Antimagic Labelings of Weighted and Oriented Graphs

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and any list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ for all $e\in E(G)$, labels of edges are pairwise distinct, and the sum of the labels on edges incident to a vertex plus the weight of that vertex is distinct from the sum at every other vertex. In this paper we prove that every graph on $n$ vertices having no $K_1$ or $K_2$ component is $\lfloor{\frac{4n}{3}}\rfloor$-weighted-list-antimagic. An oriented graph $G$ is $k$-$oriented-antimagic$ if there exists an injective edge labeling from $E(G)$ into $\{1,\dotsc,|E(G)|+k\}$ such that the sum of the labels on edges incident to and oriented toward a vertex minus the sum of the labels on edges incident to and oriented away from that vertex is distinct from the difference of sums at every other vertex. We prove that every graph on $n$ vertices with no $K_1$ component admits an orientation that is $\lfloor{\frac{2n}{3}}\rfloor$-oriented-antimagic.Comment: 10 pages, 1 figur

Weighted Modal Transition Systems

Specification theories as a tool in model-driven development processes of component-based software systems have recently attracted a considerable attention. Current specification theories are however qualitative in nature, and therefore fragile in the sense that the inevitable approximation of systems by models, combined with the fundamental unpredictability of hardware platforms, makes it difficult to transfer conclusions about the behavior, based on models, to the actual system. Hence this approach is arguably unsuited for modern software systems. We propose here the first specification theory which allows to capture quantitative aspects during the refinement and implementation process, thus leveraging the problems of the qualitative setting. Our proposed quantitative specification framework uses weighted modal transition systems as a formal model of specifications. These are labeled transition systems with the additional feature that they can model optional behavior which may or may not be implemented by the system. Satisfaction and refinement is lifted from the well-known qualitative to our quantitative setting, by introducing a notion of distances between weighted modal transition systems. We show that quantitative versions of parallel composition as well as quotient (the dual to parallel composition) inherit the properties from the Boolean setting.Comment: Submitted to Formal Methods in System Desig

A Few Considerations on Structural and Logical Composition in Specification Theories

Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms. In this short abstract, we collect results of our work in progress on describing and systematizing the algebraic assumptions in specification theories.Comment: In Proceedings FIT 2010, arXiv:1101.426

LEVENDE BILLEDER: OM DANNELSE OG OMDANNELSE AF FORESTILLINGSBILLEDER I HJERNEN

In experimental psychology the notion of a fundamental functional similarity between visual imagery and visual perception dates back to Perky ( 1910); it has gained steadily increasing popularity in modem cognitive psychology and is supported by evidence from experimental studies on visual perception of apparent motion and studies on visual transformation of mental images. Brain activation studies based on new imaging techniques like PET and fMRI has provided further evidence by locating brain mechanisms, which appears active in both visual perception and transformation of visual images with respect to size and orientation.Ideen om et dybtgående slægtskab mellem visuel forestillingsvirksomhed og visuel perception går i den eksperimentelle psykologi tilbage til Perky ( 1910 ). I moderne kognitionspsykologi vandt synspunktet stigende tilslutning fra slutningen af 60'erne, og har nu fået et langt mere præcist indhold gennem konvergerende evidens fra eksperimentelle studier over visuel perception af bevægelse og undersøgelser over mentale transformationer af forestillingsbilleder. Hjerneaktiveringsstudier, der bygger på nye billeddannelsesteknikker som PET og fMRl, har endog gjort det muligt at indkredse visuelle mekanismer i hjernen, der tilsyneladende både bidrager til at frembringe synsoplevet bevægelse og til at transformsformere visuelle forestillingsbilleder med hensyn til størrelse og orientering