Graph-based Methods for Visualization and Clustering

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In decentralized optimization, nodes of a communication network each possess a local objective function, and communicate using gossip-based methods in order to minimize the average of these per-node functions. While synchronous algorithms are heavily impac ...

Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements in the model capabilities. Yet, a theoretical characterization of how such mecha ...

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Water distribution systems (WDSs) are complex networks with numerous interconnected junctions and pipes. The robustness and reliability of these systems are critically dependent on their network structure, necessitating detailed analysis for proactive leak ...

This article focuses on spectral methods for recovering communities in temporal networks. In the case of fixed communities, spectral clustering on the simple time-aggregated graph (i.e., the weighted graph formed by the sum of the interactions over all tem ...

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interact ...

Technology mapping transforms a technology-independent representation into a technology-dependent one given a library of cells. This process is performed by means of local replacements that are extracted by matching sections of the subject graph to library ...

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

Dataset corresponding to the following manuscript: Slagter, A., Setyadji, J.A., Vogt, E.L. et al. Nanoindentation Hardness and Modulus of Al2O3–SiO2–CaO and MnO–SiO2–FeO Inclusions in Iron. Metall Mater Trans A (2024). https://doi.org/10.1007/s11661-024-0 ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

We propose a comparative study of three different methods aimed at optimizing existing groundwater monitoring networks. Monitoring piezometric heads in subsurface porous formations is crucial at regional scales to properly characterize the relevant subsurf ...

Translation elongation plays an important role in regulating protein concentrations in the cell, and dysregulation of this process has been linked to several human diseases. In this study, we use data from ribo-seq experiments to model ribosome densities, ...

This article presents a portfolio construction approach that combines the hierarchical clustering of a large asset universe with the stock price momentum. On one hand, investing in high-momentum stocks enhances returns by capturing the momentum premium. On ...

Graph-based Methods for Visualization and Clustering

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Asynchronous Speedup in Decentralized Optimization

A phase transition between positional and semantic learning in a solvable model of dot-product attention

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Non-planarity of Markoff graphs mod p

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Towards an Understanding of Hydraulic Sensitivity: Graph Theory Contributions to Water Distribution Analysis

Recovering Static and Time-Varying Communities Using Persistent Edges

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Spectral Estimators for High-Dimensional Matrix Inference

Interpret3C: Interpretable Student Clustering Through Individualized Feature Selection

Graph generative deep learning models with an application to circuit topologies

Network-based kinetic models: Emergence of a statistical description of the graph topology

In Medio Stat Virtus: Combining Boolean and Pattern Matching

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Nanoindentation hardness and modulus of Al2O3-SiO2-CaO and MnO-SiO2-FeO inclusions in iron

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Data-driven statistical optimization of a groundwater monitoring network

Towards improving full-length ribosome density prediction by bridging sequence and graph-based representations

Portfolio Construction with Hierarchical Momentum