arXiv subjects

Giuseppe Calafiore

Publications and source records attributed to Giuseppe Calafiore.

15 recordsLinked to original sources

arXiv2025

A Robust Optimization Model for Cost-Efficient and Fast Electric Vehicle Charging with L2-norm Uncertainty

In this paper, we propose a robust optimization model that addresses both the cost-efficiency and fast charging requirements for electric vehicles (EVs) at charging stations. By combining elements from traditional cost-minimization models and a fast charging objective, we construct an optimization model that balances user costs with rapid power allocation. Additionally, we incorporate L2-norm uncertainty into the charging cost, ensuring that the model remains resilient under cost fluctuations. The proposed model is tested under real-world scenarios and demonstrates its potential for efficient and flexible EV charging solutions.

eess.SY↗

arXiv2024

Flat panel laser displays enabled by large-scale visible photonic integrated circuits

Laser-based displays are highly sought after for their superior brightness and color performance, especially in advanced applications like augmented reality (AR). However, their broader adoption has been hindered by bulky projector designs and complex optical module assemblies. Here, we introduce a new laser display architecture enabled by large-scale visible photonic integrated circuits (PICs) to address these challenges. Unlike previous projector-style laser displays, this architecture features an ultra-thin, flat-panel form factor, replacing bulky free-space illumination modules with a single, high-performance photonic chip. Centimeter-scale PIC devices, which integrate thousands of distinct optical components on-chip, are carefully tailored to achieve high display uniformity, contrast, and efficiency. We demonstrate a 2 mm-thick flat-panel laser display combining the PIC with a liquid-crystal-on-silicon (LCoS) panel, achieving 211% of the color gamut and more than 80% volume reduction compared to traditional LCoS displays. We further showcase its application in a see-through AR system. Our work represents a major advancement in the integration of nanophotonics with display technology, enabling a range of new display concepts, from high-performance immersive displays to slim-panel 3D holography.

physics.optics↗

arXiv2024

Optimizing electric vehicles charging through smart energy allocation and cost-saving

As the global focus on combating environmental pollution intensifies, the transition to sustainable energy sources, particularly in the form of electric vehicles (EVs), has become paramount. This paper addresses the pressing need for Smart Charging for EVs by developing a comprehensive mathematical model aimed at optimizing charging station management. The model aims to efficiently allocate the power from charging sockets to EVs, prioritizing cost minimization and avoiding energy waste. Computational simulations demonstrate the efficacy of the mathematical optimization model, which can unleash its full potential when the number of EVs at the charging station is high.

math.OC↗

arXiv2024

Default Resilience and Worst-Case Effects in Financial Networks

In this paper we analyze the resilience of a network of banks to joint price fluctuations of the external assets in which they have shared exposures, and evaluate the worst-case effects of the possible default contagion. Indeed, when the prices of certain external assets either decrease or increase, all banks exposed to them experience varying degrees of simultaneous shocks to their balance sheets. These coordinated and structured shocks have the potential to exacerbate the likelihood of defaults. In this context, we introduce first a concept of {default resilience margin}, $\epsilon^*$, i.e., the maximum amplitude of asset prices fluctuations that the network can tolerate without generating defaults. Such threshold value is computed by considering two different measures of price fluctuations, one based on the maximum individual variation of each asset, and the other based on the sum of all the asset's absolute variations. For any price perturbation having amplitude no larger than $\epsilon^*$, the network absorbs the shocks remaining default free. When the perturbation amplitude goes beyond $\epsilon^*$, however, defaults may occur. In this case we find the worst-case systemic loss, that is, the total unpaid debt under the most severe price variation of given magnitude. Computation of both the threshold level $\epsilon^*$ and of the worst-case loss and of a corresponding worst-case asset price scenario, amounts to solving suitable linear programming problems.}

q-fin.RM↗

arXiv2022

Control of Dynamic Financial Networks (The Extended Version)

The current global financial system forms a highly interconnected network where a default in one of its nodes can propagate to many other nodes, causing a catastrophic avalanche effect. In this paper we consider the problem of reducing the financial contagion by introducing some targeted interventions that can mitigate the cascaded failure effects. We consider a multi-step dynamic model of clearing payments and introduce an external control term that represents corrective cash injections made by a ruling authority. The proposed control model can be cast and efficiently solved as a linear program. We show via numerical examples that the proposed approach can significantly reduce the default propagation by applying small targeted cash injections.

math.OC↗

arXiv2021

COVID-19 case data for Italy stratified by age class

The dataset described in this paper contains daily data about COVID-19 cases that occurred in Italy over the period from Jan. 28, 2020 to March 20, 2021, divided into ten age classes of the population, the first class being 0-9 years, the tenth class being 90 years and over. The dataset contains eight columns, namely: date (day), age class, number of new cases, number of newly hospitalized patients, number of patients entering intensive care, number of deceased patients, number of recovered patients, number of active infected patients. This data has been officially released for research purposes by the Italian authority for COVID-19 epidemiologic surveillance (Istituto Superiore di Sanità - ISS), upon formal request by the authors, in accordance with the Ordonnance of the Chief of the Civil Protection Department n. 691 dated Aug. 4 2020. A separate file contains the numerosity of the population in each age class, according to the National Institute of Statistics (ISTAT) data of the resident population of Italy as of Jan. 2020. This data has potential use, for instance, in epidemiologic studies of the effects of the COVID-19 contagion in Italy, in mortality analysis by age class, and in the development and testing of dynamical models of the contagion.

stat.ML↗

arXiv2021

Optimal Clearing Payments in a Financial Contagion Model

Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Then, we argue that the proportionality rule is one of the factors responsible for cascaded defaults, and that the overall system loss can be reduced if this rule is lifted. The proposed approach thus shifts the focus from the individual interest to the overall system's interest to control and contain adverse effects of cascaded failures, and we show that clearing payments in this setting can be computed by solving suitable convex optimization problems.

math.OC↗

arXiv2020

Recurrent Averaging Inequalities in Multi-Agent Control and Social Dynamics Modeling

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, this local averaging procedure eventually leads to global consensus, or synchronization of the values at all nodes. Applications of iterative averaging include, but are not limited to, algorithms for distributed optimization, for solution of linear and nonlinear equations, for multi-robot coordination and for opinion formation in social groups. Although these algorithms have similar structures, the mathematical techniques used for their analysis are diverse, and conditions for their convergence and differ from case to case. In this paper, we review many of these algorithms and we show that their properties can be analyzed in a unified way by using a novel tool based on recurrent averaging inequalities (RAIs). We develop a theory of RAIs and apply it to the analysis of several important multi-agent algorithms recently proposed in the literature.

eess.SY↗

arXiv2018

Learning Political DNA in the Italian Senate

Motivated by the increasing interest of the control community towards social sciences and the study of opinion formation and belief systems, in this paper we address the problem of exploiting voting data for inferring the underlying affinity of individuals to competing ideology groups. In particular, we mine key voting records of the Italian Senate during the XVII legislature, in order to extract the hidden information about the closeness of senators to political parties, based on a parsimonious feature extraction method that selects the most relevant bills. Modeling the voting data as outcomes of a mixture of random variables and using sparse learning techniques, we cast the problem in a probabilistic framework and derive an information theoretic measure, which we refer to as Political Data-aNalytic Affinity (Political DNA). The advantages of this new affinity measure are discussed in the paper. The results of the numerical analysis on voting data unveil underlying relationships among political exponents of the Italian Senate.

cs.SI↗

arXiv2017

Quantum Spin-Hall Effect of Light at Bound States in the Continuum

The discovery of the topological nature of free-space light and its quantum chiral behavior has recently raised large attention. This important scientific endeavor features spin-based integrated quantum technologies. Herein, we discuss a novel phenomenon based on a resonantly-enhanced quantum spin-Hall transport of light observed in a dielectric resonator operating near the bound-state-in-continuum (BIC) regime. The BIC mode is characterized by a transverse photonic spin angular momentum density extended on a macroscopic area. As such, the experimental excited mode in near-BIC regime generates resonant surface waves characterized by spin-momentum locking and that propagate along the symmetry axes of the structure. In addition, the generated side waves are interpreted as an abrupt nonparaxial redirection of the exciting far field light, which is responsible for the spin-to-orbital angular momentum conversion evidenced in the spin-orbit asymmetry measured in the intensity of the side waves. The experimental results are in excellent agreement with a model that combines geometric parallel transport of light polarization and spin-momentum locking. In addition, breaking the excitation symmetry leads to a total spin-directive coupling. Our results reveal the possibility of a BIC-enhanced macroscopic spin-directive coupling, a novel fundamental mechanism of light-spin manipulation that will have strong impact on emerging quantum technologies.

physics.optics↗

arXiv2016

High refractive index Fresnel lens on a fiber fabricated by nanoimprint lithography for immersion applications

In this Letter we present a Fresnel lens fabricated on the end of an optical fiber. The lens is fabricated using nanoimprint lithography of a functional high refractive index material, which is suitable for mass production. The main advantage of the presented Fresnel lens compared to a conventional fiber lens is its high refractive index (n=1.69), which enables efficient light focusing even inside other media such as water or adhesive. Measurement of the lens performance in an immersion liquid (n=1.51) shows a near diffraction limited focal spot of 810 nm in diameter at the 1/e2 intensity level for a wavelength of 660 nm. Applications of such fiber lenses include integrated optics, optical trapping and fiber probes.

physics.ins-det↗

arXiv2016

Nanoimprint of a 3D structure on an optical fiber for light wavefront manipulation

Integration of complex photonic structures onto optical fiber facets enables powerful platforms with unprecedented optical functionalities. Conventional nanofabrication technologies, however, do not permit viable integration of complex photonic devices onto optical fibers owing to their low throughput and high cost. In this paper we report the fabrication of a three dimensional structure achieved by direct Nanoimprint Lithography on the facet of an optical fiber. Nanoimprint processes and tools were specifically developed to enable a high lithographic accuracy and coaxial alignment of the optical device with respect to the fiber core. To demonstrate the capability of this new approach, a 3D beam splitter has been designed, imprinted and optically characterized. Scanning electron microscopy and optical measurements confirmed the excellent lithographic capabilities of the proposed approach as well as the desired optical performance of the imprinted structure. The inexpensive solution presented here should enable advancements in areas such as integrated optics and sensing, achieving enhanced portability and versatility of fiber optic components.

physics.optics↗

arXiv2015

Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.

cs.RO↗

arXiv2015

Pose Graph Optimization in the Complex Domain: Lagrangian Duality, Conditions For Zero Duality Gap, and Optimal Solutions

Pose Graph Optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem, and currently no known technique can guarantee the computation of an optimal solution. In this paper, we show that Lagrangian duality allows computing a globally optimal solution, under certain conditions that are satisfied in many practical cases. Our first contribution is to frame the PGO problem in the complex domain. This makes analysis easier and allows drawing connections with the recent literature on unit gain graphs. Exploiting this connection we prove non-trival results about the spectrum of the matrix underlying the problem. The second contribution is to formulate and analyze the dual problem in the complex domain. Our analysis shows that the duality gap is connected to the number of eigenvalues of the penalized pose graph matrix, which arises from the solution of the dual. We prove that if this matrix has a single eigenvalue in zero, then (i) the duality gap is zero, (ii) the primal PGO problem has a unique solution, and (iii) the primal solution can be computed by scaling an eigenvector of the penalized pose graph matrix. The third contribution is algorithmic: we exploit the dual problem and propose an algorithm that computes a guaranteed optimal solution for PGO when the penalized pose graph matrix satisfies the Single Zero Eigenvalue Property (SZEP). We also propose a variant that deals with the case in which the SZEP is not satisfied. The fourth contribution is a numerical analysis. Empirical evidence shows that in the vast majority of cases (100% of the tests under noise regimes of practical robotics applications) the penalized pose graph matrix does satisfy the SZEP, hence our approach allows computing the global optimal solution. Finally, we report simple counterexamples in which the duality gap is nonzero, and discuss open problems.

cs.RO↗

arXiv2012

Distributed Random Convex Programming via Constraints Consensus

This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas, especially in the context of decision under uncertainty, see [2],[3]. We here consider a setup in which instances of the random constraints (the scenario) are not held by a single centralized processing unit, but are distributed among different nodes of a network. Each node "sees" only a small subset of the constraints, and may communicate with neighbors. The objective is to make all nodes converge to the same solution as the centralized RCP problem. To this end, we develop two distributed algorithms that are variants of the constraints consensus algorithm [4],[5]: the active constraints consensus (ACC) algorithm, and the vertex constraints consensus (VCC) algorithm. We show that the ACC algorithm computes the overall optimal solution in finite time, and with almost surely bounded communication at each iteration. The VCC algorithm is instead tailored for the special case in which the constraint functions are convex also w.r.t. the uncertain parameters, and it computes the solution in a number of iterations bounded by the diameter of the communication graph. We further devise a variant of the VCC algorithm, namely quantized vertex constraints consensus (qVCC), to cope with the case in which communication bandwidth among processors is bounded. We discuss several applications of the proposed distributed techniques, including estimation, classification, and random model predictive control, and we present a numerical analysis of the performance of the proposed methods. As a complementary numerical result, we show that the parallel computation of the scenario solution using ACC algorithm significantly outperforms its centralized equivalent.

math.OC↗