We consider an information update system on a gossip network, where a source node encodes information intontotal keys such that any subset of at leastk+ 1 keys can fully reconstruct the original information. This encoding process follows the principles of ak-out-of-nthreshold system. The encoded updates are then disseminated across the network through peer-to-peer communication. We have two different types of nodes in a network: subscriber nodes, which receive a unique key from the source node for every status update instantaneously, and nonsubscriber nodes, which receive a unique key for an update only if the node is selected by the source, and this selection is renewed for each update. For the message structure between nodes, we consider two different schemes: a memory scheme (in which the nodes keep the source’s current and previous encrypted messages) and a memoryless scheme (in which the nodes are allowed to only keep the source’s current message). We measure thetimelinessof information updates by using a recent performance metric called, the version age of information. We present explicit formulas for the time average AoI in a scalable homogeneous network as functions of the number of subscriber nodes under a memoryless scheme. Additionally, we provide strict lower and upper bounds for the time average AoI under a memory scheme.

Interest in soft continuum arms has increased as their inherent material elasticity enables safe and adaptive interactions with the environment. However to achieve full autonomy in these arms, accurate three-dimensional shape sensing is needed. Vision-based solutions have been found to be effective in estimating the shape of soft continuum arms. In this paper, a vision-based shape estimator that utilizes a geometric strain based representation for the soft continuum arm’s shape, is proposed. This representation reduces the dimension of the curved shape to a finite set of strain basis functions, thereby allowing for efficient optimization for the shape that best fits the observed image. Experimental results demonstrate the effectiveness of the proposed approach in estimating the end effector with accuracy less than the soft arm’s radius. Multiple basis functions are also analyzed and compared for the specific soft continuum arm in use.

In this article, we study the properties of the spectral analysis of multiclass Erdös-Rényi graphs. With a view towards using the embedding afforded by the decomposition of the graph Laplacian for subsequent processing, we analyze two basic geometric properties, namely interclass intersection and interclass distance. We will first study the dyadic two-class case in details and observe the existence of a phase transition for the interclass intersection. We then focus on the general multiclass case, where we introduce an appropriate notion of diagonal concentration and derive a statistical model that allows sampling graphs whose expected diagonal concentration is fixed. The simulations provided yield useful guidelines for practitioners to choose appropriately parameters in the context of spectral clustering.