Selfish traffic allocation for server farms

We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price of selfish routing using the price of anarchy (a.k.a. the coordination ratio) and other (e.g., bicriteria) measures in the recently introduced game theoretic parallel links network model of Koutsoupias and Papadimitriou. We generalize this model toward general, monotone families of cost functions and cost functions from queueing theory. A summary of our main results for general, monotone cost functions is as follows: 1. We give an exact characterization of all cost functions having a bounded/unbounded price of anarchy. For example, the price of anarchy for cost functions describing the expected delay in queueing systems is unbounded. 2. We show that an unbounded price of anarchy implies an extremely high performance degradation under bicriteria measures. In fact, the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size. 3. We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small or negligible amount of integrality can lead to a dramatic performance degradation. 4. We unify recent results on selfish routing under different objectives by showing that an unbounded price of anarchy under the min-max objective implies an unbounded price of anarchy under the average cost objective and vice versa. Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of Transmission Control Protocol (TCP) connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload. Our analysis indicates that all queueing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates

Studies Towards the Synthesis of Thienamycin

Almost all successful syntheses of bicyclic beta-lactams involve the early synthesis of the monocyclic azetidin-2-one ring. Of the numerous methods developed to achieve this, the [2+2] cycloaddition of chlorosulphonyl isocyanate (CSI) to functionalised alkenes has proven to be particularly useful. In general, addition is performed on alkenyl acetates providing C-4 acetoxyazetidinones, which have found widespread use since the 4-acetoxy substituent can be replaced with various nucleophiles in an elimination/addition sequence. However, there are few functionalised alkenes which directly introduce the C-4 carbon substitution required for carbapenem synthesis upon cycloaddition with CSI. Earlier investigations within this group have shown that allylsilanes undergo regioselective cycloaddition with CSI to yield C-4 silylmethyl substituted beta-lactams.133,137 The regiochemistry of cycloaddition is controlled by the beta-effect of silicon, i.e., silicon's ability to stabilise the development of partial positive charge P to itself. Use of phenyldimethylsilyl substitution allows access, albeit in low yield, to the corresponding hydroxymethyl azetidinones, via oxidative cleavage of the C-Si bond. We were intrigued by reports from Fleming142 and Taddei141 that allylsilanes bearing a chiral centre directly adjacent to the double bond undergo reaction with various electrophiles, including CSI, with remarkably high stereoselectivity. The initial aim of this project was to prepare an ?-oxa-allylsilane, with such a chiral centre, which would undergo regio- and stereoselective cycloaddition with CSI to yield a C-3 hydroxyethyl substituted ?-lactam. Subsequent oxidative cleavage of the silylmethyl group would led to a useful precursor for the powerful carbapenem antibiotic Thienamycin. Unfortunately, all attempts to carry out cycloaddition with these substrates resulted in a rapid 1,4 silyl elimination to penta-l,3-diene. In an attempt to overcome this problem, an alternative allylsilane was designed and prepared. Disappointingly, however, this compound did not react with CSI. The second aim of this project was to improve the efficiency of the key oxidative cleavage step. Our interest was awakened by a report from Ito191 which briefly mentioned the use of iodine monochloride (ICl) for the iododesilylation of phenyldimethylsilyl moieties prior to oxidative cleavage. In order to study the applicability of this method to C-4 silylmethyl beta-lactams simple N-protected precursors were prepared. Gratifyingly, treatment with ICl resulted in cleavage of the Si-Ph bond and formation of the chlorodimethylsilyl beta-lactams which were hydrolysed to the corresponding silanols in high yield. Oxidation of these compounds using a modification of Tamao's191 procedure gave the potentially useful C-4 hydroxymethyl beta-lactams in good to moderate yield. Alternatively, one of the intermediate chlorosilanes could be directly oxidised using AcOOH/KF

Modelling environmental factors correlated with podoconiosis: a geospatial study of non-filarial elephantiasis

Introduction The precise trigger of podoconiosis — endemic non-filarial elephantiasis of the lower legs — is unknown. Epidemiological and ecological studies have linked the disease with barefoot exposure to red clay soils of volcanic origin. Histopathology investigations have demonstrated that silicon, aluminium, magnesium and iron are present in the lower limb lymph node macrophages of both patients and non-patients living barefoot on these clays. We studied the spatial variation (variations across an area) in podoconiosis prevalence and the associated environmental factors with a goal to better understanding the pathogenesis of podoconiosis. Methods Fieldwork was conducted from June 2011 to February 2013 in 12 kebeles (administrative units) in northern Ethiopia. Geo-located prevalence data and soil samples were collected and analysed along with secondary geological, topographic, meteorological and elevation data. Soil data were analysed for chemical composition, mineralogy and particle size, and were interpolated to provide spatially continuous information. Exploratory, spatial, univariate and multivariate regression analyses of podoconiosis prevalence were conducted in relation to primary (soil) and secondary (elevation, precipitation, and geology) covariates. Results Podoconiosis distribution showed spatial correlation with variation in elevation and precipitation. Exploratory analysis identified that phyllosilicate minerals, particularly clay (smectite and kaolinite) and mica groups, quartz (crystalline silica), iron oxide, and zirconium were associated with podoconiosis prevalence. The final multivariate model showed that the quantities of smectite (RR = 2.76, 95% CI: 1.35, 5.73; p = 0.007), quartz (RR = 1.16, 95% CI: 1.06, 1.26; p = 0.001) and mica (RR = 1.09, 95% CI: 1.05, 1.13; p < 0.001) in the soil had positive associations with podoconiosis prevalence. Conclusions More quantities of smectite, mica and quartz within the soil were associated with podoconiosis prevalence. Together with previous work indicating that these minerals may influence water absorption, potentiate infection and be toxic to human cells, the present findings suggest that these particles may play a role in the pathogenesis of podoconiosis and acute adenolymphangitis, a common cause of morbidity in podoconiosis patients

Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

Characterising sand and gravel deposits using electrical resistivity tomography (ERT) : case histories from England and Wales

Electrical Resistivity Tomography (ERT) is a rapidly developing geophysical imaging technique that is now widely used to visualise subsurface geological structure, groundwater and lithological variations. It is being increasingly used in environmental and engineering site investigations, but despite its suitability and potential benefits, ERT has yet to be routinely applied by the minerals industry to sand and gravel deposit assessment and quarry planning. The principal advantages of ERT for this application are that it is a cost-effective non-invasive method, which can provide 2D or 3D spatial models of the subsurface throughout the full region of interest. This complements intrusive sampling methods, which typically provide information only at discrete locations. Provided that suitable resistivity contrasts are present, ERT has the potential to reveal mineral and overburden thickness and quality variations within the body of the deposit. Here we present a number of case studies from the UK illustrating the use of 2D and 3D ERT for sand and gravel deposit investigation in a variety of geological settings. We use these case studies to evaluate the performance of ERT, and to illustrate good practice in the application of ERT to deposit investigation. We propose an integrated approach to site investigation and quarry planning incorporating both conventional intrusive methods and ERT

A global perspective on drinking-water and sanitation classification: an evaluation of census content

Following the recent expiry of the United Nations’ 2015 Millennium Development Goals (MDGs), new international development agenda covering 2030 water, sanitation and hygiene (WASH) targets have been proposed, which imply new demands on data sources for monitoring relevant progress. This study evaluates drinking-water and sanitation classification systems from national census questionnaire content, based upon the most recent international policy changes, to examine national population census’s ability to capture drinking-water and sanitation availability, safety, accessibility, and sustainability. In total, 247 censuses from 83 low income and lower-middle income countries were assessed using a scoring system, intended to assess harmonised water supply and sanitation classification systems for each census relative to the typology needed to monitor the proposed post-2015 indicators of WASH targets. The results signal a lack of international harmonisation and standardisation in census categorisation systems, especially concerning safety, accessibility, and sustainability of services in current census content. This suggests further refinements and harmonisation of future census content may be necessary to reflect ambitions for post-2015 monitoring

Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence

We introduce an optimum principle for a vehicular traffic network with road bottlenecks. This network breakdown minimization (BM) principle states that the network optimum is reached, when link flow rates are assigned in the network in such a way that the probability for spontaneous occurrence of traffic breakdown at one of the network bottlenecks during a given observation time reaches the minimum possible value. Based on numerical simulations with a stochastic three-phase traffic flow model, we show that in comparison to the well-known Wardrop's principles the application of the BM principle permits considerably greater network inflow rates at which no traffic breakdown occurs and, therefore, free flow remains in the whole network.Comment: 22 pages, 6 figure

The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

On Unbounded Composition Operators in L2L^2-Spaces

Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert's characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied

Activity-specific mobility of adults in a rural region of western Kenya

Improving rural household access to resources such as markets, schools and healthcare can help alleviate poverty in low-income settings. Current models of geographic accessibility to various resources rarely take individual variation into account due to a lack of appropriate data, yet understanding mobility at an individual level is key to knowing how people access their local resources. Our study used both an activity-specific survey and GPS trackers to evaluate how adults in a rural area of western Kenya accessed local resources. We calculated the travel time and time spent at six different types of resource and compared the GPS and survey data to see how well they matched. We found links between several demographic characteristics and the time spent at different resources, and that the GPS data reflected the survey data well for time spent at some types of resource, but poorly for others. We conclude that demography and activity are important drivers of mobility, and a better understanding of individual variation in mobility could be obtained through the use of GPS trackers on a wider scale