Latest Research
Fast randomized algorithms for low-rank matrix approximations with applications in global comparative analysis of a class of data sets
Generalized singular values (GSVs) play an essential role in the comparative analysis.
Numerical Analysis Numerical Analysis
Asymptotics in infinite monoidal categories
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories.
Category Theory Combinatorics Representation Theory Primary: 11N45, 18M05, Secondary: 05C81, 15A18, 20C20
Orbits of Theta Characteristics
The theta characteristics on a Riemann surface are permuted by the induced action of the automorphism group, with the orbit structure being important for the geometry of the curve and associated manifolds.
Algebraic Geometry 14H37, 14Q05, 14H60, 20J06
Efficient discretization of the Laplacian on complex geometries
Semi-discrete stability using the new Laplace operator is proven for the acoustic wave equation in 2D.
Numerical Analysis Numerical Analysis
Asynchronous Heterogeneous Linear Quadratic Regulator Design
We address the problem of designing an LQR controller in a distributed setting, where M similar but not identical systems share their locally computed policy gradient (PG) estimates with a server that aggregates the estimates and computes a controller that, on average, performs well on all systems.
Optimization and Control
Improving Autoencoder Image Interpolation via Dynamic Optimal Transport
xue1993/dynamic-optimal-transport
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Autoencoders are important generative models that, among others, have the ability to interpolate image sequences.
Optimization and Control
Complex variable solution on over-/under-break shallow tunnelling in gravitational geomaterial with reasonable far-field displacement
With integration of a newly proposed bidirectional composite conformal mapping using Charge Simulation Method, a complex variable solution of infinite complex potential series is subsequently derived using analytic continuation to tranform the mixed boundaries into a homogenerous Riemann-Hilbert problem, which is iteratively solved to obtain the stress and displacement in geomaterial.
Numerical Analysis Numerical Analysis Complex Variables
A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph.
Optimization and Control
Bootstrap percolation is local
We show that for two of the most classical models, two-neighbour and Frob\"ose, upper bounds are sharp to essentially arbitrary precision, by linking them to their local counterparts.
Probability Statistical Mechanics Mathematical Physics Combinatorics Mathematical Physics 60C05, 60K35 (Primary) 82C20, 60-04, 60-08, 60F10, 15A12 (Secondary)
EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics
To demonstrate the potential of the approach, we address the identification of a linear non-autonomous system consisting of a shear building model excited by real seismograms, and the identification of a partially observed nonlinear system.
Dynamical Systems Systems and Control Systems and Control
