Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Scale-up of mixer granulators for effective liquid distribution

There is considerable anecdotal evidence from industry that poor wetting and liquid distribution can lead to broad granule size distributions in mixer granulators. Current scale-up scenarios lead to poor liquid distribution and a wider product size distribution. There are two issues to consider when scaling up: the size and nature of the spray zone and the powder flow patterns as a function of granulator scale. Short, nucleation-only experiments in a 25L PMA Fielder mixer using lactose powder with water and HPC solutions demonstrated the existence of different nucleation regimes depending on the spray flux Psi(a)-from drop-controlled nucleation to caking. In the drop-controlled regime at low Psi(a) values. each drop forms a single nucleus and the nuclei distribution is controlled by the spray droplet size distribution. As Psi(a) increases, the distribution broadens rapidly as the droplets overlap and coalesce in the spray zone. The results are in excellent agreement with previous experiments and confirm that for drop-controlled nucleation. Psi(a) should be less than 0.1. Granulator flow studies showed that there are two powder flow regimes-bumping and roping. The powder flow goes through a transition from bumping to roping as impeller speed is increased. The roping regime gives good bed turn over and stable flow patterns. This regime is recommended for good liquid distribution and nucleation. Powder surface velocities as a function of impeller speed were measured using high-speed video equipment and MetaMorph image analysis software, Powder surface velocities were 0.2 to 1 ms(-1)-an order of magnitude lower than the impeller tip speed. Assuming geometrically similar granulators, impeller speed should be set to maintain constant Froude number during scale-up rather than constant tip speed to ensure operation in the roping regime. (C) 2002 Published by Elsevier Science B.V.

Basal nonselective cation permeability in rat cardiac microvascular endothelial cells

The presence of a basal nonselective cation permeability was mainly investigated in primary cultures of rat cardiac microvascular endothelial cells (CMEC) by applying both the patch-clamp technique and Fura-2 microfluorimetry. With low EGTA in the pipette solution, the resting membrane potential of CMEC was -21.2 +/- 1.1 mV, and a Ca2+-activated Cl- conductance was present. When the intracellular Ca2+ was buffered with high EGTA, the membrane potential decreased to 5.5 +/- 1.2 mV. In this condition, full or partial substitution of external Na+ by NMDG(+) proportionally reduced the inward component of the basal I-V relationship. This current was dependent on extracellular monovalent cations with a permeability sequence of K+ > Cs+ > Na+ > Li+ and was inhibited by Ca2+, La3+, Gd3+, and amiloride. The K+/Na+ permeability ratio, determined using the Goldman-Hodgkin-Katz equation, was 2.01. The outward component of the basal I-V relationship was reduced when intracellular K+ was replaced by NMDG(+), but was not sensitive to substitution by Cs+. Finally, microfluorimetric experiments indicated the existence of a basal Ca2+ entry pathway, inhibited by La3+ and Gd3+. The basal nonselective cation permeability in CMEC could be involved both in the control of myocardial ionic homeostasis, according to the model of the blood-heart barrier, and in the modulation of Ca2+ -dependent processes. (C) 2002 Elsevier Science (USA).

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Revisiting the question of limited genetic variation within Schistosoma japonicum

Recent electrophoretic data have indicated that Schistosoma japonicum in mainland China may be a species complex, with the existence of a cryptic species being predicted from the analysis of schistosome populations from Sichuan province. To investigate the Sichuan form of S. japonicum, 4.9 kbp of mitochondrial DNA from each of three samples of the parasite from China (two from Sichuan and one from Hunan) and one from Sorsogon in the Philippines were amplified, sequenced and characterized. The sequence data were compared with those from the related South-east Asian species of S. mekongi (Khong Island, Laos) and S. malayensis (Baling, Malaysia) and that from S. japonicum from Anhui (China). At both the nucleotide and amino-acid levels, the variation among the five S. japonicum samples was limited ( < 1%). This was consistent with the conclusions drawn from previous molecular studies, in which minimal variation among S. japonicum populations was also detected. In contrast, S. mekongi and S. malayensis, species recognized as separate but closely related, differ from each other by about 10%, and each differs by 25%-26% from S. japonicum. Phylogenetic trees provided a graphic representation of these differences, showing all S. japonicum sequences to be very tightly clustered and distant from S. mekongi and S. malayensis, the last two being clearly distinct from each other. The results thus indicate no significant intraspecific genetic variation among S. japonicum samples collected from different geographical areas and do not support the idea of a distinct form in Sichuan.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Anomalies in the developing neural and visceral head skeleton of the Australian lungfish, Neoceratodus forsteri

Several anomalies occur in the developing neural and visceral head skeleton of young specimens of Neoceratodus forsteri that have been reared under laboratory conditions. These include anomalies of the basicranium and its derivatives, aberrations of the anterior mandible and hyoid apparatus, and abnormalities in the articulation of the jaws and the elements that produce them. Apart from the occasional absence of the basihyal, and failure of the quadrate processes to form, the anomalies are not deficiencies. Most involve malformations of parts of the neurocranium and visceral skeleton, inappropriate articulations or fusions between elements, disunity in structures that are normally fused and the appearance of supernumerary elements. The incidence of chondral anomalies, generally higher than aberrations that occur in the dermal skeleton in juvenile lungfish, ranges from 1-10% in laboratory reared individuals that have not been subjected to experimental interference. The anomalies differ from those found in many amphibian populations, in the field and in the laboratory, because they involve the cranium, and not the limbs, and the lungfish have not been exposed to the factors that cause anomalies in the amphibians. It is unlikely that the existence of those anomalies, if it is reflected in the wild population, places a selective pressure on the lungfish, because, in a normal season, less than 1% of the total number of eggs produced survive to be recruited into the adult population.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Variation in articulatory timing of three English consonants: An electropalatographic investigation

Increasingly, electropalatography (EPG) is being used in speech pathology research to identify and describe speech disorders of neurological origin. However, limited data currently exists that describes normal articulatory segment timing and the degree of variability exhibited by normal speakers when assessed with EPG. Therefore, the purpose of the current investigation was to use the Reading EPG3 system to quantify segmental timing values and examine articulatory timing variability for three English consonants. Ten normal subjects repeated ten repetitions of CV words containing the target consonants /t/, /l/, and /s/ while wearing an artificial palate. The target consonants were followed by the /i/ vowel and were contained in the carrier phrase 'I saw a __'. Mean duration of the approach, closure/constriction, and release phases of consonant articulation were calculated. In addition, inter-subject articulatory timing variability was investigated using descriptive graphs and intra-subject articulatory timing variability was investigated using a coefficient of variation. Results revealed the existence of intersubject variability for mean segment timing values. This could be attributed to individual differences in the suprasegmental features of speech and individual differences in oral cavity size and structure. No significant differences were reported for degree of intra-subject variability between the three sounds for these same phases of articulation. However, when this data set was collapsed, results revealed that the closure/constriction phase of consonant articulation exhibited significantly less intra-subject variability than both the approach and release phases. The stabilization of the tongue against the fixed structure of the hard palate during the closure phase of articulation may have reduced the levels of intra-subject variability.

Further evidence for the reliance of catalysis by rabbit muscle pyruvate kinase upon isomerization of the ternary complex between enzyme and products

Isothermal calorimetry has been used to examine the effect of thermodynamic non-ideality on the kinetics of catalysis by rabbit muscle pyruvate kinase as the result of molecular crowding by inert cosolutes. The investigation, designed to detect substrate-mediated isomerization of pyruvate kinase, has revealed a 15% enhancement of maximal velocity by supplementation of reaction mixtures with 0.1 M proline, glycine or sorbitol. This effect of thermodynamic non-ideality implicates the existence of a substrate-induced conformational change that is governed by a minor volume decrease and a very small isomerization constant; and hence, substantiates earlier inferences that the rate-determining step in pyruvate kinase kinetics is isomerization of the ternary enzyme product complex rather than the release of products. (C) 2003 Elsevier Science B.V. All rights reserved.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Linearization of a naturally occurring circular protein maintains structure but eliminates hemolytic activity

Cyclotides are a recently discovered family of disulfide rich proteins from plants that contain a circular protein backbone. They are exceptionally stable, as exemplified by their use in native medicine of the prototypic cyclotide kalata B1. The peptide retains uterotonic activity after the plant from which it is derived is boiled to make a medicinal tea. The circular backbone is thought to be in part responsible for the stability of the cyclotides, and to investigate its role in determining structure and biological activity, an acyclic derivative, des-(24-28)-kalata B1, was chemically synthesized and purified. This derivative has five residues removed from the 29-amino acid circular backbone of kalata B1 in a loop region corresponding to a processing site in the biosynthetic precursor protein. Two-dimensional NMR spectra of the peptide were recorded, assigned, and used to identify a series of distance, angle, and hydrogen bonding restraints. These were in turn used to determine a representative family of solution structures. Of particular interest was a determination of the structural similarities and differences between des-(2428)-kalata B1 and native kalata B1. Although the overall three-dimensional fold remains very similar to that of the native circular protein, removal of residues 24-28 of kalata B1 causes disruption of some structural features that are important to the overall stability. Furthermore, loss of hemolytic activity is associated with backbone truncation and linearization.

Analysis of the mouse transcriptome for genes involved in the function of the nervous system

We analyzed the mouse Representative Transcript and Protein Set for molecules involved in brain function. We found full-length cDNAs of many known brain genes and discovered new members of known brain gene families, including Family 3 G-protein coupled receptors, voltage-gated channels, and connexins. We also identified previously unknown candidates for secreted neuroactive molecules. The existence of a large number of unique brain ESTs suggests an additional molecular complexity that remains to be explored. A list of genes containing CAG stretches in the coding region represents a first step in the potential identification of candidates for hereditary neurological disorders.

A molecular phylogeny of the Australian skink genera Eulamprus, Gnypetoscincus and Nangura

Skinks from the genera Eulamprus, Gnypetoscincus and Nangura are a prominent component of the reptile fauna of the mesic forests of the east coast of Australia and have been the subject of numerous ecological studies. Highly conserved morphology and the retention of ancestral traits have limited our understanding of the relationships within and among these genera beyond an initial identification of species groups within Eulamprus. To address this deficit and to explore the relationships between Eulamprus and the monotypic genera Nangura and Gnypetoscincus, sections of two mitochondrial genes (ND4 and 16S rRNA) were sequenced and subjected to Bayesian phylogenetic analysis. This phylogenetic analysis supports recognition of the three species groups proposed for Eulamprus (murrayi, quoyii and tenuis) and indicates that this genus is paraphyletic, with Gnypetoscincus and Nangura being proximal to basal lineages of the tenuis group. To resolve these and broader problems of paraphyly, we suggest that each of the species groups from 'Eulamprus' should be recognised as a distinct genus. The phylogenetically and ecologically distinct water skinks of the quoyii group would be retained within Eulamprus and the diverse species of the tenuis group allocated to Concinnia. We suggest placing the monophyletic murrayi group, endemic to the rainforests of central eastern Australia, in a new genus ( yet to be formally described). The sequencing data also revealed the existence of a genetically divergent but morphologically cryptic lineage within E. murrayi and substantial diversity within E. quoyii. There is evidence for two major habitat shifts from rainforest towards drier habitats, one leading to the quoyii group and the second defining a clade of three species within the tenuis complex. These ecological transitions may represent adaptations to general drying across eastern Australia during the late Miocene - Pliocene. Each of the major areas of east coast tropical or subtropical rainforest contains multiple phylogenetically diverse endemic species, reflecting the long-term persistence and high conservation value of wet forest habitats in each area.