When is the Bloch-Okounkov q-bracket modular?

We obtain a condition describing when the quasimodular forms given by the Bloch-Okounkov theorem as $q$-brackets of certain functions on partitions are actually modular. This condition involves the kernel of an operator {\Delta}. We describe an explicit basis for this kernel, which is very similar to the space of classical harmonic polynomials.Comment: 12 pages; corrected typo

Quantitative Results on Diophantine Equations in Many Variables

We consider a system of integer polynomials of the same degree with non-singular local zeros and in many variables. Generalising the work of Birch (1962) we find quantitative asymptotics (in terms of the maximum of the absolute value of the coefficients of these polynomials) for the number of integer zeros of this system within a growing box. Using a quantitative version of the Nullstellensatz, we obtain a quantitative strong approximation result, i.e. an upper bound on the smallest integer zero provided the system of polynomials is non-singular.Comment: Accepted for publication in Acta Arithmetica. Added a few pages so that familiarity with Birch's work is no longer assumed; 24 page

Triply mixed coverings of arbitrary base curves: Quasimodularity, quantum curves and a mysterious topological recursions

Simple Hurwitz numbers enumerate branched morphisms between Riemann surfaces with fixed ramification data. In recent years, several variants of this notion for genus $0$ base curves have appeared in the literature. Among them are so-called monotone Hurwitz numbers, which are related to the HCIZ integral in random matrix theory and strictly monotone Hurwitz numbers which count certain Grothendieck dessins d'enfants. We generalise the notion of Hurwitz numbers to interpolations between simple, monotone and strictly monotone Hurwitz numbers to any genus and any number of arbitrary but fixed ramification profiles. This yields generalisations of several results known for Hurwitz numbers. When the target surface is of genus one, we show that the generating series of these interpolated Hurwitz numbers are quasimodular forms. In the case that all ramification is simple, we refine this result by writing this series as a sum of quasimodular forms corresonding to tropical covers weighted by Gromov-Witten invariants. Moreover, we derive a quantum curve for monotone and Grothendieck dessins d'enfants Hurwitz numbers for arbitrary genera and one arbitrary but fixed ramification profile. Thus, we obtain spectral curves via the semiclassical limit as input data for the CEO topological recursion. Astonishingly, we find that the CEO topological recursion for the genus $1$ spectral curve of the strictly monotone Hurwitz numbers compute the monotone Hurwitz numbers in genus $0$. Thus, we give a new proof that monotone Hurwitz numbers satisfy CEO topological recursion. This points to an unknown relation between those enumerants. Finally, specializing to target surface $\mathbb{P}^1$, we find recursions for monotone and Grothendieck dessins d'enfants double Hurwitz numbers, which enables the computation of the respective Hurwitz numbers for any genera with one arbitrary but fixed ramification profile.Comment: 41 page

Fear of exercise and health-related quality of life in patients with an implantable cardioverter defibrillator

Several studies have reported improved survival rates thanks to the use of an implantable cardioverter defibrillator (ICD) in the treatment of patients with life-threatening arrhythmia. However, the effects of the ICD on health-related quality of life (HR-QoL) of these patients are not clear. The aim of this study is to describe HR-QoL and fear of exercise in ICD patients. Eighty-nine ICD patients from the University Hospital in Groningen, the Netherlands, participated in this study. HR-QoL was measured using the Rand-36 and the Quality of Life After Myocardial Infarction Dutch language version questionnaires. Fear of exercise was measured using the Tampa Scale for Kinesiophobia, Dutch version and the Fear Avoidance Beliefs Questionnaire, Dutch version. Association between outcome variables was analysed by linear regression analyses. Study results show that the HR-QoL of patients with ICDs in our study population is significantly worse than that of normal healthy people. Furthermore, fear of exercise is negatively associated with HR-QoL corrected for sex, age and number of years living with an ICD. After implantation of the ICD, patients with a clear fear of exercise should be identified and interventions should be considered in order to increase their HR-QoL

Triply mixed coverings of arbitrary base curves : quasimodularity, quantum curves and a mysterious topological recursions

Simple Hurwitz numbers are classical invariants in enumerative geometry counting branched morphisms between Riemann surfaces with fixed ramification data. In recent years, several modifications of this notion for genus 0 base curves have appeared in the literature. Among them are so-called monotone Hurwitz numbers, which are related to the Harish–Chandra–Itzykson–Zuber integral in random matrix theory and strictly monotone Hurwitz numbers which enumerate certain Grothendieck dessins d’enfants. We generalise the notion of Hurwitz numbers to interpolations between simple, monotone and strictly monotone Hurwitz numbers for arbitrary genera and any number of arbitrary but fixed ramification profiles. This yields generalisations of several results known for Hurwitz numbers. When the target surface is of genus one, we show that the generating series of these interpolated Hurwitz numbers are quasimodular forms. In the case that all ramification is simple, we refine this result by writing this series as a sum of quasimodular forms corresponding to tropical covers weighted by Gromov–Witten invariants. Moreover, we derive a quantum curve for monotone and Grothendieck dessins d’enfants Hurwitz numbers for arbitrary genera and one arbitrary but fixed ramification profile. Thus, we obtain spectral curves via the semi-classical limit as input data for the Chekhov–Eynard–Orantin (CEO) topological recursion. Astonishingly, we find that the CEO topological recursion for the genus 1 spectral curve of the strictly monotone Hurwitz numbers computes the monotone Hurwitz numbers in genus 0. Thus, we give a new proof that monotone Hurwitz numbers satisfy CEO topological recursion. This points to an unknown relation between those enumerative invariants. Finally, specializing to target surface ℙ1, we find recursions for monotone and Grothendieck dessins d’enfants double Hurwitz numbers, which enables the computation of the respective Hurwitz numbers for any genera with one arbitrary but fixed ramification profile

Adapting agriculture in 2050 in Flevoland; perspectives from stakeholders

Although recently more research has gone into farm level studies, little attention has been given to the variety of responses of farmers, considering their characteristics, objectives and the socio-economic, technological and political contexts (Reidsma et al, 2010). In the Agri-Adapt project we focus on farm level adaptation within an agricultural region considering the socio-economic context of 2050

Assessing the adaptation of arable farmers to climate change using DEA and bio-economic modelling

The objective of this article is to assess the impact of climate change on arable farming systems in Flevoland (the Netherlands) and to explore the adoption of different adaptation strategies. Data Envelopment Analysis (DEA) is applied that uses empirical data from individual farms to identify “best” current farm practices and derive relationships regarding current farm managemen

Reducing the maize yield gap in Ethiopia: Decomposition and policy simulation

Maize is an important staple crop in Ethiopia. Reducing the yield gap - the difference between actual and (water-limited) potential yield - has wide implications for food security and policy. In this paper we combine stochastic frontier analysis of household survey data with agronomic information on (water-limited) potential yield to decompose the maize yield gap in Ethiopia and highlight policy solutions to reduce the yield gap. Our analysis suggests that lack of access to advanced technologies makes up the largest component of the maize yield gap but market imperfections, economic constraints and management constraints are also important determinants. Potentially, maize production can be increased almost fivefold if all these constraints would be addressed simultaneously and the yield gap could be fully closed. Another finding of the paper is measurement issues in the national household survey (LSMS-ISA), a key source of information for scientists to assess agricultural policies in Ethiopia and other African countries. A comparison with results from a crop model suggests a large number of unrealistic values related to key maize input and output variables. Combining economic and agronomic approaches is therefore not only useful to identify policies to reduce maize yield gaps, but also to assess and improve the quality of data-bases on which recommendations are made