The Voluntary Adjustment of Railroad Obligations

Automatic memory management techniques eliminate many programming errors that are both hard to find and to correct. However, these techniques are not yet used in embedded systems with hard realtime applications. The reason is that current methods for automatic memory management have a number of drawbacks. The two major ones are: (1) not being able to always guarantee short real-time deadlines and (2) using large amounts of extra memory. Memory is usually a scarce resource in embedded applications. In this paper we present a new technique, Real-Time Reference Counting (RTRC) that overcomes the current problems and makes automatic memory management attractive also for hard real-time applications. The main contribution of RTRC is that often all memory can be used to store live objects. This should be compared to a memory overhead of about 500% for garbage collectors based on copying techniques and about 50% for garbage collectors based on mark-and-sweep techniques

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

The counterphobic defense in children

The clinical data for this study were derived from the case histories of five children who consistently used the counterphobic defense either alone or in combination with phobic attitudes. The children's manifestations of this defense appeared in both verbal and nonverbal behavioral patterns. The choice of defensive style was found related to at least three factors: an early history of trauma, especially separation, parental encouragement of “toughness,” and essentially a counterphobic family style.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43947/1/10578_2005_Article_BF01433642.pd

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

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog