Irregular Sets Research Articles

Wheel–rail stochastic dynamics and rail wear analysis of small radius curved sections of a tram line based on generalized probability density evolution

Compared with ordinary railways, the curve radius of tram lines tends to be smaller, with minimum values of only 30 m. Therefore, wheel–rail interaction is more intense and complicated in sections of small radius tram line curves. Using a stochastic variable sample set based on a generalized probability density evolution method, the stochastic variable–spectrum representation method was used to generate a time-domain sample set of stochastic track irregularities. By inputting the stochastic set of track irregularities into a tram-track coupled dynamic system model, the stochastic dynamic response of the coupled dynamic system can be obtained. Moreover, by substituting the stochastic dynamic system response into the generalized probability density evolution formula, the process of probability density evolution of each evaluation index can be obtained by the finite difference method. Finally, the dynamic response of the tram-track coupled dynamic system can be evaluated by the probability distribution of each index. By setting a series of specific groove rail wear values, a tram-track coupled dynamic analysis was carried out, and compared with the specification requirements, vehicle safety limits under different wear values were obtained. This research has great engineering value for guiding the routine maintenance of small radius curve sections of trams.

Cardinality of survival set for the chaotic Tent map with holes.

The aim of this paper is to give an overview of the dynamics of one dimensionaldiscrete dynamical systems: Tent map family T3, Doubling map E2and shift map σ are investigated. Let I-intervals(Holes) lie in the interval [0,1) and let E2be a Doubling map. The survivor set Ω(I) :={x∈[0,1) :Enx /∈ I, n≥0}. Depending on location and size of the intervals we will characterize the survivor set Ω(I) infinite or finite. Also we will show conjugacy of some maps that used in this paper. By using conjugacy of functions we will show that the Survivor set is infinite or finite in another composition of maps. The Cantor sets Λ that occur as non-survivor sets for c >2 from Tent map family Tc.[1] Keywords: dynamical systems, symbolic dynamics, interval maps, survivor sets, chaos, open systems, irregular sets.

Additive, Almost Additive and Asymptotically Additive Potential Sequences Are Equivalent

Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism, dimension theory and large deviations theory have been extensively studied in the recent years. In this paper, we show that every such potential sequence is actually equivalent to a standard (additive) potential in the sense that there exists a continuous potential with the same topological pressure, equilibrium states, variational principle, weak Gibbs measures, level sets (and irregular set) for the Lyapunov exponent and large deviations properties. In this sense, our result shows that almost and asymptotically additive potential sequences do not extend the scope of the theory compared to standard potentials, and that many results in the literature about such sequences can be recovered as immediate consequences of their counterpart in the additive case. A corollary of our main result is that all quasi-Bernoulli measures are weak Gibbs.

Precarious employment and self-reported experiences of unwanted sexual attention and sexual harassment at work. An analysis of the European Working Conditions Survey.

Unwanted sexual attention (UWSA) and sexual harassment (SH) are prevalent experiences for women in working life and often accompanied by poor health. Despite increasing numbers especially of young people working in insecure and irregular employment settings, there is little empirical evidence if such precarious arrangements are associated with UWSA or SH. To investigate this, we used a representative sample of the European working population consisting of 63,966 employees in 33 countries who participated in the European Working Conditions Survey in 2010 or 2015. Precarious employment (PE) was assessed on the basis of seven indicators and a formative index derived from them: temporary employment, contractual duration < 1 year, schedule unpredictability, involuntary part-time, low information on occupational health and safety risks (OSH), low pay (wage < 60%), and multiple job-holding. We measured self-reported experiences of workplace UWSA during the last month and SH during the last 12 months each using a single-item questionnaire. Multi-level Poisson regressions were used to estimate prevalence ratios for UWSA and SH according to PE adjusted for survey year, age, education, type of household, migration background, job tenure, weekly working hours, occupational position, working sector, company size, workplace gender ratio, and visiting customers or clients. 0.8% of men reported UWSA in the last month and 2.6% of the women. SH in the last year was reported by 0.4% of the men and 1.3% of the women. For both men and women, PE was significantly associated with elevated prevalence of UWSA and SH, in particular when reporting schedule unpredictability, multiple job-holding and low information on OSH. Our results suggest that precariously employed individuals may be more prone to experience unwanted sexual behaviour at the workplace compared with workers in non-precarious settings.

Efficient statistics of the wheel-rail contact stress: cases on track geometric excitation

The wheel-rail contact stress solution is the precondition for many wheel-rail contact problems, such as wheel-rail contact fatigue, plastic deformation and wear, etc. However, vehicle-track interaction generally shows a high degree of randomness due to the uncertainty of excitations, e.g. track irregularities, in the estimation of wheel-rail contact point positions and contact stresses. Moreover, it is known that track irregularities are massive data, possessing evolution characteristics at time and space domain, thus it will consume much time if directly loading all of them into the vehicle-track interaction process. Regarding this, this work tries to introduce the track irregularity probabilistic model to select representative track irregularity sets with much smaller samples. To guarantee the representativeness of track irregularity data, track irregularities of up to five thousand kilometres are measured to ensure the ergodicity of the power spectral density function (PSD) of the track irregularities. Moreover, a fast-accurate contact model is introduced to extract the stress distribution of the wheel-rail contact patch. By effectively combing the vehicle-track dynamics method and random simulation methods, the wheel and rail contact stresses in amplitude and distribution range can be efficiently quantified from a statistical view.

TGNet: Geometric Graph CNN on 3-D Point Cloud Segmentation

Recent geometric deep learning works define convolution operations in local regions and have enjoyed remarkable success on non-Euclidean data, including graph and point clouds. However, the high-level geometric correlations between the input and its neighboring coordinates or features are not fully exploited, resulting in suboptimal segmentation performance. In this article, we propose a novel graph convolution architecture, which we term as Taylor Gaussian mixture model (GMM) network (TGNet), to efficiently learn expressive and compositional local geometric features from point clouds. The TGNet is composed of basic geometric units, TGConv, that conduct local convolution on irregular point sets and are parametrized by a family of filters. Specifically, these filters are defined as the products of the local point features and the neighboring geometric features extracted from local coordinates. These geometric features are expressed by Gaussian weighted Taylor kernels. Then, a parametric pooling layer aggregates TGConv features to generate new feature vectors for each point. TGNet employs TGConv on multiscale neighborhoods to extract coarse-to-fine semantic deep features while improving its scale invariance. Additionally, a conditional random field (CRF) is adopted within the output layer to further improve the segmentation results. Using three point cloud data sets, qualitative and quantitative experimental results demonstrate that the proposed method achieves 62.2% average accuracy on ScanNet, 57.8% and 68.17% mean intersection over union (mIoU) on Stanford Large-Scale 3D Indoor Spaces (S3DIS) and Paris-Lille-3D data sets, respectively.

Stein hypothesis and screening effect for covariances with compact support

In spatial statistics, the screening effect historically refers to the situation when the observations located far from the predictand receive a small (ideally, zero) kriging weight. Several factors play a crucial role in this phenomenon: among them, the spatial design, the dimension of the spatial domain where the observations are defined, the mean-square properties of the underlying random field and its covariance function or, equivalently, its spectral density. The tour de force by Michael L. Stein provides a formal definition of the screening effect and puts emphasis on the Matérn covariance function, advocated as a good covariance function to yield such an effect. Yet, it is often recommended not to use covariance functions with a compact support. This paper shows that some classes of covariance functions being compactly supported allow for a screening effect according to Stein’s definition, in both regular and irregular settings of the spatial design. Further, numerical experiments suggest that the screening effect under a class of compactly supported covariance functions is even stronger than the screening effect under a Matérn model.

Covariance-regularized Reconstruction of Data Cubes in Integral Field Spectroscopy and Application to MaNGA Data

Abstract Integral field spectroscopy can map astronomical objects spatially and spectroscopically. Due to instrumental and atmospheric effects, it is common for integral field instruments to yield a sampling of the sky image that is both irregular and wavelength dependent. Most subsequent analysis procedures require a regular, wavelength-independent sampling (for example a fixed rectangular grid), and thus an initial step of fundamental importance is to resample the data onto a new grid. The best possible resampling would produce a well-sampled image, with a resolution equal to that imposed by the intrinsic spatial resolution of the instrument, telescope, and atmosphere, and with no statistical correlations between neighboring pixels. A standard method in the field to produce a regular set of samples from an irregular set of samples is Shepard’s method, but Shepard’s method typically yields images with a degraded resolution and large statistical correlations between pixels. Here we introduce a new method, which improves on Shepard’s method in both these respects. We apply this method to data from the Mapping Nearby Galaxies at Apache Point Observatory survey, part of Sloan Digital Sky Survey IV, demonstrating a full width at half maximum close to that of the intrinsic spatial resolution (and ∼16% better than Shepard’s method) and low statistical correlations between pixels. These results nearly achieve the ideal resampling. This method can have broader applications to other integral field data sets and to other astronomical data sets (such as dithered images) with irregular sampling.

Wave induced motions of partially submerged bodies near a fixed structure

Wave driven impact of small icebergs with offshore structures is a design consideration in Arctic and sub-Arctic regions. The near field hydrodynamic interaction of these wave driven ice masses has been investigated through experimental and CFD studies by Sayeed et al. (2017b, 2018a, 2018b). These studies found that motions were significantly influenced by the standing wave generated due to the superposition of the incident and reflected waves in front of the fixed structure. In regular waves the small bodies may or may not impact the structure, depending on initial starting condition whereas in irregular waves the ice masses hit the structure in all cases. Spectrum analysis carried out over the entire distance travelled by the free floating ice mass in irregular waves revealed relatively small difference in surge and heave velocity due to the presence of the structure (Sayeed et al. (2018b)). The reason is attributed to insufficient data at each separation distances to capture the motion responses for all the frequencies in the spectrum. In this paper, the surge and heave motion time series data in irregular waves are reanalyzed in a similar manner as was previously done for regular waves (Sayeed et al. (2018a). The present analysis reveals correlation of significant wavelength with the motion history at variable separation distances in front of the fixed structure. A statistical approach is then adopted to both regular and irregular wave motion data sets to identify percentiles of velocity response vs position as the small floating bodies approach head on to the fixed structure. These findings enable the identification of the motions of small bodies at specific locations in front of the structure and provide understanding of how wave-induced surge and heave velocities change as small floating bodies approach a fixed structure in a realistic wave field.

An Efficient Path Planning Algorithm for Networked Robots using Modified Optimization Algorithm

Path planning has played a significant role in major numerous decision-making techniques through an automatic system involved in numerous military applications. In the last century, pathfinding and generation were carried out by multiple intelligent approaches. It is very difficult in pathfinding to reduce energy. Besides suggesting the shortest path, it has been found that optimal path planning. This paper introduces an efficient path planning algorithm for networked robots using modified optimization algorithms in combination with the η3 -splines. A new method has employed a cuckoo optimization algorithm to handle the mobile robot path planning problem. At first, η3 - splines are combined so an irregular set of points can be included alongside the kinematic parameters chosen to relate with the development and the control of mobile robots. The proposed algorithm comprises of adaptive random fluctuations (ARFs), which help to deal with the very much manageable neighborhood convergence. This algorithm carries out the process of accurate object identification along with analyzing the influence of different design choice by developing a 3D CNN architecture to determine its performance. Besides offering classification in real-time applications, the proposed algorithm outperforms the performance of state of the art in different benchmarks.

Distributional chaos in multifractal analysis, recurrence and transitivity

There is much research on the dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, the Hausdorff dimension, Lebesgue positive measure, positive or full topological entropy (and topological pressure), etc. However, this is not the case from the viewpoint of chaos. There are many results on the relationship of positive topological entropy and various chaos. However, positive topological entropy does not imply a strong version of chaos, called DC1. Therefore, it is non-trivial to study DC1 on irregular sets and level sets. In this paper, we will show that, for dynamical systems with specification properties, there exist uncountable DC1-scrambled subsets in irregular sets and level sets. Meanwhile, we prove that several recurrent level sets of points with different recurrent frequency have uncountable DC1-scrambled subsets. The major argument in proving the above results is that there exists uncountable DC1-scrambled subsets in saturated sets.

Transitively-saturated property, Banach recurrence and Lyapunov regularity

The topological entropy of upper recurrent, lower recurrent points and Birkhoff regularity were considered in Tian (2016 Adv. Math. 288 464–526) but Banach upper recurrence points are not considered. In this paper we mainly consider whether the points that are Banach upper recurrent but not upper recurrent can carry full topological entropy. Moreover, we use statistical -limit sets to obtain entropy results on the refined orbit distribution of Banach recurrence. In this process, we strengthen Pfister and Sullivan’s result of Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56) from saturated property to transitively-saturated property (and from single-saturated property to transitively-convex-saturated property). We also establish an abstract framework on the combination of Banach recurrence and multifractal analysis of general observable functions and in particular, how these results can be applied in the combination of Banach recurrence Lyapunov regularity to obtain a generalized and refined theory of Barreira and Doutor (2009 J. Math. Pures Appl. 92 1–17); Barreira and Gelfert (2006 Commun. Math. Phys. 267 393–418); Barreira and Saussol (2001 Trans. Am. Math. Soc. 353 3919–44); Feng and Huang (2010 Commun. Math. Phys. 297 1–43); Feng (2003 J. Math. 138 353–76); Feng (2009 Israel J. Math. 170 355–94); Feng and Lau (2002 Math. Res. Lett. 9 363–78) etc, on mixed Lyapunov multifractal analysis such as irregular sets and level sets of Lyapunov exponents.

Convergence of fractional diffusion processes in extension domains

We study the asymptotic behavior of anomalous fractional diffusion processes in bad domains via the convergence of the associated energy forms. We introduce the associated Robin–Venttsel’ problems for the regional fractional Laplacian. We provide a suitable notion of fractional normal derivative on irregular sets via a fractional Green formula as well as existence and uniqueness results for the solution of the Robin–Venttsel’ problem by a semigroup approach. Submarkovianity and ultracontractivity properties of the associated semigroup are proved.

An Operator Based Approach to Irregular Frames of Translates

We consider translates of functions in L 2 ( R d ) along an irregular set of points, that is, { ϕ ( · − λ k ) } k ∈ Z —where ϕ is a bandlimited function. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel, frame or Riesz sequence. We show the connection of the frame-related operators of the translates to the operators of exponentials. This is used, in particular, to find for the first time in the irregular case a representation of the canonical dual as well as of the equivalent Parseval frame—in terms of its Fourier transform.

Irregular Target Object Detection Based on Faster R-CNN

Forthe shortcomings of traditional target detection algorithms can only extract specific target features for detection, propose the Faster R-CNN target detecti-on model of deep learning, combined with VGG16 and ResNet101 convolutional neur-al network methods, to detection of irregular target objects. Experiments established two types of irregular target data sets, walnut and jujube, use the network training and testing, verified the feasibility of deep learning network for detecting irregular target objects. The experimental results show that the Faster R-CNN target detection networ-kof training on the self-built data set, the final detection result reaches 95%, which proves the effectiveness of the network for detecting irregular target objects.

Research on Simulation Analysis Method of Microbial Cemented Sand Based on Discrete Element Method

A simulation method for microbial cemented sand (MCS) based on the Two-Dimensional Particle Flow Code (PFC 2D) has been developed in this study. It consists of an identification of mesoscopic contact model for structural mesoscopic particles, development of morphological algorithm for irregular crystal particles, and classification and setting of mesoscopic parameters for compositional materials and particle size distribution simulation. Additionally, an acoustic emission algorithm based on moment tensor theory was developed for discrete element simulation analysis on fracture characteristic of cemented sand under the action of the force. The simulation method proposed in this article/paper may reflect the physical and mechanical characteristics of real microbial cemented sand based on physical experiments. Quantification of the fracture process of microbial cemented sand is possible by introducing a moment magnitude (MW) in discrete element simulation analysis. The material may have greater probability of fracture between the MW ranges of −6.8 and −6.6. The relationship between probability of fracture at different MWs and the MW follows the Gaussian curve. The research results are a new trial for fracture analysis on microbial cemented sand.

The asymptotically additive topological pressure: variational principle for non-compact and intersection of irregular sets

ABSTRACTLet be a dynamical system, where is a compact metric space and is a continuous map. Using the concepts of g-almost product property and uniform separation property introduced by Pfister and Sullivan in Pfister and Sullivan [On the topological entropy of saturated sets, Ergodic Theory Dyn. Syst. 27 (2007), pp. 929–956], we give a variational principle for certain non-compact with relation to the asymptotically additive topological pressure. We also study the set of points that are irregular for a collection finite or infinite of asymptotically additive sequences and we show that carried the full asymptotically additive topological pressure. These results are suitable for systems such as mixing shifts of finite type, β-shifts, repellers and uniformly hyperbolic diffeomorphisms.

Constrained ergodic optimization for asymptotically additive potentials

Using an asymptotically additive sequence of continuous functions as a constrained condition, this paper studies the relations of several constrained ergodic averages for asymptotically additive potentials. Basic properties of constrained maximum ergodic averages are studied. In particular, if the dynamical systems satisfy the specification property, the maximal growth rate of an asymptotically additive potential on the level sets is equal to its constrained maximum ergodic averages and the maximal growth rates on the irregular sets is its unconstrained maximum ergodic averages. Finally, the applications for suspension flows are given in the end of the paper.

The use of triangulation processing algorithms for the construction of combined model of the underwater and above-water terrain of the bed of the Bratsk Reservoir

The article summarizes the experience gained during processing of the data about the terrain of the Bratsk Reservoir bed. We discuss the available sources of information on the land and underwater terrain and justify the choice of the sources used in the project. To measure the actual depths in the regions of interest an echo-sounder of the consumer grade was applied, and we consider the processing of its measurements in some details. We describe the free, open source and custom software, which we apply for the processing of the data. We consider the use of the several algorithms that we have developed for processing of the terrain points. The main goal of this processing is to obtain the combined terrain model, which summarizes the data from the various information sources: the topographic maps, the pilot charts and the echo sounder measurements. All the algorithms considered build and process the triangulations of irregular sets of points. The algorithms used are: constrained Delaunay triangulation construction; removal of artefacts of triangulation, constructed from the terrain isolines; map morphing to reconcile the terrain models: and triangulation fragment replacement. The resulting combined terrain model contains all the information about the terrain in the area of interest and allows to use the model for the further hydrological calculations.

Speech Genre: A Study of Gossip in Australian English Speaking Context

A gossip as a casual conversation usually occurs in diverse context or a wide range of social situations; has distinct and various topics; and involve an irregular set of participants. The scholars scrutinize that conversation has highly structured activity of which people tacitly realize that there are some basic conventions to follow – such as when to speak or to stay silent and to listen. In this study, I specifically discuss one of the speech genre – a gossip, in Australia English speaking context. The gossip data of the study is taken from the research conducted by Thornburry, Scott, and Slade, Diana (2006). In a discussion, I focus the analysis of the generic structure of the gossip and how it establishes the social function (within) the speech members. Several findings conveyed that: 1) there is a leeway of shifting from one genre to another – e.g. narrative to gossip, within the same participants; 2) conversation can be successful if all the participants aware of and follow the basic conventions – when to talk or to listen, support to judgement or reluctant to the focus of conversation; 3) the genre, e.g. narrative or gossip, could motivate people to leave or to join the conversation which then could establish and reinforce the group membership and maintain the values of the social group.