Degree Of Singularity Research Articles

Unsupervised Machine Learning-Based Singularity Models: A Case Study of the Taiwan Strait Basin

The identification of geochemical anomalies in oil and gas indicators is a fundamental task in oil and gas exploration, as the process of oil and gas accumulation is a low probability event. Machine learning algorithms for anomaly detection are applicable to the identification of oil and gas geochemical anomalies related to oil and gas accumulation. However, when using oil and gas indicators for anomaly detection, the diversity of these indicators often leads to the influence of the indicator redundancy on the identification of such features. Therefore, it is particularly important to select appropriate oil and gas indicators for anomaly detection. In this study, a hybrid model combining unsupervised machine learning methods and singularity analysis methods was used to evaluate oil and gas indicator anomalies using geochemical data from the Taiwan Strait Basin. The models used in this study include the singularity index model (LSP), the principal component model combined with the singularity index model (PCA and LSP), and the cluster analysis combined with the principal component model and the singularity index model (CLA-PCA-LSP). PCA models can reduce the dimensions of the data and retain as much information as possible. CLA divides data samples into different groups, so that samples within the same group are more similar and samples between different groups are less similar. LSP is mainly used for measuring the setting and singular degree of local anomalies in multi-scale geochemistry, geophysics, and other types of local anomalies, and it has a unique advantage in extracting low and weak anomalies and nonlinear characteristics. The results of the study show that the results obtained using the CLA-PCA-LSP hybrid model are very similar to those obtained by performing PCA on the entire index and then calculating the singularity index. This also verifies that, for the study areas of the Jiulongjiang Depression and Jinjiang Depression, we can select oil and gas indicators that are favorable for exploration analysis, without including all indicators in the analysis scope, thereby improving the computational efficiency. The application of a singularity analysis method and generalized self-similarity principle in extracting the geochemical information of oil and gas indicators in the Taiwan Strait Basin highlights key technologies such as the identification of weak anomalies, decomposition of composite anomalies, and integration of spatial information. The combination anomalies delineated by the singularity analysis method and S-A method not only reflect the spatial relationship with known oil and gas reservoir distribution, but also show the multiple combination anomalies in unknown areas, providing favorable guidance for the next exploration direction in the Taiwan Strait Basin.

Closing duality gaps of SDPs completely through perturbation when singularity degree is one

Let ( P , D ) be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, P and D are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function v as a function of the perturbation is not well-defined at zero (i.e. at the unperturbed data). Nevertheless, under the assumption that both P and D have singularity degree one, we show that a limiting version v a of v is a well-defined monotone decreasing continuous bijective function with domain [ 0 , π / 2 ] and image [ v ( P ) , v ( D ) ] , where v ( P ) and v ( D ) are the optimal values of P and D , respectively. The domain [ 0 , π / 2 ] corresponds to directions of perturbation defined in a certain manner. Thus, v a ‘completely fills’ the nonzero duality gap under a mild regularity condition. Our result is tight in that there exists an instance with singularity degree two for which v a is not continuous.

Structural Design and Analysis of Multi-Directional Foot Mobile Robot

Traditional mobile robots have limited mobility in complex terrain environments. Generally, the closed-chain leg structure of a foot-type robot relies on the speed difference to turn, but it is difficult to complete the turning action in narrow spaces. Therefore, this study proposes a closed-chain foot-type robot that can move in multiple directions, inspired by the WATT-I leg structure. Firstly, the closed-chain single-leg structure is designed, and the leg structure is analyzed in terms of the degrees of freedom, kinematics, and singularity. A simulation is also carried out. Secondly, based on the present trajectory, a heuristic algorithm is used to solve the inverse trajectory problem, and the size of the mechanism is optimized. Finally, the steering mechanism of the leg with a zero turning radius is designed and analyzed, which achieves the steering function of the whole robot and satisfies the goal of enabling the foot robot to walk in all directions. This study provides theoretical guidance for the structural dimension optimization of the proposed foot mobile robot and its application in engineering fields such as rescue, exploration, and the military.

Preliminary Study on Current Research Status and Clinical Application of Lower Limb Rehabilitation Robot Mechanisms

As an assistive device to restore lower limb athletic ability, human lower limb rehabilitation robots are becoming increasingly important in the field of rehabilitation and clinical applications. With the advancement of science and technology, both domestic and foreign research in this field has been developed. This study provides a detailed overview of the development of lower limb rehabilitation robots and reviews the current status of clinical applications, with a focus on mechanism research, from the perspectives of degrees of freedom, workspace, singularity, gait simulation, kinematic simulation and human-robot interaction, etc. The results show that domestic research on lower limb rehabilitation robots focus on the design and optimization of the mechanism configuration, while foreign research focus on the improvement and innovation of the control system and training mode based on human-computer interaction. Finally, the current state of research is combined with an outlook on future trends.

A formula for the degree of singularity of plane algebroid curves

A formula for the degree of singularity of plane algebroid curves

An analytical approach for evaluation of linear elastic stress fields around sharp V-shaped notches in plates

In the context of the theory of elasticity, the stress state at a sharp notch is singular, and the degree of stress singularity depends on the notch opening angle. Most existing analytical approaches for evaluating asymptotic linear elastic stress fields ahead of V-notches rely on notch stress intensity factors (N-SIFs). This paper presents an alternative analytical approach for evaluating notch stress fields by taking advantage of traction-based structural stress and Williams’ eigenfunction methods. To better represent notch stress fields, the first order and higher order terms of eigenfunction are included in the present study. The analytical solutions are then compared to the stress fields resulting from finite element analysis for validation purposes. The stress contours evaluated by the analytical approach are nearly identical to the numerical results corresponding to three distinguishing notch opening angles under pure Mode I loading, which signifies the effectiveness and robustness of the analytical solution methodology developed in the present study. Subsequently, the approach is extended to accommodate Mode II loading by introducing a skew-symmetric term in the stress function. The generalized method is then applied on a welded cruciform joint, which precisely captures the notch fields compared to FEA results.

Nonlinear kinematics of space parallel robot with Bricard mechanism

The space parallel robot with Bricard mechanism (SPRBM) is a complex mechanical device used for capturing free-floating space debris. It consists of a 3-RRS (Revolute-Revolute-Spherical Joints) parallel mechanism and a Bricard mechanism. Space debris can be captured by the interior space of the SPRBM. Compared with the conventional manipulator system, the SPRBM can capture a target with an arbitrary shape and motion state if the target can be enwrapped by the mechanism. In addition, it does not impose any stringent requirement on the locations of the capture points on the debris. However, the SPRBM has complex configurations and therefore nonlinear kinematics. This paper presents a detailed kinematics analysis of the SPRBM. The analysis involves the degrees of freedom, singularity, forward and inverse kinematics, workspace, and the trajectory planning method. These analyses and the results provide the fundamentals for modeling and controlling the SPRBM.

Modeling and experimental characterization of contact boundary tractions in non-conforming contact with random defects

An experimental characterization method for the non-conforming contact with random defects is developed in this paper. The method consists of the mechanics modeling and the parameters inversion algorithm. In the modeling, a new contact boundary description method is developed, which can sensitively characterize the discontinuous contact area caused by random defects. In the parameters inversion algorithm, an innovative objective function is designed by comprehensively considering the matching degree of displacements, the stability and singularity of boundary tractions. Combined with an iterative optimization method, the inversion algorithm can accurately identify random defects at different scales and characterize the evolution of contact boundary tractions. Numerical and experimental examples demonstrate that the method can provide reliable reconstruction results based on the displacement data.

Dexterity distribution design for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition

This paper presents a dexterity distribution design method for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition (SWD). The requirement of attitude adjustment for platform is described by time-varying Euler angles, by which the structural prototyping of universal-prismatic-spherical + spherical (UPS + S) parallel robot body can be generated via mechanism concept design. According to Kutzbach-Grubler formula regarding degree of freedom (DOF), the forward kinematics model is built, meanwhile, the reachable posture workspace of the robot can be depicted in 3D space by exploiting tilt-and-torsion method. The Jacobian matrix is extracted to reckon dexterous performance of the mechanism, including condition number, minimum singular value, manipulability and comprehensive evaluation index. The singularity degree within the design domain, from singularity-free to fully singularity, is comparatively ranked in polar coordinates, which constitutes the essence of SWD, the performance spectrum corresponding to the structural parameters can hereby be acquired for larger workspace and smaller singularity. The impedance control errors with parameter perturbation further validate the consistency of the singularity-free attitude from the perspective of dynamics. The physical experiments are carried out to verify the outcomes by virtue of multi-axis pose sensor array. Hence the presented SWD method has important application prospects regarding DOF coupling, especially in medical rehabilitation, industrial robotics, aerospace manufacturing and so forth.

Convergence Analysis under Consistent Error Bounds

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and Hölderian error bounds and includes logarithmic and entropic error bounds found in the exponential cone. It also includes the error bounds obtainable under the theory of amenable cones. Our main result is that the convergence rate of several projection algorithms for feasibility problems can be expressed explicitly in terms of the underlying consistent error bound function. Another feature is the usage of Karamata theory and functions of regular variations which allows us to reason about convergence rates while bypassing certain complicated expressions. Finally, applications to conic feasibility problems are given and we show that a number of algorithms have convergence rates depending explicitly on the singularity degree of the problem.

Facial reduction for symmetry reduced semidefinite and doubly nonnegative programs

We consider both facial reduction, FR, and symmetry reduction, SR, techniques for semidefinite programming, SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers, ADMM, approach. In fact, this approach allows for simply adding on nonnegativity constraints, and solving the doubly nonnegative, DNN , relaxation of many classes of hard combinatorial problems. We also show that the singularity degree remains the same after SR, and that the DNN relaxations considered here have singularity degree one, that is reduced to zero after FR. The combination of FR and SR leads to a significant improvement in both numerical stability and running time for both the ADMM and interior point approaches. We test our method on various DNN relaxations of hard combinatorial problems including quadratic assignment problems with sizes of more than n=500. This translates to a semidefinite constraint of order 250, 000 and 625times 10^8 nonnegative constrained variables, before applying the reduction techniques.

Multimedia Image Data Compression Based on Wavelet Analysis

In order to improve the compression technology of multimedia image data, a compression method of multimedia image data based on wavelet analysis was proposed. By combining Fourier transform and wavelet packet multithreshold denoising method, the image data was denoised and compressed through the transform of wavelet analysis and multithreshold processing, so as to realize the compression of image data with high quality. The experimental results showed that it was effective to analyze signal singularity, singularity position, and singularity degree by using wavelet analysis. And the signal mutation position near t = 0 could be seen clearly from the wavelet coefficient diagram, while the Fourier transform diagram did not provide any information about when the frequency mutation occurred. It was concluded that the method of multimedia image data compression based on wavelet analysis could promote the development of multimedia image data compression technology effectively.

Using the multi-precision fast Hankel transformation to calculate the constant current field of wide-area layered earth

The constant current field of wide-area layered earth has adverse effects on many industries. But it presents a high degree of numerical singularity, resulting in difficulty in solving. In this paper, the derivation of Green’s function and the fast Hankel transformation are presented based on the basic principle of linear filtering method for Green’s function of wide-area layered earth. A method of Multi-Precision Fast Hankel Transformation (MP-FHT) is proposed, which solves the problem of numerical singularity of integral kernel function in Green’s function by multi-precision algorithm, thus ensuring the accuracy of Hankel integral. The accuracy and reliability of the MP-FHT are proved by comparison of MP-FHT, commercial software CDEGS and improved version of high-order complex image method (HCIM). Compared with the existing algorithms, this method has high precision and low difficulty in algorithm implementation, which is a new method with high practical value.

Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment.

A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon-anomalous dissipation-is sometimes called the 'zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions [Formula: see text] exhibit persistent power-law scaling in the inertial range, namely [Formula: see text] for exponents [Formula: see text] over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that [Formula: see text] for all [Formula: see text] and Onsager's 1949 theory establishes the requirement that [Formula: see text] for [Formula: see text] for consistency with the zeroth law. Empirically, [Formula: see text] and [Formula: see text], suggesting that turbulent Navier-Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

A strengthened Barvinok-Pataki bound on SDP rank

The Barvinok-Pataki bound provides an upper bound on the rank of extreme points of a spectrahedron. This bound depends solely on the number of affine constraints of the problem, i.e., on the algebra of the problem. Specifically, the triangular number of the rank r is upper bounded by the number of affine constraints. We revisit this bound and provide a strengthened upper bound on the rank using the singularity degree of the spectrahedron. Thus we bring in the geometry and stability of the spectrahedron, i.e., increased instability as seen by higher singularity degree, yields a lower, strengthened rank bound.

The Effects of Temporary Clipping as an Expression of Circulatory Individuality: Online Measurement of Temporal Lobe Oxygen Levels During Surgery for Middle Cerebral Artery Aneurysms

Despite its widespread use, much is left to understand about the repercussions of parent artery temporary clipping in neurosurgery. This study seeks a better comprehension of the subject by aiming at the online measurement of brain tissue oxygen pressure (PbtO2) during such events. This was a prospective observational study. Patients submitted to surgery for middle cerebral artery aneurysms (both ruptured and unruptured) were continuously monitored under Intensive Care Monitoring+ software, in order to obtain temporal (downstream) PbtO2 levels while temporary clips were applied. Separate PbtO2 curve events were identified, extracted, and processed. These were studied for assessing intraindividual and interindividual variability and the potential impact of repeated clipping and previous aneurysmal rupture. Eighty-six temporary clippings (from 20 patients) were recorded with a mean duration of 140.8 (41- 238) seconds. Temporary arterial occlusion at the M1 segment of the middle cerebral artery produced specifically shaped trajectories, characterized by a preclipping PbtO2 level, rapid downward sigmoid-shaped curve, succession of progressively angled slopes, and lower plateau. The steepest slope of the curve correlated strongly with PbtO2 range (P < 0.001, r= 0.944). These features were highly reproducible only intraindividually and did not vary significantly with repeated clippings. The effects of temporary arterial occlusion on temporal lobe oxygenation demonstrate a high degree of singularity, highlighting the potential benefits of assessing individual available collateral circulation intraoperatively. The "PbtO2 steepest slope" predicted the severity of PbtO2 decrease and was available within the first minute.

Design and Analysis of an Intelligent Toilet Wheelchair Based on Planar 2DOF Parallel Mechanism with Coupling Branch Chains.

Due to the fixed size of the structure or the possibility of only simple manual adjustment, the traditional toilet wheelchair cannot easily be adapted to the size of the user or the toilet. In this paper, a planar two-degree-of-freedom parallel mechanism with coupling branch chains is proposed to enable both seat height adjustment and body posture adjustment of a toilet chair, solving the problems of posture adaptability between the user and the machine, and height matching in the process of using the wheelchair-assisted toilet. The model of the parallel mechanism was designed after analyzing the general rules of posture transformation in the human body before and after the toilet process, and the dimensions of each linkage were then determined according to the constraint conditions. By analyzing the degree of freedom, kinematics, workspace, singularity and position of the center of gravity, the rationality of the design was ensured. The weighted average function was used to find the optimal fixed point of the horizontal moving slider, and the actual trajectory at the end of the single driving mode was close to the ideal trajectory. The experimental results show that the adjustable seat height range is 290~550 mm and the adjustable angle range is 0~90°, which can enable disabled people to use the toilet independently.

Chitopentaose inhibits hepatocellular carcinoma by inducing mitochondrial mediated apoptosis and suppressing protective autophagy

Hepatocellular carcinoma (HCC) is one of the most prevalent and deadliest cancers. In this study, the anti-tumor effect of singular degree of polymerization (DP) chitooligosaccharides (COS) (DP 2–5) and the underlay molecular mechanisms were investigated on HCC cell line HepG2. MTT assay showed that (GlcN)5 have the best anti-proliferation effect among the different DP of COS (DP2-5). Furthermore, the administration of (GlcN)5 could decrease mitochondrial membrane potential, release cytochrome c into cytoplasm, activate the cleavage of Caspases9/3, thus inducing mitochondrial-mediated apoptosis in HepG2 cells (accounting for 24.57 ± 2.25%). In addition, (GlcN)5 treatment could increase the accumulation of autophagosomes. Further investigation showed that (GlcN)5 suppressed protective autophagy at the fusion of autophagosomes and lysosomes. Moreover, the inhibition of protective autophagy flux by (GlcN)5 could further decrease cell viability and increase the apoptosis rate. Our findings suggested that (GlcN)5 suppressed HepG2 proliferation through inducing apoptosis via the intrinsic pathway and impairing cell-protective autophagy. COS might have the potential to be an agent for lowering the risk of HCC.

Error Bounds and Singularity Degree in Semidefinite Programming

In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discr...

The calculation of singular orders for composite material anti-plane propagating V-notches

Because of geometric or material discontinuities, stress singularities can occur around the vertex of a V-notch. The singular order is an important parameter for characterizing the degree of the stress singularity. The present paper focuses on the calculation of the singular order for the anti-plane propagating V-notch in a composite material structure. Starting from the governing equation of elastodynamics and the displacement asymptotic expansion, an ordinary differential eigen equation with respect to the singular order is proposed. The interpolating matrix method is then employed to solve the established eigen equation to conduct the singular orders. The effects of the material principal axis direction, shear modulus, and propagation velocity and acceleration on the singular orders of the V-notch are respectively investigated, and some conclusions are drawn. The singular orders of the V-notches decrease with an increase in the material principal axis direction angle, except for the crack, whose singular orders do not change with the principal axis direction. The singular orders increase with an increase in the shear modulus $$G_{13} $$ , while they decrease with an increase in the shear modulus $$G_{23} $$ . The singular orders increase as the magnitude of the propagation velocity increases, while they decrease as the direction of the propagation velocity increases. The singular orders increase with an increase in the value of the propagation acceleration, while they decrease with an increase in the direction of the propagation acceleration. The singular orders become larger when the ratio of $$G_{13}^{(2)} /G_{13}^{(1)} $$ increases, while they become smaller when the ratio of $$G_{23}^{(2)} /G_{23}^{(1)} $$ increases, and they increase with an increase in the mass density ratio for the bi-material V-notch.