Statistical Theory Research Articles

Complexity synchronization in living matter: a mini review

Fractal time series have been argued to be ubiquitous in human physiology and some of the implications of that ubiquity are quite remarkable. One consequence of the omnipresent fractality is complexity synchronization (CS) observed in the interactions among simultaneously recorded physiologic time series discussed herein. This new kind of synchronization has been revealed in the interaction triad of organ-networks (ONs) consisting of the mutually interacting time series generated by the brain (electroencephalograms, EEGs), heart (electrocardiograms, ECGs), and lungs (Respiration). The scaled time series from each member of the triad look nothing like one another and yet they bear a deeply recorded synchronization invisible to the naked eye. The theory of scaling statistics is used to explain the source of the CS observed in the information exchange among these multifractal time series. The multifractal dimension (MFD) of each time series is a measure of the time-dependent complexity of that time series, and it is the matching of the MFD time series that provides the synchronization referred to as CS. The CS is one manifestation of the hypothesis given by a “Law of Multifractal Dimension Synchronization” (LMFDS) which is supported by data. Therefore, the review aspects of this paper are chosen to make the extended range of the LMFDS hypothesis sufficiently reasonable to warrant further empirical testing.

Illegal Activities of Cartel Organizations in the Field of Public Procurement as a New Object of Statistical Study

The sphere of public procurement and the disbursement of budget funds in all countries is an environment that attracts not only respectable entrepreneurs who want to make guaranteed money, but also various “criminal white-collar elements.” According to various estimates, the volume of financing for public procurement in the Russian Federation occupies up to one third of the total GDP. A large number of labor and financial resources are involved in this area, while regularly changing legislation in this area, as well as the complexity of procurement procedures for different categories of goods, works, and services create favorable conditions and allow unscrupulous bidders, as well as corrupt customer representatives, to obtain unjustified profits and illegal remuneration. In the current situation, the introduction of new control measures becomes vital to ensure fair competition and efficient use of budget funds. That is why additional research and measures aimed at eliminating these problems and the preconditions for their occurrence are an integral part of ensuring the effectiveness of the public procurement system and protecting public interests.Purpose of the research is to study the genesis of cartel agreements in public procurement and their impact on the implementation of national projects in the Russian Federation, as well as the impact of cartel agreements on the presence of healthy competition and the efficiency of spending budget funds. As part of the paper, the state of crime in this area was examined; the signs of cartel agreements, methods for identifying cartels, as well as signs of collusion between the customer and the participant in public procurement were identified.Methods and materials. The author in his paper applies a comprehensive methodological approach, including analysis of statistical data, methods of the general theory of statistics, as well as methods of synthesis and analysis. The main attention is paid to the analysis of the current legal regulation in the field of public procurement. Graphical and tabular methods were used to visualize statistical data. The study is based on data provided by the Ministry of Internal Affairs of Russia, the Federal Antimonopoly Service of Russia, the Federal Treasury of the Russian Federation, the Prosecutor General’s Office of the Russian Federation and the Judicial Department of the Supreme Court.Results of the study. The paper made a quantitative assessment of the scope of public procurement in recent years, and assessed the work carried out by law enforcement officials and the antimonopoly service. Typical violations of antimonopoly legislation during public procurement are given and methods for identifying them are proposed. The illegal schemes used by cartel participants in electronic trading are analyzed, as well as problematic issues and ways to resolve them that arise in practice. The paper proposes various approaches to increasing the efficiency of law enforcement and control agencies. An analysis of law enforcement practice revealed problems associated with proving crimes in this area, and noted an insufficient level of interaction between law enforcement agencies and the Federal Antimonopoly Service of the Russian Federation.Conclusion. In the study, the author analyzed the main features of cartels, proposed methods for identifying them, as well as ways to improve the verification activities carried out. The presented measures do not exhaust the topic of the study, and to effectively combat cartels, a systematic approach is recommended, including not only improving the quality of work of law enforcement and control agencies, but also improving the software and hardware used in carrying out inspections. Cartels in public procurement are a relatively new phenomenon for Russia; statistical data obtained from the Russian Ministry of Internal Affairs and the Judicial Department of the Supreme Court of the Russian Federation indicate that law enforcement and control authorities are just beginning their work to counter the criminal behavior of participants in cartel agreements. Only the fruitful joint work of law enforcement and control agencies will ensure the economic security of the state and protect the national interests of the Russian Federation.

A multiscale and multicriteria generative adversarial network to synthesize 1-dimensional turbulent fields

This article introduces a new neural network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of (1) energy distribution, (2) energy cascade and (3) intermittency across scales in agreement with experimental observations. The model is a generative adversarial network (GAN) with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field, that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the GAN criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence’s studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model, we use turbulent velocity signals from grid turbulence at Modane wind tunnel.

Statistical theory of fluids confined in quenched disordered porous media.

We develop a theory to calculate structural correlations and thermodynamic properties of a fluid confined in a random porous solid medium (matrix). We used density functional formalism to derive an annealed averaged expression for the density profile and excess free energy of fluid arising due to random fields of a particular realization of the matrix. After performing the second average over the quenched-disordered variables, the excess free energy is organized to give one- and two-body potentials for fluid particles. The average over disorder reduces the system to an effective one-component system of fluid in which particles feel one-body (external) potential and interact via effective pair potential. The effective pair potential is a sum of the bare (the one in the pure fluid) and the matrix-induced potential. The resulting partition function involves only fluid variables. Equations are derived for fluid-fluid and fluid-matrix correlation functions and for free energy, pressure, and chemical potential of the fluid. The theory is applied to a model system of hard spheres and results for the effective pair potential, correlation functions, and thermodynamic properties are reported. The effective pair potential is found to be attractive at the contact and develops a repulsive peak before decaying to zero. Results for pair correlation function and structure factor are compared with simulation results for several fluid densities at two matrix densities. In all the cases, a very good agreement has been found.

A mechanistic deterioration point assignment model for water pipe condition assessment

ABSTRACT A pipe condition assessment model is required to implement effective and economical planned maintenance of the water distribution system. The application of such a model requires sufficient accuracy, which, however, is limited by the complexity of the pipe deterioration process and data storage capacity of the water utility. The majority of previous studies have focused on the improvement of assessment algorithms for data mining. In this study, a mechanistic deterioration point assignment (MDPA) model is developed to make advancements in the modes of data input and result output to enhance the model's accuracy and application scope for cast iron and steel pipes. In this MDPA model, (1) indicators/sub-indicators on external corrosion, external load, internal corrosion, and internal load are constructed and can be obtained by data estimation or techniques and (2) assessment results include both pipe overall condition and detailed conditions on corrosion and load, offering evidence for primary maintenance measures. The weights of the indicators/sub-indicators are estimated using the Bayesian statistics theory. The modelling results of pipe samples demonstrate that this MDPA model is an effective tool for pipe condition assessment.

Some results on the odds rate order along with its statistical testing

Recently, Lando, et al. [2022. Properties of increasing odds rate distributions with a statistical application. Journal of Statistical Planning and Inference 221,313–-325 ] define the odds rate order and show that it is stronger than the usual stochastic order, but weaker than the hazard rate order. The purpose of this paper is to investigate the other properties of this new stochastic order. Some characterization and preservation results and its relationship with other well-known stochastic orders are given. In addition, two relative ordering based on the odds rate functions are also defined and their relation with the odds rate order is investigated. Applications in statistical theory of reliability and a statistical test for the odds rate order are also included.

Statistical physics investigation of the docking process of fruity odorants on Machilis hrabei MhOR5: New microscopic interpretations

In this paper, the putative phenomenon of adsorption involved in the insect olfactory perception of four fruity odorants on Machilishrabei olfactory receptor MhOR5 was studied at a molecular scale. Thus, the experimental concentration–response curves of propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate on MhOR5 were adjusted using the monolayer model of ideal gas established using the powerful statistical physics approach, which was selected as the most appropriate model among the others. The fitted model parameters were applied to stereographic and energetic analyze the four olfactory systems. Indeed, the modeling results indicated that the tested fruity key food odorants (KFOs) were docked as 2- or 3-aggregated molecules on one MhOR5 binding site via a nonparallel position (i.e., multi-molecular adsorption mechanism). Energetic parameters were used to characterize the adsorption process involved in the studied systems via the determination of the molar adsorption energies (ranging from 12.91 to 17.52 kJ/mol). Hence, the values of the molar adsorption energies are positive and inferior to 40 kJ/mol; this means that the putative adsorption mechanism presented an exothermic character and a physical type. The docking simulation results proved that the adsorption of propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate on MhOR5 may occur via physical interactions (weak interactions) like alkyl, pi-alkyl, van der Waals, carbon hydrogen bond, and conventional hydrogen bond. The statistical physics theory may also be utilized to quantitatively characterize Machilishrabei MhOR5 activated by propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate odorants via the estimation of the different site size distributions (SSDs) and site energy distributions (SEDs).

Towards algorithms and models that we can trust: A theoretical perspective

In the last decade it became increasingly apparent the inability of technical metrics such as accuracy, sustainability, and non-regressiveness to well characterize the behavior of intelligent systems. In fact, they are nowadays requested to meet also ethical requirements such as explainability, fairness, robustness, and privacy increasing our trust in their use in the wild. Of course often technical and ethical metrics are in tension between each other but the final goal is to be able to develop a new generation of more responsible and trustworthy machine learning. In this paper, we focus our attention on machine learning algorithms and associated predictive models, questioning for the first time, from a theoretical perspective, if it is possible to simultaneously guarantee their performance in terms of both technical and ethical metrics towards machine learning algorithms that we can trust. In particular, we will investigate for the first time both theory and practice of deterministic and randomized algorithms and associated predictive models showing the advantages and disadvantages of the different approaches. For this purpose we will leverage the most recent advances coming from the statistical learning theory: Complexity-Based Methods, Distribution Stability, PAC-Bayes, and Differential Privacy. Results will show that it is possible to develop consistent algorithms which generate predictive models with guarantees on multiple trustworthiness metrics.

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians’ annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA). Unlike previous shape analysis methods that directly regularize the smoothness of the displacement field, DCES-PA regularizes the first and second-order derivative of the displacement field and decomposes these vector fields according to different deformations. For the first-order elastic metric, DCES-PA orthogonally decomposes the first-order derivative of the displacement field by shearing, scaling and bending deformation, and then penalize deformations triggering proliferation formation. For the second-order elastic metric, DCES-PA encodes both intrinsic and extrinsic surface curvatures into the second-order derivative of the displacement field to control the generation of high-curvature regions. By integrating the elastic shape metric with the varifold distances, DCES-PA achieves correspondence-free shape analysis. Extensive experiments on both simulated and real clinical datasets demonstrate that DCES-PA not only shows an improved accuracy than other state-of-the-art shape-based methods applied to proliferation analysis but also produces highly sensitive proliferation annotations to assist physicians in proliferation analysis.

A two-stage monitoring scheme for multiple high-dimensional data streams

With the rapid development of data acquisition and analysis technology, the online monitoring of data streams is particularly important in modern industries. This study proposes an efficient online monitoring scheme for multiple high-dimensional data streams. We first construct a point-wise process monitoring control chart based on statistical extreme value theory. Then we use the clustering method to roughly obtain reliable data streams and suspected abnormal data streams, within the sliding window range, further identify abnormal data streams one by one over time points, and estimate the potential change points of these abnormal streams. Finally, we conduct simulations and case studies on this method, and compare it with existing competitive methods to demonstrate its effectiveness.

A new computational framework for log-concave density estimation

AbstractIn statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the log-concave maximum likelihood estimator, adoption of this method has been hampered by the complexities of the non-smooth convex optimization problem that underpins its computation. We provide enhanced understanding of the structural properties of this optimization problem, which motivates the proposal of new algorithms, based on both randomized and Nesterov smoothing, combined with an appropriate integral discretization of increasing accuracy. We prove that these methods enjoy, both with high probability and in expectation, a convergence rate of order 1/T up to logarithmic factors on the objective function scale, where T denotes the number of iterations. The benefits of our new computational framework are demonstrated on both synthetic and real data, and our implementation is available in a github repository (Log-Concave Computation).

Chaotic characterization and chaotic prediction modelling of HFSWR ionospheric echoes excited by typhoon

ABSTRACT This research explores the intricate-coupling relationship between typhoons and the ionosphere by the high-frequency surface wave radar’s (HFSWR) over-the-horizon capabilities. This letter describes the gravity wave features in travelling ionospheric disturbances (TIDs) and ionospheric drift information. Further discussion is raised on the chaotic properties of gravity wave features using the Lyapunov exponents and chaotic attractors, particularly as they are influenced by typhoon. To predict these gravity wave features more accurately, a new model is developed by synergizing phase space reconstruction theory and statistical learning theory, a chaotic prediction model for gravity wave features constructed on a third-order Volterra filter. The experimental findings confirm that the gravity waves features detected via HFSWR present the hyperchaotic behaviour. More importantly, the innovative gravity wave prediction model based on chaotic attractor can capture the dynamics of the original chaotic system. Notably, the model’s prediction accuracy has been improved by 98.6% after the introduction of phase space reconstruction modelling.

Statistical learning to identify salient factors influencing FEMA public assistance outlays

AbstractBoth the number of disasters in the U.S. and federal outlays following disasters are rising. FEMA’s Public Assistance (PA) is a key program for rebuilding damaged public infrastructure and aiding local and state governments in recovery. It is the primary post-disaster source of recovery funds. Between 2000 and 2019, more than $125B (adjusted, 2020 dollars) was awarded through PA. While all who qualify for PA should have equal opportunity to receive aid, not all do, and the factors influencing how the program has been administered are complex and multifaceted. Lacking an understanding of the factors positively associated with historical receipt of aid, there is little way to objectively evaluate the efficacy of the PA program. In this work, we evaluate the salient features that contribute to the number of county-level PA applicants and projects following disasters. We use statistical learning theory applied to repetitive flooding events in the upper Midwest between 2003 and 2018 as a case study. The results suggest that many non-disaster related indicators are key predictors of PA outlays, including the state in which the disaster occurred, the county’s prior experience with disasters, the county’s median income, and the length of time between the end of the disaster and the date when a disaster is declared. Our work suggests that indicators of PA aid are tied to exposure, bureaucratic attributes, and human behavior. For equitable distribution of aid, policymakers should explore more disaster-relevant indicators for PA distribution.

Estimation of Ultrasonic Velocity, Density, Internal Pressure, and Thermophysical Parameters of Ionic Liquid Mixtures: Application of Flory's Statistical Theory.

Flory's statistical theory (FST) has been employed to estimate the ultrasonic velocity, density, internal pressure, and several important thermophysical parameters such as the energy of vaporization, the heat of vaporization, cohesive energy density, polarity index, and solubility for eight binary mixtures of ionic liquids and water within the temperature range of 288.15 to 308.15 K. The ionic liquids chosen for this investigation are [BMim][dca], [BMim][TfO], [BMpy][TfO], [BMpyr][dca], [BMpyr][TfO], [EEPy][ESO4], [HMim][dca], and [MPy][MSO4]. The predicted values of ultrasonic velocity and density show good agreement with the data reported in the literature. It endorses the applicability of FST to these binary mixtures. A comparative analysis of the internal pressure values (Pi) determined by using FST and the standard thermodynamic approach is also presented. The results obtained for Pi using both approaches show good agreement. Besides, for the mixtures under study, the correlation between ultrasonic velocity, density, and surface tension has also been examined. The variation of thermophysical parameters with concentration and temperature changes has been utilized to explore the nature and strength of the solute-solvent interactions prevalent in these mixtures. It is pointed out that A-A-type interactions dominate over A-B-type interactions in water-rich regions of the mixtures.

Temperature dependence investigations of molecular interactions and excess thermodynamic parameters of binary mixtures of ionic liquids and water using Flory's statistical theory

Temperature dependence investigations of molecular interactions and excess thermodynamic parameters of binary mixtures of ionic liquids and water using Flory's statistical theory

Some Early Studies of Isotropic Turbulence: A Review

A re-examination of some early classic turbulence literature, mainly of isotropic turbulence, is given in this selective review. Some early studies, including original concepts and points, are reviewed or highlighted. Two earliest studies and six major original concepts are found: (i) Lord Kelvin’s pioneering elementary studies of homogeneous, isotropic turbulence; (ii) Kelvin’s early introduction of Fourier Principles into turbulence studies; (iii) the Kelvin elementary concept of the direct energy cascade; (iv) the Kelvin early concept of the symmetry of turbulence; (v) the Taylor concept of the coefficient of eddy viscosity; (vi) the Taylor concept of the ‘age’ of the eddy; (vii) the Taylor–Fage–Townend concept of small eddies or microturbulence or small scale turbulence; and (viii) the Obukhov concept of a function of the inner Reynolds number (i.e., Re dependent coefficient) in both the balance equation and the energy distribution equation (the two-thirds law). Both Kelvin and Taylor should be regarded as the co-founders of the statistical theory of homogeneous, isotropic turbulence. The notion, ‘the Maxwell–Reynolds decomposition of turbulent flow velocity’, should be used. The Kolmogorov–Obukhov scaling laws are reviewed in detail. Heisenberg’s inverse seventh power spectrum is briefly reviewed. The implications or significances of these early studies, original concepts and points are briefly discussed, with special reference to their possible links with modern approaches and theories.

Simple and complex sorption−solution isotherms for membrane polymers: A statistical thermodynamic fluctuation theory

Simple, site-specific adsorption isotherm models, such as GAB and other generalizations of BET, fit strikingly well to experimental isotherms of simple shapes for glassy and rubbery polymers. However, the structures of dense polymers do not necessarily resemble the unrestricted layer-by-layer adsorption mechanism on one type of sorption site assumed by these models. Since polymers contain micropores, sorptive likely (ad)sorbs on the internal surfaces of the free (accessible) volume voids, and dissolves in the polymer phase. While the empirical dual mode sorption model and its variants address this duality, other common models assume chiefly only one of the two mechanisms. Moreover, the simplified models do not fit complex isotherms, such as those for alcohols and poly[(trimethylsilyl)propyne] (PTMSP). The statistical thermodynamic fluctuation theory is adopted here to capture the sorption-solution duality consistently even for the complex isotherms. The statistical thermodynamic ABC isotherm derived from this theory involves the sorbate-sorbent and mono-, di-, and tri-sorbate interactions expressed by sorbate number correlations. This work shows that BET, GAB, dual-mode sorption model, Flory-Huggins, and ENSIC models are special cases of the ABC isotherm. The isotherm multiplicativity principle has been derived from the number fluctuation relationship to model complex isotherms.

Defining metrics of visual acuity from theoretical models of observers.

Many experimental studies show that metrics of visual image quality can predict changes in visual acuity due to optical aberrations. Here we use statistical decision theory and Fourier optics formalism to demonstrate that two metrics known in the field of vision sciences are approximations of two different theoretical models of linear observers. The theory defines metrics of visual acuity to potentially predict changes in visual acuity due to optical aberrations, without needing a posteriori scale or offset. We illustrate our approach with experiments, using combinations of defocus and spherical aberration, and pure coma.

Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory.

The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.

Statistical Complexity of Quantum Learning

AbstractLearning problems involve settings in which an algorithm has to make decisions based on data, and possibly side information such as expert knowledge. This study has two main goals. First, it reviews and generalizes different results on the data and model complexity of quantum learning, where the data and/or the algorithm can be quantum, focusing on information‐theoretic techniques. Second, it introduces the notion of copy complexity, which quantifies the number of copies of a quantum state required to achieve a target accuracy level. Copy complexity arises from the destructive nature of quantum measurements, which irreversibly alter the state to be processed, limiting the information that can be extracted about quantum data. As a result, empirical risk minimization is generally inapplicable. The paper presents novel results on the copy complexity for both training and testing. To make the paper self‐contained and approachable by different research communities, an extensive background material is provided on classical results from statistical learning theory, as well as on the distinguishability of quantum states. Throughout, the differences between quantum and classical learning are highlighted by addressing both supervised and unsupervised learning, and extensive pointers are provided to the literature.