7,525 research outputs found

    Online Bin Stretching with Three Bins

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    Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 11/8=1.37511/8 = 1.375 for three bins. Additionally, we present a lower bound of 45/33=1.36‾45/33 = 1.\overline{36} for Online Bin Stretching on three bins and a lower bound of 19/1419/14 for four and five bins that were discovered using a computer search.Comment: Preprint of a journal version. See version 2 for the conference paper. Conference paper split into two journal submissions; see arXiv:1601.0811

    Discovering and Certifying Lower Bounds for the Online Bin Stretching Problem

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    There are several problems in the theory of online computation where tight lower bounds on the competitive ratio are unknown and expected to be difficult to describe in a short form. A good example is the Online Bin Stretching problem, in which the task is to pack the incoming items online into bins while minimizing the load of the largest bin. Additionally, the optimal load of the entire instance is known in advance. The contribution of this paper is twofold. First, we provide the first non-trivial lower bounds for Online Bin Stretching with 6, 7 and 8 bins, and increase the best known lower bound for 3 bins. We describe in detail the algorithmic improvements which were necessary for the discovery of the new lower bounds, which are several orders of magnitude more complex. The lower bounds are presented in the form of directed acyclic graphs. Second, we use the Coq proof assistant to formalize the Online Bin Stretching problem and certify these large lower bound graphs. The script we propose certified as well all the previously claimed lower bounds, which until now were never formally proven. To the best of our knowledge, this is the first use of a formal verification toolkit to certify a lower bound for an online problem

    The applications of deep neural networks to sdBV classification

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    With several new large-scale surveys on the horizon, including LSST, TESS, ZTF, and Evryscope, faster and more accurate analysis methods will be required to adequately process the enormous amount of data produced. Deep learning, used in industry for years now, allows for advanced feature detection in minimally prepared datasets at very high speeds; however, despite the advantages of this method, its application to astrophysics has not yet been extensively explored. This dearth may be due to a lack of training data available to researchers. Here we generate synthetic data loosely mimicking the properties of acoustic mode pulsating stars and we show that two separate paradigms of deep learning - the Artificial Neural Network And the Convolutional Neural Network - can both be used to classify this synthetic data effectively. And that additionally this classification can be performed at relatively high levels of accuracy with minimal time spent adjusting network hyperparameters.Comment: 12 pages, 10 figures, originally presented at sdOB

    Online Two-Dimensional Load Balancing

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    In this paper, we consider the problem of assigning 2-dimensional vector jobs to identical machines online so to minimize the maximum load on any dimension of any machine. For arbitrary number of dimensions d, this problem is known as vector scheduling, and recent research has established the optimal competitive ratio as O((log d)/(log log d)) (Im et al. FOCS 2015, Azar et al. SODA 2018). But, these results do not shed light on the situation for small number of dimensions, particularly for d = 2 which is of practical interest. In this case, a trivial analysis shows that the classic list scheduling greedy algorithm has a competitive ratio of 3. We show the following improvements over this baseline in this paper: - We give an improved, and tight, analysis of the list scheduling algorithm establishing a competitive ratio of 8/3 for two dimensions. - If the value of opt is known, we improve the competitive ratio to 9/4 using a variant of the classic best fit algorithm for two dimensions. - For any fixed number of dimensions, we design an algorithm that is provably the best possible against a fractional optimum solution. This algorithm provides a proof of concept that we can simulate the optimal algorithm online up to the integrality gap of the natural LP relaxation of the problem

    Evaluation of the EVA Descriptor for QSAR Studies: 3. The use of a Genetic Algorithm to Search for Models with Enhanced Predictive Properties (EVA_GA)

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    The EVA structural descriptor, based upon calculated fundamental molecular vibrational frequencies, has proved to be an effective descriptor for both QSAR and database similarity calculations. The descriptor is sensitive to 3D structure but has an advantage over field-based 3D-QSAR methods inasmuch as structural superposition is not required. The original technique involves a standardisation method wherein uniform Gaussians of fixed standard deviation (σ) are used to smear out frequencies projected onto a linear scale. This smearing function permits the overlap of proximal frequencies and thence the extraction of a fixed dimensional descriptor regardless of the number and precise values of the frequencies. It is proposed here that there exist optimal localised values of σ in different spectral regions; that is, the overlap of frequencies using uniform Gaussians may, at certain points in the spectrum, either be insufficient to pick up relationships where they exist or mix up information to such an extent that significant correlations are obscured by noise. A genetic algorithm is used to search for optimal localised σ values using crossvalidated PLS regression scores as the fitness score to be optimised. The resultant models are then validated against a previously unseen test set of compounds. The performance of EVA_GA is compared to that of EVA and analogous CoMFA studies

    Conducting a virtual ensemble with a kinect device

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    This paper presents a gesture-based interaction technique for the implementation of an orchestra conductor and a virtual ensemble, using a 3D camera-based sensor to capture user’s gestures. In particular, a human-computer interface has been developed to recognize conducting gestures using a Microsoft Kinect device. The system allows the conductor to control both the tempo in the piece played as well as the dynamics of each instrument set independently. In order to modify the tempo in the playback, a time-frequency processing-based algorithmis used. Finally, an experiment was conducted to assess user’s opinion of the system as well as experimentally confirm if the features in the system were effectively improving user experience or not.This work has been funded by the Ministerio de Economia y Competitividad of the Spanish Government under Project No. TIN2010-21089-C03-02 and Project No. IPT-2011-0885-430000 and by the Junta de Andalucia under Project No. P11-TIC-7154. The work has been done at Universidad de Malaga. Campus de Excelencia Internacional Andalucia Tech
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