On Topological Minors in Random Simplicial Complexes

For random graphs, the containment problem considers the probability that a binomial random graph $G(n,p)$ contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well-known that the (sharp) threshold is at $p=1/n$. We consider a natural analogue of this question for higher-dimensional random complexes $X^k(n,p)$, first studied by Cohen, Costa, Farber and Kappeler for $k=2$. Improving previous results, we show that $p=\Theta(1/\sqrt{n})$ is the (coarse) threshold for containing a subdivision of any fixed complete $2$-complex. For higher dimensions $k>2$, we get that $p=O(n^{-1/k})$ is an upper bound for the threshold probability of containing a subdivision of a fixed $k$-dimensional complex.Comment: 15 page

On Link Homology Theories from Extended Cobordisms

This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2-dimensional cobordisms by taking into account their embedding into the three space. Secondly, we extend the underlying cobordism category to a 2-category, where the usual relations hold up to 2-isomorphisms. The corresponding abelian 2-functor is called an extended quantum field theory (EQFT). We show that the Khovanov homology, the nested Khovanov homology, extracted by Stroppel and Webster from Seidel-Smith construction, and the odd Khovanov homology fit into this setting. Moreover, we prove that any EQFT based on a Z_2-extension of the embedded cobordism category which coincides with Khovanov after reducing the coefficients modulo 2, gives rise to a link invariant homology theory isomorphic to those of Khovanov.Comment: Lots of figure

Relating geometry descriptions to its derivatives on the web

Sharing building information over the Web is becoming more popular, leading to advances in describing building models in a Semantic Web context. However, those descriptions lack unified approaches for linking geometry descriptions to building elements, derived properties and derived other geometry descriptions. To bridge this gap, we analyse the basic characteristics of geometric dependencies and propose the Ontology for Managing Geometry (OMG) based on this analysis. In this paper, we present our results and show how the OMG provides means to link geometric and non-geometric data in meaningful ways. Thus, exchanging building data, including geometry, on the Web becomes more efficient

Alltagskommunikation in der digitalen Gesellschaft: Vorschlag eines Konzepts zur Analyse zwischenmenschlicher Kommunikation

Im Beitrag wird das Konzept der Alltagskommunikation vorgeschlagen, welches darauf abzielt, die komplexe zwischenmenschliche Kommunikation in der digitalen Gesellschaft kontextualisiert zu analysieren. Das Konzept verortet die von unterschiedlichen Medien geprägten, mobilen und mitunter parallel verlaufenden Kommunikationsprozesse mit anderen Menschen in der Alltagswelt eines Individuums. Es begreift diese Prozesse als miteinander in Beziehung stehend, in überdauernde Strukturen der zwischenmenschlichen Kommunikation eingebettet und durch diese beeinflusst. Das Analysekonzept lässt sich empirisch anwenden, indem spezifische (thematische) Ausschnitte der zwischenmenschlichen Kommunikation fokussiert und ganzheitlich unter Rückgriff auf vier Analyselinsen analysiert werden. Diese Analyselinsen umfassen 1) die kommunikativen Beziehungen, innerhalb derer die zwischenmenschliche Kommunikation stattfindet, 2) die Kommunikationsmuster, durch die die Kommunikation geprägt ist, 3) die Medien- und Kommunikationsrepertoires, auf die zur Kommunikation zurückgegriffen wird sowie 4) die Funktionen, welche die Kommunikation erfüllt. Im Artikel wird das Konzept der Alltagskommunikation zunächst expliziert, bevor dessen empirische Umsetzbarkeit anhand einer Fallstudie zur Kommunikation über satirische Medieninhalte illustriert wird. In this contribution, the concept of Alltagskommunikation (everyday communication) is introduced, which aims to analyze the complex interpersonal communication entanglements in the digital society in a contextualized way. The concept locates the mobile and sometimes parallel communication processes with other individuals, which are shaped by different media, within the lifeworld of an individual. These processes are understood as interrelated, embedded in and influenced by permanent structures of interpersonal communication. To empirically apply the concept, specific (thematic) segments of interpersonal communication are examined and analyzed holistically through four analytical lenses. These analytical lenses comprise 1) the communicative relationships, in which the interpersonal communication takes place, 2) the patterns of communication by which communication is shaped, 3) the media and communication repertoires utilized for communication, and 4) the functions the communication fulfills. In this article, first, the concept of everyday communication is explicated and, second, its empirical feasibility is illustrated in a case study on interpersonal communication about satirical media content

PKS 1510-089: a rare example of a flat spectrum radio quasar with a very high-energy emission

The blazar PKS 1510-089 is an example of flat spectrum radio quasars. High-energy emissions from this class of objects are believed to have been produced by inverse Compton radiation with seed photons originating from the broad line region. In such a paradigm, a lack of very high-energy emissions is expected because of the Klein-Nishina effect and strong absorption in the broad line region. Recent detection of at least three such blazars by Cherenkov telescopes has forced a revision of our understanding of these objects. We have aimed to model the observed spectral energy distribution of PKS 1510-089 from the high-energy flares in March 2009, during which very high-energy emission were also detected by H.E.S.S. We have applied the single-zone internal shock scenario to reproduce the multiwavelength spectrum of PKS~1510-089. We have followed the evolution of the electrons as they propagate along the jet and emit synchrotron and inverse Compton radiation. We have considered two sources of external photons: the dusty torus and the broad line region. We have also examined the effects of the gamma-gamma absorption of the high-energy photons both in the AGN environment (the broad line region and the dusty torus), as well as while traveling over cosmological distances: the extragalactic background light. We have successfully modeled the observed spectrum of PKS 1510-089. In our model, the highest energy emission is the result of the Comptonization of the infrared photons from the dusty torus, thus avoiding Klein-Nishina regime, while the bulk of the emissions in the GeV range may still be dominated by the Comptonization of radiation coming from the broad line region.Comment: Accepted for publication in A&

Including widespread geometry formats in semantic graphs using RDF literals

The exchange of building data involves both geometric and non-geometric data. A promising Linked Data approach is to embed data from existing geometry formats inside Resource Description Framework (RDF) literals. Based on a study of relevant specifications and related work, this toolset-independent approach was found suitable for the exchange of geometric construction data. To implement the approach in practice, the File Ontology for Geometry formats (FOG) and accompanying modelling method is developed. In a proof-of-concept web application that uses FOG, is demonstrated how geometry descriptions of different existing formats are automatically recognised and parsed

MCHM (4-methylcyclohexane Methanol) Influences the Predator-Prey Interaction Between Danio Rerio and Daphnia Magna

Chemical contamination alters organism-level traits, such as activity and feeding, that can ultimately affect aquatic trophic interactions. Despite the importance of predator-prey relationships in aquatic communities, chemical toxicity is often tested on single species prior to use. For example, 4-methylcyclohexane methanol (MCHM) used in industrial coal-cleaning enters the environment regularly from low-level contamination during disposal and occasionally in high concentrations following accidental spills, but its effects on fish-zooplankton interactions remain unknown. It was hypothesized MCHM exposure affects zebrafish and D. magna swimming behavior differently when exposed individually or together, and ultimately affects their relationship. Zebrafish and D. magna were exposed individually and together to various environmentally relevant concentrations of MCHM. In the single-species experiments, zebrafish and D. magna swimming distance, velocity, and activity, as well as D. magna mortality, were quantified 1, 3, 5, and 7 days post-exposure to 0, 0.5, 1, 3, or 5 ppm MCHM. In single species tests, zebrafish in all MCHM treatments experienced an immediate and consistent decrease in all measured parameters. Daphnia magna swimming distance, velocity and activity also decreased by approximately 30-50%; however, unlike the zebrafish, mortality occurred after 3 days, reaching 100% by the end of the experiment. When exposed together, D. magna exhibited similar results to the individual test. In contrast, only zebrafish in the 1 and 5 ppm concentrations experienced decreased swimming distance and velocity when prey was present. To examine how decreased mobility in both organisms affected their predator-prey interaction, a feeding study was conducted. Zebrafish were exposed to MCHM concentrations of 0, 0.5, 1, 3, or 5 ppm. After 1, 3, 5, and 7 days, 15 live D. magna were released into a tank containing one fish. The number of D. magna remaining after 30 minutes and one hour was used to calculate feeding rate. The number of strikes performed by each zebrafish was also quantified. Zebrafish feeding rate decreased by 40% in the 1, 3 and 5 ppm MCHM treatments compared to the control throughout the exposure period. Zebrafish in those MCHM treatments also performed more strikes per D. magna consumed. The individual species tests suggest MCHM exposures longer than three days could lead to loss of zebrafish food resources. Short-term exposures led to decreased mobility in both organisms, and the feeding study results indicated these changes altered the zebrafish-D. magna predator-prey relationship

Using Geophysical Constraints To Determine Groundwater Travel Times, Seafloor Arrival Locations, And Saltwater Concentrations For Transition Zone Depths At Underground Nuclear Detonations On Amchitka Island

Thesis (Ph.D.) University of Alaska Fairbanks, 2007There is a great amount of radioactive material in the subsurface of Amchitka Island as a result from underground nuclear testing performed between 1965 and 1971. It is unknown how long it will take for the radionuclides to travel to the seafloor and the marine environment or where possible seepage zones will occur. The contaminant transport is greatly affected by the location of the transition zone (TZ) and the effective porosity, which were both determined by magnetotellurics (MT) in 2004. The hypothesis of this study was as follows: the groundwater travel times and seafloor arrival locations, can be estimated through groundwater modeling, with the location of the transition zone being estimated by magnetotellurics. An additional hypothesis is as follows: saltwater concentration for a TZ and the general subsurface characteristics can be quantified with groundwater modeling, using geophysical constraints in combination with saltwater and hydraulic head measurements. The groundwater travel times were estimated with groundwater modeling using the transition zone location as determined by MT. Shortest groundwater travel times are 1,200 and 2,100 years, at Long Shot and Cannikin respectively. At Long Shot, a decreased groundwater travel time of up to 55% could be seen when an enhanced hydraulic conductivity was included at the location of an assumed andesite sill layer. The seafloor arrival locations can be up to 1,000 and 2,100 m offshore at Long Shot and Cannikin respectively but will most likely occur closer to shore. This study was also successful at establishing the general characteristics of the subsurface by using geophysical constraints in combination with saltwater and hydraulic head measurements. The subsurface at Long Shot is isotropic or has mild anisotropy ratio of 1:2, which confirms the study by Fenske (1972). As represented in this study, this method has been shown to be valuable in determining the saltwater concentration of the TZ as determined by MT and can thus be used in further studies of islands and coastal areas

Beaten by the chord to nail the melody: Influence of metric and irregular submerged dissonance accents on auditory sequence learning

Dynamic attending theory (Jones, 1976; Large & Jones, 1999) suggests that isochronously repeating salient points in time are predictable and facilitate processing by synchronizing attentional oscillations in the brain. By manipulating amount and spacing of such salience, this design attempts to enhance accuracy of reproduced melodies. Salience was introduced by dissonant harmonies. All subjects seemed to get distracted by the harsh sound of dissonance. However, non-musicians seemed to benefit from a regular ¾ meter. More research with larger non-musician samples is needed to investigate how dissonance raises cognitive load but may also function as attentional refresher when predictable

A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations

Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of O(n^7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture