This paper 1 presents a practical, and theoretically well-founded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with integral operators, we propose Reduced Set KPCA (RSKPCA), which also suggests an easy-to-implement method to remove or replace samples with minimal effect on the ...

This paper presents a practical, and theoretically wellfounded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with integral operators, we propose Reduced Set KPCA (RSKPCA), which also suggests an easy-toimplement method to remove or replace samples with minimal effect on the empi...

A convolutionless equation of motion for the reduced density matrix of a system coupled to its environment, where the system1 environment is closed, may be obtained using a projection-operator technique. We show that, when both the system and the environment Hilbert spaces are finite-dimensional, it is possible to eliminate the need for the partial trace over the environment states by construct...

Exact and nonperturbative quantum master equation can be constructed via the calculus on path integral. It results in hierarchical equations of motion for the reduced density operator. Involved are also a set of well– defined auxiliary density operators that resolve not just system–bath coupling strength but also memory. In this work, we scale these auxiliary operators individually to achieve a...

The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of ‘proper’ versus ‘improper’ separability is proposed to mark the distinction. 1 Proper and Improper mixtures In many discussions of the measurement problem in quant...

An exact and nonperturbative quantum master equation can be constructed via the calculus on the path integral. It results in hierarchical equations of motion for the reduced density operator. Involved also are a set of well-defined auxiliary density operators that resolve not just the system–bath coupling strength but also memory. In this work, we scale these auxiliary operators individually to...

In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and ca...

We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov a...

The expectation values of a hermitean operator  in (2s+1) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other (2s + 1) coherent states also provide a basis for selfadjoint operators. This is proven by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious c...

We construct a (0, 2), D = 2 gauged linear sigma model on a supermanifold in both the Abelian gauge group and the non-Abelian gauge group. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operatorˆU for the Abelian gauge group. Thê U operator provides consistency conditions for satisfying the SUSY invariance. C...