Complex Dynamics in a Hysteretic Relay Feedback System with Delay

Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.     

Embryonic expression of a haematopoietic growth factor encoded by the Sl locus and the ligand for c-kit.

Mice carrying mutations at the W (Dominant white spotting) and Sl (Steel) loci develop abnormalities in three independent systems: neural crest-derived melanocytes, primordial germ cells and haematopoietic stem cells. Consequently, homozygotes of viable mutant alleles have white coats and are sterile and severely anaemic. Tissue recombination studies predict that the W gene is expressed cell autonomously, whereas the product of the Sl locus affects the microenvironment in which the stem cells migrate, proliferate and differentiate. The W locus encodes the protoncogene c-kit, a member of the tyrosine kinase receptor family. The haematopoietic growth factor SCF (stem cell factor) has been identified as the product of the Sl locus and a ligand for c-kit. Here, we report that SCF is expressed during embryogenesis in cells associated with both the migratory pathways and homing sites of melanoblasts, germ cells and haematopoietic stem cells. Both SCF and c-kit are also expressed in a variety of other tissues, including the brain and spinal cord, suggesting that the receptor-ligand system has additional roles in embryogenesis.     

Data envelopment analysis and university selection

This paper is concerned with the process of performance measurement undertaken by different stakeholders in the UK higher education sector, focusing on the perspective of the potential student. The appropriateness of the Times League Table in guiding applicants choices is considered, and a case study of applicants at a comprehensive school reported on. The contribution of data envelopment analysis as a decision support technique which can produce customised individual league tables to inform the potential student in his/her choice is illustrated.     

Co-expression of vimentin and cytokeratins in parietal endoderm cells of early mouse embryo

Of the five classes of intermediate filaments found in vertebrate tissues, the cytokeratins are considered unique to epithelial tissues, while vimentin is expressed by endothelial and mesenchymal cells. In neither case is the precise function of the filament system known. Epithelial cells in culture often express vimentin as well as cytokeratins, but co-expression in vivo, as reported for pleomorphic adenomas of the parotid gland and metastatic carcinoma cells in ascites or pleural fluid, is still controversial. Here we report the co-expression of cytokeratins and vimentin in situ, in the parietal endoderm of the mouse embryo 8.5-13.5 days old. This population of individual, motile cells seems to be derived from a conventional epithelium by migration and differentiation. Our results support the idea that vimentin expression is specifically related to reduced cell-to-cell contact, and to the independent existence of a cell following detachment from an epithelial sheet.     

Importance of DNA stiffness in protein-DNA binding specificity

From the first high-resolution structure of a repressor bound specifically to its DNA recognition sequence it has been shown that the phage 434 repressor protein binds as a dimer to the helix. Tight, local interactions are made at the ends of the binding site, causing the central four base pairs (bp) to become bent and overtwisted. The centre of the operator is not in contact with protein but repressor binding affinity can be reduced at least 50-fold in response to a sequence change there. This observation might be explained should the structure of the intervening DNA segment vary with its sequence, or if DNA at the centre of the operator resists the torsional and bending deformation necessary for complex formation in a sequence dependent fashion. We have considered the second hypothesis by demonstrating that DNA stiffness is sequence dependent. A method is formulated for calculating the stiffness of any particular DNA sequence, and we show that this predicted relationship between sequence and stiffness can explain the repressor binding data in a quantitative manner. We propose that the elastic properties of DNA may be of general importance to an understanding of protein-DNA binding specificity.     

Applications of a general convergence theory for outer approximation algorithms

Eaves and Zangwill [2] have developed a very general theory of the convergence of cutting plane algorithms. This theory is applied to prove the convergence of Geoffrion's Generalized Benders Decomposition procedure (GBD) [5]. Using the insight provided by the general theory, GBD is then modified to permit the deletion of old constraints without upsetting the infinite convergence property. Finally, certain approximations of GBD are presented and the robustness of the convergence results is indicated.This research was supported by the National Science Foundation under Grant GP-22108.     

Synthesis and cytotoxicity studies of new dimethylamino-functionalised and indolyl-substituted titanocene anti-cancer drugs

Abstract From the carbolithiation of 6-N,N-dimethylamino fulvene (3a) and different ortho-lithiated indole derivatives (5-methoxy-N-methylindole, N-methylindole and N,N-dimethylaminomethylindole), the corresponding lithium cyclopentadienide intermediate (4a–c) was formed. These three lithiated intermediates underwent a transmetallation reaction with TiCl₄ resulting in dimethylamino-functionalised titanocenes (5a–c). When these titanocenes were tested against LLC-PK cells, the IC₅₀ values obtained were of 37 and 71 μM for titanocenes 5a and 5b respectively. The most cytotoxic titanocene in this paper, 5c showed an IC₅₀ value of 8.4 μM is found to be almost as cytotoxic as cis-platin, which showed an IC₅₀ value of 3.3 μM, when tested on the LLC-PK cell line, and titanocene 5c is approximately 250 times better than titanocene dichloride itself. Graphical Abstract Bis-(N,N-dimethylamino-2-(N-methylindolyl)methylcyclopentadienyl) titanium (IV) dichloride was synthesised starting from 2-(N-methylindolyl) lithium and 6-N,N-dimethylamino fulvene. Herein, we present the synthesis and DFT structure of the titanocene and two further derivatives followed by MTT-based cytotoxicity tests on LLC-PK cells.      

Energy doubling of 42 GeV electrons in a metre-scale plasma wakefield accelerator

The energy frontier of particle physics is several trillion electron volts, but colliders capable of reaching this regime (such as the Large Hadron Collider and the International Linear Collider) are costly and time-consuming to build; it is therefore important to explore new methods of accelerating particles to high energies. Plasma-based accelerators are particularly attractive because they are capable of producing accelerating fields that are orders of magnitude larger than those used in conventional colliders. In these accelerators, a drive beam (either laser or particle) produces a plasma wave (wakefield) that accelerates charged particles. The ultimate utility of plasma accelerators will depend on sustaining ultrahigh accelerating fields over a substantial length to achieve a significant energy gain. Here we show that an energy gain of more than 42 GeV is achieved in a plasma wakefield accelerator of 85 cm length, driven by a 42 GeV electron beam at the Stanford Linear Accelerator Center (SLAC). The results are in excellent agreement with the predictions of three-dimensional particle-in-cell simulations. Most of the beam electrons lose energy to the plasma wave, but some electrons in the back of the same beam pulse are accelerated with a field of approximately 52 GV m(-1). This effectively doubles their energy, producing the energy gain of the 3-km-long SLAC accelerator in less than a metre for a small fraction of the electrons in the injected bunch. This is an important step towards demonstrating the viability of plasma accelerators for high-energy physics applications.     

Testing general relativity with atom interferometry

The unprecedented precision of atom interferometry will soon lead to laboratory tests of general relativity to levels that will rival or exceed those reached by astrophysical observations. We propose such an experiment that will initially test the equivalence principle to 1 part in 10(15) (300 times better than the current limit), and 1 part in 10(17) in the future. It will also probe general relativistic effects - such as the nonlinear three-graviton coupling, the gravity of an atom's kinetic energy, and the falling of light - to several decimals. In contrast with astrophysical observations, laboratory tests can isolate these effects via their different functional dependence on experimental variables.     

Fracture mode,microstructure and temperature-dependent elastic moduli for thermoelectric composites of PbTe–PbS with SiC nanoparticle additions

Twenty-six (Pb_0.95Sn_0.05Te)_0.92(PbS)_0.08–0.055% PbI₂–SiC nanoparticle (SiC_np) composite thermoelectric specimens were either hot pressed or pulsed electric current sintered (PECS). Bloating (a thermally induced increase in porosity, P, for as-densified specimens) was observed during annealing at temperatures >603?K for hot-pressed specimens and PECS-processed specimens from wet milled powders, but in contrast seven out of seven specimens densified by PECS from dry milled powders showed no observable bloating following annealing at temperatures up to 936?K. In this study, bloating in the specimens was accessed via thermal annealing induced changes in (i) porosity measured by scanning electron microscopy on fractured specimen surfaces, (ii) specimen volume and (iii) elastic moduli. The moduli were measured by resonant ultrasound spectroscopy. SiC_np additions (1–3.5 vol.%) changed the fracture mode from intergranular to transgranular, inhibited grain growth, and limited bloating in the wet milled PECS specimens. Inhibition of bloating likely occurs due to cleaning of contamination from powder particle surfaces via PECS processing which has been reported previously in the literature.