Related papers: Time-Frequency Analysis (Lecture Notes)

Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…

The article is a lightly edited version of my habilitation thesis at the University Wuerzburg. My aim is to give a self contained, if concise, introduction to the formal methods used when off-line learning in feedforward networks is…

These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern…

Oscillatory processes are central for the understanding of the neural bases of cognition and behaviour. To analyse these processes, time-frequency (TF) decomposition methods are applied and non-parametric cluster-based statistical procedure…

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in…

Event data is present in a variety of domains such as electronic health records, daily living activities and web clickstream records. Current visualization methods to explore event data focus on discovering sequential patterns but present…

These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.

Notes from a course taught by Palle Jorgensen in the fall semester of 2009. The course covered central themes in functional analysis and operator theory, with an emphasis on topics of special relevance to such applications as representation…

Temporal difference (TD) learning is an important approach in reinforcement learning, as it combines ideas from dynamic programming and Monte Carlo methods in a way that allows for online and incremental model-free learning. A key idea of…

These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.

Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…

Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…

This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material is mainly based on the two books of the lecturer, one…

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…

These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…

This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency…

In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…

The Fourier Transform (FT) is a fundamental tool that permeates modern science and technology. While chemistry undergraduates encounter the FT as early as second year, their courses often only mention it in passing because computers…