Proximal Operator Research Articles

Regulated dynamic subcellular GLUT4 localization revealed by proximal proteome mapping in human muscle cells.

Regulation of glucose transport, which is central for control of whole-body metabolism, is determined by the amount of GLUT4 glucose transporter (also known as SLC2A4) in the plasma membrane (PM) of fat and muscle cells. Physiologic signals [such as activated insulin receptor or AMP-activated protein kinase (AMPK)] increase PM GLUT4. Here, we show that the distribution of GLUT4 between the PM and interior of human muscle cells is dynamically maintained, and that AMPK promotes PM redistribution of GLUT4 by regulating exocytosis and endocytosis. Stimulation of exocytosis by AMPK is mediated by Rab10 and the Rab GTPase-activating protein TBC1D4. APEX2 proximity mapping reveals that GLUT4 traverses both PM-proximal and PM-distal compartments in unstimulated muscle cells, further supporting retention of GLUT4 by a constitutive retrieval mechanism. AMPK-stimulated translocation involves GLUT4 redistribution among the same compartments traversed in unstimulated cells, with a significant recruitment of GLUT4 from the Golgi and trans-Golgi network compartments. Our comprehensive proximal protein mapping provides an integrated, high-density, whole-cell accounting of the localization of GLUT4 at a resolution of ∼20 nm that serves as a structural framework for understanding the molecular mechanisms regulating GLUT4 trafficking downstream of different signaling inputs in a physiologically relevant cell type.

Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging.

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

First person – Anuttoma Ray

ABSTRACT First Person is a series of interviews with the first authors of a selection of papers published in Journal of Cell Science, helping researchers promote themselves alongside their papers. Anuttoma Ray is first author on ‘ Regulated dynamic subcellular GLUT4 localization revealed by proximal proteome mapping in human muscle cells’, published in JCS. Anuttoma conducted the research described in this article while a Postdoctoral researcher in Dr Timothy McGraw's lab at Department of Biochemistry, Weill Cornell Medicine, Cornell University, New York, USA. She is now an Editor at Cactus Communications, Princeton, NJ, USA, where she leverages her skills and expertise for the scientific community to drive the creation of high-quality, research-based manuscripts for academic publishing.

Iteratively reweighted accurate sparse low-rank matrix estimation algorithm for bearing fault diagnosis

Bearing fault diagnosis is significant to ensure the safe functioning of mechanical systems. One of the key issues in bearing fault diagnosis is the accurate and effective extraction of fault characteristic features. In order to further explore the construction of penalty function, further alleviate the problem of bias estimation and enhance the capabilities of the sparse low-rank (SLR) method in effectively diagnosing bearing faults, in this paper, an iteratively reweighted accurate sparse low-rank (IRASLR) matrix estimation algorithm is proposed. Taking the sparse and low-rank properties of fault transient signals in time–frequency domain into account, an optimization problem is formulated. Two penalty functions, derived from a core minimax-concave penalty (MCP), induce sparse and low-rank properties, respectively. Specifically, to facilitate the design of weighting schemes, we construct an equivalent variant of MCP (EVMCP). By separately extending EVMCP to matrix elements and singular values, we obtain equivalent weighted MCP and equivalent weighted matrix γ-norm. Finally, based on the proximal operators of the two penalty functions, we deduce an IRASLR algorithm under the alternating direction method of the multipliers (ADMM) framework. The performance of IRASLR is verified by processing simulated and experimental signals, while the superiority of the algorithm is confirmed through comparative experiments.

Multi-Channel Representation Learning Enhanced Unfolding Multi-Scale Compressed Sensing Network for High Quality Image Reconstruction.

Deep Unfolding Networks (DUNs) serve as a predominant approach for Compressed Sensing (CS) reconstruction algorithms by harnessing optimization. However, a notable constraint within the DUN framework is the restriction to single-channel inputs and outputs at each stage during gradient descent computations. This constraint compels the feature maps of the proximal mapping module to undergo multi-channel to single-channel dimensionality reduction, resulting in limited feature characterization capabilities. Furthermore, most prevalent reconstruction networks rely on single-scale structures, neglecting the extraction of features from different scales, thereby impeding the overall reconstruction network's performance. To address these limitations, this paper introduces a novel CS reconstruction network termed the Multi-channel and Multi-scale Unfolding Network (MMU-Net). MMU-Net embraces a multi-channel approach, featuring the incorporation of Adap-SKConv with an attention mechanism to facilitate the exchange of information between gradient terms and enhance the feature map's characterization capacity. Moreover, a Multi-scale Block is introduced to extract multi-scale features, bolstering the network's ability to characterize and reconstruct the images. Our study extensively evaluates MMU-Net's performance across multiple benchmark datasets, including Urban100, Set11, BSD68, and the UC Merced Land Use Dataset, encompassing both natural and remote sensing images. The results of our study underscore the superior performance of MMU-Net in comparison to existing state-of-the-art CS methods.

Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost

In this paper, we propose a sparse equity portfolio optimization model that aims at minimizing transaction cost by avoiding small investments while promoting diversification to help mitigate the volatility in the portfolio. The former is achieved by including the ell _{0}-norm regularization of the asset weights to promote sparsity. Subjected to a minimum expected return, the proposed model turns out to be an objective function consisting of discontinuous and nonconvex terms. The complexity of the model calls for proximal method, which allows us to handle the objective terms separately via the corresponding proximal operators. We develop an efficient algorithm to find the optimal portfolio and prove its global convergence. The efficiency of the algorithm is demonstrated using real stock data and the model is promising in portfolio selection in terms of generating higher expected return while maintaining good level of sparsity, and thus minimizing transaction cost.

A new fast ADMM for kernelless SVM classifier with truncated fraction loss

Support vector machine (SVM) is one of well-known supervised machine learning classifier and is used widely in image classification, pattern recognition, disease diagnosis, etc. However, the high computational complexity is a major issue for large-scale classification problems. To address this issue, we propose a new truncated fraction loss function to construct a new sparse and robust SVM model (Ltf-SVM). By newly developed support vectors and a working set based on the proximal operator of truncated fraction loss, we prove the sparsity and robustness to outliers of Ltf-SVM from a theoretical perspective. When it comes to solve Ltf-SVM problems, we develop an alternating direction method of multipliers with a working set for addressing Ltf-SVM. The proposed algorithm is proven to converge globally and enjoys very low computational complexity. Moreover, numerical experiments verify its superior performance with respect to its high accuracy and high computational speed in comparison with other leading solvers.

Best proximity for proximal operators on $b$-metric spaces

Best proximity for proximal operators on $b$-metric spaces

Accelerated Partially Shared Dictionary Learning With Differentiable Scale-Invariant Sparsity for Multi-View Clustering.

Multiview dictionary learning (DL) is attracting attention in multiview clustering due to the efficient feature learning ability. However, most existing multiview DL algorithms are facing problems in fully utilizing consistent and complementary information simultaneously in the multiview data and learning the most precise representation for multiview clustering because of gaps between views. This article proposes an efficient multiview DL algorithm for multiview clustering, which uses the partially shared DL model with a flexible ratio of shared sparse coefficients to excavate both consistency and complementarity in the multiview data. In particular, a differentiable scale-invariant function is used as the sparsity regularizer, which considers the absolute sparsity of coefficients as the l0 norm regularizer but is continuous and differentiable almost everywhere. The corresponding optimization problem is solved by the proximal splitting method with extrapolation technology; moreover, the proximal operator of the differentiable scale-invariant regularizer can be derived. The synthetic experiment results demonstrate that the proposed algorithm can recover the synthetic dictionary well with reasonable convergence time costs. Multiview clustering experiments include six real-world multiview datasets, and the performances show that the proposed algorithm is not sensitive to the regularizer parameter as the other algorithms. Furthermore, an appropriate coefficient sharing ratio can help to exploit consistent information while keeping complementary information from multiview data and thus enhance performances in multiview clustering. In addition, the convergence performances show that the proposed algorithm can obtain the best performances in multiview clustering among compared algorithms and can converge faster than compared multiview algorithms mostly.

A constructive approach for computing the proximity operator of the p-th power of the ℓ1 norm

A constructive approach for computing the proximity operator of the p-th power of the ℓ1 norm

Proximity Mapping of Ciliary Proteins by BioID.

The primary cilium is a highly conserved microtubule-based organelle present in most vertebrate cell types. Mutations in ciliary protein genes can lead to dysfunctional or absent cilia and are the cause of a large group of heterogeneous diseases known as ciliopathies. ARL13Bis a member of the ARF family of regulatory GTPases and is highly enriched on the ciliary membrane. The absence ofARL13B disrupts cilia architecture and mutations have been linked to several diseases; yet there remain major gaps in our understanding of the role thatARL13B plays in primary cilia function. Here, we demonstrate how in cellulo proximity-dependent biotinylation (BioID) can be used to generate a comprehensive protein proximity map of ciliary proteins by performing BioID on N- and C-terminally BirA*-taggedARL13B. This method can theoretically provide insight into any cilia protein, identifying key interactors that play a critical role in ciliary biology.

Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.

Field experience from designing and implementing a cold-chain system for the 2021 Nigeria national food consumption and micronutrient survey

Improving nutrition is a key component of efforts to promote sustainable development and improve health and well-being. However, it is impossible to effectively improve nutrition in a population without monitoring the nutrition status of vulnerable groups. Monitoring approaches such as micronutrient surveys are critical to allow stakeholders determine the prevalence of malnutrition and identify micronutrient deficiencies of public health importance and at-risk groups. In this regard, the 2021 Nigeria National Food Consumption and Micronutrient Survey (NFCMS 2021) collected biological samples from children aged 6-59 months, adolescent girls, as well as pregnant and non-pregnant women of reproductive age. The micronutrients of interest were retinol, thiamine, riboflavin, cobalamin, folate, iodine, iron, and zinc. Quantitative 24-hour dietary recall data were also collected from children aged 6-59 months, pregnant and non-pregnant women of reproductive age. To achieve its goal, the NFCMS 2021 had to overcome some hurdles. Therefore, the current study details the challenges of developing a cold-chain system for the survey and novel strategies employed to address them. The main challenges encountered included collecting, transporting, processing, storing, and analyzing over 51,143 samples from enumeration areas with unreliable electricity, difficult terrain, and far from functional health facilities. The survey successfully designed and implemented a cold-chain system across 364 enumeration areas in all 36 states and the Federal Capital Territory. This can be attributed to several factors. First, the team reviewed and documented the survey's cold-chain requirements. Second, stakeholder engagement with the federal and state governments allowed the use of Ministry of Health cold stores. This was followed by proximity mapping of survey enumeration areas to all existing cold stores, a visit to verify their suitability, and the selection of the best cold stores for the survey. The survey also procured the right equipments, and trained teams on cold-chain logistics, best practices, troubleshooting, and communication. An innovation of the survey was the use of checklists for decision-making and real-time temperature data loggers and dashboards for monitoring the cold-chain. Using detailed contingency plans for cold-chain logistics and leveraging cost-effective technologies can improve cold-chain transparency, efficiency, and integrity in resource-constrained settings, as was the case of the NFCMS 2021. The survey identified an unmet demand for a detailed manual with updated guidance on designing a cold-chain system for a nutrition survey. Key words: Cold-chain system, micronutrient survey, resource-constrained settings, Nigeria, Africa, NFCMS 2021

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

When the sparse regularizer is convex and its proximal operator has a closed‐form, first‐order iterative algorithms based on proximal operators can effectively solve the sparse optimization problems. Recently, plug‐and‐play (PnP) algorithms have achieved significant success by incorporating advanced denoisers to replace the proximal operators in iterative algorithms. However, convex sparse regularizers such as the ‐norm tend to underestimate the large values within the sparse solutions. In contrast, the convex non‐convex (CNC) sparse regularization enables the non‐convex regularizer while preserving the convexity of the objective function. In this paper, we propose several PnP algorithms for solving the CNC sparse regularization model and discuss their convergence properties. Specifically, we first derive the proximal operator for CNC sparse regularization in iterative form and subsequently integrate it with several first‐order algorithms to yield different PnP algorithms. Then, based on the monotone operator theory, we prove that the proposed PnP algorithms are convergent under the condition that the data‐fidelity term is strongly convex and the residuals of the denoisers are contractive. We also emphasized the significance of strong convexity in the data‐fidelity term for the CNC sparse regularization model. Additionally, we demonstrate the superiority of the proposed PnP algorithms through extensive image restoration tasks.

A kernel formula for regularized Wasserstein proximal operators

A kernel formula for regularized Wasserstein proximal operators

A Proximal Neurodynamic Network With Fixed-Time Convergence for Equilibrium Problems and Its Applications.

This article proposes a novel fixed-time converging proximal neurodynamic network (FXPNN) via a proximal operator to deal with equilibrium problems (EPs). A distinctive feature of the proposed FXPNN is its better transient performance in comparison to most existing proximal neurodynamic networks. It is shown that the FXPNN converges to the solution of the corresponding EP in fixed-time under some mild conditions. It is also shown that the settling time of the FXPNN is independent of initial conditions and the fixed-time interval can be prescribed, unlike existing results with asymptotical or exponential convergence. Moreover, the proposed FXPNN is applied to solve composition optimization problems (COPs), l₁-regularized least-squares problems, mixed variational inequalities (MVIs), and variational inequalities (VIs). It is further shown, in the case of solving COPs, that the fixed-time convergence can be established via the Polyak-Lojasiewicz condition, which is a relaxation of the more demanding convexity condition. Finally, numerical examples are presented to validate the effectiveness and advantages of the proposed neurodynamic network.

A Weibull gradient prior for image restoration

In image restoration, image priors with a heavy-tailed gradient distribution found in natural images have been successfully applied to address ill-posed problems such as denoising, deblurring, and super-resolution. However, existing literature has limitations in fitting well with image gradient magnitudes using widely used distributions. This paper introduces the Weibull distribution as a potential model that can better describe image gradient magnitudes compared to existing methods. Specifically, the Weibull distribution provides the best fit for describing small gradient magnitudes. Within the framework of maximum a posteriori estimation, a recovery model based on the Weibull gradient prior is introduced. The shape parameter of the Weibull prior is automatically estimated during the iterative process using the method of moments, allowing the model to better conform to the real images’ gradient distribution. The proposed model is computed using the alternating direction method of multipliers. Moreover, the properties of the solution to the sub-problem related to the Weibull prior are analyzed, and an efficient numerical algorithm for solving the multivariate proximal operator is proposed. Experimental results validate that the proposed model exhibits superior performance and is particularly well-suited for piecewise constant images compared to competing methods.

Diagnostic criteria for proximal left bundle branch block and their significance in predicting the success of cardiac resynchronization therapy

Aim. To develop diagnostic criteria for proximal left bundle branch block (LBBB) based on non-invasive methods and to determine the significance of these criteria in predicting the effect of cardiac resynchronization therapy (CRT).Material and methods. To develop criteria, 58 patients (21 men, mean age, 76,1±7,1 years) with LBBB occurred immediately after transcatheter aortic valve implantation (TAVI) were included. To assess the significance of the developed criteria, the second group included 22 patients (11 men, mean age, 57,9±9,3 years) with dilated cardiomyopathy (DCM), who had indications for CRT. The effectiveness of CRT was assessed by echocardiography 6 months after implantation. All patients in the DCM group and 15 patients in the TAVI group underwent superficial epiand endocardial non-invasive mapping using Amycard 01C EP Lab (EP Solutions SA, Switzerland). Patients in the DCM group underwent contrast-enhanced cardiac magnetic resonance imaging (MRI) before device implantation.Results. The criteria for proximal LBBB included 3 electrocardiographic features: QRS complex >130 ms in women and 140 ms in men, QSor rS-configuration in V1 lead, notch in two or more lateral leads (I, avL, V5, V6), and 2 mapping criteria: characteristic location of block line and delayed activation point. In the DCM group, the criteria were positive in 13 of 22 patients (59%). The developed criteria for proximal LBBB showed a relatively strong, significant relationship with the positive effect of CRT (сhi-square test =5,46, p=0,02, Cramer test =0,5, odds ratio (OR)=15,0, 95% confidence interval (CI), 1,32-169,9, p=0,002). An additional analysis showed that both the criteria for proximal block and CRT effect are associated with myocardial fibrosis according to MRI. In particular, intramural stria-shaped contrast accumulation in the interventricular septum leads to a change in characteristic of proximal block mapping phenomena — displacement of delayed activation point (chi-square test =13,9, p<0,001, Cramer test =0,79) and displacement or absence of conduction block lines (chi-square test =6,92, p=0,009, Cramer test =0,56) and prevents the CRT effect (OR =8,67, 95% CI, 1,05-71,57 p=0,03).Conclusion. Proximal LBBB is only one of the factors determining the effectiveness of CRT. Proximal LBBB may mask significant myocardial structural changes that prevent the CRT success.

The proximal map of the weighted mean absolute error

AbstractWe investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied to a nonsmooth energy minimization problem.

A highly efficient algorithm for solving exclusive lasso problems

The exclusive lasso (also known as elitist lasso) regularizer has become popular recently due to its superior performance on intra-group feature selection. Its complex nature poses difficulties for the computation of high-dimensional machine learning models involving such a regularizer. In this paper, we propose a highly efficient dual Newton method based proximal point algorithm (PPDNA) for solving large-scale exclusive lasso models. As important ingredients, we systematically study the proximal mapping of the weighted exclusive lasso regularizer and the corresponding generalized Jacobian. These results also make popular first-order algorithms for solving exclusive lasso models more practical. Extensive numerical results are presented to demonstrate the superior performance of the PPDNA against other popular numerical algorithms for solving the exclusive lasso problems.