24,236 research outputs found

    Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

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    Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in dd-dimensions, with d=4+ϵd=4+\epsilon.Comment: 20 pages, 3 figures This version corrects and clarifies the previous result. This version has been submitted for publicatio

    Projections, Pseudo-Stopping Times and the Immersion Property

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    Given two filtrations FG\mathbb F \subset \mathbb G, we study under which conditions the F\mathbb F-optional projection and the F\mathbb F-dual optional projection coincide for the class of G\mathbb G-optional processes with integrable variation. It turns out that this property is equivalent to the immersion property for F\mathbb F and G\mathbb G, that is every F\mathbb F-local martingale is a G\mathbb G-local martingale, which, equivalently, may be characterised using the class of F\mathbb F-pseudo-stopping times. We also show that every G\mathbb G-stopping time can be decomposed into the minimum of two barrier hitting times

    Proximity Full-Text Search with a Response Time Guarantee by Means of Additional Indexes

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    Full-text search engines are important tools for information retrieval. Term proximity is an important factor in relevance score measurement. In a proximity full-text search, we assume that a relevant document contains query terms near each other, especially if the query terms are frequently occurring words. A methodology for high-performance full-text query execution is discussed. We build additional indexes to achieve better efficiency. For a word that occurs in the text, we include in the indexes some information about nearby words. What types of additional indexes do we use? How do we use them? These questions are discussed in this work. We present the results of experiments showing that the average time of search query execution is 44-45 times less than that required when using ordinary inverted indexes. This is a pre-print of a contribution "Veretennikov A.B. Proximity Full-Text Search with a Response Time Guarantee by Means of Additional Indexes" published in "Arai K., Kapoor S., Bhatia R. (eds) Intelligent Systems and Applications. IntelliSys 2018. Advances in Intelligent Systems and Computing, vol 868" published by Springer, Cham. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-01054-6_66. The work was supported by Act 211 Government of the Russian Federation, contract no 02.A03.21.0006.Comment: Alexander B. Veretennikov. Chair of Calculation Mathematics and Computer Science, INSM. Ural Federal Universit

    Nondestructive quantitative measurement for precision quality control in additive manufacturing using hyperspectral imagery and machine learning.

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    Measuring the purity of the metal powder is essential to maintain the quality of additive manufacturing products. Contamination is a significant concern, leading to cracks and malfunctions in the final products. Conventional assessment methods focus more on physical integrity rather than material composition and can be time-consuming. By capturing spectral data from a wide frequency range along with the spatial information, hyperspectral imaging (HSI) can detect minor differences in terms of temperature, moisture, and chemical composition to tackle this challenge. In this article, we explore the application of HSI in conjunction with machine learning for nondestructive inspection of metal powders. By employing near-infrared and visible HSI cameras, we introduce the utilization of HSI for this purpose. We delve into the technical challenges encountered and present detailed solutions through three case studies, including the establishment of a spectral dictionary, contamination detection, and band selection analysis. Our experimental results demonstrate the immense potential of HSI and its synergy with machine learning for nondestructive testing in powder metallurgy, particularly in meeting the requirements of industrial manufacturing environments

    wsrf: An R Package for Classification with Scalable Weighted Subspace Random Forests

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    We describe a parallel implementation in R of the weighted subspace random forest algorithm (Xu, Huang, Williams, Wang, and Ye 2012) available as the wsrf package. A novel variable weighting method is used for variable subspace selection in place of the traditional approach of random variable sampling. This new approach is particularly useful in building models for high dimensional data - often consisting of thousands of variables. Parallel computation is used to take advantage of multi-core machines and clusters of machines to build random forest models from high dimensional data in considerably shorter times. A series of experiments presented in this paper demonstrates that wsrf is faster than existing packages whilst retaining and often improving on the classification performance, particularly for high dimensional data

    Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy

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    Automated label-free quantitative imaging of biological samples can greatly benefit high throughput diseases diagnosis. Digital holographic microscopy (DHM) is a powerful quantitative label-free imaging tool that retrieves structural details of cellular samples non-invasively. In off-axis DHM, a proper spatial filtering window in Fourier space is crucial to the quality of reconstructed phase image. Here we describe a region-recognition approach that combines shape recognition with an iterative thresholding to extracts the optimal shape of frequency components. The region recognition technique offers fully automated adaptive filtering that can operate with a variety of samples and imaging conditions. When imaging through optically scattering biological hydrogel matrix, the technique surpasses previous histogram thresholding techniques without requiring any manual intervention. Finally, we automate the extraction of the statistical difference of optical height between malaria parasite infected and uninfected red blood cells. The method described here pave way to greater autonomy in automated DHM imaging for imaging live cell in thick cell cultures

    Stability of the utility maximization problem with random endowment in incomplete markets

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    We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well-posed, in the sense the optimal wealth and the marginal utility-based prices are continuous functionals of preferences and probabilistic views.Comment: 21 pages, revised version. To appear in "Mathematical Finance"
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