Evan’s syndrome secondary to COVID-19 infection

Wide range of autoimmune diseases are known to occur following SARS-CoV-2 infection. There are very few case reports of Evan’s syndrome secondary to COVID-19. We hereby report a case of Evan’s syndrome secondary to COVID-19 infection and discuss its management

Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower Bounds

We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in $\tilde{O}(D+\sqrt{n})$ rounds in the standard CONGEST model (where $n$ is the network size and $D$ is the network diameter) and this is essentially the best possible round complexity (up to logarithmic factors). However, in resource-constrained networks such as ad hoc wireless and sensor networks, nodes spending so much time can lead to significant spending of resources such as energy. Motivated by the above consideration, we study distributed algorithms for MST under the \emph{sleeping model} [Chatterjee et al., PODC 2020], a model for design and analysis of resource-efficient distributed algorithms. In the sleeping model, a node can be in one of two modes in any round -- \emph{sleeping} or \emph{awake} (unlike the traditional model where nodes are always awake). Only the rounds in which a node is \emph{awake} are counted, while \emph{sleeping} rounds are ignored. A node spends resources only in the awake rounds and hence the main goal is to minimize the \emph{awake complexity} of a distributed algorithm, the worst-case number of rounds any node is awake. We present deterministic and randomized distributed MST algorithms that have an \emph{optimal} awake complexity of $O(\log n)$ time with a matching lower bound. We also show that our randomized awake-optimal algorithm has essentially the best possible round complexity by presenting a lower bound of $\tilde{\Omega}(n)$ on the product of the awake and round complexity of any distributed algorithm (including randomized) that outputs an MST, where $\tilde{\Omega}$ hides a $1/(\text{polylog } n)$ factor.Comment: 28 pages, 1 table, 5 figures, abstract modified to fit arXiv constraint

Sleeping is Superefficient: MIS in Exponentially Better Awake Complexity

Maximal Independent Set (MIS) is one of the central and most well-studied problems in distributed computing. Even after four decades of intensive research, the best-known (randomized) MIS algorithms take $O(\log{n})$ worst-case rounds on general graphs (where $n$ is the number of nodes), while the best-known lower bound is $\Omega\left(\sqrt{\frac{\log{n}}{\log{\log{n}}}}\right)$ rounds. Breaking past the $O(\log{n})$ worst-case bound or showing stronger lower bounds have been longstanding open problems. Our main contribution is that we show that MIS can be computed in (worst-case) awake complexity of $O(\log \log n)$ rounds that is (essentially) exponentially better compared to the (traditional) round complexity lower bound of $\Omega\left(\sqrt{\frac{\log{n}}{\log{\log{n}}}}\right)$. Specifically, we present the following results. (1) We present a randomized distributed (Monte Carlo) algorithm for MIS that with high probability computes an MIS and has $O(\log\log{n})$-rounds awake complexity. This algorithm has (traditional) {\em round complexity} that is $O(poly(n))$. Our bounds hold in the $CONGEST(O(polylog n))$ model where only $O(polylog n)$ (specifically $O(\log^3 n)$) bits are allowed to be sent per edge per round. (2) We also show that we can drastically reduce the round complexity at the cost of a slight increase in awake complexity by presenting a randomized MIS algorithm with $O(\log \log n \log^* n )$ awake complexity and $O(\log^3 n \log \log n \log^*n)$ round complexity in the $CONGEST(O(polylog n))$ model.Comment: Abstract shortened to fit arXiv constraint

Time- and Communication-Efficient Overlay Network Construction via Gossip

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph $G$ on $n$ nodes and $m$ edges, we can construct an overlay network that is a constant-degree expander in polylog $n$ rounds using only $\tilde{O}(n)$ messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only $\tilde{O}(n)$ messages, which is sublinear in $m$ (even when $m$ is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog $n$ rounds and $o(m)$ messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model.Comment: Slightly shortened abstrac

Distributed MIS in O(log log n) Awake Complexity

Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best known (randomized) MIS algorithms have O(log n) round complexity on general graphs [Luby, STOC 1986] (where n is the number of nodes), while the best known lower bound is [EQUATION] [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the O(log n) round complexity upper bound or showing stronger lower bounds have been longstanding open problems. Energy is a premium resource in various settings such as battery-powered wireless networks and sensor networks. The bulk of the energy is used by nodes when they are awake, i.e., when they are sending, receiving, and even just listening for messages. On the other hand, when a node is sleeping, it does not perform any communication and thus spends very little energy. Several recent works have addressed the problem of designing energy-efficient distributed algorithms for various fundamental problems. These algorithms operate by minimizing the number of rounds in which any node is awake, also called the (worst-case) awake complexity. An intriguing open question is whether one can design a distributed MIS algorithm that has significantly smaller awake complexity compared to existing algorithms. In particular, the question of obtaining a distributed MIS algorithm with o(log n) awake complexity was left open in [Chatterjee, Gmyr, Pandurangan, PODC 2020]. Our main contribution is to show that MIS can be computed in awake complexity that is exponentially better compared to the best known round complexity of O(log n) and also bypassing its fundamental [EQUATION] round complexity lower bound exponentially. Specifically, we show that MIS can be computed by a randomized distributed (Monte Carlo) algorithm in O(log log n) awake complexity with high probability.1 However, this algorithm has a round complexity that is O(poly(n)). We then show how to drastically improve the round complexity at the cost of a slight increase in awake complexity by presenting a randomized distributed (Monte Carlo) algorithm for MIS that, with high probability computes an MIS in O((log log n) log* n) awake complexity and O((log3 n)(log log n) log* n) round complexity. Our algorithms work in the CONGEST model where messages of size O(log n) bits can be sent per edge per round

Distributed MIS in O(log log n) Awake Complexity

Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best known (randomized) MIS algorithms have O(log n) round complexity on general graphs [Luby, STOC 1986] (where n is the number of nodes), while the best known lower bound is [EQUATION] [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the O(log n) round complexity upper bound or showing stronger lower bounds have been longstanding open problems. Energy is a premium resource in various settings such as battery-powered wireless networks and sensor networks. The bulk of the energy is used by nodes when they are awake, i.e., when they are sending, receiving, and even just listening for messages. On the other hand, when a node is sleeping, it does not perform any communication and thus spends very little energy. Several recent works have addressed the problem of designing energy-efficient distributed algorithms for various fundamental problems. These algorithms operate by minimizing the number of rounds in which any node is awake, also called the (worst-case) awake complexity. An intriguing open question is whether one can design a distributed MIS algorithm that has significantly smaller awake complexity compared to existing algorithms. In particular, the question of obtaining a distributed MIS algorithm with o(log n) awake complexity was left open in [Chatterjee, Gmyr, Pandurangan, PODC 2020]. Our main contribution is to show that MIS can be computed in awake complexity that is exponentially better compared to the best known round complexity of O(log n) and also bypassing its fundamental [EQUATION] round complexity lower bound exponentially. Specifically, we show that MIS can be computed by a randomized distributed (Monte Carlo) algorithm in O(log log n) awake complexity with high probability.1 However, this algorithm has a round complexity that is O(poly(n)). We then show how to drastically improve the round complexity at the cost of a slight increase in awake complexity by presenting a randomized distributed (Monte Carlo) algorithm for MIS that, with high probability computes an MIS in O((log log n) log* n) awake complexity and O((log3 n)(log log n) log* n) round complexity. Our algorithms work in the CONGEST model where messages of size O(log n) bits can be sent per edge per round

PageRank in scale-free random graphs

We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature

Awareness On The Management Of Iatrogenic Arterial Nicking During Dental Surgical Procedures Among Dental Students

Background: Bleeding during surgery may be a serious clinical problem which will be very disconcerting to the patient and will have serious consequences. During the course of nearly all kinds of surgery, blood vessels are going to be disrupted, causing some bleeding. The dentist should be aware of all techniques of hemorrhage control for various sorts of bleeding episodes—small vessels, large vessels, oozing, drug-induced, or when an underlying coagulation defect is present. Bleeding complications can occur in healthy also as systemically compromised patients. Aim: The aim of the current study is to analyse the awareness and knowledge on the management of iatrogenic arterial nicking among dental undergraduate students. Materials and Methods: The study was a cross-sectional questionnaire study. Survey was designed as a questionnaire in English with 2 sections. Section 1 contained demographics and section 2 had questions on various techniques on management of arterial injury, which was answered by 150 dental undergraduate students. All the obtained data were entered on Microsoft excel sheet and analysed using SPSS by IBM. Results: From the statistical analysis it is clear that almost 75% of the respondents from final year and internship were aware of different methods of management and prevention of dental injuries, yet only minimal number of students from other three years were aware of the methods and procedures to be followed at each step during dental surgical procedures, Conclusion: Within the limitations of the current study, it can be concluded that the majority of dental undergraduate students are aware of different methods of presentation and management of iatrogenic arterial nicking during dental surgical procedures. In the present study the knowledge on the methods of management such as mobilisation, deep sutures, burnishing of bone, use of bone grafting was lacking among first to third year students when compared to students pursuing their final year and internship.Saveetha Institute of Medical and Technical SciencesSaveetha Dental College and HospitalsSaveetha UniversityAkshaya Associates Private Limited, Chenna

An Almost Singularly Optimal Asynchronous Distributed MST Algorithm

A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC 2017, Elkin, PODC 2017]. However, it is open whether a singularly (near) optimal bound can be obtained for the MST construction problem in general \emph{asynchronous} CONGEST networks. We present a randomized distributed MST algorithm that, with high probability, computes an MST in \emph{asynchronous} CONGEST networks and takes $\tilde{O}(D^{1+\epsilon} + \sqrt{n})$ time and $\tilde{O}(m)$ messages, where $n$ is the number of nodes, $m$ the number of edges, $D$ is the diameter of the network, and $\epsilon >0$ is an arbitrarily small constant (both time and message bounds hold with high probability). Our algorithm is message optimal (up to a polylog$(n)$ factor) and almost time optimal (except for a $D^{\epsilon}$ factor). Our result answers an open question raised in Mashregi and King [DISC 2019] by giving the first known asynchronous MST algorithm that has sublinear time (for all $D = O(n^{1-\epsilon})$) and uses $\tilde{O}(m)$ messages. Using a result of Mashregi and King [DISC 2019], this also yields the first asynchronous MST algorithm that is sublinear in both time and messages in the $KT_1$ CONGEST model. A key tool in our algorithm is the construction of a low diameter rooted spanning tree in asynchronous CONGEST that has depth $\tilde{O}(D^{1+\epsilon})$ (for an arbitrarily small constant $\epsilon > 0$) in $\tilde{O}(D^{1+\epsilon})$ time and $\tilde{O}(m)$ messages. To the best of our knowledge, this is the first such construction that is almost singularly optimal in the asynchronous setting.Comment: 27 pages, accepted to DISC 202