# Archive 2020

**December 7, 2020**: Elena Pulvirenti

When: Monday, December 7, 16:00

Where: Zoom via link https://tudelft.zoom.us/j/98337663674

*Metastability for the dilute Curie-Weiss model with Glauber dynamics*

We analyse the metastable behaviour of the dilute Curie–Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are replaced by i.i.d. random coefficients, e.g. Bernoulli random variables with fixed parameter p. This model can be also viewed as an Ising model on the Erdos–Renyi random graph with edge probability p. The system is a Markov chain where spins flip according to a Metropolis dynamics at inverse temperature \beta. We compute the average time the system takes to reach the stable phase when it starts from a certain probability distribution on the metastable

state (called the last-exit biased distribution), in the regime where the

system size goes to infinity, the inverse temperature is larger than 1 and the magnetic field is positive and small enough. We obtain asymptotic bounds on the probability of the event that the mean metastable hitting time is approximated by that of the Curie–Weiss model. The proof uses the potential theoretic approach to metastability and concentration of measure inequalities. This is a joint work with Anton Bovier and Saeda Marello.

**November 23, 2020**: Hanne Kekkonen

When: Monday, November 23, 16:00

Where: Zoom via link https://tudelft.zoom.us/j/98337663674

*Frequentist consistency of Bayesian inversion*

Inverse problems arise from the need to gain information about an unknown object of interest from given indirect noisy measurements. The Bayesian approach to inverse problems has been particularly popular in application areas as it does not only deliver an estimator for the unknown parameter but simultaneously provides uncertainty quantification. We will show that the resulting posterior based parameter inferences are statistically optimal from an objective, information theoretic and asymptotic minimax point of view for linear inverse problems, where the data is corrupted by additive Gaussian noise. We will also discuss some results for certain nonlinear inverse problems.

**November 9, 2020**: Fernando de Oliveira Filho

When: Monday, November 9, 16:00

Where: Zoom via link https://tudelft.zoom.us/j/98337663674

*What is semidefinite programming and why you should care*

Perhaps the most powerful tool in the optimization toolbox is semidefinite programming: the ability to optimize over the entries of positive semidefinite matrices. Not only can semidefinite programs be solved efficiently in theory and practice, but many problems in combinatorics, geometry, quantum information theory etc. can be modeled as semidefinite programs.

In this talk I will give an overview of semidefinite programming, its theory and applications, guided by a few iconic examples. No prior knowledge of optimization theory will be required to follow the talk.

**October 26, 2020**: Kate Saunders (Cancelled)

When: Monday, October 26, 16:00

Where:

**October 12, 2020**: Stefan Grosskinsky

When: Monday, October 12, 16:00

Where: Zoom via link https://tudelft.zoom.us/j/98337663674

*Rare event simulation for stochastic dynamics in continuous time*

Dynamic rare events of time-additive observables in Markov processes such as empirical currents have attracted recent research interest. They can be cast in terms of Feynman-Kac semigroups generated by a tilted version of the generator of the process. So-called McKean interpretations of those semigroups lead to non-linear Markov processes, which are numerically accessible by Monte Carlo sampling via particle approximations, i.e. ensembles of processes evolving in parallel subject to a mean-field selection interaction. We discuss several choices of McKean models and particle approximations, including cloning algorithms which are used in the theoretical physics literature, and provide a mathematical framework for comparison based on the martingale characterization of (Feller) Markov processes. We adapt results from the sequential Monte Carlo literature on convergence rates and asymptotic variances of such algorithms, and illustrate those for stochastic lattice gases such as zero-range or inclusion processes.

This is joint work with Letizia Angeli, Adam Johansen and Andrea Pizzoferrato.

**June 15, 2020**: Luca Avena (Leiden University)

When: Monday, June 15, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F

**May 25, 2020**: Julian Karch (Leiden University)

When: Monday, May 25, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

*Improving on Adjusted R-squared*

The amount of variance explained is widely reported for quantifying the model fit of a multiple linear regression model. The default adjusted R-squared estimator has the disadvantage of not satisfying any theoretical optimality criterion. The Olkin-Pratt estimator, in contrast, is known to be uniformly minimum-variance unbiased. Despite this, the Olkin-Pratt estimator is not being used due to being difficult to compute. In this talk, I present an algorithm for the exact and fast computation of the Olkin-Pratt estimator, which enables using it. I compare the Olkin-Pratt, the adjusted R-squared, and 18 alternative estimators using a simulation study employing different optimality perspectives.

**April 20, 2020**: Phyllis Wan (Erasmus University)

When: Monday, April 20, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

**March 30, 2020**: Alexander Ly (CWI)

When: Monday, March 30, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

**March 16, 2020**: Ivan Kryven (University of Utrecht)

When: Monday, March 16, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

*Random graphs with fixed local constrains*

Random graphs provide theoretical foundation for methods and models in network science. However, a commonly used assumption of vertex degrees being independent and identically distributed is often undesired when random graphs are used for modelling networks. In this talk we consider a generalised random graph with a fixed multivariate degree distribution that allows edges to be coloured. In such a model the neighbourhood of a single node is described by a random vector counting numbers of coloured edges. We will show that depending on how colours are assigned, such a model can be made to exhibit (long-range) correlations between vertex degrees. Such a feature makes the coloured random graph attractive to modellers. Among interesting applications we will discuss percolation in clustered and degree-degree correlated networks and history-dependent network growth. We will also demonstrate how the size distribution of connected components in such a model can be used to explain and quantify several phenomena in polymer physics and soft matter.

**February 17, 2020**: Alessandro Zocca (VU Amsterdam)

When: Monday, February 17, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

*Rare Events in Stochastic Networks: Theory and Applications to Power Systems*

I will give an overview of my current research, which aims to develop new mathematical tools to analyze complex networks and their performance in the presence of uncertainty. In this talk, I will focus in particular on rare events analysis and large deviations techniques, which in many instances are crucial to correctly assess the network performance and the risk of failures. The main application area for the purpose of this talk will be power systems with high penetration of renewables. More specifically, I will present some novel insights into the interplay between renewable energy sources and power grid reliability: rare stochastic fluctuations of the power injections, amplified by correlations and network effects, can cause failures and possibly blackouts. I will discuss various solutions we devised to mitigate their impact and non-local propagation, using mathematical methods ranging from applied probability to optimization, including new ad-hoc MCMC methods for rare events and novel clustering techniques.

**February 3, 2020**: Christian Hirsch (University of Groningen)

When: Monday, February 3, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

*Testing goodness of fit for point processes and spatial networks via TDA*

Persistent Betti numbers form a key tool in topological data analysis as they track the appearance and disappearance of topological features in a sample. In this talk, we derive a goodness of fit test of point patterns and random networks based on the persistence diagram in large volumes. On the conceptual side, the tests rely on functional central limit theorems for the sub-level filtration in cylindrical networks and for bounded-size features of the Čech-complex of planar point patterns. The proof is based on methods from a recently developed framework for CLTs on point processes with fast decay of correlations.

We analyze the power of tests derived from this statistic on simulated point patterns and apply the tests to a point pattern from an application context in neuroscience.

Based on joint work with Christophe Biscio, Nicolas Chenavier and Anne Marie Svane.

**January 27, 2020**: Probability day

**January 13, 2020**: Katharina Proksch (University of Twente)

When: Monday, January 13, 16:00

Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F.

*Distance-based object matching: Asymptotic statistical inference*

In this talk, we aim to provide a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently computable asymptotic statistical test for pose invariant object discrimination. This is based on an empirical version of a lower bound of the Gromov-Wasserstein distance. We derive distributional limits of this test statistic. To this end, we introduce a novel U-type process and show its weak convergence. This extends known results on U- and U-quantile processes. Finally, the theory developed is investigated in Monte Carlo simulations and applied to structural protein comparisons.