Abstract:
An introduction to spatial point pattern analysis or just a few (of many) things that could be done with mapped data. The most frequent analysis of a spatial point pattern is a test of complete spatial randomness. As randomness is more of an exception than the rule in the natural world it would be usually followed by modelling the generating spatial process. Different hypothesis can be tested for marked patterns regarding the spatial dependence between marks: independence, random labelling, correlation, gradients in the value of marks, etc.

Abstract:
Structural operational semantics can be studied at the general level of distributive laws of syntax over behaviour. This yields specification formats for well-behaved algebraic operations on final coalgebras, which are a domain for the behaviour of all systems of a given type functor. We introduce a format for specification of algebraic operations that restrict to the rational fixpoint of a functor, which captures the behaviour of finite systems. In other words, we show that rational behaviour is closed under operations specified in our format. As applications we consider operations on regular languages, regular processes and finite weighted transition systems.

Abstract:
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known~\cite{abbondandoloschwarz, aizenbudzapolski,audindamian, kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolating map and flow map allows the results to generalize to local Morse homology and Morse-Conley-Floer homology. We prove Poincar\'e type duality statements for local Morse homology and Morse-Conley-Floer homology.

Abstract:
For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue of the Conley index and the Morse-Conley relations. The approach will be referred to as Morse-Conley-Floer homology.

Abstract:
Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages.

Volatile organic
compounds (VOCs) released by host plants attract gravid European corn borer
(ECB) female moths for oviposition. Despite extensive studies, little is known
about VOCs emitted by maize under natural conditions or the odorscape of a
maize field, particularly at the time of ECB oviposition. Here, we
characterized VOCs released by undamaged maize plants and VOCs in the maize
field odorscape. VOCs were collected throughout the diel cycle with solid-phase
microextraction fibres. VOCs were identified by GC-MS and quantified with
calibration curves. Four replicates per time period were collected; i.e.,
dusk, night, dawn, and day. VOC patterns differed between the maize plants and
the maize field odorscape throughout the diel cycle. At night, the period of
ECB oviposition, the VOC pattern was characterized by an increase in
monoterpenes, a decrease in sesquiterpenes, and the presence of methyl
salicylate, α-copaene, and
Z-3-hexenyl acetate. An apparent discrepancy between maize plant and field
odorscape VOC compositions was observed. Key compounds were identified as
putative host-cues, including methyl salicylate, α-pinene, 3-carene, p-cymene, limonene, and dimethyl nonatriene.
This study showed that VOCs were released by maize in a diel pattern, and
host-characteristic cues were present for nocturnal ECB oviposition.

Abstract:
Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and local variables the interactions of a program with the heap can become rather complex, as an unbounded number of objects can be allocated either on the call stack using local variables, or, anonymously, on the heap using reference fields. As such a static analysis is, in general, undecidable. In this paper we study the verification of recursive programs with unbounded allocation of objects, in a simple imperative language for heap manipulation. We present an improved semantics for this language, using an abstraction that is precise. For any program with a bounded visible heap, meaning that the number of objects reachable from variables at any point of execution is bounded, this abstraction is a finitary representation of its behaviour, even though an unbounded number of objects can appear in the state. As a consequence, for such programs model checking is decidable. Finally we introduce a specification language for temporal properties of the heap, and discuss model checking these properties against heap-manipulating programs.