Distinguishing between fractional Brownian motion with random and constant Hurst exponent using sample autocovariance-based statistics.

Fractional Brownian motion (FBM) is a canonical model for describing dynamics in various complex systems. It is characterized by the Hurst exponent, which is responsible for the correlation between FBM increments, its self-similarity property, and anomalous diffusion behavior. However, recent research indicates that the classical model may be insufficient in describing experimental observations when the anomalous diffusion exponent varies from trajectory to trajectory. As a result, modifications of the classical FBM have been considered in the literature, with a natural extension being the FBM with a random Hurst exponent. In this paper, we discuss the problem of distinguishing between two models: (i) FBM with the constant Hurst exponent and (ii) FBM with random Hurst exponent, by analyzing the probabilistic properties of statistics represented by the quadratic forms. These statistics have recently found application in Gaussian processes and have proven to serve as efficient tools for hypothesis testing. Here, we examine two statistics-the sample autocovariance function and the empirical anomaly measure-utilizing the correlation properties of the considered models. Based on these statistics, we introduce a testing procedure to differentiate between the two models. We present analytical and simulation results considering the two-point and beta distributions as exemplary distributions of the random Hurst exponent. Finally, to demonstrate the utility of the presented methodology, we analyze real-world datasets from the financial market and single particle tracking experiment in biological gels.

Testing of two-dimensional Gaussian processes by sample cross-covariance function.

In this paper, we address the issue of testing two-dimensional Gaussian processes with a defined cross-dependency structure. Multivariate Gaussian processes are widely used in various applications; therefore, it is essential to identify the theoretical model that accurately describes the data. While it is relatively straightforward to do so in a one-dimensional case, analyzing multi-dimensional vectors requires considering the dependency between the components, which can significantly affect the efficiency of statistical methods. The testing methodology presented in this paper is based on the sample cross-covariance function and can be considered a natural generalization of the approach recently proposed for testing one-dimensional Gaussian processes based on the sample autocovariance function. We verify the efficiency of this procedure on three classes of two-dimensional Gaussian processes: Brownian motion, fractional Brownian motion, and two-dimensional autoregressive discrete-time process. The simulation results clearly demonstrate the effectiveness of the testing methodology, even for small sample sizes. The theoretical and simulation results are supported by analyzing two-dimensional real-time series that describe the main risk factors of a mining company, namely, copper price and exchange rates (USDPLN). We believe that the introduced methodology is intuitive and relatively simple to implement, and thus, it can be applied in many real-world scenarios where multi-dimensional data are examined.

Weigh-in-Motion Site for Type Approval of Vehicle Mass Enforcement Systems in Poland.

The need to protect road infrastructure makes it necessary to direct the mass enforcement control of motor vehicles. Such control, in order to fulfil its role, must be continuous and universal. The only tool currently known to achieve these goals are weigh-in-motion (WIM) systems. The implementation of mass enforcement WIM systems is possible only if the requirements for their metrological properties are formulated, followed by the implementation of administrative procedures for the type approval of WIM systems, rules for their metrological examination, and administrative regulations for their practical use. The AGH University of Krakow, in cooperation with the Central Office of Measures (Polish National Metrological Institute), has been conducting research in this direction for many years, and, now, as part of a research project financed by the Ministry of Education and Science. In this paper, we describe a unique WIM system located in the south of Poland and the results of over two years of our research. These studies are intended to lead to the formulation of requirements for metrological legalisation procedures for this type of system. Our efforts are focused on implementing WIM systems in Poland for direct mass enforcement. The tests carried out confirmed that the constructed system is fully functional. Its equipment with quartz and bending plate load sensors allows for the comparison of both technologies and the measurement of many parameters of the weighed vehicle and environmental parameters affecting weighing accuracy. The tests confirmed the stability of its metrological parameters. The GVW maximal measurement error does not exceed 5%, and the single axle load maximal measurement error does not exceed 12%. The sensors of the environmental parameters allow for the search for correlations between weighing accuracy and the intensity of these parameters.

High Accuracy Weigh-In-Motion Systems for Direct Enforcement.

In many countries, work is being conducted to introduce Weigh-In-Motion (WIM) systems intended for continuous and automatic control of gross vehicle weight. Such systems are also called WIM systems for direct enforcement (e-WIM). The achievement of introducing e-WIM systems is conditional on ensuring constant, known, and high-accuracy dynamic weighing of vehicles. WIM systems weigh moving vehicles, and on this basis, they estimate static parameters, i.e., static axle load and gross vehicle weight. The design and principle of operation of WIM systems result in their high sensitivity to many disturbing factors, including climatic factors. As a result, weighing accuracy fluctuates during system operation, even in the short term. The article presents practical aspects related to the identification of factors disturbing measurement in WIM systems as well as methods of controlling, improving and stabilizing the accuracy of weighing results. Achieving constant high accuracy in weighing vehicles in WIM systems is a prerequisite for their use in the direct enforcement mode. The research results presented in this paper are a step towards this goal.

Multiclass Image Classification Using GANs and CNN Based on Holes Drilled in Laminated Chipboard.

The multiclass prediction approach to the problem of recognizing the state of the drill by classifying images of drilled holes into three classes is presented. Expert judgement was made on the basis of the quality of the hole, by dividing the collected photographs into the classes: "very fine," "acceptable," and "unacceptable." The aim of the research was to create a model capable of identifying different levels of quality of the holes, where the reduced quality would serve as a warning that the drill is about to wear down. This could reduce the damage caused by a blunt tool. To perform this task, real-world data were gathered, normalized, and scaled down, and additional instances were created with the use of data-augmentation techniques, a self-developed transformation, and with general adversarial networks. This approach also allowed us to achieve a slight rebalance of the dataset, by creating higher numbers of images belonging to the less-represented classes. The datasets generated were then fed into a series of convolutional neural networks, with different numbers of convolution layers used, modelled to carry out the multiclass prediction. The performance of the so-designed model was compared to predictions generated by Microsoft's Custom Vision service, trained on the same data, which was treated as the benchmark. Several trained models obtained by adjusting the structure and hyperparameters of the model were able to provide better recognition of less-represented classes than the benchmark.

Optimised Autocalibration Algorithm of Weigh-In-Motion Systems for Direct Mass Enforcement.

Dynamic vehicle weighing systems, also known as Weigh-In-Motion (WIM), are sensitive to factors which interfere with the measurement, including weather and climate conditions. This is a result of the sensitivity of the axle load sensors used in the systems. As a result, a significant change in the precision of weighing can be observed over short periods of time (even less than 1 h). This fact is a deterrent to the use of such systems for direct mass enforcement. In this article, we present a solution for this problem using an optimised autocalibration algorithm. We show the results of simulation studies which we conducted on the proposed algorithm. These were then verified experimentally at an in-road site. We demonstrated that autocalibration of the WIM system allows for effective limitation of the sensitivity of weighing results to interfering factors. This is, however, conditioned on a sufficiently high frequency of reference vehicles crossing the WIM site. The required frequency depends on the speed of change in the concentration of influencing factors.

Sensor Data Fusion in Multi-Sensor Weigh-In-Motion Systems.

In this paper, we present the results of a comparison of two estimators of the gross vehicle weight (GVW) and the static load of individual axles of vehicles. The estimators were used to process measurement data derived from Multi-Sensor Weigh-In-Motion systems (MS-WIM). The term estimator is understood as an algorithm according to which the dynamic axle load measurement results are processed in order to determine the static load. The result obtained is called static load estimate. As a measure of measurement uncertainty, we adopted the standard deviation of the static load estimate. The mean value and the maximum likelihood estimators were compared. Studies were conducted using simulation methods based on synthetic data and experimental data obtained from a WIM system equipped with 16 lines of polymer axle load sensors. We have shown a substantially lower uncertainty of estimates determined using the maximum likelihood estimator. The results obtained have considerable practical significance, particularly during long-term usage of multi-sensor WIM systems.

Inductive Loop Axle Detector Based on Resistance and Reactance Vehicle Magnetic Profiles.

The article presents a measurement system that captures two components of a motor vehicle's magnetic profile, which are associated with the real and imaginary part of the impedance of a narrow inductive loop sensor. The proposed algorithm utilizes both components of the impedance magnetic profile to detect vehicle axles, including lifted axles. Accuracies of no less than 71.8% were achieved for vehicles travelling with a lifted axle, and no less than 98.8% for other vehicles. The axle detection accuracy was determined during a series of experiments carried out under normal traffic conditions, using profile analysis, video footage and reference signals from an axle load detector on a total of 4000 vehicles.

Eddy-Current Sensors with Asymmetrical Point Spread Function.

This paper concerns a special type of eddy-current sensor in the form of inductive loops. Such sensors are applied in the measuring systems classifying road vehicles. They usually have a rectangular shape with dimensions of 1 × 2 m, and are installed under the surface of the traffic lane. The wide Point Spread Function (PSF) of such sensors causes the information on chassis geometry, contained in the measurement signal, to be strongly averaged. This significantly limits the effectiveness of the vehicle classification. Restoration of the chassis shape, by solving the inverse problem (deconvolution), is also difficult due to the fact that it is ill-conditioned. An original approach to solving this problem is presented in this paper. It is a hardware-based solution and involves the use of inductive loops with an asymmetrical PSF. Laboratory experiments and simulation tests, conducted with models of an inductive loop, confirmed the effectiveness of the proposed solution. In this case, the principle applies that the higher the level of sensor spatial asymmetry, the greater the effectiveness of the deconvolution algorithm.

Thermal Property Analysis of Axle Load Sensors for Weighing Vehicles in Weigh-in-Motion System.

Systems which permit the weighing of vehicles in motion are called dynamic Weigh-in-Motion scales. In such systems, axle load sensors are embedded in the pavement. Among the influencing factors that negatively affect weighing accuracy is the pavement temperature. This paper presents a detailed analysis of this phenomenon and describes the properties of polymer, quartz and bending plate load sensors. The studies were conducted in two ways: at roadside Weigh-in-Motion sites and at a laboratory using a climate chamber. For accuracy assessment of roadside systems, the reference vehicle method was used. The pavement temperature influence on the weighing error was experimentally investigated as well as a non-uniform temperature distribution along and across the Weigh-in-Motion site. Tests carried out in the climatic chamber allowed the influence of temperature on the sensor intrinsic error to be determined. The results presented clearly show that all kinds of sensors are temperature sensitive. This is a new finding, as up to now the quartz and bending plate sensors were considered insensitive to this factor.

Long term outcome of heart failure patients disqualified from heart transplantation.

BACKGROUND: The prognosis of patients with advanced heart failure is unfavourable. However, little is known about the survival of patients referred for heart transplantation but finally disqualified from transplantation due to contraindications. This study aimed to evaluate the prognosis of patients' disqualified from heart transplantation. METHODS: It was a retrospective study based on medical records of patients disqualified from heart transplantation. RESULTS: One hundred and fifty-one patients were included and 94 deaths were recorded during long-term follow-up (range 0.02-10.1 years). The survival rate at 5 years was 25%. The mean age of the studied population was 57.7 years and the majority of patients were males, 87.4%. The ischaemic aetiology (66.2%) was the most dominant aetiology of heart failure. In the Cox regression model, supervision by the specialist cardiology centre (HR 0.61;p = 0.04) and pharmacotherapy with beta-blockers (HR = 0.47;p = 0.02) positively influenced the prognosis. On the contrary, well-known heart failure risk factors like a renal failure (HR 1.59;p = 0.049), pulmonary hypertension (HR 1.55;p = 0.046), liver failure (HR 2.65;p = 0.02) were negative predictors of outcome. By Kaplan-Meier analysis, patients with other than pulmonary hypertension causes of disqualification from heart transplantation had a better survival rate, p = 0.047. CONCLUSIONS: The prognosis of patients disqualified from heart transplantation is unfavourable. However, some of the patients experience relatively long survival. Therefore, careful clinical assessment and identification of factors influencing prognosis may improve adequate patients' qualifications for heart transplantation.

Probabilistic properties of detrended fluctuation analysis for Gaussian processes.

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter.

Longevity and cardiovascular mortality of Polish elite football players.

BACKGROUND: Despite wide popularity of football, there is a paucity of scientific evidence explaining the relationship between being a competitive footballer and life expectancy. AIM: The study analyses and compares cause-specific mortality of Polish male elite footballers and the general Polish male population. METHODS: Data regarding of 455 elite footballers who died between 1990 and 2015 were retrospectively analysed. The cause of death was established based on the official data from the Polish Central Statistical Office. The control group consisted of men from the general male population in Poland who died in the sampled period at the age of 25 years or more. RESULTS: The mean age at death turned out to be higher for footballers than controls (70.2 vs. 67.4 years). Cardiovascular diseases were a more common cause of death among footballers than in the general male population, both in the subgroup of subjects who died under the age of 65 years and in those who were at least 65 years old at the time of death (46.9% vs. 32.3% and 61.3% vs. 53.3%, respectively). A detailed analysis of cause-specific cardiovascular mortality revealed that acute myocardial infarction caused more deaths (odds ratio [OR] 1.31; 95% confidence interval [CI] 1.02-1.68) and hypertensive disease caused less deaths (OR 0.20; 95% CI 0.05-0.79) among athletes than in the general male population. A trend analysis has shown that the level of cardiovascular mortality among footballers is falling. CONCLUSIONS: The study results indicate excess cardiovascular mortality among Polish elite footballers.

Improving oncoplastic breast tumor bed localization for radiotherapy planning using image registration algorithms.

Knowledge about tumor bed localization and its shape analysis is a crucial factor for preventing irradiation of healthy tissues during supportive radiotherapy and as a result, cancer recurrence. The localization process is especially hard for tumors placed nearby soft tissues, which undergo complex, nonrigid deformations. Among them, breast cancer can be considered as the most representative example. A natural approach to improving tumor bed localization is the use of image registration algorithms. However, this involves two unusual aspects which are not common in typical medical image registration: the real deformation field is discontinuous, and there is no direct correspondence between the cancer and its bed in the source and the target 3D images respectively. The tumor no longer exists during radiotherapy planning. Therefore, a traditional evaluation approach based on known, smooth deformations and target registration error are not directly applicable. In this work, we propose alternative artificial deformations which model the tumor bed creation process. We perform a comprehensive evaluation of the most commonly used deformable registration algorithms: B-Splines free form deformations (B-Splines FFD), different variants of the Demons and TV-L1 optical flow. The evaluation procedure includes quantitative assessment of the dedicated artificial deformations, target registration error calculation, 3D contour propagation and medical experts visual judgment. The results demonstrate that the currently, practically applied image registration (rigid registration and B-Splines FFD) are not able to correctly reconstruct discontinuous deformation fields. We show that the symmetric Demons provide the most accurate soft tissues alignment in terms of the ability to reconstruct the deformation field, target registration error and relative tumor volume change, while B-Splines FFD and TV-L1 optical flow are not an appropriate choice for the breast tumor bed localization problem, even though the visual alignment seems to be better than for the Demons algorithm. However, no algorithm could recover the deformation field with sufficient accuracy in terms of vector length and rotation angle differences.

Percutaneous mitral balloon valvuloplasty: beyond classic indications.

BACKGROUND AND AIM: In patients with mitral stenosis (MS) percutaneous mitral balloon valvuloplasty (PMBV) is used to im-prove symptoms and prognosis. Although there is some evidence for potential long-term benefits from PMBV in asymptomatic patients with mitral valve area (MVA) between 1.0 and 1.5 cm2, there are no follow-up data on patients with symptomatic MS with MVA > 1.5 cm2, who underwent PMBV. METHODS: We retrospectively analysed periprocedural results of 113 symptomatic patients who underwent PMBV for MS with MVA > 1.5 cm2 (group 1) and compared them with a control group of patients with MVA ≤ 1.5 cm2 (group 2). Clinical and procedural variables were compared between groups. RESULTS: In group 1, PMBV resulted in a significant increase of MVA as well as a decrease of mean and maximal mitral gradients and mean left atrial pressure (LAP), and a subsequent decrease of mean and systolic pulmonary artery pressures (PAPs). Moreover, 6.3% of patients developed moderate to severe (3+) or severe (4+) post-procedural mitral regurgitation (MR). Post-procedural increase in MVA and decrease of LAP were more pronounced in group 2 than group 1 (∆MVA 0.74 cm2 vs. 0.41 cm2, p < 0.05, and ∆LAP 8.2 mmHg vs. 6.0 mmHg, p < 0.05). Nonetheless, no significant differences were observed for ∆ of mean and systolic PAPs. The grade of post-procedural MR was comparable between groups. CONCLUSIONS: PMBV is a feasible procedure in highly selected patients without classic echocardiographic indications. None-theless, it is associated with a small but non-negligible periprocedural risk of developing severe MR.

Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis.

Protein and lipid nanodomains are prevalent on the surface of mammalian cells. In particular, it has been recently recognized that ion channels assemble into surface nanoclusters in the soma of cultured neurons. However, the interactions of these molecules with surface nanodomains display a considerable degree of heterogeneity. Here, we investigate this heterogeneity and develop statistical tools based on the recurrence of individual trajectories to identify subpopulations within ion channels in the neuronal surface. We specifically study the dynamics of the K^{+} channel Kv1.4 and the Na^{+} channel Nav1.6 on the surface of cultured hippocampal neurons at the single-molecule level. We find that both these molecules are expressed in two different forms with distinct kinetics with regards to surface interactions, emphasizing the complex proteomic landscape of the neuronal surface. Further, the tools presented in this work provide new methods for the analysis of membrane nanodomains, transient confinement, and identification of populations within single-particle trajectories.

Voice data mining for laryngeal pathology assessment.

The aim of this study was to evaluate the usefulness of different methods of speech signal analysis in the detection of voice pathologies. Firstly, an initial vector was created consisting of 28 parameters extracted from time, frequency and cepstral domain describing the human voice signal based on the analysis of sustained vowels /a/, /i/ and /u/ all at high, low and normal pitch. Afterwards we used a linear feature extraction technique (principal component analysis), which enabled a reduction in the number of parameters and choose the most effective acoustic features describing the speech signal. We have also performed non-linear data transformation which was calculated using kernel principal components. The results of the presented methods for normal and pathological cases will be revealed and discussed in this paper. The initial and extracted feature vectors were classified using the k-means clustering and the random forest classifier. We found that reasonably good classification accuracies could be achieved by selecting appropriate features. We obtained accuracies of up to 100% for classification of healthy versus pathology voice using random forest classification for female and male recordings. These results may assist in the feature development of automated detection systems for diagnosis of patients with symptoms of pathological voice.

Kramers' escape problem for fractional Klein-Kramers equation with tempered α-stable waiting times.

In this paper we extend the subdiffusive Klein-Kramers model, in which the waiting times are modeled by the α-stable laws, to the case of waiting times belonging to the class of tempered α-stable distributions. We introduce a generalized version of the Klein-Kramers equation, in which the fractional Riemman-Liouville derivative is replaced with a more general integro-differential operator. This allows a transition from the initial subdiffusive character of motion to the standard diffusion for long times to be modeled. Taking advantage of the corresponding Langevin equation, we study some properties of the tempered dynamics, in particular, we approximate solutions of the tempered Klein-Kramers equation via Monte Carlo methods. Also, we study the distribution of the escape time from the potential well and compare it to the classical results in the Kramers escape theory. Finally, we derive the analytical formula for the first-passage-time distribution for the case of free particles. We show that the well-known Sparre Andersen scaling holds also for the tempered subdiffusion.

Fractional Fokker-Planck equation with tempered α-stable waiting times: langevin picture and computer simulation.

In this paper we introduce a Langevin-type model of subdiffusion with tempered α-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales. We derive general properties of tempered anomalous diffusion from the theory of tempered α-stable processes, in particular we find the form of the fractional Fokker-Planck equation corresponding to the tempered subdiffusion. We also construct an algorithm of simulation of sample paths of the introduced process. We apply the algorithm to approximate solutions of the fractional Fokker-Planck equation and to study statistical properties of the tempered subdiffusion via Monte Carlo methods.