Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Stochastic equations in infinite dimensions

Stochastic differential equations and diffusion processes

Probability and Measure

Cryptocurrencies, such as Bitcoin and 250 similar alt-coins, embody at their core a blockchain protocol --- a mechanism for a distributed network of computational nodes to periodically agree on a set of new transactions. Designing a secure blockchain protocol relies on an open challenge in security, that of designing a highly-scalable agreement protocol open to manipulation by byzantine or arbitrarily malicious nodes. Bitcoin's blockchain agreement protocol exhibits security, but does not scale: it processes 3--7 transactions per second at present, irrespective of the available computation capacity at hand. In this paper, we propose a new distributed agreement protocol for permission-less blockchains called ELASTICO. ELASTICO scales transaction rates almost linearly with available computation for mining: the more the computation power in the network, the higher the number of transaction blocks selected per unit time. ELASTICO is efficient in its network messages and tolerates byzantine adversaries of up to one-fourth of the total computational power. Technically, ELASTICO uniformly partitions or parallelizes the mining network (securely) into smaller committees, each of which processes a disjoint set of transactions (or "shards"). While sharding is common in non-byzantine settings, ELASTICO is the first candidate for a secure sharding protocol with presence of byzantine adversaries. Our scalability experiments on Amazon EC2 with up to $1, 600$ nodes confirm ELASTICO's theoretical scaling properties.

A Secure Sharding Protocol For Open Blockchains

Pipe system diagnosis and leak detection by unsteady-state tests. 1. Harmonic analysis

Reliable and quick techniques are needed to locate and estimate leaks in pressurised pipe systems in order to reduce water loss as much as possible. The aim of the present paper is to show that the...

Detecting leaks in pressurised pipes by means of transients

Transient conditions in closed conduits have traditionally been modeled as 1D flows with the implicit assumption that velocity profile and friction losses can be accurately predicted using equivalent 1D velocities. Although more complex fluid models have been suggested, there has been little direct experimental basis for selecting one model over another. This paper briefly reviews the significance of the 1D assumption and the historical approaches proposed for improving the numerical modeling of transient events. To address the critical need for better data, an experimental apparatus is described, and preliminary measurements of velocity profiles during two transient events caused by valve operation are presented. The velocity profiles recorded during these transient events clearly show regions of flow recirculation, flow reversal, and an increased intensity of fluid turbulence. The experimental pressures are compared to a water hammer model using a conventional quasi-steady representation of head loss an...

Velocity Profiles and Unsteady Pipe Friction in Transient Flow

Transient tests can be reliably used for the diagnosis of pressurized pipe systems. As a matter of fact, the pressure signals acquired during these tests can reveal the presence of anomalies, e.g., leaks, since any irregularity in the pipe gives rise to reflected waves which in turn create discontinuities in the observed signal at the measurement section. In order to make the most of the interpretation of the pressure signals, as well as to improve the effectiveness of the location of leaks, wavelet analysis—a powerful tool within the realm of harmonic analysis—can be used. It aids in the diagnosis of pressure pipe systems by better exposing pressure signal discontinuities and precisely determining the arrival time of the pressure waves reflected by leaks, thus locating the leak itself. Since many wavelet transforms are available and the choice is driven by the specific application, both continuous and discrete wavelet transforms are considered in the paper, comparing different mother wavelets. Then the r...

Wavelets for the Analysis of Transient Pressure Signals for Leak Detection

In this paper, the reliability of transients due to pump trip as a powerful tool for the pre-localization of anomalies in real pipe systems is tested. The examined pipe system is part of the one supplying the city of Milan, Italy and is managed by Metropolitana Milanese SpA (MM). The characteristics of such a system can be considered as intermediate between those of classical transmission mains and distribution systems because of its several branches. A Lagrangian model simulating pressure wave propagation is used to evaluate the pipe pressure wave speed – associated with a genetic algorithm – and to locate possible anomalies – associated with wavelet analysis. The results of the diagnosis of the pipe system are corroborated by repairs executed by MM in the area where possible anomalies have been pre-localized.

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Marco Ferrante

Papers

Pipe system diagnosis and leak detection by unsteady-state tests. 1. Harmonic analysis

Detecting leaks in pressurised pipes by means of transients

Velocity Profiles and Unsteady Pipe Friction in Transient Flow

Wavelets for the Analysis of Transient Pressure Signals for Leak Detection

Anomaly pre-localization in distribution–transmission mains by pump trip: preliminary field tests in the Milan pipe system