Reconstructing Rational Functions with FireFly\texttt{FireFly}

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio

Education, Information, and Improved Health: Evidence from Breast Cancer Screening

While it is well known that education strongly predicts health, less is known as to why. One reason might be that education improves health-care decision making. In this paper we attempt to disentangle improved decision making from other effects of education, and to quantify how large an impact it has on both a patient’s demand for health services, and that demand’s sensitivity to objective risk factors. We do this by estimating a simple structural model of information acquisition and health decisions for data on women’s self-reported breast-cancer risk and screening behavior. This allows us to separately identify differences in the ability to process health information and differences in overall demand for health. Our results suggest that the observed education gradient in screening stems from a higher willingness-to-pay for health among the educated, but that the main reason why the educated respond more to risk factors in their screening decision is because they are much better informed about the risk factors they face.education, allocative efficiency, health

Fertility transitions along the extensive and intensive margins

This paper examines the fertility transition through a new lens: the extensive margin. Parents with high levels of children might substitute quality for quantity as the constraints on quality relax or those on quantity tighten. However, along the extensive margin, the quantity-quality trade-off cannot operate. At low levels of fertility, we expect quality and quantity to be essential complements. We apply these insights to a large school construction program in the American South during the early 20th century, the Rosenwald Rural Schools Initiative. We find that increased schooling opportunities lead to reductions in fertility among women with high fertility levels, while at the same time inducing higher levels of fertility among women with low levels of fertility. The magnitude of the fertility changes induced in the parent generation is, however, small compared to the changes in fertility induced by the Rosenwald intervention among women that were themselves treated by the intervention. The evidence from the Rosenwald intervention therefore suggests that changes in female opportunity costs induced by increased educational attainment might be among the most important driving forces of the fertility transition.Fertility

Critical behavior of the extended Hubbard model with bond dimerization

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended ($U$-$V$) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio $V/U$ between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge $c=1/2$ terminates at a tricritical point belonging to the universality class of the dilute Ising model with $c=7/10$. We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter $\beta=1/8$ (1/24) and correlation length $\nu=1$ (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.Comment: 6 pages, 7 figures, contributions to SCES 201

Effective electroweak Hamiltonian in the gradient-flow formalism

The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading-order QCD. The results are presented for two common choices of the operator basis. This allows for a consistent matching of perturbatively evaluated Wilson coefficients and nonperturbative matrix elements evaluated by lattice simulations on the basis of the gradient-flow formalism

Exotic criticality in the dimerized spin-1 XXZXXZ chain with single-ion anisotropy

We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.Comment: Received the Select label. 20 pages, 7 figures, final versio

Die Rolle der kontraläsionellen Hemisphäre für die Erholung motorischer Funktionen der Hand in der chronischen Phase nach einem Schlaganfall

In dieser Arbeit wurde die konnektivitätsabhängige Rolle des Kortex im anterioren Intraparietalsulcus (aIPS) beider Hemisphären und des kontraläsionellen primär motorischen Kortex (M1) in der Erholung motorischer Funktionen der vom Schlaganfall betroffenen Hand bei 18 Patienten in der chronischen Phase nach einem Schlaganfall und 18 Kontrollprobanden mittels fMRT, rTMS und der kinematischen Analyse von Handbewegungen untersucht. Anhand einer Clusteranalyse der Kinematikdaten unter Schein-Stimulation ließen sich die Patienten von den gesunden Kontrollprobanden unterscheiden und in zwei Subgruppen unterteilen. Eine weitgehend erholte Patientengruppe wurde anhand ihres hohen Funktionsniveaus den altersentsprechenden Kontrollprobanden zugeordnet, während sich eine andere Gruppe mit residuellen motorischen Defiziten von den gesunden Probanden unterschied. Die Gruppe der gut erholten Patienten wies im Vergleich zu den Patienten mit residuellem Defizit ipsiläsionell eine erhöhte frontoparietale funktionelle Konnektivität im Ruhezustand auf. Auch die Konnektivität zwischen dem aIPS beider Hemisphären war in der Gruppe der gut erholten Patienten signifikant höher. Durch die Interferenz mittels rTMS konnten wir zeigen, dass der kontraläsionelle M1 und der kontraläsionelle aIPS in Patienten eine unterschiedliche Rolle in Abhängigkeit von der durchgeführten Aufgabe und der Konnektivität mit der jeweils homologen Region der Gegenseite annimmt. Bei höherer interhemisphärischer Konnektivität scheinen die beiden Regionen eine unterstützende Funktion für einzelne Komponenten von Greifbewegungen zu haben, während sie bei niedrigerer Konnektivität eine gegenteilige Rolle einzunehmen scheinen. Unsere Ergebnisse lassen somit vermuten, dass sich die Qualität der motorischen Funktionserholung in spezifischen Netzwerkkonfigurationen nachvollziehen lässt