The unfolding road from dust to trust

Beiu, Valeriu

doi:10.1117/12.2601821

Cited by 2 publications

(2 citation statements)

References 40 publications

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“…One additional remark is that computations such as the ones performed for generating these images are highly demanding and an option we intend to pursue is to rely on approximations which, while not absolutely accurate, would allow us to significantly reduce the computing time (time-complexity). These could also move us forward on time-efficient approximations of the coefficients of reliability polynomials, a topic of high interest in the context of advanced nanoscale CMOS transistors fabricated using EUV lithography [35].…”

Section: Discussionmentioning

confidence: 99%

On a Surface Associated with Pascal’s Triangle

et al. 2022

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An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the classical discrete Pascal’s triangle (comprising all the binomial coefficients) to a continuous version (exhibiting infinitely many values in between the binomial coefficients) might be geometrically helpful and revealing. That is why we have decided to investigate the geometric properties of a continuous extension of Pascal’s triangle including: Gauss curvatures, mean curvatures, geodesics, and level curves, as well as their symmetries.

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Section: Discussionmentioning

confidence: 99%

On a Surface Associated with Pascal’s Triangle

et al. 2022

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“…That is how we slowly realized that the original goal of Moore and Shannon-of finding networks for enhancing the reliability of computations-has been slowly shifting over time towards networks for reliable communications [6]. Still, with scaling, both computations and communications are being affected by variations [8], so a deeper understanding of reliability polynomials should in the end prove beneficial, and Pascal's surface seems to be providing a different view which starts from their coefficients.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Approximating the Level Curves on Pascal’s Surface

Dăuş

Jianu

Nagy

et al. 2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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It is well-known that in general the algorithms for determining the reliability polynomial associated to a two-terminal network are computationally demanding, and even just bounding the coefficients can be taxing. Obviously, reliability polynomials can be expressed in Bernstein form, hence all the coefficients of such polynomials are fractions of the binomial coefficients. That is why we have very recently envisaged using an extension of the classical discrete Pascal’s triangle (which comprises all the binomial coefficients) to a continuous version/surface. The fact that this continuous Pascal’s surface has real values in between the binomial coefficients makes it appealing as being a mathematical concept encompassing all the coefficients of all the reliability polynomials (which are integers, as resulting from counting processes) and more. This means that, the coefficients of any reliability polynomial can be represented as discrete steps (on level curves of integer values) on Pascal’s surface. The equation of this surface was formulated by means of the gamma function, for which quite a few approximation formulas are known. Therefore, we have started by reviewing many of those results, and have used a selection of those approximations for the level curves problem on Pascal’s surface. Towards the end, we present fresh simulations supporting the claim that some of these could be quite useful, as being both (reasonably) easy to calculate as well as fairly accurate.

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The unfolding road from dust to trust

Cited by 2 publications

References 40 publications

On a Surface Associated with Pascal’s Triangle

On a Surface Associated with Pascal’s Triangle

Approximating the Level Curves on Pascal’s Surface

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