Needs for an Integration of Specific Data Sources and Items – First Insights of a National Survey Within the German Center for Infection Research

State-subsidized programs develop medical data integration centers in Germany. To get infection disease (ID) researchers involved in the process of data sharing, common interests and minimum data requirements were prioritized. In 06/2019 we have initiated the German Infectious Disease Data Exchange (iDEx) project. We have developed and performed an online survey to determine prioritization of requests for data integration and exchange in ID research. The survey was designed with three sub-surveys, including a ranking of 15 data categories and 184 specific data items and a query of available 51 data collecting systems. A total of 84 researchers from 17 fields of ID research participated in the survey (predominant research fields: gastrointestinal infections n=11, healthcare-associated and antibiotic-resistant infections n=10, hepatitis n=10). 48% (40/84) of participants had experience as medical doctor. The three top ranked data categories were microbiology and parasitology, experimental data, and medication (53%, 52%, and 47% of maximal points, respectively). The most relevant data items for these categories were bloodstream infections, availability of biomaterial, and medication (88%, 87%, and 94% of maximal points, respectively). The ranking of requests of data integration and exchange is diverse and depends on the chosen measure. However, there is need to promote discipline-related digitalization and data exchange.

Maximal point spaces of posets with relative lower topology

In domain theory, by a poset model of a T1 topological space X we usually mean a poset P such that the subspace Max(P) of the Scott space of P consisting of all maximal points is homeomorphic to X. The poset models of T1 spaces have been extensively studied by many authors. In this paper we investigate another type of poset models: lower topology models. The lower topology ?(P) on a poset P is one of the fundamental intrinsic topologies on the poset, which is generated by the sets of the form P\?x, x ? P. A lower topology poset model (poset LT-model) of a topological space X is a poset P such that the space Max?(P) of maximal points of P equipped with the relative lower topology is homeomorphic to X. The studies of such new models reveal more links between general T1 spaces and order structures. The main results proved in this paper include (i) a T1 space is compact if and only if it has a bounded complete algebraic dcpo LT-model; (ii) a T1 space is second-countable if and only if it has an ?-algebraic poset LT-model; (iii) every T1 space has an algebraic dcpo LT-model; (iv) the category of all T1 space is equivalent to a category of bounded complete posets. We will also prove some new results on the lower topology of different types of posets.

Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity

We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and basic results on convergence and limits, continuity, gH-differentiability, and monotonicity. We define different types of (local) minimal and maximal points and develop the basic theory for their characterization. We then consider some interesting connections with applied geometry of curves and the convexity of interval-valued functions is introduced and analyzed in detail. Further, the periodicity of interval-valued functions is described and analyzed. Several examples and pictures accompany the presentation.

An Iterative Dimension-Wise Approach to the Structural Analysis with Interval Uncertainties

The structural analysis is inevitably surrounded with uncertainties and the interval analysis is a favorable method if insufficient data is available on uncertainties. The accuracy of current interval analysis methods including the interval perturbation method (IPM), subinterval perturbation method (SIPM) and dimension-wise approach (DWA) depends on a reference point (RP), e.g., the expansion point in IPM, for some problems due to ignoring the co-operative effects of multiple interval inputs on the response. To this end, an iterative dimension-wise approach (IDWA) is proposed. Either the minimal or maximal input vector of the response is identified as an RP by a global update in which a novel RP is dimension-wisely assembled by the minimal or maximal points of all sectional curves of the response surface at a previous RP through a local update. The interval response is calculated by deterministic solvers at the minimal and maximal input vectors. An acoustic analysis problem is studied eventually to validate the effectiveness of the proposed method, from which conclusions are drawn.

Dcpo models of T1 spaces

A poset model of a topological space X is a poset P such that the subspace Max(P) of the Scott space ΣP consisting of all maximal points of P is homeomorphic to X. Every T<sub>1</sub> space has a (bounded complete algebraic) poset model. It is, however, not known whether every T<sub>1</sub> space has a dcpo model and whether every sober T<sub>1</sub> space has a dcpo model whose Scott topology is sober. In this paper we give a positive answer to these two problems. For each T<sub>1</sub> space X we shall construct a dcpo A that is a model of X, and prove that X is sober if and only if the Scott topology of A is sober. One useful by-product is a method that can be used to construct more non-sober dcpos.

Directed complete poset models of T1 spaces

A poset model of a topological space X is a poset P such that the subspace Max(P) of the Scott space ΣP is homeomorphic to X, where Max(P) is the set of all maximal points of P. Every T1 space has a (bounded complete algebraic) poset model. It was, however, not known whether every T1 space has a directed complete poset model and whether every sober T1 space has a directed complete poset model whose Scott topology is sober. In this paper we give a positive answer to each of these two problems. For each T1 space X, we shall construct a directed complete poset E that is a model of X, and prove that X is sober if and only if the Scott space Σ E is sober. One useful by-product is a method for constructing more directed complete posets whose Scott topology is not sober.

Normal approximation for statistics of Gibbsian input in geometric probability

This paper concerns the asymptotic behavior of a random variableWλresulting from the summation of the functionals of a Gibbsian spatial point process over windowsQλ↑ℝd. We establish conditions ensuring thatWλhas volume order fluctuations, i.e. they coincide with the fluctuations of functionals of Poisson spatial point processes. We combine this result with Stein's method to deduce rates of a normal approximation forWλas λ → ∞. Our general results establish variance asymptotics and central limit theorems for statistics of random geometric and related Euclidean graphs on Gibbsian input. We also establish a similar limit theory for claim sizes of insurance models with Gibbsian input, the number of maximal points of a Gibbsian sample, and the size of spatial birth-growth models with Gibbsian input.

Normal approximation for statistics of Gibbsian input in geometric probability

This paper concerns the asymptotic behavior of a random variable Wλ resulting from the summation of the functionals of a Gibbsian spatial point process over windows Qλ ↑ ℝd. We establish conditions ensuring that Wλ has volume order fluctuations, i.e. they coincide with the fluctuations of functionals of Poisson spatial point processes. We combine this result with Stein's method to deduce rates of a normal approximation for Wλ as λ → ∞. Our general results establish variance asymptotics and central limit theorems for statistics of random geometric and related Euclidean graphs on Gibbsian input. We also establish a similar limit theory for claim sizes of insurance models with Gibbsian input, the number of maximal points of a Gibbsian sample, and the size of spatial birth-growth models with Gibbsian input.