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Based on a sample of 7696 nonrecurrent and 566 recurrent sunspot groups, we have investigated the Gnevyshev–Waldmeier rule using the Catalogue of Solar Activity by R.S. Gnevysheva (1954–1978). The maximum recorded sunspot group lifetime is 160 days. The general Gnevyshev–Waldmeier rule for all lifetimes is Amax = (12.1 ± 0.70)LT (Amax is the maximum sunspot group area during the lifetime and LT is the sunspot group lifetime). However, the general rule has turned out to deviate from the derived linear form for the population of small short-living sunspot groups (SSG): it has a significant nonlinear scaling form Amax = (8.02 ± 0.41)LT(1.105±0.022). For the population of large long-living sunspot groups (LLG) there is a linear form Amax = (12.9 ± 1.1)LT. Allowance only for recurrent sunspot groups with lifetimes more than 40 days gives Amax = (13.93 ± 0.41)LT.

Few neuroimaging studies are sufficiently large to adequately describe population‐wide variations. This study's primary aim was to generate neuroanatomical norms and individual markers that consider age, sex, and brain size, from 629 cerebral measures in the UK Biobank (N = 40,028). The secondary aim was to examine the effects and interactions of sex, age, and brain allometry—the nonlinear scaling relationship between a region and brain size (e.g., total brain volume)—across cerebral measures. Allometry was a common property of brain volumes, thicknesses, and surface areas (83%) and was largely stable across age and sex. Sex differences occurred in 67% of cerebral measures (median |β| = .13): 37% of regions were larger in males and 30% in females. Brain measures (49%) generally decreased with age, although aging effects varied across regions and sexes. While models with an allometric or linear covariate adjustment for brain size yielded similar significant effects, omitting brain allometry influenced reported sex differences in variance. Finally, we contribute to the reproducibility of research on sex differences in the brain by replicating previous studies examining cerebral sex differences. This large‐scale study advances our understanding of age, sex, and brain allometry's impact on brain structure and provides data for future UK Biobank studies to identify the cerebral regions that covary with specific phenotypes, independently of sex, age, and brain size., This study's primary aim was to generate neuroanatomical norms and individual markers that consider age, sex, and brain size, from 629 cerebral measures in the UK Biobank (N = 40,028). Allometry was a common property of brain volumes, thicknesses, and surface areas (83%) and we found sex differences in 67% of the investigated brain regions. This large‐scale study advances our understanding of age, sex, and brain allometry's impact on brain structure and provides data for future UK Biobank studies to identify the cerebral regions that covary with specific phenotypes, independently of sex, age, and brain size.

Paper aims Extending the AHP abilities to new areas from explaining the famous Two-Envelope paradox to finding priorities as functions of auxiliary variables is suggested. Originality The proposed innovative and advantageous approach permits to find the non-constant priorities via regression modeling for the exponential or Cobb-Douglas production functions. Research method Transforming the ratio scale into the additive or logarithmic scales, which correspond to the multiplicative utility function, opens new possibilities in the multiple-criteria decision making. Main findings Two-Envelop problem is resolved, priority vectors are presented as functions by auxiliary variables, preferences are predicted and profiled by predictors. Implications for theory and practice The suggested techniques open novel possibilities of multiple-criteria decisions helping to researchers and managers to discover useful features of priority behavior due to the demographic, socio-economic, or technical properties of the compared alternatives, and to find optimal solutions for individual customers.

A motion cueing algorithm plays an important role in generating motion cues in driving simulators. The motion cueing algorithm is used to transform the linear acceleration and angular velocity of a vehicle into the translational and rotational motions of a simulator within its physical limitation through washout filters. Indeed, scaling and limiting should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the motion cueing algorithm. This is to decrease the effects of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation. A nonlinear scaling method based on the genetic algorithm for the motion cueing algorithm is developed in this study. The aim is to accurately produce motions with a high degree of fidelity and use the platform more efficiently without violating its physical limitations. To successfully achieve this aim, a third-order polynomial scaling method based on the genetic algorithm is formulated, tuned, and implemented for the linear quadratic regulator–based optimal motion cueing algorithm. A number of factors, which include the sensation error between the real and simulator drivers, the simulator’s physical limitations, and the sensation signal shape-following criteria, are considered in optimizing the proposed nonlinear scaling method. The results show that the proposed method not only is able to overcome problems pertaining to selecting nonlinear scaling parameters based on trial-and-error and inefficient usage of the platform workspace, but also to reduce the sensation error between the simulator and real drivers, while satisfying the constraints imposed by the platform boundaries.

We prove a subset of inequalities of Caffarelli–Kohn–Nirenberg type in the hyperbolic space \({{\mathbb {H}}^N}, N\ge 2\), based on invariance with respect to a certain nonlinear scaling group, and study existence of corresponding minimizers. Earlier results concerning the Moser–Trudinger inequality are now interpreted in terms of CKN inequalities on the Poincare disk.

Accurately predicting energy requirements form a critical component for initializing dynamic mathematical models of metabolism. The majority of such existing estimates rely on linear regression models that predict total daily energy expenditure (TDEE) from age, gender, height, and body mass, however, there is evidence these predictors obey a power function. Baseline, free-living TDEE measured by doubly labeled water (DLW) in 20 studies with no overlapping subjects were obtained from the core lab at the University of Chicago and the University of Wisconsin-Madison (N = 2501 adults, 628 males, 1873 females). Linear regression models of log-transformed equations of the form: $${\rm{TDEE}} = \alpha _1M^{\beta _1}H^{\beta _2}$$ TDEE = α 1 M β 1 H β 2 and $${\rm{TDEE}} = {\rm{ln}}\left( {\alpha _1M^{\beta _1 + \gamma _1{\rm{Sex}}}H^{\beta _2 + \gamma _2{\rm{Sex}}}} \right)$$ TDEE = ln α 1 M β 1 + γ 1 Sex H β 2 + γ 2 Sex were developed to determine the values of the exponents of body mass (M (kg)) and height (H (cm)) along with a gender effect (Sex). A nonlinear curve fit was performed to develop a power model that also includes age $${\rm{TDEE}} = \alpha _1M^{\beta _1}H^{\beta _2} + \alpha _2{\mathrm{Age}}$$ TDEE = α 1 M β 1 H β 2 + α 2 Age . The power for body mass, β1 = 0.45 and the power for height was β2 = 1.52 in the database with both genders combined. Adding gender reduced these to β1 = 0.43 and β2 = 1.04. All terms were significant (p

The surface eigenstress model was further developed to study the surface-induced size-dependent ultimate biaxial tensile strength of thin films. First-principles calculations and molecular dynamics (MD) simulations were conducted on Au and Si thin films with different thicknesses. The atomistic calculations show that the ultimate biaxial tensile strength of Au thin films increases when the film thickness decreases, a typical the thinner the stronger phenomenon, while the Si thin films exhibit the thinner the weaker behavior. Nevertheless, both behaviors were perfectly predicted by a nonlinear scaling law developed from the surface eigenstress model. Moreover, the first-principles calculations put insight into the surface induced strengthening or weakening mechanism.

International audience; It has been known for a long time that the kinetics of diffusion-limited reactions can be quantified by the time needed for a diffusing molecule to reach a target: the first-passage time (FPT). So far the general determination of the mean first-passage time to a target in confinement has left aside aging media, such as glassy materials, cellular media, or cold atoms in optical lattices. Here we consider general non-Markovian scale-invariant diffusion processes, which model a broad class of transport processes of molecules in aging media, and demonstrate that all the moments of the FPT obey universal scalings with the confining volume with nontrivial exponents. Our analysis shows that a nonlinear scaling with the volume of the mean FPT, which quantities the mean reaction time, is the hallmark of aging and provides a general tool to quantify its impact on reaction kinetics in confinement.

Maintenance of mining machinery is done by schedule or in the event of break down and this is area where it is possible to cut down in maintenance costs by lowering down time and preventing sudden break downs. Advanced on site signal processing enables early fault detection and improves maintenance planning by optimizing service intervals. This paper studies the stress affecting the load haul dumper front axle. Methods used are stress indices and cumulative stress analysis.

Crime is a major threat to society's well-being but lacks a statistical characterization that could lead to uncovering some of its underlying mechanisms. Evidence of nonlinear scaling of urban indicators in cities, such as wages and serious crime, has motivated the understanding of cities as complex systems-a perspective that offers insights into resources limits and sustainability, but that usually neglects details of the indicators themselves. Notably, since the nineteenth century, criminal activities have been known to occur unevenly within a city; crime concentrates in such way that most of the offenses take place in few regions of the city. Though confirmed by different studies, this concentration lacks broad analyses on its characteristics, which hinders not only the comprehension of crime dynamics but also the proposal of sounding counter-measures. Here, we developed a framework to characterize crime concentration which divides cities into regions with the same population size. We used disaggregated criminal data from 25 locations in the U.S. and the U.K., spanning from 2 to 15 years of longitudinal data. Our results confirmed that crime concentrates regardless of city and revealed that the level of concentration does not scale with city size. We found that the distribution of crime in a city can be approximated by a power-law distribution with exponent α that depends on the type of crime. In particular, our results showed that thefts tend to concentrate more than robberies, and robberies more than burglaries. Though criminal activities present regularities of concentration, we found that criminal ranks have the tendency to change continuously over time-features that support the perspective of crime as a complex system and demand analyses and evolving urban policies covering the city as a whole.

Scaling methods are widely used in railgun technology. But nonlinear problems are seldom studied because of the complexity and uncertainty. To employ the scaling method better, this paper brings the nonlinear drag model to the solid armature railgun circuit. Several drag models are compared including friction drag model (FDM), atmosphere drag model (ADM), and current drag model (CDM). Then, nonlinear scaling relationships of these drag models are discussed. Furthermore, a novel experiment is constructed to compare the drag models at low velocity. At last, the nonlinear scaling method is verified by an example at high velocity. FDM is accurate enough to simulate a railgun system at any condition. Coefficient $\varepsilon$ in FDM should be used considering different test conditions. Scaling relationships of FDM could not be derived at low velocity because of nonlinearity. Although at high velocity, FDM could be simplified to CDM and realize linear scaling method (LSM). Further research indicates that the FDM could use the scaling method directly and realize approximate LSM. CDM is workable which satisfies the conditions of LSM in nature. Due to the work range of the solid armature, usually under 2.5 km/s, nonlinear scaling method could be used in a railgun with FDM. For a solid armature railgun, the $f_{\rm ADM}$ is too small compared with $f_{\rm FDM}$ and it could be ignored in analysis of a railgun, especially at low velocity. What should be noted is that the velocity scaling factor must be controlled above about one-quarter to avoid the nonlinear field.

Performance improvement is taken as the primary goal in the asset management. Advanced data analysis is needed to efficiently integrate condition monitoring data into the operation and maintenance. Intelligent stress and condition indices have been developed for control and condition monitoring by combining generalized norms with efficient nonlinear scaling. These nonlinear scaling methodologies can also be used to handle performance measures used for management since management oriented indicators can be presented in the same scale as intelligent condition and stress indices. Performance indicators are responses of the process, machine or system to the stress contributions analyzed from process and condition monitoring data. Scaled values are directly used in intelligent temporal analysis to calculate fluctuations and trends. All these methodologies can be used in prognostics and fatigue prediction. The meanings of the variables are beneficial in extracting expert knowledge and representing information in natural language. The idea of dividing the problems into the variable specific meanings and the directions of interactions provides various improvements for performance monitoring and decision making. The integrated temporal analysis and uncertainty processing facilitates the efficient use of domain expertise. Measurements can be monitored with generalized statistical process control (GSPC) based on the same scaling functions.

The linear Reissner–Mindlin membrane-bending plate model is the rigourous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ 𝔰𝔬(3). We also provide formal calculations for other combinations of scalings by retrieving other plate models previously proposed in the literature by formal asymptotic methods as corresponding Γ-limits. No boundary conditions on the microrotations are prescribed.

We investigate the asymptotic behavior of solutions to semi-classical Schroedinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras., Comment: 13 pages; Version 2: Added Remark 2.2

Discounting of delayed and probabilistic rewards was examined in two relatively large samples (N s > 100). For both types of rewards, a hyperbola-like discounting function provided good fits to individual data. Amount of reward had opposite effects on temporal and probability discounting: Smaller delayed rewards were discounted more steeply than larger delayed rewards, whereas larger probabilistic rewards were discounted more steeply than smaller probabilistic rewards. The nonlinear scaling parameter of the hyperbola-like function was larger for larger probabilistic rewards, but did not vary with the amount of delayed reward. Taken together, these findings suggest that despite the similar form of the temporal and probability discounting functions, separate processes may underlie the discounting of delayed and probabilistic rewards. Finally, weak to moderate positive correlations were observed between the discounting of delayed and probabilistic rewards. This finding is inconsistent with the notion of an ‘‘impulsiveness’’ trait that links an inability to delay gratification with a tendency to gamble and take risks. 2003 Elsevier B.V. All rights reserved.

An offset nonlinear scaling is developed for the ELMy H-mode by analysing the ITER H-mode database ITERH.DB2. The offset part of the stored energy is determined by the MHD stability of ELM, and the incremental confinement time of a nonlinear function of heating power is determined by the gyro-Bohm-like transport of the core plasma. This scaling predicts a lower confinement time for ITER than that predicted by general power-law scaling.

The constituents of any network glass can be broadly classified as either network formers or network modifiers. Network formers, such as SiO2, Al2O3, B2O3, P2O5, etc., provide the backbone of the glass network and are the primary source of its rigid constraints. Network modifiers play a supporting role, such as charge stabilization of the network formers or alteration of the network topology through rupture of bridging bonds and introduction of floppy modes. The specific role of the modifiers depends on which network formers are present in the glass and the relative free energies of modifier interactions with each type of network former site. This variation of free energy with modifier speciation is responsible for the so-called mixed network former effect, i.e., the nonlinear scaling of property values in glasses having fixed modifier concentration but a varying ratio of network formers. In this paper, a general theoretical framework is presented describing the statistical mechanics of modifier speciation in mixed network glasses. The model provides a natural explanation for the mixed network former effect and also accounts for the impact of thermal history and relaxation on glass network topology.

The translational hydration dynamics within 0.5-1.5 nanometers (nm) of the surface of a DPPC liposome – a model biomacromolecular surface – is analyzed by the recently developed Overhauser dynamic nuclear polarization (ODNP) technique. We find that dramatic changes to the bulk solvent cause only weak changes in the surface hydration dynamics. Specifically, both a >10-fold increase in bulk viscosity and the restriction of diffusion by confinement on a multiple-nm length-scale change the local translational diffusion coefficient of the surface water surrounding the lipid bilayer by less than 2.5-fold. By contrast, previous ODNP studies have shown that changes to the biomacromolecular surface induced by folding, binding, or aggregation can cause local hydration dynamics to vary by factors of up to 30.1,2 We suggest that the surface topology and chemistry at the ≤ 1.5 nm scale, rather than the characteristics of the bulk fluid, nearly exclusively determine the surface hydration dynamics of aqueous macromolecular solutes.

Scaling method has been used widely in railgun technology. But nonlinear problem is seldom studied because of the complexity and uncertainty. In order to employ the scaling method better, the paper brings the nonlinear drag model to the solid armature railgun circuit.

An algorithm for unconstrained minimization is proposed which is invariant to the nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for general use. It compares favorably in numerical tests (eight test functions, dimensionality up to 1000) with the 1975 Dixon algorithm on which this new algorithm is based.

The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

Kayser, Bengt, Andrea Aliverti, Riccardo Pellegrino, Raffaele Dellaca, Marco Quaranta, Pasquale Pompilio, Giuseppe Miserocchi, and Annalisa Cogo. Comparison of a visual analogue scale and Lake Louise symptom scores for acute mountain sickness. High Alt. Med. Biol. 11:69-72, 2010.-Assessment of the presence and severity of acute mountain sickness (AMS) is based on subjective reporting of the sensation of symptoms. The Lake Louise symptom scoring system (LLS) uses categorical variables to rate the intensity of AMS-related symptoms (headache, gastrointestinal distress, dizziness, fatigue, sleep quality) on 4-point ordinal scales; the sum of the answers is the LLS self-score (range 0-15). Recent publications indicate a potential for a visual analogue scale (VAS) to quantify AMS. We tested the hypothesis that overall and single-item VAS and LLS scores scale linearly. We asked 14 unacclimatized male subjects [age 41 (14), mean (SD) yr; height 176 (3)cm; weight 75 (9)kg] who spent 2 days at 3647m and 4 days at 4560m to fill out LLS questionnaires, with a VAS for each item (i) and a VAS for the overall (o) sensation of AMS, twice a day (n=172). Even though correlated (r=0.84), the relationship between LLS(o) and VAS(o) was distorted, showing a threshold effect for LLS(o) scores below 5, with most VAS(o) scores on one side of the identity line. Similar threshold effects were seen for the LLS(i) and VAS(i) scores. These findings indicate nonlinear scaling characteristics that render difficult a direct comparison of studies done with either VAS or LLS alone. © Copyright 2010, Mary Ann Liebert, Inc. 2010.

The formation of multiplexed phase-only holograms with more weighted phase functions creates spurious cross terms and nonlinear scaling. We extend previously reported work [Appl. Opt. 25, 3767 (1986)] by proposing a normal method to analyze multiplexed holograms mathematically. We show that the output of holograms with any number weighted phase function can be written as a new linear combination for the original phase function with new weights. The relationship between the original weights and the new weights is developed for real-time optimization of hologram performance. We focus on the analysis of two and three multiplexed holograms to demonstrate the effectiveness of this approach.

We report on a systematic investigation of the critical fluctuations in the complex conductivity of epitaxially grown ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ films for $T\ensuremath{\lesssim}{T}_{c}$ using a two-coil inductive technique at zero applied field. We observe the static three-dimensional (3D) $\mathrm{XY}$ critical exponent in the superfluid density near ${T}_{c}.$ Linear scaling analysis close to the critical temperature yields a dynamic critical exponent of $z\ensuremath{\approx}2.0$ for small drive currents, but nonlinear effects are seen to be important. At ${T}_{c},$ a nonlinear scaling analysis also yields a 3D dynamic exponent of $z=2.0\ifmmode\pm\else\textpm\fi{}0.1.$

The thermodynamic behavior of a fluid near a vapor-liquid and, hence, asymmetric critical point is discussed within a general ``complete'' scaling theory incorporating pressure mixing in the nonlinear scaling fields as well as corrections to scaling. This theory allows for a Yang-Yang anomaly in which \mu_{\sigma}^{\prime\prime}(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when T\to T_{\scriptsize c}; it also generates a leading singular term, |t|^{2\beta}, in the coexistence curve diameter, where t\equiv (T-T_{\scriptsize c}) /T_{\scriptsize c}. The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which \chi^{(k)}\equiv \chi(\rho,T)/\rho^{k} (with \chi = \rho^{2} k_{\scriptsize B}TK_{T}) and C_{V}^{(k)}\equiv C_{V}(\rho,T)/\rho^{k} are maximal at fixed T, is carefully elucidated. These results are useful for analyzing simulations and experiments, since particular, nonuniversal values of k specify loci that approach the critical density most rapidly and reflect the pressure-mixing coefficient. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte. For comparison, a discussion of the classical (or Landau) theory is presented briefly and various interesting loci are determined explicitly and illustrated quantitatively for a van der Waals fluid., Comment: 21 pages in two-column format including 8 figures

The objectives for this year are the development of manual techniques for the selection of piecewise linear structure functions, to evaluate their utility for the development of statistical forecast models and to evaluate their value for the improvement of statistical forecast equations.

In 3 experiments, the authors examined movement space—time variability as a function of the force-time properties of the initial impulse in a movement timing task. In the range of motion and movement time task conditions, peak force, initial rate of force, and force duration were manipulated either independently or in combination across a range of parameter values. The findings showed that (a) impulse variability is predicted well by the elaboration of the isometric force variability scaling functions of L. G Carlton, K. H. Kim, Y. T. Liu, and K. M. Newell (1993) to movement, and (b) the movement spatial and temporal outcome variability are complementary and well predicted by an equation treating the variance of force and time in Newton's 2nd law as independent random variables. Collectively, the findings suggest that movement outcome variability is the product of a coherent space—time function that is driven by the nonlinear scaling of the force—time properties of the initial impulse.

The linear Reissner–Mindlin membrane-bending plate model is the rigourous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ 𝔰𝔬(3). We also provide formal calculations for other combinations of scalings by retrieving other plate models previously proposed in the literature by formal asymptotic methods as corresponding Γ-limits. No boundary conditions on the microrotations are prescribed.

The long-range aim of this work was to improve our understanding of the atmosphere through the development of new methods for forecasting and for extracting information from raw time series data. The specific aim of this project was to develop and refine nonlinear forecast methods as tools to analyze atmospheric field observations with a view toward the following: (1) to diagnose the underlying dynamic mechanisms driving barometric time series; (2) to determine the effectiveness of nonlinear predictive methods in forecasting atmospheric phenomena; (3) to document and better understand the scale dependence of predictability in atmospheric data.

We report on calculations of the translational and rotational short-time self-diffusion coefficients $D^t_s$ and $D^r_s$ for suspensions of charge-stabilized colloidal spheres. These diffusion coefficients are affected by electrostatic forces and many-body hydrodynamic interactions (HI). Our computations account for both two-body and three-body HI. For strongly charged particles, we predict interesting nonlinear scaling relations $D^t_s\propto 1-a_t\phi^{4/3}$ and $D^r_s\propto 1-a_r\phi^2$ depending on volume fraction $\phi$, with essentially charge-independent parameters $a_t$ and $a_r$. These scaling relations are strikingly different from the corresponding results for hard spheres. Our numerical results can be explained using a model of effective hard spheres. Moreover, we perceptibly improve the known result for $D^t_s$ of hard sphere suspensions., Comment: 8 pages, LaTeX, 3 Postscript figures included using epsf

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionw≔u−v≥0 and for small effective disorder coupling\(\bar v(l)\) on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as Open image in new window for\(\bar v(l) \ll 1\).