Estimating a mean from delayed observations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47652/1/440_2004_Article_BF00533314.pd

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Optimal Traffic Networks

Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by a strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio

Price of anarchy on heterogeneous traffic-flow networks

The efficiency of routing traffic through a network, comprising nodes connected by links whose cost of traversal is either fixed or varies in proportion to volume of usage, can be measured by the `price of anarchy'. This is the ratio of the cost incurred by agents who act to minimise their individual expenditure to the optimal cost borne by the entire system. As the total traffic load and the network variability - parameterised by the proportion of variable-cost links in the network - changes, the behaviours that the system presents can be understood with the introduction of a network of simpler structure. This is constructed from classes of non-overlapping paths connecting source to destination nodes that are characterised by the number of variable-cost edges they contain. It is shown that localised peaks in the price of anarchy occur at critical traffic volumes at which it becomes beneficial to exploit ostensibly more expensive paths as the network becomes more congested. Simulation results verifying these findings are presented for the variation of the price of anarchy with the network's size, aspect-ratio, variability and traffic load

Persistence of Natural Killer (NK) cell lymphocytosis with hyposplenism without development of leukaemia

BACKGROUND: Natural killer (NK) cell lymphocytosis usually has an indolent course and can progress into massive lymphocytosis with development of cytopenias and neoplastic diseases. NK-cells usually express one or more "NK-associated" antigens (CD16, CD56, CD57). Reactive expansions are seen in autoimmune diseases, viral infections, solid tumours and non-Hodgkin's lymphoma. CASE PRESENTATION: We report a lady with a benign clinical course over 10 years and persistent CD8+/CD3-/CD57+/CD16+ LGL proliferation with presence of Howell-Jolly bodies (functional hyposplenism), an association not previously described. CONCLUSION: We discuss the possible causes of clonal expansion and conclude that this may be part of the spectrum of immune dysregulation associated with NK-cell lymphocytosis

The Dispersal Ecology of Rhodesian Sleeping Sickness Following Its Introduction to a New Area

Tsetse-transmitted human and animal trypanosomiasis are constraints to both human and animal health in sub-Saharan Africa, and although these diseases have been known for over a century, there is little recent evidence demonstrating how the parasites circulate in natural hosts and ecosystems. The spread of Rhodesian sleeping sickness (caused by Trypanosoma brucei rhodesiense) within Uganda over the past 15 years has been linked to the movement of infected, untreated livestock (the predominant reservoir) from endemic areas. However, despite an understanding of the environmental dependencies of sleeping sickness, little research has focused on the environmental factors controlling transmission establishment or the spatially heterogeneous dispersal of disease following a new introduction. In the current study, an annually stratified case-control study of Rhodesian sleeping sickness cases from Serere District, Uganda was used to allow the temporal assessment of correlations between the spatial distribution of sleeping sickness and landscape factors. Significant relationships were detected between Rhodesian sleeping sickness and selected factors, including elevation and the proportion of land which was “seasonally flooding grassland” or “woodlands and dense savannah.” Temporal trends in these relationships were detected, illustrating the dispersal of Rhodesian sleeping sickness into more ‘suitable’ areas over time, with diminishing dependence on the point of introduction in concurrence with an increasing dependence on environmental and landscape factors. These results provide a novel insight into the ecology of Rhodesian sleeping sickness dispersal and may contribute towards the implementation of evidence-based control measures to prevent its further spread

Computation of Equilibrium Distributions of Markov Traffic-Assignment Models

Markov traffic-assignment models explicitly represent the day-to-day evolving interaction between traffic congestion and drivers' information acquisition and choice processes. Such models can, in principle, be used to investigate traffic flows in stochastic equilibrium, yielding estimates of the equilibrium mean and covariance matrix of link or route traffic flows. However, in general these equilibrium moments cannot be written down in closed form. While Monte Carlo simulations of the assignment process may be used to produce “empirical” estimates, this approach can be extremely computationally expensive if reliable results (relatively free of Monte Carlo error) are to be obtained. In this paper an alternative method of computing the equilibrium distribution is proposed, applicable to the class of Markov models with linear exponential learning filters. Based on asymptotic results, this equilibrium distribution may be approximated by a Gaussian process, meaning that the problem reduces to determining the first two multivariate moments in equilibrium. The first of these moments, the mean flow vector, may be estimated by a conventional traffic-assignment model. The second, the flow covariance matrix, is estimated through various linear approximations, yielding an explicit expression. The proposed approximations are seen to operate well in a number of illustrative examples. The robustness of the approximations (in terms of network input data) is discussed, and shown to be connected with the “volatility” of the traffic assignment process

Расчёт напряженно-деформированного состояния виброизоляторов сложной формы

Розглянуто пружно-деформований стан гумових віброізоляторів з урахуванням контактної взаємодії з деталями конструкції.Stress-strain state of rubber vibroinsulators is considered, taking into account contact interaction with construction parts

Nash Equilibria in Discrete Routing Games with Convex Latency Functions

In a discrete routing game, each of n selfish users employs a mixed strategy to ship her (unsplittable) traffic over m parallel links. The (expected) latency on a link is determined by an arbitrary non-decreasing, non-constant and convex latency function φ. In a Nash equilibrium, each user alone is minimizing her (Expected) Individual Cost, which is the (expected) latency on the link she chooses. To evaluate Nash equilibria, we formulate Social Cost as the sum of the users ’ (Expected) Individual Costs. The Price of Anarchy is the worst-case ratio of Social Cost for a Nash equilibrium over the least possible Social Cost. A Nash equilibrium is pure if each user deterministically chooses a single link; a Nash equilibrium is fully mixed if each user chooses each link with non-zero probability. We obtain: For the case of identical users, the Social Cost of any Nash equilibrium is no more than the Social Cost of the fully mixed Nash equilibrium, which may exist only uniquely. Moreover, instances admitting a fully mixed Nash equilibrium enjoy an efficient characterization. For the case of identical users, we derive two upper bounds on the Price of Anarchy: For the case of identical links with a monomial latency function φ(x) = x d, the Price of Anarchy is the Bell number of order d + 1. For pure Nash equilibria, a generic upper bound from the Wardrop model can be transfered to discrete routing games. For polynomial latency functions with non-negative coefficients and degree d, this yields an upper bound of d + 1. For th