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.

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.

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.

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.

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.

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Abstract

We develop a computational framework for risk mitigation in high population density event

As end-consumers of electricity become more proactive and as many countries around the world push for a deeper penetration of renewable resources into the power grid, critical issues and challenges arise to the design and operation of deregulated electricity markets. In this presentation, we show how one can exploit tools from game theory to address some of these critical issues. Firstly, wholesale and retail markets are becoming more integrated due to the increasing adoption of distributed energy resources, creating a large gap in the current understanding of the impact of such small-scale energy resources on the larger power system operation and electricity market outcomes. This motivates us to develop a metric, called the Price of Aggregation, which quantifies the impact of integrating distributed energy resources in the retail-level on wholesale market efficiency.  Secondly, evidence from real markets indicate that large-scale adoption of wind energy in the transmission system leads to significantly higher price volatility in wholesale markets. To mitigate the effects of price volatility, we propose an add-on centralized clearing mechanism that is applicable to any wholesale market, with the aim of allowing any market participant to hedge against profit volatilities, without changing the existing market operations. Finally, we develop a multiperiod-multicompany demand response framework in retail markets, which captures the behavior of competing companies and their price-responsive end-consumers. Using real-life data, we demonstrate potential savings that can exceed 30% for end-consumers, in addition to revealing desirable mathematical properties and deep insights.

This talk presents an overview of challenges, state-of the-art, and applications for distributed robotic systems. In distributed robotic systems, there is a group of robots that seek to achieve a collective task. Applications include environmental monitoring, search and rescue, and programmable self-assembly. Settings can range from a small team of cooperative robots to a swarm of many interacting agents. An essential feature of such systems is that individual robots make decisions based on available local information as well as limited communications with other robots. The challenge is to design local protocols that result in desired global outcomes. In contrast to a traditional centralized paradigm, both measurements and decisions are distributed among multiple actors.

As autonomy in individual robots becomes advanced, one of the next challenges is to coordinate multiple of such intelligent robots, which are then expected to innovatively transform legacy industries (e.g., warehouse automation, connected-vehicle management, etc.). Towards collaboration of multiple robots, this talk will particularly introduce a game-theoretical framework for clustering a large number of multiple robots and assigning the robot teams to given tasks, where the network of the robots is strongly connected and the individuals are asynchronous. The proposed decentralised algorithm guarantees convergence of selfish agents having social inhibition towards a Nash stable partition (i.e., social agreement) within polynomial time.

Robotics is set to play an ever increasingly important role in society, due to its influence in every aspect of life, including medicine and healthcare, manufacturing, services..etc

The emerging need to improve the quality of life for elderly and disabled individuals who rely on wheelchairs for mobility is our motivation for this work. Research on robotics wheelchair covers broad range from motion control, how to control the wheelchair movement, to complete autonomy.

Flash floods are one of the most common natural disasters worldwide, causing thousands of casualties every year. The emergence of Unmanned Aerial Vehicles (UAVs) gives the possibility to monitor these events over large geographical areas. In this talk, we focus on the problem of trajectory planning for a swarm of unmanned aerial vehicles sensing flooding conditions.

We study a simple learning dynamic model of routing (congestion) games to explore the effects of increasing the total demand on system performance. We focus on the most benign setting, non-atomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative Weights Updates with a fixed learning rate.

In this talk, I will present my research on designing multi-agent robotic systems and developing theory and algorithms for system control. The first part of the talk will present my research on designing an animal-borne remote imaging system and developing theory and algorithm for distributed sensor fusion that enables estimation and detection of animal group movements using the system. I will explain data collection capability of the system and share system deployment experiences in monitoring a wild life of African animals In the second part, I will describe my current work on developing a fleet of autonomous robotic vessels.

Game theory has become a powerful tool in engineering field to study, model and control interacting systems. This talk addresses two game theoretical approaches, i.e., evolutionary games and mean-field-type games.

Drone-based delivery systems promise to enable new important transportation applications and to solve the “last mile problem”. Drones are able to perform time-critical delivery of medicines in remote areas.

In the last years, autonomous vehicles have attracted the attention of researchers in several fields. For instance, we find unmanned vehicles for ground applications, for aerial applications and for marine applications.

The modeling paradigm builds on the theory of evolutionary game dynamics and bio-inspired collective decision making.