When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV (G;p) is a polynomial in p. We present several distinct equivalent formulations of EV (G;p), unifying prior treatments of this topic. We use results on network resilience (introduced by Co...

An acyclic edge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge colouring using k colours and is usually denoted by a′(G). Determining a ′(G) exactly is a very hard problem (both the...

In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality . this paper, we build on recent algorithmic progresses in deep learning to explore various consensus-optimality trade-offs over fixed communication topology. First, propose the incremental -based stochastic gradient descent (i-CDSGD...

We will define the notions of abstract theorem-proving graph, abstract theorem-proving problem g and search strategy E for g. These concepts generalize the usual tree (or graph) searching problem and admit Hart, Nilsson and Raphael (1968) and Pohl (1969) theories of heuristic search. In particular the admissibility and optimality theorems of Hart, Nilsson and Raphael generalize for the classes ...

This paper investigates experimental design (DoE) for the calibration of the triaxial accelerometers embedded in a wearable micro Inertial Measurement Unit (μ-IMU). Firstly, a new linearization strategy is proposed for the accelerometer model associated with the so-called autocalibration scheme. Then, an effective Icosahedron design is developed, which can achieve both D-optimality and G-optima...

It is often helpful to compute the intrinsic volumes of a set of which only a pixel image is observed. A computational efficient approach, which is suggested by several authors and used in practice, is to approximate the intrinsic volumes by a linear functional of the pixel configuration histogram. Here we want to examine, whether there is an optimal way of choosing this linear functional, wher...

In this paper we consider space-time codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also point out that lattice codes based on Q-central division algebras satisfy this optimality criterion. As...