Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

No evidence of a role for activating CDK2 mutations in melanoma

Inactivation of p16(INK4a) and/or activation of cyclin-dependent kinase-4 (CDK4) are strongly associated with both susceptibility and progression in melanoma. Activating CDK4 mutations prevent the binding and inhibition of CDK4 by p16(INK4a). A second, more indirect role for CDK4 is in late G(1), where It may sequester the inhibitors p27(KIP1) or p21(CIP1) away from CDK2, and in doing so upregulate the CDK2 activity necessary for cells to proceed completely through G(1) into S phase. As the pivotal residues around the most predominant R24C activating CDK4 mutation are invariant between CDK2 and CDK4, we speculated that the pivotal arginine (position 22 in CDK2), or a nearby residue, may be mutated in some melanomas, resulting in the diminution of its binding and inhibition by p27(KIP1) or p21(CIP1). However, except for a silent polymorphism, we detected no variants within this region of the CDK2 gene in 60 melanoma cell lines. Thus, if CDK2 activity is dysregulated in melanoma it is likely to occur by a means other than mutations causing loss of direct inhibition. We also examined the expression of the CDK2 gene in melanoma cell lines, to assess its possible co-regulation with the gene for the melanocyte-lineage antigen pmel17, which maps less than 1 kb away in head to head orientation with CDK2 and may be transcribed off the same bidirectional promoter. However, expression of the genes is not co-regulated. (C) 2001 Lippincott Williams & Wilkins.

Glutamate(NMDA) receptor NR1 subunit mRNA expression in Alzheimer's disease

We analyzed the expression profile of two NMDAR1 mRNA isoform subsets. NR1(0xx) and NR1(1xx), in discrete regions of human cerebral cortex. The subsets are characterized by the absence or presence of a 21-amino acid N-terminal cassette. Reverse transcription polymerase chain reaction for NR1 isoforms was performed on total RNA preparations from spared and susceptible regions from 10 pathologically confirmed Alzheimer's disease (AD) cases and 10 matched controls. Primers spanning the splice insert yielded two bands, 342 bp (NR1(0xx)) and 405 bp (NR1(1xx)), on agarose gel electrophoresis. The bands were visualized with ethidium and quantified by densitometry. NR1(1xx) transcript expression was calculated as a proportion of the NR1(1xx) + NR1(0xx) total. Values were significantly lower in AD cases than in controls in mid-cingulate cortex, p < 0.01, superior temporal cortex, p < 0.01 and hippocampus, p similar to 0.05. Cortical proportionate NR1(1xx) transcript expression was invariant over the range of ages acid areas of controls tested, at similar to 50%. This was also true for AD motor and occipital cortex. Proportionate NR1(1xx) expression in AD cingulate and temporal cortex was lower at younger ages and increased with age: this regression was significantly different from that in the homotropic areas of controls. Variations in NR1 N-terminal cassette expression may underlie the local vulnerability to excitotoxic damage of some areas in the AD brain. Alternatively, changes in NR1 mRNA expression may arise as a consequence of the AD disease process.

A(2)((2)) parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A(2)((2))/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)((2)) parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two. (C) 2002 Published by Elsevier Science B.V.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Reasoning about real-time repetitions: terminating and nonterminating

It is common for a real-time system to contain a nonterminating process monitoring an input and controlling an output. Hence, a real-time program development method needs to support nonterminating repetitions. In this paper we develop a general proof rule for reasoning about possibly nonterminating repetitions. The rule makes use of a Floyd-Hoare-style loop invariant that is maintained by each iteration of the repetition, a Jones-style relation between the pre- and post-states on each iteration, and a deadline specifying an upper bound on the starting time of each iteration. The general rule is proved correct with respect to a predicative semantics. In the case of a terminating repetition the rule reduces to the standard rule extended to handle real time. Other special cases include repetitions whose bodies are guaranteed to terminate, nonterminating repetitions with the constant true as a guard, and repetitions whose termination is guaranteed by the inclusion of a fixed deadline. (C) 2002 Elsevier Science B.V. All rights reserved.

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

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.

Multiple axon guidance cues establish the olfactory topographic map: how do these cues interact?

Each primary olfactory neuron stochastically expresses one of similar to1000 odorant receptors. The total population of these neurons therefore consists of similar to1,000 distinct subpopulations, each of which are mosaically dispersed throughout one of four semi-annular zones in the nasal cavity. The axons of these different subpopulations are initially intermingled within the olfactory nerve. However, upon reaching the olfactory bulb, they sort out and converge so that axons expressing the same odorant receptor typically target one or two glomeruli. The spatial location of each of these 1800 glomeruli are topographically-fixed in the olfactory bulb and are invariant from animal to animal. Thus, while odorant receptors are expressed mosaically by neurons throughout the olfactory neuroepithelium their axons sort out, converge and target the same glomerulus within the olfactory bulb. How is such precise and reproducible topographic targeting generated? While some of the mechanisms governing the growth cone guidance of olfactory sensory neurons are understood, the cues responsible for homing axons to their target site remain elusive.

The embryonic development of the bodywall and nervous system of the cestode flatworm Hymenolepis diminuta

Cestodes (tapeworms) are a derived, parasitic clade of the phylum Platyhelminthes (flatworms). The cestode body wall represents an adaptation to its endoparasitic lifestyle. The epidermis forms a nonciliated syncytium, and both muscular and nervous system are reduced. Morphological differences between cestodes and free-living flatworms become apparent already during early embryogenesis. Cestodes have a complex life cycle that begins with an infectious larva, called the oncosphere. In regard to cell number, cestode oncospheres are among the simplest multicellular organisms, containing in the order of 50-100 cells. As part of our continuing effort to analyze embryonic development in flatworms, we describe here the staining pattern obtained with acTub in embryos and larvae of the cestode Hymenolepis diminuta and, briefly, the monogenean Neoheterocotyle rhinobatidis. In addition, we labeled the embryonic musculature of Hymenolepis with phalloidin. In Hymenolepis embryos, two different cell types that we interpret as neurons and epidermal gland cells express acTub. There exist only two neurons that develop close to the midline at the anterior pole of the embryo. The axons of these two neurons project posteriorly into the center of the oncosphere, where they innervate the complex of muscles that is attached to the booklets. In addition to neurons, acTub labels a small and invariant set of epidermal gland cells that develop at superficial positions, anteriorly adjacent to the neurons, in the dorsal midline, and around the posteriorly located hooklets. During late stages of embryogenesis they spread and form a complete covering of the embryo. We discuss these data in the broader context of platyhelminth embryology.

New Zealand climate in the Neogene and implications for global atmospheric circulation

New Zealand has a good Neogene plant fossil record. During the Miocene it was without high topography and it was highly maritime, meaning that its climate, and the resulting vegetation, would be controlled dominantly by zonal climate conditions. Its vegetation record during this time suggests the climate passed from an ever-wet and cool but frostless phase in the Early Miocene in which Nothofagus subgenus Brassospora was prominent. Then it became seasonally dry, with vegetation in which palms and Eucalyptus were prominent and fires were frequent, and in the mid-Miocene, it developed a dry-climate vegetation dominated by Casuarinaceae. These changes are reflected in a sedimentological change from acidic to alkaline chemistry and the appearance of regular charcoal in the record. The vegetation then changed again to include a prominent herb component including Chenopodiaceae and Asteraceae. Sphagnum became prominent, and Nothofagus returned, but mainly as the subgenus Fuscospora (presently restricted to temperate climates). This is interpreted as a return to a generally wet, but now cold climate, in which outbreaks of cold polar air and frost were frequent. The transient drying out of a small maritime island and the accompanying vegetation/climate sequence could be explained by a higher frequency of the Sub-Tropical High Pressure (STHP) cells (the descending limbs of the Hadley cells) over New Zealand during the Miocene. This may have resulted from an increased frequency of 'blocking', a synoptic situation which occurs in the region today. An alternative hypothesis, that the global STHP belt lay at a significantly higher latitude in the early Neogene (perhaps 55degreesS) than today (about 30degreesS), is considered less likely because of physical constraints on STHP belt latitude. In either case, the difference between the early Neogene and present situation may have been a response to an increased polar-equatorial temperature gradient. This contrasts with current climate models for the geological past in which the latitude of the High Pressure belt impact is held invariant though geological time. (C) 2003 Elsevier Science B.V. All rights reserved.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.