29,703 research outputs found

    Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

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    We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

    Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs

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    Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as a measurement for estimator stability (informativeness), we provide a new estimate of the Fiedler value for these two random graph models. In the asymptotic limit as the number of vertices tends to infinity, we prove the validity of the estimate. Based on our findings, for a small number of items to be compared, we recommend a two-stage sampling strategy where a greedy sampling method is used initially and random sampling \emph{without} replacement is used in the second stage. When a large number of items is to be compared, we recommend random sampling with replacement as this is computationally inexpensive and trivially parallelizable. Experiments on synthetic and real-world datasets support our analysis

    The small and medium enterprises Act as catalyst for economic growth and development in Pakistan: Economic growth and development perspective

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    This paper explores the value of small and medium enterprises for the economic growth and development especially in Pakistan. Moreover, it assesses the usage of information technology in SMEs sector of Pakistan. According to the recent Census of Establishments conducted by the Federal Bureau of Statistics (FBS) there are about 3.2 million economic establishments in Pakistan. Out of these Small & Medium sized enterprises (SMEs) (with employment base up to 99) constitute 90% of all private enterprises employing approximately 78% of non-agriculture labor force1. SMEs contributed over 30% to GDP, 25% in export earnings besides sharing 35% in manufacturing value addition2. The paper suggests that SMEs act as a catalyst to economical growth and development where IT embedded in their operations, planning and decisions like Hong Kong, Denmark and USA. Many other societies also place great value on the small and medium enterprises and encourage their activity. In fact, wealth and a high majority of jobs are created by small & medium businesses in the world. As a result, many experienced business people, political leaders, economists, and educators believe that fostering a robust small and medium business culture will maximize individual and collective economic and social success on a local, national, and global scale. It is recommended that SMEs may be offered access to inexpensive capital, tax exemptions and management advice & experiences and IT infrastructure which further leads toward the economical growth & development. The economical growth and development in a country can brings happiness and prosperity to its nation

    Does the Culture and Practice of Allotment Holding within Oxford help to build a Sustainable Local Economy?

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    An allotment is defined as a piece of land usually about 250m² in size, which can be rented from the council in order to grow fruit and vegetables for you and your family. The study examines the culture and practice of allotment holding in Oxford and to assess if this element of self-sufficiency could benefit the community and to what extent allotments can help to build a sustainable local economy. Furthermore the study looks at the inclusion of allotments into Agenda 21 and rates Oxford City allotments using the Governments Sustainable Development Indicators. The research was based on ten face-to-face interviews with councillors and allotment holders as well as a survey of one hundred local plot holders. The findings from these interviews indicate that allotments within Oxford can be classified as sustainable when ranked against the Sustainable Development Indicators. Further to this, the study highlighted a new trend in allotment holding with a younger generation of people taking up the pastime. Due to the small sample size these findings cannot be classed as representative of the whole of Oxford, consequently generalisations cannot be made. Never the less the study provides useful insights into allotment holding and its role within sustainable development

    Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

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    We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.Comment: 31 pages, 2 figure
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