Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
Perturbation Theory for Linear Operators
10 Pith papers cite this work. Polarity classification is still indexing.
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Provides theoretical conditions for bifurcations in interior transmission eigenvalues on general and radial domains, formulated as parametric nonlinear eigenproblems and tracked numerically with a match-based adaptive contour eigensolver.
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
The paper introduces matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions that achieves quadratic residual reduction for simple eigenvalues and includes cluster stabilization.
A spectral generalized covariance measure enables conditional independence testing on non-Euclidean data with uniform bootstrap validity and power guarantees under doubly robust conditions.
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.
Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.
citing papers explorer
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Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
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Bifurcations in Interior Transmission Eigenvalues: Theory and Computation
Provides theoretical conditions for bifurcations in interior transmission eigenvalues on general and radial domains, formulated as parametric nonlinear eigenproblems and tracked numerically with a match-based adaptive contour eigensolver.
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A Diagnostic Software Suite for Auditing Learned PDE Simulators
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
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Self-Reconstructing Codazzi Defects, $\mathbb{CP}^1$ Quantization, and the Minimal Standard-Model Carrier
A local reconstruction scheme for Codazzi defects in 4D Lorentzian branches uses a lexicographic residual and CP1 Toeplitz visibility to select the S(U(3)×U(2))/Z6 form and standard one-generation SM exterior package.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
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Iterative Refinement for Diagonalizable Non-Hermitian Eigendecompositions
The paper introduces matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions that achieves quadratic residual reduction for simple eigenvalues and includes cluster stabilization.
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Testing Conditional Independence via the Spectral Generalized Covariance Measure: Beyond Euclidean Data
A spectral generalized covariance measure enables conditional independence testing on non-Euclidean data with uniform bootstrap validity and power guarantees under doubly robust conditions.
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Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
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Sum rules and a second order Feynman-Hellman theorem for abstract operators with applications
Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.
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Smoothing of operator semigroups under relatively bounded perturbations
Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.