Existence of Probability Measures With Given Marginals

We show that if f is a probability density on Rn wrt Lebesgue measure (or any absolutely continuous measure) and 0 ≤ f ≤ 1, then there is another density g with only the values 0 and 1 and with the same (n−1)-dimensional marginals in any finite number of directions. This sharpens, unifies and extends the results of Lorentz and of Kellerer. Given a pair of independent random variables 0 ≤ X, Y ≤ 1, we further study functions 0 ≤ ϕ ≤ 1 such that Z = ϕ (X,Y) satisfies E(Z|X) = X and E(Z|Y) = Y. If there is a solution then there also is a nondecreasing solution ϕ(x,y). These results are applied to tomography and baseball

Novel approaches for analysing gut microbes and dietary polyphenols: challenges and opportunities

Polyphenols, ubiquitously present in the food we consume, may modify the gut microbial composition and/or activity, and moreover, may be converted by the colonic microbiota to bioactive compounds that influence host health. The polyphenol content of fruit and vegetables and derived products is implicated in some of the health benefits bestowed on eating fruit and vegetables. Elucidating the mechanisms behind polyphenol metabolism is an important step in understanding their health effects. Yet, this is no trivial assignment due to the diversity encountered in both polyphenols and the gut microbial composition, which is further confounded by the interactions with the host. Only a limited number of studies have investigated the impact of dietary polyphenols on the complex human gut microbiota and these were mainly focused on single polyphenol molecules and selected bacterial populations. Our knowledge of gut microbial genes and pathways for polyphenol bioconversion and interactions is poor. Application of specific in vitro or in vivo models mimicking the human gut environment is required to analyse these diverse interactions. A particular benefit can now be gained from next-generation analytical tools such as metagenomics and metatranscriptomics allowing a wider, more holistic approach to the analysis of polyphenol metabolism. Understanding the polyphenol gut microbiota interactions and gut microbial bioconversion capacity will facilitate studies on bioavailability of polyphenols in the host, provide more insight into the health effects of polyphenols and potentially open avenues for modulation of polyphenol bioactivity for host health

A hybrid process combining ion exchange resin and bipolar membrane electrodialysis for reverse osmosis remineralization

A new reverse osmosis (RO) permeate remineralization process combining ion exchange resin and bipolar membrane electrodialysis (BMED) was developed. Its feasibility for hardness ions recovery and RO permeate remineralization was investigated. The effect of several operation conditions on the efficiency of the combined remineralization process was studied. Highly efficient cation exchange resin loading was achieved at a low flow rate and low feed solution concentration. The recovered calcium purity and yield considerably improved under gradient elution methods in comparison with commonly applied conventional isocratic elution methods using the same eluent quantity. The purity of the produced acid and base using BMED dropped noticeably with increasing feed NaCl concentration, presumably related to decreased permselectivity of the ion-exchange membranes. The drop in the purity of the calcium recovered when eluting the cation exchange resin with BMED-produced HCl in comparison with commercially available acid at 50 % yield was shown not to affect the remineralization process, where a dilution factor could be applied. This study confirmed the technical feasibility of the developed process for RO permeate remineralization. However, its application can be limited by the water source characteristics, the energy-intensive bipolar membrane process, and applied operational conditions, where more investigation is still needed.</p

The interplay of workplace satisfaction, activity support, and productivity support in the hybrid work context

Since the COVID-19 pandemic, more employees started to work (partially) from home. As a consequence, there is a new need to find a balance between working from home and at the office, and to optimize both workplaces to support employees’ work activities and perceived productivity. This study aims to gain insights into relationships between satisfaction with physical workplace features, perceived activity support, and productivity support in a hybrid working context. Leesman data (N=57,286), collected between March 2020 and May 2021, was used to perform a path analysis, which allows to simultaneously analyse multiple relationships. Findings suggest that the experience and the support of the work environment (either the home or the office) to perform a specific task influences employees’ location decisions. As both the perceived support of concentrative and collaborative activities at home and at the office relate to higher perceived productivity, organizations are recommended to redesign parts of the office environment to support both types of work activities

An international study of the prevalence of substance use in patients with delusional infestation

To the Editor: Delusional infestation (DI) is a disorder characterised by the belief of being infested with living organisms or objects.1 Insects and worms are the most common concerns. Objects, such as fibers or threads, are increasingly reported by patients. DI can be primary or secondary to mental illness, physical illness, prescribed medication, and misuse of substances such as amphetamines, cannabis, codeine, cocaine, or opiates. Dermatologists are usually the specialists to whom a patient with DI is referred because patients believe that they have primarily a skin diseas

On the critical pair theory in abelian groups : Beyond Chowla's Theorem

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio