This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...
We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...
Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...
This paper considers the problem of second-degree price discrimination when the type distribution is unknown or imperfectly specified by means of an ambiguity set. As robustness measure we use a performance index, equivalent to relative regret, which quant ...
Factored form is a powerful multi-level representation of a Boolean function that readily translates into an implementation of the function in CMOS technology. In particular, the number of literals in a factored form correlates strongly with the number of ...
Description (through texts, images, models or samples) played a central role in the patent regimes that emerged in the eighteenth century, first in England, later in the United States and in France. Description ensured that the contract—protection in excha ...
We consider the problem of compressing an information source when a correlated one is available as side information only at the decoder side, which is a special case of the distributed source coding problem in information theory. In particular, we consider ...
Cyclopentadienyl (Cp) metal complexes and their chiral counterparts (CpX) have enabled the development of challenging C-H activation transformations. While major progresses were made in developing new chiral CpX complexes and exploring their reactivity, th ...
Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...
With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion fo ...
We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desi ...
Current machine learning models for vision are often highly specialized and limited to a single modality and task. In contrast, recent large language models exhibit a wide range of capabilities, hinting at a possibility for similarly versatile models in co ...
This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the ...
We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...
In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...
Starting from a strong Lattice-Free Maximum Mutual Information (LF-MMI) baseline system, we explore different autoencoder configurations to enhance Mel-Frequency Cepstral Coefficients (MFCC) features. Autoencoders are expected to generate new MFCC features ...
