Forward Backward Research Articles

Group Forward–Backward Orthogonal Matching Pursuit for General Convex Smooth Functions

This paper introduces the Group Forward–Backward Orthogonal Matching Pursuit (Group-FoBa-OMP) algorithm, a novel approach for sparse feature selection. The core innovations of this algorithm include (1) an integrated backward elimination process to correct earlier misidentified groups; (2) a versatile convex smooth model that generalizes previous research; (3) the strategic use of gradient information to expedite the group selection phase; and (4) a theoretical validation of its performance in terms of support set recovery, variable estimation accuracy, and objective function optimization. These advancements are supported by experimental evidence from both synthetic and real-world data, demonstrating the algorithm’s effectiveness.

Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents {γ1,γ2,…} under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI.

Modeling environmental-born melioidosis dynamics with recurrence: An application of optimal control

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number (R0) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on R0 are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

Non-ergodic convergence rate of an inertial accelerated primal–dual algorithm for saddle point problems

In this paper, we design an inertial accelerated primal–dual algorithm to address the convex–concave saddle point problem, which is formulated as minxmaxyf(x)+〈Kx,y〉−g(y). Remarkably, both functions f and g exhibit a composite structure, combining “nonsmooth” ＋ “smooth” components. Under the assumption of partially strong convexity in the sense that f is convex and g is strongly convex, we introduce a novel inertial accelerated primal–dual algorithm based on Nesterov’s extrapolation. This algorithm can be reduced to two classical accelerated forward–backward methods for unconstrained optimization problem. We show that the proposed algorithm achieves a non-ergodic O(1/k2) convergence rate, where k represents the number of iterations. Several numerical experiments validate the efficiency of our proposed algorithm.

Efficient and Secure Management of Medical Data Sharing Based on Blockchain Technology

In the current landscape of medical data management, processing data across diverse institutions and maximizing their value are paramount. However, traditional methods lack a secure and efficient mechanism for end-to-end traceability and supervision, posing challenges in distributed scenarios lacking mutual trust. Leveraging blockchain’s decentralized, tamper-proof, and traceable features, this paper introduces a blockchain-based medical data management platform. This platform enables full-process management of raw data, operational behaviors, intermediate data, and final data, meeting the needs of trusted storage and supervision of data. We propose two methods, namely, naive method and DAG-based method, to realize forward tracking and backward tracing of medical data stored on the blockchain, respectively. We validated and analyzed the storage and query performance of the medical data management platform on real medical data, and we also conducted experimental analyses on the efficiency of the proposed traceability algorithm under different data scales and processing path lengths. The results demonstrate that our platform and traceability methods effectively meet the management needs of medical data distributed across institutions.

A fixed-time stable forward–backward dynamical system for solving generalized monotone inclusions

AbstractWe propose a forward–backward splitting dynamical system for solving inclusion problems of the form $$0\in A(x)+B(x)$$ 0 ∈ A ( x ) + B ( x ) in Hilbert spaces, where A is a maximal operator and B is a single-valued operator. Involved operators are assumed to satisfy a generalized monotonicity condition, which is weaker than the standard monotone assumptions. Under mild conditions on parameters, we establish the fixed-time stability of the proposed dynamical system. In addition, we consider an explicit forward Euler discretization of the dynamical system leading to a new forward backward algorithm for which we present the convergence analysis. Applications to other optimization problems such as constrained optimization problems, mixed variational inequalities, and variational inequalities are presented and some numerical examples are given to illustrate the theoretical results.

Adaptive Sparse Regular Split Gaussian Kernel Least Mean Square Algorithm for Super-Low-Frequency Motion-Induced Noise Cancellation

In super-low-frequency (SLF) submarine communication, the motion-induced noise of the towed antenna is the primary noise source, and below 500 Hz, it increases with increasing speed. We propose an improved quadratic Approximate Forward–Backward Split Gaussian Kernel Least Mean Square Algorithm (ASRSG–KLMS) based on the forward–backward split criterion using noise approximation of the nonlinear kernel least mean square, which introduces an L2-paradigm regularization term and has good sparsity while maintaining optimization stability. The ASRSG–KLMS algorithm could improve the narrowband signal-to-noise ratio by approximately 6.93 dB in the frequency range of 45–55 Hz, making it suitable for motion-induced noise cancellation in the SLF band.

Modeling the transmission dynamics of the co-infection of COVID-19 and Monkeypox diseases with optimal control strategies and cost–benefit analysis

This study explores a mathematical model in continuous time, elucidating the transmission dynamics of the co-infection of COVID-19 and Monkeypox. We implemented an optimal control strategy that includes adherence to wearing nose/face masks, practicing social distancing, employing rodenticides, and getting vaccinated against these lethal illnesses. The goal is to reduce their spread among people, consequently lessening their impact on the human population. Utilizing the discrete-time Pontryagin maximum principle, we determined optimal control strategies through an iterative approach to solve the optimal system. By utilizing the MATLAB optimization toolbox with the Runge–Kutta forward–backward sweep technique, we performed numerical simulations to demonstrate how these control parameters impact different sections of the human population, including both infected and uninfected compartments. We conducted a comprehensive cost–benefit analysis to identify the control measures that would produce the best outcome in minimizing both the expenses and the incidence of co-infection cases involving COVID-19 and Monkeypox diseases. Our analyses indicated that intensifying the utilization of nose/facemasks, rodenticides, personal protective equipments (PPEs) in Monkeypox treatment facilities, immunization, and implementing social distancing measures can notably diminish the prevalence of COVID-19, Monkeypox, and their concurrent infections among the human populace.

Analysis of posture and balance impairments in individuals with chronic nonspecific neck pain-an observational study.

Neck pain is one of the most burdensome chronic musculoskeletal problems globally. Impaired proprioception is associated with Chronic Nonspecific neck pain as the structures of the cervical spine are crucial for proprioception and balance. There is a paucity of literature examining objective measures of balance and postural sway in patients with Nonspecific neck pain. This study was observational and consisted of 126 samples (63 cases and 63 controls who were recruited using convenience sampling. The demographics of the samples were collected and the postural and balance impairment was assessed using Biodex Balance SD. Mean, Median, and SD were obtained and the inferential analysis was done using the Whitney U Test and the level of significance was accepted at p < 0.05. The subjects with neck pain showed had a lower static stability index, static sway index, static stability index- forward backward and static sway index lateral scores than the normal counterparts. There are significant differences in the overall static stability index, (p < 0.001). There was a significant difference in static sway index(p = 0.003), and static stability index lateral (p = 0.004). There was no significant difference for static sway index forward and backward (p = 0.550) and lateral sway index (p = 0.711). Subjects with neck pain showed had a lower static stability index, static sway index, static stability index- forward backward and static sway index lateral scores than the normal counterparts and there was a significant difference between the static sway and static stability index in forward and backward directions as well as in lateral direction. These findings may help to assess the specific balance parameters and address the underlying causes of balance issues in patients with neck pain and also provide a comprehensive care to the patients. The trial was registered with CTRI India with registration number: CTRI/2022/07/044222.

Diagnostic value of imaging in patients with clear cell papillary renal cell carcinoma: A case series and literature review.

Clear cell papillary renal cell carcinoma (CCPRCC) is a newly classified renal cell carcinoma with a low degree of malignancy. Its imaging features have not been studied deeply. Therefore, we reviewed the imaging features of CCPRCC. Solid CCPRCC shows high echo or isoecho mass on conventional ultrasound. Contrast enhanced ultrasound shows "fast forward and slow backward, uneven high enhancement". Computed tomography shows high enhancement and maximum enhancement in the cortical-medullary phase. Magnetic resonance imaging shows slightly low T1WI and high T2WI. This article aims to improve the understanding of CCPRCC by clinical radiologists and promote the accurate.

Generalizability of foot placement control strategies during unperturbed and perturbed gait.

Control of foot placement is an essential strategy for maintaining balance during walking. During unperturbed, steady-state walking, foot placement can be accurately described as a linear function of the body's centre of mass (CoM) state at midstance. However, it is uncertain if this mapping from CoM state to foot placement generalizes to larger perturbations that could potentially cause falls. Recovery from these perturbations may require reactive control strategies not observed during unperturbed walking. Here, we used unpredictable changes in treadmill belt speed to assess the generalizability of foot placement mappings identified during unperturbed walking. We found that foot placement mappings generalized poorly from unperturbed to perturbed walking and differed for forward perturbation versus backward perturbation. We also used the singular value decomposition of the mapping matrix to reveal that people were more sensitive to backward versus forward perturbations. Together, these results indicate that a single linear mapping cannot describe the foot placement control during both forward and backward losses of balance induced by treadmill belt speed perturbations. Better characterization of human balance control strategies could improve our understanding of why different neuromotor disorders result in heightened fall risk and inform the design of controllers for balance-assisting devices.

Weak solutions to coupled quadratic forward backward stochastic differential equations and Sobolev solutions to their related partial differential equations

We establish existence and uniqueness of a weak (in law sense) solution to coupled forward–backward stochastic differential equations (FBSDEs), with possibly discontinuous diffusion coefficient. We assume that the coefficient of the backward component is of quadratic growth. We first prove the existence of a Sobolev solution for the related partial differential equation (PDE) in the Sobolev space , by using compactness arguments. Next, we use Itô–Krylov's formula to get the existence of weak solution to our considered FBSDE. For the uniqueness part, we first establish the weak uniqueness of the FBSDEs then deduce the uniqueness of its related PDE by using the Feynmann–Kac formula.

Deep Learning Backward Recognition Model to Improve Pronunciation Accuracy in the Teaching of Spoken English

The advent of speech recognition algorithms has opened new avenues for enhancing pronunciation accuracy in the teaching of spoken English. As English continues to be a global lingua franca, proficiency in spoken communication holds paramount importance for individuals across diverse professional and academic domains. This paper introduces Forward Backward Recognition Deep Learning (FBRDL), a novel approach aimed at leveraging speech recognition algorithms to enhance pronunciation accuracy in the teaching of spoken English. FBRDL incorporates advanced deep learning techniques such as recurrent neural networks (RNNs) and transformers, which excel in modeling sequential data and capturing long-range dependencies. By leveraging these powerful architectures, FBRDL can effectively handle the inherent variability and complexity of speech signals, enabling robust and accurate recognition even in noisy or adverse environments. Moreover, FBRDL is characterized by its adaptability and scalability, making it well-suited for a wide range of applications across industries. Whether in the realm of virtual assistants, automatic transcription, or voice-controlled devices, FBRDL offers a versatile solution capable of meeting the demands of modern speech recognition tasks. FBRDL integrates principles from deep learning with advanced speech recognition techniques to provide learners with real-time feedback and guidance on their pronunciation. By analyzing spoken English inputs and identifying phonetic discrepancies, FBRDL offers targeted interventions tailored to individual learners' needs. FBRDL achieves an average increase in pronunciation accuracy of 20% compared to traditional teaching methods. Moreover, qualitative assessments underscore the effectiveness of FBRDL in facilitating more precise and efficient acquisition of spoken English skills.

Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models

We consider the classical problem of maximizing the expected utility of terminal net wealth with a final random liability in a simple jump-diffusion model. In the spirit of Horst et al. (Stoch Process Appl 124(5):1813–1848, 2014) and Santacroce and Trivellato (SIAM J Control Optim 52(6):3517–3537, 2014), under suitable conditions the optimal strategy is expressed in implicit form in terms of a forward backward system of equations. Some explicit results are presented for the pure jump model and for exponential utilities.

Is spinopelvic compensation associated with unstable gait?: Analysis using whole spine X-rays and a two-point accelerometer during gait in healthy adults

BackgroundPelvic incidence (PI)–lumbar lordosis (LL) mismatch has a significant destabilizing effect on the center of gravity sway in the static standing position. However, the association between spinopelvic alignment and balance during gait in healthy volunteers is poorly understood. Research questionThe degree of PI–LL mismatch and trunk anterior tilt in the static standing posture influences dynamic balance during gait. MethodsIn this study, 131 healthy volunteers were divided into two groups: harmonious group (PI − LL ≤ 10°; n = 91) and unharmonious group (PI − LL > 10°; n = 40). A two-point accelerometer system was used for gait analysis; accelerometers were attached to the pelvis and upper trunk to measure acceleration in the forward–backward, right–left, and vertical directions so that sagittal (front–back) deviation width, coronal (right–left) width, and vertical width and their ratios were calculated. Measurements were compared between the two groups, and correlations between alignment and accelerometer data were examined. ResultsThe harmonious group showed a negative correlation between pelvic sagittal width and PI – LL, pelvic tilt (PT), and sagittal vertical axis (SVA) (correlation coefficient ρ = −0.42, −0.38, and −0.4, respectively), and a positive correlation between sagittal ratio and PI − LL (ρ = 0.35). The unharmonious group showed a positive correlation between pelvic sagittal width and PI and PT (ρ = 0.43 and 0.33, respectively) and between sagittal ratio and SVA (ρ = 0.32). The unharmonious group showed a positive correlation between upper trunk sagittal width and PI − LL and PT (ρ = 0.38 and 0.36, respectively). SignificanceThe association between spinal alignment and gait parameters differs depending on the presence or absence of PI–LL mismatch. The degree of pelvic compensation and trunk anterior tilt during static standing were associated with unstable gait balance.

A Relaxed Inertial Method for Solving Monotone Inclusion Problems with Applications

We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of a continuous-time dynamical system is established under suitable conditions. Given the challenges associated with computing the resolvent of the composite operator, the proposed method is employed to tackle the composite monotone inclusion problem. Additionally, a convergence analysis is conducted under certain conditions. To demonstrate the effectiveness of the algorithm, numerical experiments are performed on the image deblurring problem.

Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations

The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high-dimensional cases, has stagnated. The development of deep learning provides ideas for its high-dimensional solution. In this paper, our focus lies on the fully coupled forward–backward stochastic differential equation. We design a neural network structure tailored to the characteristics of the equation and develop a hybrid BiGRU model for solving it. We introduce the time dimension based on the sequence nature after discretizing the FBSDE. By considering the interactions between preceding and succeeding time steps, we construct the BiGRU hybrid model. This enables us to effectively capture both long- and short-term dependencies, thus mitigating issues such as gradient vanishing and explosion. Residual learning is introduced within the neural network at each time step; the structure of the loss function is adjusted according to the properties of the equation. The model established above can effectively solve fully coupled forward–backward stochastic differential equations, effectively avoiding the effects of dimensional catastrophe, gradient vanishing, and gradient explosion problems, with higher accuracy, stronger stability, and stronger model interpretability.

STEM: Unleashing the Power of Embeddings for Multi-Task Recommendation

Multi-task learning (MTL) has gained significant popularity in recommender systems as it enables simultaneous optimization of multiple objectives. A key challenge in MTL is negative transfer, but existing studies explored negative transfer on all samples, overlooking the inherent complexities within them. We split the samples according to the relative amount of positive feedback among tasks. Surprisingly, negative transfer still occurs in existing MTL methods on samples that receive comparable feedback across tasks. Existing work commonly employs a shared-embedding paradigm, limiting the ability of modeling diverse user preferences on different tasks. In this paper, we introduce a novel Shared and Task-specific EMbeddings (STEM) paradigm that aims to incorporate both shared and task-specific embeddings to effectively capture task-specific user preferences. Under this paradigm, we propose a simple model STEM-Net, which is equipped with an All Forward Task-specific Backward gating network to facilitate the learning of task-specific embeddings and direct knowledge transfer across tasks. Remarkably, STEM-Net demonstrates exceptional performance on comparable samples, achieving positive transfer. Comprehensive evaluation on three public MTL recommendation datasets demonstrates that STEM-Net outperforms state-of-the-art models by a substantial margin. Our code is released at https://github.com/LiangcaiSu/STEM.