Related papers: Delocalization transition for the Google matrix
The rise of social media and recommendation algorithms has sparked concerns about their role in fostering opinion polarization and echo chambers. We study these phenomena using an adaptive voter model to compare two connection mechanisms:…
The effect of regularizers such as weight decay when training deep neural networks is not well understood. We study the influence of weight decay as well as $L2$-regularization when training neural network models in which parameter matrices…
This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents.…
We consider $N\times N$ Hermitian random band matrices $H=(H_{xy})$, whose entries are centered complex Gaussian random variables. The indices $x,y$ range over the $d$-dimensional discrete torus $(\mathbb Z/L\mathbb Z)^d$ with $d\in…
The evolution of information-seeking processes, driven by search engines like Google, has transformed the access to information people have. This paper investigates how individuals' preexisting attitudes influence the modern…
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…
Time series forecasting is vital in many real-world applications, yet developing models that generalize well on unseen relevant domains -- such as forecasting web traffic data on new platforms/websites or estimating e-commerce demand in new…
The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…
A new characterization of the Anderson phase transition, based on the response of the system to the boundary conditions is introduced. We change the boundary conditions from periodic to antiperiodic and look for its effects on the…
In this paper, we consider a problem of learning supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank algorithm. Due to huge hidden dimension of the…
We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other…
We propose a dynamical system that captures changes to the network centrality of nodes as external interest in those nodes vary. We derive this system by adding time-dependent teleportation to the PageRank score. The result is not a single…
Reranking, as the final stage of multi-stage recommender systems, refines the initial lists to maximize the total utility. With the development of multimedia and user interface design, the recommendation page has evolved to a multi-list…
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a…
Web-enabled LLM agents are changing how online information influences search outcomes. \ Existing Generative Engine Optimization (GEO) studies mainly focus on individual webpages. \ However, agentic web search is not a single-document…
The Airbnb search system grapples with many unique challenges as it continues to evolve. We oversee a marketplace that is nuanced by geography, diversity of homes, and guests with a variety of preferences. Crafting an efficient search…