Singular Regions Research Articles

Multifractal and singularity analysis of weighted road networks

Road is an important element of modern traffic infrastructures in national economic construction. Accurately, road networks might be multifractal systems. The mathematics of multifractal can be used to provide a quantitative signature in many fields. The roads in this paper are endowed with weights according to their respective traffic abilities. With the aim in mind, the weighted road networks in three country-level cities (Danyang, Yangzhong and Jurong) which belong to Zhenjiang, China, are studied. We analyze the heterogeneities of the three weighted road networks with multifractal spectrum, which correspond to their socio-geographical contexts. Besides, we extract the singularity regions of three country-level cities with the annular segmentation method and the singularity exponent method, which can be helpful in further transportation planning.

Principal-vector-directed fringe-tracking technique.

Fringe tracking is one of the most straightforward techniques for analyzing a single fringe pattern. This work presents a principal-vector-directed fringe-tracking technique. It uses Gaussian derivatives for estimating fringe gradients and uses hysteresis thresholding for segmenting singular points, thus improving the principal component analysis method. Using it allows us to estimate the principal vectors of fringes from a pattern with high noise. The fringe-tracking procedure is directed by these principal vectors, so that erroneous results induced by noise and other error-inducing factors are avoided. At the same time, the singular point regions of the fringe pattern are identified automatically. Using them allows us to determine paths through which the "seed" point for each fringe skeleton is easy to find, thus alleviating the computational burden in processing the fringe pattern. The results of a numerical simulation and experiment demonstrate this method to be valid.

Theoretical and numerical analysis of learning dynamics near singularity in multilayer perceptrons

The multilayer perceptron is one of the most widely used neural networks in applications, however, its learning behavior often becomes very slow, which is due to the singularities in the parameter space. In this paper, we analyze the learning dynamics near singularities in multilayer perceptrons by using traditional methods. We obtain the explicit expressions of the averaged learning equations which play a significant role in theoretical and numerical analysis. After obtaining the best approximation on overlap singularity, the stability of overlap singularity is analyzed. Then we take the numerical analysis on singular regions. Real averaged dynamics near the singularities are obtained in comparison with the theoretical learning trajectories near singularity. In the simulation we analyze the averaged learning dynamics, batch mode learning dynamics and on-line learning dynamics, respectively.

Multimodal imaging in autism: an early review of comprehensive neural circuit characterization.

There is accumulating evidence that the neurobiology of autism spectrum disorders (ASD) is linked to atypical neural communication and connectivity. This body of work emphasizes the need to characterize the function of multiple regions that comprise neural circuits rather than focusing on singular regions as contributing to deficits in ASD. Multimodal neuroimaging - the formal combination of multiple functional and structural measures of the brain - is extremely promising as an approach to understanding neural deficits in ASD. This review provides an overview of the multimodal imaging approach, and then provides a snapshot of how multimodal imaging has been applied in the study of ASD to date. This body of work is separated into two categories: one concerning whole brain connectomics and the other focused on characterizing neural circuits implicated as altered in ASD. We end this review by highlighting emerging themes from the existing body of literature, and new resources that will likely influence future multimodal imaging studies.

Heat kernels for generalized Ornstein–Uhlenbeck operators

In this article, we use the Hamiltonian and Lagrangian formalism to study the -dimensional extended Ornstein–Uhlenbeck operator where is an real matrix, is a real parameter and means the gradient. Given the boundary conditions, we find the solutions of the associated Hamiltonian system of . Then, we construct the action function by the Lagrangian function and use the van Vleck’s formula to obtain the volume element of the heat kernel. Finally, we discuss the regular and singular regions of this operator.

Mixed-mode thermal stress intensity factors from the finite element discretized symplectic method

A finite element discretized symplectic method is introduced to find the thermal stress intensity factors (TSIFs) under steady-state thermal loading by symplectic expansion. The cracked body is modeled by the conventional finite elements and divided into two regions: near and far fields. In the near field, Hamiltonian systems are established for the heat conduction and thermoelasticity problems respectively. Closed form temperature and displacement functions are expressed by symplectic eigen-solutions in polar coordinates. Combined with the analytic symplectic series and the classical finite elements for arbitrary boundary conditions, the main unknowns are no longer the nodal temperature and displacements but are the coefficients of the symplectic series after matrix transformation. The TSIFs, temperatures, displacements and stresses at the singular region are obtained simultaneously without any post-processing. A number of numerical examples as well as convergence studies are given and are found to be in good agreement with the existing solutions.

A new approach to singularity-free inverse kinematics using dual-quaternionic error chains in the Davies method

SUMMARYThe manipulation in singular regions promotes an instantaneous reduction in mechanism mobility, which can result in some disturbances in the trajectory tracking. The application of the quaternionic elements for motion representation not only guarantees an orthonormal transformation but also results in the smallest variance and minimizes the acceleration peaks. The use of a unit quaternion avoids these phenomena, but there are dimensional limitations that make it impossible to translate the representation. This work presents a methodology for using dual quaternions in the analysis of robot kinematics using the Davies method, which avoids kinematic singularities and ensures the optimal torque profiles.

Gestational Iron Deficiency Differentially Alters the Structure and Function of White and Gray Matter Brain Regions of Developing Rats

Gestational iron deficiency (ID) has been associated with a wide variety of central nervous system (CNS) impairments in developing offspring. However, a focus on singular regions has impeded an understanding of the CNS-wide effects of this micronutrient deficiency. Because the developing brain requires iron during specific phases of growth in a region-specific manner, we hypothesized that maternal iron deprivation would lead to region-specific impairments in the CNS of offspring. Female rats were fed an iron control (Fe+) or iron-deficient (Fe−) diet containing 240 or 6 μg/g iron during gestation and lactation. The corpus callosum (CC), hippocampus, and cortex of the offspring were analyzed at postnatal day 21 (P21) and/or P40 using structural and functional measures. In the CC at P40, ID was associated with reduced peak amplitudes of compound action potentials specific to myelinated axons, in which diameters were reduced by ∼20% compared with Fe+ controls. In the hippocampus, ID was associated with a 25% reduction in basal dendritic length of pyramidal neurons at P21, whereas branching complexity was unaffected. We also identified a shift toward increased proximal branching of apical dendrites in ID without an effect on overall length compared with Fe+ controls. ID also affected cortical neurons, but unlike the hippocampus, both apical and basal dendrites displayed a uniform decrease in branching complexity, with no significant effect on overall length. These deficits culminated in significantly poorer performance of P40 Fe− offspring in the novel object recognition task. Collectively, these results demonstrate that non-anemic gestational ID has a significant and region-specific impact on neuronal development and may provide a framework for understanding and recognizing the presentation of clinical symptoms of ID.

Topological evolution of laminar juncture flows under different critical parameters

Horseshoe vortex topological structure has been studied extensively in the past, traditional “saddle of separation” and new “attachment saddle point” topologies found in literature both have theoretical basis and experimental and computational evidences for support. The laminar incompressible juncture flows at low Reynolds numbers especially are observed to have new topology. Studies concerning the existence of the new topology though found in literature, the topological evolution and its dependency on various critical flow parameters require further investigation. A Particle Image Velocimetry based analysis is carried out to observe the effect of aspect ratio, δ*/D and shape of the obstacle on laminar horseshoe vortex topology for small obstacles. Rise in aspect ratio evolves the topology from the traditional to new for all the cases observed. The circular cross section obstacles are found more apt to having the new topology compared to square cross sections. It is noted that the sweeping effect of the fluid above the vortex system in which horseshoe vortex is immersed plays a critical role in this evolution. Topological evolution is observed not only in the most upstream singular point region of horseshoe vortex system but also in the corner region. The corner vortex topology evolves from the traditional type to new one before the topological evolution of the most upstream singular point, resulting in a new topological pattern of the laminar juncture flows “separation-attachment combination”. The study may help extend the understanding of the three-dimensional boundary layer separation phenomenon.

Game of Singular Stochastic Control and Strategic Exit

We investigate a game of singular control and strategic exit in a model of competitive market share control. In the model, each player can make irreversible investments to increase his market share which is modeled as a diffusion process. In addition, each player has an option to exit the market at any point in time. We formulate a verification theorem for best responses of the game and characterize Markov perfect equilibria (MPE) under a set of verifiable assumptions. We find a class of MPEs with a rich structure. In particular, each player maintains up to two disconnected intervals of singular control regions, one of which plays a defensive role while the other plays an offensive role. We also identify a set of conditions under which the outcome of the game may be unique despite the multiplicity of the equilibria.

Likelihood inference in some finite mixture models

Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is well known that likelihood inference in mixture models is complicated due to (1) lack of point identification, and (2) parameters (for example, mixing probabilities) whose true value may lie on the boundary of the parameter space. These issues cause the profiled likelihood ratio (PLR) statistic to admit asymptotic limits that differ discontinuously depending on how the true density of the data approaches the regions of singularities where there is lack of point identification. This lack of uniformity in the asymptotic distribution suggests that confidence intervals based on pointwise asymptotic approximations might lead to faulty inferences. This paper examines this problem in details in a finite mixture model and provides possible fixes based on the parametric bootstrap. We examine the performance of this parametric bootstrap in Monte Carlo experiments and apply it to data from Beauty Contest experiments. We also examine small sample inferences and projection methods.

A mesoscale eddy detection method of specific intensity and scale from SSH image in the South China Sea and the Northwest Pacific

Mesoscale eddies exist almost everywhere in the ocean and play important roles in the ocean circulation of the world. These eddies may cause sound spread singular regions and bring great influences to the upwater ship and underwater aircraft. Due to the lack of hydrographic survey datasets, study of mesoscale eddies has been greatly restricted. Fortunately, satellite altimeter provided an effective way to study mesoscale eddies. An automatic detection algorithm is introduced to detect mesoscale eddies of specific intensity and spatial/temporal scale based on satellite sea surface height (SSH) data and the algorithm is applied in a strong eddy activity region: the South China Sea and the Northwest Pacific. The algorithm includes four steps. The first step is preprocessing of the SSH image, which includes elimination of error SSH data and interpolation. The second step is to detect suspected mesoscale eddies from preprocessed SSH images by dynamic threshold adjustment and morphological method, and the suspected mesoscale eddy detection includes two procedures: suspected mesoscale eddy core region detection and suspected mesoscale eddy brim extraction. The third step is to pick out mesoscale eddies satisfied with specified criteria from suspected mesoscale eddies. The criteria include three items, that is, intensity criterion, spatial scale, criterion and temporal scale criterion. The last step is algorithm performance analysis and verification. The algorithm has the capability of adaptive parameter adjustment, and can extract mesoscale eddies of interested intensity and spatial/temporal scale. The paper can provide a basis for analyzing space-time characteristics of mesoscale eddy in the South China Sea and the Northwest Pacific.

Singularities in the identification of dynamic systems

As is well known, the parameter spaces of hierarchical systems such as multilayer perceptrons include singularities and the plateau phenomenon is ubiquitous in the process of learning. In the singular regions, the Fisher information matrix degenerates and the loss function is almost unchanged when the parameters arrive in the singular regions, which is called the plateau phenomenon. We wonder about whether the singularities and the plateau phenomenon exist in the parameter identification process of the linear and the ordinary nonlinear systems. In this paper, we can see that in some of the parameter identification of the nonlinear systems, the Fisher information matrix degenerates, the singularities exist and we can see the plateau phenomenon in the learning curves. A simulation example is provided to demonstrate the theoretical analysis in Section 3.

Laplace-domain wave-equation modeling and full waveform inversion in 3D isotropic elastic media

Abstract The 3D elastic problem has not been widely studied because of the computational burden. Over the past few years, 3D elastic full waveform inversion (FWI) techniques in the time and frequency domains have been proposed by some researchers based on developments in computer science. However, these techniques still have the non-uniqueness and high nonlinearity problems. In this paper, we propose a 3D elastic FWI algorithm in the Laplace domain that can mitigate these problems. To efficiently solve the impedance matrix, we adopt a first-order absorbing boundary condition that results in a symmetric system. A conjugate gradient (CG) solver can be used because the Laplace-domain wave equation is naturally positive definite. We apply the Jacobi preconditioner to increase the convergence speed. We identify the permissible range of Laplace damping constants through dispersion analysis and accuracy tests. We perform the Laplace-domain FWI based on a logarithmic objective function, and the inversion examples are designed for a land setting, which means that the source is vertically excited and multi-component data are considered. The inversion results indicate that the inversion that uses only the vertical component performs slightly better than the multi-component inversion. This unexpected result is obtained partly because we use a vertically polarized source. We analyze the residuals and Frechet derivatives for each component to examine the characteristics of the Laplace-domain multi-component FWI. The results indicate that the residuals and Frechet derivatives for the horizontal component have a singularity problem. The numerical examples demonstrate that the singularity problem is related to the directivity of the displacement and to taking the logarithm of Laplace-domain wave fields. To avoid this singularity problem, we use a simple method that excludes the data near the singular region. Although we can use either simultaneous or sequential strategies to invert the Laplace-domain data, we apply a simultaneous inversion strategy in this paper. Nonetheless, the numerical examples demonstrate that our inversion algorithm yields reasonable long-wavelength velocity structures.

Synergetic structure–control design via a hybrid gradient-evolutionary algorithm

This paper proposes a synergetic approach to design a planar parallel robot with its control system. In this proposal, the design problem is stated as a dynamic optimization problem with dynamic and static constraints on both the robot parameters and the control input to the robot. Control parameterization via PID controllers is used to rewrite the dynamic optimization problem as a nonlinear programming problem, which is solved by using a hybrid gradient-evolutionary optimization technique. The dynamic optimization problem presents singularity regions in the design space requiring the use of the proposed hybrid gradient-evolutionary optimization technique. The rationale behind the proposed hybrid algorithm lies in using a exploratory search mechanism for finding the initial guess to the fine search mechanism, which is used to search in a local region of a solution. We discuss both the results of the proposed optimization technique and the experimental results of the robot designed with the proposed approach. In addition, the result provided by the proposed synergetic design approach is compared with a sequential design approach, showing the advantages of the synergetic approach.

Resolution of type IV singularities in quantum cosmology

We discuss the fate of classical type IV singularities in quantum cosmology. The framework is Wheeler-DeWitt quantization applied to homogeneous and isotropic universes with a perfect fluid described by a generalized Chaplygin gas. Such a fluid can be dynamically realized by a scalar field. We treat the cases of a standard scalar field with positive kinetic energy and of a scalar field with negative energy (phantom field). We first present the classical solutions. We then discuss in detail the Wheeler-DeWitt equation for these models. We are able to give analytic solutions for a special case and to draw conclusions for the general case. Adopting the criterion that singularities are avoided if the wave function vanishes in the region of the classical singularity, we find that type IV singularities are avoided only for particular solutions of the Wheeler-DeWitt equation. We compare this result with earlier results found for other types of singularities.

Thermal stress and relieving method of the ITER lower vertical stabilization coil

Structural analysis of the ITER lower vertical stabilization (VS) coil has concluded thermal stress concentration is a serious issue obstructing the coil design. To optimize the lower VS coil, its structural performance has been studied in detail to find methods of solving the stress concentration issues. Apparently, increasing filet radius and decreasing the notch depth are the means commonly used to deal with stress concentrations in the singular regions. However, the real effects are not so simple due to very limited optimization space of the coil geometry. Larger filet radius will significant mitigate the stress concentration but still not enough if the material keeps original. On the other hand, stress concentration at the interface between the conductor jacket and clamp also needs to be mitigated. Changing the clamp size or distance is an obvious and effective way to solve this issue. However, introducing sliding contact at the interface is more effective and simpler. It requires the jacket and clamp are not tightly welded together but connected by bolts or other analogous means with which local sliding is permitted. Additionally, the effect of gap between conductor, spine and clamp is also researched. All in all, the stress concentrations of ITER lower VS coil can be mitigated to meet the acceptance criteria based on the specific optimizations and combining them together.

Computational Analysis of Fatigue Crack Growth based on Stress Intensity Factor Approach in Axial Flow Compressor Blades

Gas turbine compressor blades are subjected to centrifugal, gas bending and vibratory loads. This repeated loading and unloading can reduce the life of compressor blades. This research aims at the estimation of fatigue crack growth and fatigue life of various three dimensional crack in a compressor blade considering the stress intensity factor calculations for a half-elliptical crack, subjected to centrifugal loading. Static stress analysis was carried out to ascertain the critical region or crack zone of the blade. The maximum Von - Mises stress was found at the fillet region near the root of the blade, the predicted state of stress has helped in identifying the region of singularity which may lead to crack initiation. Finite Element Method was used to evaluate the range of stress intensity factor solutions in the blade with a half-elliptical flaw. Semi-elliptical crack lengths ranging from 0.2mm to 6mm were considered in the crack zone. Stress intensity factor was evaluated for different rotational velocity of 5000, 10000 and 20000rpm. The stress intensity factor range obtained is employed to predict fatigue crack growth behavior and fatigue crack life estimation by using Paris law. The maximum Mode I stress intensity factor of 61.4 Mpa√m was found at the surface interception point, for a crack length of 6mm and crack depth of 2.4mm. With the increase in rotational velocity of 5000rpm, 10000rpm and 20000rpm, fatigue crack length growth rate was estimated to be and 1.95 x 10-09, 1.65 x 10-07 m/cycle and 4.15 x 10-05 m/cycle and the fatigue crack propagation life was estimated to be of 4.3 x 108 cycles, 7.3 x 106 cycles and 5 x 103 cycles respectively. It was concluded that at the surface crack interception point, fatigue crack growth rate increases with increase in crack depth and the fatigue crack propagation life tends to decrease with increase in the rotational velocity of the compressor blade.

Leaf image segmentation method based on multifractal detrended fluctuation analysis

To identify singular regions of crop leaf affected by diseases, based on multifractal detrended fluctuation analysis (MF-DFA), an image segmentation method is proposed. In the proposed method, first, we defend a new texture descriptor: local generalized Hurst exponent, recorded as LHq based on MF-DFA. And then, box-counting dimension f(LHq) is calculated for sub-images constituted by the LHq of some pixels, which come from a specific region. Consequently, series of f(LHq) of the different regions can be obtained. Finally, the singular regions are segmented according to the corresponding f(LHq). Six kinds of corn diseases leaf's images are tested in our experiments. Both the proposed method and other two segmentation methods—multifractal spectrum based and fuzzy C-means clustering have been compared in the experiments. The comparison results demonstrate that the proposed method can recognize the lesion regions more effectively and provide more robust segmentations.

The International Politics of Water Security in Central Asia

The article examines the international politics of water security in Central Asia with a particular focus on the level of regionalism. Are the five Central Asian states evolving into a region capable of solving water management problems on a regional basis? To examine the extent to which water has shaped the structure of Central Asian relations, I use water-related events. The empirical findings suggest that international relations of the Central Asian states are characterised by at least two sets of triads rather than a singular region. The presence of regional fragmentation is likely to exacerbate existing disputes over water and possibly destabilise the region.