Law Exponent Research Articles

Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood.

Pulmonary artery (PA) morphometry has been extensively explored in adults, with particular focus on intra-acinar arteries. However, scaling law relationships for length and diameter of extensive preacinar PAs by age have not been previously reported for in vivo human data. To understand preacinar PA growth spanning children to adults, we performed morphometric analyses of all PAs visible in the computed tomography (CT) and magnetic resonance (MR) images from a healthy subject cohort [n = 16; age: 1-51 yr; body surface area (BSA): 0.49-2.01 m2]. Subject-specific anatomic PA models were constructed from CT and MR images, and morphometric information-diameter, length, tortuosity, bifurcation angle, and connectivity-was extracted and sorted into diameter-defined Strahler orders. Validation of Murray's law, describing optimal scaling exponents of radii for branching vessels, was performed to determine how closely PAs conform to this classical relationship. Using regression analyses of vessel diameters and lengths against orders and patient metrics (BSA, age, height), we found that diameters increased exponentially with order and allometrically with patient metrics. Length increased allometrically with patient metrics, albeit weakly. The average tortuosity index of all vessels was 0.026 ± 0.024, average bifurcation angle was 28.2 ± 15.1°, and average Murray's law exponent was 2.92 ± 1.07. We report a set of scaling laws for vessel diameter and length, along with other morphometric information. These provide an initial understanding of healthy structural preacinar PA development with age, which can be used for computational modeling studies and comparison with diseased PA anatomy.NEW & NOTEWORTHY Pulmonary artery (PA) morphometry studies to date have focused primarily on large arteries and intra-acinar arteries in either adults or children, neglecting preacinar arteries in both populations. Our study is the first to quantify in vivo preacinar PA morphometry changes spanning infants to adults. For preacinar arteries > 1 mm in diameter, we identify scaling laws for vessel diameters and lengths with patient metrics of growth and establish a healthy PA morphometry baseline for most preacinar PAs.

Taylor's Law in Innovation Processes.

Taylor’s law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor’s law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson–Dirichlet processes and demonstrate how a non-trivial Taylor’s law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus); (ii) an online music website (Last.fm); (iii) Twitter hashtags; (iv) an online collaborative tagging system (Del.icio.us). While Taylor’s law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor’s law is a fundamental complement to Zipf’s and Heaps’ laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.

Stein’s Method for Asymmetric $$\alpha $$-stable Distributions, with Application to the Stable CLT

This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the Wasserstein distance between $Z$ and any integrable random variable $X$, in terms of an operator that reduces to the classical fractional Laplacian in the symmetric case. Then, in the second part we apply the aforementioned bound to compute error rates in the stable central limit theorem, when the entries are in the domain $\mathcal{D}_\alpha$ of normal attraction of a stable law of exponent $\alpha$. To conclude, we study the specific case where the entries are Pareto like multiplied by a slowly varying function, which provides an example of random variables that do not belong to $\mathcal{D}_\alpha$, but for which our approach continues to apply.

Investigation of structural and physical properties of Eu3+ ions substituted Ni0.4Cu0.2Zn0.4Fe2O4 spinel ferrite nanoparticles prepared via sonochemical approach

Green and facile process for Ni0.4Cu0.2Zn0.4Fe2−xEuxO4 (x = 0.00–0.10) spinel ferrite nanoparticles (SNPs) prepared via ultrasonic irradiation (without any post annealing process) has been deeply investigated. The influence of Eu3+ substitutions on the structure, morphological, optical, magnetic, electrical and dielectric traits of NiCuZn SNPs was assessed. Tauc plots revealed direct optical band gaps in a very tight interval of 1.86–1.90 eV. Magnetization measurements exposed a superparamagnetic behavior at room temperature and below the blocking temperature (TB) a superparamagnetic-ferromagnetic transition was noticed. The saturation magnetization (Ms) value is highest for pure Ni0.4Cu0.2Zn0.4Fe2O4 (i.e. x = 0.00) SNP with Ms ~ 58.9 emu/g at room temperature. The saturation magnetization (Ms) declines with rising Eu3+ substituting content. AC conductivity decreases as a function of exponent power base law. Maximum variation in dc conductivity is observed to be around the substitution ratio of x = 0.02. It is found that activation energy is highly dependent on both Eu ions substitution ratios and temperature ranges. The frequency dependence of dielectric functions is explained by Koop's models based on Maxwell-Wagner theory.

Electrical transport properties of polyaniline grafted radiation crosslinked chitosan

Present work reports about electrical properties of polyaniline (PANI) grafted with electron beam crosslinked chitosan. Measurement of temperature dependent dc & ac conductivity shows a significant improvement in the ac and dc conductivity after doping with 1 M HCl for different time intervals. The dc conductivity results were analyzed using Mott’s variable range hopping mechanism. The ac conductivity of grafted polymer obeys power law and behavior of frequency exponent‘s’ has been interpreted by the correlated barrier hopping (CBH) model. The variation of dielectric constant with temperature and frequency is consistent with the Debye type dispersion.

Fast scalable construction of ([compressed] static | minimal perfect hash) functions

Recent advances in the analysis of random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing techniques. The main obstacle for any practical application of these results is the time required to solve such linear systems: despite they can be made very small, the computation is still too slow to be feasible.In this paper, we describe in detail a number of heuristics and programming techniques to speed up the solution of these systems by orders of magnitude, making the overall construction competitive with the standard and widely used MWHC technique, which is based on hypergraph peeling. In particular, we introduce broadword programming techniques for fast equation manipulation and a lazy Gaussian elimination algorithm. We also describe a number of technical improvements to the data structure which further reduce space usage and improve lookup speed.Our implementation of these techniques yields a minimal perfect hash function data structure occupying 2.24 bits per element, compared to 2.68 for MWHC-based ones, and a static function data structure which reduces the multiplicative overhead from 1.23 to 1.024. For functions whose output has low entropy, we are able to implement feasibly for the first time the Hreinsson–Krøyer–Pagh approach, which makes it possible, for example, to store a function with an output of 106 values distributed following a power law of exponent 2 in just 2.76 bits per key instead of 20.

Instrumento de medición para diagnosticar las habilidades algebraicas de los estudiantes en el Curso de Cálculo Diferencial en ingeniería

A highly reliable algebraic skill measurement instrument with content and approach validity was developed. Its content focusses on the algebraic skills engineering students require to successfully follow a Differential Calculus Course. A team of 10 teachers, each with minimum of a master’s degree and teaching experience in differential calculus, participated in the design of this instrument. The measurement instrument is a large-scale multiple-choice criteria test comprising 25 test items. Its quality is described and analysed on the basis of the answers given by engineering students during the first and second semesters of the 2018-2019 academic year. The results show that topics that can predict student success and have the greatest power of discrimination in the measurement instrument are strongly related to skills students acquire in primary and secondary education, such as operating with fractions and the laws of exponents. It was also found that the main shortcomings in the algebraic skills of students are rationalisation, division of polynomials, factoring sums, and difference of cubes.

Analysis of Free Vibrations of Axisymmetric Functionally Graded Generalized Viscothermoelastic Cylinder Using Series Solution

The analysis of free vibrations of axisymmetric functionally graded isotropic viscothermoelastic hollow cylinder has been investigated in the radial direction. The material of viscothermoelastic cylinder has been assumed to be graded in the radial direction due to simple exponent law. The governing partial differential equations are transformed into ordinary differential equations with th e help of time harmonic vibrations. The extended power series solution of matrix Frobenius method has been applied to derive the analytical solutions for stresses, displacement and temperature change. The frequency equations of various types of modes of vibrations have been derived in a compact form. To investigate the numerical features of vibrations, the analytical results of frequency equations have been further solved with the help of fixed-point numerical iteration technique using MATLAB software tools. The polymethyl methacrylate material has been used for numerical computations. The numerical results have been presented for frequency shift, natural frequencies, thermoelastic damping, stresses, displacement and variation of temperature. With the increase in the values of grading index, variation of vibrations in field functions go on decreasing. The numerical results show alternate variations in homogenous materials in contrast to inhomogeneous materials. The behaviour of deformation, temperature change, frequency shift and thermoelastic damping have been monitored (increase or decrease) with the help of grading index (in-homogeneity parameter).

Education for Sustainability: Lessons from Living Systems Governance

Abstract To survive that is to eat and not to be eaten. Whatever its spatial and temporal level of organisation, every living system owns 7 invariant capacities (the gauge invariance paradigm). Emerging by embedments and juxtapositions of previous systems, every living system-of-systems is both dependent and independent from its new global level of organisation and past and present local situations of emergence. Mass growth governs growth phase duration. Local actors, modules of past, present and new modules of modules become mutually integrated (percolation process) into a new Whole through their merging into an ARMSADA (Association for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages). Reversely (systemic constructal law) the global Whole is integrating the local parceners. Whatever the organisation level, the living systems obey the same principle of evolution and emergence, the volume and time of generation of the adult system obey a correlation: The mass controlled duration of acquisition of the reproductive capacity and the volume at its acquisition are linked by a 3/2 exponent power law. This dynamic fractal law is invariant, between and within le- vels of organisation. Brownian motion is the basic phenomenon of growth control: Matter and energy are exchanged at a constant flow rate. A Pareto-like relationship governs limits and limitations: Mutual survival depends on reciprocal limitations, through interactive feedbacks, for the best and for the worst. To survive that is to transform disadvantages into advantages and to avoid advantages turn to disadvantages.

Forced Vibration Analysis in Axisymmetric Functionally Graded Viscothermoelastic Hollow Cylinder Under Dynamic Pressure

The forced vibrations of axisymmetric inhomogenous isotropic viscothermoelastic hollow cylinder under periodic dynamic pressure have been studied. The material was taken inhomogenous due to easy exponent law in radial direction. By applying time harmonics variation technique, the partial differential equations were converted into ordinary differential equations. These ordinary differential equations were solved by applying series solution of matrix Frobenius method analytically to represent displacement, temperature and stresses. Numerically simulated outcomes were presented graphically to express the effect of functionally graded material disk for different values of grading parameter. With the increase in value of grading index, variation of field functions go on decreasing. The variation of field functions show high variation in homogenous materials in contrast to low variation in inhomogeneous materials.

Evaluation method for the measuring comprehensive suitability of chelating agents: a study of the temporal dynamics of heavy metal activation

The effects of chelating agents on heavy metal activation in Cd- and Pb-contaminated soils were studied through a dynamic activation experiment. An evaluation method for the measuring comprehensive suitability of chelating agent was established by calculating indexes for the degree of activation effect suitability and activated heavy metals’ half-life suitability. The following results were obtained: in Cd- and Pb-contaminated soils, heavy metal activation effects reached or approached maximum activating effects within 1 d and subsequently showed different levels of decline in all chelating agent treatment conditions. Declines in activation effects similarly subjected to the law of exponents over time and to the goodness of fit in DTPA, NTA, and GLDA ranged from 0.80 to 0.98. For Cd- and Pb-contaminated soils, chelating agents' levels of comprehensive suitability (H) were recorded as follows: NTA(1.40) > GLDA(1.31) > DTPA(1.14) > EDTA(1.00) > EDDS(0.14) > CA(0.06) and GLDA(1.56) > DTPA(1.48) > EDTA(1.00) > NTA(0.78) > EDDS(0.26) > CA (0.02). GLDA and DTPA are both suitable for Cd and Pb phytoextraction. Moreover, NTA and GLDA are optimal chelating agents for Cd and Pb phytoextraction, respectively.

Kinetic Model of Aging Biological Species in Natural Habitat

It was found that the rate of change (kinetics) of the probability of death of representatives of living systems (LS) of different biological species - Drosophila, mice, rats, dogs, horses and people in the wild in their residence in different geographical areas, is described by a kinetic equation with similar values of the parameters. However, the kinetics of the probability of death of young people and rats, starting from birth, is more accurately described by the kinetic equation of a slightly different species, taking into account the prevailing process of development and adaptation of the organism to the environment. On the basis of a single kinetic approach to the description of the probability of death, an analytical model of the intensity of mortality in LS (approximation of the death rate - CS). It is shown that the approximation proposed by Gompertz to CS by an increasing exponent (law of Gompertz) is a special case of the unified mathematical model proposed in this paper.

Cognitive Effect of Tracing Gesture in the Learning from Mathematics Worked Examples

The present study attempted to replicate the previous results of Hu et al. (Learning and Instruction 35:85–93 2015) and further examined the boundary condition of tracing gesture whether its cognitive effect is merely comparable with other attention-guiding means, i.e., textual attention cueing, in two different learning tasks in nature. In two experiments, 11- to 13-year-old students were asked to study the worked examples on angles relationships involving parallel lines (experiment 1) and laws of exponents (experiment 2) either without tracing instruction, with textual attention cueing instruction, or tracing instruction. The tracing group outperformed the other two groups on a subsequent test and reported lower levels of test difficulty in experiment 1 but not in experiment 2, suggesting that the cognitive effect of tracing gesture was beyond guiding attention in the learning from highly visuospatial-based worked examples but not in the materials that are less obviously visuospatial in nature. The present findings suggested that tracing gesture offers a simple yet effective embodied technique that may further enhance the worked example-based learning through its cognitive effect specifically on the task involved with spatial information.

Finite-size scaling phenomenon of nuclear liquid-gas phase transition probes

Based on the isospin-dependent quantum molecular dynamics model, finite-size scaling effects on nuclear liquid--gas phase transition probes are investigated by studying the de-excitation processes of six thermal sources of different sizes with the same initial density and similar $N/Z$. Using several probes including the total multiplicity derivative ($dM_{tot}/dT$), second moment parameter ($M_2$), intermediate mass fragment (IMF) multiplicity ($N_{IMF}$), Fisher's power-law exponent ($\tau$), and Ma's nuclear Zipf's law exponent ($\xi$), the relationship between the phase transition temperature and the source size has been established. It is observed that the phase transition temperatures obtained from the IMF multiplicity, Fisher's exponent, and Ma's nuclear Zipf's law exponent have a strong correlation with the source size. Moreover, by employing the finite-size scaling law, the critical temperature $T_c$ and the critical exponent $\nu$ have been obtained for infinite nuclear matter.

Microstructural interpretation of charge transport dynamics of chemically derived ZnCo2O4 under mechanical milling

In this work, milling effect on chemically synthesized nanocrystalline Zinc Cobaltite (ZnCo2O4) has been investigated and we report how the structural and electrical properties vary with the milling span. Phase pure ZnCo2O4 has been successfully synthesized via simple and cost-effective co-precipitation method and then it has been milled for one, four and 8 h respectively. XRD confirms formation of single phase cubic structure for both milled and unmilled nano-powders. Different microstructural parameters has been estimated from Rietveld analysis, which shows particle size reduction from ∼29.64 nm for unmilled sample to ∼18.13 nm for 8 h milled sample. TGA-DSC curve of as prepared sample shows good temperature stability that helps to estimate the appropriate sintering temperature for the samples. TEM analysis also gives values of grain size in agreement with Reitveld analysis. Frequency dependent ac conductivity curve obeys universal Jonscher power law and temperature dependence of frequency exponent is explained by small polaron transaction. Comparable activation energies from hopping mechanism and relaxation process indicates similar transport mechanism. Superimposed scaling spectra obeys TTSP principle. AC conductivity increases with frequency as a result of hopping of the charge carriers. Smaller particles with reduced strain gives enhanced conductivity as well as enhanced value of hopping frequency. This further suggests creation of excess charge carriers in milled samples. Cole-Cole plot shows non-Debye type behaviour of the samples. The dielectric loss factor increases with lowering of particle size since smaller grains contributes to faster charge conduction.

Узгодження параметрів зварювальних імпульсів з програмою тиску електродів та електрофізичними процесами в зварювальному контакті

Resistance welding is an important technological operation for many modern industries, including mechanical engineering, electronics and instrument making. Micro resistance welding is used in producing of micro-structures for critical purposes, such as electronic components, circuits, etc. It is obvious that welded joints in such structures should be characterized by such high quality indicators as the absence of solid metal splashes, burnouts, faulty fusions, and the repetitiveness of dimensions of welding spots, which are achieved by coordinating the parameters of welding current pulses with electrophysical processes in welding contact. Thus, in this paper, the authors analyze electrophysical processes taking place in the welding contact and the effect of the welding current pulse parameters on these processes, in order to mutually coordinate them. This allows specifying the law of pulse power change, which makes it possible to take into account the features of electrophysical processes in the welding contact to the full extent. The smooth rise of the pulse power, obtained according to the exponent law with selection of the optimal exponent n value, provides gradual input of energy required for welding during the most unstable phase of primary contact formation. Due to the flat top of the welding pulse, the constant energy input to the contact is maintained during a rather stable phase of welding core formation. Finally, the smooth pulse fall obtained by selecting the optimal exponent m value of the power change law provides the proper cooling of the welding spot, which guarantees the strength and uniformity of the joint structure. To achieve the best welding quality, the recommendations are given regarding the formation of rise and fall of the pulse, depending on specific welding conditions, parameters of the welded parts and requirements for the obtained joints. The paper shows that it is a useful practice to coordinate the pulse power change law with the program of changing the pressure of the electrodes, and with changing the resistance of the welding zone. The proposed example of coordination between welding pulse power change, welding electrode pressure and electrophysical processes in the welding contact (resistance of the welding zone) is substantiated in terms of the influence of the electrode pressure on the welding process. This practice can provide the highest quality of welded joints and thus the highest quality of the end products manufactured by welding.

Universality of active wetting transitions

Four on-lattice and six off-lattice models for active matter are studied numerically, showing that in contact with a wall, they display universal wetting transitions between three distinctive phases. The particles, which interact via exclusion volume only, move persistently and, depending on the model, change their direction either via tumble processes or rotational diffusion. When increasing the turning rate $\nu_T$, the systems transit from total wetting, to partial wetting and dewetted phases. In the first phase, a wetting film covers the wall, with increasing heights while decreasing $\nu_T$. The second phase is characterized by wetting droplets on the walls. And, finally, the walls dries with few particles in contact with it. These phases present two continuous non-equilibrium transitions. For the first transition, from partial to total wetting, the fraction of dry sites vanishes continuously when decreasing $\nu_T$, with a power law of exponent 1. And, for the second transition, an order parameter proportional to the excess mass in droplets decreases continuously with a power law of exponent 3 when approaching a critical value of $\nu_T$. The critical exponents are the same for all the models studied.

Electrical Properties of Cerium and Yttrium Co-substituted Strontium Nanohexaferrites

Ce and Y substituted SrFe12O19 (x = 0.4 and 0.5) nanohexaferrites have been synthesised by sol–gel auto-combustion. The pure hexagonal SrFe12O19 phase was confirmed by XRD, FE-SEM and HR-TEM. The ac conductivity and dielectric properties of Ce and Y substituted Sr:Fe12O19 nanohexaferrites were studied by using complex impedance technique. Dielectric properties such as dielectric constant, dielectric loss, dielectric tangent loss, as well as ac conductivity are measured at various bias potentials in a varying frequency range from 10 Hz to 10 MHz. The frequency dependency of the ac conductivity could be evaluated by a power exponent law at higher frequencies, which is a characteristic mechanism for electrical charge transport by tunnelling processes with which it is more dispersive at lower frequencies. The conduction mechanisms were also investigated at various dc bias potentials, mainly being an indicative of hopping type conduction. So, the dielectric dispersion behaviour can be well elucidated in terms of Maxwell–Wagner polarization in accordance with the Koop’s phenomenological theory. Utilizing an electrical equivalent circuit model, impedance studies were carried out in a specific frequency domain to characterize all the contributions of the dielectric response between the grains and grain boundaries to the dielectric parameters.

Ac conductivity of transition metal oxide doped glassy nanocomposite systems: temperature and frequency dependency

Transition metal oxide (TMO) doped different types of semiconducting glassy systems of the common terminology as 0.3V2O5–0.7 (0.05AmOn–0.95ZnO) for AmOn = MoO3, SeO2, Nd2O3, and CdO have been prepared by melt quenching route. The frequency and temperature dependent conductivity of all the as-quenched glass nanocomposite samples has been investigated over a wide temperature and frequency range. Conductivity, depending on temperature and frequency, is well established using Jonscher’s universal power law and Almond-West formalism. The values of DC conductivity (σdc), polaron hopping frequency (ωH), frequency exponent (n), and power law exponent (s) have been computed. The value of n indicates three-dimensional motions of charge carriers or polarons, which is the main reason for high-frequency dispersion in the ac conductivity. The estimated values of activation energy of ac conduction (Eac), free energy of polaron migration (EH) and activation energy of DC conductivity (Edc) are mainly owing to polaron transport with the energy level in the optical band gap. Ac conductivity and temperature dependent power-law exponent (s) of the as-prepared glassy samples containing MoO3 and Nd2O3 are dominated by non-overlapping small polaron tunneling (NSPT). Conversely, correlated barrier hopping (CBH) solely controls the ac conductivity and temperature dependent power-law exponent (s) of the glassy samples containing SeO2 and CdO. It is ascertained that mobile charge carrier concentration is independent of temperature and only 20%–25% of the total charge carriers (polarons) contribute to the ac conductivity of the presently studied glassy systems.

Sensitivity study of experimental measures for the nuclear liquid-gas phase transition in the statistical multifragmentation model

The experimental measures of the multiplicity derivatives, the moment parameters, the bimodal parameter, the fluctuation of maximum fragment charge number (NVZ), the Fisher exponent ($\tau$) and Zipf's law parameter ($\xi$), are examined to search for the liquid-gas phase transition in nuclear multifragmention processes within the framework of the statistical multifragmentation model (SMM). The sensitivities of these measures are studied. All these measures predict a critical signature at or near to the critical point both for the primary and secondary fragments. Among these measures, the total multiplicity derivative and the NVZ provide accurate measures for the critical point from the final cold fragments as well as the primary fragments. The present study will provide a guide for future experiments and analyses in the study of nuclear liquid-gas phase transition.