The error function erf is a special function. It is widely used in statistical computations for instance, where it is also known as the standard normal cumulative probability. The complementary error function is defined as erfc(x) = 1 − erf(x). In this paper, the computation of erf(x) and erfc(x) in arbitrary precision is detailed: our algorithms take as input a target precision t′ and deliver ...

We introduce a new way of defining metric temporal logic on a real-numbers flow of time. The idea is based on having semantics which allow us to refer to a single universal clock of arbitrary precision in order to impose metric constraints. This gives us a new metric temporal logic which is very expressive, is natural to use, can be applied in very general situations, affords a wide range of us...

For a triangle in the hyperbolic plane, let α, β, γ denote the angles opposite the sides a, b, c, respectively. Also, let h be the height of the altitude to side c. Under the assumption that α, β, γ can be chosen uniformly in the interval (0, π) and it is given that α + β + γ < π, we show that the strong triangle inequality a + b > c + h holds approximately 79% of the time. To accomplish this, ...

decreased water holding capacity are believed to skin barrier dysfunction. It was surprising that we found positive correlation between TEWL and water holding capacity in AD. Conclusions: The results of TEWL and water holding capacity suggest that the barrier function of stratum corneum is impaired in AD patients. On the one hand, further studies should be required to explain the unexpected cor...

The graphicsQC package is a new R package developed for extending Quality Control for Graphics in R. It is capable of evaluating arbitrary code to produce plots in different file formats, while recording information about them. Sets of these plots are then able to be compared, with plots of differences produced (when available). Lastly, information about these comparisons can be transformed int...

Kurzfassung: In diesem Beitrag wird eine umfassende Bibliothek mit arithmetischen und kryptographischen Funktionen vorgestellt. Diese Bibliothek wurde in VHDL entwickelt und unterstützt sowohl Langzahlarithmetik als auch Multiple Precision Arithmetic (MPA). Dadurch eignet sich die Bibliothek insbesondere zur simulatorunabhängigen Simulation und Verifikation kryptographischer Prozessoren, die au...

Simulated estimates for several proportions are needed in many simulation studies. We propose a method for controlling the length of a simulation run so that the proportions estimated satisfy a prespeciied precision requirement. The method applies the arcsin transform in order to generate conndence intervals with the desired width. The Bonferroni inequality is applied in a new way to construct ...

We present an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library. Rapid convergence is ensured for piecewise complex analytic integrals by use of the Petras algorithm, which combines adaptive bisection with adaptive Gaussian quadrature where error bounds are determined via complex magnitudes without evaluating derivatives. The code is gener...

Consider a system consisting of a sender that wants to send a value to certain receivers. Byzantine agreement protocols [7, 6, 2] have been proposed to achieve this in the presence of arbitrary failures. The imposed requirement typically is that the fault-free receivers must all agree on the same value [7, 6]. (Dolev [2] analyzes a seemingly weaker form of agreement). It has been shown that suc...

We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastabl...