Related papers: Two minicourses on analytic microlocal analysis
The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare…
These are notes for a mini-course given at the summer school and conference "The Six-Functor Formalism and Motivic Homotopy Theory" in Milan 9/2021. They provide an introduction to the formalism of Grothendieck's six operations in algebraic…
The objective of this Ph.D. thesis is the implementation of the Worldline Formalism in the frame of Noncommutative Quantum Field Theories. The result is a master formula for the 1-loop effective action that is applied to a number of scalar…
This article is a short survey of the history of functional analysis for topologists.
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…
Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the paper…
The broad adoption of machine learning (ML)-based automated and autonomous experiments (AE) in physical characterization and synthesis requires development of strategies for understanding and intervention in the experimental workflow. Here,…
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA),…
Dynamic analysis enables detecting Windows malware by executing programs in a controlled environment and logging their actions. Previous work has proposed training machine learning models, i.e., convolutional and long short-term memory…
This report provides a summary of the outcomes of the Interdisciplinary Workshop on Mechanical Intelligence held in 2024. Mechanical Intelligence (MI) represents the phenomenon that novel structural features of material/biological/robotic…
This volume contains the papers presented at the 1st workshop on Quantitative Formal Methods: Theory and Applications, which was held in Eindhoven on 3 November 2009 as part of the International Symposium on Formal Methods 2009. This volume…
These notes give a brief introduction to differential Harnack inequalities and summarise the main results of the mini-course ``Li-Yau and Harnack estimates for nonlocal diffusion problems'', presented by the author at the Seasonal School on…
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…
We present NanoFlux, a novel adversarial framework for generating targeted training data to improve LLM reasoning, where adversarially-generated datasets containing fewer than 200 examples outperform conventional fine-tuning approaches. The…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
Meta-analysis employs statistical techniques to synthesize the results of individual studies, providing an estimate of the overall effect size for a specific outcome of interest. The direction and magnitude of this estimate, along with its…
The Macroscopic Fundamental Diagram is a popular tool used to describe traffic dynamics in an aggregated way, with applications ranging from traffic control to incident analysis. However, estimating the MFD for a given network requires…
Cortical minicolumns are considered a model of cortical organization. Their function is still a source of research and not reflected properly in modern architecture of nets in algorithms of Artificial Intelligence. We assume its function…
Agentic Al systems are increasingly deployed as personal assistants and are likely to become a common object of digital investigations. However, little is known about how their internal state and actions can be reconstructed during forensic…