Special functions, transcendentals and their numerics

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.Comment: 13 pages LATEX, one style file, Proceedings of Loops and Legs in Quantum Field Theory -- LL2014,27 April 2014 -- 02 May 2014 Weimar, German

A toolbox to solve coupled systems of differential and difference equations

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter \ep (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t.\ \ep and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package \texttt{SolveCoupledSystem} which is based on the packages \texttt{Sigma}, \texttt{HarmonicSums} and \texttt{OreSys}. In all applications the representation in $x$-space is obtained as an iterated integral representation over general alphabets, generalizing Poincar\'{e} iterated integrals

Development of the Coach Autonomy Support Beliefs Scale

Coaches’ autonomy support is one of the most meaningful influences on the satisfaction of athletes’ basic psychological needs of competence, autonomy, and relatedness (Mageau & Vallerand, 2003). Fostering these needs cultivates self-determined motivation (Deci & Ryan, 2000), which has been found to positively affect individuals’ effort, persistence when faced with adversity, performance, performance-related anxiety, and well-being (Gillet, Berjot, & Gobance, 2009; Mack et al., 2011; Podlog & Dionigi, 2010; Vallerand & Losier, 1999). The reasoned action approach (Fishbein & Ajzen, 2010) suggests that coaches’ attitude, perceived behavioral control, and perceived norm toward autonomy support influences their use of autonomysupportive behaviors. However, prior to this study, no instrument has been developed that measured these behavioral antecedents. Consequently, the purpose of the current research was to develop a scale that assesses coaches’ attitude, perceived behavioral control, and perceived norm toward autonomy-supportive behaviors when working with student-athletes during practice. Exploratory Factor Analysis procedures with data from 497 National Collegiate Athletic Association Division I and II head coaches’ revealed adequate model fit for a two-factor solution (RMSEA = .042, 99% CI [.020; .063], p = .703; CFI = .99). The Autonomy Support Belief Scale (ASBS) is an eight item measure with two subscales: personal belief (five items) and social influence (three items). Subsequent correlation and regression analysis further validated the ASBS. Personal belief and social influence were both found to be statistically significant predictors for coaches’ behaviors, accounting for 25.9% and 20.3% of the total variance in participants’ use of autonomy-supportive behaviors respectively. The ASBS allows researchers, sport psychology professionals, and coach educators to gain insight into coaches’ beliefs about autonomy supportive behaviors and can help them shape interventions with coaches, evaluate the effectiveness of such programs, and ultimately impact coaches’ use of autonomy support

Fisher Information in Noisy Intermediate-Scale Quantum Applications

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning

Massive three loop form factors in the planar limit

We present the color planar and complete light quark QCD contributions to the three loop heavy quark form factors in the case of vector, axial-vector, scalar and pseudo-scalar currents. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for any first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.Comment: 10 pages; Proceedings of the Loops and Legs in Quantum Field Theory, 29th April 2018 - 4th May 2018, St. Goar, Germany; Report number modifie