Average Consensus in the Presence of Delays and Dynamically Changing Directed Graph Topologies

Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practical settings due to varying delays that might affect transmissions at different times, as well as possible changes in the underlying interconnection topology (e.g., due to component mobility). In this work, we propose protocols to overcome these limitations. We first consider a fixed interconnection topology (captured by a - possibly directed - graph) and propose a discrete-time protocol that can reach asymptotic average consensus in a distributed fashion, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its outgoing links (i.e., the number of components to which it sends information). We subsequently extend the protocol to also handle changes in the underlying interconnection topology and describe a variety of rather loose conditions under which the modified protocol allows the components to reach asymptotic average consensus. The proposed algorithms are illustrated via examples.Comment: 37 page

Comments on the entropic gravity proposal

Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the entropic gravity proposal cannot account for the gravitational force in generic situations.Comment: v2, 20pp, 1fig; added references and discussions; improved presentation; accepted in EPJ

L-configuration re-attachment of distal biceps tendon rupture

In distal biceps tendon ruptures, re-attachment to the radial tuberosity should ensure adequate tendon to bone contact for optimal healing

Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method, utilizes the total variation distance to discriminate the transition probabilities of a high dimensional Markov process and a reduced order Markov process. The approximation is obtained by optimizing a linear functional defined in terms of transition probabilities of the reduced order Markov process over a total variation distance constraint. The transition probabilities of the approximated Markov process are given by a water-filling solution. The second method, utilizes total variation distance to discriminate the invariant probability of a Markov process and that of the approximating process. The approximation is obtained via two alternative formulations: (a) maximizing a functional of the occupancy distribution of the Markov process, and (b) maximizing the entropy of the approximating process invariant probability. For both formulations, once the reduced invariant probability is obtained, which does not correspond to a Markov process, a further approximation by a Markov process is proposed which minimizes the Kullback-Leibler divergence. These approximations are given by water-filling solutions. Finally, the theoretical results of both methods are applied to specific examples to illustrate the methodology, and the water-filling behavior of the approximations.Comment: 38 pages, 17 figures, submitted to IEEE-TA

ARQ-based Average Consensus over Unreliable Directed Network Topologies

In this paper, we address the discrete-time average consensus problem, where nodes exchange information over unreliable communication links. We enhance the Robustified Ratio Consensus algorithm by exploiting features of the Automatic Repeat ReQuest (ARQ) protocol used for error control of data transmissions, in order to allow the nodes to reach asymptotic average consensus even when operating within unreliable directed networks. This strategy, apart from handling time-varying delays induced by retransmissions of erroneous packets, can also handle packet drops that occur when exceeding a predefined packet retransmission limit imposed by the ARQ protocol. Invoking the ARQ protocol allows nodes to: (a) exploit the incoming error-free acknowledgement feedback to initially acquire or later update their out-degree, (b) know whether a packet has arrived or not, and (c) determine a local upper-bound on the delays imposed by the retransmission limit. By augmenting the network's corresponding weight matrix, we show that nodes utilizing our proposed ARQ-based Ratio Consensus algorithm can reach asymptotic average consensus over unreliable networks, while maintaining low running sum values

Comorbidities of deformational plagiocephaly in infancy:a scoping review protocol

Introduction Deformational plagiocephaly (DP) is one of the most common cranial shape disorders in infancy. It is characterised by unilateral flattening of the skull due to head preference to one side. The literature suggests that DP is associated with comorbidities such as developmental delay, but the nature and prevalence of the comorbid impairments are still unclear and controversial. Therefore, our scoping review (ScR) aims to explore systematically the extent and nature of literature by identifying, mapping and categorising the most relevant comorbidities of DP in children up to the age of 2 years.Methods and analysis This protocol is based on the framework outlined by Arksey and O’Malley. A systematic search will be conducted to identify relevant full text studies from 1992 to 2021 using the databases of Cochrane, MEDLINE, Google Scholar, EMBASE, PubMed and University of Nicosia EBSCO. Two independent reviewers will screen abstracts and full articles in parallel, using specific inclusion and exclusion criteria. Specifically, this review will consider studies investigating DP and relevant comorbidities in children up to the age of 2 years of life without craniosynostosis, torticollis and any other diagnosed neurodevelopmental deficiency.The Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for ScR Checklist will be considered for results’ analysis and reporting. The results will be described in a narrative form in relation to the research question and in the context of the overall study purpose.Ethics and dissemination Research ethics approval is not required for this ScR since data will be retrieved from publicly available studies. Dissemination activities will include research findings’ submission for publication in a relevant peer-reviewed journal and presentation of the results at relevant conferences.Registration Our protocol was registered prospectively with the Open Science Framework (https://osf.io/48am3/)