Search results for "kernel"

2021

Fluctuation–dissipation relations or “theorems” (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to …

Efficient formulation of Multimode Equivalent Networks for 2-D waveguide steps through Kummer's transformation

2017

In this paper we present a new and improved formulation for the Multimode Equivalent Network (MEN) representation of arbitrary waveguide junctions. In the new formulation the Kummer's transformation is used to separate the kernel into dynamic and static parts, by introducing higher order extraction terms. The main difference with respect to the old formulation is that the approximation of the kernel is more accurate and the numerical computations are more efficient. In addition to theory, both formulations are compared in terms of efficiency and convergence thereby fully validating the proposed new formulation.

Analysis of compatibility between lighting devices and descriptive features using Parzen’s kernel: application to flaw inspection by artificial vision

2000

We present a supervised method, developed for industrial inspections by artificial vision, to obtain an adapted combination of descriptive features and a lighting device. This method must be implemented under real-time constraints and therefore a minimal number of features must be selected. The method is based on the assessment of the discrimination power of many descriptive features. The objective is to select the combination of descriptive features and lighting system best able to discriminate flawed classes from defect-free classes. In the first step, probability densities are computed for flawed and defect-free classes and for each tested combination. The discrimination power of the fea…

Multiplicative Loops of Quasifields Having Complex Numbers as Kernel

2017

We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to $$Spin_3({\mathbb {R}})$$ . Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.

Multiset Kernel CCA for multitemporal image classification

2013

The analysis of multitemporal remote sensing images is becoming an increasingly important problem because of the upcoming scenario of multispectral satellite constellations monitoring our Planet. Algorithms that can analyze such amount of heterogeneous information are necessary. While linear techniques have been extensively deployed, this work considers a kernel method that finds nonlinear correlations between all image sources and the class labels. We introduce in this context the Kernel Canonical Correlation Analysis (KCCA) to exploit the wealth of temporal image information and to handle nonlinear relations in a natural way via kernels. To achieve this goal, we use the generalization of …

Kernel intensity for space-time point processes with application to seismological problems

2010

Dealing with data coming from a space-time inhomogeneous process, there is often the need of semi-parametric estimates of the conditional intensity function; isotropic or anisotropic multivariate kernel estimates can be used, with windows sizes h. The properties of the intensities estimated with this choice of h are not always good for specific fields of application; we could try to choose h in order to have good predictive properties of the estimated intensity function. Since a direct ML approach cannot be followed, we propose an estimation procedure, computationally intensive, based on the subsequent increments of likelihood obtained adding an observation at time. The first results obtain…

Signal-to-noise ratio in reproducing kernel Hilbert spaces

2018

This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications}. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful signal-to-noise regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed inde…

Softness Kernel and Nonlinear Electronic Responses

2021

A nonlocal problem arising from heat radiation on non-convex surfaces

1997

We consider both stationary and time-dependent heat equations for a non-convex body or a collection of disjoint conducting bodies with Stefan-Boltzmann radiation conditions on the surface. The main novelty of the resulting problem is the non-locality of the boundary condition due to self-illuminating radiation on the surface. Moreover, the problem is nonlinear and in the general case also non-coercive. We show that the non-local boundary value problem admits a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. This result is then applied to prove existence under some hypotheses that guarantee the existence of sub- and…

Measurement of azimuthal asymmetries associated with deeply virtual Compton scattering on a longitudinally polarized deuterium target

2010

Azimuthal asymmetries in exclusive electroproduction of a real photon from a longitudinally polarized deuterium target are measured with respect to target polarization alone and with respect to target polarization combined with beam helicity and/or beam charge. The asymmetries appear in the distribution of the real photons in the azimuthal angle $\phi$ around the virtual photon direction, relative to the lepton scattering plane. The asymmetries arise from the deeply virtual Compton scattering process and its interference with the Bethe-Heitler process. The results for the beam-charge and beam-helicity asymmetries from a tensor polarized deuterium target with vanishing vector polarization ar…