Statistical Laws Research Articles

Quantum Chaos in the Dynamics of Molecules.

Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.

Factors of Volitional Attributiveness of the Legal Transaction based on International Experience

The aim of the study was to determine the most effective model of legal regulation of the form of declaration of will in legal transactions from the survey of the legislation of several countries and their respective jurisprudence. The research covered the methods of statistical analysis, comparative law, dialectics and legal epistemology, as well as data selection and legal modeling. It is shown that the model of legal regulation of the form of declaration of will, which is based on the principle of free choice of the form of declaration of will, is the most effective in terms of these indicators in the case of: (Greece, Poland, Czech Republic). At the same time, these States provide for strict requirements for challenging legal transactions and provide for the prohibition of abuse of rights. It is concluded that it is justified that in the majority of states the principle of valid will is applied when concluding legal transactions. Moreover, the results of this study can be used to develop proposals for the improvement of legislation in the field of regulation of the forms of declaration of will in the conclusion of legal transactions in their various forms and modalities.

Extraction and characterization of novel natural lignocellulosic fibers from Malva sylvestris L.

The main goal of this study is to characterize natural lignocellulosic fibers extracted from Malva Sylvestris. The experimental approach used is consisted to analyze the morphological, physical, chemical, thermal and mechanical characteristics of Malva sylvistris fibers. The stem anatomy showed that the bark of Malva is rich in fiber cells. Based on ATR-FTIR and X-ray analysis, the obtained results illustrated that the fiber contained mainly cellulose, hemicellulose and lignin. The crystallinity index of fiber is about 55.12 %, which indicated a high cellulose content. The Thermo-gravimetric analysis (TGA) analysis test point out that Malva Sylvestris fibers are thermally stable until 225°C and an apparent activation energy about of 111 kJ.mol−1 was recorded. Tensile strength of Malva fibers is about of 236.64 ± 93.33 MPa whilst its young’s modulus is about of 26.07 ± 5.14 GPa. In view of the dispersion in the obtained experimental results, the latter were analyzed using the Weibull statistical laws with two parameters.

A study of ancient glass classification problem based on multiple logistic regression

The Silk Road was a commercial route linking China and the West in ancient times, and was an important window for China to open up to the outside world during the Han Dynasty, strongly promoting cultural exchange between China and the West. Ancient glass is susceptible to weathering by the burial environment, and in the process the proportions of its various chemical components change. This paper studies the chemical composition content of ancient glass objects, establishes a classification model, analyses the correlation between various parameters of different types of glass objects, gives statistical laws and specific classification methods, and uses glass objects to help the exchange and mutual appreciation between Eastern and Western civilizations and the longevity of Chinese civilization.

A study on the classification of the composition of ancient glassware based on statistical law analysis

Ancient glass is highly susceptible to weathering by the environment in which it is buried, and weathering can cause changes in the proportions of its chemical composition, which can affect the correct determination of its category. In this paper, we solve the problem by studying the chemical composition of ancient glass artefacts to establish a mathematical model. We first used the Spearman correlation test and obtained that the weathering of the surface of the artefacts had no relationship with the color and decoration of the glass, and a negative weak correlation with the type of glass; then we analyzed the statistical pattern of the chemical composition content of the surface of the artefact samples with and without weathering, and conducted the Mann-Whitney test on the chemical composition of the sample data. The mean values of , , , , , and in lead-barium glass were not significantly different before and after weathering, while the mean values of other oxides were significantly different, e.g. the CaO content increased from 1.89% to 4.49% after weathering; finally, the chemical composition of surface weathered glass before weathering was predicted. By analyzing the discrete degree coefficients of each component, we found that the component content is stochastic, and proposed the index of random variation to quantify the stochasticity, and combined with the inevitable variation in the weathering process to establish a mathematical model of the chemical component content before and after weathering for prediction.

Analytical identification model of ancient glass based on density clustering and PSO-SVM

In this paper, the correlation between the indicators of glass artifacts is explored in depth by establishing relevant mathematical models, giving the statistical laws of weathering for high potassium glass and lead-barium glass, and classifying a series of glass artifacts. In this paper, a support vector machine (PSO-SVM) model based on particle swarm optimization is developed. Firstly, the SVM model is proposed to achieve binary classification for the model, while the particle swarm model is established, and the hyperparameters c and g are optimized by adding adaptive particle variation operation and velocity contraction factor, and the optimal values of both are 0.248 and 2.244, respectively. and the training and validation sets are continuously changed by K-fold cross-validation, and the accuracy of the model classification is obtained as 100%. The model was then used to classify the Form 3 data, and the results were that the artifacts in groups 2, 3, 4, 5, and 8 were lead-barium glass; the artifacts in groups 1, 6, and 7 were high-potassium glass. Finally, the sensitivity analysis of the model was carried out to adjust the values of hyperparameters c and g. It was found that the model sensitivity was very low and the results were satisfactory. In addition, the spearman correlation coefficients between the individual chemical compositions of the two types of glasses were calculated, plotted thermodynamically and interpreted. Then, a gray correlation analysis model was developed to investigate the relationship between other chemical components and it by using silica as the parent sequence, and conclusions were drawn. And based on the results, the differences in the correlation between the chemical components of the two types of glasses were analyzed, and it was found that the correlation between some components in the two types of glasses and the silica content were significantly different.

Based on the analysis and identification of ancient glass products

The chemical composition of ancient glass in China is diverse, and it is very vulnerable to weathering under the influence of burial environment. This weathering will aggravate the difficulty of identifying ancient glass types. There are a number of relevant data on ancient glass products in China. Archaeologists have divided these cultural relics into two types: high potassium glass and lead barium glass according to their chemical composition and other detection methods. In this paper, Kappa consistency test, statistical law, principal component analysis, k-means clustering analysis, logical regression model, gray correlation analysis and other methods or models are used to analyze the composition of these glass samples and identify their types.The Kappa coefficient is used to test the consistency of these three groups of disordered classification variables, and the Kappa value is used to judge the correlation degree of the three groups of disordered classification variables. Through the test, it is found that the surface weathering of glass relics has a certain relationship with its glass type; Later, we tried to explore whether there would be a more obvious rule when the surface weathering was affected by two variables at the same time. It was found that when the glass type was fixed to high potassium, the type of its decoration would have an impact on its weathering.

The classification method of different glasses is clear and composition analysis

With the development of the Silk Road, this paper mainly studies the glass category, glass pattern decoration, weathering, glass color, chemical composition content as the indicators to make statistical rules and analysis rules, and analyze and summarize the relationship between chemical components content,For question 1, it is divided into three problems. Preprocess the attached data, process its invalid data, and integrate the data. The first question first uses bivariate correlation analysis, using Spearman correlation coefficient and Pearson correlation coefficient, and then using chi-square test to test the results of the correlation analysis. The result is: there is a strong correlation between category and weathering, while there is no correlation between color, ornamentation and weathering.[1]The second question is based on the statistical analysis model of the first question, under the condition of glass type and surface weathering, and the vertical sample T test obtained the statistical law of silica, potassium oxide, calcium oxide and lead oxide. The third question established a predictive model and used multiple linear regression to obtain the prediction results.

Composition Analysis and Identification of Ancient Glass Products

In this paper, aiming at the problem of composition analysis and identification of ancient glass products, a correlation analysis model based on chi square test is established to solve the relationship between the surface weathering of cultural relics and glass types, patterns and colors; ARMA model is established to solve the statistical law of chemical composition content with or without weathering and the problem of predicting chemical composition content before weathering; A classification model based on K-means++clustering is established to solve the problem of classification rules; An evaluation model based on principal component analysis is established to solve the problem of type identification of glass relics.

Bielefeld May In Fact Not Exist – Empirical Evidence From Official Population Data

Abstract The “Bielefeld conspiracy” has long disputed the existence of Bielefeld, a (supposed) German city. In this paper, an approach is developed to test such a theory empirically by auditing officially reported population numbers, arguing that real cities would not fake these. It is shown that Bielefeld’s data, in fact, violate the Benford law, a statistical law that they should follow if they were genuine. This anomaly is found only for Bielefeld, in contrast to all other tested similar and dissimilar cities, across two decades, and with highest significance by five statistical tests. The Bielefeld conspiracy remains as the most or even only plausible explanation for these findings.

A novel probabilistic model to explain drainage network evolution

River channels self-organize to form tree-like networks that follow certain statistical laws, such as Horton's laws and Hack's law, which is perhaps the reason why simple statistical models are often used to explain river network evolution. However, statistical models generally do not attempt to explain the differences between network structures. Here we address this issue by incorporating certain physically meaningful variables in a statistical modeling framework. The model allows the network to grow in a headward direction via probabilistic decisions based on two free parameters. Simulations performed over a planar matrix result in tree-like networks exhibiting power-law scaling relationships as displayed by real river networks. The two parameters are shown to be capable of explaining the variation of key network characteristics such as compactness coefficient and Hack's exponent. The uniqueness of the model thus lies in its ability to generate networks with different shapes and characteristics.

Errors and recommended practices that should be identified to reduce suspected concentrations of microplastics in soil and groundwater: A review

Over the last decade, many studies on microplastics (MPs) have only focused on the marine environment, and scientist have recently begun to document soil and groundwater MP contamination. However, many of these studies have included errors that should be addressed. Therefore, the aim of this study is to identify multiple errors in internationally reported soil and groundwater MPs studies and to provide recommendations. Over 185 original research papers on soil and groundwater MPs published between 2017 and 2022 from seven database categories in the Web of Science were sorted. These papers were manually sorted to identify errors in (i) sample quantity, (ii) quality assurance and equipment used, (iii) microplastic identification, and (iv) microplastic classification. The majority of studies were found not to use blank samples, classified MPs incorrectly by mixing MP shapes and forms, used filters with either larger pore sizes, or materials that could be potential sources of MP. In some of these studies, the statistical package or law used for statistical analysis was not specified, with some other studies using problematic MP analysis procedures. As a remediation method to address these errors, MP studies should consider using blank soil samples and metallic filters. Statistical software packages should be used, and the statistical prerequisite laws should be verified prior to analysis. Stereo microscopes should be used simultaneously with Raman or Fourier transform infrared (FTIR) spectroscopy to identify MPs in soils and groundwater. • It is essential plastic kits are not used for storing soil and groundwater after sampling. • Accurate microplastic analysis requires at least one trip and a device blank sample each time. • Film and fragment should be classified as the same microplastics shape, not separate shapes. • A glass filter is preferable to a cellulose filter for accurate microplastics analysis. • It is critical to collect soil weight in the range of 200–1000 g for accurate microplastic analysis.

ANALYTICAL ASPECTS OF CRISIS REPORTING

The article discusses the analytical aspects of crisis reporting relevant in the conditions of uncertainty and crisis manifestations in the economy, reflected in the indicators of financial statements, unprofitability of activities, in trends of indicative analytical indicators. Some analytical aspects of crisis reporting have been considered, expressed in the presence of negative absolute indicators in reporting, in the frequency of occurrence and negative dynamics. The indicators of a crisis situation, absolute analytical indicators, include insufficiency of own working capital, the presence and proportion of own working capital. It is a criterion indicator of the financial condition as a whole; its insufficiency may indicate an unstable position of the organization; the insufficiency of net working capital and its negative value signals the unsatisfactory solvency and liquidity of the organization, the unprofitability of production activities; the negative value of the balance of cash flows reflects the current insolvency and financial problems in the organization, indicates the absence of temporarily free funds in the organization; the insufficiency of net assets indicates an unstable situation, the negative dynamics of the indicator indicates a deterioration. In crisis reporting, unprofitability of activities is reflected in the appearance of various losses and the presence of negative analytical relative indicators, which are indicative. In a trend economy, monitoring and their impact on the financial position of an organization is a necessary tool. In analytical practice, there are difficulties in reading and understanding trends in the presence of losses in various periods of activity. The variability of economic situations in the presence of unprofitable activity has been considered; the conditions for trends in balance sheet profit (loss) in diagnosing the financial situation have been justified from the point of view of the laws of statistics and economic analysis.

ANALYTICAL ASPECTS OF CRISIS REPORTING

The article discusses the analytical aspects of crisis reporting relevant in the conditions of uncertainty and crisis manifestations in the economy, reflected in the indicators of financial statements, unprofitability of activities, in trends of indicative analytical indicators. Some analytical aspects of crisis reporting have been considered, expressed in the presence of negative absolute indicators in reporting, in the frequency of occurrence and negative dynamics. The indicators of a crisis situation, absolute analytical indicators, include insufficiency of own working capital, the presence and proportion of own working capital. It is a criterion indicator of the financial condition as a whole; its insufficiency may indicate an unstable position of the organization; the insufficiency of net working capital and its negative value signals the unsatisfactory solvency and liquidity of the organization, the unprofitability of production activities; the negative value of the balance of cash flows reflects the current insolvency and financial problems in the organization, indicates the absence of temporarily free funds in the organization; the insufficiency of net assets indicates an unstable situation, the negative dynamics of the indicator indicates a deterioration. In crisis reporting, unprofitability of activities is reflected in the appearance of various losses and the presence of negative analytical relative indicators, which are indicative. In a trend economy, monitoring and their impact on the financial position of an organization is a necessary tool. In analytical practice, there are difficulties in reading and understanding trends in the presence of losses in various periods of activity. The variability of economic situations in the presence of unprofitable activity has been considered; the conditions for trends in balance sheet profit (loss) in diagnosing the financial situation have been justified from the point of view of the laws of statistics and economic analysis.

Analogy of scaling law for heterogeneous interfacial fracture to explain the Gutenberg–Richter formula for earthquakes

We propose a new approach for the statistical law due to the fracture of a heterogeneous interface involving spatial correlation of disorders. The dynamic process of interfacial fracture is governed by three coupled integral equations, which further become a system of linear algebraic equations after discretizing the interface to a set of prismatic elements. By tuning parameters, this model covers the whole cases of interfacial fracture from local-load-sharing to almost equal-load-sharing, extending the classical fiber bundle models to a general form. Numerical simulations present that in all cases, the statistical frequency distribution of bursts follows a power law with the exponent in the range (1.5, 2.5), the corresponding b-value in (0.75, 2.25), which well explains the empirical Gutenberg–Richter scaling. The exponent depends on stiffness of elastic spaces, heterogeneous properties of interface, and the distribution of displacements induced by loading. Furthermore, the exponent drops temporally with the evolution of fracture, to its final value before rupture of interface, a phenomenon that may be treated as a precursor for imminent catastrophic failure.

Einstein on measurement theory: A heuristic point of view

Einstein did not contribute significantly to the quantum mechanics we are familiar with, but he did contribute to its theoretical foundations. In a seminal theory on black body radiation, he used two physically distinct sets of coordinates, a classical set to describe the continuity of heat energy with Maxwell Boltzmann statistics and an atomic set to describe discrete energy states required by the Planck radiation law. His methods are extended here to reveal that matrix mechanics is an incomplete description of atomic structure. In addition to the discrete energy states of the diagonal matrix elements, classically derived components of kinetic energy are necessary. We conclude that the diagonalized matrix elements and eigenvalues of the Schrödinger equation both describe characteristics of the steady states, but the physical variables they describe are different, because they are measured with respect to different coordinate systems. Einstein’s assumptions lead to a resolution of the measurement problem by introducing statistical laws at the microscopic level.

Strong Heterogeneity in Shallow Lunar Subsurface Detected by Apollo Seismic Data

AbstractExperiencing heavy impacting, the Moon preserves a megaregolith in its shallow subsurface with physical properties that carry implications for lunar history. A strong scattering of seismic waves associated with the heterogeneous lunar megaregolith appears to be systematic, but deriving a statistical law of the random heterogeneities has remained elusive. Apollo seismic data are characterized by ultra‐long coda waves with weak amplitude decay that provide an opportunity to explore the extent of heterogeneity in the lunar crust. We obtain by numerical simulation the appropriate parameters for seismic velocity and density perturbation of the shallow lunar crust that match Apollo seismic data. The perturbations of the shallow lunar crust identified here, which are at least 50%, are much larger than previously thought. This physical behavior thus both confirms a strongly heterogeneous surface layer as well as provides a new constraint on the structural characteristics of the megaregolith.

Altered distribution of resting periods of daily locomotor activity in patients with delayed sleep phase disorder.

Delayed sleep phase disorder (DSPD) and mood disorders have a close relationship. However, the shared mechanisms by DSPD and mood disorders have not been well-elucidated. We previously found that micro-fluctuations in human behaviors are organized by robust statistical laws (behavioral organization), where the cumulative distributions of resting and active period durations take a power-law distribution form and a stretched exponential functional form, respectively. Further, we found that the scaling exponents of resting period distributions significantly decreased in major depressive disorder (MDD). In this study, we hypothesized that DSPD had similar characteristics of the altered behavioral organization to that of MDD. Locomotor activity data were acquired for more than 1 week from 17 patients with DSPD and 17 age- and gender-matched healthy participants using actigraphy. We analyzed the cumulative distributions of resting and active period durations in locomotor activity data and subsequently derived fitting parameters of those distributions. Similar to patients with MDD, we found that resting period distributions took a power-law form over the range of 2–100 min, with significantly lower values of scaling exponents γ in patients with DSPD compared with healthy participants. The shared alteration in γ suggests the existence of similar pathophysiology between DSPD and MDD.

The Future of Climate Modelling: Weather Details, Macroweather Stochastics—Or Both?

Since the first climate models in the 1970s, algorithms and computer speeds have increased by a factor of ≈1017 allowing the simulation of more and more processes at finer and finer resolutions. Yet, the spread of the members of the multi-model ensemble (MME) of the Climate Model Intercomparison Project (CMIP) used in last year’s 6th IPCC Assessment Report was larger than ever: model uncertainty, in the sense of MME uncertainty, has increased. Even if the holy grail is still kilometric scale models, bigger may not be better. Why model structures that live for ≈15 min only to average them over factors of several hundred thousand in order to produce decadal climate projections? In this commentary, I argue that alongside the development of “seamless” (unique) weather-climate models that chase ever smaller—and mostly irrelevant—details, the community should seriously invest in the development of stochastic macroweather models. Such models exploit the statistical laws that are obeyed at scales longer than the lifetimes of planetary scale structures, beyond the deterministic prediction limit (≈10 days). I argue that the conventional General Circulation Models and these new macroweather models are complementary in the same way that statistical mechanics and continuum mechanics are equally valid with the method of choice determined by the application. Candidates for stochastic macroweather models are now emerging, those based on the Fractional Energy Balance Equation (FEBE) are particularly promising. The FEBE is an update and generalization of the classical Budyko–Sellers energy balance models, it respects the symmetries of scaling and energy conservation and it already allows for both state-of-the-art monthly and seasonal, interannual temperature forecasts and multidecadal projections. I demonstrate this with 21st century FEBE climate projections for global mean temperatures. Overall, the projections agree with the CMIP5 and CMIP6 multi-model ensembles and the FEBE parametric uncertainty is about half of the MME structural uncertainty. Without the FEBE, uncertainties are so large that climate policies (mitigation) are largely decoupled from climate consequences (warming) allowing policy makers too much “wiggle room”. The lower FEBE uncertainties will help overcome the current “uncertainty crisis”. Both model types are complementary, a fact demonstrated by showing that CMIP global mean temperatures can be accurately projected using such stochastic macroweather models (validating both approaches). Unsurprisingly, they can therefore be combined to produce an optimum hybrid model in which the two model types are used as copredictors: when combined, the various uncertainties are reduced even further.

Enterprise risk arising from legacy production systems: a probabilistic perspective

The model of estimation of effective minimization of strategic risks arising at modernization of the software of legacy production systems is presented. It is shown that incompatible hypotheses of strategic risks of the enterprise in the digital economy form a complete group of pairwise incompatible independent events, and their probabilities are found by mathematical methods of processing an inversely symmetric matrix, made by experts in pairwise comparison on a 5-point scale of relative importance errors of calculations of the constructed matrix (no more than 15 %). For these matrices, solutions of characteristic equations are found to determine the maximum values of the eigenvalues of matrices, which appear in the assessment of the adequacy of composite expert matrices together with the corresponding orders of matrices.
 To substantiate the statistical measurement under the condition of quantitative or qualitative assessment of the risk of occurrence of events, the a priori value of the probabilities of occurrence of risk in the occurrence of events is taken. The full probability formula is the formula for the probability of occurrence of an event of effective minimization of strategic risks. It is shown that to determine the a priori values of conditional probabilities of hypotheses of effective minimization of strategic risks of the enterprise it is necessary to make statistically significant sections of these hypotheses at selected enterprises for several periods, which may be subject to statistical distribution laws. Thus, the presented model for quantitative measurement, comprehensive analysis of the level of software modernization of legacy production systems of the enterprise is the initial theoretical basis for improving the system of strategic management of the enterprise in terms of digitalization.