Search

Traditional round-trip car rental systems mandate users to return vehicles to their point of origin, limiting the system adaptability to meet diverse mobility demands. This constraint often leads to fleet under-utilization and incurs high parking costs for idle vehicles. To address this inefficiency, we propose a N-user matching algorithm which is designed to facilitate one-way trips within the round-trip rental framework. Our algorithm addresses the joint problem of optimal pricing and user matching through a Two-Stage Integer Linear Programming (ILP)-based formulation. In the first stage, optimal rental prices are determined by setting a risk factor that governs the likelihood of matching a set of N-user. The second stage involves maximizing expected profit through a novel ILP-based user-matching formulation. Testing our algorithm on real-world scenarios demonstrates an approximate 35\% increase in demand fulfillment. Additionally, we assess the model robustness under uncertainty by varying factors such as the risk factor (probability of user ride acceptance at the offered price), cost factor (rental cost-to-fare ratio), and maximum chain length.

The flow of information through a complex system can be readily understood with category theory. However, negative information (e.g., what is not possible) does not have an immediately evident categorical representation. The formalization of nategories using unconventional composition addresses this issue, and lets imposed limitations on categories be considered. However, traditional nategories abandon core categorical constructs and rely on extensive mathematical development. This creates a divide between the consideration of positive and negative information composition. In this work, we show that negative information can be considered in a natural categorical manner. This is aided by functor string diagrams, a novel flexible diagrammatic approach that can intuitively show the operation of hom-functors and natural transformations in expressions. This insight reveals how to consider the composition of negative information with foundational categorical constructs without relying on enrichment. We present diagrammatic means to consider not only nategories, but preorders more broadly. This paper introduces diagrammatic methods for the consideration of triangle inequalities and co-designs $\mathbf{DP/Feas_{Bool}}$, showing how important cases of negative information composition can be categorically and diagrammatically approached. In particular, we develop systematic tools to rigorously consider imposed limitations on systems, advancing our mathematical understanding, and present intuitive diagrams which motivate widespread adoption and usage for various applications.

The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of diverse theoretical and applied systems. Complex algebraic structures - otherwise represented by a forest of symbols - can be encoded into diagrams with intuitive graphical rules. The prevailing paradigm for diagrammatic category theory are monoidal string diagrams whose specification reflects the axioms of monoidal categories. However, such diagrams struggle in accurately portraying crucial categorical constructs such as functors or natural transformations, obscuring central concepts such as the Yoneda lemma or the simultaneous consideration of hom-functors and products. In this work, we introduce functor string diagrams, a systematic approach for the development of categorical diagrams which allows functors, natural transformations, and products to be clearly represented. We validate their practicality in multiple dimensions. We show their usefulness for theoretical manipulations by proving the Yoneda lemma, show that they encompass monoidal string diagrams and hence their helpful properties, and end by showing their exceptional applied utility by leveraging them to underpin neural circuit diagrams, a method which, at last, allows deep learning architectures to be comprehensively and rigorously expressed.

Support vector machines (SVMs) are widely used machine learning models (e.g., in remote sensing), with formulations for both classification and regression tasks. In the last years, with the advent of working quantum annealers, hybrid SVM models characterised by quantum training and classical execution have been introduced. These models have demonstrated comparable performance to their classical counterparts. However, they are limited in the training set size due to the restricted connectivity of the current quantum annealers. Hence, to take advantage of large datasets (like those related to Earth observation), a strategy is required. In the classical domain, local SVMs, namely, SVMs trained on the data samples selected by a k-nearest neighbors model, have already proven successful. Here, the local application of quantum-trained SVM models is proposed and empirically assessed. In particular, this approach allows overcoming the constraints on the training set size of the quantum-trained models while enhancing their performance. In practice, the FaLK-SVM method, designed for efficient local SVMs, has been combined with quantum-trained SVM models for binary and multiclass classification. In addition, for comparison, FaLK-SVM has been interfaced for the first time with a classical single-step multiclass SVM model (CS SVM). Concerning the empirical evaluation, D-Wave's quantum annealers and real-world datasets taken from the remote sensing domain have been employed. The results have shown the effectiveness and scalability of the proposed approach, but also its practical applicability in a real-world large-scale scenario., Comment: 12 pages, 1 figure, 11 tables

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubits requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, the ensembles have turned out to be able to mitigate both unsuitable data normalizations and repeated measurement inaccuracies, making quantum classifiers more stable., Comment: 24 pages, 11 figures

An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning., Comment: 25 pages, 9 figures, updated to the version published on SciPost

The time varying reproduction number R is a critical variable for situational awareness during infectious disease outbreaks, but delays between infection and reporting hinder its accurate estimation in real time. We propose a nowcasting method for improving the timeliness and accuracy of R estimates, based on comparisons of successive versions of surveillance databases. The method was validated against COVID-19 surveillance data collected in Italy over an 18-month period. Compared to traditional methods, the nowcasted reproduction number reduced the estimation delay from 13 to 8 days, while maintaining a better accuracy. Moreover, it allowed anticipating the detection of periods of epidemic growth by between 6 and 23 days. The method offers a simple and generally applicable tool to improve situational awareness during an epidemic outbreak, allowing for informed public health response planning.

The evolution of existing transportation systems,mainly driven by urbanization and increased availability of mobility options, such as private, profit-maximizing ride-hailing companies, calls for tools to reason about their design and regulation. To study this complex socio-technical problem, one needs to account for the strategic interactions of the heterogeneous stakeholders involved in the mobility ecosystem and analyze how they influence the system. In this paper, we focus on the interactions between citizens who compete for the limited resources of a mobility system to complete their desired trip. Specifically, we present a game-theoretic framework for multi-modal mobility systems, where citizens, characterized by heterogeneous preferences, have access to various mobility options and seek individually-optimal decisions. We study the arising game and prove the existence of an equilibrium, which can be efficiently computed via a convex optimization problem. Through both an analytical and a numerical case study for the classic scenario of Sioux Falls, USA, we illustrate the capabilities of our model and perform sensitivity analyses. Importantly, we show how to embed our framework into a "larger" game among stakeholders of the mobility ecosystem (e.g., municipality, Mobility Service Providers, and citizens), effectively giving rise to tools to inform strategic interventions and policy-making in the mobility ecosystem., Comment: 8 pages, 5 figures, to appear in the proceedings of the 2023 IEEE 26th International Conference on Intelligent Transportation Systems

The k-nearest neighbors (k-NN) is a basic machine learning (ML) algorithm, and several quantum versions of it, employing different distance metrics, have been presented in the last few years. Although the Euclidean distance is one of the most widely used distance metrics in ML, it has not received much consideration in the development of these quantum variants. In this article, a novel quantum k-NN algorithm based on the Euclidean distance is introduced. Specifically, the algorithm is characterised by a quantum encoding requiring a low number of qubits and a simple quantum circuit not involving oracles, aspects that favor its realization. In addition to the mathematical formulation and some complexity observations, a detailed empirical evaluation with simulations is presented. In particular, the results have shown the correctness of the formulation, a drop in the performance of the algorithm when the number of measurements is limited, the competitiveness with respect to some classical baseline methods in the ideal case, and the possibility of improving the performance by increasing the number of measurements., Comment: 35 pages, 12 figures, 15 tables

This paper presents the details and testing of two implementations (in C++ and Python) of the hybrid quantum-classical algorithm Quantum Annealing Learning Search (QALS) on a D-Wave quantum annealer. QALS was proposed in 2019 as a novel technique to solve general QUBO problems that cannot be directly represented into the hardware architecture of a D-Wave machine. Repeated calls to the quantum machine within a classical iterative structure and a related convergence proof originate a learning mechanism to find an encoding of a given problem into the quantum architecture. The present work considers the Number Partitioning Problem (NPP) and the Travelling Salesman Problem (TSP) for the testing of QALS. The results turn out to be quite unexpected, with QALS not being able to perform as well as the other considered methods, especially in NPP, where classical methods outperform quantum annealing in general. Nevertheless, looking at the TSP tests, QALS has fulfilled its primary goal, i.e., processing QUBO problems not directly mappable to the QPU topology., Comment: 26 pages, 1 figure

In many engineering applications it is useful to reason about "negative information". For example, in planning problems, providing an optimal solution is the same as giving a feasible solution (the "positive" information) together with a proof of the fact that there cannot be feasible solutions better than the one given (the "negative" information). We model negative information by introducing the concept of "norphisms", as opposed to the positive information of morphisms. A "nategory" is a category that has "nom"-sets in addition to hom-sets, and specifies the interaction between norphisms and morphisms. In particular, we have composition rules of the form morphism + norphism $\to$ norphism. Norphisms do not compose by themselves; rather, they use morphisms as catalysts. After providing several applied examples, we connect nategories to enriched category theory. Specifically, we prove that categories enriched in de Paiva's dialectica categories GC, in the case C = Set and equipped with a modified monoidal product, define nategories which satisfy additional regularity properties. This formalizes negative information categorically in a way that makes negative and positive morphisms equal citizens., Comment: In Proceedings ACT 2022, arXiv:2307.15519

In the current era, quantum resources are extremely limited, and this makes difficult the usage of quantum machine learning (QML) models. Concerning the supervised tasks, a viable approach is the introduction of a quantum locality technique, which allows the models to focus only on the neighborhood of the considered element. A well-known locality technique is the k-nearest neighbors (k-NN) algorithm, of which several quantum variants have been proposed. Nevertheless, they have not been employed yet as a preliminary step of other QML models, whereas the classical counterpart has already proven successful. In this paper, we present (i) an implementation in Python of a QML pipeline for local classification, and (ii) its extensive empirical evaluation. Specifically, the quantum pipeline, developed using Qiskit, consists of a quantum k-NN and a quantum binary classifier. The results have shown the quantum pipeline's equivalence (in terms of accuracy) to its classical counterpart in the ideal case, the validity of locality's application to the QML realm, but also the strong sensitivity of the chosen quantum k-NN to probability fluctuations and the better performance of classical baseline methods like the random forest., Comment: 33 pages, 8 figures, 9 tables

Bayesian networks are widely used probabilistic graphical models, whose structure is hard to learn starting from the generated data. O'Gorman et al. have proposed an algorithm to encode this task, i.e., the Bayesian network structure learning (BSNL), into a form that can be solved through quantum annealing, but they have not provided an experimental evaluation of it. In this paper, we present (i) an implementation in Python of O'Gorman's algorithm, (ii) a divide et impera approach that allows addressing BNSL problems of larger sizes in order to overcome the limitations imposed by the current architectures, and (iii) their empirical evaluation. Specifically, several problems with an increasing number of variables have been used in the experiments. The results have shown the effectiveness of O'Gorman's formulation for BNSL instances of small sizes, and the superiority of the divide et impera approach on the direct execution of O'Gorman's algorithm., Comment: 29 pages, 6 figures

When designing autonomous systems, we need to consider multiple trade-offs at various abstraction levels, and the choices of single (hardware and software) components need to be studied jointly. In this work we consider the problem of designing the control algorithm as well as the platform on which it is executed. In particular, we focus on vehicle control systems, and formalize state-of-the-art control schemes as monotone feasibility relations. We then show how, leveraging a monotone theory of co-design, we can study the embedding of control synthesis problems into the task-driven co-design problem of a robotic platform. The properties of the proposed approach are illustrated by considering urban driving scenarios. We show how, given a particular task, we can efficiently compute Pareto optimal design solutions., Comment: 8 pages, 7 figures. Proceedings of the 2022 IEEE 61th Conference on Decision and Control

Background School closures and distance learning have been extensively applied to control SARS-CoV-2 transmission. Despite evidence of viral circulation in schools, the contribution of students and of in-person schooling to the transmission remains poorly quantified. Methods We analyze 976 exposure events, involving 460 positive individuals, as identified in early 2021 by routine surveillance and through an extensive screening conducted on students, school personnel, and their household members during an outbreak in a small municipality of Italy. Results From the analysis of potential transmission chains, we estimated that, on average, 55.1%, 17.3% and 27.6% infection episodes were linked to household, school, and community contacts, respectively. Clusters originated from students or school personnel showed a larger average cluster size (3.32 vs 1.15), a larger average number of generations in the transmission chain (1.56 vs 1.17) and a larger set of associated close contacts (11.3 vs 3.15, on average). We found substantial transmission heterogeneities, with 20% positive individuals seeding 75-80 of all transmission. A higher proportion of infected individuals causing onward transmission was found among students (48.8% vs 29.9%, on average), who also caused a markedly higher number of secondary cases (mean: 1.3 vs 0.5). Conclusions Uncontrolled transmission at school could disrupt the regular conduct of teaching activities, likely seeding the transmission into other settings, and increasing the burden on contact-tracing operations.

Background. During 2021, the COVID-19 pandemic was characterized by the emergence of lineages with increased fitness. For most of these variants, quantitative information is scarce on epidemiological quantities such as the incubation period and generation time, which are critical for both public health decisions and scientific research. Method. We analyzed a dataset collected during contact tracing activities in the province of Reggio Emilia, Italy, throughout 2021. We determined the distributions of the incubation period using information on negative PCR tests and the date of last exposure from 282 symptomatic cases. We estimated the distributions of the intrinsic generation time (the time between the infection dates of an infector and its secondary cases under a fully susceptible population) using a Bayesian inference approach applied to 4,435 SARS-CoV-2 cases clustered in 1,430 households where at least one secondary case was recorded. Results. We estimated a mean incubation period of 4.9 days (95% credible intervals, CrI, 4.4-5.4; 95 percentile of the mean distribution: 1-12) for Alpha and 4.5 days (95%CrI 4.0-5.0; 95 percentile: 1-10) for Delta. The intrinsic generation time was estimated to have a mean of 6.0 days (95% CrI 5.6-6.4; 95 percentile: 1-15) for Alpha and of 6.6 days (95%CrI 6.0-7.3; 95 percentile: 1-18) for Delta. The household serial interval was 2.6 days (95%CrI 2.4-2.7) for Alpha and 2.4 days (95%CrI 2.2-2.6) for Delta, and the estimated proportion of pre-symptomatic transmission was 54-55% for both variants. Conclusions. These results indicate limited differences in the incubation period and intrinsic generation time of SARS-CoV-2 variants Alpha and Delta compared to ancestral lineages., Comment: 11 pages, 3 figures, 2 tables, supplementary material

Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a partially ordered set of metrics. This allows one to combine hierarchical priorities of each player with the interactive nature of the environment. By contextualizing standard game theoretical notions, we provide two sufficient conditions on the preference of the players to prove existence of pure Nash Equilibria in finite action sets. Moreover, we define formal operations on the preference structures and link them to a refinement of the game solutions, showing how the set of equilibria can be systematically shrunk. The presented results are showcased in a driving game where autonomous vehicles select from a finite set of trajectories. The results demonstrate the interpretability of results in terms of minimum-rank-violation for each player., Comment: 8 pages

It is estimated that around 80\% of the world's population live in areas susceptible to at-least one major vector borne disease, and approximately 20% of global communicable diseases are spread by mosquitoes. Furthermore, the outbreaks of such diseases are becoming more common and widespread, with much of this driven in recent years by socio-demographic and climatic factors. These trends are causing significant worry to global health organisations, including the CDC and WHO, and-so an important question is the role that technology can play in addressing them. In this work we describe the integration of an epidemiology model, which simulates the spread of mosquito-borne diseases, with the VESTEC urgent computing ecosystem. The intention of this work is to empower human health professionals to exploit this model and more easily explore the progression of mosquito-borne diseases. Traditionally in the domain of the few research scientists, by leveraging state of the art visualisation and analytics techniques, all supported by running the computational workloads on HPC machines in a seamless fashion, we demonstrate the significant advantages that such an integration can provide. Furthermore we demonstrate the benefits of using an ecosystem such as VESTEC, which provides a framework for urgent computing, in supporting the easy adoption of these technologies by the epidemiologists and disaster response professionals more widely., Comment: Preprint of paper in 2021 IEEE/ACM HPC for Urgent Decision Making (UrgentHPC)

Challenged by urbanization and increasing travel needs, existing transportation systems need new mobility paradigms. In this article, we present the emerging concept of autonomous mobility-on-demand, whereby centrally orchestrated fleets of autonomous vehicles provide mobility service to customers. We provide a comprehensive review of methods and tools to model and solve problems related to autonomous mobility-on-demand systems. Specifically, we first identify problem settings for their analysis and control, from both operational and planning perspectives. We then review modeling aspects, including transportation networks, transportation demand, congestion, operational constraints, and interactions with existing infrastructure. Thereafter, we provide a systematic analysis of existing solution methods and performance metrics, highlighting trends and trade-offs. Finally, we present various directions for further research., Comment: To appear in Annual Review of Control, Robotics, and Autonomous Systems

Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system., Comment: In Proceedings ACT 2021, arXiv:2211.01102

Designing optimal soft modular robots is difficult, due to non-trivial interactions between morphology and controller. Evolutionary algorithms (EAs), combined with physical simulators, represent a valid tool to overcome this issue. In this work, we investigate algorithmic solutions to improve the Quality Diversity of co-evolved designs of Tensegrity Soft Modular Robots (TSMRs) for two robotic tasks, namely goal reaching and squeezing trough a narrow passage. To this aim, we use three different EAs, i.e., MAP-Elites and two custom algorithms: one based on Viability Evolution (ViE) and NEAT (ViE-NEAT), the other named Double Map MAP-Elites (DM-ME) and devised to seek diversity while co-evolving robot morphologies and neural network (NN)-based controllers. In detail, DM-ME extends MAP-Elites in that it uses two distinct feature maps, referring to morphologies and controllers respectively, and integrates a mechanism to automatically define the NN-related feature descriptor. Considering the fitness, in the goal-reaching task ViE-NEAT outperforms MAP-Elites and results equivalent to DM-ME. Instead, when considering diversity in terms of "illumination" of the feature space, DM-ME outperforms the other two algorithms on both tasks, providing a richer pool of possible robotic designs, whereas ViE-NEAT shows comparable performance to MAP-Elites on goal reaching, although it does not exploit any map., Comment: To be published in the proceedings of ACM Genetic and Evolutionary Computation Conference (GECCO) 2021

Increasing urbanization and exacerbation of sustainability goals threaten the operational efficiency of current transportation systems and confront cities with complex choices with huge impact on future generations. At the same time, the rise of private, profit-maximizing Mobility Service Providers leveraging public resources, such as ride-hailing companies, entangles current regulation schemes. This calls for tools to study such complex socio-technical problems. In this paper, we provide a game-theoretic framework to study interactions between stakeholders of the mobility ecosystem, modeling regulatory aspects such as taxes and public transport prices, as well as operational matters for Mobility Service Providers such as pricing strategy, fleet sizing, and vehicle design. Our framework is modular and can readily accommodate different types of Mobility Service Providers, actions of municipalities, and low-level models of customers choices in the mobility system. Through both an analytical and a numerical case study for the city of Berlin, Germany, we showcase the ability of our framework to compute equilibria of the problem, to study fundamental tradeoffs, and to inform stakeholders and policy makers on the effects of interventions. Among others, we show tradeoffs between customers satisfaction, environmental impact, and public revenue, as well as the impact of strategic decisions on these metrics., Comment: 8 pages, 6 figures, Published in the Proceedings of the 2021 IEEE International Conference on Intelligent Transportation Systems (Awarded the Best Paper Award - First Place)

Solid estimates describing the clinical course of SARS-CoV-2 infections are still lacking due to under-ascertainment of asymptomatic and mild-disease cases. In this work, we quantify age-specific probabilities of transitions between stages defining the natural history of SARS-CoV-2 infection from 1,965 SARS-CoV-2 positive individuals identified in Italy between March and April 2020 among contacts of confirmed cases. Infected contacts of cases were confirmed via RT-PCR tests as part of contact tracing activities or retrospectively via IgG serological tests and followed-up for symptoms and clinical outcomes. In addition, we provide estimates of time intervals between key events defining the clinical progression of cases as obtained from a larger sample, consisting of 95,371 infections ascertained between February and July 2020. We found that being older than 60 years of age was associated with a 39.9% (95%CI: 36.2-43.6%) likelihood of developing respiratory symptoms or fever >= 37.5 {\deg}C after SARS-CoV-2 infection; the 22.3% (95%CI: 19.3-25.6%) of the infections in this age group required hospital care and the 1% (95%CI: 0.4-2.1%) were admitted to an intensive care unit (ICU). The corresponding proportions in individuals younger than 60 years were estimated at 27.9% (95%CI: 25.4-30.4%), 8.8% (95%CI: 7.3-10.5%) and 0.4% (95%CI: 0.1-0.9%), respectively. The infection fatality ratio (IFR) ranged from 0.2% (95%CI: 0.0-0.6%) in individuals younger than 60 years to 12.3% (95%CI: 6.9-19.7%) for those aged 80 years or more; the case fatality ratio (CFR) in these two age classes was 0.6% (95%CI: 0.1-2%) and 19.2% (95% CI: 10.9-30.1%), respectively. The median length of stay in hospital was 10 (IQR 3-21) days; the length of stay in ICU was 11 (IQR 6-19) days. The obtained estimates could be instrumental to refine mathematical modeling work supporting public health decisions., Comment: 20 pages, 4 figures

A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types, all within a unified, sheaf-theoretic formalism. We take robotic systems as an exemplar of complex systems and rigorously describe actuators, sensors, and algorithms using this framework., Comment: In Proceedings ACT 2020, arXiv:2101.07888. arXiv admin note: substantial text overlap with arXiv:2005.04715

We consider the problem of co-designing embodied intelligence as a whole in a structured way, from hardware components such as propulsion systems and sensors to software modules such as control and perception pipelines. We propose a principled approach to formulate and solve complex embodied intelligence co-design problems, leveraging a monotone co-design theory. The methods we propose are intuitive and integrate heterogeneous engineering disciplines, allowing analytical and simulation-based modeling techniques and enabling interdisciplinarity. We illustrate through a case study how, given a set of desired behaviors, our framework is able to compute Pareto efficient solutions for the entire hardware and software stack of a self-driving vehicle., Comment: 8 pages, 9 figures, To appear in the Proceedings of the 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems

Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the control algorithm as well as the platform around it. In particular, we leverage a monotone theory of co-design to formalize variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot behaviors, we can compute Pareto efficient design solutions., Comment: 8 pages, 6 figures, to appear in the proceedings of the 20th European Control Conference (ECC21)

We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the presence of a fitness trade-off between resistance to infection and proliferative potential are incorporated into the model. The model comprises an ODE for the number of infected individuals that is coupled with a partial integrodifferential equation for the population density of susceptibles through an integral term. The expression for the basic reproduction number $\mathcal{R}_0$ is derived, the disease-free and endemic equilibrium of the model are characterised and a threshold theorem is proved. Analytical results are integrated with numerical simulations of a calibrated version of the model based on the results of artificial selection experiments in a host-parasite system. The results of our mathematical study disentangle the impact of different evolutionary parameters on the spread of infectious diseases and the consequent phenotypic adaption of susceptible individuals. In particular, these results provide a theoretical basis for the observation that infectious diseases exerting stronger selective pressures on susceptibles and being characterised by higher infection rates are more likely to spread. Moreover, our results indicate that spontaneous phenotypic changes in proliferative potential and resistance to infection can either promote or prevent the spread of diseases depending on the strength of selection acting on susceptible individuals prior to infection. Finally, we demonstrate that, when an endemic equilibrium is established, higher levels of resistance to infection and lower degrees of phenotypic heterogeneity are to be expected in the presence of infections which are characterised by lower rates of death and exert stronger selective pressures., Comment: 29 pages, 8 figures

The design of future mobility solutions and the design of the mobility systems they enable are closely coupled. Indeed, knowledge about the intended service of novel mobility solutions would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management policies. This requires tools to study such a coupling and co-design mobility systems in terms of different objectives. We present a framework to address such co-design problems, leveraging a mathematical theory of co-design to frame and solve the problem of designing and deploying an intermodal mobility system, whereby autonomous vehicles service travel demands jointly with micromobility solutions and public transit, in terms of fleets sizing, vehicle characteristics, and public transit service frequency. Our framework is modular and compositional, allowing one to describe the design as the interconnection of simple components and to tackle it from a systemic perspective. Moreover, it requires general monotonicity assumptions and naturally handles multiple objectives, delivering rational, actionable solutions for policy makers. We showcase our methodology in a case study of Washington D.C., USA. Our work suggests the possibility to create user-friendly optimization tools to systematically assess costs and benefits of interventions, and to inform policy-making in the future., Comment: Accepted for publication in the IEEE Transactions of Network Science and Engineering. arXiv admin note: text overlap with arXiv:2003.04739, arXiv:1910.07714

A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types, all within a unified, sheaf-theoretic formalism. We take robotic systems as an exemplar of complex systems and rigorously describe actuators, sensors, and algorithms using this framework., Comment: 24 pages