A counterexample to Thiagarajan's conjecture on regular event structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular event structures correspond exactly to event structures obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded $\natural$-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects. Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs; from a geometric point of view, these domains are in bijection with CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of regular event structures (with bounded $\natural$-cliques) admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded $\natural$-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling. We prove that other counterexamples to Thiagarajan's conjecture arise from aperiodic 4-way deterministic tile sets of Kari and Papasoglu (1999) and Lukkarila (2009). On the positive side, using breakthrough results by Agol (2013) and Haglund and Wise (2008, 2012) from geometric group theory, we prove that Thiagarajan's conjecture is true for regular event structures whose domains occur as principal filters of hyperbolic CAT(0) cube complexes which are universal covers of finite nonpositively curved cube complexes

1-Safe Petri nets and special cube complexes: equivalence and applications

Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net $N$ unfolds into an event structure $\mathcal{E}_N$. By a result of Thiagarajan (1996 and 2002), these unfoldings are exactly the trace regular event structures. Thiagarajan (1996 and 2002) conjectured that regular event structures correspond exactly to trace regular event structures. In a recent paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on the striking bijection between domains of event structures, median graphs, and CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we proved that Thiagarajan's conjecture is true for regular event structures whose domains are principal filters of universal covers of (virtually) finite special cube complexes. In the current paper, we prove the converse: to any finite 1-safe Petri net $N$ one can associate a finite special cube complex ${X}_N$ such that the domain of the event structure $\mathcal{E}_N$ (obtained as the unfolding of $N$) is a principal filter of the universal cover $\widetilde{X}_N$ of $X_N$. This establishes a bijection between 1-safe Petri nets and finite special cube complexes and provides a combinatorial characterization of trace regular event structures. Using this bijection and techniques from graph theory and geometry (MSO theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that the monadic second order logic of a 1-safe Petri net is decidable if and only if its unfolding is grid-free. Our counterexample is the trace regular event structure $\mathcal{\dot E}_Z$ which arises from a virtually special square complex $\dot Z$. The domain of $\mathcal{\dot E}_Z$ is grid-free (because it is hyperbolic), but the MSO theory of the event structure $\mathcal{\dot E}_Z$ is undecidable

Bucolic Complexes

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In particular, we characterize bucolic complexes by some properties of their 2-skeleta and 1-skeleta (that we call bucolic graphs), by which several known results are generalized. We also show that locally-finite bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties.Comment: 45 pages, 4 figure

Habitatval och rörelsemönster hos ren (Rangifer t. tarandus) : en jämförelse mellan fritt bete och stödutfodring

Reindeer (Rangifer tarandus tarandus) husbandry mainly relies on natural pastures to ensure a sustainable animal production. In Sweden, coniferous forest areas are most commonly utilized as grazing grounds during winter. Additionally, supplementary feeding is sometimes provided for free-ranging animals to ensure their survival. The main reasons for the provision of supplementary feeding are loss of lichen pastures due to modern forestry practices and climate change. It is important to understand habitat selection of reindeer and how this selection differs when supplementary food is provided during winter. To answer these questions, GPS collared reindeer data was analyzed for winters between years 2007 – 2010 and 2014 – 2016, comparing time periods when animals relied on natural pasture with periods when animals were provided with supplementary feeding. The study area is situated within Malå herding district in Västerbotten County in northern Sweden. The aim of this project was to investigate 1) habitat selection and space use pattern, 2) differences in home range size between supplementary fed and naturally grazing reindeer, 3) to what extent reindeer move during the winter period when they are not supplementary fed, and 4) how often they re-visit and stay close to the feeding stations when they are supplementary fed. The results clearly showed that reindeer select for lichen-rich forests, open areas and clear cuts both when freely ranging or supplementary fed. The choice of lichen-rich forest habitat becomes stronger when animal were not supplementary fed. The results also showed that reindeer avoided roads during winter. In addition, utility distribution covered a larger geographical area when they were feeding on natural pastures as reindeer covered large geographical area. The frequency of revisitations and time spent around the feeding stations varied between years. The findings of this research can be useful to face the future challenges associated with reindeer husbandry management in different areas with respect to their home range size, habitat selectivity, re-visitation frequency and time spend inside the feeding stations. The study results could be compared with the herders’ knowledge and shared with them for coordination and dialogue between different sectors

Cocompactly cubulated crystallographic groups

We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually \integers^n group is isomorphic to the hyperoctahedral triangulation of $S^{n-1}$, providing a class of groups $G$ for which the simplicial boundary of a $G$-cocompact cube complex depends only on $G$. We also use this result to show that the cocompactly cubulated crystallographic groups in dimension $n$ are precisely those that are \emph{hyperoctahedral}. We apply this result to answer a question of Wise on cocompactly cubulating virtually free abelian groups.Comment: Several correction

Change and variation in a hyer-arid cultural landscape: A merhodological approach using remote sensing timeseries (Landsat MSS and TM, 1973-1996) from the Wadi vegetation of the eastern desert of Egypt

Nine wadi localities in a hyper-arid environment have been registered in the field and studied using earth observation data. Branch height, crown – and trunk – diameter, and indicators of land-use such as present traces of browsing, lopping and charcoal production were registered for arboreal vegetation, mostly Acacia tortilis and Balanites aegyptiaca. A point mapping (GPS) was selected to optimise subsequent integration with raster data and to facilitate a detailed interpretation of change images. Field data and change images are interpreted according to two gradients, one cultural and one hydrological. Derived tree maps are overlaid referenced TM data in order to detect differences between pixels with and without vegetation. The Red band is the most consistent spectral band in its content of vegetation information. Nevertheless it is apparent that several methodological and technical factors constrain the possibilities to register vegetation in this environment of very scarce vegetation cover. Similar problems are also recognised in the change analysis which is based on the difference between Red bands of the years compared. Four different datasets are part of the analysis: 1973, 1979, 1984 (all Landsat MSS images) and 1996 (TM). Field data indicate that changes are taking place in the cultural landscape of the Eastern Desert, and the change is primarily due to processes that both in causes and consequences is associated with ‘deforestation’. Although several sources of errors introduce variations in the change images, the images do reflect the field observations

Behavioural development in wild Western lowland gorillas (gorilla gorilla gorilla)

Behavioural development has received little attention in primates, despite having important influences on infant mortality, interbirth intervals, and therefore, growth of populations. Gorillas have long developmental periods, exhibit strong maternal bonds and integrate into intricate social systems, making them an ideal species in which to investigate non-human primate development. Gorillas exist across a range of habitats, and differences in behaviour, both within and between species reflect socioecological differences, for example, in the availability and distribution of food. Consequently, by using gorillas as a model, opportunities also exist to investigate environmental constraints on the development of independence. This study provides the first detailed analysis, with reference to ecological factors, of the development of behavioural skills and relationships in wild western lowland gorillas (Gorilla gorilla gorilla). Behavioural development of western lowland gorillas is then compared with published accounts of development in mountain gorillas (Gorilla beringei beringei) to determine the extent to which differing ecology influences behaviour. The study was conducted at Mbeli Bai in the Republic of Congo, a large, marshy clearing, visited by gorillas predominantly for feeding purposes. Data were collected using scan, focal, all-occurrence and ad libitum sampling methods from 58 gorillas below 8 years of age. Spatial relationships, suckling, and the nature of interactions involving immature individuals were analysed. The distribution of time between different behaviours by immatures, and the development of independent feeding and travelling behaviour was also investigated, and all were tested for differences as a result of immature age, sex and social group, or the mother's parity. Towards the end of infancy, individuals showed competent feeding behaviour in the bai. However, western lowland gorillas were not weaned until the juvenile period, and until this time, close association was common between mothers and offspring. With increasing independence from the mother there was limited investment in relationships with other individuals, and instead, a greater emphasis was placed on developing skills through play, alloparenting and agonistic interactions. When results were compared with those of mountain gorillas, there was evidence of increased investment in relationships, particularly with the silverback, by immature mountain gorillas, which was assumed to reflect lower rates of natal dispersal by mountain gorillas, and the greater likelihood that relationships with individuals in the natal group could prove useful in the future. Suckling and close proximity to the mother continued until later ages in western lowland gorillas, resulting in clear differences between them mountain gorillas in the duration of investment by mothers. More frugivorous western lowland gorillas required increased levels of investment by the mother before independence could be achieved, demonstrating the effect that resource availability can have on behavioural development in species where resources are widely and unpredictably dispersed

Effects of ant predation on the efficacy of biological control agents Hypena Laceratalis Walker (Lepidoptera : noctuirdae) ; Falconia intermedia Distant (Hemiptera : Miridae and Teleonemia scrupulosa Stål (Hemiptera: Tingidae) on Lantana Camara (Verbenaceae) in South Africa

Lantana camara L. (Verbenaceae) remains a highly invasive and ecologically damaging weed in South Africa, despite some 50 years of biological control efforts. Lack of success has been ascribed to varietal differences, climate and predation of agents but these have not been tested. In this study, the effects of ant predation were tested on populations of three biological control agents for L. camara. Colonies of two species, Crematogaster sp. 1 and 2 were investigated. Crematogaster sp. 1 colonies were offered no choice between immature stages of the agents Hypena laceratalis Walker (Lepidoptera: Noctuidae), Falconia intermedia Distant (Hemiptera: Miridae) or Teleonemia scrupulosa Stål (Hemiptera: Tingidae) on lantana shoots. Density-dependent predation on F. intermedia and T. scrupulosa nymphs on lantana shoots was tested using Crematogaster sp. 2 colonies. In choice experiments Crematogaster sp. 2 colonies were offered F. intermedia or T. scrupulosa nymphs on potted lantana plants. Preliminary food trials confirmed that colonies foraged for protein, thereby validating results of no-choice experiments. Crematogaster sp.1 foragers removed 50% of F. intermedia nymphs, followed by 45% of H. laceratalis larvae and only 9% of T. scrupulosa nymphs. Foragers recruited most actively to H. laceratalis larvae and significantly more H. laceratalis biomass was removed than either F. intermedia or T. scrupulosa. A trade-off existed in prey size selection because larger larvae provided considerably more biomass but required forager cooperation and a longer time to subdue than did smaller prey. This increases both forager energy expense and mortality risk by other predators. This study showed that all Crematogaster sp. 1 colonies removed small (≤10mm) H. laceratalis larvae more frequently than larvae larger than 10mm. Thus, of these biological control agents, predators probably prefer small H. laceratalis larvae. Significantly more F. intermedia than T. scrupulosa nymphs were removed by Crematogaster sp. 1, while Crematogaster sp. 2 colonies removed comparable numbers of both agent species. Falconia intermedia nymphs' fast movement triggered a predatory response by these ant species. In contrast, the relatively immobile behaviour of T. scrupulosa nymphs was identified as a highly effective predator avoidance strategy. Since T. scrupulosa nymphs are unable to escape predators by moving, they appear to depend on the presence of alternative prey attracting predator attention. At high agent and/or forager density, T. scrupulosa nymphs attempted escape, but foragers identified them as prey once they moved and caught them. Predation on F. intermedia was also density dependent in that at high nymph and/or forager densities, escape routes were congested and nymphs were more easily caught. Survival of F. intermedia and T. scrupulosa nymphs in particular was low on ant-accessed shrubs in choice experiments and high on ant-excluded shrubs. It is likely that ants significantly depress F. intermedia populations in the field since besides predation, ant foragers probably interrupt F. intermedia feeding and ovipositioning. The combination of parasitism and predation on early instar larvae may explain why H. laceratalis occurs across lantana's range in South Africa but populations remain low. It is unlikely that T. scrupulosa nymphs are habitually preyed on by ant species unless they attract attention by being mobile. Although biological control of L. camara is influenced by climate and physiological defence mechanisms, this study has shown that predation by two ant species severely impacts leaf-feeding agents for L. camara. Thus, it is recommended that future selection of additional agents to control lantana should exclude leaf-feeding