The impact of randomization in smoothing networks

We revisit randomized smoothing networks (Herlihy and Tirthapura in J Parallel Distrib Comput 66(5):626–632, 2006), which are made up of balancers and wires. We assume that balancers are oriented independently and uniformly at random. Tokens arrive arbitrarily on w input wires and propagate asynchronously through the network; each token is served on the output wire it arrives at. The smoothness is the maximum discrepancy among the numbers of tokens arriving at the w output wires. We present a collection of lower and upper bounds on smoothness, which are to some extent surprising: (1) The smoothness of a single block network is lg lg w+Θ(1) (with high probability), where the additive constant is between ?2 and 3. This tight bound improves vastly over the upper bound of ${\mathcal{O}(\sqrt{lg\, w})}$ from Herlihy and Tirthapura (2006), and it essentially settles our understanding of the smoothing properties of the block network. Further, this lg lg w+Θ(1) bound cannot be extended to universal smoothing a property stronger than smoothing that we introduce. (2) Most significantly, the smoothness of the cascade of two block networks is no more than 17 (with high probability); this is the first known randomized network with so small depth (2 lg w) and so good (constant) smoothness. The proof introduces some combinatorial and probabilistic structures and techniques which may be further applicable; the result demonstrates the full power of randomization in smoothing networks. (3) There is no randomized 1-smoothing network of width w and depth d that achieves 1-smoothness with probability better than ${\frac{\mathsf{d}} {w-1} }$ . In view of the deterministic, Θ(lg w)-depth, 1-smoothing network in Klugerman and Plaxton (Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 1992), this result implies the first separation between deterministic and randomized smoothing networks. These results demonstrate an unexpected limitation on the power of randomization for smoothing networks: although it yields constant smoothness using small depth, going down to smoothness of 1 requires linear depth.     

Book Review

Abstract

COMPUTER ABUSE, by Donn B. Parker, Susan Nycum, and S. Stephen Oura; National Science Foundation, 1973, 131 pages, $4.75. (Obtain from National Technical Information Service, U.S. Department of Commerce, Springfield, VA, 22151. Order No. PB-231–320.)     

Direct routing: Algorithms and complexity

Direct routing is the special case ofbufferless routing whereN packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing:

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

Inflammation in Coronary Microvascular Dysfunction

Chronic low-grade inflammation is involved in coronary atherosclerosis, presenting multiple clinical manifestations ranging from asymptomatic to stable angina, acute coronary syndrome, heart failure and sudden cardiac death. Coronary microvasculature consists of vessels with a diameter less than 500 μm, whose potential structural and functional abnormalities can lead to inappropriate dilatation and an inability to meet the required myocardium oxygen demands. This review focuses on the pathogenesis of coronary microvascular dysfunction and the capability of non-invasive screening methods to detect the phenomenon. Anti-inflammatory agents, such as statins and immunomodulators, including anakinra, tocilizumab, and tumor necrosis factor-alpha inhibitors, have been assessed recently and may constitute additional or alternative treatment approaches to reduce cardiovascular events in atherosclerotic heart disease characterized by coronary microvascular dysfunction.     

Quantification of uncertainty modelling in stochastic analysis of FRP composites

The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.     

Probabilistic Models for Spatially Varying Mechanical Properties of In-Service GFRP Cladding Panels

The physical uncertainty associated with fiber-reinforced polymer composites has to be quantified and dealt with for their widespread use to be reliable. Developing probabilistic models based on experimental studies form an important part of this task. In the present paper, such models are developed for glass fiber-reinforced polymer (GFRP) composites based on an experimental study on panels obtained from Mondial House, a 32?year old building demolished in 2006 in London. Having an average size of 1.5?m×1.7?m and made of chopped strand mat composites, these panels have been exposed to varying ambient conditions, protected only by a fire retardant gel coat for self-cleaning. Tensile and compressive tests are performed to quantify the variability in stiffness and strength properties of these panels. Intra- and interpanel effects and correlations between random variables are studied using statistical methods. A range of probability distributions is tested and suggestions are made with regard to their suitability for modeling different mechanical and geometric properties.     

Biometric verification with correlation filters

Using biometrics for subject verification can significantly improve security over that of approaches based on passwords and personal identification numbers, both of which people tend to lose or forget. In biometric verification the system tries to match an input biometric (such as a fingerprint, face image, or iris image) to a stored biometric template. Thus correlation filter techniques are attractive candidates for the matching precision needed in biometric verification. In particular, advanced correlation filters, such as synthetic discriminant function filters, can offer very good matching performance in the presence of variability in these biometric images (e.g., facial expressions, illumination changes, etc.). We investigate the performance of advanced correlation filters for face, fingerprint, and iris biometric verification.