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About 10,000 papers for “Partial function”

Fine’s function and partial theta function

Heng Huat Chan, Song Heng Chan, Kuo-Jye Chen et al. · Proceedings of the American Mathematical Society · 2021

In this article, we use identities found in N.J. Fine’s book <italic>Basic hypergeometric series and its applications</italic> to derive a one-parameter generalization of the product of two partial theta functions discovered by G.E. Andrews and S.O. Warnaar. We also give two different proofs of this generalization, one of which is motivated by the work of A. Berkovich and the other is given by M.E.H. Ismail.

Cited by 1

The partial K function

Jake P. Grainger, Tuomas Rajala, David J. Murrell et al. · ArXiv.org · 2025

The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or between two different types of points. In this paper, introduce a partial K function, enabling us to account for some of the effects of the other point types when analysing point-point interactions. The partial K function we introduce reduces to the usual K function when the other points are independent of the points of interest and has a similar interpretation. Using examples, we demonstrate how the partial K function can unpick dependence between point types that would otherwise be hidden in the usual K function. We also discuss important bias correction steps and hyperparameter selection. In addition, we discuss an extension to account for other spatial covariates, and demonstrate the methodology on the Lansing Woods dataset.

Cited by 0Open access

Penalized function-on-function partial leastsquares regression

Hernandez Roig, Harold Antonio, Aguilera Morillo, María del Carmen, Aguilera, Ana M. et al. · e-Archivo (Carlos III University of Madrid) · 2023

This paper deals with the "function-on-function'" or "fully functional" linear regression problem. We address the problem by proposing a novel penalized Function-on-Function Partial Least-Squares (pFFPLS) approach that imposes smoothness on the PLS weights. Our proposal introduces an appropriate finite-dimensional functional space with an associated set of bases on which to represent the data and controls smoothness with a roughness penalty operator. Penalizing the PLS weights imposes smoothness on the resulting coefficient function, improving its interpretability. In a simulation study, we demonstrate the advantages of pFFPLS compared to non-penalized FFPLS. Our comparisons indicate a higher accuracy of pFFPLS when predicting the response and estimating the true coefficient function from which the data were generated. We also illustrate the advantages of our proposal with two case studies involving two well-known datasets from the functional data analysis literature. In the first one, we predict log precipitation curves from the yearly temperature profiles recorded in 35 weather stations in Canada. In the second case study, we predict the hip angle profiles during a gait cycle of children from their corresponding knee angle profiles.

Cited by 0Open access

Function Outlining and Partial Inlining

Peng Zhao, José Nelson Amaral · 2006

Frequently invoked large functions are common in non-numeric applications. These large functions present challenges to modern compilers not only because they require more time and resources at compilation time, but also because they may prevent optimizations such as function inlining. However, usually it is the case that large portions of the code in a hot function f/sub host/ are executed much less frequently than f/sub host/ itself. Partial inlining is a natural solution to the problems caused by including cold code segments that are seldom executed into hot functions that are frequently invoked. When applying partial inlining, a compiler outlines cold statements from a hot function f/sub host/. After outlining, f/sub host/ becomes smaller and thus can be easily inlined. This paper presents a framework for function outlining and partial inlining that includes several innovations: (1) an abstract-syntax-tree-based analysis and transformation to form cold regions for outlining; (2) a set of flexible heuristics to control the aggressiveness of function outlining; (3) several possible function outlining strategies; (4) alias agent, a new technique that overcomes negative side-effects of function outlining. With the proper strategy, partial inlining improves performance by up to 5.75%. A performance study also suggests that partial inlining is not effective on enabling more aggressive in-lining. The performance improvement from partial in-lining actually comes from better code placement and better code generation.

Cited by 19

Kidney function after partial nephrectomy

Simon P. Kim, R. Houston Thompson · Current Opinion in Urology · 2013

Partial nephrectomy should remain the standard of care for small renal masses, if the renal tumor size and complexity are amenable to such a surgical approach. Efforts to minimize ischemia time are important for long-term renal functional recovery, and hypothermia should be considered if longer warm ischemia times are anticipated (i.e. >25 min). Although the preliminary results of zero ischemia partial nephrectomy are promising, further research is needed to determine if these surgical techniques are safely adaptable in the broader urologic community.

Cited by 26

About a partial theta function

Vladimir Petrov Kostov · HAL (Le Centre pour la Communication Scientifique Directe) · 2013

International audience

Cited by 1

Thyroid function following partial thyroidectomy

N J Griffiths, R. S. Murley, R. Gulin et al. · British journal of surgery · 1974

Abstract The main objective of this investigation was to establish the incidence of hypothyroidism and recurrent goitre following partial thyroidectomy. Accurate measurements of the thyroid remnants and resected specimens have been made in all cases. The postoperative thyroid status has been assessed clinically and also biochemically by serum thyroxine as iodine, T3 resin uptake, free thyroxine index and thyroid-stimulating hormone estimations. Serum calcium and phosphorus have also been measured and the necessary histological material reviewed. Postoperative hypothyroidism occurred in approximately 11 per cent of previously toxic and 6.5 per cent of non-toxic patients, becoming evident in most cases within a year of operation. The T3 resin uptake measurement following operation in this and previous series suggests that in many patients there is a compensation process which is maintained by increased secretion of thyroid-stimulating hormone. No evidence has been adduced that patients who show this compensation mechanism are, as some have suggested, in a state of ‘subclinical hypothyroidism’ or that they become overtly hypothyroid later. In this series hypothyroidism was more closely related to small remnant size than the presence of lymphadenoid change. A significantly higher proportion of patients with small thyroid remnants became hypothyroid in both toxic and non-toxic groups. Remnants of about 8–16 ml ‘cuboid’ volume (roughly 8–16 g by weight) have seemed reasonable for our patients.

Cited by 29