A guaranteed-convergence framework for passivity enforcement of linear macromodels

Passivity enforcement is a key step in the extraction of linear macromodels of electrical interconnects and packages for Signal and Power Integrity applications. Most state-of-the-art techniques for passivity enforcement are based on suboptimal or approximate formulations that do not guarantee convergence. We introduce in this paper a new rigorous framework that casts passivity enforcement as a convex non-smooth optimization problem. Thanks to convexity, we are able to prove convergence to the optimal solution within a finite number of steps. The effectiveness of this approach is demonstrated through various numerical example

Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels

This paper presents a class of nonsmooth convex optimization methods for the passivity enforcement of reduced-order macromodels of electrical interconnects, packages, and linear passive devices. Model passivity can be lost during model extraction or identification from numerical field solutions or direct measurements. Nonpassive models may cause instabilities in transient system-level simulation, therefore a suitable postprocessing is necessary in order to eliminate any passivity violations. Different from leading numerical schemes on the subject, passivity enforcement is formulated here as a direct frequency-domain ${{cal H}_infty}$ norm minimization through perturbation of the model state-space parameters. Since the dependence of this norm on the parameters is nonsmooth, but continuous and convex, we resort to the use of subdifferentials and subgradients, which are used to devise two different algorithms. We provide a theoretical proof of the global optimality for the solution computed via both schemes. Numerical results confirm that these algorithms achieve the global optimum in a finite number of iterations within a prescribed accuracy leve

Robust localization methods for passivity enforcement of linear macromodels

In this paper we solve a non-smooth convex formulation for passivity enforcement of linear macromodels using robust localization based algorithms such as the ellipsoid and the cutting plane methods. Differently from existing perturbation based techniques, we solve the formulation based on the direct ℌ∞ norm minimization through perturbation of state-space model parameters. We provide a systematic way of defining an initial set which is guaranteed to contain the global optimum. We also provide a lower bound on the global minimum, that grows tighter at each iteration and hence guarantees δ - optimality of the computed solution. We demonstrate the robustness of our implementation by generating accurate passive models for challenging examples for which existing algorithms either failed or exhibited extremely slow convergenc

Quantum spin Hall effect in bound states in continuum

Moving the polarization of the incident wave along a meridian of the Poincaré sphere, experimentally we show that the coupling with the fundamental Bloch's surface waves of the mode, provide a spatially coherent, macroscopic spinmomentum locked propagation along the symmetry axes of the PhCM. This novel mechanism of light-spin manipulation enables a versatile implementation of spin-optical structures that may pave the way to novel strategies for light spin technology and photonic multiplatform implementations

A review of the role of ultrasound biomicroscopy in glaucoma associated with rare diseases of the anterior segment

Ultrasound biomicroscopy is a non-invasive imaging technique, which allows high-resolution evaluation of the anatomical features of the anterior segment of the eye regardless of optical media transparency. This technique provides diagnostically significant information in vivo for the cornea, anterior chamber, chamber angle, iris, posterior chamber, zonules, ciliary body, and lens, and is of great value in assessment of the mechanisms of glaucoma onset. The purpose of this paper is to review the use of ultrasound biomicroscopy in the diagnosis and management of rare diseases of the anterior segment such as mesodermal dysgenesis of the neural crest, iridocorneal endothelial syndrome, phakomatoses, and metabolic disorders

Data-driven extraction of uniformly stable and passive parameterized macromodels

A Robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we solve the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either overconservative or heuristic and possibly unreliable methods

Convex Passivity Enforcement of Linear Macromodels via Alternate Subgradient Iterations

This paper introduces a new algorithm for passivity enforcement of linear lumped macromodels in scattering form. As typical in most state of the art passivity enforcement methods, we start with an initial non-passive macromodel obtained by a Vector Fitting process, and we perturb its parameters to make it passive. The proposed scheme is based on a convex formulation of both passivity constraints and objective function for accuracy preservation, thus allowing a formal proof of convergence to the unique optimal passive macromodel. This is a distinctive feature that differentiates the new scheme with respect to most state of the art methods, which either do not guarantee convergence or are not able to provide the most accurate solution. The presented algorithm can thus be safely used for those cases for which existing techniques fail. We illustrate the advantages of proposed method on a few benchmarks

Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions

We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is asymptotically necessary and sufficient. Our results are also generalized to detect all different types of multipartite entanglement.Comment: 4 pages, 2 figures, submitted to Physical Review Letters. Revised version with new calculation

From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving

Survival and Neural Models for Private Equity Exit Prediction

Within the Private Equity (PE) market, the event of a private company undertaking an Initial Public Offering (IPO) is usually a very high-return one for the investors in the company. For this reason, an effective predictive model for the IPO event is considered as a valuable tool in the PE market, an endeavor in which publicly available quantitative information is generally scarce. In this paper, we describe a data-analytic procedure for predicting the probability with which a company will go public in a given forward period of time. The proposed method is based on the interplay of a neural network (NN) model for estimating the overall event probability, and Survival Analysis (SA) for further modeling the probability of the IPO event in any given interval of time. The proposed neuro-survival model is tuned and tested across nine industrial sectors using real data from the Thomson Reuters Eikon PE database