A bound for Dickson's lemma

We consider a special case of Dickson's lemma: for any two functions $f,g$ on the natural numbers there are two numbers $i<j$ such that both $f$ and $g$ weakly increase on them, i.e., $f_i\le f_j$ and $g_i \le g_j$. By a combinatorial argument (due to the first author) a simple bound for such $i,j$ is constructed. The combinatorics is based on the finite pigeon hole principle and results in a descent lemma. From the descent lemma one can prove Dickson's lemma, then guess what the bound might be, and verify it by an appropriate proof. We also extract (via realizability) a bound from (a formalization of) our proof of the descent lemma. Keywords: Dickson's lemma, finite pigeon hole principle, program extraction from proofs, non-computational quantifiers

Irrational behavior in the Brown-von Neumann-Nash dynamics

We present a class of games with a pure strategy being strictly dominated by another pure strategy such that the former survives along most solutions of the Brown-von Neumann-Nash dynamics.Nash map, BNN dynamics, Dominated strategies

Brouwer’s Fan Theorem and Convexity

In the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of , the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f satisfies a weak convexity condition

Long term trends of mesopheric ice layers: A model study

Trends derived from the Leibniz-Institute Middle Atmosphere Model (LIMA) and the MIMAS ice particle model (Mesospheric Ice Microphysics And tranSport model) are presented for a period of 138 years (1871–2008) and for middle, high, and arctic latitudes, namely 58°N, 69°N, and 78°N, respectively. We focus on the analysis of mesospheric ice layers (NLC, noctilucent clouds) in the main summer season (July) and on yearly mean values. Model runs with and without an increase of carbon dioxide and water vapor (from methane oxidation) concentrations are performed. Trends are most prominent after ~1960 when the increase of both CO2 and H2O accelerates. It is important to distinguish between tendencies on geometric altitudes and on given pressure levels converted to altitudes (‘pressure altitudes’). Negative trends of (geometric) NLC altitudes are primarily due to cooling below NLC altitudes caused by CO2 increase. Increases of ice particle radii and NLC brightness with time are mainly caused by an enhancement of water vapor. Several ice layer and background parameter trends are similar at high and arctic latitudes but are substantially different at middle latitudes. This concerns, for example, occurrence rates, ice water content (IWC), and number of ice particles in a column. Considering the time period after 1960, geometric altitudes of NLC decrease by approximately 260 m per decade, and brightness increases by roughly 50% (1960–2008), independent of latitude. NLC altitudes decrease by approximately 15–20 m per increase of CO2 by 1 ppmv. The number of ice particles in a column and also at the altitude of maximum backscatter is nearly constant with time. At all latitudes, yearly mean NLC appear at altitudes where temperatures are close to 145±1 K. Ice particles are present nearly all the time at high and arctic latitudes, but are much less common at middle latitudes. Ice water content and maximum backscatter (βmax) are highly correlated, where the slope depends on latitude. This allows to combine data sets from satellites and lidars. Furthermore, IWC and the concentration of water vapor at βmax are also strongly correlated. Nearly all trends depend on a lower limit applied for βmax, e.g., IWC and occurrence rates. Results from LIMA/MIMAS are in very good agreement with observations

Städtewappen des Viertels unter dem Manhartsberg (Weinviertel)

Durch meine Ausbildung zum Malermeister wurde mein Interesse für heraldische Darstellungen geweckt. Da ich angrenzend zum Weinviertel im Weinort Stammersdorf lebe und seit Jahren einen großen Bezug zum Weinviertel habe, wählte ich dieses Thema. Ziel der Untersuchung: Thema dieser Diplomarbeit ist die Aufarbeitung der geschichtlichen Entwicklung der Städtewappen des Viertels unter dem Manhartsberg (Weinviertel), mit dem Bezug auf die heutigen Bezirke, die im nordöstlichen Niederösterreich liegen. Es werde die Städtewappen und ihre Geschichte aus den Bezirken Gänserndorf, Hollabrunn, Korneuburg, Mistelbach und der Stadt Gerasdorf beleuchtet. Diese Arbeit hat sich das Ziel gesetzt, Vergleiche zwischen den Wappen durch Blasonierungen aufzustellen. Im ersten Teil setzt sich die Diplomarbeit mit der Geschichte der Städte auseinander. Dabei wird das Hauptaugenmerk insbesondere auf die historische Entwicklung der Städtewappen gelegt sowie auf die Namensgebung eingegangen. Auch Erkenntnisse über die Städte fließen in die Arbeit ein. Der zweite Teil ist eine wissenschaftliche Untersuchung. In dieser werden die Metalle und Farben in den Wappen des Weinviertels in einer statistischen Aufstellung dargestellt. Besonderes Augenmerk wurde auf die farblichen Zusammenhänge im Hinblick auf die Region gelegt. Methodik: Es werden die farblichen Zusammenhänge der Wappen im Weinviertel untersucht. Außerdem erfolgt eine Auflistung der Städte- und Gemeindewappen mit historischem Einblick. Ergebnisse: Die Diplomarbeit kommt zum Ergebnis, dass die meisten Städtewappen herrschaftliche Zusammenhänge besitzen. Ferner werden zwischen den einzelnen Wappen heraldische Verknüpfungen ersichtlich, die zeigen, dass die Bezirke des Weinviertels früher eine andere Aufteilung hatten. Zur Bearbeitung des Themas wurden Buchquellen und Dokumente herangezogen. Dies ist der Anfang einer Forschung, die noch nicht abgeschlossen ist, da es noch viele offene Fragen gibt. Schlüsselwörter: Weinviertel, Markt –und Stadtwappen, Heraldik, Deutsch-Wagram, Gänserndorf, Gerasdorf, Groß-Enzersdorf, Hardegg, Hollabrunn, Korneuburg, Laa an der Thaya, Marchegg, Maissau, Mistelbach, Poysdorf, Pulkau, Retz, Schrattenthal, Stockerau, Wolkersdorf, Zistersdorf, Kolonisation, Herrschafts- und Besitzgeschichte.My education as master painter has evoked my interest in heraldic representations. I chose this as the topic for my thesis because I live next to the Weinviertel in the wine village Stammersdorf and thus have a close relation to the Weinviertel. Aim of the study: The thesis‘ aim is to portray the historical development of the district below the Manhartsberg (Weinviertel) in relation to today’s administrative regions in north-eastern Lower Austria. The coats of arms of the administrative regions Gänserndorf, Hollabrunn, Korneuburg, Mistelbach and the city of Gerasdorf as well as their history will be examined. The thesis aims at contrasting the coats of arms by blazoning them. The first part of this thesis deals with the towns‘ history. The main focus is thereby on the historical development of the towns‘ coats of arms and their naming. Also knowledge about the towns will be included in the thesis. The second part of the thesis is a scientific investigation presenting metals and colours of the coats of arms in a statistic table. It concentrates on the colour contexts with regard to the region. Methodology: The thesis examines the colour contexts of the Weinviertel’s coats of arms and gives an historical overview about the regional town and municipality coats of arms. Results: One of the study’s main results is that most of the towns‘ coats of arms have manorial connections. There are also heraldic links between the single coats of arms that show that the administrative regions of the Weinviertel once were distributed differently. Books and other documents were used as source for this thesis. It can be seen as the beginning of a research process that has not been finished yet as there are still a lot of open questions. Keywords: Weinviertel, market and town coats of arms, heraldic, Deutsch-Wagram, Gänserndorf, Gerasdorf, Groß-Enzersdorf, Hardegg, Hollabrunn, Korneuburg, Laa an der Thaya, Marchegg, Maissau, Mistelbach, Poysdorf, Pulkau, Retz, Schrattenthal, Stockerau, Wolkersdorf, Zistersdorf, colonisation, history of reign, power and ownership

Statin effect on thrombin inhibitor effectiveness during percutaneous coronary intervention: a post-hoc analysis from the ISAR-REACT 3 trial

Objective: To determine whether statin therapy influences the efficacy of thrombin inhibitor bivalirudin or unfractionated heparin (UFH) during PCI. Setting and patients: The post-hoc analysis of the ISAR-REACT 3 Trial included 4,570 patients: 3,106 patients were on statin therapy and 1,464 patients were not on statin therapy at the time of PCI procedure. Main outcome measures: The primary outcome of this analysis was the 30-day composite of death, myocardial infarction, target vessel revascularization (TVR) or major bleeding. Results: The primary outcome occurred in 7.9% patients (n=246) in the statin group versus 9.8% (n=143) in the non-statin group (P=0.036). There was an interaction in univariate (P=0.028) and multivariable (P=0.026) analysis between pre-PCI statin therapy and the type of antithrombotic therapy regarding myocardial infarction. In the statin group, bivalirudin significantly reduced the incidence of major bleeding (2.6 vs. 4.3%, P=0.013) with no significant difference in the incidence of myocardial infarction (4.9 vs. 5.2%; P=0.73) compared with UFH. In the non-statin group, bivalirudin was inferior to UFH regarding the incidence of myocardial infarction (7.1 vs. 4.1%, P=0.013), yet major bleeding remained lower among bivalirudin-treated patients (4.0 vs. 5.2%, P=0.25). Conclusion: This post-hoc analysis suggests the existence of an interaction between statin therapy before PCI and antithrombotic therapy during PCI. Patients receiving bivalirudin therapy at the time of PCI showed less periprocedural myocardial infarction when on pre-PCI statin therapy which has to be investigated in further studie

Community phenology of insects on oak:Local differentiation along a climatic gradient

Climate change is advancing the onset of phenological events, with the rate of advance varying among species and trophic levels. In addition, local populations of the same species may show genetic differences in their response to seasonal cues. If populations of interacting species differ in their response, then climate change may result in geographically varying shifts in the community-level distribution of interaction strength. We explored the magnitude of trophic- and species-level responses to temperature in a tritrophic system comprising pedunculate oak, insect herbivores, and their associated parasitoids. We sampled local realizations of this community at five sites along a transect spanning fifteen degrees of latitude. Samples from each trophic level at each site were exposed to the same set of five climatic regimes during overwintering in climate chambers. We then recorded the number of days and degree-days required for oak acorns to develop and insects to emerge. In terms of dates of events, phenology differed among populations. In terms of degree-days, we found that for two species pairs, the heat sum required to develop in spring differed by an additional similar to 500 degree-days between trophic levels when overwintering at the highest temperature. For three species, within-population variation in the number of degree-days required for emergence was higher at warmer temperatures. Our findings suggest that changing temperatures can modify interactions within a community by altering the relative phenology of interacting species and that some interactions are more vulnerable than others to a shift in temperature. The geographic variation in the phenological response of a species suggests that there is a genetic component in determining the phenology of local populations. Such local variation blended with interspecific differences in responses makes it complex to understand how communities will respond to warmer temperatures