Reallocation of an infinetely divisible good

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.mathematical economics and econometrics ;

Physics with Coherent Matter Waves

This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future

Cholinergic white matter pathways along the Alzheimer's disease continuum

Nemy et al. investigate cholinergic white matter projections along the Alzheimer's disease continuum. They show that alterations are already present in individuals with subjective cognitive decline, preceding the more widespread alterations seen in mild cognitive impairment and Alzheimer's disease dementia. Previous studies have shown that the cholinergic nucleus basalis of Meynert and its white matter projections are affected in Alzheimer's disease dementia and mild cognitive impairment. However, it is still unknown whether these alterations can be found in individuals with subjective cognitive decline, and whether they are more pronounced than changes found in conventional brain volumetric measurements. To address these questions, we investigated microstructural alterations of two major cholinergic pathways in individuals along the Alzheimer's disease continuum using an in vivo model of the human cholinergic system based on neuroimaging. We included 402 participants (52 Alzheimer's disease, 66 mild cognitive impairment, 172 subjective cognitive decline and 112 healthy controls) from the Deutsches Zentrum für Neurodegenerative Erkrankungen Longitudinal Cognitive Impairment and Dementia Study. We modelled the cholinergic white matter pathways with an enhanced diffusion neuroimaging pipeline that included probabilistic fibre-tracking methods and prior anatomical knowledge. The integrity of the cholinergic white matter pathways was compared between stages of the Alzheimer's disease continuum, in the whole cohort and in a CSF amyloid-beta stratified subsample. The discriminative power of the integrity of the pathways was compared to the conventional volumetric measures of hippocampus and nucleus basalis of Meynert, using a receiver operating characteristics analysis. A multivariate model was used to investigate the role of these pathways in relation to cognitive performance. We found that the integrity of the cholinergic white matter pathways was significantly reduced in all stages of the Alzheimer's disease continuum, including individuals with subjective cognitive decline. The differences involved posterior cholinergic white matter in the subjective cognitive decline stage and extended to anterior frontal white matter in mild cognitive impairment and Alzheimer's disease dementia stages. Both cholinergic pathways and conventional volumetric measures showed higher predictive power in the more advanced stages of the disease, i.e. mild cognitive impairment and Alzheimer's disease dementia. In contrast, the integrity of cholinergic pathways was more informative in distinguishing subjective cognitive decline from healthy controls, as compared with the volumetric measures. The multivariate model revealed a moderate contribution of the cholinergic white matter pathways but not of volumetric measures towards memory tests in the subjective cognitive decline and mild cognitive impairment stages. In conclusion, we demonstrated that cholinergic white matter pathways are altered already in subjective cognitive decline individuals, preceding the more widespread alterations found in mild cognitive impairment and Alzheimer's disease. The integrity of the cholinergic pathways identified the early stages of Alzheimer's disease better than conventional volumetric measures such as hippocampal volume or volume of cholinergic nucleus basalis of Meynert

Amyloid pathology but not APOE ε4 status is permissive for tau-related hippocampal dysfunction

We investigated whether the impact of tau-pathology on memory performance and on hippocampal/medial temporal memory function in non-demented individuals depends on the presence of amyloid pathology, irrespective of diagnostic clinical stage. We conducted a cross-sectional analysis of the observational, multicentric DZNE-Longitudinal Cognitive Impairment and Dementia Study (DELCODE). Two hundred and thirty-five participants completed task functional MRI and provided CSF (92 cognitively unimpaired, 100 experiencing subjective cognitive decline and 43 with mild cognitive impairment). Presence (A+) and absence (A-) of amyloid pathology was defined by CSF amyloid-β42 (Aβ42) levels. Free recall performance in the Free and Cued Selective Reminding Test, scene recognition memory accuracy and hippocampal/medial temporal functional MRI novelty responses to scene images were related to CSF total-tau and phospho-tau levels separately for A+ and A- individuals. We found that total-tau and phospho-tau levels were negatively associated with memory performance in both tasks and with novelty responses in the hippocampus and amygdala, in interaction with Aβ42 levels. Subgroup analyses showed that these relationships were only present in A+ and remained stable when very high levels of tau (>700 pg/ml) and phospho-tau (>100 pg/ml) were excluded. These relationships were significant with diagnosis, age, education, sex, assessment site and Aβ42 levels as covariates. They also remained significant after propensity score based matching of phospho-tau levels across A+ and A- groups. After classifying this matched sample for phospho-tau pathology (T-/T+), individuals with A+/T+ were significantly more memory-impaired than A-/T+ despite the fact that both groups had the same amount of phospho-tau pathology. ApoE status (presence of the E4 allele), a known genetic risk factor for Alzheimer's disease, did not mediate the relationship between tau pathology and hippocampal function and memory performance. Thus, our data show that the presence of amyloid pathology is associated with a linear relationship between tau pathology, hippocampal dysfunction and memory impairment, although the actual severity of amyloid pathology is uncorrelated. Our data therefore indicate that the presence of amyloid pathology provides a permissive state for tau-related hippocampal dysfunction and hippocampus-dependent recognition and recall impairment. This raises the possibility that in the predementia stage of Alzheimer's disease, removing the negative impact of amyloid pathology could improve memory and hippocampal function even if the amount of tau-pathology in CSF is not changed, whereas reducing increased CSF tau-pathology in amyloid-negative individuals may not proportionally improve memory function

Improving 3D convolutional neural network comprehensibility via interactive visualization of relevance maps: Evaluation in Alzheimer's disease

Background: Although convolutional neural networks (CNN) achieve high diagnostic accuracy for detecting Alzheimer's disease (AD) dementia based on magnetic resonance imaging (MRI) scans, they are not yet applied in clinical routine. One important reason for this is a lack of model comprehensibility. Recently developed visualization methods for deriving CNN relevance maps may help to fill this gap. We investigated whether models with higher accuracy also rely more on discriminative brain regions predefined by prior knowledge. Methods: We trained a CNN for the detection of AD in N=663 T1-weighted MRI scans of patients with dementia and amnestic mild cognitive impairment (MCI) and verified the accuracy of the models via cross-validation and in three independent samples including N=1655 cases. We evaluated the association of relevance scores and hippocampus volume to validate the clinical utility of this approach. To improve model comprehensibility, we implemented an interactive visualization of 3D CNN relevance maps. Results: Across three independent datasets, group separation showed high accuracy for AD dementia vs. controls (AUC$\geq$0.92) and moderate accuracy for MCI vs. controls (AUC$\approx$0.75). Relevance maps indicated that hippocampal atrophy was considered as the most informative factor for AD detection, with additional contributions from atrophy in other cortical and subcortical regions. Relevance scores within the hippocampus were highly correlated with hippocampal volumes (Pearson's r$\approx$-0.86, p<0.001). Conclusion: The relevance maps highlighted atrophy in regions that we had hypothesized a priori. This strengthens the comprehensibility of the CNN models, which were trained in a purely data-driven manner based on the scans and diagnosis labels.Comment: 24 pages, 9 figures/tables, supplementary material, source code available on GitHu

Fornix fractional anisotropy mediates the association between Mediterranean diet adherence and memory four years later in older adults without dementia

Here, we investigated whether fractional anisotropy (FA) of hippocampus-relevant white-matter tracts mediates the association between baseline Mediterranean diet adherence (MeDiAd) and verbal episodic memory over four years. Participants were healthy older adults with and without subjective cognitive decline and patients with amnestic mild cognitive impairment from the DELCODE cohort study (n = 376; age: 71.47 ± 6.09 years; 48.7 % female). MeDiAd and diffusion data were obtained at baseline. Verbal episodic memory was assessed at baseline and four yearly follow-ups. The associations between baseline MeDiAd and white matter, and verbal episodic memory's mean and rate of change over four years were tested with latent growth curve modeling. Baseline MeDiAd was associated with verbal episodic memory four years later (95 % confidence interval, CI [0.01, 0.32]) but not with its rate of change over this period. Baseline Fornix FA mediated - and, thus, explained - that association (95 % CI [0.002, 0.09]). Fornix FA may be an appropriate response biomarker of Mediterranean diet interventions on verbal memory in older adults.</p