A construction principle for proper scoring rules

Proper scoring rules enable decision-theoretically principled comparisons of probabilistic forecasts. New scoring rules can be constructed by identifying the predictive distribution with an element of a parametric family and then applying a known scoring rule. We introduce a condition which ensures propriety in this construction and thereby obtain novel proper scoring rules.

Constructing Node-Independent Spanning Trees in Augmented Cubes

For a network, edge/node-independent spanning trees (ISTs) can not only tolerate faulty edges/nodes, but also be used to distribute secure messages. As important node-symmetric variants of the hypercubes, the augmented cubes have received much attention from researchers. The n-dimensional augmented cube AQn is both (2n ‒ 1)-edge-connected and (2n ‒ 1)-nodeconnected (n ≢ 3), thus the well-known edge conjecture and node conjecture of ISTs are both interesting questions in AQn. So far, the edge conjecture on augmented cubes was proved to be true. However, the node conjecture on AQn is still open. In this paper, we further study the construction principle of the node-ISTs by using the double neighbors of every node in the higher dimension. We prove the existence of 2k − 1 node-ISTs rooted at node 0 in A Q n ( 00...0 ︸ n−k )(n≥k≥4) by proposing an ingenious way of construction and propose a corresponding O(NlogN) time algorithm, where N = 2k is the number of nodes in A Q n ( 00...0 ︸ n−k ) .

»Mehr als das« – ein programmatischer Titel auch in gattungstheoretischer Hinsicht

Artikelbeginn:[English title and abstract below] Dieses Buch ist so Mindfuck. [...] [D]ieses Buch lebt davon, dass man keinen Plan hat. Dass man, genau wie der Protagonist, keine Ahnung hat, was da eigentlich abgeht. [...] Wie der Protagonist hinterfragt man das, was man kennt, denkt sich zwischendurch »wtf« und ist sich einschließlich des Endes nie so ganz sicher, was jetzt eigentlich Sache ist. (Weltentraeumerin 2019) Dieses Urteil der LovelyBooks-Rezensentin Weltentraeumerin über Patrick Ness’ Mehr als das (engl. EA More Than This) ist insofern repräsentativ, als fast alle der etwas ausführlicheren Rezensionen auf der Plattform hervorheben, dass die Lektüre dieses Buches mehr Fragen aufwirft als sie beantwortet. Patrick Ness’s More Than ThisA Hybrid of Postmodern Utopia and Adolescent Novel The novel More Than This (2013) by Patrick Ness is an enthralling but potentially disconcerting text; the construction principle of which seems to be deliberate confusion. It tells the story of 16-year-old Seth who drowns in the first chapter of the book and then finds himself in a desolate, abandoned place, wondering whether he is still alive or in some version of hell – or somewhere in between – and dreaming his last dream in the moment of death. Or might Seth have woken up from what could be called a collective dream, a virtual reality that has become the safe haven for humanity after the physical world has become uninhabitable? Neither the protagonist nor the reader is given a conclusive answer. This article addresses the literary strategies that are deployed in the novel to create this plurality of possible readings. Specific attention is paid to the way in which structural elements of the utopian novel and the adolescent novel are combined and hybridised. Drawing on the concept of heterotopia as a postmodern utopian subgenre, it is argued that More Than This can be read as an aesthetic realisation of a post-modern frame of mind, generating what Jean-François Lyotard calls the differend, and thereby offering readers the opportunity to consciously endure radical plurality.

Mutually Unbiased Bases and Their Symmetries

We present and generalize the basic ideas underlying recent work aimed at the construction of mutually unbiased bases in finite dimensional Hilbert spaces with the help of group and graph theoretical concepts. In this approach finite groups are used to construct maximal sets of mutually unbiased bases. Thus the prime number restrictions of previous approaches are circumvented and this construction principle sheds new light onto the intricate relation between mutually unbiased bases and characteristic geometrical structures of Hilbert spaces.

Well-order as a construction principle for physical theories

Physics has up to now missed to express in mathematical terms the fundamental idea of events of a path in time and space uniquely succeeding one another. An appropriate mathematical concept that reflects this idea is a well-ordered set. In such a set every subset has a least element. Thus every element of a well-ordered set has as its definite successor the least element of the subset of all elements larger than itself. This is apparently contradictory to the densely ordered real number lines which conventionally constitute the coordinate axes in any representation of time and space and in which between any two numbers exists always another number. In this article it is shown how decomposing this disaccord in favour of well-ordered sets causes spacetime to be discontinuous.

Form Finding of Shell Bridges Using the Pneumatic Forming of Hardened Concrete Construction Principle

Concrete shells are fascinating structures. Even thin shells can span over large areas without requiring any columns. If a form-defining load case exists, the shape of the shell can be designed to ensure that the forces in the structure are transferred primarily by the membrane action, which leads to an even distribution of the stresses across the shell surface. Concrete as a material, characterized by high compressive strength and low tensile strength, can be used with a very high degree of utilization. A fundamental problem with building concrete shells is the high effort required for the production of the complicated formwork. A new construction principle called Pneumatic Forming of Hardened Concrete (PFHC) was invented at TU Wien and requires no traditional formwork or falsework during the construction process. An air cushion is used to lift a flat hardened concrete plate, and at the same time, additional post-tensioning cables are tightened to support the transformation of the flat plate into a double-curved shell. One possible application of PFHC is the construction of shell bridges. Here, the shape of the shell has to be designed according to the acting loads and the boundary conditions of the construction method. This paper describes the partly conflicting factors involved in the form-finding process for practical application and the semiautomated workflow for optimizing the geometry of shell bridges. In the first optimization step, the final bridge shape is determined using a particle-spring system or alternatively a thrust-network approach. In the second optimization step, the shell is completed to form a full dome—this is called the reference geometry and is required for the new construction method. Finally, the reference geometry is discretized into single-curved panels by using a mesh-based optimization framework. To frame the presented work, an overview of different experimental and computer-aided form-finding methods is given.