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We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly,…

Physics and Society · Physics 2009-07-03 Xiaofeng Gong , Shuguang Guan , C. -H. Lai

This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…

Quantum Physics · Physics 2024-09-04 William Kirby

Network inference, the task of reconstructing interactions in a complex system from experimental observables, is a central yet extremely challenging problem in systems biology. While much progress has been made in the last two decades,…

Quantitative Methods · Quantitative Biology 2024-09-12 Stephen Y Zhang

Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…

Numerical Analysis · Mathematics 2016-08-09 Daniel Stone , Gabriel Lord

Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…

Machine Learning · Computer Science 2018-11-21 Kar-Ann Toh

In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to…

Optimization and Control · Mathematics 2022-08-09 Mohammad Pirani , Saber Jafarpour

We present a novel data-driven reformulation of the iterative SVD-rational Krylov algorithm (ISRK), in its original formulation a Petrov-Galerkin (two-sided) projection-based iterative method for model reduction combining rational Krylov…

Numerical Analysis · Mathematics 2024-07-19 Ion Victor Gosea , Serkan Gugercin , Christopher Beattie

Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…

Disordered Systems and Neural Networks · Physics 2015-05-30 Dane Taylor , Juan G. Restrepo

Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…

Methodology · Statistics 2021-12-07 Suman Majumder , Yawen Guan , Brian J. Reich , Arvind K. Saibaba

Compared with relational database (RDB), graph database (GDB) is a more intuitive expression of the real world. Each node in the GDB is a both storage and logic unit. Since it is connected to its neighboring nodes through edges, and its…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-09-06 Chen Yuan , Guangyi Liu , Renchang Dai , Zhiwei Wang

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a…

Optimization and Control · Mathematics 2019-10-01 Yue Chen , Andrey Bernstein , Adithya Devraj , Sean Meyn

We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying…

Social and Information Networks · Computer Science 2020-07-14 William Brown , Utkarsh Patange

The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour integration in the complex plane to obtain the eigenvectors of a matrix for the eigenvalues that are located in any user-defined search interval. By…

Numerical Analysis · Mathematics 2017-06-05 Brendan Gavin , Eric Polizzi

We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…

Materials Science · Physics 2008-02-07 Takeo Fujiwara , Takeo Hoshi , Susumu Yamamoto

Integration of Inverter Based Resources (IBRs) which lack the intrinsic characteristics such as the inertial response of the traditional synchronous-generator (SG) based sources presents a new challenge in the form of analyzing the grid…

Optimization and Control · Mathematics 2024-07-31 Satish Vedula , Ayobami Olajube , Olugbenga Anubi

We study iterative methods based on Krylov subspaces for low-rank approximation under any Schatten-$p$ norm. Here, given access to a matrix $A$ through matrix-vector products, an accuracy parameter $\epsilon$, and a target rank $k$, the…

Data Structures and Algorithms · Computer Science 2022-06-20 Ainesh Bakshi , Kenneth L. Clarkson , David P. Woodruff

Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16)…

Numerical Analysis · Mathematics 2025-05-28 Kengo Suzuki , Takeshi Iwashita

We study the dynamics of matrix-valued time series with observed network structures by proposing a matrix network autoregression model with row and column networks of the subjects. We incorporate covariate information and a low rank…

Methodology · Statistics 2023-02-07 Xuening Zhu , Feifei Wang , Zeng Li , Yanyuan Ma

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

Numerical Analysis · Mathematics 2022-02-17 Eda Oktay , Erin Carson

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two…

Machine Learning · Computer Science 2020-01-07 Colin Graber , Alexander Schwing