Categorical Semantics for Functional Reactive Programming with Temporal Recursion and Corecursion

Functional reactive programming (FRP) makes it possible to express temporal aspects of computations in a declarative way. Recently we developed two kinds of categorical models of FRP: abstract process categories (APCs) and concrete process categories (CPCs). Furthermore we showed that APCs generalize CPCs. In this paper, we extend APCs with additional structure. This structure models recursion and corecursion operators that are related to time. We show that the resulting categorical models generalize those CPCs that impose an additional constraint on time scales. This constraint boils down to ruling out $\omega$-supertasks, which are closely related to Zeno's paradox of Achilles and the tortoise.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Tree size and herbivory determine below-canopy grass quality and species composition in savannahs

Large single-standing trees are rapidly declining in savannahs, ecosystems supporting a high diversity of large herbivorous mammals. Savannah trees are important as they support both a unique flora and fauna. The herbaceous layer in particular responds to the structural and functional properties of a tree. As shrubland expands stem thickening occurs and large trees are replaced by smaller trees. Here we examine whether small trees are as effective in providing advantages for grasses growing beneath their crowns as large trees are. The role of herbivory in this positive tree-grass interaction is also investigated. We assessed soil and grass nutrient content, structural properties, and herbaceous species composition beneath trees of three size classes and under two grazing regimes in a South African savannah. We found that grass leaf content (N and P) beneath the crowns of particularly large (ca. 3. 5 m) and very large trees (ca. 9 m) was as much as 40% greater than the same grass species not growing under a tree canopy, whereas nutrient contents of grasses did not differ beneath small trees

Generalized disks of contractivity for explicit and implicit Runge-Kutta methods

The A-contractivity of Runge-Kutta methods with respect to an inner product norm was investigated thoroughly by Butcher and Burrage (who used the term B-stability). Their theory is extended to contractivity in a region bounded by a circle through the origin. The largest possible circle is calculated for many known explicit Runge-Kutta methods. As a rule it is considerably smaller than the stability region, and in several cases it degenerates to a point. It is shown that an explicit Runge-Kutta method cannot be contractive in any circle of this class if it is more than fourth order accurate

Reducibility and contractivity of Runge-Kutta methods revisited

The exact relation between a Cooper-like reducibility concept and the reducibilities introduced by Hundsdorfer, Spijker and by Dahlquist and Jeltsch is given. A shifted Runge-Kutta scheme and a transplanted differential equation is introduced in such a fashion that the input/output relation remains unchanged under these transformations. This gives a technique to prove stability and contractivity results. This is demonstrated on the example of contractivity disk

On curl-preserving finite volume discretizations for shallow water equations

The preservation of intrinsic or inherent constraints, like divergence-conditions, has gained increasing interest in numerical simulations of various physical evolution equations. In Torrilhon and Fey, SIAM J. Numer. Anal. (42/4) 2004, a general framework is presented how to incorporate the preservation of a discrete constraint into upwind finite volume methods. This paper applies this framework to the wave equation system and the system of shallow water equations. For the wave equation a curl-preservation for the momentum variable is present and easily identified. The preservation in case of the shallow water system is more involved due to the presence of convection. It leads to the vorticity evolution as generalized curl-constraint. The mechanisms of vorticity generation are discussed. For the numerical discretization special curl-preserving flux distributions are discussed and their incorporation into a finite volume scheme described. This leads to numerical discretizations which are exactly curl-preserving for a specific class of discrete curl-operators. The numerical experiments for the wave equation show a significant improvement of the new method against classical schemes. The extension of the curl-free numerical discretization to the shallow water case is possible after isolating the pressure flux. Simulation examples demonstrate the influence of the modification. The vortex structure is more clearly resolve

The role of active movement in fungal ecology and community assembly

Movement ecology aims to provide common terminology and an integrative framework of movement research across all groups of organisms. Yet such work has focused on unitary organisms so far, and thus the important group of filamentous fungi has not been considered in this context. With the exception of spore dispersal, movement in filamentous fungi has not been integrated into the movement ecology field. At the same time, the field of fungal ecology has been advancing research on topics like informed growth, mycelial translocations, or fungal highways using its own terminology and frameworks, overlooking the theoretical developments within movement ecology. We provide a conceptual and terminological framework for interdisciplinary collaboration between these two disciplines, and show how both can benefit from closer links: We show how placing the knowledge from fungal biology and ecology into the framework of movement ecology can inspire both theoretical and empirical developments, eventually leading towards a better understanding of fungal ecology and community assembly. Conversely, by a greater focus on movement specificities of filamentous fungi, movement ecology stands to benefit from the challenge to evolve its concepts and terminology towards even greater universality. We show how our concept can be applied for other modular organisms (such as clonal plants and slime molds), and how this can lead towards comparative studies with the relationship between organismal movement and ecosystems in the focus

Proofs about Network Communication: For Humans and Machines

Many concurrent and distributed systems are safety-critical and therefore have to provide a high degree of assurance. Important properties of such systems are frequently proved on the specification level, but implementations typically deviate from specifications for practical reasons. Machine-checked proofs of bisimilarity statements are often useful for guaranteeing that properties of specifications carry over to implementations. In this paper, we present a way of conducting such proofs with a focus on network communication. The proofs resulting from our approach are not just machine-checked but also intelligible for humans.Comment: In Proceedings ICE 2023, arXiv:2308.0892

Correctness of Broadcast via Multicast: Graphically and Formally

Maintaining data consistency among multiple parties requires nodes to repeatedly send data to all other nodes. For example, the nodes of a blockchain network have to disseminate the blocks they create across the whole network. The scientific literature typically takes the ideal perspective that such data distribution is performed by broadcasting to all nodes directly, while in practice data is distributed by repeated multicast. Since correctness and security of consistency maintenance protocols usually have been established for the ideal setting only, it is vital to show that these properties carry over to real-world implementations. Therefore, it is desirable to prove that the ideal and the real behavior are equivalent. In the work described in this paper, we take an important step towards such a proof by proving a simpler variant of this equivalence statement. The simplification is that we consider only a concrete pair of network topologies, which nevertheless illustrates important phenomena encountered with arbitrary topologies. For describing systems that distribute data, we use a domain-specific language of processes that corresponds to a class of Petri nets and is embedded in a general-purpose process calculus. This way, we can outline our proof using an intuitive graphical notation and leverage the rich theory of process calculi in the actual proof, which is machine-checked using the Isabelle proof assistant.Comment: In Proceedings FROM 2022, arXiv:2209.09208. arXiv admin note: substantial text overlap with arXiv:2208.1124

The lymphangiogenic growth factors VEGF-C and VEGF-D : Part 1: Basic principles and embryonic development

This journal is listed by Scopus and EMBASE/Excerpta Medica, but not by Web of Science...VEGF-C and VEGF-D are the two central signaling molecules that stimulate the development and growth of the lymphatic system. Both belong to the vascular endothelial growth factor (VEGF) protein family, which plays important roles in the growth of blood vessels (angiogenesis) and lymphatic vessels (lymphangiogenesis). In mammals, the VEGF family comprises five members: VEGF-A, PlGF, VEGF-B, VEGF-C and VEGF-D. The family was named after VEGF-A, the first member to be discovered. VEGF-C and VEGF-D form a subgroup within this family in terms of function and structure. Their distinctive biosynthesis differentiates them from the other VEGFs: they are produced as inactive precursors and need to be activated by proteolytic removal of their long N- and C-terminal propeptides. Unlike the other VEGFs, VEGF-C and VEGF-D are direct stimulators of lymphatic vessel growth. They exert their lymphangiogenic function via VEGF receptor 3, which is expressed in the adult organism almost exclusively on lymphatic endothelial cells. In this review, we provide an overview of the VEGF protein family and their receptors. We focus on the lymphangiogenic VEGF-C and VEGF-D, discussing their biosynthesis and their role in embryonic lymphangiogenesis.Peer reviewe