Proximal Operator Research Articles

Scalable precision wide-field imaging in radio interferometry – II. AIRI validated on ASKAP data

ABSTRACT Accompanying Part I, this sequel delineates a validation of the recently proposed AI for Regularization in radio-interferometric Imaging (AIRI) algorithm on observations from the Australian Square Kilometre Array Pathfinder (ASKAP). The monochromatic AIRI-ASKAP images showcased in this work are formed using the same parallelized and automated imaging framework described in Part I: ‘uSARA validated on ASKAP data’. Using a Plug-and-Play approach, AIRI differs from uSARA by substituting a trained denoising deep neural network (DNN) for the proximal operator in the regularization step of the forward–backward algorithm during deconvolution. We build a trained shelf of DNN denoisers that target the estimated image dynamic ranges of our selected data. Furthermore, we quantify variations of AIRI reconstructions when selecting the nearest DNN on the shelf versus using a universal DNN with the highest dynamic range, opening the door to a more complete framework that not only delivers image estimation but also quantifies epistemic model uncertainty. We continue our comparative analysis of source structure, diffuse flux measurements, and spectral index maps of selected target sources as imaged by AIRI and the algorithms in Part I – uSARA and WSClean. Overall, we see an improvement over uSARA and WSClean in the reconstruction of diffuse components in AIRI images. The scientific potential delivered by AIRI is evident in further imaging precision, more accurate spectral index maps, and a significant acceleration in deconvolution time, whereby AIRI is four times faster than its subiterative sparsity-based counterpart uSARA.

PO-01-104 3D MODELING OF PRE-PROCEDURE CT SCAN TO PREDICT SEVERE ESOPHAGEAL HEATING DURING HIGH POWER SHORT DURATION ATRIAL FIBRILLATION ABLATION

The degree of esophageal heating during left atrial posterior wall (LAPW) ablation is a powerful predictor of esophageal injury. Esophageal temperature monitoring has not been shown, however, to reduce esophageal injury risk related to atrial fibrillation (AF) ablation. Esophageal proximity modeling based on pre-procedure CT scan using ADAS 3D software (ADAS3D Medical, Barcelona, Spain) is a novel method of identifying left atrial locations at high risk for severe esophageal heating. Given the mobile nature of the esophagus relative to the LAPW, the predictive value of esophageal proximity mapping is unclear. To determine the predictive value of esophageal proximity mapping to identify LAPW ablation sites at risk for severe esophageal heating. Pre-procedure CT scans were analyzed using ADAS 3D software in 10 patients undergoing AF ablation to create a 3D esophageal proximity model and left atrial tissue thickness map that were merged with a catheter based left atrial electroanatomic map (Ensite X, Abbott, Inc.). Esophageal proximity was defined as: Zone 1 – overlying esophagus, Zone 2 – within 5 mm of esophagus, or Zone 3 – > 5 mm from esophagus. LAPW ablation lesions were created with a contact-force sensing radiofrequency ablation catheter (Tacticath, Abbott, Inc.) at 45W, 10-20g of force, and 6 seconds duration. A 12 sensor esophageal temperature probe (Circa, Circa Scientific, Inc.) recorded the temperature increase related to each LAPW lesion. Ablation lesions in Zone 3 resulted in significantly lower esophageal temperature rise (degrees Celsius) as compared to either Zone 1 (mean 0.11 ± 0.27 vs 1.61 ± 1.39, p value <0.0001) or Zone 2 (mean 0.11 ± 0.27 vs 0.84 ± 1.1, p value <0.0001) (Fig A). Lesions in Zone 2 resulted in lower temperature rise as compared to Zone 1 (mean 0.84 ±1.1 vs. 1.61 ± 1.39, p value <0.0001) (Fig A). Within Zones 1 and 2, lesions with LAPW thickness > 2 mm resulted in significantly less esophageal temperature rise as compared to those on tissue with thickness of ≤ 2 mm (Fig B). Ablation lesions delivered >5mm from esophageal location at time of pre-procedure CT scan are very unlikely to result in significant esophageal heating. Ablation sites overlying esophagus with LAPW thickness ≤ 2mm were at greatest risk of significant esophageal heating. Analysis of pre-procedure CT scans to determine esophageal proximity and LAPW thickness may be useful in developing strategies to avoid esophageal injury during LAPW RF ablation.

A fixed step distributed proximal gradient push‐pull algorithm based on integral quadratic constraint

AbstractIn order to solve the distributed optimization problem with smooth + nonsmooth structure of the objective function on unbalanced directed networks, this article uses the proximal operator to deal with the nonsmooth part of the objective function, and designs and analyzes the fixed step proximal gradient Push‐Pull (PG‐Push‐Pull) algorithm. Firstly, the Integral Quadratic Constraint (IQC) suitable for proximal gradient Push‐Pull algorithm is given. When the smooth part of the objective function is strongly convex and the gradient satisfies the Lipchitz condition, the convergence of the algorithm is proved, and the convergence analysis is transformed into solving a linear matrix inequality by using this IQC framework. Its feasibility can ensure that the proposed algorithm has linear convergence rate, which is the same as that of Push‐Pull gradient algorithm. Then, the upper bound of convergence rate can be found by solving a Non‐Linear Programming problem. Finally, an example is given to analyze the upper bound of the convergence rate and verify the effectiveness of the proposed algorithm.

Best Proximity Point Results in Fuzzy Normed Spaces

Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been developed in numerous ways. Nevertheless, all of these results are reliant on the existence and uniqueness of a FP on some suitable space. Because the FP problem could not have a solution in the case of nonself-mappings, the idea of the best proximity point (briefly Bpp) is offered to approach the best solution. This paper investigates the existence and uniqueness of the Bpp of nonself-mappings in fuzzy normed space(briefly FN space) to arrive at the best solution. Following the introduction of the definition of the Bpp, the existence, and uniqueness of the Bpp are shown in a FN space for diverse fuzzy proximal contractions such as ?????? fuzzy proximal contractive mapping and ????h ????h - fuzzy proximal contractive mapping.

Best Proximity Points for Generalized Geraghty Quasi-Contraction Type Mappings in Metric Spaces

In this paper, we introduce a new concept of α-φ-Geraghty proximal quasi-contraction type mappings and establish best proximity point theorems for those mappings in proximal T-orbitally complete metric spaces. This generalizes and complements the proofs of some known fixed and best proximity point results.

Stochastic variable metric proximal gradient with variance reduction for non-convex composite optimization

This paper introduces a novel algorithm, the Perturbed Proximal Preconditioned SPIDER algorithm (3P-SPIDER), designed to solve finite sum non-convex composite optimization. It is a stochastic Variable Metric Forward–Backward algorithm, which allows approximate preconditioned forward operator and uses a variable metric proximity operator as the backward operator; it also proposes a mini-batch strategy with variance reduction to address the finite sum setting. We show that 3P-SPIDER extends some Stochastic preconditioned Gradient Descent-based algorithms and some Incremental Expectation Maximization algorithms to composite optimization and to the case the forward operator can not be computed in closed form. We also provide an explicit control of convergence in expectation of 3P-SPIDER, and study its complexity in order to satisfy the approximate epsilon-stationary condition. Our results are the first to combine the non-convex composite optimization setting, a variance reduction technique to tackle the finite sum setting by using a minibatch strategy and, to allow deterministic or random approximations of the preconditioned forward operator. Finally, through an application to inference in a logistic regression model with random effects, we numerically compare 3P-SPIDER to other stochastic forward–backward algorithms and discuss the role of some design parameters of 3P-SPIDER.

A Hamilton–Jacobi-based proximal operator

First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit proximal formulas are known for only limited classes of functions. We provide an algorithm, HJ-Prox, for accurately approximating such proximals. This is derived from a collection of relations between proximals, Moreau envelopes, Hamilton-Jacobi (HJ) equations, heat equations, and Monte Carlo sampling. In particular, HJ-Prox smoothly approximates the Moreau envelope and its gradient. The smoothness can be adjusted to act as a denoiser. Our approach applies even when functions are accessible only by (possibly noisy) black box samples. We show that HJ-Prox is effective numerically via several examples.

Discrete potential mean field games: duality and numerical resolution

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows hard constraints on the distribution of the agents. We analyze the connection between the MFG problem and two optimal control problems in duality. We present two families of numerical methods and detail their implementation: (i) primal-dual proximal methods (and their extension with nonlinear proximity operators), (ii) the alternating direction method of multipliers (ADMM) and a variant called ADM-G. We give some convergence results. Numerical results are provided for two examples with hard constraints.

Proximity proteome mapping reveals PD-L1-dependent pathways disrupted by anti-PD-L1 antibody specifically in EGFR-mutant lung cancer cells

BackgroundPD-L1, a transmembrane ligand for immune checkpoint receptor PD1, has been successfully targeted to activate an anti-tumor immune response in a variety of solid tumors, including non-small cell lung cancer (NSCLC). Despite the success of targeting PD-L1, only about 20% of patients achieve a durable response. The reasons for the heterogeneity in response are not understood, although some molecular subtypes (e.g., mutant EGF receptor tumors) are generally poor responders. Although PD-L1 is best characterized as a transmembrane PD1 ligand, the emerging view is that PD-L1 has functions independent of activating PD1 signaling. It is not known whether these cell-intrinsic functions of PD-L1 are shared among non-transformed and transformed cells, if they vary among cancer molecular subtypes, or if they are impacted by anti-PD-L1 therapy.MethodsHere we use quantitative microscopy techniques and APEX2 proximity mapping to describe the behavior of PD-L1 and to identify PD-L1's proximal proteome in human lung epithelial cells.ResultsOur data reveal growth factor control of PD-L1 recycling as a mechanism for acute and reversible regulation of PD-L1 density on the plasma membrane. In addition, we describe novel PD-L1 biology restricted to mutant EGFR cells. Anti-PD-L1 antibody treatment of mutant EGFR cells perturbs cell intrinsic PD-L1 functions, leading to reduced cell migration, increased half-life of EGFR and increased extracellular vesicle biogenesis, whereas anti-PD-L1 antibody does not induce these changes in wild type EGFR cells.ConclusionsGrowth factor acute regulation of PD-L1 trafficking, by contributing to the control of plasma membrane density, might contribute to the regulation of PD-L1's immune checkpoint activity, whereas the specific effects of anti-PD-L1 on mutant EGFR cells might contribute to the poor anti-PD-L1 response of mutant EGFR tumors.5zzQ_mo5e1oawe5DznU6q-Video

On Douglas-Rachford splitting that generally fails to be a proximal mapping: a degenerate proximal point analysis

Based on a degenerate proximal point analysis, we show that the Douglas-Rachford splitting can be reduced to a well-defined resolvent, but generally fails to be a proximal mapping. This extends the recent result of [Bauschke, Schaad and Wang. Math. Program. 2018;168:55–61] to more general setting. The related concepts and consequences are also discussed. In particular, the results regarding the maximal and cyclic monotonicity are instrumental for analysing many operator splitting algorithms.

Proximal Decoding for LDPC Codes

This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced. After that, the best proximity point theorem for such type of mapping in a fuzzy normed space is state and prove. In addition, the idea of α ̃–ϕ ̃-proximal contractive mapping is presented in a fuzzy normed space and under specific conditions, the best proximity point theorem for such type of mappings is proved. Furthermore, some examples are offered to show the results' usefulness.

High-Dimensional Covariance Estimation via Constrained Lq-Type Regularization

High-dimensional covariance matrix estimation is one of the fundamental and important problems in multivariate analysis and has a wide range of applications in many fields. In practice, it is common that a covariance matrix is composed of a low-rank matrix and a sparse matrix. In this paper we estimate the covariance matrix by solving a constrained Lq-type regularized optimization problem. We establish the first-order optimality conditions for this problem by using proximal mapping and the subspace method. The proposed stationary point degenerates to the first-order stationary points of the unconstrained Lq regularized sparse or low-rank optimization problems. A smoothing alternating updating method is proposed to find an estimator for the covariance matrix. We establish the convergence of the proposed calculation method. The numerical simulation results show the effectiveness of the proposed approach for high-dimensional covariance estimation.

Construction and applications of proximal maps for typical cocycles

AbstractFor typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal linear map. Using this result, we show that suitable assumptions on the periodic orbits have consequences over the entire subshift.

Evaluation of Scapholunate Injury and Repair with Dynamic (4D) CT: A Preliminary Report of Two Cases.

Background In predynamic or dynamic scapholunate (SL) instability, standard diagnostic imaging may not identify SL interosseous ligament (SLIL) injury, leading to delayed detection and intervention. This study describes the use of four-dimensional computed tomography (4DCT) in identifying early SLIL injury and following injured wrists to 1-year postoperatively. Description of Technique 4DCT acquires a series of three-dimensional volume data with high temporal resolution (66 ms). 4DCT-derived arthrokinematic data can be used as biomarkers of ligament integrity. Patients and Methods This study presents the use of 4DCT in a two-participant case series to assess changes in arthrokinematics following unilateral SLIL injury preoperatively and 1-year postoperatively. Patients were treated with volar ligament repair with volar capsulodesis and arthroscopic dorsal capsulodesis. Arthrokinematics were compared between uninjured, preoperative injured, and postoperative injured (repaired) wrists. Results 4DCT detected changes in interosseous distances during flexion-extension and radioulnar deviation. Generally, radioscaphoid joint distances were greatest in the uninjured wrist during flexion-extension and radioulnar deviation, and SL interval distances were smallest in the uninjured wrist during flexion-extension and radioulnar deviation. Conclusion 4DCT provides insight into carpal arthrokinematics during motion. Distances between the radioscaphoid joint and SL interval can be displayed as proximity maps or as simplified descriptive statistics to facilitate comparisons between wrists and time points. These data offer insight into areas of concern for decreased interosseous distance and increased intercarpal diastasis. This method may allow surgeons to assess whether (1) injury can be visualized during motion, (2) surgery repaired the injury, and (3) surgery restored normal carpal motion. Level of Evidence Level IV, Case series.

Graph Convergence, Algorithms, and Approximation of Common Solutions of a System of Generalized Variational Inclusions and Fixed-Point Problems

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in the proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The main contribution of this work is the establishment of a new equivalence relationship between the graph convergence of a sequence of general strongly H-monotone mappings and their associated proximal mappings, respectively, to a given general strongly H-monotone mapping and its associated proximal mapping by using the notions of graph convergence and proximal mapping concerning a general strongly H-monotone mapping. By employing the concept of proximal mapping relating to general strongly H-monotone mapping, some iterative algorithms are proposed, and as an application of the obtained equivalence relationship mentioned above, a convergence theorem for approximating a common element of the set of solutions of a system of generalized variational inclusions involving general strongly H-monotone mappings and the set of fixed points of an ({an},{bn},ϕ)-total uniformly L-Lipschitzian mapping is proved. It is significant to emphasize that our results are new and improve and generalize many known corresponding results.

A Primal-Dual Forward-Backward Splitting Algorithm for Distributed Convex Optimization

Motivated by modern large-scale information processing problems in engineering, this paper concentrates on studying distributed constrained convex optimization problems over a connected undirected network. The problem involves a sum of a differentiable convex function with Lipschitz continuous gradient and two non-smooth convex functions with a linear operator. To solve such a problem, we propose a novel distributed primal-dual forward-backward splitting algorithm, called D-PDFBS. Each agent locally computes the Lipschitz continuous gradient and two proximal operators, and exchanges information with its neighbors. D-PDFBS adopts non-identical stepsizes, and we reveal the relationship between selection of stepsizes and parameters of objective functions. The simulation results verify the feasibility of D-PDFBS and the correctness of theoretical findings.

Suitability mapping of solid waste disposal sites in Obio/Akpor local government area: rivers state of Nigeria

Obio/Akpor Local Government Area of Rivers State have constantly witnessed Rapid City growth and increased urbanization due to persistence rural-urban migration and the quest for human to meet their needs and wants. This has increased solid waste generation and unregulated dumping of solid wastes in unapproved sites. This prompted the need for this study which is aimed at mapping the suitability of solid waste sites in the study area with the objective of identifying the spatial locations and development of a database of suitability or otherwise of solid waste disposal sites. Ground survey and Geospatial techniques were utilized for data acquisition, manipulation and processing. Garmin 78csx GNSS receiver was used in observing the coordinates of ground positions of all solid waste disposal sites in the study area, the obtain coordinates were charted on the Google earth imagery (2022) and Open Street Map (OSM) (2022) to ensure the positions falls within the shape-file of the study area, On-Screen vectorization was perform using the point, line and polygon spatial tools in the QGIS 3.22 bialowieza software environment to determine the position and extent of solid waste sites under study. Proximity analysis was performed in QGIS environment for buffer of 200m, 500m and 1km to ascertain the suitability of solid waste collection centers and dumpsites base on global standard and proximity maps were produced. A total of (114) solid waste disposal sites were mapped, with (27) legal and (73) illegal collection points and (2) suitable and (12) unsuitable dumpsites respectively. The study also revealed that Elelenwo community in ward 6 has the highest (12) whereas Egbelu Ozodo community in ward 16 has the lowest (1) number of collection sites in the study area. Immediate review and enforcement of solid waste disposal and management laws is needed to forestall likely environmental hazards resulting from indiscriminate dumping of refuse in the study area.

Evaluating the accuracy and usefulness of commercially-available proximal soil mapping services for grassland nutrient management planning and soil health monitoring

Grasslands play an important role in global food security. However, there are increasing pressures to improve the sustainability of ruminant farming. Precision nutrient management tools (e.g., proximal soil sensors for soil mapping) offer opportunities to improve nutrient use efficiency through spatially-variable nutrient application rate maps. Despite little research validating these technologies on grasslands, commercial companies promote these technologies to grassland farmers. In this study, the accuracy of commercial companies offering these services was evaluated by comparing soil pH, P, K, Mg and SOM measurements derived from conventional soil sampling and laboratory analyses to measurements derived from the commercial operators, across a range of soils that are typical found in UK grasslands. Results showed that soil mapping services utilising gamma-ray spectroscopy (GRS) were not sufficiently accurate to predict soil pH, P, K and Mg on grasslands, and subsequently inappropriate for nutrient management planning for variable rate lime and nutrient application. Conversely, both GRS and visible-near infrared spectroscopy (Vis–NIR) accurately predicted between-field SOM variations in grassland soils but not within-field variation. This study emphasises the need for further research to explore the limitations of, and opportunities for, the universal application of these technologies across different soil types and/or land uses before their commercial application. It is therefore highly recommended that commercially-available soil mapping services are subject to certification, similar to centralised soil testing laboratories, to ensure data are accurate for soil management interpretation. The lack of reliability of such systems risks farmers’ confidence in the value of soil mapping, which could severely hinder future adoption of potentially valuable technologies.

Proximity Mapping of CCP6 Reveals Its Association with Centrosome Organization and Cilium Assembly.

The cytosolic carboxypeptidase 6 (CCP6) catalyzes the deglutamylation of polyglutamate side chains, a post-translational modification that affects proteins such as tubulins or nucleosome assembly proteins. CCP6 is involved in several cell processes, such as spermatogenesis, antiviral activity, embryonic development, and pathologies like renal adenocarcinoma. In the present work, the cellular role of CCP6 has been assessed by BioID, a proximity labeling approach for mapping physiologically relevant protein-protein interactions (PPIs) and bait proximal proteins by mass spectrometry. We used HEK 293 cells stably expressing CCP6-BirA* to identify 37 putative interactors of this enzyme. This list of CCP6 proximal proteins displayed enrichment of proteins associated with the centrosome and centriolar satellites, indicating that CCP6 could be present in the pericentriolar material. In addition, we identified cilium assembly-related proteins as putative interactors of CCP6. In addition, the CCP6 proximal partner list included five proteins associated with the Joubert syndrome, a ciliopathy linked to defects in polyglutamylation. Using the proximity ligation assay (PLA), we show that PCM1, PIBF1, and NudC are true CCP6 physical interactors. Therefore, the BioID methodology confirms the location and possible functional role of CCP6 in centrosomes and centrioles, as well as in the formation and maintenance of primary cilia.