Continuous Branching Research Articles

Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone Problems

We suggest and study iteration procedures converging from below and above to robust stable solutions and to robust stable continuous branches of solutions for quasilinear boundary-value problems with continuous non-monotone non-linearities. The iterations are constructed by modifications of the shuttle iteration method, which is used in problems with monotone operators leaving invariant a cone interval.

Phylogenetic identification of Sparganum proliferum as a pseudophyllidean cestode by the sequence analyses on mitochondrial COI and nuclear sdhB genes

Sparganum proliferum is a larval cestode for which the adult stage is unknown. It is characterized by the continuous branching and budding when parasitized to humans, and causes fatal human sparganosis. However, the biological features of S. proliferum, including its taxonomic status, still remain obscure. Our previous investigation suggested that S. proliferum might be phylogenetically distinct from Spirometra erinaceieuropaei, by the analysis on mitochondrial NADH dehydrogenase subunit 3 (ND3) gene. However, mitochondrial DNA sequence in Platyhelminth is known to have heteroplasmy within a species. Therefore, in the present study, we have investigated the complete nucleotide sequences of mitochondrial cytochrome c oxidase subunit I (COI) gene and the partial nucleotide sequences of nuclear coded succinate dehydrogenase iron–sulfur protein subunit gene ( sdhB). The results clearly demonstrated that S. proliferum is a distinct species from S. erinaceieuropaei, and that S. proliferum belongs to the order Pseudophyllidea.

VORTEX-INDUCED VIBRATION OF A FLEXIBLE CANTILEVER

This study is concerned with the vortex-induced vibrations of a flexible cantilever in a fluid flow. Our cantilever comprises a leaf spring encased within a rubber flexible cylinder, restricting the vibrations of the body in a water channel flow to principally transverse motion. It is found that the transverse amplitude response of the cantilever has a marked similarity with transverse vibrations of an elastically mounted rigid cylinder, in that there is a clear initial branch extending to high amplitudes, with a jump to a lower branch response, as normalized velocity is increased. The continuous initial branch suggests that a distinct upper branch does not exist for the cantilever, as is found for a rigid cylinder under similar conditions of low mass and damping. Good agreement is found between the response amplitude and frequency for two identical cantilevers, one set up by Pesce and Fujarra, where strain is measured to infer the body dynamics, and the other arrangement by Flemming and Williamson, where the tip motion is measured using optical techniques. An interesting large-amplitude response mode is found at higher normalized velocities (U*>12) outside the principal synchronization regime (typicallyU* =4–8), which is observed for an increasing velocity, or may be triggered by manual streamwise disturbances of the body. This vibration mode is due to a coupled streamwise-transverse motion, where the streamwise amplitude becomes non-negligible, and may be related to a further vibration mode at high normalized speed, found for a vibrating pivoted rod, by Kitagawa et al. (1999).

Stability of stationary solutions for a degenerate parabolic system

The paper is devoted to the stability of stationary solutions of an evolution system, describing heat explosion in a two-phase medium, where a parabolic equation is coupled with an ordinary differential equation. Spectral properties of the problem linearized about a stationary solution are analyzed and used to study stability of continuous branches of solutions. For the convex nonlinearity specific to combustion problems it is shown that solutions on the first increasing branch are stable, solutions on all other branches are unstable. These results remain valid for the scalar equation and they generalize the results obtained before for heat explosion in the radially symmetric case [1].

Estimation in continuous state-space branching processes

Extinction probability of a continuous-time continuous state-space branching process is a function of first two moments of the process. These moments are estimated on the basis of a discrete skeleton of the process. Estimators of smooth functions of the first two moments and in particular of extinction probability are proposed. Martingale limit theory is utilised to establish the optimal properties of the estimators.

Acetylcholine receptors and neuronal nitric oxide synthase distribution at the neuromuscular junction of regenerated muscle fibers.

We investigated whether the changes in acetylcholine receptor (AChR) distribution and neuronal nitric oxide synthase (nNOS) expression reported for the skeletal muscle of mdx mice were a consequence of muscle fiber regeneration rather than of the absence of dystrophin. Degenerative-regenerative changes in muscle fibers of the sternomastoid muscle of normal mice were induced by injecting lidocaine hydrochloride. Twenty-one days later, AChRs were labeled with alpha-bungarotoxin and nNOS with anti-nNOS antibody, and observed under a confocal microscope. AChRs were distributed in continuous branches in normal fibers. Regenerated fibers showed disruption of AChRs distribution similar to that seen in muscle of mdx mice. This suggests that changes in AChRs distribution seen in mdx mice were probably a consequence of muscle fiber degeneration and regeneration, rather than a symptom of dystrophin deficiency. Conversely, there were no changes in nNOS distribution and expression in normal regenerated fibers, suggesting that the decrease in nNOS expression reported for mdx mice might be attributed to the absence of dystrophin.

Killing spinors and SYM on curved spaces

We construct two families of globally supersymmetric counterparts of standard Poincar\'e supersymmetric SYM theories on curved space-times admitting Killing spinors, in all dimensions less than six and eight respectively. The former differs from the standard theory only by mass terms for the fermions and scalars and modified supersymmetry transformation rules, the latter in addition has cubic Chern-Simons like couplings for the scalar fields. We partially calculate the supersymmetry algebra of these models, finding R-symmetry extensions proportional to the curvature. We also show that generically these theories have no continuous Coulomb branch of maximally supersymmetric vacua, but that there exists a half-BPS Coulomb branch approaching the standard Coulomb branch in the Ricciflat limit.

Scanning Electron Microscopy of the Microcotyledonary Placenta of the Horse (Equus caballus) in the Latter Half of Gestation

Scanning electron microscopy was used to examine the microstructure of the maternal and fetal placenta from 25 pregnant ponies (Equus caballus) throughout the second half of gestation. Samples of placenta, 2–6cm2in area, were collected from the antimesometrial region of the pregnant horn at 105 days (n=1), 165–219 days (n=5), 260 days (n=3), 270–277 days (n=3), 313–337 days (n=11) and immediately after spontaneous delivery at term (n=2). The maternal microcaruncle appears to be created from a clustering of about 16 uterine crypts encapsulated in a connective tissue sheath. There is a gestational increase in the depth of the microcaruncle during the second half of pregnancy. The fetal microcotyledon appears to be formed by a clustering of individual fetal villi. The length and branching of the villi increased considerably during the last 2–3 months of gestation. Tufts of from three to six branches were seen arising from close to the base of a villous stem. Branching of the villous stem occurred not only at the base but also along the secondary and tertiary branches. There was evidence of continued branching at the tips of the villi in the few days before birth.

Geometric aspects of Sturm—Liouville problems I. Structures on spaces of boundary conditions

We consider some geometric aspects of regular Sturm—Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm—Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for separated boundary conditions and those for coupled boundary conditions, or the eigenvalues for self-adjoint boundary conditions and those for non-self-adjoint boundary conditions, are closely related under this structure. Then we give complete characterizations of several subsets of boundary conditions such as the set of self-adjoint boundary conditions that have a given real number as an eigenvalue, and determine their shapes. The shapes are shown to be independent of the differential equation in question. Moreover, we investigate the differentiability of continuous eigenvalue branches under this structure, and discuss the relationships between the algebraic and geometric multiplicities of an eigenvalue.

Asymptotic Behaviour of Continuous Time and State Branching Processes

AbstractWe prove some limit theorems for contiunous time and state branching processes. The non-degenerate limit laws are obtained in critical and non-critical cases by conditioning or introducing immigration processes. The limit laws in non-critical cases are characterized in terms of the cononical measure of the cumulant semigroup. The proofs are based on estimates of the cumulant semigroup derived from the forward and backward equations, which are easier than the proffs in the classical setting.

Different Modes of Rayleigh–Bénard Instability in Two- and Three-Dimensional Rectangular Enclosures

The article describes a complete numerical solution of a recently formulated benchmark problem devoted to the parametric study of Rayleigh–Bénard instability in rectangular two- and three-dimensional boxes. The solution is carried out by the spectral Galerkin method with globally defined, three-dimensional, divergent-free basis functions, which satisfy all boundary conditions. The general description of these three-dimensional basis functions, which can be used for a rather wide spectrum of problems, is presented. The results of the parametric calculations are presented as neutral curves showing the dependence of the critical Rayleigh number on the aspect ratio of the cavity. The neutral curves consist of several continuous branches, which belong to different modes of the most dangerous perturbation. The patterns of different perturbations are also reported. The results obtained lead to some new conclusions about the patterns of the most dangerous perturbations and about the similarities between two- and three-dimensional models. Some extensions of the considered benchmark problem are discussed.

Oxygen and placental vascular development.

Human embryogenesis takes place in a hypoxic environment because the trophoblast shell excludes entry of maternal blood. The first fetal-placental villi develop as trophoblast sprouts. These are invaded by allantoic mesoderm to form secondary villi and are transformed, by vasculogenesis, into tertiary villi. The placental barrier to maternal blood is gradually breached between 8-12 weeks of gestation, due to invasion of placental-bed uteroplacental spiral arteries by the extravillous trophoblast (EVT). Placental oxygen tension thus rises and a phase of branching angiogenesis continues until 24 weeks. Thereafter a gradual shift takes place favoring non-branching angiogenesis. Gas-exchanging terminal villi thus form which are essential for rapid fetal growth and development of a high-flow, low-resistance fetal-placental circulation. Inadequate invasion of the uteroplacental spiral arteries by EVT results in placental ischemia and the development of obstetrical complications--preeclampsia and/or intrauterine growth restriction (IUGR). Placental villi often show evidence of continued branching angiogenesis, as is the case with anemic pregnancy, and pregnancy at high altitude. These structural alterations may reflect continued hypoxia-driven activity of vascular endothelial growth factor (VEGF). By contrast, a minority of severe early-onset IUGR pregnancies exhibit reduced fetal-placental blood flow with elongated maldeveloped villous capillaries. Placenta-like growth factor (PIGF) expression is increased while trophoblast proliferation is reduced, suggesting "hyperoxia" in the placental villous tree. IUGR may thus have two phenotypes--a more common hypoxic and a rarer hyperoxic type. While this concept is gaining acceptance, we have no insight as to the initiating mechanism(s).

Estimation for Continuous Branching Processes

The maximum‐likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels

Branching processes in Lévy processes: the exploration process

The main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure. The exploration process appears as a simple local time functional of a Levy process with no negative jumps, whose Laplace exponent coincides with the branching mechanism function. This new relation between spectrally positive Levy processes and continuous branching processes provides a unified perspective on both theories. In particular, we derive the adequate formulation of the classical Ray–Knight theorem for such Levy processes. As a consequence of this theorem, we show that the path continuity of the exploration process is equivalent to the almost sure extinction of the branching process.

Phylogenetic identification of Sparganum proliferum as a pseudophyllidean cestode

Sparganum proliferum is characterized by continuous branching and budding, the resulting progeny invading all tissues of the human body, causing fatal sparganosis. Its life cycle, definitive hosts and the route of infection to humans have not yet been disclosed. Because its morphology is similar to Spirometra erinacei, the phylogeny of S. proliferum has been thought to be identical to or closely related to S. erinacei. However, the taxonomy of S. proliferum has not been established up to present due to the lack of definitive observations. In order to clarify the phylogenetic relationship between S. proliferum and S. erinacei, nucleotide sequences of mitochondrial NADH dehydrogenase subunit 3 gene (ND3) and four mitochondrial tRNA coding genes of S. proliferum and other pseudophyllidean cestodes were analyzed. The sequences of S. proliferum showed high similarity to those of S. erinacei, although they were clearly different from each other, indicating that the phylogeny of S. proliferum and S. erinacei is distinct. This is the first report showing the phylogenetic relationship among S. proliferum and other pseudophyllidean cestodes at the DNA sequence level.

Branching Process Models for Mutant Genes in Nonstationary Populations

A deleterious gene achieves a population balance between the opposing forces of selection and mutation. In this paper we explore the nature of this stochastic balance when the surrounding normal population is not at equilibrium. Assuming that new mutations occur according to a Poisson process and thereafter evolve by the rules of a continuous time branching process, we derive explicit formulas and recurrence relations determining the probability distribution of the current number of mutant individuals. In fact, we compute expectations for a variety of interesting random variables for genetic models involving autosomal dominant andX-linked diseases. We can also handle haplotype information on linked markers. This feature will be especially helpful in understanding the linkage disequilibrium strategy of positional cloning in population isolates. In the presence of exponential growth of the normal population, our formulas reduce to the evaluation of certain Laplace transforms.

Fractal random measures generated by time continuous branching and diffusion

Fractal measures are often defined in a constructive way. The most of these constructions lead to fractal measures with compact support. In this paper we regard fractal random measures with not necessarily compact support as limits of measure valued processes generated by time continuous branching and diffusion. For the special case of time transformed symmetric Γ-stable motions the almost sure existence of the carrying dimension is proved and an explicit formula for its computation is derived

Cauchy's Principal Value of Local Times of Lévy Processes with no Negative Jumps via Continuous Branching Processes

Let $X$ be a recurrent Lévy process with no negative jumps and $n$ the measure of its excursions away from $0$. Using Lamperti's connection that links $X$ to a continuous state branching process, we determine the joint distribution under $n$ of the variables $C^+_T=\int_{0}^{T}{\bf 1}_{{X_s>0}}X_s^{-1}ds$ and $C^-_T=\int_{0}^{T}{\bf 1}_{{X_s<0}}|X_s|^{-1}ds$, where $T$ denotes the duration of the excursion. This provides a new insight on an identity of Fitzsimmons and Getoor on the Hilbert transform of the local times of $X$. Further results in the same vein are also discussed.

Localized and Non-Localized Nonlinear Normal Modes in a Multi-Span Beam With Geometric Nonlinearities

The nonlinear normal modes of a geometrically nonlinear multi-span beam consisting of n segments, coupled by means of torsional stiffeners are examined. Assuming that the stiffeners possess large torsional stiffness, the beam displacements are decomposed into static and flexible components. It is shown that the static components are much smaller in magnitude than the flexible ones. A Galerkin approximation is subsequently employed to discretize the problem, whereby the computation of the nonlinear normal modes of the multi-span beam is reduced to the study of the periodic solutions of a set of weakly coupled, weakly nonlinear ordinary differential equations. Numerous stable and unstable, localized and non-localized nonlinear normal modes of the multi-span beam are detected. Assemblies consisting of n = 2, 3, and 4 beam segments are examined, and are found to possess stable, strongly localized nonlinear normal modes. These are free synchronous oscillations during which only one segment of the assembly vibrates with finite amplitude. As the number of periodic segments increases, the structure of the nonlinear normal modes becomes increasingly more complicated. In the multi-span beams examined, nonlinear mode localization is generated through two distinct mechanisms: through Pitchfork or Saddle-node mode bifurcations, or as the limit of a continuous mode branch when a coupling parameter tends to zero.

Seasonal variation in the intertidal seagrass Zostera noltii Hornem.: coupling demographic and physiological patterns

The considerable seasonal variation in biomass (2–130 g ash-free dry weight (AFDW) m −2) and cover of intertidal Zostera noltii Hornem. in the Zandkreek estuary (SW Netherlands) was mainly caused by changes in shoot density (1000–23000 m −2) and not in shoot size (shoot weight 1–3.6 mg AFDW, shoot leaf area 0.3–1.5 cm 2). The spring increase in shoot density was realised through continuous monopodial branching of the rhizome, which commenced when light available during low tide increased above 15 E m −2 day −1, in mid April. Branching stopped by the end of July, about 6 weeks before the onset of the annual biomass decline, due to a combination of: (a) self-shading during low tide; (b) high respiratory demand by the expanded rhizome network; (c) the seasonal decline in light availability during late summer. Nutrients were probably not limiting since concentrations in shoots remained high: 3.6% N and 0.6% P of dry weight are seasonal means. During the period of maximal biomass the primary rhizome axes decayed, leaving single shoots on short pieces of rhizome, the former secondary axes. The rapid decline in biomass from mid September onwards could be attributed to grazing by herbivorous migratory waterfowl. It was estimated that brent geese, Branta bernicla (L.), and wigeon, Anas penelope L. (about 200 and 300 birds, respectively, on the bed of 30 ha) together removed 45 g AFDW m −2 month −1, whilst autumn storms were insignificant. As established experimentally, winter survival was by single shoots enclosing an active meristem, and not by rhizome fragments without leaves. Sucrose was the main storage carbohydrate. The rhizome was the main storage organ, with maximal carbohydrate content observed in mid July (190 mg g −1 dry weight, sucrose + starch in glucose weight equivalents), and a gradual decline during autumn and winter. We estimated that the storage carbohydrates could cover 28% of the respiratory needs during winter, which would necessitate a substantial photosynthesis to meet the remaining 72%. From iteratively fitted photosynthesis-light curves we conclude that this intertidal Z. noltii population is high-light adapted compared with permanently submerged seagrasses and freshwater angiosperms: estimates for the light compensation point (LCP) and half-saturation constant ( K m) were comparatively high (July LCP and K m: 98 μE m −2 s −1 and 236 μE m −2 s −1, respectively), maximum photosynthetic rate was high ( P max: 236 μg O 2 g −1 AFDW min −1) and the initial slope of the curve was low (α: 0.63 μg O 2 g −1 AFDW min −1/μE m −2 s −1). Estimated daily oxygen balances confirmed that positive net photosynthesis was largely limited to low tide daylight in this turbid estuary (mean high tide light attenuation coefficient: 2.1 m −1).