Recursive Scheme Research Articles

Numerical Solution of the Problem of Filtering Estimates Information Impact on the Electorate

The formulation and numerical scheme for solving the problem of filtering estimates of the informational impact of mass media on the electorate, allowing with a high degree of accuracy at a given observation interval to estimate the number of individuals in society who prefer a certain political subject (opinion), are proposed in the article. A mathematical model for assessing the information impact on the electorate during election campaigns, which boils down to solving a stochastic differential equation – the equation of state, forms the basis of the formulation of the problem. When compiling a model for filtering information impact estimates, it is proposed to reduce the study of the equation of state to a numerical solution of the Duncan–Mortensen–Zakai equation by introducing an additional observation equation, which is obtained from the equation of state when evaluating its stochastic components (observed agitation intensities) by methods of polyspectral analysis. In the projection formulation of the Galerkin method, when reducing to a system of linear differential equations and obtaining its solution in a recursive estimation scheme when sampling the analysis interval into subintervals and using the matrix exponential method, the Duncan–Mortensen–Zakai equation is solved. For a visual comparison of the effectiveness of the generated numerical solution to the problem of filtering information impact assessments, calculations were carried out on test examples.

Distributed recursive filtering under random access protocols: A multirate strategy

AbstractThis article addresses the distributed recursive filtering problem for a class of time‐varying multirate systems in sensor networks with randomly occurring nonlinearities and the communication protocol. A multirate model is considered where the sampling period of the sensors is slower than the updating period of the system state. Accordingly, the lifting technique is proposed to transform the multirate system into a single‐rate system. In order to avoid data collisions, the random access protocol (RAP) scheduling is applied to determine which signal/packet selected by RAP scheduling can access the shared network for each sensor. Attention is focused on the design of a distributed recursive filter such that, in the simultaneous presence of randomly occurring nonlinearities, the multirate strategy and the RAP scheduling, an upper bound for the filtering error covariance is obtained with the help of the mathematical induction method. Furthermore, by utilizing a novel matrix simplification technique, the filter parameters are recursively calculated by minimizing the obtained upper bound. Finally, the effectiveness of the proposed distributed recursive filtering scheme is demonstrated via a numerical example.

Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting

We study the fluctuations of the area under a self-similar Gaussian process x(τ) with Hurst exponent H > 0 (e.g., standard or fractional Brownian motion, or the random acceleration process) that stochastically resets to the origin at rate r. Typical fluctuations of A(t) scale as for large t and on this scale the distribution is Gaussian, as one would expect from the central limit theorem. Here our main focus is on atypically large fluctuations of A(t). In the long-time limit t → ∞, we find that the full distribution of the area takes the form with anomalous exponents α = 1/(2H + 2) and β = (2H + 3)/(4H + 4) in the regime of moderately large fluctuations, and a different anomalous scaling form in the regime of very large fluctuations. The associated rate functions Φ(y) and Ψ(w) depend on H and are found exactly. Remarkably, Φ(y) has a singularity that we interpret as a first-order dynamical condensation transition, while Ψ(w) exhibits a second-order dynamical phase transition above which the number of resetting events ceases to be extensive. The parabolic behavior of Φ(y) around the origin y = 0 correctly describes the typical, Gaussian fluctuations of A(t). Despite these anomalous scalings, we find that all of the cumulants of the distribution grow linearly in time, , in the long-time limit. For the case of reset Brownian motion (corresponding to H = 1/2), we develop a recursive scheme to calculate the coefficients c n exactly and use it to calculate the first six nonvanishing cumulants.

The optimal decomposition method (ODM) for nonlinear problems

The herein coined Optimal Decomposition Method (ODM) is presented; an analytic decomposition approach to solve nonlinear problems that circumvents the well-known convergence barrier within nonlinear decomposition methods, e.g., Adomian Decomposition Method (ADM) and Duan –Rach ADM. ODM initially concerns removing the unknown coefficients from the recursion scheme. In addition, it is powered by multiple Convergence-Control Parameters (CCP) through insertion of an ‘artificial’ parameter. The series of CCPs results in the deployment of the entire convergence potential of the decomposition method. It is shown, in a detailed manner, that ADM and Duan-Rach ADM, i.e., a modified approach preventing the appearance of the unknown coefficients in the Adomian recursion scheme for an l-point BVP ( l≥2), can be generalized only as the special cases of ODM. Therefore, ODM, by itself, moves beyond generalization of the aforementioned methods. The CCPs are computed by minimizing the universal system error. For this purpose, a gradient-based contraction search is exploited together with Genetic Algorithm (GA) to facilitate procuring the CCPs in strongly divergent examples involving several CCPs. Indeed, through examples, namely, a generalized Boundary Value Problem (BVP) test case, the Falkner-Skan equation, a two-state optimal control problem, the Burgers’ equation and a strongly nonlinear problem governing electrohydrodynamic flow of a fluid in a circular cylindrical conduit, it is exemplified that CCPs expand the radius of convergence substantially. In the considered examples, ADM and D-R ADM are strictly divergent with the addition of series terms; on the contrary, ODM serves as a successful remedy on these occasions. In practice, it was found that for most of the nonlinearities, minimizing the system error containing CCPs for lower orders of approximation gives rise to a natural minimization of the system error in higher orders of approximation, i.e., natural convergence.

An iterative technique based on HPM for a class of one dimensional Bratu’s type problem

An effective iterative computational technique is developed for the nonlinear initial and boundary value problems and employed on a class of one dimensional Bratu’s type problems. In the proposed technique, we use the homotopy concepts (similar as homotopy perturbation method (HPM)) for the recursive scheme which is obtained in terms of Green’s function with the support of the Picard’s iterative method and boundary/initial conditions. It generates, estimated solutions in the form of series, which is extremely useful in terms of computing. The suggested technique is also subjected to a convergence and error analysis. To highlight the method’s ease of implementation and usefulness, certain numerical examples have been provided and also compared our results with other existing results.

Surface Finite Element Approximation of Spherical Whittle--Matérn Gaussian Random Fields

Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part of the operator is solved by a recursive scheme, a quadrature of the Dunford--Taylor integral representation is employed for the fractional part. Strong error analysis is performed, and the computational complexity is bounded in terms of the accuracy. Numerical experiments for different choices of parameters confirm the theoretical findings.

Automatically Deployable Robust Control of Modular Reconfigurable Robot Manipulators

We propose an automatically deployable robust control scheme for modular reconfigurable robot manipulators, which accounts for noisy velocity measurements, yet it maximizes the tracking performance while avoiding chattering effects. Our proposed control approach automatically adapts to any of the possible robot compositions of given sets of modules. The robust stability is guaranteed by exploiting the use of a recursive Newton-Euler scheme with interval arithmetic computations. Moreover, the robust performance is maximized via an online regulation of the control parameters by analyzing the power spectral density of the commanded torque signal. Being fully automatic, the proposed approach allows for a quick deployment and reconfiguration of modular reconfigurable manipulators. The algorithm is validated via simulations and experiments on a commercially available robot.

Recursive Centerline- and Direction-Aware Joint Learning Network with Ensemble Strategy for Vessel Segmentation in X-ray Angiography Images

Background and objectiveAutomatic vessel segmentation from X-ray angiography images is an important research topic for the diagnosis and treatment of cardiovascular disease. The main challenge is how to extract continuous and completed vessel structures from XRA images with poor quality and high complexity. Most existing methods predominantly focus on pixel-wise segmentation and overlook the geometric features, resulting in breaking and absence in segmentation results. To improve the completeness and accuracy of vessel segmentation, we propose a recursive joint learning network embedded with geometric features. MethodsThe network joins the centerline- and direction-aware auxiliary tasks with the primary task of segmentation, which guides the network to explore the geometric features of vessel connectivity. Moreover, the recursive learning strategy is designed by passing the previous segmentation result into the same network iteratively to improve segmentation. To further enhance connectivity, we present a complementary-task ensemble strategy by fusing the outputs of the three tasks for the final segmentation result with majority voting. ResultsTo validate the effectiveness of our method, we conduct qualitative and quantitative experiments on the XRA images of the coronary artery and aorta including aortic arch, thoracic aorta, and abdominal aorta. Our method achieves F1 scores of 85.61±3.48% for the coronary artery, 89.02±2.89% for the aortic arch, 88.22±3.33% for the thoracic aorta, and 83.12±4.61% for the abdominal aorta. ConclusionsCompared with six state-of-the-art methods, our method shows the most complete and accurate vessel segmentation results.

Deep contrastive learning based tissue clustering for annotation-free histopathology image analysis.

Deep convolutional neural networks (CNNs) have yielded promising results in automatic whole slide images (WSIs) processing for digital pathology in recent years. Training supervised CNNs usually requires a large amount of annotated samples. However, manual annotation of gigapixel WSIs is labor-intensive and error-prone, i.e., the shortage of annotations has become the major bottleneck of WSI diagnosis model development. In this work, we aim to develop a deep learning based self-supervised histopathology image analysis workflow that can classify tissues without any annotation. Inspired by the contrastive learning methods that have achieved state-of-the-art results on unsupervised representation learning for natural images, we adopt the self-supervised training scheme to generate discriminative embeddings from annotation-free WSI patches and simultaneously obtain initial clusters, which are further refined by a silhouette coefficient based recursive scheme to divide tissue mixture clusters. A multi-scale encoder network is specifically designed to extract pathology-specific contextual features. A tissue dictionary composed by the tissue clusters is then built for cancer diagnosis. Experiments show that our method can identify different tissues in annotation-free conditions with competitive results (achieving the accuracy of 0.9364/0.9325 in human colorectal/sentinel lymph WSIs) as the supervised methods (with the corresponding accuracy of 0.9806/0.9494) and surpass other unsupervised baselines. Our method is also evaluated in a cohort of 20 clinical patients and get an AUC score of 0.99 to distinguish benign/malignant polyps. Our proposed deep contrastive learning based tissue clustering method can learn from raw WSIs without annotation to distinguish different tissues. The method are tested in three different datasets and show the potential to help pathologists diagnosing diseases as a quantitative and qualitative tool.

Effective improvement of multi-step-ahead flood forecasting accuracy through encoder-decoder with an exogenous input structure

Accurate and reliable multi-step-ahead flood forecasting is beneficial for reservoir operation and water resources management. The Encoder-Decoder (ED) that can tackle sequence-to-sequence problems is suitable for multi-step-ahead flood forecasting. This study proposes a novel ED with an exogenous input (EDE) structure for multi-step-ahead flood forecasting. The exogenous input can be the outputs of process-based hydrological models. This study constructs four multi-step-ahead flood forecasting approaches, including the Xinanjiang (XAJ) hydrological model, the single-output long short-term memory (LSTM) neural network with recursive strategies, the recursive ED combined with the LSTM neural network (LSTM-RED), and the LSTM-EDE models. The performance of these four models is evaluated and compared by the long-term 3 h hydrologic data series of the Lushui and Jianxi basins in China. The results show that the LSTM-RED model that integrates recursive strategies into the training process of neural networks is more advantageous than the LSTM model. The proposed LSTM-EDE model can overcome the exposure bias problem, simplify its model structure, increase the computational efficiency in the validation process, and improve the multi-step-ahead flood forecasting accuracy, as compared to the LSTM-RED model.

A new recursive scheme for solving the general fractional differential equation of the nonlinear Lienard’s equation

PurposeThe purpose of this paper is to solve an initial-value problem for the general fractional differential equation of the nonlinear Lienard's equation.Design/methodology/approachA new recursive scheme is presented by combining the Adomian decomposition method with a magnificent recurrence formula and via the solutions of the well-known generalized Abel equation.FindingsIt is shown that the proposed method may offer advantages in computing the components yn; n = 1; 2; … in an easily computed formula. Also, the numerical experiments show that with few iterations of the recursive method, this technique converges swiftly and accurately.Originality/valueThe approach is original, and a reasonably accurate solution can be achieved with only two components. Moreover, the proposed method can be applied to several nonlinear models in science and engineering.

Recursive Enhancement of Weak Subsurface Boundaries and Its Application to SHARAD Data

Sedimentary layers are composed of alternately deposited compositions in different periods, reflecting the geological evolution history of a planet. Orbital radar can detect sedimentary layers, but the radargram is contaminated by varying background noise levels. Traditional denoising methods, such as median filter, have difficulty dealing with such kinds of noise. We propose a recursive signal enhancement scheme to identify weak reflections from intense background noise. Numerical experiments with synthetic data and SHARAD radargrams illustrate that the proposed method can enhance the clarity of the radar echoes and reveal delicate sedimentary structures previously buried in the background noise. The denoising result presents better horizontal continuity and higher vertical resolution compared with those of the traditional methods.

Recursive grain remapping scheme for phase‐field models of additive manufacturing

AbstractThe phase‐field method is an attractive tool in modeling microstructural evolution due to rapid solidification under additive manufacturing conditions, but typical polycrystalline models are prone to grain coalescence. Grain tracking and remapping schemes can eliminate artificial coalescence and increase the number of grains and crystallographic orientations that may be considered in a simulation, but previous tracking and remapping schemes may not efficiently capture the complex grain morphologies that form during additive manufacturing. A new recursive scheme is derived from a binary tree of axis‐aligned bounding boxes that can efficiently represent columnar and irregularly shaped grains. We demonstrate the power of this approach by simulating microstructures with hundreds to thousands of grains and quantify the reduction in the number of order parameters required to represent the microstructure. The new scheme leads to orders of magnitude fewer computational resources as compared to the naïve paradigm of one grain per order parameter, and also offers a substantial improvement over algorithms derived from bounding spheres.

Efficient deep neural network for photo-realistic image super-resolution

Recent progress in deep learning-based models has improved photo-realistic (or perceptual) single-image super-resolution significantly. However, despite their powerful performance, many methods are difficult to apply to real-world applications because of the heavy computational requirements. To facilitate the use of a deep model under such demands, we focus on keeping the network efficient while maintaining its performance. In detail, we design an architecture that implements a cascading mechanism on a residual network to boost the performance with limited resources via multi-level feature fusion. In addition, our proposed model adopts group convolution and recursive schemes in order to achieve extreme efficiency. We further improve the perceptual quality of the output by employing the adversarial learning paradigm and a multi-scale discriminator approach. The performance of our method is investigated through extensive internal experiments and benchmarks using various datasets. Our results show that our models outperform the recent methods with similar complexity, for both traditional pixel-based and perception-based tasks.

Improvement in design and training of feature pyramid network for contour refinement

• A simplified feature pyramid architecture, called Edge Pyramid Network, applied for the first time to edge detection. • A recursive fine-tuning strategy introducing a new weighted negative loss to detect accurate and thin edges. • State-of-the-art results on the benchmark datasets for semantic and category-agnostic edge detection. Semantic edge detection is a challenging problem which aims to produce multiple edge maps corresponding to different object categories. The design and the training of the related network are the two most powerful levers to optimize its accuracy. To this end, we first refine existing semantic edge detection architectures with low and high level features inside our Edge Pyramid Network, which already outperforms state-of-the-art networks on popular benchmark datasets. Then, we apply an ingenious fine-tuning strategy, which incrementally improves edge detection accuracy through a few alternated training cycles, using various loss functions to perform thick and thin edge detection. We observe that applying separately any of these refinements outperforms such networks as SEAL and STEAL for category-aware edge detection. More remarkable is the fact that these two refinements provide accumulated benefits on the edge detection performance (+0.85% and +1.78% on MF-scores compared to STEAL on SBD and Cityscapes datasets respectively). This improvement is visible in the edge maps in which EPN architecture results in smoother edges and the fine-tuning strategy is responsible for thinner edges. Furthermore, we show that EPN architecture achieves competitive performance (ODS F-measure of 0.828) against the state-of-the-art category-agnostic edge detection networks on the BSDS500 dataset.

Teacher Mobility: What Is It, How Is It Measured and What Factors Determine It? A Scoping Review.

Teacher mobility represents a serious problem due to the instability of the teaching force that has persisted over time in many countries. Therefore, retaining qualified teachers represents a challenge given the difficulty of having the necessary workforce to face the educational challenges of each year. Our objective was trying to identify how mobility is understood and measured, that is, teacher turnover and attrition, and to identify the results of the related factors according to the different perspectives. The PRISMA-Scr protocol was used, which establishes the information that should be included in a systematic review. The following key phrases were used: “teacher rotation” or “teacher mobility” or “teacher desertion” or teacher leavers or teacher stayers. The databases used were Web of Science, Scielo Citation Index and Google Scholar, which yielded an initial total of 760 documents published between 2008 and 2018, that after identification, screening, eligibility, and inclusion processes, were reduced to 213. The selection of articles was carried out independently by two researchers using a structured and recursive hierarchical strategy. The existence of multiple ways of defining and measuring teacher mobility was identified and a definition based on two perspectives was proposed that summarizes the conceptual and operational findings, which are indirect and direct mobility. The first refers to the intention to leave and the second to leave. We have identified more evidence related to direct studies of a quantitative approach and focused on teachers with medium or short experience. The factors associated with mobility were identified based on the approaches used and a key element was identified when distinguishing teacher mobility, which is voluntary and involuntary mobility. We identified multiple factors associated with teacher mobility, among which the precarious working environment, poor organizational conditions such as lack of leadership and support among colleagues, excessive workload and low self-efficacy stand out. The limitations of this study are discussed. The findings of this study are highly relevant since they allow proposing medium or short-term policies, such as improving the organizational conditions of the school to promote the retention of the teaching workforce.

Bounding Box Stabilization for Visual Object Tracking Using Kalman and FIR Filters

In visual object tracking, the estimation of the trajectory of a moving object is a widely studied problem. In the object tracking process, there are usually variations between the real position of the objet in the scene and the estimated position, that is, the object is not exactly followed throughout its trajectory. These variations can be considered as color measurement noise (CMN) caused by the object and the camera frame movement. In this paper, we treat such differences as Gauss-Markov coloring measurement noise. We use Finite Impulse Response filters and Kalman filter with a recursive strategy in tracking: predict and update. To demonstrate the best performance, tests were carried out with simulated trajectories and with benchmarks from a database available online. The OUFIR and UFIR algorithms showed favorable results with high precision and accuracy in the object tracking task.

A training-free recursive multiresolution framework for diffeomorphic deformable image registration

Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural networks (CNNs) have yielded well-suited approaches for image registration by learning the transformation priors from a large dataset. The improvement in the performance of these methods is related to their ability to learn information from several sample medical images that are difficult to obtain and bias the framework to the specific domain of data. In this paper, we propose a novel diffeomorphic training-free approach; this is built upon the principle of an ordinary differential equation. Our formulation yields an Euler integration type recursive scheme to estimate the changes of spatial transformations between the fixed and the moving image pyramids at different resolutions. The proposed architecture is simple in design. The moving image is warped successively at each resolution and finally aligned to the fixed image; this procedure is recursive in a way that at each resolution, a fully convolutional network (FCN) models a progressive change of deformation for the current warped image. The entire system is end-to-end and optimized for each pair of images from scratch. In comparison to learning-based methods, the proposed method neither requires a dedicated training set nor suffers from any training bias. We evaluate our method on three cardiac image datasets. The evaluation results demonstrate that the proposed method achieves state-of-the-art registration accuracy while maintaining desirable diffeomorphic properties.

The Macroeconomic Impact of Fiscal Policy Shocks: What do the Indian Data Say?

This article examines the impact of fiscal policy shocks on a set of macroeconomic variables in India, using a seasonally adjusted quarterly dataset for the period 2003–2019. The Gregory-Hansen residual-based test for cointegration and the vector error correction model (VECM) are applied, and impulse responses based on a recursive identification scheme (Cholesky decomposition) is used to assess the effects of a gross tax revenue shock and a government spending shock on economic activity, while accounting for the possibility of structural breaks. The findings indicate that an unexpected fiscal policy shock has an immediate expansionary impact on real GDP and a sudden positive effect on inflation (WPI) and the repo rate; and that the impact is permanent and away from the zero equilibrium. The careful design of policies by the central bank and the government as crucial macroeconomic stabilisation tools is imperative. JEL Classification: E6, H20, H30

Deep Recursive Embedding for High-Dimensional Data.

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this article, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding. We introduce a generic deep embedding network (DEN) framework, which is able to learn a parametric mapping from high-dimensional space to low-dimensional space, guided by well-established objectives such as Kullback-Leibler (KL) divergence minimization. We further propose a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance. We exemplify the flexibility of DRE by different architectures and loss functions, and benchmarked our method against the two most popular embedding methods, namely, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP). The proposed DRE method can map out-of-sample data and scale to extremely large datasets. Experiments on a range of public datasets demonstrated improved embedding performance in terms of local and global structure preservation, compared with other state-of-the-art embedding methods. Code is available at https://github.com/tao-aimi/DeepRecursiveEmbedding.