Anti-tumour and anti-metastatic activity of 3-(P-Chlorophenyl)-2,3-Dihydro-3-Hydroxythiazolo (3,2-A)-Benzimidazole-2-acetic acid (WY-13,876).

Extensive investigation of 3-(p-chlorophenyl)-2,3-dihydro-3-hydroxythiazolo(3,2-alpha)-benzimidazole-2-acetic acid (Wy-13,876) in BDF1 mice implanted with Lewis lung tumour has shown that it is an effective anti-tumour and anti-metastatic agent. In vitro examination using HEp-2 human epidermal tumour cells has indicated that Wy-13,876 is not cytotoxic. When mice implanted with Lewis lung tumour and treated with Wy-13,876 are also injected with anti-thymocyte serum, an increase in lung metastases is observed suggesting that thymocyte activity is involved in the drug's mechanism of action. An increase in peripheral T lymphocytes observed in rats 18 h after a single oral dose of Wy-13,876 further supports this possibility. When Wy-13,876 is given to tumour -bearing mice in combination with low, ineffective doses of 5-fluorouracil or cyclophosphamide, further reduction of primary tumour growth is observed

Subthreshold oscillations in a map-based neuron model

Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are considered. We discuss bifurcation scenarios explaining the birth of these oscillations and their transformation into tonic spikes. Specific features of these transitions caused by the discrete-time dynamics of the model and the influence of external noise are discussed.Comment: To be published in Physics Letters

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic. Erratum follows references in this versio

Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Accounting for the increasing benefits from scarce ecosystems

Governments are catching up with economic theory and practice by increasingly integrating ecosystem service values into national planning processes, including benefitcost analyses of public policies. Such analyses require information not only about today’s benefits from ecosystem services but also on how benefits change over time. We address a key limitation of existing policy guidance, which assumes that benefits from ecosystem services remain unchanged. We provide a practical rule that is grounded in economic theory and evidence-based as a guideline for how benefits change over time: They rise as societies get richer and even more so when ecosystem services are declining. Our proposal will correct a substantial downward bias in currently used estimates of future ecosystem service values. This will help governments to reflect the importance of ecosystems more accurately in benefit-cost analyses and policy decisions they inform

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove