Related papers: Lecture Notes on Spectral Graph Methods
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
This material complements David Chandler's Introduction to Modern Statistical Mechanics (Oxford University Press, 1987) in a graduate-level, one-semester course I teach in the Department of Chemistry at Duke University. Students enter this…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…
Graph-structured data commonly have node annotations. A popular approach for inference and learning involving annotated graphs is to incorporate annotations into a statistical model or algorithm. By contrast, we consider a more direct…
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…
Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and…
These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.
We present a review of the status of $W$ string theories, their physical spectra, and their interactions. (Based on review talks given at the Trieste Spring Workshop, and the Strings 93 meeting at Berkeley, May 1993.)
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman's graduate statistical mechanics course at Berkeley from the 1972-1973 academic year. Part 1 addresses equilibrium statistical mechanics with topics:…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation,…
We propose to study the problem of few shot graph classification in graph neural networks (GNNs) to recognize unseen classes, given limited labeled graph examples. Despite several interesting GNN variants being proposed recently for node…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
These notes are based on some lectures that the author gave at the University of Campinas - UNICAMP. The notes are in Portuguese, and deal with some methods of mathematics applied to Fluid Mechanics.