810 research outputs found
Existence and stability of hole solutions to complex Ginzburg-Landau equations
We consider the existence and stability of the hole, or dark soliton,
solution to a Ginzburg-Landau perturbation of the defocusing nonlinear
Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau
equation (CGL). By using dynamical systems techniques, it is shown that the
dark soliton can persist as either a regular perturbation or a singular
perturbation of that which exists for the NLS. When considering the stability
of the soliton, a major difficulty which must be overcome is that eigenvalues
may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may
occur. Since the continuous spectrum for the NLS covers the imaginary axis, and
since for the CGL it touches the origin, such a bifurcation may lead to an
unstable wave. An additional important consideration is that an edge
bifurcation can happen even if there are no eigenvalues embedded in the
continuous spectrum. Building on and refining ideas first presented in Kapitula
and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we
show that when the wave persists as a regular perturbation, at most three
eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we
precisely track these bifurcating eigenvalues, and thus are able to give
conditions for which the perturbed wave will be stable. For the NLS the results
are an improvement and refinement of previous work, while the results for the
CGL are new. The techniques presented are very general and are therefore
applicable to a much larger class of problems than those considered here.Comment: 41 pages, 4 figures, submitte
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
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
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
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
Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian Flow
Equation-free methods make possible an analysis of the evolution of a few
coarse-grained or macroscopic quantities for a detailed and realistic model
with a large number of fine-grained or microscopic variables, even though no
equations are explicitly given on the macroscopic level. This will facilitate a
study of how the model behavior depends on parameter values including an
understanding of transitions between different types of qualitative behavior.
These methods are introduced and explained for traffic jam formation and
emergence of oscillatory pedestrian counter flow in a corridor with a narrow
door
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
An Application of the Concept of the Therapeutic Alliance To Sadomasochistic Pathology
This paper traces the history of the therapeutic alliance concept, examining how it has been used and misused, at times elevated to a central position and at others rejected altogether. The loss of this concept created a vacuum in classical psychoanalysis that has been filled by rival theories. The continuing usefulness of looking at the treatment process through the lens of the therapeutic alliance, particularly in relation to the manifold difficulties of working with sadomasochistic pathology, is suggested. To this end, revisions of the theory of the therapeutic alliance are suggested to address some of the difficulties that have arisen in conceptualizing this aspect of the therapeutic relationship, and to provide an integrated dynamic model for working with patients at each phase of treatment. This revised model acknowledges the complexity of the domain and encompasses the multiple tasks, functions, partners, and treatment phases involved. The utility of the revised theory is illustrated in application to understanding the sadomasochistic, omnipotent resistances of a female patient through the phases of her analysis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66889/2/10.1177_00030651980460031301.pd
Designing Medical Informatics Research and Library--Resource Projects to Increase What Is Learned
Careful study of medical informatics research and library-resource projects is necessary to increase the productivity of the research and development enterprise. Medical informatics research projects can present unique problems with respect to evaluation. It is not always possible to adapt directly the evaluation methods that are commonly employed in the natural and social sciences. Problems in evaluating medical informatics projects may be overcome by formulating system development work in terms of a testable hypothesis; subdividing complex projects into modules, each of which can be developed, tested and evaluated rigorously; and utilizing qualitative studies in situations where more definitive quantitative studies are impractical
- …