Conditional Reactive Systems

We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; second, it turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done very elegantly in the more general setting

Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a framework which includes the tropical and arctic type graphs introduced in a previous paper and a new variant of arithmetic type graphs. These type graphs can be used to assign weights to graphs and to show that these weights decrease in every rewriting step in order to prove termination. We present an example involving counters and discuss the implementation in the tool Grez

Decidability and Expressiveness of Finitely Representable Recognizable Graph Languages

Recognizable graph languages are a generalization of regular (word) languages to graphs (as well as arbitrary categories). Recently automaton functors were proposed as acceptors of recognizable graph languages. They promise to be a useful tool for the verification of dynamic systems, for example for invariant checking. Since automaton functors may contain an infinite number of finite state sets, one must restrict to finitely representable ones for implementation reasons. In this paper we take into account two such finite representations: primitive recursive automaton functors - in which the automaton functor can be constructed on-the-fly by a primitive recursive function -, and bounded automaton functors - in which the interface size of the graphs (cf. path width) is bounded, so that the automaton functor can be explicitly represented. We show that the language classes of both kinds of automaton functor are closed under boolean operations, and compare the expressiveness of the two paradigms with hyperedge replacement grammars. In addition we show that the emptiness and equivalence problem are decidable for bounded automaton functors, but undecidable for primitive recursive automaton functors

Treewidth, Pathwidth and Cospan Decompositions

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small width are used to efficiently decide graph properties, for instance via graph automata

The role of forage availability on diet choice and body condition in American beavers (\u3ci\u3eCastor canadensis\u3c/i\u3e)

Forage availability can affect body condition and reproduction in wildlife.Weused terrestrial and aquatic vegetation sampling, stable isotope analysis, and livetrapping to investigate the influence of estimated forage biomass on diet, body condition, and reproduction in American beavers (Castor canadensis) in the Namakan Reservoir, Voyageurs National Park, Minnesota, USA, May 2008–September 2009. Available terrestrial and emergent aquatic forage varied greatly among territories, but floating leaf aquatic forage was low in abundance in all territories. Variation in estimated biomass of available emergent and terrestrial vegetation did not explain variation in respective assimilated diets, but variation in floating leaf vegetation explained 31% of variation in assimilated floating leaf diets. No models using available vegetation explained variation in body condition. Body condition of individual females in spring did not affect kit catch per unit effort, and overwinter body condition of subadults and adults was similar between territories with and without kits. We found no evidence that available aquatic vegetation affected beaver body condition or fitness. Available forage may be above minimum thresholds to detect differences in diet choice or body condition. Other factors such as water level fluctuations or climatic variables may also explain variation in beaver body condition

A Logic on Subobjects and Recognizability

Abstract. We introduce a simple logic that allows to quantify over the subobjects of a categorical object. We subsequently show that, for the category of graphs, this logic is equally expressive as second-order monadic graph logic (msogl). Furthermore we show that for the more general setting of hereditary pushout categories, a class of categories closely related to adhesive categories, we can recover Courcelle's result that every msogl-expressible property is recognizable. This is done by giving an inductive translation of formulas of our logic into so-called automaton functors which accept recognizable languages of cospans

A semi-automatic three-dimensional technique using a regionalized facial template enables facial growth assessment in healthy children from 1.5 to 5.0 years of age.

Objectives To develop a semi-automatic technique to evaluate normative facial growth in healthy children between the age of 1.5 and 5.0 years using three-dimensional stereophotogrammetric images. Materials and Methods Three-dimensional facial images of healthy children at 1.5, 2.0, 2.5, 3.0, 4.0 and 5.0 years of age were collected and positioned based on a reference frame. A general face template was used to extract the face and its separate regions from the full stereophotogrammetric image. Furthermore, this template was used to create a uniform distributed mesh, which could be directly compared to other meshes. Average faces were created for each age group and mean growth was determined between consecutive groups for the full face and its separate regions. Finally, the results were tested for intra- and inter-operator performance. Results The highest growth velocity was present in the first period between 1.5 and 2.0 years of age with an average of 1.50 mm (±0.54 mm) per six months. After 2.0 years, facial growth velocity declined to only a third at the age of 5.0 years. Intra- and inter-operator variability was small and not significant. Conclusions The results show that this technique can be used for objective clinical evaluation of facial growth. Example normative facial averages and the corresponding facial growth between the age 1.5 and 5.0 years are shown. Clinical Relevance This technique can be used to collect and process facial data for objective clinical evaluation of facial growth in the individual patient. Furthermore, these data can be used as normative data in future comparative studies

Ileal transposition:A non-restrictive bariatric surgical procedure that reduces body fat and increases ingestion-related energy expenditure

Background: Ileal Transposition (IT) was developed as a model to study body weight reduction without the restrictive or malabsorptive aspects of other bariatric surgeries, but the exact mechanisms of the alterations in body weight after IT are not completely understood. Objective: To provide a detailed description of the surgical procedure of IT, and describe its effect on energy balance parameters. Methods: Adult male Lewis rats underwent either IT (IT+) or sham (IT-) surgery. Following surgery body weight and energy intake were monitored. After attaining weight stability (> 30 days), energy expenditure and its components were assessed using indirect calorimetry at a day of fasting, limited intake, and ad libitum intake. At the end of the study body composition analysis was performed. Results: IT+ resulted in transiently reduced energy intake, increased ingestion-related energy expenditure (IEE) and decreased body and adipose tissue weight when compared to IT-. At weight stability, neither energy budget (i.e., energy intake - energy expenditure), nor energy efficiency was different in IT+ rats compared to IT-. Conclusion: Our data show that the primary cause of weight reduction following IT+ is a transient reduction in energy intake. If the increased IEE is related to a higher level of satiety, compensatory feeding to bridge body weight difference between IT+ and IT- rats is less likely to occur