21 papers · ranked by Valyu relevance
Heiko Becker, Mohit Tekriwal, Eva Darulová, Anastasia Volkova + 1 more
'Jean-Baptiste Jeannin'] Elementary function operations such as sin and exp cannot in general be computed exactly on today's digital computers, and thus have to be approximated. The standard approximations in library functions typically provide only a limited set of precisions, and are too inefficient for many…
Morten Overgaard, Jesper Mogensen
This article proposes a new model to interpret seemingly conflicting evidence concerning the correlation of consciousness and neural processes. Based on an analysis of research of blindsight and subliminal perception, the reorganization of elementary functions and consciousness framework suggests that mental…
Alexander Goncearenco, Igor N Berezovsky
Background Despite recent progress in studies of the evolution of protein function, the questions what were the first functional protein domains and what were their basic building blocks remain unresolved. Previously, we introduced the concept of elementary functional loops (EFLs), which are the functional units of…
Emil Jeřábek
It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, and their inverse functions) are computable in the weak complexity class TC0 . We show how to formalize the construction and basic properties of these functions in the corresponding theory of…
Victor Nijimbere
The non-elementary integrals Siβ,α = R [sin (λxβ)/(λxα)]dx, β ≥ 1, α ≤ β + 1 and Ciβ,α = R [cos (λxβ)/(λxα)]dx, β ≥ 1, α ≤ 2β + 1, where {β, α} ∈ R, are evaluated in terms of the hypergeometric R functions 1F2 and 2F3, and their asymptotic expressions for |x| ≫ 1 are also derived. The integrals of the form [sinn…
James M. Chappell, Azhar Iqbal, Lachlan J. Gunn, Derek Abbott + 1 more
'Cheng-Yi Xia'] As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field…
Victor Nijimbere
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, R x αe ηxβ dx, R x α cosh ηxβ dx, R x α sinh ηxβ dx, R x α cos ηxβ dx and R x α sin ηxβ dx where α, η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the…
Victor Nijimbere
A formula for the non-elementary integral R e λxα dx where α is real and greater or equal two, is obtained in terms of the confluent hypergeometric function 1F1 by expanding the integrand as a Taylor series. This result is verified by directly evaluating the area under the Gaussian Bell curve, corresponding to α = 2…
Brian D. Wood
Scientists and engineers are, by definition, problem solvers. But, it is curious to reflect on how they become problem solvers. While it is possible that early in one's academic career, a course whose title included the words "problem solving" might have been taken, but this is not likely to have been where students…
B. C. Carlson
Three improvements in reduction and computation of elliptic integrals are made. 1. Reduction formulas, used to express many elliptic integrals in terms of a few standard integrals, are simplified by modifying the definition of intermediate “basic integrals.” 2. A faster than quadratically convergent series is given for…
Siyu Sun, Dandan Sun, Tianshu Xu
Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist teachers and curriculum developers in implementing instruction that…
Radoslav Dimitrić
continuous at 0? If we open any elementary calculus textbook in use, the answer will almost invariably be "no" to both questions. Moreover with some textbooks, these are the only "discontinuities" various functions seem to have. The daily calculus teaching practice follows the same party line. We will give correct…
Philippe Dague
Metabolic pathway analysis is a key method to study a metabolism in its steady state and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the…
Hend Dawood, Nefertiti Megahed, Nicholas Higham
Acquiring reliable knowledge amidst uncertainty is a topical issue of modern science. Interval mathematics has proved to be of central importance in coping with uncertainty and imprecision. Algorithmic differentiation, being superior to both numeric and symbolic differentiation, is nowadays one of the most celebrated…
Nicole Voges, Johannes Hausmann, Andrea Brovelli, Demian Battaglia
Cognitive functions arise from the coordinated activity of neural populations distributed over large-scale brain networks. However, it is challenging to understand and measure how specific aspects of neural dynamics translate into operations of information processing, and, ultimately, cognitive functions. An obstacle…
Yun Min Song, Hyukpyo Hong, Jae Kyoung Kim
Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with…
Anoop Kumar Kushwaha
In recent years, the applications of first-principles density functional theory (DFT) is diversified and expanded in a wide range due to the development of robust algorithms and more powerful computer systems. In general, DFT is used in condensed matter physics, chemistry, material science and biology to predict and…
Dai-Nghia Vy, Van-Thuan Nguyen, Quyet-Thang Huynh, Trung-Nghia Phung + 2 more
Context: Many models based on S-shaped functions demonstrate their advantages in non-homogeneous Poisson process software reliability modeling. However, three well-known types have been used without deep mathematical evaluation. Furthermore, some other promising S-shaped functions should be aimed at. Objectives: (1)…
Authors not listed
Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…
Eric Schulz, Joshua B. Tenenbaum, David Duvenaud, Maarten Speekenbrink + 1 more
How do people recognize and learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is achieved by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian…
Authors not listed
Finding microkinetic parameters for heterogeneously catalyzed processes with conventional methods is a challenging task. Recently, the use of artificial neural networks has been described as a promising and flexible tool for kinetic parameter estimation. In this work, an extension to the methodology of chemical reaction…