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Buck, Marshall W.; Coley, Raymond; Robbins, David P.

doi:10.1023/a:1022468019197

Cited by 12 publications

(2 citation statements)

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“…The present work could be considered a sequel to earlier works by the fourth author [Ven22], and the first three authors [GKN23]. The work [Ven22] relies heavily on the polynomial method using Alon's Combinatorial Nullstellensatz [Alo99] (also see Buck, Coley, and Robbins [BCR92], and Alon and Tarsi [AT92]), and the work [GKN23] relies heavily on a recent multiplicity extension of the Combinatorial Nullstellensatz given by Sauermann and Wigderson [SW22]. The problems of concern, in the two earlier works as well as in the present work, belong to a larger class of questions that have been of interest for a long time, and have rich literature.…”

Section: Motivationmentioning

confidence: 99%

Institute of Child Health, Kolkata, 1956–2022

2022

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Institute of Child Health, Kolkata is an iconic pediatric institution of India, which had its inception as one of the first pediatric hospital of the country. Pediatrics, as a separate branch of medicine, different from the principles and practices of adult medicine, was conceptualized and materialized in India by the founder of this institution, who is referred to as one of the Father of Indian Pediatrics, Dr. Kshirode Chandra Chaudhuri. This article portrays the journey of ICH, the popular acronym of the famed Institute, through the last seven decades from 1956 till the present, trying to capture the initial years of its establishment in the late 1950s, followed by its gradual evolution to an institution of central importance in pediatric healthcare, medical education, research and development, and service to the society, particularly in Eastern India.

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Section: Motivationmentioning

confidence: 99%

Institute of Child Health, Kolkata, 1956–2022

2022

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“…. , 𝜆 𝑟 ) follows from an explicit factorization of its determinant [16], [21,Eq. (2.18)]; therefore 𝐾 𝑚,𝑟 has rank at least 𝜈 𝑚 .…”

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confidence: 99%

Faster Modular Composition

Neiger¹,

Salvy²,

Schost³

et al. 2021

Preprint

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A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by 𝑛, the algorithm uses 𝑂 (𝑛 1.43 ) field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require 𝑂 (𝑛 1.63 ) field operations in general, and 𝑛 3/2+𝑜 (1) field operations in the particular case of power series over a field of large enough characteristic. If using cubic-time matrix multiplication, the new algorithm runs in 𝑛 5/3+𝑜 (1) operations, while previous ones run in 𝑂 (𝑛 2 ) operations.Our approach relies on the computation of a matrix of algebraic relations that is typically of small size. Randomization is used to reduce arbitrary input to this favorable situation.

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Advanced Determinant Calculus

Krattenthaler

2001

The Andrews Festschrift

291

389

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The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research. Second, it lists a number of such determinants that have been already evaluated, together with explanations which tell in which contexts they have appeared. Third, it points out references where further such determinant evaluations can be found.1991 Mathematics Subject Classification. Primary 05A19; Secondary 05A10 05A15 05A17 05A18 05A30 05E10 05E15 11B68 11B73 11C20 15A15 33C45 33D45.

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Cited by 12 publications

References 1 publication

Institute of Child Health, Kolkata, 1956–2022

Institute of Child Health, Kolkata, 1956–2022

Faster Modular Composition

Advanced Determinant Calculus

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