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The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation, energy, and mathematical biology. A very recent development in the use of AIMD is its application in solving large-scale optimisation and distributed control problems without the need for inter-agent communication. In this context, an interesting problem arises when multiple AIMD networks are coupled in some sense (usually through a nonlinearity). The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks. This result has important consequences for the convergence of the aforementioned optimisation algorithms. The arguments in the paper also correct conceptual and technical errors in Alam et al. (2020, The convergence of finite-averaging of AIMD for distributed heterogeneous resource allocations. arXiv:2001.08083 [math.OC].). [ABSTRACT FROM AUTHOR]

The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

In this paper we present the design for a smart-mask to mitigate the impact of an airborne virus such as COVID-19. The design utilises recent results from feedback control theory over a distributed ledger that have been developed to enforce compliance in a pseudo-anonymous manner. The design is based on the use of the IOTA distributed ledger. A hardware-in-the-loop simulation based on indoor positioning, paired with Monte-Carlo simulations, is developed to demonstrate the efficacy of the designed prototype. [ABSTRACT FROM AUTHOR]

I-nteract is a cyber-physical system that enables real-time interaction with both virtual and real artifacts to design 3D models for additive manufacturing by leveraging mixed-reality technologies. This paper presents novel advances in the development of the interaction platform to generate 3D models using both constructive solid geometry and artificial intelligence. In specific, by taking advantage of the generative capabilities of deep neural networks, the system has been automated to generate 3D models inferred from a single 2D image captured by the user. Furthermore, a novel generative neural architecture, SliceGen, has been proposed and integrated with the system to overcome the limitation of single-type genus 3D model generation imposed by differentiable-rendering-based deep neural architectures. The system also enables the user to adjust the dimensions of the 3D models with respect to their physical workspace. The effectiveness of the system is demonstrated by generating 3D models of furniture (e.g., chairs and tables) and fitting them into the physical space in a mixed reality environment. The presented developmental advances provide a novel and immersive form of interaction to facilitate the inclusion of a consumer into the design process for personal fabrication. [ABSTRACT FROM AUTHOR]

It is well known that two-sided markets are unfair in a number of ways. For example, female drivers on ride-hailing platforms earn less than their male colleagues per mile driven. Similar observations have been made for other minority subgroups in other two-sided markets. Here, we suggest a novel market-clearing mechanism for two-sided markets, which promotes equalization of the pay per hour worked across multiple subgroups, as well as within each subgroup. In the process, we introduce a novel notion of subgroup fairness (which we call Inter-fairness), which can be combined with other notions of fairness within each subgroup (called Intra-fairness), and the utility for the customers (Customer-Care) in the objective of the market-clearing problem. Although the novel non-linear terms in the objective complicate market clearing by making the problem non-convex, we show that a certain non-convex augmented Lagrangian relaxation can be approximated to any precision in time polynomial in the number of market participants using semidefinite programming, thanks to its "hidden convexity". This makes it possible to implement the market-clearing mechanism efficiently. On the example of driver-ride assignment in an Uber-like system, we demonstrate the efficacy and scalability of the approach and trade-offs between Inter- and Intra-fairness. [ABSTRACT FROM AUTHOR]

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in timeseries forecasting problems: subgroup fairness and instantaneous fairness. These notion extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods. [ABSTRACT FROM AUTHOR]

A stochastic algorithm is presented for a class of optimisation problems that arise when a group of agents compete to share a single constrained resource in an optimal manner. The approach uses intermittent single-bit feedback, which indicates a constraint violation and does not require inter-agent communication. The algorithm is based on a positive matrix model of AIMD,which is extended to the nonhomogeneous Markovian case. The key feature is the assignment of back-off probabilities to the individual agents as a function of the past average access to the resource. This leads to a nonhomogeneous Markov chain in an extended state space, and we show almost sure convergence of the average access to the social optimum. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for Positive Realness of general transfer function matrices are derived. The conditions are expressed in terms of eigenvalues of matrix functions of the state matrices representation of the LTI system. Illustrative numerical examples are provided. Index Terms--Conditions, passivity, positive real (PR), spectral methods.

In this paper, we present a probabilistic synchronization algorithm whose convergence properties are examined using tools of rowstochastic matrices. The proposed algorithm is particularly well suited for wireless sensor network applications, where connectivity is not guaranteed at all times, and energy efficiency is an important design consideration. The tradeoff between the convergence speed and the energy use is studied. Index Terms--Common Lyapunov function, consensus, scrambling matrix, switched systems, synchronization.

Necessary and sufficient conditions for strict positive realness and positive realness of strictly proper functions are derived. The conditions are expressed in terms of eigenvalues of the state matrices representation of the system. Previous results rendered conditions which were significantly more complex than those for proper (but not strictly proper) functions. The present conditions for strictly proper functions are simpler than the ones for proper functions, which is consistent with intuition in this case. Illustrative numerical examples are provided. Index Terms--Circle criterion, eigenvalues locations, positive real (PR) conditions, state--space representation, time varying systems.

In this note, we introduce the concepts of best case and worst-case convergence rates for switched linear systems. Their connections to the problems of stability and stabilization are briefly discussed. For simultaneously triangularizable switched systems, explicit formulas are presented for the convergence rates in terms of the system eigenvalues. Index Terms--Convergence rate, simultaneous triangularization, switched linear systems, switching path, stability, stabilization.

Mycobacterium tuberculosis isolates cultured from 6 patients associated with an isoniazid-resistant M. tuberculosis outbreak acquired rifampicin resistance. The rpoB gene sequence showed that resistance was associated with rare mutations in [...]

In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices [A.sub.1] and [A.sub.2] are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product [A.sub.1] [A.sub.2] does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result. Index Terms--Quadratic stability, stability theory, switched linear systems.

In this note, we define strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the nonexistence of a strong CQLF, for a pair of LTI systems, is characterized by easily verifiable algebraic conditions. These conditions are found to play an important role in proving the existence of strong CQLFs for general LTI systems. Index Terms--Quadratic stability, stability theory, switched linear systems.

We introduce a permissioned distributed ledger technology (DLT) design for crowdsourced smart mobility applications. This architecture is based on a directed acyclic graph architecture (similar to the IOTA tangle) and uses both Proof-of-Work and Proof-of-Position mechanisms to provide protection against spam attacks and malevolent actors. In addition to enabling individuals to retain ownership of their data and to monetize it, the architecture is also suitable for distributed privacy-preserving machine learning algorithms, is lightweight, and can be implemented in simple internet-of-things (IoT) devices. To demonstrate its efficacy, we apply this framework to reinforcement learning settings where a third party is interested in acquiring information from agents. In particular, one may be interested in sampling an unknown vehicular traffic flow in a city, using a DLT-type architecture and without perturbing the density, with the idea of realizing a set of virtual tokens as surrogates of real vehicles to explore geographical areas of interest. These tokens, whose authenticated position determines write access to the ledger, are thus used to emulate the probing actions of commanded (real) vehicles on a given planned route by “jumping” from a passing-by vehicle to another to complete the planned trajectory. Consequently, the environment stays unaffected (i.e., the autonomy of participating vehicles is not influenced by the algorithm), regardless of the number of emitted tokens. The design of such a DLT architecture is presented, and numerical results from large-scale simulations are provided to validate the proposed approach. [ABSTRACT FROM AUTHOR]