Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

Distributed aggregative optimization is a recently emerged framework in which the agents of a network want to minimize the sum of local objective functions, each one depending on the agent decision variable (e.g., the local position of a team of robots) and an aggregation of all the agents' variables (e.g., the team barycentre). In this paper, we address a distributed feedback optimization framework in which agents implement a local (distributed) policy to reach a steady-state minimizing an aggregative cost function. We propose Aggregative Tracking Feedback, i.e., a novel distributed feedback optimization law in which each agent combines a closed-loop gradient flow with a consensus-based dynamic compensator reconstructing the missing global information. By using tools from system theory, we prove that Aggregative Tracking Feedback steers the network to a stationary point of an aggregative optimization problem with (possibly) nonconvex objective function. The effectiveness of the proposed method is validated through numerical simulations on a multi-robot surveillance scenario

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss their implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots

Distributed Online Optimization via Gradient Tracking with Adaptive Momentum

This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient tracking with adaptive momentum estimation (GTAdam) distributed algorithm, which combines a gradient tracking mechanism with first and second order momentum estimates of the gradient. The algorithm is analyzed in the online setting for strongly convex and smooth cost functions. We prove that the average dynamic regret is bounded and that the convergence rate is linear. The algorithm is tested on a time-varying classification problem, on a (moving) target localization problem and in a stochastic optimization setup from image classification. In these numerical experiments from multi-agent learning, GTAdam outperforms state-of-the-art distributed optimization methods

ADMM-Tracking Gradient for Distributed Optimization over Asynchronous and Unreliable Networks

In this paper, we propose (i) a novel distributed algorithm for consensus optimization over networks and (ii) a robust extension tailored to deal with asynchronous agents and packet losses. The key idea is to achieve dynamic consensus on (i) the agents' average and (ii) the global descent direction by iteratively solving an online auxiliary optimization problem through a distributed implementation of the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. First, in the case of ideal networks, by using tools from system theory, we prove the linear convergence of the scheme with strongly convex costs. Then, by exploiting the averaging theory, we extend such a first result to prove that the robust extension of our method preserves linear convergence in the case of asynchronous agents and packet losses. Further, by using the notion of Input-to-State Stability, we also guarantee the robustness of the schemes with respect to additional, generic errors affecting the agents' updates. Finally, some numerical simulations confirm our theoretical findings and show that the proposed methods outperform the existing state-of-the-art distributed methods for consensus optimization

Tracking-based distributed equilibrium seeking for aggregative games

We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms

Morphology and paleobiology of the Late Cretaceous large-sized shark Cretodus crassidens (Dixon, 1850) (Neoselachii; Lamniformes)

The definition of the Cretaceous shark genus Cretodus Sokolov, 1965 is primarily based on isolated teeth. This genus includes five species. Among these, Cretodus houghtonorum Shimada and Everhart, 2019 is the only species based on a partially preserved skeleton. Here, the taxonomic attribution of a virtually complete skeleton of Cretodus from the Turonian of northeastern Italy is discussed, together with a few specimens from the Turonian of England. One of the latter is investigated through micropaleontological analysis to determine its stratigraphic position. The material is referred to Cretodus crassidens (Dixon, 1850), the diagnosis of which is emended herein. The dentition is tentatively reconstructed, exhibiting strong similarities with congeneric species, although it differs in having strong vertical folds on the main cusp labial face, a mesiodistally broad tooth aspect, weak and well-spaced 'costulae' at crown base, and a different dental formula in the number of parasymphyseal and lateral rows. Some tooth malformations are interpreted as feeding-related or senile characters. The Italian specimen suggests that Cretodus crassidens had a wide and laterally expanded mouth and head, a stout body, and attained a gigantic size. Cretodus crassidens was a moderate-speed swimming shark ecologically like the extant tiger shark Galeocerdo cuvier (Péron and Lesueur in Lesueur, 1822). The age estimate from vertebral-band counting suggests that the Italian individual was at least 23 years old and the growth model indicates a longevity of 64 years and a maximum attainable total length of 9-11 m. Cretodus crassidens occurs both in Boreal and Tethyan domains, implying a broad paleobiogeographic distribution and a preference toward offshore settings

Arranging Small Molecules with Subnanometer Precision on DNA Origami Substrates for the Single‐Molecule Investigation of Protein–Ligand Interactions

DNA origami nanostructures are versatile substrates for the single‐molecule investigation of biomolecular interactions as they enable the display of molecular species in complex arrangements. Herein, the fundamental limitations of this approach are explored by displaying pairs of small‐molecule ligands of the protein trypsin on DNA origami substrates and adjusting their ligand–ligand spacing with subnanometer precision. Bidentate binding of trypsin to the ligand pairs is investigated by atomic force microscopy (AFM), microscale thermophoresis (MST), and molecular dynamics simulations. Bidentate trypsin binding is strongly affected by the distance of the ligand pairs and the accessibility of the protein's binding pockets. MST cannot resolve the differences in bidentate trypsin binding because of the nonspecific binding of trypsin to the DNA origami substrates, rendering the AFM‐based single‐molecule detection of binding events superior to ensemble measurements. Finally, even monodentate binding to a single ligand may be affected by subnanometer variations in its position, highlighting the importance of local microenvironments that vary even over molecular distances. While this single‐molecule approach can provide viable information on the effects of ligand arrangements on bidentate protein binding, in‐depth investigations into the nature of local microenvironments will be required to exploit its full potential

Oxidative stress and gut-derived lipopolysaccharides in children affected by paediatric autoimmune neuropsychiatric disorders associated with streptococcal infections

BACKGROUND: Paediatric autoimmune neuropsychiatric disorders associated with streptococcal infections syndrome (PANDAS) identifies patients with acute onset of obsessive-compulsive and tic disorders. The objective of this study was to evaluate serum NOX2 levels, as well as 8-iso-prostaglandin F2α (8-iso-PGF2α) and lipopolysaccharide (LPS) of PANDAS patients. METHODS: In this study we wanted to compare serum levels of soluble NOX2-dp (sNOX-2-dp), iso-PGF2α and LPS in 60 consecutive subjects, including 30 children affected by PANDAS and 30 controls (CT) matched for age and gender. Serum zonulin was used as intestinal permeability assay. RESULTS: Compared with CT, PANDAS children had increased serum levels of sNOX-2-dp, 8-iso-PGF2α and LPS. Bivariate analysis showed that serum sNOX2-dp was significantly correlated with LPS (Rs = 0.359; p = 0.005), zonulin (Rs = 0.444; p < 0.001) and 8-iso-PGF2α (Rs = 0.704; p < 0.001). Serum LPS significantly correlated with zonulin (Rs = 0.610; p < 0.001), and 8-iso-PGF2α (Rs = 0.591; p = 0.001). Finally, a multiple linear regression analysis showed that serum 8-iso-PGF2α and zonulin were the only independent variables associated with sNOX2-dp (R2 = 68%). CONCLUSION: This study shows that children affected by PANDAS have high circulating levels of sNOX2-dp, isoprostanes and of LPS that could be involved in the process of neuroinflammation

Management and treatment of decompensated hepatic fibrosis and severe refractory Schistosoma mansoni ascites with transjugular intrahepatic portosystemic shunt

This study aimed to report the first case of a patient with hepatosplenic schistosomiasis mansoni, refractory ascites and portal vein thrombosis treated with a transjugular intrahepatic portosystemic shunt (TIPS), at the Instituto de Radiologia, Hospital das Clinicas, Faculdade de Medicina, Universidade de Sao Paulo, Brazil. After the procedure, the patient recovered favorably and progressed with portal pressure reduction and no deterioration of the liver function. Endovascular shunt modification is a conservative medical approach that often helps in reducing symptoms significantly, making it a less invasive and a safer alternative to liver transplantation for the treatment of schistosomiasis with portal hypertension