Rare, low-probability events often lead to the biggest impacts. Therefore, the development of statistical approaches for modeling, predicting and quantifying environmental risks associated with natural hazards is of utmost importance. In this seminar, I will show how statistical deep-learning methods can help solve challenges that arise when modeling complex and massive spatiotemporal extremes data.

Given the complex nature of brain signals and the challenges involved in estimating its dependence and analyzing the emerging topological patterns, this dissertation introduces innovative statistical tools designed to explore both the functional and effective connectivity within brain networks. It sheds light on frequency-specific patterns in ADHD subjects and introduces a novel approach for examining the hierarchical structure of brain regions during seizures. Our work provides a novel perspective on the organization of brain networks and presents insight into how various conditions influence their complex structure.

We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating distribution and do not require model refitting.

Artificial intelligence (AI) has focused on a paradigm in which intelligence inheres in a single, autonomous agent. Social issues are entirely secondary in this paradigm. When AI systems are deployed in social contexts, however, the overall design of such systems is often naive --- a centralized entity provides services to passive agents and reaps the rewards. Such a paradigm need not be the dominant paradigm for information technology. In a broader framing, agents are active, they are cooperative, and they wish to obtain value from their participation in learning-based systems. Agents may supply data and other resources to the system, only if it is in their interest to do so. Critically, intelligence inheres as much in the overall system as it does in individual agents, be they humans or computers. This is a perspective that is familiar in the social sciences, and a key theme in my work is that of bringing economics into contact with foundational issues in computing and data sciences. I'll emphasize some of the mathematical challenges that arise at this tripartite interface.

Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms.

Despite the significant advancements deep learning models have brought to solving complex problems in the real world, their lack of transparency remains a significant barrier, particularly in deploying them within safety-critical contexts.

Neural ODEs have surfaced in the last decade as a new perspective on modelling dynamics by learning the time-derivative that drives the system evolution forward as a neural network.

As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

In this work, we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF).

When pressure acoustic waves interact with rotating scatterers, they undergo peculiar and intriguing characteristics. In this talk, I will discuss our recent findings on the physics of acoustic scattering and propagation in spinning fluids.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Neural networks have achieved impressive performance in many applications such as image and speech recognition and generation. State-of-the-art performance is usually achieved via a series of engineered modifications to existing neural architectures and their training procedures. However, a common feature of these systems is their large-scale nature: modern neural networks usually contain Billions - if not 10's of Billions - of trainable parameters, and empirical evaluations (generally) support the claim that increasing the scale of neural networks (e.g. width and depth) boosts the model performance if done correctly. However, given a neural network model, it is not straightforward to address the crucial question `how do we scale the network?'. In this talk, I will show how we can leverage different mathematical results to efficiently scale neural networks, with empirically confirmed benefits.

Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the unit circle, although the latter objects frequently arise in many applications. In this talk, the problem of clustering circular time series is discussed.

Brain activity over the entire network is complex. A full understanding of brain activity requires careful study of its multi-scale spatial-temporal organization. Motivated by these challenges, we will explore some characterizations of dependence between components of a multivariate time series and then apply these to the study of brain functional connectivity.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

Partial differential equations are a mathematical tool widely used to model phenomena in several different fields. A stochastic partial differential equation (SPDE) introduces random forcing to take the nature of real-world observations.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

In this talk, we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus on the case of neuroscience.

Many problems in applied geometry amount to the solution of a typically nonlinear partial differential equation. We will discuss why it may not be a good idea to discretize the equation, but to take the viewpoint of discrete differential geometry and discretize the theory.

Clinical research often requires the simultaneous study of longitudinal repeated measurements and time-to-event (i.e., survival) data. Joint models, which can combine these two types of data, are invaluable tools in this context.

We are all familiar with the tendency of water waves to break in shallow water, for instance at the beach. Indeed, breaking is a universal behavior of solutions to first-order nonlinear hyperbolic PDEs, and manifests itself in phenomena ranging from traffic jams to shock waves.

This workshop will cover the statistical essentials to designing experiments including power analysis, sample size calculation, regression, and variance analysis. A statistically sound experimental design is essential in applying for research grants. Detailed syllabi will be sent to those who register. Limited seats. Sign up now!