Events

Abstract:

Recent advances in cell-free DNA (cfDNA) analysis have focused on the multimodal integration of genetic (e.g., copy number aberrations, variants) and epigenetic (e.g., fragmentomics, methylation) profiles for cancer detection. We hypothesized that combining cfDNA modalities would enhance detection sensitivity and developed a novel analytical framework for their joint analysis.We conducted enzymatic conversion and whole-genome methylation sequencing on blood samples from breast and colorectal cancer patients (predominantly stage I), multiple myeloma patients, and healthy controls, with sequencing depths ranging from 1x to 10x. Enzymatic conversion was chosen for its expected lower GC and fragmentation biases, facilitating the combined analysis of methylome and fragmentome data. A new analytical pipeline was designed for simultaneous methylation calling, copy number aberration analysis, and fragmentomic analysis. These derived modalities were then utilized for downstream analysis using a problem-specific machine learning approach.We report an area under the receiver operating characteristic curve (AUROC) of 0.834 on our colorectal cancer test cohort, and AUROCs of 0.970 and 0.999 cross-validation performance for breast cancer and multiple myeloma detection, respectively. Our results demonstrated significant performance improvements when combining cfDNA properties, underscoring their synergy and complementarity. Furthermore, correlations between modalities suggested that changes in fragmentomic and methylation profiles were influenced not only by the presence of circulating tumor DNA but also by alterations in nuclease activity. These findings emphasize the critical role of orthogonal biomarkers, as their joint analysis can elucidate the underlying causes of changes in genetic and epigenetic profiles.

Dr. Igor V. Tetko (Institute of Structural Biology, Molecular Targets and Therapeutics Center - Helmholtz Munich-Forschungszenrum für Gesundheit und Umweld (GmbH), Germany) will give a lecture on "Advanced Machine Learning in Drug Discovery".

Abstract: Modern Machine Learning (ML) based on deep neural networks (DNNs), which form the basis of Artificial Intelligence (AI), is gaining popularity in the field of drug discovery. These methods can digest large amounts of information and provide reliable predictions for new molecules. Notably, such methods need not rely anymore on descriptors, but can learn their internal representations based on text or molecular graphs. They can also incorporate non-traditional information, such as images produced by high content screening, to better utilize results of in vitro measurements. Emerging solutions include the use of meta- and transfer-learning approaches, which enable the pre-training of models on a large corpus of chemical data of different modalities, and then efficiently applies the models to small datasets. The estimation of the accuracy of such predictions, which allows for the discrimination between reliable vs non-reliable predictions, is another important direction of the development of these methods. Being considered for a long time as black boxes, DNNs can become interpretable via eXplainable AI (XAI) methods. These developments open new perspectives for the use of ML in chemistry.

Following the lecture, there will be opportunity for young researchers to interact with him.

Abstract
The essence of successful Quantitative Structure-Activity Relationship (QSAR) modeling for drug discovery lies in the availability of diverse and high-quality data. However, acquiring such data in the pharmaceutical industry is not only challenging and expensive but also constrained by its proprietary nature, limiting sharing opportunities. To overcome these challenges, this dissertation introduces innovative methods aimed at accessing literature and cross-pharma data, thereby enabling the utilization of larger datasets for the training of machine learning models.

An integral component of this research involves the introduction of the Optical Chemical Structure Recognition (OCSR) technique, known as ChemGrapher. While showcasing its potential, a notable limitation comes to light, emphasizing the indispensability of atom-level entity labels. These labels, providing precise details about the localization of individual elements within chemical compounds, prove essential for effective training. The treatment of atom-level entities as discrete objects highlights the convergence of OCSR with object detection methodologies, underlining the significance of identifying and categorizing individual atomic elements within chemical depictions. The subsequent sections of this dissertation delve into the continual progress and enhancement of object detection methods, directly contributing to the refinement and advancement of ChemGrapher.

"Multivalued Robust Control: Monotonicity and well-posedness"

Fernando Castanos, Department of Automatic Control, CINVESTAV-IPN, Mexico

Abstract:

Motivated by physical devices that exhibit multivalued characteristics, we look at the feedback interconnection of dynamical systems with multivalued control laws.

The property of monotonicity ensures that the closed-loop system is well-posed, that is, that state trajectories exist and are unique.

On the other hand, the multivalued nature of the controller provides robustness in the face of uncertainty.

Monotonicity also guarantees that the controller is implementable in discrete-time devices such as microcontrollers.

Abstract

Molecular biology delves into how DNA controls cell functions, aiming to understand complex processes at a molecular level. Thanks to recent technological advances, we can now study biomolecules like DNA, RNA, proteins, and metabolites on a large scale using "omics" technologies. These advances have led to significant improvements in diagnostics, treatments, genetically modified organisms, and personalized medicine. "Omics" refers to fields such as genomics (DNA), transcriptomics (RNA), proteomics (proteins), and metabolomics (metabolites). Each generates vast amounts of data that require sophisticated analysis tools. This thesis focuses on three advanced techniques—mass spectrometry imaging (MSI), multiplexed immunohistochemistry (mIHC), and chromatin conformation capture (3C)—and addresses the challenge of analyzing these complex data sets. To simplify and interpret these data, we utilized non-negative matrix factorization (NMF), which breaks down large data sets into smaller, understandable components. In MSI, used to study proteins and metabolites in tissues, we found that NMF methods considering Poisson noise performed best. We also employed a visualization tool to reveal detailed structures in mouse pancreas data and developed a hierarchical NMF approach to uncover subtle signals. For the analysis of mIHC data, which measures protein markers with high spatial resolution, we created a pipeline combining NMF with machine learning to analyze melanoma and kidney samples more efficiently. Finally, for chromatin structure analysis in mouse brain cells, we used NMF to identify crucial chromatin contacts linked to specific cell types, despite noisy data.

Overall, this research demonstrates how advanced computational methods like NMF can extract valuable insights from complex biological data, enhancing our understanding of molecular biology.

Dr. Gamze Gürsoy (Columbia University & New York Genome Center, USA) will give a lecture on "Overcoming distributional shifts in federated learning and applications in biomedicine".

Following the lecture, there will be opportunity for young researchers to interact with her

•     Venue: ESAT B91.200
•     Date: 5 July 2024, 10:30 - 11:30
•     Dr. Gamze Gürsoy is visiting KU Leuven at the occasion of the PhD defence of Melanie Nijs. See also: https://forms.gle/DLc729o1vAJt8bAY8 

https://set.kuleuven.be/phd/seminars/gursoy


Abstract:
Federated learning has been proposed as a potential solution to overcome the institutional barriers to data sharing in biomedical AI. Federated learning allows multiple parties to train the same model on their own data, without having to share the data with each other. However, there still remain unanswered challenges, especially in the domain of biomedicine: Federated learning relies on the assumption that the data at each party are independent and identically distributed. In particular, heterogeneity between different local datasets might propagate the bias that each institution might have with respect to patient population, given that the size of local datasets may vary significantly. To mitigate these issues, we present frameworks for assessing and overcoming distribution shifts while preserving privacy.

Biography:
Gamze Gürsoy, PhD, is a Core Faculty Member at the New York Genome Center. She holds a joint appointment as Assistant Professor in the Departments of Biomedical Informatics and Computer Science at Columbia University. Dr. Gürsoy’s lab’s overarching research goal is to harmonize diverse fields such as biology, bioinformatics, molecular biology, engineering, and cryptography to achieve two fundamental aims: (1) to increase biomedical data access to a wider group of scientists while preserving privacy of research participants; and (2) to uncover the molecular underpinnings of gene dysregulation via knowledge gained from functional genomics data. They create modular and privacy-enhancing omics and clinical data analysis tools, which can be adapted to new data modalities and analysis needs as they arise, by combining knowledge in molecular biology and applied cryptography. They also develop computational and biochemical technologies to pinpoint genetic and epigenetic determinants of chromatin organization.

Abstract:

Patients suffering from end stage osteoarthritis commonly have to cope with pain, joint instability, reduced range of motion, and joint stiffness. Total knee arthroplasty (TKA) is a surgical procedure aimed to treat patients suffering from end stage osteoarthritis. In the last decade several technological advancements have helped surgeons in increasing their efficiency and attempt to improve patient outcome. 3D preoperative planning allows surgeons to be better prepared for the surgery by planning the required implant types, sizes and their position in advance. These preoperative plans can be used in combination with patient specific instruments, navigation systems, robotics platforms or augmented reality to transfer the plan to the surgery. In the process, these systems collect large amounts of data.

The purpose of this thesis is to investigate ways to improve the preoperative planning process based on retrospectively collected preoperative plans using machine learning (ML). Therefore, we will investigate automatic knee MRI segmentation, the variability in preoperative planning styles, and surgeon specific preoperative planning. Manual segmentation of knee MRI scans is time consuming, taking up to 6 hours per scan, and is prone to inter-observer variability. As a result, several methods have been proposed over the last decade to automate the segmentation procedure based on atlas approaches, shape models, and recently deep learning. Two deep learning approaches were compared based on 3D and 2.5D convolutional neural networks. Our methods outperform state-of-the-art methods in terms of bone segmentation. The 3D and 2.5D methods were compared to a shape model based automatic segmentation based on 3000 scans and yielded a 22.9% and 35.4% reduction in manual segmentation time, respectively. As a result, the cost associated with preoperative planning can be decreased, facilitating the adoption of 3D based preoperative planning.

For decades, mechanical alignment has been the gold standard in knee alignment targeted during TKA. However, in recent years, new scientific and clinical insights have led to new planning philosophies. We investigated the variation in preoperative planning styles between 42 surgeons through the use of machine learning. A machine learning method was proposed that predicted the surgeon who planned a case based on the selected implant sizes, their position and orientation. Our method was able to predict with 84% accuracy which surgeon planned a case. Furthermore, our method was able to find surgeons with similar planning style. Based on these results, we concluded that preoperative planning should happen in a way that is both patient and surgeon specific.

Several studies in the literature have demonstrated the need to make changes to the proposed implant size, position or orientation in manufacturer’s preoperative plans. Therefore, a machine learning method was proposed that predicts the preoperative planning parameters in a surgeon and patient specific manner. The ML generated preoperative plans required 39.7% less corrections compared to manufacturer’s default preoperative plans. The femoral and tibial implant sizes in the default plan were correct in 68.4% and 73.1% of cases respectively, while in the ML plan they were correct in 82.2% and 85.0% of cases. These ML generated preoperative plans can enhance the efficiency and user experience of the surgeon.

Determining the required implant size preoperatively has clinical and logistical advantages. Several methods in the literature have investigated predicting femoral implant size based on demographic data with an accuracy up to 56%. We proposed a novel method to predict femoral implant size based on the 3D mesh of the femoral bone. Our method, the hypergraph regularized group lasso significantly outperformed previously reported methods with an accuracy of 70.1%. This can be beneficial in increasing the efficiency of hospital logistics, by reducing instrument and implant sterilization cost, and operating room setup time. In this thesis state-of-the-art machine learning approaches were investigated to improve the efficiency of the preoperative planning process. Improved medical image segmentation can reduce lead times and the cost of personalized total knee arthroplasty. Machine learning methods can capture surgical planning styles of experienced surgeons. Towards the future the biggest opportunity of machine learning in total knee arthroplasty lies in optimizing the patient reported outcome. If more data, such as data related to patient outcome, is collected on a larger scale, these models can help establish surgical plans that attempt to maximize the patient’s post-operative outcome.

Register:

Please confirm your attendance before Wednesday 5 June 2024
through this link.

Participate online

The defence will also be livestreamed through the following link (PIN: 533559)

Speaker: Claudia Lindner, PhDSenior Research Fellow, Sir Henry Dale Fellow  

This seminar investigates the integration of artificial intelligence (AI) into musculoskeletal image analysis and its transition from laboratory research to clinical implementation. Through case studies, the seminar showcases how AI algorithms can automate medical image analysis, benefiting diagnosis and treatment in musculoskeletal disorders. Moreover, the seminar explores the translational challenges inherent in bringing AI technologies from research environments to clinical settings, covering validation processes, integration strategies, and clinical acceptance. In summary, the seminar aims to highlight AI's potential in advancing musculoskeletal healthcare and improving patient outcomes, while also emphasising the need for careful consideration of translation into clinical practice right from the outset.

Participate online:
The symposium can be livestreamed through the following link (PIN: 823347)

Guillaume Mercère University of Poitiers, France

Abstract
In numerous industrial projects, engineers face the crucial task of extracting physical parameters and signals from real-world data. When employing gray box state space model learning, a key challenge lies in generating reliable initial estimates to ensure convergence towards precise parameter values. Similarly, in utilizing Kalman filtering for signal reconstruction, a common obstacle is selecting reliable covariance matrices to attain accurate estimates. This presentation delves into how subspace-based model identification can effectively address these challenges. These solutions, relying solely on linear algebra, center on determining the similarity transformation between various state space realizations. Through both simulated and real data demonstrations, we illustrate the efficacy of these approaches.

Everyone is welcome to attend in person.

The presentation will be streamed and can be followed by using this link: https://eu.bbcollab.com/guest/6c0b700cbe744161975e8cce8ed0c9cb

The slides and recordings of the previous seminars are available on our website.

The challenge of understanding the Universe's dynamics, particularly the Hubble tension, requires precise measurements of the Hubble constant. Building upon the existing spectral siren method, which capitalizes on population information from gravitational wave sources, this talk explores an alternative way to analyse the population data to obtain the cosmological parameters. We'll focus on how non-parametric methods, which are flexible models that can be used to agnostically reconstruct arbitrary probability densities, can be incorporated in this framework and leverage on the detector-frame mass distribution to infer the cosmological parameters

Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials. They arise naturally when solving polynomial equations expressed in the Chebyshev basis. More precisely, when passing from monomials to Chebyshev polynomials, Chebyshev varieties replace toric varieties. I will introduce these objects, discuss their defining equations and present key properties. Via examples, I will motivate their use in practical computations. This is joint work with Zaïneb Bel-Afia and Chiara Meroni.

Neural networks have achieved remarkable success in various domains such as
computer vision, natural language processing, reinforcement learning, robotics,
autonomous driving, etc. With the increase in computer computing power,
neural networks have evolved over the past decades from simple multi-layer
perceptrons to convolutional neural networks, and till now, large language
models based on Transformers. However, the increasing architecture capacities
of neural networks can also lead to overconfident predictions which might result
in severe consequences in real-world situations. To this end, in addition to
improve their prediction in a clean-data scenario, in this thesis, we consider
neural networks in settings assembling the real-world scenarios with noise resided
in the datasets. To be more exact, we focus on improving the robustness and
generalization abilities of neural networks in different learning tasks.
In this thesis, we study the robustness of convolutional neural networks against
label noise, where a significant portion of training data labels are incorrect.
To address over-fitting to noisy labels, we introduce compression inductive
bias, leveraging classical regularizations such as Dropout and Nested Dropout
to the networks. Additionally, we enhance performance by combining these
constraints with Co-teaching, a classical ensemble method for learning with
noisy labels. Theoretical validation includes a bias-variance decomposition
under compression regularization. Experimental results demonstrate that our
approach performs comparably or even better than state-of-the-art methods on
benchmarks including datasets with real-world label noise.
Given the ubiquitous use of Transformers and their outstanding performance in
various tasks, our focus shifts to exploring the robustness and generalization
of Vision Transformers (ViTs). In particular, we explore leveraging the jigsaw
puzzle solving problem as a self-supervised auxiliary loss of a standard ViT,
named Jigsaw-ViT for enhancing the robustness and generalization of ViTs.
In addition to the standard classification flow during the end-to-end training,
we introduce a jigsaw flow aiming to predict the absolute positions of input
patches by solving a classification problem. Despite its simplicity, Jigsaw-ViT
demonstrates improvements in both generalization and robustness over the
standard ViT, which is usually rather a trade-off. The efficacy of Jigsaw-ViT
is validated across benchmarks, including clean image datasets, learning with
noisy labels, and adversarial examples.
Next, we delve into the core mechanism that brings Transformer success, namely,
the self-attention mechanism. Specifically, we provide a novel perspective to
interpret self-attention with a primal-dual representation based on asymmetric
Kernel Singular Value Decomposition (KSVD), which fills the gap of dismissing
the asymmetry between theory and implementation. In this unsupervised setup,
we propose to remodel self-attention in the primal representation of the duality,
namely, Primal-Attention and to optimize it accordingly. The generalization
and efficiency of our new self-attention mechanism are validated on a series
of benchmarks, including time series, long sequence modelling, reinforcement
learning, image classification and language modelling.
Last, we find that due to large architecture capacities, Transformers can be
prone to suffering from poor robustness where the erratic outputs are over-
confident. To this end, we consider building uncertainty-aware Transformers so
as to make them more suitable for safety-critical tasks which have a high demand
for making rational decision under uncertainty. Specifically, we propose a new
self-attention mechanism for Transformer based on Sparse Variational Gaussian
Processes with kernel-eigen features to obtain better uncertainty quantification,
where the eigenvectors and eigenvalues of the attention matrix are obtained
by Primal-Attention. This leads to our Kernel-Eigen Pair Sparse Variational
Gaussian Processes (KEP-SVGP).

Please fill in this form if you are going to attend:

• https://forms.gle/SbpNVgmdoFsiLFsv9

To follow the defense online, please use the following Google Meet link: 

• https://calendar.app.google/kS9c2JcGcncByYHR6

A seminar by VSC team aiming in steering the researchers from ESAT towards using abundant compute/GPU resources which is available at the Flemish Tier-1 level or even European Tier-0 level.

Speaker: Ehsan Moravveji

Abstract

This project investigates the design of controllers for dynamic systems. These are systems whose state evolves over time. Examples, include cars, drones, power distribution networks, biochemical reactions, etc. When controlling such systems, it is essential to predict future behavior. In many applications, these predictions can be made using models based on physics. However, in some cases, these models are not available due to the inherent complexity of the system. Examples include human interactions crucial in self-driving cars, aerodynamic effects on drones flying close to objects, etc. If a model cannot be used, uncertainty arises that we must actively mitigate by learning about the environment based on examples of past behavior. Our goal is then to exploit this learned behavior in a controller.

To learn safely, we employ a three-step procedure. We start by using data to estimate a distribution of future trajectories. Then we evaluate the errors in this distribution due to the limited amount of available data. Finally, we ensure that our controller performs well under all possible errors. To predict these errors, we leverage existing fundamental results from the statistical literature. We also extend these by examining how data sorting can be used to estimate errors. This also has independent applications in areas such as machine learning, where it allows for more learning from the same amount of data. To make the controller robust against distributional errors, we use distributionally robust optimization. We describe a flexible and rigorous framework to computationally solve the resulting problems.

These tools are then applied to a broad, abstract class of dynamics where we can guarantee that the learning controller will meet certain conditions. Specifically, we demonstrate that the controller is stable, and thus, the state will converge to a specific value. We can also design controllers that constrain the state to a particular region. We describe how the controller becomes more cautious as more data becomes available, until we can make nearly perfect predictions and exploit them optimally. We also provide an upper bound on a quantitative measure of performance. Since we are working with statistical models, there is always a small probability that the data is not representative of the system's behavior, invalidating the aforementioned guarantees. Therefore, we also provide a quantitative prediction of this probability.

The entire framework serves as a bridge between system identification and optimal control, giving it a unique position in the literature. In the project, we also describe various challenges in establishing this bridge, which open up further research directions. One of the most crucial aspects in estimating errors in statistical learning techniques. Therefore, we offer concrete suggestions on how existing methods can be improved in the future.

Abstract: Multimodal deep learning systems, utilizing multiple modalities, have demonstrated superior performance over unimodal systems. However, prevalent assumptions in multimodal machine learning, such as all the modalities are present, well aligned, and noiseless during both training process and deployment, usually do not hold in real-world scenarios. To address these challenges, various methodologies have been proposed, including modality imputation, generation, zero-shot learning, and Cross-Modal Transfer Learning. This seminar starts with a general overview of these methodologies, followed by a discussion of their respective advantages, disadvantages, and suitability within biomedical contexts. Moreover, the seminar will demonstrate a novel solution tailored for biomedical signals. By showcasing its advantages in biomedical settings, this seminar aims to underscore the potential of robust multimodal machine learning techniques for advancing biomedical applications.

Abstract

In this talk I will introduce tensor network kernel machines. These models are able to learn nonlinear patterns from data for both regression and classification tasks and are described by an exponential amount of model parameters. Live-demos will show that such models can be learned efficiently and at the same time achieve state-of-the art performance on validation data.

Abstract
In this talk, I will present an efficient approach for counting roots of polynomial systems, where each polynomial is a general linear combination of fixed, prescribed polynomials. Our tools primarily rely on the theory of Khovanskii bases, combined with toric geometry.

I will demonstrate the application of this approach to the problem of counting the number of approximate stationary states for coupled Duffing oscillators. We have derived a Khovanskii basis for the corresponding polynomial system and determined the number of its complex solutions for an arbitrary degree of nonlinearity in the Duffing equation and an arbitrary number of oscillators. This is the joint work with Viktoriia Borovik, Mateusz Michalek, Javier del Pino, and Oded Zilberberg.

Everyone is welcome to attend in person.
The presentation will be streamed and can be followed by using this link: https://eu.bbcollab.com/guest/fc9cf8d95e2b43ffbc125adb60662444

Speaker: Professor Arjan Van der Schaft, University of Groningen

Title: Kron reduction of nonlinear networks

Abstract: Kron reduction is concerned with the elimination of interior nodes of physical network systems. Simplest example is an electrical circuit only containing linear resistors, where part of the nodes are boundary nodes (terminals). Elimination of the interior nodes results in a reduced electrical circuit with newly defined resistors between the terminals. This reduced network is equivalent to the original one in the sense of having the same voltage-current behavior at the terminals. Furthermore, by Maxwell’s minimum heat theorem the reduced network exhibits the same dissipated power. The Kron reduced network is obtained by computing a Schur complement of the Laplacian (or Kirchhoff) matrix of the network, which again defines a Laplacian matrix. Special case of Kron reduction is the computation of the effective resistance, where only two terminals are selected.In this talk we will consider Kron reduction of nonlinear networks, such as electrical circuits consisting of nonlinear resistors/conductors. Under two technical assumptions it will be shown how Kron reduction can still be performed, resulting in an equivalent nonlinear network. Key tool will be a function intrinsically defined by the network, whose Hessian matrix is again a Laplacian matrix, with weights depending on the variables of the network. A second application concerns the Kron reduction of memristor networks.

The MSCA European Training Networks SOUNDS and I-SPOT are jointly organizing this Seasonal School on "Machine Learning for Speech and Audio Processing". Targeting MSc and PhD students with a basic background in machine learning and a keen interest in audio, acoustics, and speech applications, this school aims to offer a timely overview of how machine learning has been shaping academic research as well as industry practice in these application domains.

The school consists of four course days, starting Monday April 8, 2024 up till and including Thursday April 11, 2024. The first course day will provide a recap of fundamentals of machine learning and deep learning, and each of the next three course days will zoom in on one of three applications areas: speech, audio, and acoustics. The primary course activity consists in guest lectures delivered by experts from academia and industry. Students who aim to develop a deeper understanding of the subject matter and a more intense interaction with other participants, can opt in for the practical sessions that will be organized Monday to Wednesday, and/or for the poster session on Thursday where they can present a research topic of their own choice.

https://www.sounds-etn.eu/index.php/4th-seasonal-school

Abstract: Achieving reliable performance in deep learning usually requires the ability of learning against label noise. This challenge is generally addressed by identifying incorrectly labelled instances through the memorization effect, wherein networks prioritize learning patterns from correctly labelled instances before memorizing incorrectly labelled data. However, these methods often encounter difficulties when faced with imbalanced datasets, a common scenario in real-world applications. This presentation dives into the reasons why existing methods may struggle with imbalanced datasets, attributing discrepancies in loss distribution among classes. Subsequently, the presentation provides some insights into strategies for addressing label noise in imbalanced dataset learning.

Abstract

A classical approach to solving polynomial systems is to linearize the problem and reduce it to an eigenvalue calculation. For this purpose, certain families of special matrices are used, e.g., Sylvester and Dixon matrices. Their size and structure determine how far these methods can go; therefore, it is essential to construct better matrices for the specific systems that arise in practice. In this talk, we focus on polynomial systems coming from the multiparameter eigenvalue problem and certain generalizations. Using the theory of resultants and Weyman complexes, we present new matrices of optimal size for solving these systems. This talk is based on joint work with Jean Charles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas.

Abstract: The diffusion model has recently gained considerable attention in the field of Generative Artificial Intelligence (GAI) and has showcased its potential to drive future AI innovations. This presentation will offer a concise overview of diffusion models, a breakthrough in generative AI that enables the production of high-quality, diverse outputs across various domains by refining random noise into structured patterns. The presentation will cover the fundamental principles of diffusion models, their advantages over other generative approaches, and their applications in cutting-edge technologies such as Dall-E and Sora. Through theoretical explanations and practical examples, we will demonstrate the versatility of diffusion models in generating images and text, among other tasks, underscoring their pivotal role in advancing creative and content generation technologies.

Abstract
Central in this talk is the so-called Macaulay matrix that arises in the problem of solving systems of polynomial equations. We discuss its algebraic properties and the computational challenges that one faces when computing its right null space. With the goal of designing asymptotically faster null space algorithms, we zoom-in on the (quasi-)Toeplitz structures of the matrix and examine how they may be exploited in computation. To this end, we review the theory of low-displacement rank matrices and particularly the Schur algorithm for Cauchy-like matrices developed by Gohberg, Kailath, and Olshevsky (GKO). We show that the GKO algorithm may be used to reduce the complexity of computing the Macaulay null space from O(dΣ^6) to O(dΣ^5) (where dΣ is the total degree of the polynomial equations) in the case of a (possibly overdetermined) bivariate polynomial system. This is achieved by computing a rank-revealing LU factorisation using a total pivoting strategy introduced by Ming Gu. We discuss several implementation issues to keep the algorithm fast and stable. Additionally, we also discuss extensions of the fast null space algorithm to polynomial systems expressed in the Chebyshev systems. The final part of the talk is dedicated to the challenges of extending the algorithm to systems of more than two variables. A key open problem that will be discussed is the lack-of-understanding of the displacement equation for a multi-level Toeplitz matrix and its properties under Gaussian elimination.

Everyone is welcome to attend in person.
The presentation will be streamed and can be followed by using this link: https://eu.bbcollab.com/guest/3cebcc23414f42b2b1d1cf23ab30c082

The slides and recordings of the previous seminars are available on our website.

13h00 – 13h30 Welcome Coffee 

13h30 – 14h15 Plenary Talk: “GC1: AI-driven Data Science”   

14h15 – 15h00 Responsible AI 

15h00 – 15h15 Q&A session 

15h15 -16h00 Poster Session + Coffee Break 

16h00 – 17h15 Breakout sessions: 

• BO1: Use cases - Health 

• BO2: Use cases - Health and Society 

• BO3: Use cases - Industry 

• BO4: Use cases – Planet, Energy & Society 

17h15 – 18h30 Networking + Drinks 

Registration 

Follow this link:  https://forms.gle/CuuGDXtG1gGGeSNRA 

The Einstein Telescope, a proposed next-generation gravitational-wave observatory, is expected to revolutionize the field of fundamental physics and astrophysics. With its unparalleled sensitivity, this detector has the potential to detect a million gravitational-wave events per year, including both known and new types of events. The talk will focus on the challenges encountered in analyzing and processing data from the observatory. It will provide an overview of the advanced techniques and algorithms necessary to extract valuable scientific information from the intricate and noisy signals captured by the detector.

Abstract

Polynomial optimization consists of minimizing a polynomial of many real variables subject to polynomial equality and inequality constraints. Its special case is the problem of finding real solutions of a system of polynomial equations. This difficult problem has many applications in fields such as statistics, signal processing, machine learning, computer vision, computational geometry, and control engineering. The Moment-SOS hierarchy is an approach to polynomial optimization that solves it globally at the price of solving a family of convex (semidefinite) optimization problems of increasing size. The lecture introduces the approach and describes its main milestones during the last two decades. The focus is on the computational features of the Moment-SOS hierarchy, its limitations and current efforts to overcome them.

Abstract

We present a fast and stable algorithm for computing roots of polynomials. The roots are found by computing the eigenvalues of the associated companion matrix. A companion matrix is an upper Hessenberg matrix that is of unitary-plus-rank-one form, that is, it is the sum of a unitary matrix and a rank-one matrix. When running Francis’s implicitly-shifted QR algorithm this property is preserved, and exactly that is exploited here.

To compactly store the matrix we will show that only 3n-1 rotators are required, so the storage space is O(n). In fact, these rotators only represent the unitary part, but we will show that we can retrieve the rank-one part from the unitary part with a trick. It is thus not necessary to store the rank-one part explicitly. Francis’s algorithm tuned for working on this representation requires only O(n) flops per iteration and thus O(n²) flops in total. The algorithm is normwise backward stable and is shown to be about as accurate as the (slow) Francis QR algorithm applied to the companion matrix without exploiting the structure. It is also faster than other O(n²) methods that have been proposed, and its accuracy is comparable or better.

The paper accompanying this research received SIAM’s outstanding paper prize in 2017.
https://www.siam.org/prizes-recognition/major-prizes-lectures/detail/siam-outstanding-paper-prizes

The representation of non-negative functions as sums of squares has become an important tool in many modeling and optimization tasks. Traditionally applied to polynomial functions, it requires rich tools from algebraic geometry that led to many developments in the last twenty years. In this lecture, I will look at this problem from a functional analysis point of view, leading to new applications and new results on the performance of sum-of-squares optimization.

This presentation is given in the framework of ERC project "Spikycontrol"

A small reception will follow this seminar. Please fill in the form if you plan to participate:

https://docs.google.com/forms/d/e/1FAIpQLSfYHdGlRhXHeMVQK2uUplJsksBYTjtG0oP87INcdLxXkO2s5A/viewform