Joint distribution of first exit times of a two dimensional Wiener process with jumps with application to a pair of coupled neurons

Motivated by a neuronal modeling problem, a bivariate Wiener process with two independent components is considered. Each component evolves independently until one of them reaches a threshold value. If the first component crosses the threshold value, it is reset while the dynamics of the other component remains unchanged. But, if this happens to the second component, the first one has a jump of constant amplitude; the second component is then reset to its starting value and its evolution restarts. Both processes evolve once again until one of them reaches again its boundary. In this work, the coupling of the first exit times of the two connected processes is studied.     

Heuristics for the Hodgkin–Huxley system

Hodgkin and Huxley (HH) discovered that voltages control ionic currents in nerve membranes. This led them to describe electrical activity in a neuronal membrane patch in terms of an electronic circuit whose characteristics were determined using empirical data. Due to the complexity of this model, a variety of heuristics, including relaxation oscillator circuits and integrate-and-fire models, have been used to investigate activity in neurons, and these simpler models have been successful in suggesting experiments and explaining observations. Connections between most of the simpler models had not been made clear until recently. Shown here are connections between these heuristics and the full HH model. In particular, we study a new model (Type III circuit): It includes the van der Pol-based models; it can be approximated by a simple integrate-and-fire model; and it creates voltages and currents that correspond, respectively, to the h and V components of the HH system.     

Comparing vector–host and SIR models for dengue transmission

Various simple mathematical models have been used to investigate dengue transmission. Some of these models explicitly model the mosquito population, while others model the mosquitoes implicitly in the transmission term. We study the impact of modeling assumptions on the dynamics of dengue in Thailand by fitting dengue hemorrhagic fever (DHF) data to simple vector–host and SIR models using Bayesian Markov chain Monte Carlo estimation. The parameter estimates obtained for both models were consistent with previous studies. Most importantly, model selection found that the SIR model was substantially better than the vector–host model for the DHF data from Thailand. Therefore, explicitly incorporating the mosquito population may not be necessary in modeling dengue transmission for some populations.     

Arbuscular mycorrhizal fungi reduce growth and infect roots of the non‐host plant Arabidopsis thaliana

The arbuscular mycorrhizal (AM) symbiosis is widespread throughout the plant kingdom and important for plant nutrition and ecosystem functioning. Nonetheless, most terrestrial ecosystems also contain a considerable number of non‐mycorrhizal plants. The interaction of such non‐host plants with AM fungi (AMF) is still poorly understood. Here, in three complementary experiments, we investigated whether the non‐mycorrhizal plant Arabidopsis thaliana, the model organism for plant molecular biology and genetics, interacts with AMF. We grew A. thaliana alone or together with a mycorrhizal host species (either Trifolium pratense or Lolium multiflorum) in the presence or absence of the AMF Rhizophagus irregularis. Plants were grown in a dual‐compartment system with a hyphal mesh separating roots of A. thaliana from roots of the host species, avoiding direct root competition. The host plants in the system ensured the presence of an active AM fungal network. AM fungal networks caused growth depressions in A. thaliana of more than 50% which were not observed in the absence of host plants. Microscopy analyses revealed that R. irregularis supported by a host plant was capable of infecting A. thaliana root tissues (up to 43% of root length colonized), but no arbuscules were observed. The results reveal high susceptibility of A. thaliana to R. irregularis, suggesting that A. thaliana is a suitable model plant to study non‐host/AMF interactions and the biological basis of AM incompatibility.     

Paradigmatic pragmatism and the politics of diversity

How migration and mobilizations of difference are accommodated at the local level is a burning question. Concepts adopted by local governments and the capacities of cities to formulate and implement these have received increasing attention, but often without examining the ideas and norms that underlie local concepts and practices. This article assesses the hypothesis of local-level pragmatism, which it rejects, and develops the notion of ‘paradigmatic pragmatism’ to characterize how local-level politics address mobilizations of difference. Based on empirical findings from Amsterdam, Antwerp and Leeds, and comparing the content and the implementation of ‘diversity policies’, I argue against a dichotomy of pragmatic vs ideational politics. Instead, these cities draw on a variety of ideas and pragmatically combine them under the header of diversity. This paradigmatic pragmatism invites further research on the effects of potential incompatibilities of immigrant policy ideas.     

Mechanical behavior of bovine nasal cartilage under static and dynamic loading

Abnormal mechanical loading may trigger cartilage degeneration associated with osteoarthritis. Tissue response to load has been the subject of several in vitro studies. However, simple stimuli were often applied, not fully mimicking the complex in vivo conditions. Therefore, a rolling/plowing explant test system (RPETS) was developed to replicate the combined in vivo loading patterns. In this work we investigated the mechanical behavior of bovine nasal septum (BNS) cartilage, selected as tissue approximation for experiments with RPETS, under static and dynamic loading. Biphasic material properties were determined and compared with those of other cartilaginous tissues. Furthermore, dynamic loading in plowing modality was performed to determine dynamic response and experimental results were compared with analytical models and Finite Elements (FE) computations. Results showed that BNS cartilage can be modeled as a biphasic material with Young's modulus E=2.03±0.7 MPa, aggregate modulus H_A=2.35±0.7 MPa, Poisson's ratio ν=0.24±0.07, and constant hydraulic permeability k₀=3.0±1.3×10⁻¹⁵ m⁴ (N s)⁻¹. Furthermore, dynamic analysis showed that plowing induces macroscopic reactions in the tissue, proportionally to the applied loading force. The comparison among analytical, FE analysis and experimental results showed that predicted tangential forces and sample deformation lay in the range of variation of experimental results for one specific experimental condition. In conclusion, mechanical properties of BNS cartilage under both static and dynamic compression were assessed, showing that this tissue behave as a biphasic material and has a viscoelastic response to dynamic forces.     

Optimal growth strategies under divergent predation pressure

The conditions leading to gigantism in nine‐spined sticklebacks Pungitius pungitius were analysed by modelling fish growth with the von Bertalanffy model searching for the optimal strategy when the model's growth constant and asymptotic fish size parameters are negatively related to each other. Predator‐related mortality was modelled through the increased risk of death during active foraging. The model was parameterized with empirical growth data of fish from four different populations and analysed for optimal growth strategy at different mortality levels. The growth constant and asymptotic fish size were negatively related in most populations. Optimal fish size, fitness and life span decreased with predator‐induced mortality. At low mortality, the fitness of pond populations was higher than that of sea populations. The differences disappeared at intermediate mortalities, and sea populations had slightly higher fitness at extremely high mortalities. In the scenario where all populations mature at the same age, the pond populations perform better at low mortalities and the sea populations at high mortalities. It is concluded that a trade‐off between growth constant and asymptotic fish size, together with different mortality rates, can explain a significant proportion of body size differentiation between populations. In the present case, it is a sufficient explanation of gigantism in pond P. pungitius.     

Nicotinic acid and DP1 blockade: studies in mouse models of atherosclerosis

The use of nicotinic acid to treat dyslipidemia is limited by induction of a “flushing” response, mediated in part by the interaction of prostaglandin D₂ (PGD₂) with its G-protein coupled receptor, DP1 (Ptgdr). The impact of DP1 blockade (genetic or pharmacologic) was assessed in experimental murine models of atherosclerosis. In Ptgdr^−/−ApoE^−/− mice versus ApoE^−/− mice, both fed a high-fat diet, aortic cholesterol content was modestly higher (1.3- to 1.5-fold, P < 0.05) in Ptgdr^−/−ApoE^−/− mice at 16 and 24 weeks of age, but not at 32 weeks. In multiple ApoE^−/− mouse studies, a DP1-specific antagonist, L-655, generally had a neutral to beneficial effect on aortic lipids in the presence or absence of nicotinic acid treatment. In a separate study, a modest increase in some atherosclerotic measures was observed with L-655 treatment in Ldlr^−/− mice fed a high-fat diet for 8 weeks; however, this effect was not sustained for 16 or 24 weeks. In the same study, treatment with nicotinic acid alone generally decreased plasma and/or aortic lipids, and addition of L-655 did not negate those beneficial effects. These studies demonstrate that inhibition of DP1, with or without nicotinic acid treatment, does not lead to consistent or sustained effects on plaque burden in mouse atherosclerotic models.     

Species Diversity,Phylogeny and Large Scale Biogeographic Patterns of the Genus Padina (Phaeophyceae,Dictyotales)

The brown algal genus Padina (Dictyotales, Phaeophyceae) is distributed worldwide in tropical and temperate seas. Global species diversity and distribution ranges, however, remain largely unknown. Species‐level diversity was reassessed using DNA‐based, algorithmic species delineation techniques based on cox3 and rbcL sequence data from 221 specimens collected worldwide. This resulted in estimates ranging from 39 to 61 putative species (ESUs), depending on the technique as well as the locus. We discuss the merits, potential pitfalls, and evolutionary and biogeographic significance of algorithmic species delineation. We unveil patterns whereby ESUs are in all but one case restricted to either the Atlantic or Indo‐Pacific Ocean. Within ocean basins we find evidence for the vast majority of ESUs to be confined to a single marine realm. Exceptions, whereby ESUs span up to three realms, are located in the Indo‐Pacific Ocean. Patterns of range‐restricted species likely arise by repeated founder events and subsequent peripatric speciation, hypothesized to dominate speciation mechanisms for coastal marine organisms in the Indo‐Pacific. Using a three‐gene (cox3, psaA and rbcL), relaxed molecular clock phylogenetic analysis we estimated divergence times, providing a historical framework to interpret biogeographic patterns.