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.

Over the past decades, Jeff has been lucky enough to follow some of these developments from a front-row seat. He will share selected perspectives on current and past research including the various pendulum swings over the years between extremes, such as expertise-based knowledge engineering vs. data-centric machine learning, autonomous vs. mixed-initiative systems, publicly available chatbot capabilities vs. personalized, policy-governed multi-agent systems. In this talk, I will show what past research in AI has to teach us about the future.

Coffee Time: 15:30 - 16:00. The phase-field model, a powerful modeling tool for dealing with interface problems, has been widely used in various fields such as computational physics, computational biology, materials engineering, and even image processing. The dissipation of free energy is an important and fundamental property of the phase-field model.

We provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity. This is a joint work with A. Biswas and J. Tian.

Let us consider an elliptic equation of second order in variational form i.e. div(A(x)∇u) = divf in a bounded domain Ω ⊂ Rn where the function f belongs to some suitable function space.

Splitting methods have been shown to a useful tool in solving phase field equations. However, rigorous nonlinear stability analysis has not been available. In this short course, we will discuss some recent development in this direction.

Coffee Time: 15:30 - 16:00. Splitting methods are a well-established tool for numerically integrating time-dependent partial differential equations. These methods split the vector field into disjoint components, which are integrated separately using an appropriate time step. The individual flows are then combined to obtain the desired numerical approximation.

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.

A fascination with symmetric forms seems to be an innate feature of human perception and for millennia it has influenced art and natural philosophy. The concept of symmetry is one of the very few on which mathematicians and physicists agree, namely that Symmetry ≡ Groups. We describe some special symmetries and related problems including symmetric polynomials and monstrous moonshine.

We will give an overview of the development of Abstract Algebra from Galois to our time. The talk will be accessible to general audience with basic mathematical background.

The studies in numerical approximation of partial differential equations are characterized by the necessity of managing complex geometries and their discretization. We focus our attention on two different fields where complex geometries are very common: the mathematical modeling of fluid-structure interaction problems and the family of virtual element methods.

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.

Abstract

Cells make fate decisions in response to dynamic environments, and multicellular structur

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.

Tensor network techniques are known for their ability to approximate low-rank structures and beat the curse of dimensionality. They are also increasingly acknowledged as fundamental mathematical tools for efficiently solving high-dimensional Partial Differential Equations (PDEs). In this talk, we present a novel method that incorporates the Tensor Train (TT) and Quantized Tensor Train (QTT) formats for the computational resolution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian coordinates.

A Schrödinger equation for the system’s wavefunctions in a parallelepiped unit cell subject to Bloch-periodic boundary conditions must be solved repeatedly in quantum mechanical computations to derive the materials’ properties.

Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning optimizers.

Free boundary problems arise naturally in a range of mathematical models that describe physical, biological or financial phenomena, such as the melting of ice into water, the dynamics of a population or the behavior of stock markets, to mention just a few.

Xanadu is a Canadian quantum computing company with the mission to build quantum computers that are useful and available to people everywhere. Xanadu is one of the world’s leading quantum hardware and software companies and also leads the development of PennyLane, an open-source software library for quantum computing and application development.

This talk begins with the problem of pricing American basket options in a multivariate setting. In high dimensions, nonlinear PDE methods for solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation become expensive due to the curse of dimensionality.

Abstract

The COVID-19 pandemic produced excess mortality in many countr

The Euler equation does not possess a unique solution for the flow over a two-dimensional object. This problem has serious repercussions in aerodynamics; it implies that the inviscid aero-hydrodynamic lift force over a two-dimensional object cannot be determined from first principles; a closure condition must be provided. The Kutta condition has been ubiquitously considered for such closure in the literature, even in cases where it is not applicable (e.g. unsteady).

Spatial data analysis commonly needs to deal with spatial data derived from multiple sources (e.g. satellites, stations, survey samples) with different supports, but associated with the same properties of a spatial phenomenon under interest. Usually, predictors are also measured on different spatial supports than the response variable.

Quantinuum is the world’s largest integrated quantum computing company. Quantinuum has developed the H-Series quantum computers based on a trapped-ion architecture using the unique and highly-scalable QCCD architecture (QCCD = Quantum Charge-Coupled Device), and released its first two generations: the System Model H1 and H2. The H-Series QPUs are well-known for their superior, low noise performance and differentiating capabilities such as all-to-all connectivity and mid-circuit measurement with very low qubit cross talk.  Dr. Brian Neyenhuis will discuss how the QCCD architecture enables these differentiators and what researchers can do with the H-Series quantum computers that they cannot do on other commercially available quantum computers.  As a full stack quantum computing company, Quantinuum also makes TKET, an open source SDK compiler and optimizer, as well as algorithm and application layers for applications in Machine Learning, Finance, Chemistry, and modeling of Quantum Systems.  Anand Shah will review the application and algorithm activities at Quantinuum.

In this talk we propose and validate a Space Multiscale model for the description of particle diffusion in the presence of trapping boundaries. We start from a drift diffusion equation in which the drift term describes the effect of bubble traps, and it is simulated by the Lennard–Jones potential.