This paper deals with the application of the support vector machine (SVM) and the leastsquares SVM regressions to the uncertainty quantification of complex systems with a high-dimensional parameter space. The above regression techniques are used to build accurate and compact surrogate models of the system responses from a limited set of training samples. The accuracy and the feasibility of the proposed modeling techniques are then investigated by comparing their results with the ones predicted by a sparse polynomial chaos expansion by considering two real-life problems with 8 and 30 random variables, respectively. INDEX TERMS Machine learning, uncertainty quantification, parameterized modeling, surrogate models, SVM regression, LS-SVM regression, sparse PC expansion, integrated voltage regulator (IVR), wireless power transfer (WPT). I. INTRODUCTION

Simultaneous PET/MR/EEG (Positron Emission Tomography - Magnetic Resonance - Electroencephalography), a new tool for the investigation of neuronal networks in the human brain, is presented here within the framework of the European Union Project TRIMAGE. The trimodal, cost-effective PET/MR/EEG imaging tool makes use of cutting edge technology both in PET and in MR fields. A novel type of magnet (1.5T, non-cryogenic) has been built together with a PET scanner that makes use of the most advanced photodetectors (i.e., SiPM matrices), scintillators matrices (LYSO) and digital electronics. The combined PET/MR/EEG system is dedicated to brain imaging and has an inner diameter of 260 mm and an axial Field-of-View of 160 mm. It enables the acquisition and assessment of molecular metabolic information with high spatial and temporal resolution in a given brain simultaneously. The dopaminergic system and the glutamatergic system in schizophrenic patients are investigated via PET, the same physiological/pathophysiological conditions with regard to functional connectivity, via fMRI, and its electrophysiological signature via EEG. In addition to basic neuroscience questions addressing neurovascular-metabolic coupling, this new methodology lays the foundation for individual physiological and pathological fingerprints for a wide research field addressing healthy aging, gender effects, plasticity and different psychiatric and neurological diseases. The preliminary performances of two components of the imaging tool (PET and MR) are discussed. Initial results of the search of possible candidates for suitable schizophrenia biomarkers are also presented as obtained with PET/MR systems available to the collaboration.

This letter addresses the simulation of the steadystate response of switching power converters. The proposed approach is based on the interpretation of the voltage and current variables of a periodically switched linear circuit in terms of a series expansion and on the generation of augmented timeinvariant constitutive relations of the circuit elements. The circuit solution is obtained from an augmented time-invariant nodal equation generated from topological information and circuit inspection only. The feasibility and strength of the approach are demonstrated on a DC-DC boost converter.

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time-and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.

This paper presents an alternative solution for the power-flow analysis of power systems with distributed generation provided by heterogeneous sources. The proposed simulation approach relies on a suitable interpretation of the power network in terms of a nonlinear circuit in the phasor domain. The above circuit interpretation can be solved directly in the frequency-domain via the combination of a standard tool for circuit analysis with an iterative numerical scheme, providing directly the steady-state solution of the power-flow of a generic distribution network. At each iteration, the resulting circuit turns out to be composed by two decoupled subnetworks, a large linear part and a set of smaller nonlinear pieces accounting for the load characteristics, with evident benefits in terms of the computational time. The feasibility and strength of the proposed simulation scheme have been verified on a large benchmark consisting of the IEEE 8500-node test feeder. Then it is applied to the statistical simulation of a power network accounting for the variability effects of renewable generators. According to the results, the proposed tool provides an effective alternative to the state-of-the-art approaches for power-flow analysis further highlighting the benefits of the application of well-established tools for circuit analysis to power-flow problems.