"Force-deformation laws, Love numbers, and the Association Principle". This lecture contains a discussion about realistic force-deformation relations used for celestial bodies, their empirical description by means of Love numbers, and their mathematical modelling by means of the "Association Principle''.

This Ph.D. research focuses on proposing new statistical methods for two types of time series data: integer-valued data and multivariate nonstationary extreme data. For the former, the researcher proposes a novel approach to building an integer-valued autoregressive (INAR) model that offers the flexibility to specify both marginal and innovation distributions, leading to several new INAR processes. For the latter, the researcher proposes new extreme value theory methods for analyzing multivariate nonstationary extreme data, specifically EEG recordings from patients with epilepsy. Two extreme-value methods, Conex-Connect and Club Exco, are proposed to study alterations in the brain network during extreme events such as epileptic seizures.

In this talk, we discuss problems and numerical methods arising in the calculus of variations and energy minimization. Among numerous applications, energy minimization is a core element of Machine Learning algorithms. Within the field of nonlinear PDEs, the calculus of variations has received a lot of attention from the analysis point of view.  Although quite interesting and challenging,  the numerical analysis of these problems is much less developed.

Delivering healthcare to patients in their homes is shaping the future of healthcare, as it offers better access to healthcare for people who live far from hospitals. It also facilitates the early detection of diseases and the prevention of complications that might otherwise require hospitalization, while simultaneously reducing costs for patients and healthcare systems. Nevertheless, the utilization of machine learning and health sensors for clinical purposes within the home environment requires addressing certain challenges, such as simplifying compliance procedures, ensuring that the digital representations of patients are comparable to the established medical gold standard, and preserving data privacy. In this talk, I will discuss how to develop new algorithms and models with health sensors to capture rich, continuous representations for in-home healthcare applications that address all these challenges.

"Translation, rotation and Deformation". In this lecturer, we will present the simplest possible model for the motion of two extended rigid bodies interacting by gravity.

This talk will review the recent shift in the construction and modern analysis of a large class of spatially and temporally adaptive methods whose properties are very close to our current analytical knowledge about hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. Thus these algorithms can be regarded as the elite methods in the field. Next, we will show examples of how the robustness and efficiency of the fully-discrete representation of PDEs can be enhanced using computational science's smithy, i.e., "modern" numerical analysis. The talk will showcase complex flow problems in aeronautics, aerospace, and automotive sectors, provide preliminary results in other fields, and present an outlook for future research directions where data science can currently be the linesman.

"Qualitative theory of tides and their effects." It contains a qualitative explanation of tides and their effects: phase lags, forces that dissipate energy but do not dissipat angular momentum, circularization of orbits, spin-orbit synchronization and collision.

Abstract

Non-Abelian-based theories are one of the foundations of modern physics.

We study the use of a nonlinear projection operator in the development of a novel function space approach for the optimization of trajectory functionals.

This talk reviews recent results concerning the inviscid limit for the 2D Euler equations with unbounded vorticity. In particular, by using techniques from the theory of transport equation with no smooth vector fields, we show that the solutions obtained in the vanishing viscosity limit satisfy a representation formula in terms of the flow of the velocity and that the strong convergence of the vorticity holds and we give a rate of convergence.

Cloud storage is pervasive nowadays; surprisingly, how to secure cloud storage that is usable in the real world is in fact still open. In this work, we propose a novel system called End-to-Same-End Encryption (E2SEE) that can be deployed directly on existing infrastructure and provide both security and usability. Our system can be flexibly used to augment any App with secure storage, for users to create a personal digital lockbox, and for the cloud to provide secure storage service. A preliminary version of E2SEE was deployed in Snapchat, serving hundreds of millions of users, and the research result was published at USENIX Security 22.

Risk assessment for natural hazards and financial extreme events requires the statistical analysis of extreme events, often beyond observed levels. The characterization and extrapolation of the probability of rare events rely on assumptions about the extremal dependence type and about the specific structure of statistical models. In this thesis, we develop models with flexible tail dependence structures, in order to provide a reliable estimation of tail characteristics and risk measures. Our novel methodologies are illustrated by a range of applications to financial, climatic, and health data.

After a brief introduction to the field of Computational Cardiology and cardiac reentry, we introduce and study some scalable domain decomposition preconditioners for cardiac reaction-diffusion models, discretized with splitting semi-implicit techniques in time and isoparametric finite elements in space.

This talk will present recent approaches for mitigation and adaptation, for which data analytics and ML are parts of the solution in a larger context of interdisciplinary and methodological research and innovations.

Complex systems and software engineering, and associated challenges become increasingly important for the well-being and safety of our society of humans. Motivated by this push towards ever more complex systems and software of all sizes, spectacular failures, and decades of questioning in a variety of contexts and endeavors, this talk presents a theory of complex systems engineering, that is, a scientific theory in which an engineered system or software can be seen as a validated scientific hypothesis arising from a convergent mix of mathematical and validated experimental constructs. In its simplest form, a complex engineered system is a manufactured, validated scientific hypothesis arising from a mathematical theorem similar to those found in theoretical physics. This observation provides suggestions for improving system design, especially system architecture, by leveraging advanced mathematical and / or scientific concepts. In return, mathematicians and computer scientists can benefit from this bridge to engineering by bringing to bear many of their automated and manual theorem proving techniques to help with the design of complex systems.

The transfer of information between non-matching meshes is an important ingredient for coupled multi-physics simulations. For most coupled problems information, such as displacements or stresses, has to be exchanged between, two different meshes. As an example consider fluid-structure interaction (FSI) problem, where information has to be transferred between a fluid and an elastic body (the "S"tructure in FSI).

Complex systems and software engineering, and associated challenges become increasingly important for the well-being and safety of our society of humans.

Emergence of nontrivial patterns via collective actions of many individual entities is an ever-present phenomenon in physics, biology and social sciences. It has numerous applications in engineering, for instance, in swarm robotics. I shall demonstrate how tools from mathematical modeling and analysis help us gain understanding of fundamental principles and mechanisms of emergence. I will present my recent results in consensus formation and flocking models, taking into account their realistic aspects - noise, latency, finite speed of information propagation and anticipation. Moreover, I will introduce a continuum modeling framework for biological network formation, where emergence takes place through the interaction of structure and medium. The models are formulated in terms of ordinary, stochastic and partial differential equations. I shall explain how mathematical analysis of the respective models contributes to the understanding of how individual rules generate and influence the patterns observed on the global scale. Finally, I will explain how requirements on robustness of the network can be incorporated into the mathematical model.

Federated learning (FL) is increasingly deployed among multiple clients to train a shared model over decentralized data. To address the privacy concerns, FL systems need to protect the clients' data from being revealed during training, and also control data leakage through trained models when exposed to untrusted domains. However, existing FL systems (with distributed differential privacy) work impractically in the presence of client dropout, resulting in either poor privacy guarantees or degraded training accuracy. In addition, existing FL systems focus on safeguarding the privacy of training data, but not on protecting the confidentiality of the models being trained, which are increasingly of high business value. In this talk, I will present two pieces of our recent work that aim to address these aforementioned issues.

This presentation addresses the challenges associated with trusting Neural Networks due to their black-box nature and limited ability to answer important questions on how they behave. The thesis proposes techniques that increase the trustworthiness of Neural Network models by employing approaches to overcome their black-box nature. The techniques include efficient extraction and verification of weights and decisions to ensure correctness with regards to pre-existing properties, continuous and exact explanations of the model behavior, and scalable training techniques providing strong, theoretically provable guarantees of privacy. We provide strong, approximation-free guarantees about Neural Networks, improving their trustworthiness to make it more likely that users will be willing to deploy them in the real world.

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of iterative fixed-point algorithms known as proximal splitting algorithms is particularly adequate: they consist of simple operations, handling the terms in the objective function separately. I will present a selection of recent primal-dual algorithms within a unified framework, which consists in solving monotone inclusions with well-chosen spaces and metrics.

In this presentation we will explain how we can solve linear, semi-linear as well as nonlinear partial differential equations by the concept of backward stochastic differential equations and Fourier cosine expansions. We will discuss the highly efficient pricing of financial options in the Fourier context by means of the COS method. Particularly, we also present a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion of stock prices.

Despite long-ago predictions (e.g., see Bill Gates, 2004) that other user-authentication technologies would replace passwords, passwords remain not only pervasive but have flourished as the dominant form of account protection, especially at websites such as retailers that require a low-friction user experience. This talk will describe our research on methods to tackle three key ingredients of account takeovers for password-protected accounts today: (i) site database breaches, which is the largest source of stolen passwords for internet sites; (ii) the tendency of users to reuse the same or similar passwords across sites; and (iii) credential stuffing, in which attackers submit breached credentials for one site in login attempts for the same users' accounts at another.