Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in $\epsilon$ if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the $\epsilon$-expansion of a ladder graph with 6 massive fermion lines

The Complete O(αs2)O(\alpha_s^2) Non-Singlet Heavy Flavor Corrections to the Structure Functions g1,2ep(x,Q2)g_{1,2}^{ep}(x,Q^2), F1,2,Lep(x,Q2)F_{1,2,L}^{ep}(x,Q^2), F1,2,3ν(νˉ)(x,Q2)F_{1,2,3}^{\nu(\bar{\nu})}(x,Q^2) and the Associated Sum Rules

We calculate analytically the flavor non-singlet $O(\alpha_s^2)$ massive Wilson coefficients for the inclusive neutral current non-singlet structure functions $F_{1,2,L}^{ep}(x,Q^2)$ and $g_{1,2}^{ep}(x,Q^2)$ and charged current non-singlet structure functions $F_{1,2,3}^{\nu(\bar{\nu})p}(x,Q^2)$, at general virtualities $Q^2$ in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales $Q^2$ and the effects of the power corrections due to the heavy quark mass are of the size of the known $O(\alpha_s^4)$ corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region $Q^2 \gg m_{c,b}^2$. We also study the target mass corrections to the above sum rules.Comment: 50 pages LATEX, 35 figure

Urbano o rural: ¿Dónde es más feliz la gente y por qué?

Using data from a worldwide sample, we investigate how happy people look like and if these “happiness characteristics” are more present in big urban towns or in small rural villages. We found evidence that (i) people seem to be slightly happier in rural settlements, (ii) happier people have some particular characteristics (e.g., higher levels of trust in others and being more interested in politics) and (iii) these positive attitudes are slightly more present in rural contexts. Then, we discuss some conceivable explanations to what we have seen.Utilizando datos de una muestra mundial, investigamos cómo es la gente feliz y si estas “características de felicidad” están más presentes en las grandes ciudades urbanas o en los pequeños pueblos rurales. Encontramos pruebas de que (i) la gente parece ser ligeramente más feliz en los asentamientos rurales, (ii) las personas más felices tienen algunas características particulares (por ejemplo, mayores niveles de confianza en los demás y estar más interesados en la política) y (iii) estas actitudes positivas están ligeramente más presentes en los contextos rurales. A continuación, se discuten algunas explicaciones concebibles a lo que hemos visto.Instituto Complutense de Estudios InternacionalesTRUEpu

An Analysis on the Experimental Design of “My Money or Yours: House Money Payment Effects"

Considering the expanding usage of experiments in Economics, the present article chooses one published paper in the area, dealing with the house money effect and analyzes it in a didactic way as concepts relating to the experimental design of lab experiments are evoked and discussed. In order to do so, three sections are outlined. First of all, the house money effect is explained and the article under scrutiny is placed in the context of what had already been done before; secondly, some of the experimental design concepts are summarised and then applied to soundly describe the experimental design of their experiment. Finally, after briefly presenting their results, there is an analytical overview of what has been done after their work and a personal take on possible lines for further research

Integration of GMR sensors with different technologies

Less than thirty years after the giant magnetoresistance (GMR) effect was described, GMR sensors are the preferred choice in many applications demanding the measurement of low magnetic fields in small volumes. This rapid deployment from theoretical basis to market and state-of-the-art applications can be explained by the combination of excellent inherent properties with the feasibility of fabrication, allowing the real integration with many other standard technologies. In this paper, we present a review focusing on how this capability of integration has allowed the improvement of the inherent capabilities and, therefore, the range of application of GMR sensors. After briefly describing the phenomenological basis, we deal on the benefits of low temperature deposition techniques regarding the integration of GMR sensors with flexible (plastic) substrates and pre-processed CMOS chips. In this way, the limit of detection can be improved by means of bettering the sensitivity or reducing the noise. We also report on novel fields of application of GMR sensors by the recapitulation of a number of cases of success of their integration with different heterogeneous complementary elements. We finally describe three fully functional systems, two of them in the bio-technology world, as the proof of how the integrability has been instrumental in the meteoric development of GMR sensors and their applications.Peer ReviewedPostprint (published version

Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory

We present the two-loop QCD helicity amplitudes for quark-quark and quark-antiquark scattering. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization and present the scheme dependence of the results. We verify that the finite remainder, after subtracting the divergences using Catani's formula, are in agreement with previous results. We also provide the amplitudes for gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We describe ambiguities in continuing the Dirac algebra to D dimensions, including ones which violate fermion helicity conservation. The finite remainders after subtracting the divergences using Catani's formula, which enter into physical quantities, are free of these ambiguities. We show that in the FDH scheme, for gluino-gluino scattering, the finite remainders satisfy the expected supersymmetry Ward identities.Comment: arXiv admin note: substantial text overlap with arXiv:hep-ph/030416