Design Theory and the Australian Tula Adze

The tula adze is a distinctive composite tool that was used in the Australian arid zone during the late Holocene. In this paper we use design theory to investigate why this particular tool form was so pervasive across time and space. Design theory provides a rational means for classifying tool designs and for determining why particular tool design classes were employed over others. We draw upon ethnographic and archaeological evidence to characterize the design of the tula adze and conclude that it is consistently the product of a “reliable” design strategy. We further determine that the high cost of a reliable design was chosen because the tula adze was employed in situations where failure could not be tolerated. Specifically, we argue that an important role of the tula adze was to manufacture wooden goods for not only personal use but more significantly for trade. The quantity and quality of these goods had an extremely strong bearing on the economic sustainability of arid zone Aboriginal groups

Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model

Co-limitation of marine phytoplankton growth by light and nutrient, both of which are essential for phytoplankton, leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlorophyll maxima, or DCMs, which are structures localized in a finite depth interior to the water column. From an ecological point of view, DCMs are evocative of a balance between the inflow of light from the water surface and of nutrients from the sediment. From a (linear) bifurcational point of view, they appear through a transcritical bifurcation in which the trivial, no-plankton steady state is destabilized. This article is devoted to the analytic investigation of the weakly nonlinear dynamics of these DCM patterns, and it has two overarching themes. The first of these concerns the fate of the destabilizing stationary DCM mode beyond the center manifold regime. Exploiting the natural singularly perturbed nature of the model, we derive an explicit reduced model of asymptotically high dimension which fully captures these dynamics. Our subsequent and fully detailed study of this model - which involves a subtle asymptotic analysis necessarily transgressing the boundaries of a local center manifold reduction - establishes that a stable DCM pattern indeed appears from a transcritical bifurcation. However, we also deduce that asymptotically close to the original destabilization, the DCM looses its stability in a secondary bifurcation of Hopf type. This is in agreement with indications from numerical simulations available in the literature. Employing the same methods, we also identify a much larger DCM pattern. The development of the method underpinning this work - which, we expect, shall prove useful for a larger class of models - forms the second theme of this article

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

Synthesis of glycopeptides and glycopeptide conjugates

Protein glycosylation is a key post-translational modification important to many facets of biology. Glycosylation can have critical effects on protein conformation, uptake and intracellular routing. In immunology, glycosylation of antigens has been shown to play a role in self/non-self distinction and the effective uptake of antigens. Improperly glycosylated proteins and peptide fragments, for instance those produced by cancerous cells, are also prime candidates for vaccine design. To study these processes, access to peptides bearing well-defined glycans is of critical importance. In this review, the key approaches towards synthetic, well-defined glycopeptides, are described, with a focus on peptides useful for and used in immunological studies. Special attention is given to the glycoconjugation approaches that have been developed in recent years, as these enable rapid synthesis of various (unnatural) glycopeptides, enabling powerful carbohydrate structure/activity studies. These techniques, combined with more traditional total synthesis and chemoenzymatic methods for the production of glycopeptides, should help unravel some of the complexities of glycobiology in the near future.NWOBBoL grantBio-organic Synthesi

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Spatial polarization modulators: distinguishing diffraction effects from spatial polarization modulation

Are we alone? In our quest to find life beyond Earth, we use our own planet to develop and verify new methods and techniques to remotely detect life. Our Life Signature Detection polarimeter (LSDpol), a snapshot full-Stokes spectropolarimeter to be deployed in the field and in space, looks for signals of life on Earth by sensing the linear and circular polarization states of reflected light. Examples of these biosignatures are linear polarization resulting from O2-A band and vegetation, e.g. the Red edge and the Green bump, as well as circular polarization resulting from the homochirality of biotic molecules. LSDpol is optimized for sensing circular polarization. To this end, LSDpol employs a spatial light modulator in the entrance slit of the spectrograph, a liquid-crystal quarter-wave retarder where the fast axis rotates as a function of slit position. The original design of LSDpol implemented a dual-beam spectropolarimeter by combining a quarter-wave plate with a polarization grating. Unfortunately, this design causes significant linear-to-circular cross-talk. In addition, it revealed spurious polarization modulation effects. Here, we present numerical simulations that illustrate how Fresnel diffraction effects can create these spurious modulations. We verified the simulations with accurate polarization state measurements in the lab using 100% linearly and circularly polarized light.Instrumentatio

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

The role of peatland degradation, protection and restoration for climate change mitigation in the SSP scenarios

Peatlands only cover a small fraction of the global land surface (∼3%) but store large amounts of carbon (∼600 GtC). Drainage of peatlands for agriculture results in the decomposition of organic matter, leading to greenhouse gas (GHG) emissions. As a result, degraded peatlands are currently responsible for 2%–3% of global anthropogenic emissions. Preventing further degradation of peatlands and restoration (i.e. rewetting) are therefore important for climate change mitigation. In this study, we show that land-use change in three SSP scenarios with optimistic, recent trends, and pessimistic assumptions leads to peatland degradation between 2020 and 2100 ranging from −7 to +10 Mha (−23% to +32%), and a continuation or even an increase in annual GHG emissions (−0.1 to +0.4 GtCO2-eq yr−1). In default mitigation scenarios without a specific focus on peatlands, peatland degradation is reduced due to synergies with forest protection and afforestation policies. However, this still leaves large amounts of GHG emissions from degraded peatlands unabated, causing cumulative CO2 emissions from 2020 to 2100 in an SSP2-1.5 °C scenario of 73 GtCO2. In a mitigation scenario with dedicated peatland restoration policy, GHG emissions from degraded peatlands can be reduced to nearly zero without major effects on projected land-use dynamics. This underlines the opportunity of peatland protection and restoration for climate change mitigation and the need to synergistically combine different land-based mitigation measures. Peatland location and extent estimates vary widely in the literature; a sensitivity analysis implementing various spatial estimates shows that especially in tropical regions degraded peatland area and peatland emissions are highly uncertain. The required protection and mitigation efforts are geographically unequally distributed, with large concentrations of peatlands in Russia, Europe, North America and Indonesia (33% of emission reductions are located in Indonesia). This indicates an important role for only a few countries that have the opportunity to protect and restore peatlands with global benefits for climate change mitigation