Single Scaling Research Articles

Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation.

We systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series, which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations. First, we decompose artificial long-range power-law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series, and we study their correlation properties. We find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series. Such expressions are necessary for modeling surrogate time series with desired scaling properties. Next, we study linear and nonlinear correlation properties of series composed as products of independent magnitude and sign series. These surrogate series can be considered as a zero-order approximation to the analysis of the coupling of magnitude and sign in real data, a problem still open in many fields. We find analytical results for the scaling behavior of the composed series as a function of the correlation exponents of the magnitude and sign series used in the composition, and we determine the ranges of magnitude and sign correlation exponents leading to either single scaling or to crossover behaviors. Finally, we obtain how the linear and nonlinear properties of the composed series depend on the correlation exponents of their magnitude and sign series. Based on this information we propose a method to generate surrogate series with controlled correlation exponent and multifractal spectrum.

Bioinformatic scaling of allosteric interactions in biomedical isozymes

Allosteric (long-range) interactions can be surprisingly strong in proteins of biomedical interest. Here we use bioinformatic scaling to connect prior results on nonsteroidal anti-inflammatory drugs to promising new drugs that inhibit cancer cell metabolism. Many parallel features are apparent, which explain how even one amino acid mutation, remote from active sites, can alter medical results. The enzyme twins involved are cyclooxygenase (aspirin) and isocitrate dehydrogenase (IDH). The IDH results are accurate to 1% and are overdetermined by adjusting a single bioinformatic scaling parameter. It appears that the final stage in optimizing protein functionality may involve leveling of the hydrophobic limits of the arms of conformational hydrophilic hinges.

On scaling of soft-thresholding estimator

LASSO is known to have a problem of excessive shrinkage at a sparse representation. To analyze this problem in detail, in this paper, we consider a positive scaling for soft-thresholding estimators that are LASSO estimators in an orthogonal regression problem. We especially consider a non-parametric orthogonal regression problem which includes wavelet denosing. We first gave a risk (generalization error) of LARS (least angle regression) based soft-thresholding with a single scaling parameter. We then showed that an optimal scaling value that minimizes the risk under a sparseness condition is 1+O(logn/n), where n is the number of samples. The important point is that the optimal value of scaling is larger than one. This implies that expanding soft-thresholding estimator shows a better generalization performance compared to a naive soft-thresholding. This also implies that a risk of LARS-based soft-thresholding with the optimal scaling is smaller than without scaling. We then showed their difference is O(logn/n). This also shows an effectiveness of the introduction of scaling. Through simple numerical experiments, we found that LARS-based soft-thresholding with scaling can improve both of sparsity and generalization performance compared to a naive soft-thresholding.

Influence of the aspect ratio and boundary conditions on universal finite-size scaling functions in the athermal metastable two-dimensional random field Ising model.

This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂.

Universal Scaling of Spectral Fluctuation Transitions for Interacting Chaotic Systems.

The statistical properties of interacting strongly chaotic systems are investigated for varying interaction strength. In order to model tunable entangling interactions between such systems, we introduce a new class of random matrix transition ensembles. The nearest-neighbor-spacing distribution shows a very sensitive transition from Poisson statistics to those of random matrix theory as the interaction increases. The transition is universal and depends on a single scaling parameter only. We derive the analytic relationship between the model parameters and those of a bipartite system, with explicit results for coupled kicked rotors, a dynamical systems paradigm for interacting chaotic systems. With this relationship the spectral fluctuations for both are in perfect agreement. An accurate approximation of the nearest-neighbor-spacing distribution as a function of the transition parameter is derived using perturbation theory.

Imperceptibility—Robustness tradeoff studies for ECG steganography using Continuous Ant Colony Optimization

ECG Steganography ensures protection of patient data when ECG signals embedded with patient data are transmitted over the internet. Steganography algorithms strive to recover the embedded patient data entirely and to minimize the deterioration in the cover signal caused by the embedding. This paper presents a Continuous Ant Colony Optimization (CACO) based ECG Steganography scheme using Discrete Wavelet Transform and Singular Value Decomposition. Quantization techniques allow embedding the patient data into the ECG signal. The scaling factor in the quantization techniques governs the tradeoff between imperceptibility and robustness. The novelty of the proposed approach is to use CACO in ECG Steganography, to identify Multiple Scaling Factors (MSFs) that will provide a better tradeoff compared to uniform Single Scaling Factor (SSF). The optimal MSFs significantly improve the performance of ECG steganography which is measured by metrics such as Peak Signal to Noise Ratio, Percentage Residual Difference, Kullback–Leibler distance and Bit Error Rate. Performance of the proposed approach is demonstrated on the MIT-BIH database and the results validate that the tradeoff curve obtained through MSFs is better than the tradeoff curve obtained for any SSF. The results also advocate appropriate SSFs for target imperceptibility or robustness.

Improving the Network Scale-Up Estimator: Incorporating Means of Sums, Recursive Back Estimation, and Sampling Weights.

Researchers interested in studying populations that are difficult to reach through traditional survey methods can now draw on a range of methods to access these populations. Yet many of these methods are more expensive and difficult to implement than studies using conventional sampling frames and trusted sampling methods. The network scale-up method (NSUM) provides a middle ground for researchers who wish to estimate the size of a hidden population, but lack the resources to conduct a more specialized hidden population study. Through this method it is possible to generate population estimates for a wide variety of groups that are perhaps unwilling to self-identify as such (for example, users of illegal drugs or other stigmatized populations) via traditional survey tools such as telephone or mail surveys—by asking a representative sample to estimate the number of people they know who are members of such a “hidden” subpopulation. The original estimator is formulated to minimize the weight a single scaling variable can exert upon the estimates. We argue that this introduces hidden and difficult to predict biases, and instead propose a series of methodological advances on the traditional scale-up estimation procedure, including a new estimator. Additionally, we formalize the incorporation of sample weights into the network scale-up estimation process, and propose a recursive process of back estimation “trimming” to identify and remove poorly performing predictors from the estimation process. To demonstrate these suggestions we use data from a network scale-up mail survey conducted in Nebraska during 2014. We find that using the new estimator and recursive trimming process provides more accurate estimates, especially when used in conjunction with sampling weights.

Critical behavior in polycrystalline La0.7Sr0.3CoO3 from bulk magnetization study

The critical behavior of hole-doped perovskite cobaltite La0.7Sr0.3CoO3 has been investigated around the second-order paramagnetic-ferromagnetic (PM-FM) phase transition based on the static magnetization. Reliable critical exponents (β = 0.272 ± 0.001, γ = 1.291 ± 0.004, and δ = 5.54 ± 0.02 with critical point TC = 227.2 ± 0.2 K) have been determined by using different techniques, including the Modified Arrott plot, the Kouvel–Fisher method, and critical isotherm analysis. The obtained critical exponents not only obey the Widom relation δ = 1+γ/β, but also can collapse the magnetization data M(H,T) into two curves below and above TC following a single scaling equation M(H,ε) = εβf±(H/εβ+γ), which implies the reliability and accuracy of the exponents. Temperature variation of the effective exponents resemble with those for disordered ferromagnets. The exponents analysis related to the magnetocaloric effect is studied. The field dependence of the relative cooling power (RCP) is found to obey RCP∝H1+1/δ with the exponent δ. The asymptotic critical exponents (βeff and γeff) are close to those predicted by 3D-Ising model with the exchange interaction J(r) decaying as r−4.97 in the system, which reflects the existence of short-range FM coupling.

Critical behavior study in GdNiAl2 intermetallic compound

The critical behavior of the ternary intermetallic compound GdNiAl2 has been investigated around the second-order paramagnetic–ferromagnetic (PM–FM) phase transition TC based on the static magnetization data. Both the Modified Arrott plot and the Kouvel-Fisher method yield nearly the same critical exponents β = 0.368 ± 0.006 and γ = 1.042 ± 0.001, along with TC = 28.34 ± 0.01 K. Critical isotherm analysis at 30 K gives the result for the critical exponent δ = 3.59 ± 0.04. All three obtained critical exponents obey the Widom relation δ = 1 + γ/β and can also collapse the isothermal magnetization M-H-T data into two branches below and above TC in accordance with the single scaling equation M(H, ε) = εβf±(H/εβ+γ). This implies the self-consistence and accuracy of the exponents. The asymptotic critical exponents (βeff and γeff) are found to approach those of mean-field model, reflecting the existence of long-range magnetic interactions. The exchange interaction J(r) is found to decay as r−4.57 in the system. The long-range FM coupling in the system is suggested to be governed by the synergetic effect of hybridization and RKKY interactions.

“Equivalent” permeability and flow in compliant porous media

Resin flow modeling for liquid composite molding processes is generally based on assumptions of rigid porous media. This is invalid for process variations utilizing compliant mold. Yet the models built on rigid porous media assumption are used with some success in analyzing such infusions.Previous work showed that for certain porous media the one dimensional flow patterns are similar to those in rigid porous media and the deformation effects can be included in a scaling factor for permeability.This note analyzes the one-dimensional linear and radial flows in porous media with generic constitutive relations between resin pressure, thickness and permeability. It shows that as long as the deformation remains moderate, the effect of deforming porous medium may be incorporated in a single scaling factor for material permeability. This scaling factor depends on material and applied injection pressure, but does not change with time, flow-front position or type of infusion (linear or radial).

Strong and weak localization in a ballistic quantum chain

We study coherent electron transport in a quantum network or superlattice formed by connecting chaotic ballistic quantum dots via barriers of arbitrary transparencies in a chain topology. We show that the emergence of localization effects, both weak and strong, depend on the way the infinite dot scaling limit is taken. In the localized regime, we found evidence of single parameter scaling and deviations from uniformity in the distribution of the unitary matrices in the polar decomposition of the system’s transfer-matrix. In the metallic regime, we show that recent predictions of anomalous properties in a double scaling limit, in which the barriers’ transparencies are changed along with the number of dots, can be interpreted as a two-parameter scaling theory, which cannot be derived from the Dorokhov–Mello–Pereyra–Kumar equation.

Mammalian Brains Are Made of These: A Dataset of the Numbers and Densities of Neuronal and Nonneuronal Cells in the Brain of Glires, Primates, Scandentia, Eulipotyphlans, Afrotherians and Artiodactyls, and Their Relationship with Body Mass

Comparative studies amongst extant species are one of the pillars of evolutionary neurobiology. In the 20th century, most comparative studies remained restricted to analyses of brain structure volume and surface areas, besides estimates of neuronal density largely limited to the cerebral cortex. Over the last 10 years, we have amassed data on the numbers of neurons and other cells that compose the entirety of the brain (subdivided into cerebral cortex, cerebellum, and rest of brain) of 39 mammalian species spread over 6 clades, as well as their densities. Here we provide that entire dataset in a format that is readily useful to researchers of any area of interest in the hope that it will foster the advancement of evolutionary and comparative studies well beyond the scope of neuroscience itself. We also reexamine the relationship between numbers of neurons, neuronal densities and body mass, and find that in the rest of brain, but not in the cerebral cortex or cerebellum, there is a single scaling rule that applies to average neuronal cell size, which increases with the linear dimension of the body, even though there is no single scaling rule that relates the number of neurons in the rest of brain to body mass. Thus, larger bodies do not uniformly come with more neurons - but they do fairly uniformly come with larger neurons in the rest of brain, which contains a number of structures directly connected to sources or targets in the body.

Critical behavior and magnetic entropy change in Nd0.7Sr0.1Ba0.1Ca0.1MnO3−δ perovskite manganite

The aim of our study was to investigate the critical exponents of Nd0.7Sr0.1Ba0.1Ca0.1MnO3−δ material around its paramagnetic to ferromagnetic phase transition. Reliable critical exponents i.e. β=0.355, γ=1.329, and δ=4.867 at the critical temperature TC=117K were refined using modified Arrott plot and Kouvel–Fisher methods. The critical exponent δ=4.760±0.129 was further separately determined from the isothermal magnetization data. Finally these critical exponents fulfill the Widom scaling relation δ=1+γ/β. Based on these analysis, the magnetization–field–temperature (M–H–T) data around TC collapses into two independent curves obeying the single scaling equation M(H,ε)=|ε|βf±(H/|ε|β+γ), with ε=(T−TC)/TC is the reduced temperature. Once again, the critical exponents are confirmed by the field dependence of the magnetic entropy change relation ∆SM|T=TC ∞Hn with n=1+(β−1)/(β+1). The obtained critical exponents for Nd0.7Sr0.1Ba0.1Ca0.1MnO3−δ manganite are in accordance with the prediction of the 3D-Heisenberg model with short-range magnetic interactions. The temperature dependence of specific heat and magnetic entropy change ΔSM further supports second order PM–FM phase transition and shed light the A-site-disordered perovskite effect on the magnetocaloric properties.

Quantum criticality and emergence of the T/B scaling in strongly correlated metals

A new type of scaling observed in heavy-electron metal β-YbAlB4, where the magnetic susceptibility is expressed as a single scaling function of the ratio of temperature T and magnetic field B over four decades, is examined theoretically. We develop the mode-coupling theory for critical Yb-valence fluctuations under a magnetic field, verifying that the T/B scaling behavior appears near the QCP of the valence transition. Emergence of the T/B scaling indicates the presence of the small characteristic temperature of the critical Yb-valence fluctuation due to the strong local correlation effect. It is discussed that the T/B scaling as well as the unconventional criticality is explained from the viewpoint of the quantum valence criticality in a unified way.

Investigation of the critical behaviour and magnetocaloric effect in γ-Fe49Ni29Cr22 disordered austenitic stainless steel alloy by using the field dependence of magnetic entropy change

We have reported here the critical behaviour and magnetocaloric effect (MCE) around the ferromagnetic (FM) → paramagnetic (PM) phase transition temperature (Tc) in a γ-Fe49Ni29Cr22 disordered austenitic stainless steel alloy system through detailed ac and dc magnetization study. The value of critical exponents have been estimated using the recorded M−H isotherms SQUID data using different techniques such as modified Arrott plots, Kouvel–Fisher plots, and critical isotherm analysis. The critical exponents values of γ-Fe49Ni29Cr22 alloy are found to be β = 0.440 (7), γ = 1.340 (16) and δ = 3.336 (5) with Tc = (124.82 ± 0.01) K. From the detailed DC magnetization study, the observed non-hysteretic M-T data in FCC and FCW mode, positive slope in the entire range of the Arrott plots near TC (Banerjee criterion), it confirms a second order FM → PM phase transition at TC. Though the nature of this transition is found to be of second order, the estimated critical exponent values β, γ, and δ are in between the theoretically predicted values for 3d Heisenberg and mean-field spin interaction models. However, it is important that these critical exponents obeyed the single scaling relations [M(H,ε)=|ε|βf±(H,|ε|−(β+γ))] indicating renormalization of interactions around the Curie temperature (TC). Temperature variation in effective critical exponents (βeff and γeff) resemble with those for various disordered ferromagnets as found in our γ-Fe49Ni29Cr22 alloy system. We have also estimated the normal MCE with maximum entropy change of 1.8 J/kg-K at 125.5 K under an external magnetic field change of 5 T in the austenite phase of the alloy.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation.

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

The density and thermal expansion of dysprosium in the temperature range 110–1950 K

The results of dilatometric studies of thermal coefficient of linear expansion of dysprosium in the temperature range 110-1950 K are presented. The measurements were performed with an accuracy of (1.5-2.0)·10-7 K-1. The approximation dependences of thermal coefficient of linear expansion were obtained. The reference tables of dysprosium thermal properties for the range 110-1950 K of solid and liquid states were constructed using the previous results obtained by the gamma method. The character of thermal coefficient of linear expansion changes in the area of the Neel point has been established. Its critical exponents and the critical amplitudes have been determined. It is shown that both above and below the Neel temperature, the experimental data cannot be processed with a single scaling equation. A comparison with the published data has been performed.

The application of life-history and predation allometry to population dynamics to predict the critical density of extinction

Strong Allee effects entail the existence of the Allee threshold A, a population density, below which the population will go extinct, even in absence of environmental stochasticity. To examine Allee effects by observation or experiment is, however, very difficult. This study provides a mechanistic model to quantify Allee effects by breaking down population dynamics into three density-dependent ecological processes: the biomass fluxes due to production, natural death, and predation. The model is calibrated by empirical life-history scalings to species body mass M with a temperature of 20°C. Calibration reveals three new findings: (i) a single scaling of biomass production at the optimal or steady status, smooth across body mass regardless of reproduction pattern, (ii) a positive response of biomass production to population density, and (iii) allometry regarding predation process. Calculations demonstrate a new A scaling to M with an identical exponent of carrying capacity K scaling. In particular, a constant ratio A/K is of order 0.01, relatively stable to environmental stochasticity. This new protocol could be of wide applicability to invasion biology and conservation biology. The modeling methodology and revealed A–K linearity would be broadly applicable beyond Tuesday Lake, which is used as a reference of carrying capacity in this study. This provides a convenient way to estimate a system-dependent Allee threshold given specific carrying capacity. As a specific example, we show its implication for evaluating ballast water discharge standards in temperate mesotrophic water.

Size‐related scaling of tree form and function in a mixed‐age forest

Summary Many morphological, physiological and ecological traits of trees scale with diameter, shaping the structure and function of forest ecosystems. Understanding the mechanistic basis for such scaling relationships is key to understanding forests globally and their role in Earth's changing climate system. Here, we evaluate theoretical predictions for the scaling of nine variables in a mixed‐age temperate deciduous forest (CTFS‐ForestGEO forest dynamics plot at the Smithsonian Conservation Biology Institute, Virginia, USA) and compare observed scaling parameters to those from other forests world‐wide. We examine fifteen species and various environmental conditions. Structural, physiological and ecological traits of trees scaled with stem diameter in a manner that was sometimes consistent with existing theoretical predictions – more commonly with those predicting a range of scaling values than a single universal scaling value. Scaling relationships were variable among species, reflecting substantive ecological differences. Scaling relationships varied considerably with environmental conditions. For instance, the scaling of sap flux density varied with atmospheric moisture demand, and herbivore browsing dramatically influenced stem abundance scaling. Thus, stand‐level, time‐averaged scaling relationships (e.g., the scaling of diameter growth) are underlain by a diversity of species‐level scaling relationships that can vary substantially with fluctuating environmental conditions. In order to use scaling theory to accurately characterize forest ecosystems and predict their responses to global change, it will be critical to develop a more nuanced understanding of both the forces that constrain stand‐level scaling and the complexity of scaling variation across species and environmental conditions.

Critical phenomena in La0.6Pr0.1Sr0.3MnO3 perovskite manganese oxide

We report a study of the critical phenomena of perovskite-manganite compound La0.6Pr0.1Sr0.3MnO3 around the Curie temperature. Experimental results based on magnetic measurements using Banerjee criterion reveals that the sample exhibits a second-order paramagnetic–ferromagnetic transition. The critical behavior analysis and the Kouvel–Fisher method suggests that the critical phenomena around the critical point can be correctly described by the 3D-Heisenberg model. Critical exponents were estimated and found β=0.354±0.009 and γ=1.264±0.035 at TC=325.5±0.443K. The critical exponent δ is determined separately from the isothermal magnetization at TC and evaluated to δ=4.934±0.0004. These critical exponents obey the Widom scaling relation δ=1‏+γ/β. Based on the critical exponents, the magnetization–field–temperature (M–H–T) data around TC collapses into two curves obeying the single scaling equationM(H,ε)=|ε|βf±(H/|ε|β+γ) where ε=(T−TC)/TC is the reduced temperature.