Fast Multiscale Neighbor Embedding de Bodt, Cyril; Mulders, Dounia; Verleysen, Michel ...
IEEE transaction on neural networks and learning systems,
04/2022, Letnik:
33, Številka:
4
Journal Article
Dimension reduction (DR) computes faithful low-dimensional (LD) representations of high-dimensional (HD) data. Outstanding performances are achieved by recent neighbor embedding (NE) algorithms such ...as <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula>-SNE, which mitigate the curse of dimensionality. The single-scale or multiscale nature of NE schemes drives the HD neighborhood preservation in the LD space (LDS). While single-scale methods focus on single-sized neighborhoods through the concept of perplexity, multiscale ones preserve neighborhoods in a broader range of sizes and account for the global HD organization to define the LDS. For both single-scale and multiscale methods, however, their time complexity in the number of samples is unaffordable for big data sets. Single-scale methods can be accelerated by relying on the inherent sparsity of the HD similarities they involve. On the other hand, the dense structure of the multiscale HD similarities prevents developing fast multiscale schemes in a similar way. This article addresses this difficulty by designing randomized accelerations of the multiscale methods. To account for all levels of interactions, the HD data are first subsampled at different scales, enabling to identify small and relevant neighbor sets for each data point thanks to vantage-point trees. Afterward, these sets are employed with a Barnes-Hut algorithm to cheaply evaluate the considered cost function and its gradient, enabling large-scale use of multiscale NE schemes. Extensive experiments demonstrate that the proposed accelerations are, statistically significantly, both faster than the original multiscale methods by orders of magnitude, and better preserving the HD neighborhoods than state-of-the-art single-scale schemes, leading to high-quality LD embeddings. Public codes are freely available at https://github.com/cdebodt .
Artykuł bada wpływ awangardowej prozy Djuny Barnes na twórczość współczesnej polskiej artystki Ewy Kuryluk, kierując szczególną uwagę na grę intertekstualną między powieściami Ostępy nocy (Barnes) a ...Wiek 21 (Kuryluk). Pisarstwo Barnes, będące, mówiąc za Julie Taylor, reprezentacją „afektywnego modernizmu”, stylu emocji, za którym stoi doświadczane i doświadczające ciało, staje się dla Kuryluk jednym z głównych źródeł przeżywania traumy oraz miłości. Współczesna polska pisarka niejako stąpa po śladach Barnes: zarówno na poziomie języka i sposobu obrazowania, jak i tematyki oraz symboliki dotyczących zagadnień kobiecości, macierzyństwa, seksualności. Artystka przechwytuje plastyczną i fotograficzną wyobraźnię Barnes, pozostającą w korelacji z innymi twórcami pierwszej połowy XX wieku (np. Hansem Bellmerem), do budowania obrazu miłości z końca ubiegłego stulecia.
In this paper, we study certain interesting and useful properties of incomplete
ℵ‐functions. The incomplete
ℵ‐function is an extension of the
ℵ‐function. We find several useful classical integral ...transforms of these functions. Further, we examine the fractional calculus with the incomplete
ℵ‐functions and point out several special cases. Finally, we give the applications of incomplete
ℵ‐functions in detecting glucose supply in human blood.
Individual variation in responses to commonly used tests of anxiety and spatial memory is often reported. While this variation is frequently considered to be ‘noise’, evidence suggests that it is, at ...least partially, related to consistent individual differences in behavioral responses (i.e., personality). The same tests used to assess anxiety are often used to profile personality traits, but personality differences are rarely considered when testing treatment differences in anxiety. Focusing on the rat literature, we describe fundamental principles involved in anxiety and spatial memory tests and we discuss how personality differences and housing conditions can influence behavioral responses in these tests. We propose that an opportunity exists to increase stress resiliency in environmentally sensitive individuals by providing environmental enrichment. We conclude by discussing different approaches to incorporating personality measures into the design and analysis of future studies; given the potential that variation masks research outcomes, we suggest that a strategy which considers the individual and its housing can contribute to improving research reproducibility.
•Individual rat personality and housing conditions generate test response variation.•Variation in responses to anxiety and cognition tests masks treatment differences.•The same tests used to assess anxiety can be used to profile personality traits.•Enriched housing increases resiliency in environmentally sensitive individuals.•Study design should incorporate personality measures to improve reproducibility.
Among the methods valuable for assessing spatial learning and memory impairments in rodents, the Barnes maze (BM) task deserves special attention. It is based on the assumption that the animal placed ...into the aversive environment should learn and remember the location of an escape box located below the surface of the platform. Different phases of the task allow to measure spatial learning, memory retrieval, and cognitive flexibility. Herein, we summarize current knowledge about the BM procedure, its variations and critical parameters measured in the task. We highlight confounding factors which should be taken into account when conducting BM task, discussing briefly its advantages and disadvantages. We then propose an extended version of the BM protocol which allows to measure different aspects of spatial learning and memory in rodents. We believe that this review will help to standardize the BM methodology across the laboratories and eventually make the results comparable.
In this paper, we reconsider the large-a asymptotic expansion of the Hurwitz zeta function ζ(s,a). New representations for the remainder term of the asymptotic expansion are found and used to obtain ...sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G-function and the s-derivative of the Hurwitz zeta function ζ(s,a) are provided. A detailed discussion on the sharpness of our error bounds is also given.
We argue that the Mellin–Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary ...powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.
Determining glucose supply in blood using the incomplete I-function Bhatter, Sanjay; Jangid, Kamlesh; Shyamsunder ...
Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters,
June 2024, 2024-06-00, 2024-06-01, Letnik:
10
Journal Article
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In this paper, we delve into the realm of mathematical modeling as a powerful theoretical tool to understand essential aspects of medical-biological phenomena. This study focuses on developing a ...mathematical model incorporating the incomplete I-function (IIF) and estimating glucose supply in the human bloodstream. The results of our investigations are far-reaching, revealing many exciting scenarios across the various parameters under investigation. These results are not only practical but can also play an essential role in the contexts of medical and biological fields.
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