scholarly journals Euler–Maclaurin expansions without analytic derivatives

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200441
Author(s):  
Bengt Fornberg
Keyword(s):  
Trapezoidal Rule ◽  
Step Size ◽  
Trade Off ◽  
Runge Phenomenon ◽  
Present Context ◽  
Infinite Sums ◽  
Derivatives Of ◽  
Special Case ◽  
Very High ◽  
Excellent Accuracy

The Euler–Maclaurin (EM) formulae relate sums and integrals. Discovered nearly 300 years ago, they have lost none of their importance over the years, and are nowadays routinely taught in scientific computing and numerical analysis courses. The two common versions can be viewed as providing error expansions for the trapezoidal rule and for the midpoint rule, respectively. More importantly, they provide a means for evaluating many infinite sums to high levels of accuracy. However, in all but the simplest cases, calculating very high-order derivatives analytically becomes prohibitively complicated. When approximating such derivatives with finite differences (FD), the choice of step size typically requires a severe trade-off between errors due to truncation and to rounding. We show here that, in the special case of EM expansions, FD approximations can provide excellent accuracy without the step size having to go to zero. While FD approximations of low-order derivatives to high orders of accuracy have many applications for solving ODEs and PDEs, the present context is unusual in that it relies on FD approximations to derivatives of very high orders. The application to infinite sums ensures that one can use centred FD formulae (which are not subject to the Runge phenomenon).

Glucuronidierung von Hydroxy-testosteron- und Hydroxy-androstendion-Verbindungen durch die mikrosomale UDP-Glucuronyl-Transferase der Rattenleber / Glucuronidation of Hydroxy-compounds of Testosterone and Androstenedione by the Microsomal UDP Glucuronyl Transferase of Rat Liver

1972 ◽  
Vol 27 (1) ◽  
pp. 49-52
Author(s):  
Herbert Schriefers ◽  
Rüdiger Ghraf ◽  
Birgit Lehnen
Keyword(s):  
High Specificity ◽  
Hydroxyl Group ◽  
Hydroxyl Groups ◽  
Testosterone Metabolism ◽  
Glucuronyl Transferase ◽  
Hydroxy Compounds ◽  
Derivatives Of ◽  
Special Case ◽  
Free Steroid ◽  
Very High

The microsomal UDP glucuronyl transferase exhibits activities against hydroxy derivatives of androstenedione (hydroxyl groups in the positions 2β, 6β or 16α) between 5% and 27% of the extent shown against testosterone. 2β-, 6β· and 16α-hydroxyl groups are much less efficient in accepting the glucuronic acid than the 17β-hydroxyl group.However, the acceptor function of the 17β-hydroxyl group is restricted by other hydroxy substituents in the testosterone molecule to an increasing extent represented by the following sequence: 2α, 6β, 6α, 16α, and 7α. A special case is represented by 2β-hydroxy-testosterone. The transferase displays a higher activity against this compound than against testosterone.Apparently the transferase approaches the steroid molecule from the α-side (with the β-side there is also contact at the C-6 atom) requires the 17β-hydroxyl group and the 3-oxo-4-ene system to display full activity.Thus the very high specificity of the transferase for testosterone explains the selective action of this enzyme on testosterone metabolism in the liver. This action is expressed by the fact, that in liver perfusates the percentage of testosterone in the glucuronide fraction is twice as large as the percentage of testosterone in the free steroid fraction.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

The Turbulence of Our Times

2020 ◽  
pp. 1-22
Keyword(s):  
Economic Development ◽  
Business Leaders ◽  
Trade Off ◽  
The Arts ◽  
Talented People ◽  
Rural And Urban ◽  
Turbulent Times ◽  
Full Swing ◽  
Very High

We are full swing into the era of turbulence, and at this time, our creativity is more important than ever. We have heard many scholars and business leaders ask the question, “Can we invent and innovate effectively to keep up with the fast changes happening around us?” This chapter explores how to develop a heightened creativity and help weak economic areas by using technology, the arts, and our unique cultures to ignite economic development. Attracting tourism; young, talented people; and entrepreneurs to rural and urban cores is essential to thrive in turbulent times. In times of turbulence, organizations often navigate on autopilot, failing to see unintended circumstances and implications. However, every time a decision is made there is a trade-off. A true understanding of the trade-off may determine success or failure. Failure could mean very high cost either monetarily or the organizational future in the marketplace.

Distributed Systems

2020 ◽  
pp. 143-198
Author(s):  
Andreas Bolfing
Keyword(s):  
Distributed Systems ◽  
Fault Tolerant ◽  
Deterministic Algorithm ◽  
Impossibility Result ◽  
Software Systems ◽  
Trade Off ◽  
Byzantine Failures ◽  
The Individual ◽  
Special Case

Chapter 5 considers distributed systems by their properties. The first section studies the classification of software systems, which is usually distinguished in centralized, decentralized and distributed systems. It studies the differences between these three major approaches, showing there is a rather multidimensional classification instead of a linear one. The most important case are distributed systems that enable spreading of computational tasks across several autonomous, independently acting computational entities. A very important result of this case is the CAP theorem that considers the trade-off between consistency, availability and partition tolerance. The last section deals with the possibility to reach consensus in distributed systems, discussing how fault tolerant consensus mechanisms enable mutual agreement among the individual entities in presence of failures. One very special case are so-called Byzantine failures that are discussed in great detail. The main result is the so-called FLP Impossibility Result which states that there is no deterministic algorithm that guarantees solution to the consensus problem in the asynchronous case. The chapter concludes by considering practical solutions that circumvent the impossibility result in order to reach consensus.

scholarly journals Improving weather and climate predictions by training of supermodels

2019 ◽  
Author(s):  
Francine Schevenhoven ◽  
Frank Selten ◽  
Alberto Carrassi ◽  
Noel Keenlyside
Keyword(s):  
Time Derivative ◽  
Learning Rule ◽  
Training Methods ◽  
Model Errors ◽  
Climate Simulations ◽  
Weather And Climate ◽  
Present Context ◽  
Training Schemes ◽  
The Individual ◽  
Derivatives Of

Abstract. Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so called "supermodel". Here we focus on the weighted supermodel – the supermodel's time derivative is a weighted superposition of the time-derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here we apply two different training methods to a supermodel of up to four different versions of the global atmosphere-ocean-land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called Cross Pollination in Time (CPT), where models exchange states during the training. The second method is a synchronization based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used Multi-Model Ensemble (MME) mean. Furthermore we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance all models are warm with respect to the truth). In principle the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation for instance) and to evaluate cases for which the truth falls outside of the model class.

scholarly journals Kinetics of saccharose fermentation by Kombucha

2014 ◽  
Vol 20 (3) ◽  
pp. 345-352 ◽  
Author(s):  
Eva Loncar ◽  
Katarina Kanuric ◽  
Radomir Malbasa ◽  
Mirjana Djuric ◽  
Spasenija Milanovic
Keyword(s):  
Empirical Model ◽  
Black Tea ◽  
Reaction Rates ◽  
Yeast Cells ◽  
Inoculum Concentration ◽  
Viable Cells ◽  
Rate Of Reaction ◽  
Kinetics Of ◽  
Derivatives Of ◽  
Very High

Kinetics of saccharose fermentation by Kombucha is not yet well defined due to lack of knowledge of reaction mechanisms taking place during this process. In this research kinetics of saccharose fermentation by Kombucha was analysed using the suggested empirical model. The data were obtained on 1.5 g L-1 of black tea, with 66.47 g L-1 of saccharose and using 10% (v/v) or 15% (v/v) of Kombucha. Total number of viable cells was as follows: approximately 5x105 of yeast cells per mL of the inoculum and approximately 2x106 of bacteria cells per mL of the inoculum. The samples were analysed after 0, 3, 4, 5, 6, 7 and 10 days. Their pH values and contents of saccharose, glucose, fructose, total acids and ethanol were determined. A saccharose concentration model was defined as sigmoidal function at 22oC and 30oC, and with 10% (v/v) and 15% (v/v) of inoculum quantity. Determination coefficients of the functions were very high (R2>0.99). Reaction rates were calculated as first derivatives of Boltzmann?s functions. No simple correlation between rate of reaction and independent variables (temperature and inoculum concentration) was found. Analysis of empirical model indicated that saccharose fermentation by Kombucha occurred according to very complex kinetics.

scholarly journals The evolution of constitutive and induced defences to infectious disease

2018 ◽  
Vol 285 (1883) ◽  
pp. 20180658 ◽  
Author(s):  
Mike Boots ◽  
Alex Best
Keyword(s):  
Infectious Disease ◽  
Infectious Period ◽  
Induced Defence ◽  
Trade Off ◽  
Disease Mortality ◽  
Induced Defences ◽  
High Virulence ◽  
Constitutive Defence ◽  
Very High

In response to infectious disease, hosts typically mount both constitutive and induced defences. Constitutive defence prevents infection in the first place, while induced defence typically shortens the infectious period. The two routes to defence, therefore, have very different implications not only to individuals but also to the epidemiology of the disease. Moreover, the costs of constitutive defences are likely to be paid even in the absence of disease, while induced defences are likely to incur the most substantial costs when they are used in response to infection. We examine theoretically the evolutionary implications of these fundamental differences. A key result is that high virulence in the parasite typically selects for higher induced defences even if they result in immunopathology leading to very high disease mortality. Disease impacts on fecundity are critical to the relative investment in constitutive and induced defence with important differences found when parasites castrate their hosts. The trade-off between constitutive and induced defence has been cited as a cause of the diversity in defence, but we show that the trade-off alone is unlikely to lead to diversity. Our models provide a framework to examine relative investment in different defence components both experimentally and in the field.

scholarly journals Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 174-187 ◽  
Author(s):  
William Rodi ◽  
Randall L. Mackie
Keyword(s):  
Inverse Problems ◽  
Objective Function ◽  
Complete Solution ◽  
Model Space ◽  
Conjugate Gradients ◽  
Nonlinear Inversion ◽  
Spatial Derivatives ◽  
Computationally Intensive ◽  
Derivatives Of ◽  
Special Case

We investigate a new algorithm for computing regularized solutions of the 2-D magnetotelluric inverse problem. The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity. We compare this algorithm theoretically and numerically to two previous algorithms for constructing such “minimum‐structure” models: the Gauss‐Newton method, which solves a sequence of linearized inverse problems and has been the standard approach to nonlinear inversion in geophysics, and an algorithm due to Mackie and Madden, which solves a sequence of linearized inverse problems incompletely using a (linear) conjugate gradients technique. Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie‐Madden) are more efficient than the Gauss‐Newton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size. This owes largely to the fact that the conjugate gradients‐based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss‐Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space. The numerical tests also show that the Mackie‐Madden algorithm reduces the objective function more quickly than our new NLCG algorithm in the early stages of minimization, but NLCG is more effective in the later computations. To help understand these results, we describe the Mackie‐Madden and new NLCG algorithms in detail and couch each as a special case of a more general conjugate gradients scheme for nonlinear inversion.

Geochronology of Middle and Upper Pleistocene Loess Sections in Hungary

1997 ◽  
Vol 48 (3) ◽  
pp. 291-312 ◽  
Author(s):  
Manfred Frechen ◽  
Erzsébet Horváth ◽  
Gyula Gábris
Keyword(s):  
Accumulation Rate ◽  
Luminescence Dating ◽  
Glacial Cycle ◽  
Last Interglacial ◽  
High Accumulation ◽  
Oxygen Isotope Stage ◽  
Infrared Stimulated Luminescence ◽  
Derivatives Of ◽  
Very High ◽  
The Last Glacial

The application of both thermoluminescence and infrared stimulated luminescence dating to the extensively studied “classical” Hungarian loess/paleosol sequences from Basaharc, Mende, and Paks provides a reliable chronological framework and climatostratigraphic reconstruction for the last interglacial/glacial cycle. Based on this combined luminescence dating study a new chronology is proposed for the “Young Loess” in Hungary. Luminescence dating suggests that the loess below the MF2 horizon formed during the penultimate glaciation. The MF1 horizon probably formed during an interstade within oxygen isotope stage 3. For the youngest loess, overlying MF1, a very high accumulation rate was determined. Large time gaps occur above MF2 and MF1, indicating that most of the record of the last glaciation is missing in the standard sections at Basaharc, Mende, and Paks. Either large discontinuities or a very low accumulation rate occurred in all three type sections during the soil-forming periods. High-resolution studies of climatic proxies using this combined luminescence dating approach provide a reliable chronological framework for loess and loess derivatives of the last glacial cycle in Hungary, although a precise and complete chronostratigraphic reconstruction cannot be achieved from the incomplete records found at these sites.

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