Which neural networks can be computed by an algorithm? – Generalised hardness of approximation meets Deep Learning

Classical hardness of approximation (HA) is the phenomenon that, assuming P ≠ NP, one can easily compute an ϵ-approximation to the solution of a discrete computational problem for ϵ > ϵ0 > 0, but for ϵ 0, there are AI problems for which provably there exist stable neural networks (NNs) that solve the problem, but no algorithm can compute any NN that approximates the AI problem to ϵ1-accuracy. Moreover, this issue is independent of the P vs NP question and thus is a rather different mathematical phenomenon than HA. GHA implies that the universal approximation theorem for NNs only provides a partial understanding of the power of NNs in AI. Thus, a classification theory describing which NNs can be computed by algorithms to particular accuracies is needed to fill this gap. We initiate such a theory by showing the correspondence between the functions that can be computed to ϵ-accuracy by an algorithm and those functions that can be approximated by NNs which can be computed to ϵ̂-accuracy by an algorithm. In particular, the approximation thresholds ϵ and ϵ̂ cannot differ by more than a factor of 12. This means that computing function approximations through NNs will be optimal – in the sense of best approximation accuracy achievable by an algorithm – up to a small constant, compared to any other computational technique

Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing

Abstract: Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature level. However, for binary measurements via the Walsh transform, the theory has long been merely non-existent, despite the large number of applications such as fluorescence microscopy, single pixel cameras, lensless cameras, compressive holography, laser-based failure-analysis etc. Binary measurements are a mainstay in signal and image processing and can be modelled by the Walsh transform and Walsh series that are binary cousins of the respective Fourier counterparts. We help bridging the theoretical gap by providing non-uniform recovery guarantees for infinite-dimensional compressed sensing with Walsh samples and wavelet reconstruction. The theoretical results demonstrate that compressed sensing with Walsh samples, as long as the sampling strategy is highly structured and follows the structured sparsity of the signal, is as effective as in the Fourier case. However, there is a fundamental difference in the asymptotic results when the smoothness and vanishing moments of the wavelet increase. In the Fourier case, this changes the optimal sampling patterns, whereas this is not the case in the Walsh setting

Pneumocystis Pneumonia in HIV-positive Adults, Malawi1

In a prospective study of 660 HIV-positive Malawian adults, we diagnosed Pneumocystis jirovecii pneumonia (PcP) using clinical features, induced sputum for immunofluorescent staining, real-time PCR, and posttreatment follow-up. PcP incidence was highest in patients with the lowest CD4 counts but uncommon compared with incidences of pulmonary tuberculosis and bacterial pneumonia

Metabolomics Profile in Depression:A Pooled Analysis of 230 Metabolic Markers in 5283 Cases With Depression and 10,145 Controls

Background: Depression has been associated with metabolic alterations, which adversely impact cardiometabolic health. Here, a comprehensive set of metabolic markers, predominantly lipids, was compared between depressed and nondepressed persons. Methods: Nine Dutch cohorts were included, comprising 10,145 control subjects and 5283 persons with depression, established with diagnostic interviews or questionnaires. A proton nuclear magnetic resonance metabolomics platform provided 230 metabolite measures: 51 lipids, fatty acids, and low-molecular-weight metabolites; 98 lipid composition and particle concentration measures of lipoprotein subclasses; and 81 lipid and fatty acids ratios. For each metabolite measure, logistic regression analyses adjusted for gender, age, smoking, fasting status, and lipid-modifying medication were performed within cohort, followed by random-effects meta-analyses. Results: Of the 51 lipids, fatty acids, and low-molecular-weight metabolites, 21 were significantly related to depression (false discovery rate q <.05). Higher levels of apolipoprotein B, very-low-density lipoprotein cholesterol, triglycerides, diglycerides, total and monounsaturated fatty acids, fatty acid chain length, glycoprotein acetyls, tyrosine, and isoleucine and lower levels of high-density lipoprotein cholesterol, acetate, and apolipoprotein A1 were associated with increased odds of depression. Analyses of lipid composition indicators confirmed a shift toward less high-density lipoprotein and more very-low-density lipoprotein and triglyceride particles in depression. Associations appeared generally consistent across gender, age, and body mass index strata and across cohorts with depressive diagnoses versus symptoms. Conclusions: This large-scale meta-analysis indicates a clear distinctive profile of circulating lipid metabolites associated with depression, potentially opening new prevention or treatment avenues for depression and its associated cardiometabolic comorbidity

Investigating the relationships between unfavourable habitual sleep and metabolomic traits:evidence from multi-cohort multivariable regression and Mendelian randomization analyses

BACKGROUND: Sleep traits are associated with cardiometabolic disease risk, with evidence from Mendelian randomization (MR) suggesting that insomnia symptoms and shorter sleep duration increase coronary artery disease risk. We combined adjusted multivariable regression (AMV) and MR analyses of phenotypes of unfavourable sleep on 113 metabolomic traits to investigate possible biochemical mechanisms linking sleep to cardiovascular disease.METHODS: We used AMV (N = 17,368) combined with two-sample MR (N = 38,618) to examine effects of self-reported insomnia symptoms, total habitual sleep duration, and chronotype on 113 metabolomic traits. The AMV analyses were conducted on data from 10 cohorts of mostly Europeans, adjusted for age, sex, and body mass index. For the MR analyses, we used summary results from published European-ancestry genome-wide association studies of self-reported sleep traits and of nuclear magnetic resonance (NMR) serum metabolites. We used the inverse-variance weighted (IVW) method and complemented this with sensitivity analyses to assess MR assumptions.RESULTS: We found consistent evidence from AMV and MR analyses for associations of usual vs. sometimes/rare/never insomnia symptoms with lower citrate (- 0.08 standard deviation (SD)[95% confidence interval (CI) - 0.12, - 0.03] in AMV and - 0.03SD [- 0.07, - 0.003] in MR), higher glycoprotein acetyls (0.08SD [95% CI 0.03, 0.12] in AMV and 0.06SD [0.03, 0.10) in MR]), lower total very large HDL particles (- 0.04SD [- 0.08, 0.00] in AMV and - 0.05SD [- 0.09, - 0.02] in MR), and lower phospholipids in very large HDL particles (- 0.04SD [- 0.08, 0.002] in AMV and - 0.05SD [- 0.08, - 0.02] in MR). Longer total sleep duration associated with higher creatinine concentrations using both methods (0.02SD per 1 h [0.01, 0.03] in AMV and 0.15SD [0.02, 0.29] in MR) and with isoleucine in MR analyses (0.22SD [0.08, 0.35]). No consistent evidence was observed for effects of chronotype on metabolomic measures.CONCLUSIONS: Whilst our results suggested that unfavourable sleep traits may not cause widespread metabolic disruption, some notable effects were observed. The evidence for possible effects of insomnia symptoms on glycoprotein acetyls and citrate and longer total sleep duration on creatinine and isoleucine might explain some of the effects, found in MR analyses of these sleep traits on coronary heart disease, which warrant further investigation.</p

Effect of food-related behavioral activation therapy on food intake and the environmental impact of the diet: results from the MooDFOOD prevention trial

This is the final version. Available on open access from Springer via the DOI in this recordPurpose: Food-based dietary guidelines are proposed to not only improve diet quality, but to also reduce the environmental impact of diets. The aim of our study was to investigate whether food-related behavioral activation therapy (F-BA) applying Mediterranean-style dietary guidelines altered food intake and the environmental impact of the diet in overweight adults with subsyndromal symptoms of depression. Methods: In total 744 adults who either received the F-BA intervention (F-BA group) or no intervention (control group) for 12 months were included in this analysis. Food intake data were collected through a food frequency questionnaire at baseline and after 6 and 12 months. Greenhouse gas emissions (GHGE), land use (LU), and fossil energy use (FEU) estimates from life-cycle assessments and a weighted score of the three (pReCiPe score) were used to estimate the environmental impact of each individual diet at each timepoint. Results: The F-BA group reported increased intakes of vegetables (19.7 g/day; 95% CI 7.8–31.6), fruit (23.0 g/day; 9.4–36.6), fish (7.6 g/day; 4.6–10.6), pulses/legumes (4.0 g/day; 1.6–6.5) and whole grains (12.7 g/day; 8.0–17.5), and decreased intake of sweets/extras (− 6.8 g/day; − 10.9 to − 2.8) relative to control group. This effect on food intake resulted in no change in GHGE, LU, and pReCiPe score, but a relative increase in FEU by 1.6 MJ/day (0.8, 2.4). Conclusions: A shift towards a healthier Mediterranean-style diet does not necessarily result in a diet with reduced environmental impact in a real-life setting. Trial registration: ClinicalTrials.gov. Number of identification: NCT02529423. August 2015.European Union FP7National Institute for Health Research (NIHR

Large-scale plasma metabolome analysis reveals alterations in HDL metabolism in migraine

Objective To identify a plasma metabolomic biomarker signature for migraine. Methods Plasma samples from 8 Dutch cohorts (n = 10,153: 2,800 migraine patients and 7,353 controls) were profiled on a 1H-NMR-based metabolomics platform, to quantify 146 individual metabolites (e.g., lipids, fatty acids, and lipoproteins) and 79 metabolite ratios. Metabolite measures associated with migraine were obtained after single-metabolite logistic regression combined with a random-effects meta-analysis performed in a nonstratified and sex-stratified manner. Next, a global test analysis was performed to identify sets of related metabolites associated with migraine. The Holm procedure was applied to control the family-wise error rate at 5% in single-metabolite and global test analyses. Results Decreases in the level of apolipoprotein A1 (β −0.10; 95% confidence interval [CI] −0.16, −0.05; adjusted p = 0.029) and free cholesterol to total lipid ratio present in small high-density lipoprotein subspecies (HDL) (β −0.10; 95% CI −0.15, −0.05; adjusted p = 0.029) were associated with migraine status. In addition, only in male participants, a decreased level of omega-3 fatty acids (β −0.24; 95% CI −0.36, −0.12; adjusted p = 0.033) was associated with migraine. Global test analysis further supported that HDL traits (but not other lipoproteins) were associated with migr

Intercultural communication in German-Dutch business contexts

Contains fulltext : 161468.pdf (publisher's version ) (Open Access)Radboud University, 23 november 2016Promotores : Mulken, M.J.P. van, Gerritsen, M., Wielenga, F.325 p