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Class (philosophy)

About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.


Papers
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Journal ArticleDOI
01 Sep 2022-Optik
TL;DR: In this paper , a class of (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation soliton solutions with optical features is presented. But the spectral properties of these solutions are unknown.

25 citations

Journal ArticleDOI
TL;DR: The results indicate that the introduction of mobile access collaborative homework to a second language English class in Japan does have observable effects on students, including changes in use of space, time and method for mobile collaborative homework.
Abstract: This research is designed to explore the areas of collaborative learning and the use of smartphones as a support for collaborative learning through a year-long exploratory multiple case study approach integrating both qualitative and quantitative data analysis Qualitative exploratory interviews are combined with Multidimensional Scaling Analysis to provide a detailed image of students' mobile use during collaborative activities The Multidimensional Scaling MDS reliability is supported by a second resampling that produced similar results independent of time of subjects The results are triangulated across the qualitative and quantitative data and key issues are interpreted and discussed The results indicate that the introduction of mobile access collaborative homework to a second language English class in Japan does have observable effects on students, including changes in use of space, time and method for mobile collaborative homework

25 citations

Journal ArticleDOI
TL;DR: In this article , the authors discuss classes of exact and perturbative spherically symmetric solutions in f(T,B)-gravity, and present general methods and strategies, like generalized Bianchi identities, to find spheically solutions in modified teleparallel theories of gravity.
Abstract: Abstract Spherically symmetric solutions of theories of gravity built one fundamental class of solutions to describe compact objects like black holes and stars. Moreover, they serve as starting point for the search of more realistic axially symmetric solutions which are capable to describe rotating compact objects. Theories of gravity that do not possess spherically symmetric solutions which meet all observational constraints are easily falsified. In this article, we discuss classes of exact and perturbative spherically symmetric solutions in f(T,B)-gravity. The perturbative solutions add to the ones which have already been found in the literature, while the exact solutions are presented here for the first time. Moreover, we present general methods and strategies, like generalized Bianchi identities, to find spherically solutions in modified teleparallel theories of gravity.

25 citations

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate that definitional loops are created in order to introduce new concepts into a language and use etymological data to show that elements of loops tend to be added to the English lexicon simultaneously and incorporate their results into a simple model for language evolution.
Abstract: Dictionaries link a given word to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that definitions loop back upon themselves. We demonstrate that such definitional loops are created in order to introduce new concepts into a language. In contrast to the expectations for a random lexical network, in graphs of the dictionary, meaningful loops are quite short, although they are often linked to form larger, strongly connected components. These components are found to represent distinct semantic ideas. This observation can be quantified by a singular value decomposition, which uncovers a set of conceptual relationships arising in the global structure of the dictionary. Finally, we use etymological data to show that elements of loops tend to be added to the English lexicon simultaneously and incorporate our results into a simple model for language evolution that falls within the ‘‘rich-get-richer’’ class of network growth.

25 citations

Posted Content
TL;DR: This paper investigates a class of functions, called PAP functions, that includes nearly all (possibly non-differentiable) functions in deep learning nowadays, and proposes a new type of derivatives, called intensional derivatives, and proves that these derivatives always exist and coincide with standard derivatives for almost all inputs.
Abstract: Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable functions, but in practice, they are commonly applied to functions with non-differentiabilities. For instance, neural networks using ReLU define non-differentiable functions in general, but the gradients of losses involving those functions are computed using autodiff systems in practice. This status quo raises a natural question: are autodiff systems correct in any formal sense when they are applied to such non-differentiable functions? In this paper, we provide a positive answer to this question. Using counterexamples, we first point out flaws in often-used informal arguments, such as: non-differentiabilities arising in deep learning do not cause any issues because they form a measure-zero set. We then investigate a class of functions, called PAP functions, that includes nearly all (possibly non-differentiable) functions in deep learning nowadays. For these PAP functions, we propose a new type of derivatives, called intensional derivatives, and prove that these derivatives always exist and coincide with standard derivatives for almost all inputs. We also show that these intensional derivatives are what most autodiff systems compute or try to compute essentially. In this way, we formally establish the correctness of autodiff systems applied to non-differentiable functions.

24 citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202311,771
202223,753
2021380
2020186
201962