Distribution Of Increments Research Articles

Large deviations for the right-most position of a last progeny modified branching random walk

In this work, we consider a modification of the usual Branching Random Walk (BRW), where we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the $n$-th generation, which may be different from the driving increment distribution. This model was first introduced by Bandyopadhyay and Ghosh (2021) and they termed it as Last Progeny Modified Branching Random Walk (LPM-BRW). Under very minimal assumptions, we derive the large deviation principle (LDP) for the right-most position of a particle in generation $n$. As a byproduct, we also complete the LDP for the classical model, which complements the earlier work by Gantert and H\"{o}felsauer (2018).

The Regularity of Stress Shielding in Internal Fixation Characterized by Hydromechanics.

Stress shielding is an important factor in the internal fixation of a fracture. To explore the regularity of stress shielding in internal fixation, a simplified model of a comminuted femoral shaft fracture bridged by a locking plate was established and finite element analysis was performed to analyze the load distribution between the plate and femur from the proximal end of the femur to the fracture line and investigate the stress shielding degree of the plate on the bone. The stress, deformation, and axial compressive force distribution of four internal fixation schemes under compression were obtained, and the stress shielding degrees on each section was calculated. To compare the regularity of stress shielding and flow distribution, the relationship between the compressive force increment and stress shielding degree was established. The normalized curves of compressive force increment with the plate section position were compared with the flow distribution in a Z-type manifold, a parallel pipe system similar to an internal fixation system in structure and working characteristics. For quantitative comparison, the similarity between normalized curves of the compressive force increment and simulated flow distribution was calculated. The regularity of load distribution along the section position of the plate was similar to the flow distribution in the Z-type manifold. Therefore, the flow distribution pattern of the Z-type manifold can be used to characterize the regularity of load distribution in internal fixation. This study provided a new method to characterize the stress shielding degree of a locking plate on bone.

On a limit behaviour of a random walk penalised in the lower half-plane

We consider a random walk Ŝ which has different increment distributions in positive and negative half-planes. In the upper half-plane the increments are mean-zero i.i.d. with finite variance. In the lower half-plane we consider two cases: increments are positive i.i.d. random variables with either a slowly varying tail or with a finite expectation. For the distributions with a slowly varying tails, we show that {Ŝ(nt)/√n} has no weak limit in D([0,1]); alternatively, the weak limit is a reflected Brownian motion.

Multifractal magnetoconductance fluctuations in mesoscopic systems.

We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresponding "stochastic time series," with the magnetic field playing the role of a fictitious time. More specifically, we show that the distributions of conductance increments are well fitted by q Gaussians and that the value of the parameter q is a useful quantitative measure of multifractality in magnetoconductance fluctuations.

Anomalous diffusion in the citation time series of scientific publications

We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse anomalously, their variance scales with time ∝t 2H , where H ≠ 1/2. We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution. The papers exhibit a high degree of heterogeneity across the various fields, as the statistics of the highest cited papers is fundamentally different from that of the lower ones. The citation data is shown to be highly correlated and non-stationary; as all the papers except the small percentage of them with high number of citations, die out in time.

Additive Processes on the Unit Circle and Loewner Chains

Abstract This paper defines the notion of generators for a class of decreasing radial Loewner chains that are only continuous with respect to time. For this purpose, “Loewner’s integral equation”, which generalizes Loewner’s differential equation, is defined and analyzed. The definition of generators is motivated by the Lévy–Khintchine representation for additive processes on the unit circle. Actually, we can and do introduce a homeomorphism between the above class of Loewner chains and the set of the distributions of increments of additive processes equipped with suitable topologies. On the other hand, from the viewpoint of non-commutative probability theory, the above generators also induce bijections with some other objects: in particular, monotone convolution hemigroups and free convolution hemigroups. Finally, the generators of Loewner chains constructed from free convolution hemigroups via subordination are computed.

Consolidation deformation of hydrate-bearing sediments: A pore-scale computed tomography investigation

Consolidation deformation is prevalent in hydrate-bearing sediments due to oceanic currents, the erection of jack-up drilling rig platforms, depressurization exploitation, etc. However, the microstructural behavior of hydrate-bearing sediment during consolidation remains unclear because of experimental challenges. Herein, using a novel microfocus X-ray CT-based triaxial testing apparatus, we present a series of results to reveal the microstructural evolution of hydrate-bearing sediment using the pixel-tracking technique at the submillimeter level. Initially, a stepped cone-shaped incremental displacement distribution with a relatively large deformation was observed, a rapid decline in the total number and radii of pores was noted, and the hydrate-sand interfacial area was greatly enlarged. Later, only some scattered large incremental displacement zones were found, the decline in the total number and radii of pores slowed, and the increase in the hydrate-sand interfacial area also slowed. The deformation pattern inside the hydrate-bearing sediment presented a strong relationship with the hydrate saturation; however, no obvious hydrate crushing occurred within 3 MPa of effective confining pressure, either visually or quantitatively. The consolidation could lead to a more complex pore system and lower coordination number between the pore and the throat, which led to a decrease in absolute permeability.

Exploring the manifestation of distributed leadership in Chinese Higher Education

ABSTRACT Distributed leadership has become one of the most popular and important leadership models in the West, particularly in the field of education. However, both theoretical and empirical research into distributed leadership in the Chinese Higher Education context is rare. This dearth of literature on the subject has motivated the authors to carry out a research project focusing, from a Chinese perspective, on distributed leadership at the departmental level in one Chinese university. This article aims to determine the extent to which leadership is distributed at the departmental level, and the mechanism of leadership distribution in the Chinese context through the perceptions of Chinese Heads and other members of their departments. By conducting mixed methods research, which comprises questionnaires followed by semi-structured interviews, the findings of this study suggest that although the organizational structure is primarily hierarchical, leadership has been distributed to some extent within the departments. Leadership responsibilities are distributed mainly through formal distribution, and also through other top-down approaches, such as pragmatic and incremental distribution, implying the beginning of the practice of distributed leadership. The findings also suggest that leadership in this Chinese context is distributed through allocative practice, which is seen as more appropriate for centralized contexts.

A machine learning-driven stochastic simulation of underground sulfide distribution with multiple constraints

Abstract The increase of sulfide (S2−) during the water flooding process has been regarded as an essential and potential risk for oilfield development and safety. Kriging and stochastic simulations are common methods for assessing the element distribution. However, these traditional simulation methods are not able to predict the continuous changes of underground S2− distribution in the time domain by limited known information directly. This study is a kind of attempt to combine stochastic simulation and the modified probabilistic neural network (modified PNN) for simulating short-term changes of S2− concentration. The proposed modified PNN constructs the connection between multiple indirect datasets and S2− concentration at sampling points. These connections, which are treated as indirect data in the stochastic simulation processes, is able to provide extra supports for changing the probability density function (PDF) and enhancing the stability of the simulation. In addition, the simulation process can be controlled by multiple constraints due to which the simulating target has been changed into the increment distribution of S2−. The actual data test provides S2− distributions in an oil field with good continuity and accuracy, which demonstrate the outstanding capability of this novel method.

Increment analysis in black locust (Robinia pseudoacacia L.) stand – a case study

The study on the diameter and volume increment of black locust (Robinia pseudoacacia L.) stand (age 10-27 years, yield class II) have shown that in comparison to the periodic annual increment of the breast height diameter of tree in height class I, trees in height class II have reached 83.3%, while in class III only 43.9. The same relations for volume were found 59.0% and 24.5%, respectively. The mean values of the whole stand were close to those of height class II. According to the distribution of the periodic annual increment of volume between 10 and 27 years of age, 50% of the values were between 2.00 and13.88 dm3, 73% were between 2.00 and19.82 dm3, and 96% were between 2.00 and 37.64 dm3. The range of 13.88–19.82 dm3 had the highest occurrence (24.5%).

Fractional Lévy stable motion with LRD for RUL and reliability analysis of li-ion battery

The Remaining Useful Life (RUL) is important for reliability analysis of li-ion battery. Reliability of li-ion battery decreases with shortened the RUL. The RUL of li-ion battery can be revealed by the capacity change. The future change of the capacity is related to the current and the historical states, namely, the capacity change of li-ion battery has Long-Range Dependence (LRD). This article describes a RUL prediction method based on fractional order Lévy stable motion (fLsm), which solves the LRD was not obvious caused by the excessive difference of the integer-order model. First, the LRD of the fLsm is revealed by stability index and integral kernel function with Hurst parameter. Then, the fLsm is used as a diffusion term, which reflects the stochastic and LRD of the RUL degradation, to establish a degradation prediction model. The iterative form of the prediction model is established through the incremental distribution of the fLsm. Finally, the RUL is predicted by the Monte Carlo simulation and degradation prediction model. The predictive performance of the fLsm degradation model is verified by battery data in different operating environments. The reliability of li-ion battery is analyzed by the RUL.

Changes in the Radial Increment and CO2 Distribution in Larches that Survived the Explosion of the Tunguska Space Body

Changes in the Radial Increment and CO2 Distribution in Larches that Survived the Explosion of the Tunguska Space Body

Control design based on multi-index nonlinear control method

Firstly, a nonlinear control system based on the Riemannian manifold is defined from the perspective of holism, and the expression of the system’s state equation in the local coordinate system of the Riemannian manifold is given. The geometric structure of the Riemannian manifold is discussed. The influence of nonlinear systems is studied. The controllability and observability of nonlinear systems is studied. Secondly, using the properties of involute distribution and fully geodesic submanifolds, the local parts of nonlinear systems based on Riemannian manifolds are given. Controllable structured decomposition, local observable structure decomposition and Kalman decomposition. Thirdly, using the properties of orthogonal involute distribution family, incremental involute distribution family and fully geodesic submanifold family, the research is based on Riemannian manifolds. The parallel decoupling problem and cascade decoupling problem of nonlinear control systems on the above, as well as the local disturbance decoupling problem of affine nonlinear control systems.

Correlation Analysis of Influencing Factors and the Monthly Displacement Increment of a Hydrodynamic Landslide Using a Pseudo-Maximum-Likelihood-Estimation-Mixed-Copula Approach

Heavy rainfall and changes in the water levels of reservoirs directly affect the degree of landslide disasters in major hydropower project reservoir areas. Correlation analyses of rainfall- and water-level fluctuations with landslide displacement changes can provide a scientific basis for the prevention and early warning of landslide disasters in reservoir areas. Because of the shortcomings of the traditional correlation analysis based on linear assumptions, this study proposed the use of a pseudo-maximum-likelihood-estimation-mixed-Copula (MLE-M-Copula) method instead of linear assumptions. We used the Bazimen landslide in the Three Gorges Reservoir Area as a case study to carry out the correlation analysis of the rainfall, water-level fluctuations, and landslide displacement. First, we selected several appropriate influencing factors to construct four candidate Copula models and estimated the parameters using the pseudo-MLE method. After the goodness-of-fit test, we selected the M-Copula model as the optimal model and used this model to study correlations between the monthly displacement increment of the landslide and influencing factors. We then established the joint distribution functions of these correlations. We computed and analyzed the overall and tail correlations between the displacement increment and the influencing factors, and we constructed the conditional probability distribution of the monthly displacement increment for different given conditions. The results showed that the pseudo-MLE-M-Copula method effectively quantified the correlation between the rainfall, reservoir-level fluctuations, and landslide displacement changes, and we obtained the return periods and value at risk of the influencing factors of the Bazimen landslide under different rainfall conditions and reservoir-level changes. Furthermore, the tail correlations between the monthly displacement increment of the landslide and the rainfall- and reservoir-level changes were higher than the overall correlations.

Generalized Cauchy Process: Difference Iterative Forecasting Model

The contribution of this article is mainly to develop a new stochastic sequence forecasting model, which is also called the difference iterative forecasting model based on the Generalized Cauchy (GC) process. The GC process is a Long-Range Dependent (LRD) process described by two independent parameters: Hurst parameter H and fractal dimension D. Compared with the fractional Brownian motion (fBm) with a linear relationship between H and D, the GC process can more flexibly describe various LRD processes. Before building the forecasting model, this article demonstrates the GC process using H and D to describe the LRD and fractal properties of stochastic sequences, respectively. The GC process is taken as the diffusion term to establish a differential iterative forecasting model, where the incremental distribution of the GC process is obtained by statistics. The parameters of the forecasting model are estimated by the box dimension, the rescaled range, and the maximum likelihood methods. Finally, a real wind speed data set is used to verify the performance of the GC difference iterative forecasting model.

Vasculitis on Heart Transplant as an Emerging Prognostic Factor

Purpose Vasculitis had been considered a histopathological marker in severe form of both cellular and humoral rejection. However, in mild forms of rejections, it has not been considered a diagnostic and prognostic histopathologic criterion. Aim of this study is to assess clinical relevance of vasculitis, in terms of mortality and cardiac allograft vasculopathy development, in the mild forms of rejection in heart transplanted patients. Methods We reviewed 2794 monitoring endomyocardial biopsies from 170 adult heart transplanted pts at our center. On endomyocardial biopsies, we evaluated the presence of vasculitis in the different types of rejection . Clinical data were collected during follow up. A Multi-State Markov model was applied to describe the rejection dynamic profile and hazard for mortality, persistence of rejection and CAV development.. We used as reference population the registry data of patients who underwent HTX from 2004 to 2018 provided by the International Society for Heart and Lung Transplantation (ISHLT) Thoracic Organ Transplant Registry Results Vasculitis was detected in 442 endomyocardial biopsies ( 442/2794, 15,8%) with an incremental percent distribution according to the severity of rejection. In ACR, vasculitis significantly increased the risk of mortality by 9% (HR [95% CI]: 1.09; [1.00-1.18]) the hazard of mortality if the patient was negative for ACR and by 14% (HR [95% CI]: 1.14; [1.02-1.37], if the patients was negative for ACR, and by 14% in a mild form of rejection (1R). Similar results were obtained for pAMR and mixed rejection. In ACR, pAMR and mixed rejection patients with vasculitis have a shorter life expectancy than patients without with a loss of four months at ten year follow up for ACR, and of 9 months for pAMR and mixed rejection. Conclusion Vasculitis when present, independently from the grade and type of rejection, carries a negative prognostic value. The worse histopathological feature was represented by the association of pAMR+ACR and vasculitis.

Reliability Evaluation by a Dependent Competing Failure Model Including a Time-Varying Rate for Sudden Degradation Increments

In this study, an effective dependent competing failure model is proposed for systems suffering from shocks. Under worse system degradation, shocks with the same magnitudes can bring larger sudden degradation increments. However, this relationship was ignored in most existing research. To address this problem, in the proposed failure model, a time-dependent rate is included for the sudden degradation increments by shocks. This time-varying rate is applied for the consideration that system degradation is closely related to operation time. Two dependent competing failure processes, i.e., soft failure and hard failure, are involved in the dependent competing failure model. The distribution of the total sudden degradation increments is then deduced, and its accuracy is verified by Monte Carlo simulation. The developed reliability model is illustrated by the reliability analysis of a microelectromechanical system. The sensitivity analyses of important parameters are also performed. The analysis results show that the proposed time-varying model effectively considers the impact of system degradation on sudden degradation increments, and by using this model, the change of sudden degradation increments can be well reflected under different system performances. These advantages make the reliability model more practical and help achieve more effective maintenance policies.

Exploring spatial distributions of increments in soil heavy metals and their relationships with environmental factors using GWR

Due to human activities and industrial production, heavy metals accumulate continuously in soils, resulting in environmental ecological risks. Thus, it is critical to reveal the spatial patterns of the increments in soil heavy metals and their influencing factors to prevent the continuous deterioration of soil due to heavy metal pollution. In this study, based on soil samples collected in 2016 and 2019 at the same sites in the southern part of Daye city, the spatial distributions of increments in soil heavy metals were obtained using spatial interpolation and overlap methods. Then, the geographically weighted regression (GWR) model was used to analyze the influence of various environmental factors in three categories (location characteristics, topographical factors, and soil properties) on the increments in soil heavy metals. The results showed the following: (1) The soils in the study region were severely polluted with Cd, Cu, Pb, and Zn. Throughout almost the whole study region, the concentrations of these four heavy metals in soil exceeded local background values. (2) The concentrations of Cd, Cu, Pb, and Zn increased from 2016 to 2019 in 77.38%, 59.71%, 68.42%, and 49.21% of the study region, respectively. According to the spatial distribution of comprehensive change index values, soil heavy metal pollution continued to deteriorate in 74.4% of the study region from 2016 to 2019. (3) The GWR model revealed spatially varying relationships between the increases in soil heavy meals and environmental factors, and the results indicated that location characteristics and topographical factors had the largest and smallest influences, respectively, on the spatiotemporal increments in soil heavy metals. The influences of soil properties on the increments in soil heavy metals were similar to the influences on their concentrations. The GWR model had a higher R2 and lower AICc than the ordinary least square regression model, indicating that GWR had a stronger ability to explain the relationships between the increments in soil heavy metals and environmental factors.

Moses, Noah and Joseph effects in Lévy walks

We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the ‘Joseph effect’ (Mandelbrot and Wallis 1968 Water Resour. Res. 4 909), fat-tails of the increment probability density lead to a ‘Noah effect’ (Mandelbrot and Wallis 1968 Water Resour. Res. 4 909), and non-stationarity, to the ‘Moses effect’ (Chen et al 2017 Phys. Rev. E 95 042141). After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Lévy walk, compare our results to theoretical predictions, and discuss the generality of the method.

Generalized Cauchy difference iterative forecasting model for wind speed based on fractal time series

The local irregularity and global correlation of wind speed can be described by the fractal dimension D and the Hurst parameter H. However, the existing mathematical models imply a linear relationship between the fractal dimension D and the Hurst parameter H, which is not adequate to describe the complete characteristics of the wind speed. To overcome the descriptive limitations of the $$D-H$$ linearity assumption, in this paper, we introduce novel model, based on the generalized Cauchy (GC) process, for simulation and forecasting of wind speed. In the model, the fractal dimension D and Hurst parameter H can be combined arbitrarily to describe the local irregularity and global correlation of the wind speed. Furthermore, the GC process is taken as the disturbance fluctuation term in the forecasting model, and a difference iteration form is obtained as difference equation and incremental distribution. In such model, the maximum forecasting range of the wind speed is determined by the maximum Lyapunov exponent. To illustrate the properties of the model and its performance, simulating and forecasting of the actual wind speeds in two regions are reported.