It is well known that the polar magnetic field is at its maximum during solar minima, and that the behaviour during this time acts as a strong predictor of the strength of the following solar cycle. This relationship relies on the action of differential rotation (the Omega effect) on the poloidal field, which generates the toroidal flux observed in sunspots and active regions. We measure the helicity flux into both the northern and the southern hemispheres using a model that takes account of the Omega effect, which we apply to data sets covering a total of 60 years. We find that the helicity flux offers a strong prediction of solar activity up to five years in advance of the next solar cycle. We also hazard an early guess as to the strength of Solar Cycle 25, which we believe will be of similar amplitude and strength to Cycle 24.

Aims. We estimate the injection of relative magnetic helicity into the solar atmosphere by surface flux transport over 27 solar cycles (1700–2009). Methods. We determine the radial magnetic field evolution using two separate surface flux transport models: one driven by magnetogram inputs and another by statistical active region insertion guided by the sunspot number record. The injection of relative magnetic helicity is then computed from this radial magnetic field together with the known electric field in the flux transport models. Results. Neglecting flux emergence, solar rotation is the dominant contributor to the helicity injection. At high latitudes, the injection is always negative/positive in the northern/southern hemisphere, while at low latitudes the injection tends to have the opposite sign when integrated over the full solar cycle. The overall helicity injection in a given solar cycle depends on the balance between these two contributions. This net injected helicity correlates well with the end-of-cycle axial dipole moment.

Context. Magnetic helicity is approximately conserved in resistive MHD models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both the dynamo in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement.Aims. There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods. We apply a multiresolution wavelet decomposition to the magnetic field and demonstrate how it can be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity which allows these quantities to be calculated for fields with arbitrary boundary conditions. Results. It is shown that the multiresolution decomposition of helicity has the crucial property of local additivity and demonstrate a general linear energy-topology conservation law which is a significant generalisation of the two point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation. Conclusions. The multiresolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further its applicability in aperiodic models significantly increase the range of potential applications.

Human genetic studies have provided substantial insight into the biological mechanisms governing ovarian ageing, yet previous approaches have been largely restricted to assessing common genetic variation. Here we report analyses of rare (MAF<0.1%) protein-coding variants in the exomes of 106,973 women from the UK Biobank study, implicating novel genes with effect sizes up to ~5 times larger than previously discovered in analyses of common variants. These include protein truncating variants in ZNF518A, which shorten reproductive lifespan by promoting both earlier age at natural menopause (ANM, 5.61 years [4.04-7.18], P=2*10-12) and later puberty timing in girls (age at menarche, 0.56 years [0.15-0.97], P=9.2*10-3). By integrating ChIP-Seq data, we demonstrate that common variants associated with ANM and menarche are enriched in the binding sites of ZNF518A. We also identify further links between ovarian ageing and cancer susceptibility, highlighting damaging germline variants in SAMHD1 that delay ANM and increase all-cause cancer risk in both males (OR=2.1 [1.7-2.6], P=4.7*10-13) and females (OR=1.61 [1.31-1.96], P=4*10-6). Finally, we demonstrate that genetic susceptibility to earlier ovarian ageing in women increases de novo mutation rate in their offspring. This provides direct evidence that female mutation rate is heritable and highlights an example of a mechanism for the maternal genome influencing child health.

It is known that the poloidal field is at its maximum during solar minima, and that the behaviour during this time acts as a strong predictor of the strength of the following solar cycle. This relationship relies on the action of differential rotation (the Omega effect) on the poloidal field, which generates the toroidal flux observed in sunspots and active regions. We measure the helicity flux into both the northern and southern hemispheres using a model that takes account of the omega effect, which we find offers a strong quantification of the above relationship. We find that said helicity flux offers a strong prediction of solar activity up to 5 years in advance of the next solar cycle.

Determining how high body-mass index (BMI) at different time points influences the risk of developing type two diabetes (T2D), and affects insulin secretion and insulin sensitivity, is critical. By estimating childhood BMI in 441,761 individuals in the UK Biobank, we identified which genetic variants had larger effects on adulthood BMI than on childhood BMI, and vice-versa. All genome-wide significant genetic variants were then used to separate the independent genetic effects of high childhood BMI from high adulthood BMI on the risk of T2D and insulin related phenotypes using Mendelian randomisation and studies of T2D, and oral and intravenous measures of insulin secretion and sensitivity. We found that a 1.s.d. (= 1.97kg/m2) higher childhood BMI, corrected for the independent genetic liability to adulthood BMI, was associated with a protective effect for seven measures of insulin sensitivity and secretion, including an increased insulin sensitivity index (β = 0.15 [0.067, 0.225], p = 2.79E-4), and reduced fasting glucose (β = -0.053 [-0.089, -0.017], p = 4.31E-3). There was however little to no evidence of a direct protective effect on T2D (OR = 0.94 [0.85 - 1.04], p = 0.228), independently of genetic liability to adulthood BMI. Our results thus cumulatively provide evidence of the protective effect of higher childhood BMI on insulin secretion and sensitivity, which are crucial intermediate diabetes traits. However, we stress that our results should not currently lead to any change in public health or clinical practice, given the uncertainty in biological pathway of these effects, and the limitations of this type of study.

Aims/hypothesis Determining how high BMI at different time points influences the risk of developing type 2 diabetes and affects insulin secretion and insulin sensitivity is critical. Methods By estimating childhood BMI in 441,761 individuals in the UK Biobank, we identified which genetic variants had larger effects on adulthood BMI than on childhood BMI, and vice versa. All genome-wide significant genetic variants were then used to separate the independent genetic effects of high childhood BMI from those of high adulthood BMI on the risk of type 2 diabetes and insulin-related phenotypes using Mendelian randomisation. We performed two-sample MR using external studies of type 2 diabetes, and oral and intravenous measures of insulin secretion and sensitivity. Results We found that a childhood BMI that was one standard deviation (1.97 kg/m2) higher than the mean, corrected for the independent genetic liability to adulthood BMI, was associated with a protective effect for seven measures of insulin sensitivity and secretion, including increased insulin sensitivity index (β=0.15; 95% CI 0.067, 0.225; p=2.79×10−4) and reduced fasting glucose levels (β=−0.053; 95% CI −0.089, −0.017; p=4.31×10−3). However, there was little to no evidence of a direct protective effect on type 2 diabetes (OR 0.94; 95% CI 0.85, 1.04; p=0.228) independently of genetic liability to adulthood BMI. Conclusions/interpretation Our results provide evidence of the protective effect of higher childhood BMI on insulin secretion and sensitivity, which are crucial intermediate diabetes traits. However, we stress that our results should not currently lead to any change in public health or clinical practice, given the uncertainty regarding the biological pathway of these effects and the limitations of this type of study. Graphical Abstract

No abstract