A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

What Works in School-Based Programs for Child Abuse Prevention? The Perspectives of Young Child Abuse Survivors

Previous research has shown that youth consider school-based child abuse prevention programs as one of the most important strategies for preventing child abuse and neglect. This study asked young child abuse survivors how school-based child abuse prevention programs should be shaped and what program components they perceive as essential. Semi-structured interviews were conducted with 13 Dutch young adults that were a victim of child abuse or neglect. A literature review that resulted in 12 potential program components was used to guide the interviews. All young adults agreed that school-based child abuse prevention programs are important and have positive effects on children’s awareness of child abuse. Teaching children that they are never to blame for child abuse occurrences was considered one of the most important components of school-based programs, next to teaching children how to escape from threatening situations and to find help, increasing children’s social–emotional skills, promoting child abuse related knowledge, recognizing risky situations, and increasing children’s self-esteem. Further, the participants found it important to provide children with aftercare when a school program has ended. Overall, young child abuse survivors have a strong view on what should be addressed in school-based child abuse prevention programs to effectively prevent child abuse

The effect of a sport-based intervention to prevent juvenile delinquency in at-risk adolescents

Despite the wide implementation of sport-based crime prevention programs, there is a lack of empirical knowledge on the effectiveness of these interventions. This study evaluated a Dutch sport-based program in N = 368 youth at risk for juvenile delinquency. Intervention effects were tested in a quasi-experimental study, comparing the intervention group with a comparison group using multiple sources of information. The study was conducted under conditions that resemble real-life implementation, thereby enhancing the relevance of this contribution to practitioners. The primary outcome was juvenile delinquency, measured by official police data. The secondary outcomes were risk and protective factors for delinquency, assessed with self- and teacher reports. A significant effect was found on one delinquency measure. The intervention group consisted of fewer youth with police registrations as a suspect than the comparison group (d = −0.34). We did not find an intervention effect on the number of registrations as a suspect in each group. In addition, no significant intervention effects were found on the secondary outcomes. Implications for theory and practice concerning the use of sport-based crime prevention programs are discussed

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page

Improving Access to Mental Health Care and Psychosocial Support within a Fragile Context: A Case Study from Afghanistan

As one article in a series on Global Mental Health Practice, Peter Ventevogel and colleagues provide a case study of their efforts to integrate brief, practice-oriented mental health training into the Afghanistan health care system at a time when the system was being rebuilt from scratch

Holonomy of the Ising model form factors

We study the Ising model two-point diagonal correlation function $C(N,N)$ by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of Wu, McCoy, Tracy and Barouch. We extend this expansion, weighting, by powers of a variable $\lambda$, the $j$-particle contributions, $f^{(j)}_{N,N}$. The corresponding $\lambda$ extension of the two-point diagonal correlation function, $C(N,N; \lambda)$, is shown, for arbitrary $\lambda$, to be a solution of the sigma form of the Painlev{\'e} VI equation introduced by Jimbo and Miwa. Linear differential equations for the form factors $f^{(j)}_{N,N}$ are obtained and shown to have both a ``Russian doll'' nesting, and a decomposition of the differential operators as a direct sum of operators equivalent to symmetric powers of the differential operator of the elliptic integral $E$. Each $f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $E$ and $K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll'' structure. The previous $\lambda$-extensions, $C(N,N; \lambda)$ are, for singled-out values $\lambda= \cos(\pi m/n)$ ($m, n$ integers), also solutions of linear differential equations. These solutions of Painlev\'e VI are actually algebraic functions, being associated with modular curves.Comment: 39 page