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Effective Dimensionality Reduction Using Kernel Locality Preserving Partial Least Squares Discriminant Analysis
Partial least squares discriminant analysis (PLS-DA) is one the popular tool for the analysis of data in chemometrics and bioinformatics. As a...
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On Orbits of 4-Dimensional Representations of 3-Dimensional Solvable Lie Algebras
AbstractIn a 4-dimensional real space, we discuss linearly homogeneous hypersurfaces that are the orbits of 3-dimensional solvable Lie algebras. A...
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Development and analysis of massive parallelization of a lattice basis reduction algorithm
The security of lattice-based cryptography relies on the hardness of solving lattice problems. Lattice basis reduction is a strong tool for solving...
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Registration-Based Model Reduction in Complex Two-Dimensional Geometries
We present a general—i.e., independent of the underlying equation—egistration procedure for parameterized model order reduction. Given the spatial...
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The Odd-Dimensional Surgery Obstruction
It turns out that the problem in this case is both harder and easier than in the even-dimensional case. It is harder because the algebra that...
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Reduction to a One-Body Problem
In this chapter we show that the spectral analysis of a generalized N-body operator H near a two-cluster threshold can be reduced to the analysis of...
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Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances
The present paper considers the quantum scattering problem for three one-dimensional particles with pair Coulomb repulsion potentials at large...
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Coarse-grid operator optimization in multigrid reduction in time for time-dependent Stokes and Oseen problems
Multigrid reduction in time (MGRIT), one of the most popular parallel-in-time approaches, extracts temporal parallelism by constructing coarse grids...
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Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators RAMSES
This volume is focused on the review of recent algorithmic and mathematical advances and the development of new research directions for Mathematical...
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Global-local multiscale model reduction using GMsFEM
Our previous studies focused on local model reduction techniques. In these approaches, we develop local (space and time) reduced-order models to...
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A theory for three-dimensional response of micropolar plates
Through combined applications of the transfer-matrix method and asymptotic expansion technique, we formulate a theory to predict the...
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Advanced Stochastic Monte Carlo Optimization Methods for Two-Dimensional European Style Options
Multidimensional option pricing poses significant challenges and is a fundamental area in large-scale finance. A European call option grants the...
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Model Order Reduction for Optimal Control Problems
These lecture notes comprise lectures on Model Order Reduction (MOR) for optimal control problems which were given by the author within the CIME...
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Silting Reduction in Exact Categories
Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently, which are generalizations of...
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A Factor-GARCH Model for High Dimensional Volatilities
This paper proposes a method for modelling volatilities (conditional covariance matrices) of high dimensional dynamic data. We combine the ideas of...
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Dictionary-based model reduction for state estimation
We consider the problem of state estimation from a few linear measurements, where the state to recover is an element of the manifold
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High-dimensional robust inference for censored linear models
Due to the direct statistical interpretation, censored linear regression offers a valuable complement to the Cox proportional hazards regression in...
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Integrable (3 + 1)-Dimensional Generalization for the Dispersionless Davey–Stewartson System
This paper introduces a (3 + 1)-dimensional dispersionless integrable system, utilizing a Lax pair involving contact vector fields, in alignment with...
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Machine Learning Classification and Reduction of CAD Parts
We demonstrate machine learning methods to reduce bottlenecks in CAD-to-simulation workflows for critical analysis. Classification of common...