Twists of newforms

AbstractLet Sk0(N, ψ) denote the subspace generated by newforms in the space of cuspforms of weight k and character ψ on Σ0(N). In this paper we study decompositions of Sk0(N, ψ) into direct sums of twists (by Dirichlet characters) of other spaces of newforms. Applied to individual newforms, these results immediately yield information on the behavior of newforms under character twists. Most of the results follow from applications of the Eichler Selberg formula for the traces of the Hecke operators. A version of this formula is given in the paper. A sample result is: Let p be a prime and let M be a positive integer prime to p. Let ω be a character mod pv with e = ordpf(ω) > v2 and let φ be a character mod M. Then Sk0(pvM, ωφ) = ⊕χ Sk0(peM, ωχ2φ)χ where the sum ⊕χ is over all primitive characters χ modulo pv − e and where Sk0(N, ψ)χ denotes the twist of Sk0(N,ψ) by χ

Quantitative measurement of blood flow in paediatric brain tumours. A comparative study of dynamic susceptibility contrast and multi-timepoint arterial spin-labelled MRI

OBJECTIVE: Arterial spin-labelling (ASL) MRI uses intrinsic blood water to quantify the cerebral blood flow (CBF), removing the need for the injection of a gadolinium-based contrast agent used for conventional perfusion imaging such as dynamic susceptibility contrast (DSC). Owing to the non-invasive nature of the technique, ASL is an attractive option for use in paediatric patients. This work compared DSC and multi-timepoint ASL measures of CBF in paediatric brain tumours. METHODS: Patients (n = 23; 20 low-grade tumours and 3 high-grade tumours) had DSC and multi-timepoint ASL with and without vascular crushers (VC). VC removes the contribution from larger vessel blood flow. Mean perfusion metrics were extracted from control and T(1)-enhanced tumour regions of interest (ROIs): arterial arrival time (AAT) and CBF from the ASL images with and without VC, relative cerebral blood flow (rCBF), relative cerebral blood volume, delay time (DT) and mean transit time (MTT) from the DSC images. RESULTS: Significant correlations existed for: AAT and DT (r = 0.77, p = 0.0002) and CBF and rCBF (r = 0.56, p = 0.02) in control ROIs for ASL-noVC. No significant correlations existed between DSC and ASL measures in the tumour region. Significant differences between control and tumour ROI were found for MTT (p < 0.001) and rCBF (p < 0.005) measures. CONCLUSION: Significant correlations between ASL-noVC and DSC measures in the normal brain suggest that DSC is most sensitive to macrovascular blood flow. The absence of significant correlations within the tumour ROI suggests that ASL is sensitive to different physiological mechanisms compared with DSC measures. ADVANCES IN KNOWLEDGE: ASL provides information which is comparable with that of DSC in healthy tissues, but appears to reflect a different physiology in tumour tissues

Rethinking the Kyoto Protocol: Are There Legal Solutions to Global Warming and Climate Change?

Professor Williams moderates a panel discussion of the Kyoto Protocol and potential solutions to climate change. Other participants include Anita Halvorssen, J. Kevin Healy, William Pizer, and Jacob Werksman

Post-operative pediatric cerebellar mutism syndrome and its association with hypertrophic olivary degeneration

Background: The dentato-thalamo-cortical (DTC) pathway is recognized as the anatomical substrate for postoperative pediatric cerebellar mutism (POPCMS), a well-recognized complication affecting up to 31% of children undergoing posterior fossa brain tumour resection. The proximal structures of the DTC pathway also form a segment of the Guillain and Mollaret triangle, a neural network which when disrupted causes hypertrophic olivary degeneration (HOD) of the inferior olivary nucleus (ION). We hypothesize that there is an association between the occurrence of POPCMS and HOD and aim to evaluate this on MR imaging using qualitative and quantitative analysis of the ION in children with and without POPCMS. Methods: In this retrospective study we qualitatively analysed the follow up MR imaging in 48 children who underwent posterior fossa tumour resection for presence of HOD. Quantitative analysis of the ION was possible in 28 children and was performed using semi-automated segmentation followed by feature extraction and feature selection techniques and relevance of the features to POPCMS were evaluated. The diagnosis of POPCMS was made independently based on clinical and nursing assessment notes. Results: There was significant association between POPCMS and bilateral HOD (P=0.002) but not unilateral HOD. Quantitative analysis showed that hyperintensity in the left ION was the most relevant feature in children with POPCMS. Conclusions: Bilateral HOD can serve as a reliable radiological indicator in establishing the diagnosis of POPCMS particularly in equivocal cases. The strong association of signal change due to HOD in the left ION suggests that injury to the right proximal efferent cerebellar pathway plays an important role in the causation of POPCMS. Keywords: Cerebellar mutism syndrome (CMS); hypertrophic olivary degeneration; posterior fossa syndrome (PFS); postoperative pediatric cerebellar mutism syndrom

Cellular memory of hypoxia elicits neuroblastoma metastasis and enables invasion by non-aggressive neighbouring cells

Therapies targeting cancer metastasis are challenging owing to the complexity of the metastatic process and the high number of effectors involved. Although tumour hypoxia has previously been associated with increased aggressiveness as well as resistance to radio- and chemotherapy, the understanding of a direct link between the level and duration of hypoxia and the individual steps involved in metastasis is still missing. Using live imaging in a chick embryo model, we have demonstrated that the exposure of neuroblastoma cells to 1% oxygen for 3 days was capable of (1) enabling cell migration towards blood vessels, (2) slowing down their velocity within blood vessels to facilitate extravasation and (3) promoting cell proliferation in primary and secondary sites. We have shown that cells do not have to be hypoxic anymore to exhibit these acquired capabilities as a long-term memory of prior hypoxic exposure is kept. Furthermore, non-hypoxic cells can be influenced by neighbouring hypoxic preconditioned cells and be entrained in the metastatic progression. The acquired aggressive phenotype relies on hypoxia-inducible factor (HIF)-dependent transcription of a number of genes involved in metastasis and can be impaired by HIF inhibition. Altogether, our results demonstrate the need to consider both temporal and spatial tumour heterogeneity because cells can 'remember' an earlier environment and share their acquired phenotype with their close neighbours. As a consequence, it is necessary to monitor the correct hypoxic markers to be able to predict the consequences of the cells' history on their behaviour and their potential response to therapies

p53-mediated delayed NF-κB activity enhances etoposide-induced cell death in medulloblastoma

Medulloblastoma (MB) is an embryonic brain tumour that arises in the cerebellum. Using several MB cell lines, we have demonstrated that the chemotherapeutic drug etoposide induces a p53- and caspase-dependent cell death. We have observed an additional caspase-independent cell death mechanism involving delayed nuclear factor κB (NF-κB) activity. The delayed induction was controlled by a p53-dependent transcription step and the production of death receptors (especially CD95/Fas). We further demonstrated that in both MB and glioblastoma (GM) cell lines, in which the p53 pathway was not functional, no p65 activation could be detected upon etoposide treatment. MB cell lines that have mutations in p53 or NF-κB are either less sensitive (NF-κB mutant) or even completely resistant (p53 mutant) to chemotherapeutic intervention. The optimal cell death was only achieved when both p53 and NF-κB were switched on. Taken together, our results shed light on the mechanism of NF-κB activation by etoposide in brain tumours and show that the genetic background of MB and GM cells determines their sensitivity to chemotherapy and has to be taken into account for efficient therapeutic intervention

PARP inhibitors affect growth, survival and radiation susceptibility of human alveolar and embryonal rhabdomyosarcoma cell lines

PARP inhibitors (PARPi) are used in a wide range of human solid tumours but a limited evidence is reported in rhabdomyosarcoma (RMS), the most frequent childhood soft-tissue sarcoma. The cellular and molecular effects of Olaparib, a specific PARP1/2 inhibitor, and AZD2461, a newly synthesized PARP1/2/3 inhibitor, were assessed in alveolar and embryonal RMS cells both as single-agent and in combination with ionizing radiation (IR)

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Skeletal Shape Correspondence Through Entropy

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object's interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes' geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points

Longitudinal assessment of ataxia in children following surgical resection of posterior fossa tumours

OBJECTIVES To report the natural history of ataxia in the first two years following surgical resection of a posterior fossa tumour (PFT). METHODS 20 children (mean age 9.9 years, range 5-15 years) who had undergone resection of a posterior fossa tumour were assessed using the Scale for the Assessment and Rating of Ataxia (SARA), Brief Ataxia Rating Scale (BARS) and the Pediatric Evaluation of Disability Index (PEDI) at the following time points; initial post-operative period, then at 3 months, 1 and 2 years post operatively. RESULTS The assessments demonstrated a rapid improvement in ataxia between initial and 3 months post-operative assessments, quantified by both the SARA and BARS (mean reduction in scores 4.8, 4.6 respectively). There were additional gradual improvements at 1 year (mean reduction SARA 0.6, BARS 0.2) and 2 years post operatively (mean reduction SARA 0.9, BARS 0.9). Return of function behaved similarly, quantified by a rapid increase in PEDI scores between initial and 3 month assessments (mean increase in score 26) and gradual increases at 1 and 2 years (mean increase 2, 2.5 respectively). There was a trend for children with medulloblastoma to demonstrate higher ataxia scores than children with low grade gliomas (mean initial post-operative scores 13.4 and 8.5 respectively). CONCLUSIONS The largest change in ataxia scores and functional mobility scores (PEDI) is demonstrated within the first 3 months post operatively. Ongoing gradual improvement in ataxia and mobility function was observed at 2 years. These results have implications for management of children with PFT