Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

Implementation and role of device management Solutions to the end users

This research is based on consumer complaints with respect to recently purchased consumer electronics. This research document will investigate the instances of development and device management as a tool used to aid consumer and manage consumer’s mobile products in order to resolve issues in or before the consumers is aware one exists. The problem at the present time is that mobile devices are becoming very advanced pieces of technology, and not all manufacturers and network providers have kept up the support element of End users. As such, the subject of the research is to investigate how device management could possibly be used as a method to promote research and development of mobile devices, and provide a better experience for the consumer. The wireless world is becoming increasingly complex as revenue opportunities are driven by new and innovative data services. We can no longer expect the customer to have the knowledge or ability to configure their own device. Device Management platforms can address the challenges of device configuration and support through new enabling technologies. Leveraging these technologies will allow a network operator to reduce the cost of subscriber ownership, drive increased ARPU (Average Revenue per User) by removing barriers to adoption, reduce churn by improving the customer experience and increase customer loyalty. DM technologies provide a flexible and powerful management method but are managing the same device features that have historically been configured manually through call centers or by the end user making changes directly on the device. For this reason DM technologies must be treated as part of a wider support solution. The traditional requirement for discovery, fault finding, troubleshooting and diagnosis are still as relevant with DM as they are in the current human support environment yet the current generation of solutions do little to address this problem. In the deployment of an effective Device Management solution the network operator must consider the integration of the DM platform, interfacing with many areas of the business, supported by knowledge of the relationship between devices, applications, solutions and services maintained on an ongoing basis. Complementing the DM solution with published device information, setup guides, training material and web based tools will ensure the quality of the customer experience, ensuring that problems are completely resolved, driving data usage by focusing customer education on the use of the wireless service In this way device management becomes a tool used both internally within the network or device vendor and by the customer themselves, with each user empowered to effectively manage the device without any prior knowledge or experience, confident that changes they apply will be relevant, accurate, stable and compatible. The value offered by an effective DM solution with an expert knowledge service will become a significant differentiator for the network operator in an ever competitive wireless market. This research document is intended to highlight some of the issues the industry faces as device management technologies become more prevalent, and offers some potential solutions to simplify the increasingly complex task of managing devices on the network, where device management can be used as a tool to aid customer relations and manage customer’s mobile products in order to resolve issues before the user is aware one exists. The research is broken down into the following, Customer Relationship Management, Device management, the role of knowledge with the DM, Companies that have successfully implemented device management, and the future of device management and CRM. And it also consists of questionnaires aimed at technical support agents and mobile device users. Interview was carried out with CRM managers within support centre to further the evidence gathered. To conclude, the document is to consider the advantages and disadvantages of device management and attempt to determine the influence it will have over customer support centre, and what methods could be used to implement it.

What aspects of rehabilitation provision contribute to self-reported met needs for rehabilitation one year after stroke - amount, place, operator or timing?

BACKGROUND AND OBJECTIVE: To a large extent, people who have suffered a stroke report unmet needs for rehabilitation. The purpose of this study was to explore aspects of rehabilitation provision that potentially contribute to self-reported met needs for rehabilitation 12 months after stroke with consideration also to severity of stroke. METHODS: The participants (n = 173) received care at the stroke units at the Karolinska University Hospital, Sweden. Using a questionnaire, the dependent variable, self-reported met needs for rehabilitation, was collected at 12 months after stroke. The independent variables were four aspects of rehabilitation provision based on data retrieved from registers and structured according to four aspects: amount of rehabilitation, service level (day care rehabilitation, primary care rehabilitation and home-based rehabilitation), operator level (physiotherapist, occupational therapist, speech therapist) and time after stroke onset. Multivariate logistic regression analyses regarding the aspects of rehabilitation were performed for the participants who were divided into three groups based on stroke severity at onset. RESULTS: Participants with moderate/severe stroke who had seen a physiotherapist at least once during each of the 1st, 2nd and 3rd-4th quarters of the first year (OR 8.36, CI 1.40-49.88 P = 0.020) were more likely to report met rehabilitation needs. CONCLUSION: For people with moderate/severe stroke, continuity in rehabilitation (preferably physiotherapy) during the first year after stroke seems to be associated with self-reported met needs for rehabilitation.

Endogenous collateral: arbitrage and equilibrium without bounded short sales

We study the implications of the absence of arbitrage in an two period economy where default is allowed and assets are secured by collateral choosen by the borrowers. We show that non arbitrage sale prices of assets are submartingales, whereas non arbitrage purchase prices of the derivatives (secured by the pool of collaterals) are supermartingales. We use these non arbitrage conditions to establish existence of equilibrium, without imposing bounds on short sales. The nonconvexity of the budget set is overcome by considering a continuum of agents. Our results are particularly relevant for the collateralized mortgage obligations(CMO) markets.

Strategic manipulation of empirical tests

Theories can be produced by individuals seeking a good reputation of knowledge. Hence, a significant question is how to test theories anticipating that they might have been produced by (potentially uninformed) experts who prefer their theories not to be rejected. If a theory that predicts exactly like the data generating process is not rejected with high probability then the test is said to not reject the truth. On the other hand, if a false expert, with no knowledge over the data generating process, can strategically select theories that will not be rejected then the test can be ignorantly passed. These tests have limited use because they cannot feasibly dismiss completely uninformed experts. Many tests proposed in the literature (e.g., calibration tests) can be ignorantly passed. Dekel and Feinberg (2006) introduced a class of tests that seemingly have some power of dismissing uninformed experts. We show that some tests from their class can also be ignorantly passed. One of those tests, however, does not reject the truth and cannot be ignorantly passed. Thus, this empirical test can dismiss false experts.We also show that a false reputation of knowledge can be strategically sustained for an arbitrary, but given, number of periods, no matted which test is used (provided that it does not reject the truth). However, false experts can be discredited, even with bounded data sets, if the domain of permissible theories is mildly restricted.