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.

Machine learning (ML) has witnessed remarkable advancements in recent years, demonstrating its effectiveness in a wide array of applications, including intrusion detection systems (IDS). However, when operating in adversarial environments, ML-based systems are susceptible to a range of attacks.

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.

This talk presents a method for obtaining good accuracy of the measured rotational speed and discusses the control algorithms and modulation technique of the high-speed BLDC motor.

Our society keeps entrusting ICT systems with high value cyber-only assets, such as our most sensitive data, finances, etc. However, when it comes to cyber-physical systems and their ability to act in and with the physical world, lifes are at risk and require rigorous protection against accidental faults and cyberattacks.

Light can be controlled through different degrees of freedom. An optical field is described through frequency, amplitude, phase, polarization, and wave-front structure. Many applications have been explored using these degrees of freedom, and some have great importance in our daily life.

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.

In the first part of this thesis, we have discussed the Cram ́er-Rao lower bound (CRLB) to evaluate the performance of beam tracking for a joint beam tracking and symbol detection scheme in deep-space optical communications.

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.

We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small.

The Internet and Communication Technology (ICT) have undeniably revolutionized various aspects of human life. As the standardization of the fifth generation (5G) of wireless communication systems (WCSs) has been completed, 6G is expected to be the next focus in wireless communication and networking and aims to provide new superior communication services to meet the future hyper-connectivity demands in the 2030s. With this background, this Summit aims to go over the recently proposed solutions not only to connect the unconnected/under-connected but also to super-connect the connected.

InGaN-based monolithic RGB LED arrays would be the key to producing micro-LED displays. The micro-LED displays will reduce the frequency of battery charging for mobiles and make head-mount displays thinner and lighter weight. It will become a game changer.

Due to a variety of potential barriers to sample acquisition, many of the datasets encountered in important classification applications, ranging from tumor identification to facial recognition, are characterized by small samples of high-dimensional data. In such situations, linear classifiers are popular as they have less risk of overfitting while being faster and more interpretable than non-linear classifiers. They are also easier to understand and implement for the inexperienced practitioner.

Federated Learning (FL) is a distributed machine learning approach that allows multiple parties to train a model collaboratively without sharing sensitive data.

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.

Generative models for language generation, particularly based on transformers have shown remarkable performance in domains dealing with language.

The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well-known solution concepts such as Nash Equilibrium (NE).

One of the fundamental problems in population genetics and molecular evolution is to understand the drivers of genetic change in a population: which mutations affect the ability of an organism to survive, reproduce, and pass its genes to the next generation, while which mutations are mere "passengers" that do not affect this ability? In principle, the evolutionary history of a population contains information of the effects of mutations (deleterious, beneficial or neutral) occurring in the population.

Currently, attention mechanism becomes a standard fixture in most state-of-the-art NLP, Vision and GNN models, not only due to outstanding performance it could gain, but also due to plausible innate explanation for the behaviors of neural architectures it provides, which is notoriously difficult to analyze. However, recent studies show that attention is unstable against randomness and perturbations during training or testing, such as random seeds and slight perturbation of input or embedding vectors, which impedes it from becoming a faithful explanation tool. Thus, a natural question is whether we can find some substitute of the current attention which is more stable and could keep the most important characteristics on explanation and prediction of attention.

Quantum theory and relativity have shown the solid path for solid-state computation in the early 20th century. Since then, many theoretical breakthroughs accompanied by experimental discoveries have ultimately led us to this modern-day electronic society.