The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics.

We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of ‘category’ for which equality and equivalence of categories agree. Such categories satisfy a version of the univalence axiom, saying that the type of isomorphisms between any two objects is equivalent to the identity type between these objects; we call them ‘saturated’ or ‘univalent’ categories. Moreover, we show that any category is weakly equivalent to a univalent one in a universal way. In homotopical and higher-categorical semantics, this construction corresponds to a truncated version of the Rezk completion for Segal spaces, and also to the stack completion of a prestack.

Dyke-Davidoff-Masson syndrome, or cerebral hemiatrophy, is a pre- or perinatally acquired entity characterized by predominantly neurologic symptoms, such as seizures, facial asymmetry, contralateral hemiplegia, and mental retardation. Psychiatric symptoms are rarely reported. We report the first case of left cerebral hemiatrophy and a late onset of treatment-resistant schizoaffective disorder after a stressful life event. The patient finally responded well to clozapine. The clinical history and results from structural neuroimaging are highlighted to discuss the possible developmental bias for psychotic disorders.

The mechanical properties of porous ceramics are greatly influenced by their microstructure. Therefore, mechanical behavior of highly porous ceramics is different from that of dense ceramics. In this work, we evaluate different mechanical testing methods such as static compression, Brazilian disc test and 3-point bending on their suitability for comparison of highly porous ceramic materials. It is shown that 3-point bending is more suitable than static compression or Brazilian disc testing, as the material exhibits no critical crack propagation under compressive loading. With 3-point bending tests, a quantitative comparison of the mechanical properties of foams with different microstructures and porosities is possible. Under cyclic compression the foams exhibit a very high degree of crack tolerance in combination with preservation of their structural integrity even at high strains of 10%.

Various wireless applications are currently under development for the unlicensed 60 GHz band. This paper describes three examples with different system requirements. The first two are point-to-multipoint wireless networks (in an airplane and in a car) and the third one is a short range point-to-point connection. Special requirements of the applications are a high number of users for the point-to-multipoint connection and a high data rate of 10 Gbit/s for the point-to-point connection system. Implementation aspects are pointed out, which are important to demonstrate the functionality of the system in a relevant environment and are key aspects to develop the related products. For example, integration aspects of the antenna into an airplane passenger seat and the receiver concept of the radio frequency-(RF) front-end to reducing the power consumption at ultrahigh data rates are described. Additionally, to determine the geometrical system architecture, ray-tracing simulations inside an aircraft and inside a car were performed.

This work deals with the expressive power of logics on finite graphs with access to an additional “arbitrary” linear order. The queries that can be expressed this way are the order-invariant queries for the logic. For the standard logics used in computer science, such as first-order logic, it is known that access to an arbitrary linear order increases the expressiveness of the logic. However, when we look at the separating examples, we find that they have satisfying models whose Gaifman Graph is complex – unbounded in valence and in treewidth. We thus explore the expressiveness of order-invariant queries over well-behaved graphs. We prove that first-order order-invariant queries over strings and trees have no additional expressiveness over first-order logic in the original signature. We also prove new upper bounds on order-invariant queries over bounded treewidth and bounded valence graphs. Our results make use of a new technique of independent interest: the application of algebraic characterizations of definability to show collapse results.

GaN based pH-sensors were used to measure the reaction and the kinetics of a lipase assay producing caprylic acid. Sensor structures consist of an AlGaN/GaN-heterostructure grown by plasma-induced molecular beam epitaxy with a thin GaN cap layer. The carrier concentration of the two-dimensional electron gas is manipulated by changing the surface potential due to changes in pH value.

We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small restrictions on the semi-linear sets considered.

We study classes of ultrafilters on ω defined by a natural property of the Loeb measure in the Nonstandard Universe corresponding to the ultrafilter. This class, the Property M ultrafilters, is shown to contain all ultrafilters built up by taking iterated products over collections of pairwise nonisomorphic selective ultrafilters. Results on Property M ultrafilters are applied to the construction of extensions of probability measures, and to the study of measurable reductions between ultrafilters.