Monotonic Shape Research Articles

Kawahara solitons in Boussinesq equations using a robust Christov–Galerkin spectral method

We develop a robust Christov–Galerkin spectral technique for computing interacting localized wave solutions of and fourth and sixth-order generalized wave equations. To this end, a special complete orthonormal system of functions in L2(-∞,∞) is used whose rate of convergence is shown to be exponential for the cases under consideration. For the time-stepping, an implicit algorithm is chosen which makes use of the banded structure of the matrices representing the different spatial derivatives.As featuring examples, the head-on collision of solitary waves is investigated for a sixth-order generalized Boussinesq equation and a fourth-order Boussinesq type equation with a linear term. Its solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). The numerical results are validated against published data in the literature using the method of variational imbedding.

Worst-case actuarial calculations consistent with single- and multiple-decrement life tables

The present work complements the recent paper by Barz and Müller (2012). Specifically, upper and lower bounds are derived for the force of mortality when one-year death probabilities are given, assuming a monotonic, convex or concave shape. Based on these bounds, worst-case scenarios are derived depending on the mix of benefits in the case of survival and of death comprised in a specific insurance policy.

EVOLUTION OF STATIC ALLOMETRIES: ADAPTIVE CHANGE IN ALLOMETRIC SLOPES OF EYE SPAN IN STALK-EYED FLIES

Julian Huxley showed that within-species (static) allometric (power-law) relations can arise from proportional growth regulation with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow-sense allometry. Here, we present the first phylogenetic comparative study of narrow-sense allometric exponents based on a reanalysis of data on eye span and body size in stalk-eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong evidence that male slopes were tracking "optima" based on sexual dimorphism and relative male trait size. This tracking was slow, however, with estimated times of 2-3 million years for adaptation to exceed ancestral influence on the trait. Our results are therefore consistent with adaptive evolution on million-year time scales, but cannot rule out that static allometry may act as a constraint on eye-span adaptation at shorter time scales.

Water Sorption Isotherm Characteristics of Seeds of Six Indigenous Forest Tree Species in Ghana

The relationship between storage temperature, relative humidity and seed water content was investigated for six indigenous forest tree seed species, namely Garcinia kola, Terminalia superba, Terminalia ivorensis, Mansonia altissima, Entandrophragma angolense and Khaya anthotheca in Ghana. Seeds were equilibrated over a series of lithium chloride solutions with relative humidities ranging from 12 to 93% and silica gel with relative humidity of 3% at 20 ºC. Seeds reached equilibrium with different days depending on seed size and structure, ranging from 13 days for E. angolense to 91 days for G. kola. When seeds equilibrated, moisture contents were determined gravimetrically, and values of moisture contents were then plotted against relative humidity to construct moisture sorption isotherms for the species. Seeds of T. superba, T. ivorensis, M. altissima, E. angolense and K. anthotheca, exhibited a sigmoidal relationship between seed water content and relative humidity indicative of three regions of water binding. Contrarily to other reports, the shape of the isotherm curve for G. kola – a desiccation sensitive species – also showed the reversed sigmoid pattern similar to isotherm curves of orthodox species rather than the monotonic shape. The isotherms showed that seed moisture content increased with increasing relative humidity. Seed samples of G. kola, placed at all relative humidities chambers, lost water(desorption) as the initial water content of 58% was very high and, therefore, possessed a higher water potential than the environments. Seeds of the other species either lost water (desorption) to the relative humidity chambers, or absorbed water from the chambers depending on the relative humidity of the environment they were placed.

Computer Design of Robust I-controller

AbstractThis paper shows new possibility of the robust design of simple controllers based on computer analysis of closed loop transient responses achieved over predefined grid of possibly normalized loop parameters by simulation, or by measurement. Evaluation of the collected transients according to chosen performance measures related to monotonicity and time yields the so called Performance Portrait (PP). Based on the PP, controller tuning satisfying desired robust performance may be derived what is illustrated by tuning simple integral (I) controllers for the simplest uncertain 2-parameter plant model. Achieved results that extend the simple tuning proposed by Skogestad (2003) to a broader spectrum of nearly monotonic shapes are compared with the analytical controller tuning based on the double real dominant closed loop pole and then, on an example of a higher order dead-time dominant plant, with the results achieved by the Filtered Smith Predictor. Possible extension to PI control is briefly mentioned.

Silicon self‐diffusion of MgSiO3 perovskite by molecular dynamics and its implication for lower mantle rheology

The pressure effect of silicon self‐diffusion of MgSiO3 perovskite was investigated by molecular dynamics (MD). The viscosity variation of MgSiO3 perovskite in the lower mantle was derived by the Nabarro‐Herring (Herring‐Nabarro) model. For the MD calculation, the spontaneous jumping of atoms by self‐diffusion was reproduced without using artificial forces, and the consistency of migration enthalpy (Hm*) with experimental data was improved. The results showed that migration enthalpy increases monotonically with increasing pressure. The viscosity of MgSiO3 perovskite in the lower mantle increases monotonically with increasing depth. The obtained depth profile is distinguishable from that of MgO periclase and can be utilized to determine which mineral dominates the lower mantle rheology. Depending upon the assumed shape of the depth profile for lower mantle viscosity, we considered the dominant mineral as (1) MgSiO3 perovskite for the monotonic shape case or (2) MgO periclase for the hill shape case that has the highest‐viscosity zone in the middle of the lower mantle.

Flexible estimation of price response functions using retail scanner data

Kalyanam and Shively [1998. Estimating irregular pricing effects: a stochastic spline regression approach. Journal of Marketing Research 35 (1), 16–29] and van Heerde et al. [2001. Semiparametric analysis to estimate the deal effect curve. Journal of Marketing Research 38 (2), 197–215] have demonstrated the usefulness of nonparametric regression to estimate pricing effects flexibly. The empirical results of these two studies, however, also revealed that nonparametric regression may suffer from too much flexibility leading to nonmonotonic shapes for price effects. In this paper, we show how the problem of nonmonotonicity can be dealt with without losing the power of flexible estimation techniques. We propose a semiparametric approach based on Bayesian P-splines with monotonicity constraints imposed on own- and cross-price effects. In an empirical application, we illustrate that flexible estimation of own- and cross-price effects can improve the predictive validity of a sales response model substantially, even when price response curves were constrained to show a monotonic shape, as suggested by economic theory. We also discuss the consequences from an unconstrained estimation of price effects.

The Bump Hunting Method Using the Genetic Algorithm with the Extreme-Value Statistics

In difficult classification problems of the z-dimensional points into two groups giving 0-1 responses due to the messy data structure, we try to find the denser regions for the favorable customers of response 1, instead of finding the boundaries to separate the two groups. Such regions are called the bumps, and finding the boundaries of the bumps is called the bump hunting. The main objective of this paper is to find the largest region of the bumps under a specified ratio of the number of the points of response 1 to the total. Then, we may obtain a trade-off curve between the number of points of response 1 and the specified ratio. The decision tree method with the Gini's index will provide the simple-shaped boundaries for the bumps if the marginal density for response 1 shows a rather simple or monotonic shape. Since the computing time searching for the optimal trees will cost much because of the NP-hardness of the problem, some random search methods, e.g., the genetic algorithm adapted to the tree, are useful. Due to the existence of many local maxima unlike the ordinary genetic algorithm search results, the extreme-value statistics will be useful to estimate the global optimum number of captured points; this also guarantees the accuracy of the semi-optimal solution with the simple descriptive rules. This combined method of genetic algorithm search and extreme-value statistics use is new. We apply this method to some artificial messy data case which mimics the real customer database, showing a successful result. The reliability of the solution is discussed.

Analyzing lifetime data with long-tailed skewed distribution: the logistic-sinh family

A new two-parameter family of distribution is presented. It is derived to model the highly negatively skewed data with extreme observations. The new family of distribution is referred to as the logistic-sinh distribution, as it is derived from the logistic distribution by appropriately replacing an exponential term with a hyperbolic sine term. The resulting family provides not only negatively skewed densities with thick tails but also variety of monotonic density shapes. The space of shape parameter, lambda greater than zero is divided by boundary line of lambda equals one, into two regions over which the hazard function is, respectively, increasing and bathtub shaped. The maximum likelihood parameter estimation techniques are discussed by providing approximate coverage probabilities for uncensored samples. The advantages of using the new family are demonstrated and compared by illustrating well known examples.

Isometric and Isotensional Force‐Length Profiles in Polymethylene Chains

AbstractSummary: The force‐length curves and related thermodynamic quantities of single polymethylene (PM) chains in the high‐force region were calculated by the statistical mechanics. Two statistical mechanics ensembles (isometric and isotensional) were used to represent the chain stretching under the conditions, respectively, of the fixed length L or of the fixed force F in single‐chain experiments by AFM and related techniques. The input deformation potentials of highly extended conformations of PM chains were obtained from the molecular‐mechanics calculations. Variations of the energy, entropy, and Helmholtz energy with the end‐to‐end length L of chains were computed under the condition of fixed length. The ensuing isometric profile of the mean force 〈F〉(L) is non‐monotonic, featuring a sawtooth‐like pattern of ascending peaks. In contrast, the mechanical equation under isotensional conditions, given by the variation of the mean length 〈L〉(F), shows a conventional monotonous shape with a distinct plateau region at low temperatures. The considerable difference in the shapes of 〈F〉(L) and 〈L〉(F) curves arises from the large fluctuations of mean values due to the small number of conformers present in molecules at high strains. The computed data should be relevant to the AFM stretching experiments on short polyethylenes or on other soft matter materials involving linear paraffinic chains. It is argued that the dual character of elastic response described by the conjugated force profiles is a universal feature of mechanochemistry of chain molecules whenever the chain length discontinuously increases at a transition.Force‐length curves of short polymethylene chains at 300 K.magnified imageForce‐length curves of short polymethylene chains at 300 K.

Thermal dynamics of VO2 films within the metal–insulator transition: Evidence for chaos near percolation threshold

The thermal dynamics of thin vanadium dioxide films at the martensitic metal–insulator phase transition has been evaluated experimentally by thermal excitation spectroscopy. Over the transition region, the device becomes highly nonlinear, and its bolometric performance is affected. At low thermal cycling rates for a temperature around the percolation threshold, the device stochastically switches into an unusual pattern. The originally smooth and monotonic shape of the R(T) curve for minor loops suddenly becomes unstable and unpredictable. By direct observation of at least two strange attractors, the phenomenon clearly has been identified as chaotic. Bolometric performance of VO2 based devices in the transition region may suffer strong degradation for low thermal cycling rates. In this region, sensor responsivity for periodic thermal excitation is significantly reduced. Resistance noise is 1/f-type and self-generated oscillations were observed at frequency <10−2 Hz.

Water sorption properties inCoffeaspp. seeds and embryos

The relationships among water content, relative humidity and temperature were documented in both seeds and excised embryos ofCoffeaspp. using water sorption isotherms. Isotherms were constructed at 5, 15 and 25°C and calculated for lower temperatures. There were no apparent differences in sorption characteristics among whole seeds of several cultivars ofC. arabicaand among different species ofCoffea. Excised embryos of genetically diverseCoffeagermplasm also exhibited similar sorption characteristics, though there were substantial differences observed between embryos and whole seeds. The shape of isotherms of coffee seed tissues was intermediate to the reverse sigmoidal shape observed for orthodox seeds and the monotonic shape observed for desiccation intolerant plant tissues. The heats of sorption calculated for RH ≤ 25% for whole seeds ofCoffeaspp. were similar to orthodox seeds. In contrast, the heats of sorption calculated in the same RH range for excised embryos were intermediate between those of orthodox and recalcitrant embryos. Our observations are consistent with earlier observations that desiccation sensitivity or poor longevity is linked with low levels of water sorption at relative humidities less than 25%. An explanation for this remains elusive.

Preserving monotonic shape of the data using piecewise rational cubic functions

A C 1 monotonically shape preserving scheme has been developed. This scheme uses piecewise rational cubic functions. An algorithm has been developed, for economical curve implementation and pleasant demonstration, which ultimately replaces the rational cubic locally in each of the intervals by a constant, linear, rational quadratic or rational cubic function according to the nature of the slopes and parameters in that interval. A detailed description of the algorithm implementation has been made in tabular as well as pictorial form. Furthermore, an O( h 4) convergence result is also obtained with appropriate derivative approximations.

X-ray diffraction from low temperature ion implanted silicon

Double-crystal X-ray diffraction rocking curves (RCs) have been measured at 77 K for silicon wafers implanted with 3 MeV Ni ions at 130 K. Rather symmetric broadening of RC of the sample implanted with 1 × 10 14 Ni 3+ /cm 2 was observed. It may be a kind of distortion scattering caused by vacancies, interstitials and their agglomerates. Modulated profile of the sample implanted with 4 × 10 14 Ni 3+ /cm 2 is a result of the nonuniform strain distribution. By further implantation, the modulating profile changes to a rather monotonous shape. It is considered to be a result of the strain fluctuation in an identical depth and the increasing of amorphous region reducing the coherency of X-rays. The annealing experiments were also carried out up to 1073 K. The change of RCs started even below room temperature and is rather continuous. It leads to the fact that the recovery of defects is rather continuous in temperatures. The recovery was completed at 1073 K. Numerical calculations for the depth profiles of the strain were carried out from the fitting of the simulated RCs to those observed.

Shaping static elbow torque-angle relationships by spinal cord circuits: A theoretical study

Static torque-angle relationships (invariant characteristics) as measured by Feldman [Feldman A. G. (1980) Neuroscience 5, 81–90] at the human elbow joint for constant descencling excitatory drive have a monotonic convex shape determining joint angle-dependent stiffness. In contrast, for constant activation of elbow flexors, the torque increases, peaks and decreases again with increasing angle because of related moment arm alterations [Hasan Z. and Enoka R. M. (1985) Expl Brain Res. 59, 441–450]. Conversion of such constant-excitation torque-angle shapes into an invariant characteristic might result from action of the stretch reflex which adds excitation with increasing joint angle. To test whether a simple linear model of the stretch reflex could convert constant excitation torque-angle relationships into invariant characteristics, the following assumptions were made. (1) Muscle fibre length increases linearly with joint angle. (2) Reflex muscle excitation (electromyogram) is linearly related to muscle (fibre) length. With these assumptions, invariant characteristic shape cannot be derived from constant excitation torque-angle relationships because it would be sigmoid at low and nearly straight at large joint angles, whilst real flexor invariant characteristics are more convex at large than small angles. It is suggested that recurrent inhibition via Renshaw cells contributes to bend the invariant characteristics into their right shape. Renshaw cells show a nonlinear saturating dependence on motor axon input rate and amount of excitation, i.e. number of active axon collateral synapses. These relationships can contribute to shape motoneuron output so as to yield convex invariant characteristics. Whilst it is not quite clear whether the gain of recurrent inhibition from and to skeleto-motoneurons is high enough to co-determine the invariant characteristic shape significantly, recurrent inhibition of Ia inhibitory interneurons mediating reciprocal inhibition between antagonists is supposed to be quite strong and may influence joint stiffness by interacting with reciprocal inhibition. The arguments presented here extend those of Feldman and co-workers concerning the role of recurrent inhibition and in addition provide a possible explanation for the functional role of mutual inhibition between Renshaw cells. Together with reflex feedback, recurrent inhibition thus contributes to fine-regulate force output and joint stiffness. To account for this cooperation and to make another step towards a general theory of spinal cord circuits, major traits of a new concept are briefly outlined.

Parameter estimation and reconstruction of digital conics in normal positions

Reconstruction of the original curve (and the estimation of its parameters) from its digitization is a challenging problem as quantization always causes some loss of information. So we often estimate at least one (or all) continuous curve(s) which is (are) isomorphic to the original one under discretization. Some work has already been done in this respect on straight lines, circles, squares, etc. In this paper, we have attempted this problem for a specialized class of conics which are said to be in normal positions. In normal position the center of the conic is situated at a grid point and its axes are parallel to the coordinate axes. For circles and parabolas, we can directly formulate the domain, i.e., the entire set of continuous curves which produces the same digitization. For ellipses (and this can be extended to hyperbolas too), we first compute the smallest rectangle containing the domain of the given digitization and then estimate the domain itself. The major contribution of this paper lies in the development of a new method of analysis (via the iterative refinement of parameter bounds) which can be easily extended to other 1- or 2-parameter piecewise monotonic shapes such as straight lines or circles with known radius.

A Method for Constructing Local Monotone Piecewise Cubic Interpolants

A method is described for producing monotone piecewise cubic interpolants to monotone data which is completely local and which is extremely simple to implement.

Magma reservoir systems inferred from tilt patterns

Inflation patterns based on water-tube tiltmeter and levelling observation show different features for Krafla Volcano in Iceland and Kilauea Volcano in Hawaii. Monotonous sawtooth shape inflation is observed at Krafla, while inflation curves at Kileauea are more or less complicated. The difference was attributed to differences in the system of magma reservoir for the two volcanoes. By using the electrical equivalent of a magma reservoir and volcanic conduit as a capacitor and a resistor, an electrical oseillator was considered to be a possible model for a magma reservoir system. In the case of Krafla, the magma reservoir system is replaced with one electric oscillator called «Single system» or «Icelandic type» system.

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β‐benzyl L‐aspartate)

AbstractSimple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix‐coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β‐benzyl L‐aspartate) (PBLA) with the result: σ = 1.6 × 10−4 and ΔH = −450 cal/mole for PBLA in m‐cresol; σ = 0.6 × 10−4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol‐% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m‐cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean‐square radius of gyration, 〈S2〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S2〉.