number of traps occupying the same position. In dimension d=1, it was previously shown that under the annealed law of the random walk conditioned on survival up to time t,the walk is sub-diffusive. We show that in d>=6 and under diffusive scaling, this annealed law satisfies an invariance principle with a positive diffusion constant if the killing rate is small. Our proof is based on the theory of thermodynamic formalism, where we extend some classic results for Markov shifts with a finite alphabet and a potential of summable variation to the case of an uncountable non-compact alphabet. Based on joint work with S. Athreya and A. Drewitz.
SSDW01 - Self-interacting processes
- Speaker: Rongfeng Sun (National University of Singapore)
- Tuesday 09 July 2024, 11:45-12:45
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Fri 14 Jun 14:50: Extensile-Contractile Phase Separation in Dry and Wet Active Nematic Vertex Models ADIW04 - Anti-Diffusion in Multiphase and Active Flows
Authors: Jan Rozman and Julia M. Yeomans We study a mixture of extensile and contractile cells using a vertex model extended to include active nematic stresses [1]. The two cell populations phase separate over time. While an increase in contractile activity always aids phase separation, sufficiently high extensile activity reduces the extent of sorting. This can be understood by analysing a small contractile droplet in an extensile bulk: Increasing extensile activity results in the droplet being torn apart by the activity of the bulk, whereas greater contractile activity leads to cells “sticking” together, maintaining a connected droplet for longer. We compare these results with a “wet” vertex model in which substrate-vertex friction is replaced by vertex-vertex friction [2] as a proxy for internal dissipation. This significantly changes the dynamics of the vertex model, allowing, e.g., long range velocity correlations and unidirectional flows in a channel due to nematic activity [3]. References
S.-Z. Lin, M. Merkel, and J.-F. Rupprecht, Phys. Rev. Lett. 130, 058202 (2023). S. Tong, R. Sknepnek, and A. Košmrlj, Phys. Rev. Research 5, 013143 (2023). J. Rozman, Chaithanya K. V. S., J. M. Yeomans, and R. Sknepnek, arXiv:2312.11756 (2023).
ADIW04 - Anti-Diffusion in Multiphase and Active Flows
- Speaker: Jan Rozman (University of Oxford)
- Friday 14 June 2024, 14:50-15:20
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Mon 05 Aug 10:00: On convergence to obliquely reflected Brownian motion in the quarter plane SSDW02 - Stochastic reflection
Several approaches have been developed over the years for proving convergence to RBM . In this talk we focus on a setting in which these approaches have not been fruitful. This is the case of an RBM in the quarter plane with constant reflection direction on each of the two faces, where the set of strictly positive combinations of the two reflection directions does not intersect the closed quarter plane. Our results close this gap by proving convergence of a family of diffusively scaled planar Markov processes to such an RBM . This is joint work with Amarjit Budhiraja, UNC .
SSDW02 - Stochastic reflection
- Speaker: Rami Atar (Technion - Israel Institute of Technology)
- Monday 05 August 2024, 10:00-11:00
- Venue: External.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 11 Jul 09:15: Reinforced Galton-Watson processes. SSDW01 - Self-interacting processes
In a reinforced Galton-Watson process with reproduction law $\nu$ and memory parameter $q\in(0,1)$, the number of children of a typical individual either, with probability$q$, repeats that of one of its forebears picked uniformly at random, or, with complementary probability $1-q$, is given by an independent sample from $\nu$. We estimate the average size of the population at a large generation, and in particular, we determine explicitly the Malthusian growth rate in terms of $\nu$ and $q$. Our approach via the analysis of transport equations owes much to works by Flajolet and co-authors. This talk is based on joint works with Bastien Mallein (Toulouse)
SSDW01 - Self-interacting processes
- Speaker: Jean Bertoin (Universität Zürich)
- Thursday 11 July 2024, 09:15-10:15
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 11 Jul 14:30: First passage percolation for random interlacements SSDW01 - Self-interacting processes
In this talk, I will study the probability that there exists a path of large radius which intersects a random walk a sublinear number of times. This question can be reformulated in terms of first passage percolation for the vacant set of random interlacements, and I will also present corresponding results for the interlacement set. The long-range correlations of the model play an important role here, especially in dimension three. There are many applications of this result, for instance for the capacity of random walks, local uniqueness of random interlacements, and critical exponents for the Gaussian free field on the cable system.
SSDW01 - Self-interacting processes
- Speaker: Alexis Prévost (University of Geneva)
- Thursday 11 July 2024, 14:30-15:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 11 Jul 14:00: Height gaps of planar Brownian motion and Brownian loop soup SSDW01 - Self-interacting processes
This talk will be focused on two recent results with Titus Lupu and Wei Qian where we derive height gap properties of certain fields across CLE /SLE loops. The first result below can be heuristically thought of as a limiting case of the second result. Firstly, we show that the occupation measure of planar Brownian motion exhibits a constant height gap of 5/π across its outer boundary. Secondly, we construct a field naturally coupled with a subcritical Brownian loop soup and show that it exhibits a constant height gap across CLE κ loops. This latter result is a generalisation of the celebrated results of Schramm—Sheffield and Miller—Sheffield concerning the height gap of the Gaussian free field across SLE4 /CLE4 curves.
SSDW01 - Self-interacting processes
- Speaker: Antoine Jego (EPFL - Ecole Polytechnique Fédérale de Lausanne)
- Thursday 11 July 2024, 14:00-14:30
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Mon 08 Jul 15:30: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Alexandre Stauffer (King's College London)
- Monday 08 July 2024, 15:30-16:30
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Thu 11 Jul 16:00: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Stanislav Volkov (Lund University)
- Thursday 11 July 2024, 16:00-16:30
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Wed 03 Jul 10:45: On approximate Wiener-Hopf factorization of 2 × 2 matrices WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
We present a novel algorithm for the factorization of triangular polynomial 2×2 matrices. Our algorithm offers flexibility in choosing between ‘exact’ and ‘natural’ pairs of partial indices. Integrated into the general Winer-Hopf factorization algorithm for 2×2 matrices, as described in https://doi.org/10.1098/rspa.2020.0027, the approach offers a versatile method applicable to practical scenarios. Specifically, given a matrix function S, our method enables the construction of a Wiener-Hopf factorization for an approximate matrix with manageable factors, even when the exact factorization of S may involve large factors. These large factors of S are presumed to arise due to inaccuracies in the construction process of S, rendering its exact factorization impractical. The cases where S or its approximation have unstable partial indices are not excluded. Thus, selecting a reasonable factorization of the approximated matrix function S emerges as a natural choice, facilitating an automatic determination of the partial indices, which in turn, could serve as a novel regularization procedure. (Co-Authors: G. Mishuris, I. Spitkovsky)
WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
- Speaker: Lasha Ephremidze (Tbilisi State University)
- Wednesday 03 July 2024, 10:45-11:15
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Fri 26 Apr 11:35: Generative Modelling Under Differential Privacy OFBW65 - Connecting Heavy Tails and Differential Privacy in Machine Learning
OFBW65 - Connecting Heavy Tails and Differential Privacy in Machine Learning
- Speaker: Sahra Ghalebikesabi (Google)
- Friday 26 April 2024, 11:35-12:15
- Venue: External.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Wed 01 May 14:00: Title to be confirmed
Abstract not available
- Speaker: Juliana Marson, University of Manitoba
- Wednesday 01 May 2024, 14:00-15:00
- Venue: BAS Seminar Room 1; zoom.
- Series: British Antarctic Survey - Polar Oceans seminar series; organiser: Dr Birgit Rogalla.
Wed 10 Jul 10:15: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Pierre-Francois Rodriguez (Imperial College London)
- Wednesday 10 July 2024, 10:15-11:15
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Wed 10 Jul 09:15: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Eyal Neuman (Imperial College London)
- Wednesday 10 July 2024, 09:15-10:15
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 16:00: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Dor Elboim (Institute for Advanced Study, Princeton)
- Tuesday 09 July 2024, 16:00-16:30
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 15:30: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Yucheng Liu (University of British Columbia)
- Tuesday 09 July 2024, 15:30-16:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 14:00: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Daniel Kious (University of Bath)
- Tuesday 09 July 2024, 14:00-15:00
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.
Tue 09 Jul 11:45: TBA SSDW01 - Self-interacting processes
SSDW01 - Self-interacting processes
- Speaker: Rongfeng Sun (National University of Singapore)
- Tuesday 09 July 2024, 11:45-12:45
- Venue: Seminar Room 1, Newton Institute.
- Series: Isaac Newton Institute Seminar Series; organiser: nobody.