Visual properties of generalized Kloosterman sums

For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena

An Exhibition of Exponential Sums: Visualizing Supercharacters

We discuss a simple mathematical mechanism that produces a variety of striking images of great complexity and subtlety. We briefly explain this approach and present a selection of attractive images obtained using this technique

Blocking and its response to climate change

Purpose of review: Atmospheric blocking events represent some of the most high-impact weather patterns in the mid-latitudes, yet they have often been a cause for concern in future climate projections. There has been low confidence in predicted future changes in blocking, despite relatively good agreement between climate models on a decline in blocking. This is due to the lack of a comprehensive theory of blocking and a pervasive underestimation of blocking occurrence by models. This paper reviews the state of knowledge regarding blocking under climate change, with the aim of providing an overview for those working in related fields. Recent Findings: Several avenues have been identified by which blocking can be improved in numerical models, though a fully reliable simulation remains elusive (at least, beyond a few days lead time). Models are therefore starting to provide some useful information on how blocking and its impacts may change in the future, although deeper understanding of the processes at play will be needed to increase confidence in model projections. There are still major uncertainties regarding the processes most important to the onset, maintenance and decay of blocking and advances in our understanding of atmospheric dynamics, for example in the role of diabatic processes, continue to inform the modelling and prediction efforts. Summary: The term ‘blocking’ covers a diverse array of synoptic patterns, and hence a bewildering range of indices has been developed to identify events. Results are hence not considered fully trustworthy until they have been found using several different methods. Examples of such robust results are the underestimation of blocking by models, and an overall decline in future occurrence, albeit with a complex regional and seasonal variation. In contrast, hemispheric trends in blocking over the recent historical period are not supported by different methods, and natural variability will likely dominate regional variations over the next few decades

Modifying effect of dual antiplatelet therapy on incidence of stent thrombosis according to implanted drug-eluting stent type

Aim To investigate the putative modifying effect of dual antiplatelet therapy (DAPT) use on the incidence of stent thrombosis at 3 years in patients randomized to Endeavor zotarolimus-eluting stent (E-ZES) or Cypher sirolimus-eluting stent (C-SES). Methods and results Of 8709 patients in PROTECT, 4357 were randomized to E-ZES and 4352 to C-SES. Aspirin was to be given indefinitely, and clopidogrel/ticlopidine for ≥3 months or up to 12 months after implantation. Main outcome measures were definite or probable stent thrombosis at 3 years. Multivariable Cox regression analysis was applied, with stent type, DAPT, and their interaction as the main outcome determinants. Dual antiplatelet therapy adherence remained the same in the E-ZES and C-SES groups (79.6% at 1 year, 32.8% at 2 years, and 21.6% at 3 years). We observed a statistically significant (P = 0.0052) heterogeneity in treatment effect of stent type in relation to DAPT. In the absence of DAPT, stent thrombosis was lower with E-ZES vs. C-SES (adjusted hazard ratio 0.38, 95% confidence interval 0.19, 0.75; P = 0.0056). In the presence of DAPT, no difference was found (1.18; 0.79, 1.77; P = 0.43). Conclusion A strong interaction was observed between drug-eluting stent type and DAPT use, most likely prompted by the vascular healing response induced by the implanted DES system. These results suggest that the incidence of stent thrombosis in DES trials should not be evaluated independently of DAPT use, and the optimal duration of DAPT will likely depend upon stent type (Clinicaltrials.gov number NCT00476957

Rheumatoid arthritis - treatment: 180. Utility of Body Weight Classified Low-Dose Leflunomide in Japanese Rheumatoid Arthritis

Background: In Japan, more than 20 rheumatoid arthritis (RA) patients died of interstitial pneumonia (IP) caused by leflunomide (LEF) were reported, but many of them were considered as the victims of opportunistic infection currently. In this paper, efficacy and safety of low-dose LEF classified by body weight (BW) were studied. Methods: Fifty-nine RA patients were started to administrate LEF from July 2007 to July 2009. Among them, 25 patients were excluded because of the combination with tacrolimus, and medication modification within 3 months before LEF. Remaining 34 RA patients administered 20 to 50 mg/week of LEF were followed up for 1 year and enrolled in this study. Dose of LEF was classified by BW (50 mg/week for over 50 kg, 40 mg/week for 40 to 50 kg and 20 to 30 mg/week for under 40 kg). The average age and RA duration of enrolled patients were 55.5 years old and 10.2 years. Prednisolone (PSL), methotrexate (MTX) and etanercept were used in 23, 28 and 2 patients, respectively. In case of insufficient response or adverse effect, dosage change or discontinuance of LEF were considered. Failure was defined as dosages up of PSL and MTX, or dosages down or discontinuance of LEF. Last observation carried forward method was used for the evaluation of failed patients at 1 year. Results: At 1 year after LEF start, good/ moderate/ no response assessed by the European League Against Rheumatism (EULAR) response criteria using Disease Activity Score, including a 28-joint count (DAS28)-C reactive protein (CRP) were showed in 14/ 10/ 10 patients, respectively. The dosage changes of LEF at 1 year were dosage up: 10, same dosage: 5, dosage down: 8 and discontinuance: 11 patients. The survival rate of patients in this study was 23.5% (24 patients failed) but actual LEF continuous rate was 67.6% (11 patients discontinued) at 1 year. The major reason of failure was liver dysfunction, and pneumocystis pneumonia was occurred in 1 patient resulted in full recovery. One patient died of sepsis caused by decubitus ulcer infection. DAS28-CRP score was decreased from 3.9 to 2.7 significantly. Although CRP was decreased from 1.50 to 0.93 mg/dl, it wasn't significant. Matrix metalloproteinase (MMP)-3 was decreased from 220.0 to 174.2 ng/ml significantly. Glutamate pyruvate transaminase (GPT) was increased from 19 to 35 U/l and number of leukocyte was decreased from 7832 to 6271 significantly. DAS28-CRP, CRP, and MMP-3 were improved significantly with MTX, although they weren't without MTX. Increase of GPT and leukopenia were seen significantly with MTX, although they weren't without MTX. Conclusions: It was reported that the risks of IP caused by LEF in Japanese RA patients were past IP history, loading dose administration and low BW. Addition of low-dose LEF is a potent safe alternative for the patients showing unsatisfactory response to current medicines, but need to pay attention for liver function and infection caused by leukopenia, especially with MTX. Disclosure statement: The authors have declared no conflicts of interes

Genetic architecture of subcortical brain structures in 38,851 individuals

Subcortical brain structures are integral to motion, consciousness, emotions and learning. We identified common genetic variation related to the volumes of the nucleus accumbens, amygdala, brainstem, caudate nucleus, globus pallidus, putamen and thalamus, using genome-wide association analyses in almost 40,000 individuals from CHARGE, ENIGMA and UK Biobank. We show that variability in subcortical volumes is heritable, and identify 48 significantly associated loci (40 novel at the time of analysis). Annotation of these loci by utilizing gene expression, methylation and neuropathological data identified 199 genes putatively implicated in neurodevelopment, synaptic signaling, axonal transport, apoptosis, inflammation/infection and susceptibility to neurological disorders. This set of genes is significantly enriched for Drosophila orthologs associated with neurodevelopmental phenotypes, suggesting evolutionarily conserved mechanisms. Our findings uncover novel biology and potential drug targets underlying brain development and disease

Genetic architecture of subcortical brain structures in 38,851 individuals

Subcortical brain structures are integral to motion, consciousness, emotions and learning. We identified common genetic variation related to the volumes of the nucleus accumbens, amygdala, brainstem, caudate nucleus, globus pallidus, putamen and thalamus, using genome-wide association analyses in almost 40,000 individuals from CHARGE, ENIGMA and UK Biobank. We show that variability in subcortical volumes is heritable, and identify 48 significantly associated loci (40 novel at the time of analysis). Annotation of these loci by utilizing gene expression, methylation and neuropathological data identified 199 genes putatively implicated in neurodevelopment, synaptic signaling, axonal transport, apoptosis, inflammation/infection and susceptibility to neurological disorders. This set of genes is significantly enriched for Drosophila orthologs associated with neurodevelopmental phenotypes, suggesting evolutionarily conserved mechanisms. Our findings uncover novel biology and potential drug targets underlying brain development and disease

Case Reports1. A Late Presentation of Loeys-Dietz Syndrome: Beware of TGFβ Receptor Mutations in Benign Joint Hypermobility

Background: Thoracic aortic aneurysms (TAA) and dissections are not uncommon causes of sudden death in young adults. Loeys-Dietz syndrome (LDS) is a rare, recently described, autosomal dominant, connective tissue disease characterized by aggressive arterial aneurysms, resulting from mutations in the transforming growth factor beta (TGFβ) receptor genes TGFBR1 and TGFBR2. Mean age at death is 26.1 years, most often due to aortic dissection. We report an unusually late presentation of LDS, diagnosed following elective surgery in a female with a long history of joint hypermobility. Methods: A 51-year-old Caucasian lady complained of chest pain and headache following a dural leak from spinal anaesthesia for an elective ankle arthroscopy. CT scan and echocardiography demonstrated a dilated aortic root and significant aortic regurgitation. MRA demonstrated aortic tortuosity, an infrarenal aortic aneurysm and aneurysms in the left renal and right internal mammary arteries. She underwent aortic root repair and aortic valve replacement. She had a background of long-standing joint pains secondary to hypermobility, easy bruising, unusual fracture susceptibility and mild bronchiectasis. She had one healthy child age 32, after which she suffered a uterine prolapse. Examination revealed mild Marfanoid features. Uvula, skin and ophthalmological examination was normal. Results: Fibrillin-1 testing for Marfan syndrome (MFS) was negative. Detection of a c.1270G > C (p.Gly424Arg) TGFBR2 mutation confirmed the diagnosis of LDS. Losartan was started for vascular protection. Conclusions: LDS is a severe inherited vasculopathy that usually presents in childhood. It is characterized by aortic root dilatation and ascending aneurysms. There is a higher risk of aortic dissection compared with MFS. Clinical features overlap with MFS and Ehlers Danlos syndrome Type IV, but differentiating dysmorphogenic features include ocular hypertelorism, bifid uvula and cleft palate. Echocardiography and MRA or CT scanning from head to pelvis is recommended to establish the extent of vascular involvement. Management involves early surgical intervention, including early valve-sparing aortic root replacement, genetic counselling and close monitoring in pregnancy. Despite being caused by loss of function mutations in either TGFβ receptor, paradoxical activation of TGFβ signalling is seen, suggesting that TGFβ antagonism may confer disease modifying effects similar to those observed in MFS. TGFβ antagonism can be achieved with angiotensin antagonists, such as Losartan, which is able to delay aortic aneurysm development in preclinical models and in patients with MFS. Our case emphasizes the importance of timely recognition of vasculopathy syndromes in patients with hypermobility and the need for early surgical intervention. It also highlights their heterogeneity and the potential for late presentation. Disclosures: The authors have declared no conflicts of interes