Free Fitting Research Articles

An Interpretation of Evolutionary Dynamics in in vitro Molecular Evolution from Thermodynamical and Informational View Point

In vitro protein evolution is comprehended as a hill-climbing process on a fitness landscape in sequence space, just like the protein folding is comprehended as a valley-descending process on an energy landscape in comformation space. In this review, based on a mathematical model for in vitro molecular evolution, we demonstrated an analogy between evolutionary dynamics and thermodynamics and then many concepts in evolutionary dynamics became comprehensible. By introducing thermodynamics-like concepts such as “free fitness”, it is interpreted that evolution is driven in the direction in which free fitness increases. In this process, the evolving population climbs the fitness landscape by absorbing “fitness information” as the negative entropy from the surroundings as an experimental set-up.

Single Walled Carbon Nanotube Analysis by Photoluminescence and Raman Microscopy: Rapid, Robust Acquisition and Simulation of Quantum and Chiral Maps to Ease Structural Assignments

ABSTRACTThis paper describes improved methods for both data acquisition and analysis that are pertinent to interpreting the structural composition of single-walled carbon nanotube (SWNT) mixtures and suspensions.Rapid data acquisition of photoluminescence is made possible with a specially configured spectrofluorometer which uses a liquid nitrogen-cooled InGaAs array detector, imaging spectrograph, excitation reference photodiode and tunable xenon excitation source to collect seamless, instrument-corrected, excitation-emission quantum maps. The preferred instrument configuration with the InGaAs array can generate a quantum map with both high S/N levels and spectral resolution in only seconds to minutes; previous single-channel InGaAs photodiode and photomultiplier detector measurements took hours to days. The standard spectral range for excitation and emission is from 250 nm to 1700 nm with an option to extend to 2200 nm. Robust analysis of the quantum maps is facilitated by a custom global analysis program (US Patent Pending) which incorporates a powerful ‘double-convolution integral’ DCI algorithm to simultaneously model the excitation and emission spectral bands for each SWNT species. The patented DCI algorithm reduces the number of free fitting parameters for the spectral simulation by up to a factor of 1000 compared to conventional 2 D spectral simulators. The global analysis yields quantitative information on the chirality and diameter parameters of SWNT species in a given mixture. Together the acquisition hardware and analysis software constitute significant developments with respect to enhanced sensitivity and statistical significance for quantifying the components of complex SWNT mixtures.Raman maps of SWNT's were collected from dispersions plated onto substrates such as silicon plates using multiple excitation wavelengths. Identification of the chirality of the tubes was made using the Kataura plot. In many instances single lines in the radial breathing mode region were recorded indicating the presence of a single tube. The implication for this observation is that there is more than adequate sensitivity to detect and identify single-walled tubes. More recently Raman excitation on an AFM using a gold-coated tip to induce surface enhancement has been achieved. In this configuration it will be possible to map the topology of the tubes using detailed information on their structural composition.

Change in Self-Efficacy following a Single Strength Training Session Predicts Sedentary Older Adults' Subsequent Motivation to Join a Strength Training Program

To determine whether performance accomplishment and perceived exertion predict change in self-efficacy following a single strength training session and whether change in self-efficacy predicts subsequent motivation to join a strength training program. Fifty-nine sedentary older adults participated in a single strength training session at a seniors' exercise center, completed measures of perceived exertion and self-efficacy, and received a voucher for a free fitness consultation. Regression analyses indicated that perceived exertion predicted change in self-efficacy. In turn, greater change in self-efficacy was associated with a greater likelihood of using the voucher for a fitness consultation. Sedentary older adults can be motivated toward joining a strength training program after an initial strength training session that required low exertion. Practitioners could increase strength training initiation by providing such experiences.

Investigating of snow wetness parameter using a two-phase backscattering model

A two-phase backscattering model with nonsymmetrical inclusions is applied to calculate radar backscatter from a half-space of wet snow using strong fluctuation theory. Wet snow is assumed to consist of dry snow (host) and liquid water (inclusions). The shape and size of water inclusions are considered using an anisotropic and azimuth symmetric correlation function. The relationship between correlation lengths and snow wetness is presented by comparing strong fluctuation theory with the experimental data at 1.2, 8.6, 17, and 35.6 GHz. In the comparisons, correlation lengths are used as free fitting parameters. The effect of snow wetness on the backscattering coefficient is investigated. Numerical results of comparison between the two-phase backscattering model with nonsymmetrical inclusions and the experimental data are illustrated at 1.2, 8.6, 17, and 35.6 GHz. The effect of size and shape of water inclusions at different snow wetness values to backscatter level is shown. The comparison of angular response of backscattering coefficient (decibels) to wet snow between the model and the experimental data is presented at 2.6, 8.6, 17, and 35.6 GHz.

Elasticity of San Carlos olivine to 8 GPa and 1073 K

Elasticity of San Carlos olivine, (Mg0.9, Fe0.1)2SiO4, has been measured at simultaneous high pressure and high temperature to 8.2 GPa and 1073 K using ultrasonic interferometry in conjunction with synchrotron X‐radiation. The elastic moduli and their pressure and temperature derivatives are precisely determined using a pressure standard free fit using third‐order finite strain equations to the velocity and unit cell volume data in the entire pressure and temperature range, yielding KS0 = 130.3(4) GPa, G0 = 77.4(2) GPa, K′S0 = 4.61(11), G′0 = 1.61(4), ∂KS/∂T = −0.0164(5) GPa/K, and ∂G/∂T = −0.0130(3) GPa/K. Combined with previous thermoelastic data on wadsleyite, the velocity contrasts between α‐ and β‐(Mg, Fe)2SiO4 at 410‐km depth are calculated along a 1673 K adiabatic geotherm with plausible iron partition between the two phases. The fraction of olivine consistent with a ∼5% seismic discontinuity in an anhydrous mantle is constrained to be less than ∼50% with the possibility that a hydrous or a cooler mantle increases the olivine content towards pyrolitic composition.

The application of statistical physics to evolutionary biology.

A number of fundamental mathematical models of the evolutionary process exhibit dynamics that can be difficult to understand analytically. Here we show that a precise mathematical analogy can be drawn between certain evolutionary and thermodynamic systems, allowing application of the powerful machinery of statistical physics to analysis of a family of evolutionary models. Analytical results that follow directly from this approach include the steady-state distribution of fixed genotypes and the load in finite populations. The analogy with statistical physics also reveals that, contrary to a basic tenet of the nearly neutral theory of molecular evolution, the frequencies of adaptive and deleterious substitutions at steady state are equal. Finally, just as the free energy function quantitatively characterizes the balance between energy and entropy, a free fitness function provides an analytical expression for the balance between natural selection and stochastic drift.

Constitutive equations for dilute bubble suspensions and rheological behavior in simple shear and uniaxial elongational flow fields

A theoretical model is proposed in order to investigate rheological behavior of bubble suspension with large deformation. Theoretical constitutive equations for dilute bubble suspensions are derived by applying a deformation theory of ellipsoidal droplet [1] to a phenomenological suspension theory [2]. The rate of deformation tensor within the bubble and the time evolution of interface tensor are predicted by applying the proposed constitutive equations, which have two free fitting parameters. The transient and steady rheological properties of dilute bubble suspensions are studied for several capillary numbers (Ca) under simple shear flow and uniaxial elongational flow fields. The retraction force of the bubble caused by the interfacial tension increases as bubbles undergo deformation. The transient and steady relative viscosity decreases asCa increases. The normal stress difference (NSD) under the simple shear has the largest value whenCa is around 1 and the ratio of the first NSD to the second NSD has the value of 3/4 for largeCa but 2 for smallCa. In the uniaxial elongational flow, the elongational viscosity is three times as large as the shear viscosity like the Newtonian fluid.

Model to Predict Gate Tunneling Current of Plasma Oxynitrides

Two key parameters for silicon MOSFET scaling, equivalent oxide thickness (EOT) and gate leakage current density (J/sub g/) are measured and modeled for silicon oxynitride (Si-O-N) gate dielectrics formed by plasma nitridation of SiO/sub 2/. It is found that n-MOSFET inversion J/sub g/ is larger than p-MOSFET inversion J/sub g/ when the gate dielectric consists of less than 27% nitrogen atoms, indicating substrate injection of electrons is dominant for this range of plasma nitrided Si-O-N. To examine the intrinsic scaling of Si-O-N, we model EOT and n-MOSFET J/sub g/ for sub-2-nm physically thick gate dielectrics as a function of film physical thickness and nitrogen content. The model has four free fitting parameters and unlike existing models does not assume a priori the values of the oxide and nitride dielectric constant, barrier height, or effective mass. It indicates that at a given EOT, leakage current of n-MOSFETs with Si-O-N gate dielectrics reaches a minimum at a specific nitrogen content. Through the use of this model, we find that plasma nitrided Si-O-N can meet the 65-nm International Technology Roadmap for Semiconductors specifications for J/sub g/, and we estimate the nitrogen concentration required for each node and application.

Fidelity amplitude of the scattering matrix in microwave cavities

The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the ‘scattering fidelity’ is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength, could be determined independently from level dynamics of the system, thus providing agreement between theory and experiment without any free fit parameter.

An improved BEM model for the power curve prediction of stall-regulated wind turbines

Blade element momentum (BEM) theory is the standard computational technique for the prediction of power curves of wind turbines; it is based on the two-dimensional aerodynamic properties of aerofoil blade elements and some corrections accounting for three-dimensional wing aerodynamics. Although most BEM models yield acceptable results for low-wind and pitch-controlled regimes where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the power curve in the stall regime for a variety of blade properties and operating conditions. In this article we present a modified BEM model which satisfactorily reproduces the power curves of four experimental wind turbines reported in the literature, using no free fit parameters. Since these four experimental cases comprehend a great variety of conditions (wind tunnel vs field experiments, different air densities) and blade parameters (no twist and no taper, no taper but twist, both twist and taper, different aerofoil families), it is believed that our model represents a useful working tool for the aerodynamic design of stall-regulated wind turbines. Copyright © 2004 John Wiley & Sons, Ltd.

Influence of local anisotropic magnetoresistance on the total magnetoresistance of mesoscopicNiFerings

The magnetoresistance of mesoscopic $\mathrm{NiFe}$ rings is studied by low temperature magnetotransport measurements and numerical simulations. In order not to disturb the magnetic states in the electrical transport measurements, nonmagnetic gold wires are attached to individual rings. The simulations compute the change in resistance that is caused by the anisotropic magnetoresistance (AMR) effect and are based on a combination of magnetostatics for the magnetic domain configuration and electrostatics for the current distribution. Measurements as well as simulations reveal the presence of two stable ``onion'' states at remanence and a stable ``vortex'' state near the switching fields. Moreover, a quantitative comparison between experiment and simulation is possible without the use of any free fitting parameters. Apart from the AMR effect, no additional domain wall resistance has to be introduced for the onion state. In the switching region, experiment and simulation reveal the presence of a ``stressed vortex'' configuration which plays a key role in the quantitative description of the magnetoresistance. The switching behavior of the $\mathrm{NiFe}$ rings can be modified by introducing a wedge shaped notch at the expected position of one of the domain walls in the onion state of the rings.

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor, II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371-1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the 'free fitness' as the sum of a fitness term and an entropy term and 'evolutionary force' as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing 'effective' quantities such as the effective mutation distance or the effective screening size.

Theory of deformation in small volumes of material

It has long been controversial as to whether small volumes of material are, or should be, more resistant to plastic deformation than is implied by the yield strength of bulk material. We generalize the established theory of critical thickness for strained layers to show that there is an increase in the initial yield stress for geometrical reasons wherever there is a strain gradient. The theory is in quantitative agreement, without free fitting parameters, with the classic experimental data on the torsion of thin wires and on the bending of thin beams.

Effective low-energy theory of superconductivity in carbon nanotube ropes

We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature ${T}_{c}$ below the mean-field value, and a temperature-dependent resistance below ${T}_{c}$. We compare our theoretical results to recent experimental data of Kasumov et al. [Phys. Rev. B 68, 214521 (2003)] for the sub-${T}_{c}$ resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit.

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in a evolution reactor, I

A theory for describing evolution as adaptive walks by a finite population with M walkers (M > or = 1) on an anisotropic Mt. Fuji-type fitness landscape is presented, from a thermodynamical point of view. Introducing the 'free fitness' as the sum of a fitness term and an entropy term and 'evolutionary force' as the gradient of free fitness on a fitness coordinate, we demonstrate that the behavior of these theoretical walkers is almost consistent with the thermodynamical schemes. The major conclusions are as follows: (1) an adaptive walk (=evolution) is driven by an evolutionary force in the direction in which free fitness increases; (2) the expectation of the climbing rate obeys an equation analogous to the Einstein relation in Brownian motion; (3) the standard deviation of the climbing rate is a quantity analogous to the mean thermal energy of a particle, kT (x constant). In addition, on the interpretation that the walkers climb the landscape by absorbing 'fitness information' from the surroundings, we succeeded in quantifying the fitness information and formulating a macroscopic scheme from an informational point of view.

Thermodynamical interpretation of an adaptive walk on a Mt. Fuji-type fitness landscape: Einstein relation-like formula holds in a stochastic evolution

We have theoretically studied the statistical properties of adaptive walks (or hill-climbing) on a Mt. Fuji-type fitness landscape in the multi-dimensional sequence space through mathematical analysis and computer simulation. The adaptive walk is characterized by the "mutation distance" d as the step-width of the walker and the "population size" N as the number of randomly generated d-fold point mutants to be screened. In addition to the fitness W, we introduced the following quantities analogous to thermodynamical concepts: "free fitness" G(W) is identical with W+T x S(W), where T is the "evolutionary temperature" T infinity square root of d/lnN and S(W) is the entropy as a function of W, and the "evolutionary force" X is identical with d(G(W)/T)/dW, that is caused by the mutation and selection pressure. It is known that a single adaptive walker rapidly climbs on the fitness landscape up to the stationary state where a "mutation-selection-random drift balance" is kept. In our interpretation, the walker tends to the maximal free fitness state, driven by the evolutionary force X. Our major findings are as follows: First, near the stationary point W*, the "climbing rate" J as the expected fitness change per generation is described by J approximately L x X with L approximately V/2, where V is the variance of fitness distribution on a local landscape. This simple relationship is analogous to the well-known Einstein relation in Brownian motion. Second, the "biological information gain" (DeltaG/T) through adaptive walk can be described by combining the Shannon's information gain (DeltaS) and the "fitness information gain" (DeltaW/T).

MONTE CARLO SIMULATION OF ADSORPTION PROBABILITIES: THE CASE OF CO/DISORDERED–Cu(110) AND CO/O–Ir(110)

Recently [M. Kunat et al., Surf. Sci.474, 114 (2001)] a quenching of adsorbate-assisted adsorption ("autocatalytic adsorption") by defects has been observed for the system CO/Cu(110). A conceptually similar effect for CO adsorption on O–Ir(110) had additionally been reported before [U. Burghaus et al., Surf. Sci.384, L869 (1997)]. Presented is a simple Monte Carlo simulation (MCS) scheme which includes basically one free fit parameter and can reproduce both effects consistently.

604 3 次元点群データに基づく自由曲面生成法

604 3 次元点群データに基づく自由曲面生成法

Adaptive Monotone Rational Approximation on Finite Sets

The problem of uniform approximation on a finite set of real numbers by rational functions whose first derivative is required to be positive (negative) and denominator is required to be positive on the smallest interval containing the points is considered. An earlier non-adaptive computational code is now extended to the present adaptive code by coupling it with a positivity checker for polynomials on intervals (INCHWORM) developed herein. This new code allows for an intelligent selection of additional constraining points beyond the initial data points to enforce monotonicity preserving pole free fits to monotone data sets. In addition, it also provides the option of enforcing pole-free fits while ignoring monotonicity.

X-ray diffraction study on surface modified complex strontium titanate microparticles

A novel surface modified complex strontium titanate used as dispersion particles in an electrorhelogical fluid with an extraordinary high yield stress was synthesized by means of a modified sol–gel technique and characterized by X-ray powder diffraction. The structure model free full profile fitting technique was used to derive the crystallographic data of the compound, which crystallized in a monoclinic lattice with a =13.6822(7), b =14.5549(6), c =12.7423(5) Å and β =91.803(2)°. Deliberate examination of the XRD pattern indicates that the most probable space group of the compound is P2 1 / n . A possible composition of the complex strontium titanate is Sr[TiO 4 (C 2 O 4 ) 2 ].3H 2 O with eight chemical formula units per unit cell, leading to a calculated density of D X =2.25 g/cm 3 in good agreement with the measured density of D m =2.28(5) g/cm 3 .