Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. If you are using a template in Microsoft Word, ensure that the font is correctly set for all. Basis Decompositions and a Mathematica Package for Modular Graph Forms When writing symbols, use common, standard fonts where possible. All the calculations in this article are available in uc(Mathematica) and uc(Python) files in the supplementary material, allowing readers to experiment with their own variants. (Yes, the 1, 3 themecomplete with the fact that it’s the 13th of the month todayis amusing, if coincidental. plotly line plot with title and axis title In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. To set the legend size for the font, we need to use the very confusing: LabelStyle -> DirectiveFontSize -> 24. Just a few weeks ago it was 1/3 of a century since Mathematica 1.0 was released.Today I’m excited to announce the latest results of our long-running R&D pipeline: Version 13 of Wolfram Language and Mathematica. For three random directions, hidden-variable theories are impossible (we show) exactly 2/3 of the time. The reason is that Mathematica s plotting program assumes that the ratio of width to height is equal to 1/the golden ratio. With hidden variables, Eve can succeed when Alice and Bob limit themselves to two Stern-Gerlach directions, but always fails for some choices of three directions. This article reviews the predictions of quantum mechanics (QM) for one- and two-particle Stern-Gerlach experiments and then frames Bell's results, which rule out hidden-variable alternatives to QM, as attempts by a skeptical Eve to fool Alice and Bob with (first example) classical probability mixtures of non-entangled quantum states and (second example) a classical hidden-variable theory. Publication: American Journal of Physics.Solution method: Appropriate variable changes for given square roots are constructed by parametrizing algebraic hypersurfaces associated to these square roots by families of lines. The computation of these integrals often involves square roots that need to be rationalized via suitable variable transformations. Nature of problem: Analytic solutions for Feynman integrals are critical for accurate theoretical predictions in high energy particle physics. Licensing provisions: GNU General Public License 3
#WOLFRAM MATHEMATICA PLOT SET POINT SIZE HOW TO#
After an introduction to the theoretical background, we explain in detail how to use the program in practice. We present a program that can be used to find such transformations. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. The computation of Feynman integrals often involves square roots.
#WOLFRAM MATHEMATICA PLOT SET POINT SIZE SOFTWARE#
RationalizeRoots: Software package for the rationalization of square roots