Visible parts of fractal percolation

We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.Comment: 22 pages, 3 figure

Packing dimension of mean porous measures

We prove that the packing dimension of any mean porous Radon measure on $\mathbb R^d$ may be estimated from above by a function which depends on mean porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum value. This result was stated in \cite{BS}, and in a weaker form in \cite{JJ1}, but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example of a mean porous measure $\mu$ on $\mathbb R$ such that $\mu(A)=0$ for all mean porous sets $A\subset\mathbb R$.Comment: Revised versio

Porosities and dimensions of measures

We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.Comment: Jarvenpaa = J\"arvenp\"a\"

The Dutch Healthy Diet Index : development, evaluation, and application

The Dutch Healthy Diet index – Development, Evaluation, and Application Linde van Lee Abstract Background: Dietary indices evaluate the conformity of an individual’s diet with pre-defined standards. Generally, dietary guidelines are used for this purpose. As no index based on the current dietary guidelines was available in the Netherlands, the aim of the present thesis was to develop, evaluate, and apply a dietary index for use in the country. Methods and results: The Dutch Healthy Diet index (DHD-index) was developed on the basis of the 2006 Dutch dietary guidelines using data relating to 749 young adults who completed two 24-hour recalls in the Dutch national food consumption survey 2003. The index comprises ten components on physical activity, vegetables, fruit, dietary fibre, saturated fatty acids, trans fatty acids, consumption occasions with acidic drinks and foods, sodium, and alcohol. Scores for each component range between 0 (no adherence) and 10 (complete adherence) points. The DHD-index was inversely associated with energy intake and positively associated with most micronutrient intakes when adjusted for energy intake. We compared the DHD-index score based on two 24-hour recalls with the index based on the food frequency questionnaires (FFQ) of 121 adults from the European Food Consumption Validation study. We revealed an acceptable correlation (r=0.48) and absolute agreement between the indices based on the two methods. The prospective relationship with mortality outcomes was studied in 3593 of the Rotterdam Study participants who were followed for 20 years. The DHD-index per 10 points increment was associated with a 9% (95% CI 0.87-0.96) risk reduction for all-cause mortality, and non-significantly associated with risk reductions for cardiovascular disease, coronary heart disease, and stroke mortality. Among women, shared dinners were associated with lower DHD-index scores for that day than solo dinners in 1740 participants who contributed multiple 24-hour recalls in the Nutrition Questionnaires plus study. Among men and women, dinners shared with family members were associated with a higher DHD-index score on that day than dinners shared with others. Furthermore, in a subsample of 1235 participants in the Nutrition Questionnaires plus study, we evaluated the DHD-index based on the newly developed 34-item DHD-FFQ, a short questionnaire to assess diet quality in time-limited settings. The DHD-index based on the DHD-FFQ showed an acceptable correlation (r=0.56) with the index based on a 180-item FFQ, but showed a large variation in bias at individual level. Conclusions: The DHD-index based on an FFQ, on multiple 24-hour recalls, or on the DHD-FFQ was considered a valid tool to rank participants according to their diet quality. The DHD-index was therefore considered useful to monitor populations, study diet–disease associations, and identify subpopulations at risk of poor diet quality.</p

Slicing Sets and Measures, and the Dimension of Exceptional Parameters

We consider the problem of slicing a compact metric space \Omega with sets of the form \pi_{\lambda}^{-1}\{t\}, where the mappings \pi_{\lambda} \colon \Omega \to \R, \lambda \in \R, are \emph{generalized projections}, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that \Omega has Hausdorff dimension strictly greater than one, what is the dimension of the 'typical' slice \pi_{\lambda}^{-1}{t}, as the parameters \lambda and t vary. In the special case of the mappings \pi_{\lambda} being orthogonal projections restricted to a compact set \Omega \subset \R^{2}, the problem dates back to a 1954 paper by Marstrand: he proved that for almost every \lambda there exist positively many $t \in \R$ such that \dim \pi_{\lambda}^{-1}{t} = \dim \Omega - 1. For generalized projections, the same result was obtained 50 years later by J\"arvenp\"a\"a, J\"arvenp\"a\"a and Niemel\"a. In this paper, we improve the previously existing estimates by replacing the phrase 'almost all \lambda' with a sharp bound for the dimension of the exceptional parameters.Comment: 31 pages, three figures; several typos corrected and large parts of the third section rewritten in v3; to appear in J. Geom. Ana

Phase transition and correlation decay in Coupled Map Lattices

For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures

Bayesian Computation with Intractable Likelihoods

This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent developments in pseudo-marginal methods, approximate Bayesian computation (ABC), the exchange algorithm, thermodynamic integration, and composite likelihood, paying particular attention to advancements in scalability for large datasets. We also mention R and MATLAB source code for implementations of these algorithms, where they are available.Comment: arXiv admin note: text overlap with arXiv:1503.0806

Deep brain stimulation of the anterior nucleus of the thalamus in drug-resistant epilepsy in the MORE multicenter patient registry

Copyright © 2023 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the American Academy of Neurology. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (CC BY), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background and objectives: The efficacy of deep brain stimulation of the anterior nucleus of the thalamus (ANT DBS) in patients with drug-resistant epilepsy (DRE) was demonstrated in the double-blind Stimulation of the Anterior Nucleus of the Thalamus for Epilepsy randomized controlled trial. The Medtronic Registry for Epilepsy (MORE) aims to understand the safety and longer-term effectiveness of ANT DBS therapy in routine clinical practice. Methods: MORE is an observational registry collecting prospective and retrospective clinical data. Participants were at least 18 years old, with focal DRE recruited across 25 centers from 13 countries. They were followed for at least 2 years in terms of seizure frequency (SF), responder rate (RR), health-related quality of life (Quality of Life in Epilepsy Inventory 31), depression, and safety outcomes. Results: Of the 191 patients recruited, 170 (mean [SD] age of 35.6 [10.7] years, 43% female) were implanted with DBS therapy and met all eligibility criteria. At baseline, 38% of patients reported cognitive impairment. The median monthly SF decreased by 33.1% from 15.8 at baseline to 8.8 at 2 years (p 10 implantations) had 42.8% reduction in median monthly SF by 2 years in comparison with 25.8% in low-volume center. In patients with cognitive impairment, the reduction in median monthly SF was 26.0% by 2 years compared with 36.1% in patients without cognitive impairment. The most frequently reported adverse events were changes (e.g., increased frequency/severity) in seizure (16%), memory impairment (patient-reported complaint, 15%), depressive mood (patient-reported complaint, 13%), and epilepsy (12%). One definite sudden unexpected death in epilepsy case was reported. Discussion: The MORE registry supports the effectiveness and safety of ANT DBS therapy in a real-world setting in the 2 years following implantation. Classification of evidence: This study provides Class IV evidence that ANT DBS reduces the frequency of seizures in patients with drug-resistant focal epilepsy.The MORE registry was sponsored and funded by Medtronic, plc.info:eu-repo/semantics/publishedVersio

The impact of language barriers on trust formation in multinational teams

This study systematically investigates how language barriers influence trust formation in multinational teams (MNTs). Based on 90 interviews with team members, team leaders, and senior managers in 15 MNTs in three German automotive corporations, we show how MNT members’ cognitive and emotional reactions to language barriers influence their perceived trustworthiness and intention to trust, which in turn affect trust formation. We contribute to diversity research by distinguishing the exclusively negative language effects from the more ambivalent effects of other diversity dimensions. Our findings also illustrate how surface-level language diversity may create perceptions of deep-level diversity. Furthermore, our study advances MNT research by revealing the specific influences of language barriers on team trust, an important mediator between team inputs and performance outcomes. It thereby encourages the examination of other team processes through a language lens. Finally, our study suggests that multilingual settings necessitate a reexamination and modification of the seminal trust theories by Mayer, Davis and Schoorman (1995) and McAllister (1995). In terms of practical implications, we outline how MNT leaders can manage their subordinates’ problematic reactions to language barriers and how MNT members can enhance their perceived trustworthiness in multilingual settings