On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

A short screener is valid for assessing mediterranean diet adherence among older spanish men and women

Ensuring the accuracy of dietary assessment instruments is paramount for interpreting diet-disease relationships. The present study assessed the relative and construct validity of the 14-point Mediterranean Diet Adherence Screener (MEDAS) used in the Prevencio´n con Dieta Mediterra´nea (PREDIMED) study, a primary prevention nutrition-intervention trial. A validated FFQ and the MEDAS were administered to 7146 participants of the PREDIMED study. The MEDASderived PREDIMED score correlated significantly with the corresponding FFQ PREDIMED score (r = 0.52; intraclass correlation coefficient = 0.51) and in the anticipated directions with the dietary intakes reported on the FFQ. Using Bland Altman"s analysis, the average MEDAS Mediterranean diet score estimate was 105% of the FFQ PREDIMED score estimate. Limits of agreement ranged between 57 and 153%. Multiple linear regression analyses revealed that a higher PREDIMED score related directly (P , 0.001) to HDL-cholesterol (HDL-C) and inversely (P , 0.038) to BMI, waist circumference, TG, the TG:HDL-C ratio, fasting glucose, and the cholesterol:HDL-C ratio. The 10-y estimated coronary artery disease risk decreased as the PREDIMED score increased (P , 0.001). The MEDAS is a valid instrument for rapid estimation of adherence to the Mediterranean diet and may be useful in clinical practice.

A short screener is valid for assessing mediterranean diet adherence among older spanish men and women

Ensuring the accuracy of dietary assessment instruments is paramount for interpreting diet-disease relationships. The present study assessed the relative and construct validity of the 14-point Mediterranean Diet Adherence Screener (MEDAS) used in the Prevencio´n con Dieta Mediterra´nea (PREDIMED) study, a primary prevention nutrition-intervention trial. A validated FFQ and the MEDAS were administered to 7146 participants of the PREDIMED study. The MEDASderived PREDIMED score correlated significantly with the corresponding FFQ PREDIMED score (r = 0.52; intraclass correlation coefficient = 0.51) and in the anticipated directions with the dietary intakes reported on the FFQ. Using Bland Altman"s analysis, the average MEDAS Mediterranean diet score estimate was 105% of the FFQ PREDIMED score estimate. Limits of agreement ranged between 57 and 153%. Multiple linear regression analyses revealed that a higher PREDIMED score related directly (P , 0.001) to HDL-cholesterol (HDL-C) and inversely (P , 0.038) to BMI, waist circumference, TG, the TG:HDL-C ratio, fasting glucose, and the cholesterol:HDL-C ratio. The 10-y estimated coronary artery disease risk decreased as the PREDIMED score increased (P , 0.001). The MEDAS is a valid instrument for rapid estimation of adherence to the Mediterranean diet and may be useful in clinical practice.

Congenital Nystagmus Gene FRMD7 Is Necessary for Establishing a Neuronal Circuit Asymmetry for Direction Selectivity.

Neuronal circuit asymmetries are important components of brain circuits, but the molecular pathways leading to their establishment remain unknown. Here we found that the mutation of FRMD7, a gene that is defective in human congenital nystagmus, leads to the selective loss of the horizontal optokinetic reflex in mice, as it does in humans. This is accompanied by the selective loss of horizontal direction selectivity in retinal ganglion cells and the transition from asymmetric to symmetric inhibitory input to horizontal direction-selective ganglion cells. In wild-type retinas, we found FRMD7 specifically expressed in starburst amacrine cells, the interneuron type that provides asymmetric inhibition to direction-selective retinal ganglion cells. This work identifies FRMD7 as a key regulator in establishing a neuronal circuit asymmetry, and it suggests the involvement of a specific inhibitory neuron type in the pathophysiology of a neurological disease. VIDEO ABSTRACT.

Effect of short-duration lipid supplementation on fat oxidation during exercise and cycling performance.

The effect of intramyocellular lipids (IMCLs) on endurance performance with high skeletal muscle glycogen availability remains unclear. Previous work has shown that a lipid-supplemented high-carbohydrate (CHO) diet increases IMCLs while permitting normal glycogen loading. The aim of this study was to assess the effect of fat supplementation on fat oxidation (Fox) and endurance performance. Twenty-two trained male cyclists performed 2 simulated time trials (TT) in a randomized crossover design. Subjects cycled at ∼53% maximal voluntary external power for 2 h and then followed 1 of 2 diets for 2.5 days: a high-CHO low-fat (HC) diet, consisting of CHO 7.4 g·kg(-1)·day(-1) and fat 0.5 g·kg(-1)·day(-1); or a high-CHO fat-supplemented (HCF) diet, which was a replication of the HC diet with ∼240 g surplus fat (30% saturation) distributed over the last 4 meals of the diet period. On trial morning, fasting blood was sampled and Fox was measured during an incremental exercise; a ∼1-h TT followed. Breath volatile compounds (VOCs) were measured at 3 time points. Mental fatigue, measured as reaction time, was evaluated during the TT. Plasma free fatty acid concentration was 50% lower after the HCF diet (p < 0.0001), and breath acetone was reduced (p < 0.05) "at rest". Fox peaked (∼0.35 g·kg(-1)) at ∼42% peak oxygen consumption, and was not influenced by diet. Performance was not significantly different between the HCF and HC diets (3369 ± 46 s vs 3398 ± 48 s; p = 0.39), nor were reaction times to the attention task and VOCs (p = NS for both). In conclusion, the short-term intake of a lipid supplement in combination with a glycogen-loading diet designed to boost intramyocellular lipids while avoiding fat adaptation did not alter substrate oxidation during exercise or 1-hour cycling performance.

Short Report: Spinal Cord Stimulation in Thromboangiitis Obliterans and Secondary Raynaud's-Syndrome

Introduction: Spinal cord stimulation (SCS) may be a treatment option in limb ischemia occurring as a result of Thromboangiitis obliterans (TAO) or secondary Raynaud's-Syndrome (SRS). The impact of SCS on disease progression and micro-perfusion was prospectively evaluated during a follow-up (FU) of 4 years. Report: Under SCS, a significant increase in trans-cutaneous oxygen tension (tcpO2) was observed in TAO and a significant increase in systolic perfusion pressure at plethysmography was observed in SRS. Complete limb preservation was achieved in all patients who had reduced tobacco consumption. Discussion: SCS is an efficient therapeutic tool in TAO and SRS. Patient selection criteria are crucial for success.