934 resultados para Geometric Sum
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We introduce a function which measures the number of distinct ways in which a number can be expressed as the sum of Fibonacci numbers. Using a binary table and other devices, we explore the values that can take and reveal some interesting patterns. The article shows how standard spreadsheet functionalities make it possible to reveal quite striking patterns in data, and is intended to be used in the classroom.
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In two earlier papers, an intricate Jackpot structure and analysis of pseudo-random numbers for Keno in the Australian state of Queensland circa 2000 were described. Aspects of the work were also reported at an international conference . Since that time, many aspects of the game in Australia have changed. The present paper presents more up-to-date details of Keno throughout the states of Queensland, New South Wales and Victoria. A much simpler jackpot structure is now in place and this is described. Two add-ons or side-bets to the game are detailed: the trivial Heads or Tails and the more interesting Keno Bonus, which leads to consideration of the subset sum problem. The most intricate structure is where Heads or Tails and Keno Bonus are combined, and here, the issue of independence arises. Closed expressions for expected return to player (ERTP) are presented in all cases.
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Deterministic synthesis of self-organized quantum dot arrays for renewable energy, biomedical, and optoelectronic applications requires control over adatom capture zones, which are presently mapped using unphysical geometric tessellation. In contrast, the proposed kinetic mapping is based on simulated two-dimensional adatom fluxes in the array and includes the effects of nucleation, dissolution, coalescence, and process parameters such as surface temperature and deposition rate. This approach is generic and can be used to control the nanoarray development in various practical applications. © 2009 American Institute of Physics.
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Here we report on an unconventional Ni-P alloy-catalyzed, high-throughput, highly reproducible chemical vapor deposition of ultralong carbon microcoils using acetylene precursor in the temperature range 700-750 °C. Scanning electron microscopy analysis reveals that the carbon microcoils have a unique double-helix structure and a uniform circular cross-section. It is shown that double-helix carbon microcoils have outstanding superelastic properties. The microcoils can be extended up to 10-20 times of their original coil length, and quickly recover the original state after releasing the force. A mechanical model of the carbon coils with a large spring index is developed to describe their extension and contraction. Given the initial coil parameters, this mechanical model can successfully account for the geometric nonlinearity of the spring constants for carbon micro- and nanocoils, and is found in a good agreement with the experimental data in the whole stretching process.
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The quick detection of an abrupt unknown change in the conditional distribution of a dependent stochastic process has numerous applications. In this paper, we pose a minimax robust quickest change detection problem for cases where there is uncertainty about the post-change conditional distribution. Our minimax robust formulation is based on the popular Lorden criteria of optimal quickest change detection. Under a condition on the set of possible post-change distributions, we show that the widely known cumulative sum (CUSUM) rule is asymptotically minimax robust under our Lorden minimax robust formulation as a false alarm constraint becomes more strict. We also establish general asymptotic bounds on the detection delay of misspecified CUSUM rules (i.e. CUSUM rules that are designed with post- change distributions that differ from those of the observed sequence). We exploit these bounds to compare the delay performance of asymptotically minimax robust, asymptotically optimal, and other misspecified CUSUM rules. In simulation examples, we illustrate that asymptotically minimax robust CUSUM rules can provide better detection delay performance at greatly reduced computation effort compared to competing generalised likelihood ratio procedures.
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The controlled growth of ultra-small Ge/Si quantum dot (QD) nuclei (≈1 nm) suitable for the synthesis of uniform nanopatterns with high surface coverage, is simulated using atom-only and size non-uniform cluster fluxes. It is found that seed nuclei of more uniform sizes are formed when clusters of non-uniform size are deposited. This counter-intuitive result is explained via adatom-nanocluster interactions on Si(100) surfaces. Our results are supported by experimental data on the geometric characteristics of QD patterns synthesized by nanocluster deposition. This is followed by a description of the role of plasmas as non-uniform cluster sources and the impact on surface dynamics. The technique challenges conventional growth modes and is promising for deterministic synthesis of nanodot arrays.
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We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.
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The US National Institute of Standards and Technology (NIST) showed that, in 2004, owners and operations managers bore two thirds of the total industry cost burden from inadequate interoperability in construction projects from inception to operation, amounting to USD10.6 billion. Building Information Modelling (BIM) and similar tools were identified by Engineers Australia in 2005 as potential instruments to significantly reduce this sum, which in Australia could amount to total industry-wide cost burden of AUD12 billion. Public sector road authorities in Australia have a key responsibility in driving initiatives to reduce greenhouse gas emissions from the construction and operations of transport infrastructure. However, as previous research has shown the Environmental Impact Assessment process, typically used for project approvals and permitting based on project designs available at the consent stage, lacks Key Performance Indicators (KPIs) that include long-term impact factors and transfer of information throughout the project life cycle. In the building construction industry, BIM is widely used to model sustainability KPIs such as energy consumption, and integrated with facility management systems. This paper proposes that a similar use of BIM in early design phases of transport infrastructure could provide: (i) productivity gains through improved interoperability and documentation; (ii) the opportunity to carry out detailed cost-benefit analyses leading to significant operational cost savings; (iii) coordinated planning of street and highway lighting with other energy and environmental considerations; iv) measurable KPIs that include long-term impact factors which are transferable throughout the project life cycle; and (v) the opportunity for integrating design documentation with sustainability whole-of-life targets.
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We propose and evaluate a novel methodology to identify the rolling shutter parameters of a real camera. We also present a model for the geometric distortion introduced when a moving camera with a rolling shutter views a scene. Unlike previous work this model allows for arbitrary camera motion, including accelerations, is exact rather than a linearization and allows for arbitrary camera projection models, for example fisheye or panoramic. We show the significance of the errors introduced by a rolling shutter for typical robot vision problems such as structure from motion, visual odometry and pose estimation.
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This paper presents a full system demonstration of dynamic sensorbased reconfiguration of a networked robot team. Robots sense obstacles in their environment locally and dynamically adapt their global geometric configuration to conform to an abstract goal shape. We present a novel two-layer planning and control algorithm for team reconfiguration that is decentralised and assumes local (neighbour-to-neighbour) communication only. The approach is designed to be resource-efficient and we show experiments using a team of nine mobile robots with modest computation, communication, and sensing. The robots use acoustic beacons for localisation and can sense obstacles in their local neighbourhood using IR sensors. Our results demonstrate globally-specified reconfiguration from local information in a real robot network, and highlight limitations of standard mesh networks in implementing decentralised algorithms.
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Twenty-three non-methane hydrocarbons were captured from the exhaust of a car operating on unleaded petrol (ULP) and 10% ethanol fuels at steady speed on a chassis dynamometer. The compounds were identified and quantified by GC/MS/FID and their emission concentrations at 60 km/h, 80km/h and idle speed were evaluated. The most abundant compounds in the exhaust included n-hexane, n-heptane, benzene, toluene, ethyl benzene, m- and p-xylenes, and methylcyclopentane. Because of the large number of compounds involved, no attempt was made to compare the emission concentrations of the compounds. Rather the sum of the emission concentrations for the suite of compounds identified was compared when the car was powered by ULP and 10% ethanol fuel. It was evident from the results that the emission concentrations and factors were generally higher with ULP than with 10% ethanol fuel. The total emission concentrations with the ULP fuel were 2.8, 4.2 and 2.6 times the corresponding values for the 10% ethanol fuel at 60km/h, 80km/h and idle speed, respectively. The implications of the results on the environment are discussed in the paper.
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Purpose To establish whether the use of a passive or active technique of planning target volume (PTV) definition and treatment methods for non-small cell lung cancer (NSCLC) deliver the most effective results. This literature review assesses the advantages and disadvantages in recent studies of each, while assessing the validity of the two approaches for planning and treatment. Methods A systematic review of literature focusing on the planning and treatment of radiation therapy to NSCLC tumours. Different approaches which have been published in recent articles are subjected to critical appraisal in order to determine their relative efficacy. Results Free-breathing (FB) is the optimal method to perform planning scans for patients and departments, as it involves no significant increase in cost, workload or education. Maximum intensity projection (MIP) is the fastest form of delineation, however it is noted to be less accurate than the ten-phase overlap approach for computed tomography (CT). Although gating has proven to reduce margins and facilitate sparing of organs at risk, treatment times can be longer and planning time can be as much as 15 times higher for intensity modulated radiation therapy (IMRT). This raises issues with patient comfort and stabilisation, impacting on the chance of geometric miss. Stereotactic treatments can take up to 3 hours to treat, along with increases in planning and treatment, as well as the additional hardware, software and training required. Conclusion Four-dimensional computed tomography (4DCT) is superior to 3DCT, with the passive FB approach for PTV delineation and treatment optimal. Departments should use a combination of MIP with visual confirmation ensuring coverage for stage 1 disease. Stages 2-3 should be delineated using ten-phases overlaid. Stereotactic and gated treatments for early stage disease should be used accordingly; FB-IMRT is optimal for latter stage disease.
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This paper presents our system to address the CogALex-IV 2014 shared task of identifying a single word most semantically related to a group of 5 words (queries). Our system uses an implementation of a neural language model and identifies the answer word by finding the most semantically similar word representation to the sum of the query representations. It is a fully unsupervised system which learns on around 20% of the UkWaC corpus. It correctly identifies 85 exact correct targets out of 2,000 queries, 285 approximate targets in lists of 5 suggestions.
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INTRODUCTION: I want to argue that understanding masculinity is an important part of understanding gender and sexuality as it relates to information and communications technologies (ICTs), specifically those under the lens of the information-systems community. In order to do this, the landscape of gender and sexuality research in general is referred to along with such research in the field of information systems (IS), with reference as necessary to masculinity studies. I will then suggest some possible areas where a more thorough going theorization may prove useful. In sum, future research might focus on the relation-ship between marginalised masculinities and the construction and consumption of is in work organisations and society…
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With increased consolidation and a few large vendors dominating the market, how can software vendors distinguish themselves in order to maintain profitability and gain market share? Increasingly customers are becoming more proactive in selecting a vendor and a product, drawing upon various publications, market surveys, mailing lists, and, of course, other users. In particular, though, a company's Web site is the obvious place to begin information gathering. In sum, it may seem that the days of the uninformed customer prepared to be "sold to" are potentially all but gone.