Incorrect Convergence Research Articles

Heter-Train: A Distributed Training Framework Based on Semi-Asynchronous Parallel Mechanism for Heterogeneous Intelligent Transportation Systems

Transportation big data (TBD) are increasingly combined with artificial intelligence to mine novel patterns and information due to the powerful representational capabilities of deep neural networks (DNNs), especially for anti-COVID19 applications. The distributed cloud-edge-vehicle training architecture has been applied to accelerate DNNs training while ensuring low latency and high privacy for TBD processing. However, multiple intelligent devices (e.g., intelligent vehicles, edge computing chips at base stations) and different networks in intelligent transportation systems lead to computing power and communication heterogeneity among distributed nodes. Existing parallel training mechanisms perform poorly on heterogeneous cloud-edge-vehicle clusters. The synchronous parallel mechanism may force fast workers to wait for the slowest worker for synchronization, thus wasting their computing power. The asynchronous mechanism has communication bottlenecks and can exacerbate the straggler problem, causing increased training iterations and even incorrect convergence. In this paper, we introduce a distributed training framework, Heter-Train. First, a communication-efficient semi-asynchronous parallel mechanism (SAP-SGD) is proposed, which can take full advantage of acceleration effect of asynchronous strategy on heterogeneous training and constrain the straggler problem by using global interval synchronization. Second, Considering the difference in node bandwidth, we design a solution for heterogeneous communication. Moreover, a novel weighted aggregation strategy is proposed to aggregate the model parameters with different versions. Finally, experimental results show that our proposed strategy can achieve up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.74 \times$</tex-math> </inline-formula> speedups on training time, with almost no accuracy decrease.

Sensorless Control and Inductances Estimation of IPMSMs Using FPGA and High Bandwidth Current Measurement

This paper presents a sensorless control method and a very fast on-line inductances identification of an IPMSM. The current slopes (derivatives) at one active-voltage vector and one zero-voltage vector are measured every PWM cycle to estimate the rotor speed and position with the aim of increasing the estimation accuracy and reducing total harmonic distortion. In addition to these current slopes, the DC bus voltage of the inverter is measured to estimate the machine inductances on-line. The proposed on-line parameter identification method can overcome the drawback of the existing off-line methods, such as: the requirement of a robust mechanical clamping system and test signal generators. The proposed on-line method also addresses the limit of the existing on-line methods, such as slow update and the possibility of incorrect convergence of the estimated parameters. Extensive experimental studies were conducted to verify the effectiveness and robustness of the proposed sensorless control and parameters identification of the IPMSM.

Cognitive model of phonological awareness focusing on errors and formation process through Shiritori

Language acquisition is supported by phonological awareness, which intentionally makes children aware of phonological units. By understanding the internal processes of children during language acquisition, this study aims to elucidate factors that can correct erroneous phonological generation. Therefore, we developed a cognitive model using innate and experiential factors of the memory retrieval in the cognitive architecture–ACT-R. Furthermore, we performed simulations using Shiritori, a Japanese word game, as an interaction task. The simulation included the observation of effects of the experiential factor of repeating a task and innate factors of different settings. It showed that repeating a single task causes incorrect convergence, and this convergence can be prevented by comprehensive activation of overall phonological knowledge during the interval of Shiritori tasks. Moreover, the simulation in specific innate settings exhibited commonalities with cases of developmental disorder by showing errors like consonant deletion. In the future, we will examine the correlation of the aforementioned findings with actual language development to realize the use of cognitive architecture in real world.

Optical polarization division multiplexing fiber-wireless integration system at Ka-band based on a low-cost dual-drive MZM.

In this paper, a low-cost dual-drive Mach-Zehnder modulator (DDMZM) based 40 Gbit/s polarization division multiplexing (PDM) fiber-wireless-integration system at Ka-band is experimentally demonstrated. Since the DDMZM is biased at the quadrature point for electro-to-optical (E/O) conversion, a high-power direct current (DC)/radio frequency (RF) component will appear within the received signal bandwidth. This high-power component becomes a narrowband interference due to the phase noise of lasers, which will lead to the incorrect convergence of the constant-modulus algorithm (CMA) during equalization at the receiver side. In order to deal with the broadened DC component, twin-single-sideband (twin-SSB) signal with bandwidth interleave and RF-pilot based phase noise compensation scheme are adopted. Enabled by the combination of optical PDM technique and heterodyne coherent detection, a 40 Gbit/s PDM twin-SSB Nyquist-shaped quadrature-phase-shift-keying (QPSK) signal transmitting over 20-km single mode fiber (SMF) and 1-m 2×2 multiple-input multiple-output (MIMO) wireless distance is achieved with the bit error rate (BER) below the hard-decision forward-error-correction (HD-FEC) threshold of 3.8×10-3.

Ultrasound Computed Tomography of Knee Joint

Ultrasound computed tomography (UCT) is considered to have great potential for the early diagnosis of knee joint injuries. Combining prior knowledge and sound speeds of tissues, UCT can diagnose a variety of symptoms and the extent of tissue lesion. However, no existing studies can reconstruct the sound speed distributions of knee joints in UCT. Therefore, in this study, sound speed distributions of knee joints are reconstructed to provide an imaging basis for the formulation of a treatment plan. In addition, Full waveform inversion (FWI) methods are utilized to estimate highresolution images. However, for media with large variations in sound speeds, traditional FWI methods may lead to a cycle-skipping phenomenon and incorrect convergence direction. Hence, this study proposes a multi-centerfrequency source based FWI method to overcome the above limitations. A penalized least-squares optimization problem is constructed to obtain a numerical solution of the sound speed distribution. Computer simulations are conducted to prove the effectiveness and robustness of the proposed method. Furthermore, the reasons for selecting the center frequencies of sources are analyzed. Two numerical knee joint phantoms are used to evaluate the performance. The results suggest that the biases of the reconstructed images are less than 1% under a 5% noise condition.

A sea-sky-line detection method based on Gaussian mixture models and image texture features

This article presents a sea-sky-line detection algorithm in a sea-sky environment for unmanned surface vehicles. Obstacle detection is a vital branch for unmanned surface vehicles on the ocean. Because of the specificity and complexity of the marine navigation environment, we first apply semantic segmentation for marine images. The complete marine scene is divided into sky area, middle mixture area, and seawater area before sea-sky-line detection. Segmenting the marine environment is beneficial for narrowing the obstacle search area, accelerating the rate of obstacle detection, and improving detection accuracy. Therefore, a fast, robust, and accurate sea-sky image segmentation method is urgently required. Therefore, we present a method that lies in a probabilistic graphical model for segmenting marine images. The Gaussian mixture model is introduced as the probability distribution model for the marine image. The sky, middle mixture, and seawater areas are generated by three Gaussian models. The expectation–maximization algorithm is utilized to maximize the log-likelihood function, and the parameters of the Gaussian mixture probability density function that recover the marine image distribution are available after several iterations. Furthermore, to solve the problem of incorrect convergence direction caused by unsatisfactory initialization conditions, the gray level co-occurrence matrix is referenced to initialize the Gaussian components. The coarse segmentation results rely on the gray level co-occurrence matrix and are used to calculate the prior initialization parameters of Gaussian components and obtain the prior distribution information of marine images, which mitigates the harmful influence of poor initialization. The algorithm is tested on a data set consisting of the marine obstacle detection dataset (MODD) public data set and our collected images. The results on this data set demonstrate that the proposed method is more robust and that a superior initialization condition can effectively accelerate the convergence velocity of the iterative process for Gaussian components.

An Adaptive Wake-Up-Interval to Enhance Receiver-Based Ps-Mac Protocol for Wireless Sensor Networks.

Many receiver-based Preamble Sampling Medium Access Control (PS-MAC) protocols have been proposed to provide better performance for variable traffic in a wireless sensor network (WSN). However, most of these protocols cannot prevent the occurrence of incorrect traffic convergence that causes the receiver node to wake-up more frequently than the transmitter node. In this research, a new protocol is proposed to prevent the problem mentioned above. The proposed mechanism has four components, and they are Initial control frame message, traffic estimation function, control frame message, and adaptive function. The initial control frame message is used to initiate the message transmission by the receiver node. The traffic estimation function is proposed to reduce the wake-up frequency of the receiver node by using the proposed traffic status register (TSR), idle listening times (ILTn, ILTk), and “number of wake-up without receiving beacon message” (NWwbm). The control frame message aims to supply the essential information to the receiver node to get the next wake-up-interval (WUI) time for the transmitter node using the proposed adaptive function. The proposed adaptive function is used by the receiver node to calculate the next WUI time of each of the transmitter nodes. Several simulations are conducted based on the benchmark protocols. The outcome of the simulation indicates that the proposed mechanism can prevent the incorrect traffic convergence problem that causes frequent wake-up of the receiver node compared to the transmitter node. Moreover, the simulation results also indicate that the proposed mechanism could reduce energy consumption, produce minor latency, improve the throughput, and produce higher packet delivery ratio compared to other related works.

Steering Orbital Optimization out of Local Minima and Saddle Points Toward Lower Energy.

The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored that multiple self-consistent solutions can exist, several of which may correspond to minima of the energy functional. In addition to the difficulty sometimes encountered to converge the calculation to a self-consistent solution, one must ensure that the correct self-consistent solution was found, typically the one with the lowest electronic energy. Convergence to an unwanted solution is in general not trivial to detect and will deliver incorrect energy and molecular properties and accordingly a misleading description of chemical reactivity. Wrong conclusions based on incorrect self-consistent field convergence are particularly cumbersome in automated calculations met in high-throughput virtual screening, structure optimizations, ab initio molecular dynamics, and in real-time explorations of chemical reactivity, where the vast amount of data can hardly be manually inspected. Here, we introduce a fast and automated approach to detect and cure incorrect orbital convergence, which is especially suited for electronic structure calculations on sequences of molecular structures. Our approach consists of a randomized perturbation of the converged electron density (matrix) intended to push orbital convergence to solutions that correspond to another stationary point (of potentially lower electronic energy) in the variational parameter space of an electronic wave function approximation.

A yarn interaction model for circular braiding

Machine control data for the automation of the circular braiding process has been generated using previously published mathematical models that neglect yarn interaction. This resulted in a significant deviation from the required braid angle at mandrel cross-sectional changes, likely caused by an incorrect convergence zone length, in turn caused by this neglect. Therefore the objective is to use a new model that includes the yarn interaction, assuming an axisymmetrical biaxial process with a cylindrical mandrel and Coulomb friction. Experimental validation with carbon yarns and a 144 carrier machine confirms a convergence zone length decrease of 25% with respect to a model without yarn interaction for the case analyzed, matching the model prediction using a coefficient of friction of around 0.3.

A note on the paper “A new general eighth-order family of iterative methods for solving nonlinear equations”

In this work, we briefly talk about the incorrect convergence order presented in the paper Khan et al. (Appl. Math. Lett. 25:2262–2266, 2012). Accordingly, we first show that their convergence theorem includes major errors, and it is attempted to provide the correct error equation of their method having fifth-order not eighth-order convergence. Finally, to support our assertion, some numerical examples are tested.

Complex Langevin dynamics for chiral random matrix theory

We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.

Thirring model at finite density in2+1dimensions with stochastic quantization

We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate the results and compare to the (0+1)-dimensional case.

On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential

The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at larger chemical potential by comparison with the world line method. While complex Langevin works for larger beta, we find that it fails for smaller beta, in the region of the phase diagram corresponding to the disordered phase. Diagnostic tests are developed to identify symptoms correlated with incorrect convergence. We argue that the erroneous behaviour at smaller beta is not due to the sign problem, but rather resembles dynamics observed in complex Langevin simulations of simple models with complex noise.

Template-driven segmentation of confocal microscopy images

High quality 3D visualization of anatomic structures is necessary for many applications. The anatomic structures first need to be segmented. A variety of segmentation algorithms have been developed for this purpose. For confocal microscopy images, the noise introduced during the specimen preparation process, such as the procedure of penetration or staining, may cause images to be of low contrast in some regions. This property will make segmentation difficult. Also, the segmented structures may have rugged surfaces in 3D visualization. In this paper, we present a hybrid method that is suitable for segmentation of confocal microscopy images. A rough segmentation result is obtained from the atlas-based segmentation via affine registration. The boundaries of the segmentation result are close to the object boundaries, and are regarded as the initial contours of the active contour models. After convergence of the snake algorithm, the resulting contours in regions of low contrast are locally refined by parametric bicubic surfaces to alleviate the problem of incorrect convergence. The proposed method increases the accuracy of the snake algorithm because of better initial contours. Besides, it can provide smoother segmented results in 3D visualization.

A framework for evolutionary optimization with approximate fitness functions

It is not unusual that an approximate model is needed for fitness evaluation in evolutionary computation. In this case, the convergence properties of the evolutionary algorithm are unclear due to the approximation error of the model. In this paper, extensive empirical studies are carried out to investigate the convergence properties of an evolution strategy using an approximate fitness function on two benchmark problems. It is found that incorrect convergence will occur if the approximate model has false optima. To address this problem, individual- and generation-based evolution control are introduced and the resulting effects on the convergence properties are presented. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization, which is able to guarantee the correct convergence of the evolutionary algorithm, as well as to reduce the computation cost as much as possible. Control of the evolution and updating of the approximate models are based on the estimated fidelity of the approximate model. Numerical results are presented for three test problems and for an aerodynamic design example.

Computational Simulation of Flow Localization Behavior

The present article provides a perspective for computational predictions relating to flow localization under a wide range of deformation rates for a variety of materials characterized by constitutive equations incorporating the strain-rate and temperature sensitivities, and strain-rate-history, temperature-history, and strain-gradient dependences of the flow stress. The regularization schemes to remedy the problems associated with spurious mesh sensitivity and incorrect convergence in finite-element prediction of flow localization behavior are reviewed. Various aspects of flow localization behavior of plane strain blocks with different shapes and sizes under a wide range of tension rate are discussed on the basis of computational simulations.

Simulations of Plastic Instabilities in Solid Mechanics

The purpose of the present article is provide a perspective for computational predictions related to such plastic instabilities as buckling, necking and flow localization including shear–banding under a wide range of deformation rates for a variety of materials, including single– and polycrystals. Computational bifurcation analyses for general cases, axisymmetric to nonaxisymmetric deformation, very thin–walled bodies, and specific materials with nonstandard constitutive equations are given. The postbifurcation analyses and regularization schemes to remedy the problems associated with spurious mesh sensitivity and incorrect convergence in finite element prediction of flow localization behavior are discussed. The instability behavior of thick circular tubes deformed under pressure and combined loading of internal/external pressure and axial force, neck and bulge propagations in polymeric materials, wrinkling of thin plates and shells under sheet metal forming processes, flow localization of thermo–elasto–viscoplastic materials under a wide range of deformation rates including adiabatic shear banding, and flow localization behavior of mono– and polycrystalline solids are reviewed with illustrative examples.

Nonlocal Smeared Cracking Model for Concrete Fracture

The classical smeared cracking model widely used in finite‐element analysis of concrete and rock cannot describe the size effect experimentally observed in brittle failures and exhibits spurious mesh sensitivity with incorrect convergence to zero energy dissipation at failure. The crack band model circumvents these deficiencies but has limitations with respect to mesh refinement, shear locking on zig‐zag crack bands, and directional bias of the mesh. It is shown that all of these problems can be avoided by a nonlocal generalization, in which the damage that characterizes strain softening is considered to be a function of the spatial average of the positive part of the maximum principal strain. Two alternatives are presented: (1) Smeared cracking whose direction is fixed when cracks start to form; and (2) smeared cracking whose orientation rotates with the maximum principal strain. Furthermore, fracture tests on specimens of various sizes are analyzed by finite elements. It is shown that the model correctl...

Nonlocal Damage Theory

In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh sensitivity and proper convergence are demonstrated by numerical examples, including static strain softening in a bar, longitudinal wave propagation in strain‐softening material, and static layered finite element analysis of a beam. In the last case, the size of the representative volume serving in one dimension as the averaging length for damage must not be less than the beam depth, due to the hypothesis of plane cross sections. It is also shown that averaging of the fracturing strain leads to an equivalent formulation, which could be extended to anisotropic damage due to highly oriented cracking.

Convergence theory for fuzzy c-means: Counterexamples and repairs

A counterexample to the original incorrect convergence theorem for the fuzzy c-means (FCM) clustering algorithms (see J.C. Bezdak, IEEE Trans. Pattern Anal. and Math. Intell., vol.PAMI-2, no.1, pp.1-8, 1980) is provided. This counterexample establishes the existence of saddle points of the FCM objective function at locations other than the geometric centroid of fuzzy c-partition space. Counterexamples previously discussed by W.T. Tucker (1987) are summarized. The correct theorem is stated without proof: every FCM iterate sequence converges, at least along a subsequence, to either a local minimum or saddle point of the FCM objective function. Although Tucker's counterexamples and the corrected theory appear elsewhere, they are restated as a caution not to further propagate the original incorrect convergence statement.