Proximal Point Research Articles

Automatic Identification and Suppression of Random Noise and Methods for Profile Splicing in the Sub-Bottom Profile of Deep Water

The complex topography of deep sea presents numerous challenges for the accurate exploration of sub-bottom profiles. These include real-time tracking of seafloor reflectors, acquisition and storage of deep-sea long-term reflection data, and splicing of successive profiles. Based on the actual survey data of deep sea, we have developed automatic positioning and noise suppression algorithms, namely the double-difference threshold of proximity points. Furthermore, we have created automatic algorithms, namely content expansion and group data moving, based on extremum in seafloor’s depth. These have been designed to automatically suppress the random noise and effectively splice the sub-bottom profile data in deep water. The aforementioned processing techniques facilitate the enhancement of the quality of deep-water sub-bottom profile data, thereby enabling the provision of a comprehensive and successively long profile for interpretation in the context of deep-water sub-bottom profile data.

Some Results on Multivalued Proximal Contractions with Application to Integral Equation

In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance ϕ, we discuss some multivalued (ϕ−Fτ)CP and (ϕ−Fτ)BP−proximal contractions in the context of rectangular metric spaces. To ascertain the coincidence best proximity point, best proximity point, and the fixed point for single-valued mappings, we reduce these findings using (Fτ)CP and (Fτ)BP−proximal contractions. To make our work more understandable, examples of both single- and multivalued mappings are provided. These examples support our core findings, which rely on coincidence points, as well as the corollaries that address fixed point conclusions. In the final phase of our study, we use the obtained results to verify that a solution to a Fredholm integral equation exists. This application highlights the theoretical framework we built throughout our study.

Proximal-stabilized semidefinite programming

AbstractA regularized version of the primal-dual Interior Point Method (IPM) for the solution of Semidefinite Programming Problems (SDPs) is presented in this paper. Leveraging on the proximal point method, a novel Proximal Stabilized Interior Point Method for SDP (PS-SDP-IPM) is introduced. The method is strongly supported by theoretical results concerning its convergence: the worst-case complexity result is established for the inner regularized infeasible inexact IPM solver. The new method demonstrates an increased robustness when dealing with problems characterized by ill-conditioning or linear dependence of the constraints without requiring any kind of pre-processing. Extensive numerical experience is reported to illustrate advantages of the proposed method when compared to the state-of-the-art solver.

Existence Results of Some Nonlinear Minimization Problems with Application to a System of PDE

A new class of non-self mappings, called proximal condensing operators, is introduced and used to investigate the existence of best proximity points for non-self mappings in reflexive Banach spaces by applying an appropriate measure of noncompactness. In this way, we present generalizations of well-known Schauder and Darbo fixed point problems. We then define the notion of best proximity points for multiplication of two non-self mappings in the setting of Banach algebras and present some sufficient conditions to ensure the existence of such points. Finally, we renorm a Banach space consists of all real valued and continuous functions with two variables to obtain the strict convexity condition and then we survey the existence of an optimal solution for a system of partial differential equations.

Steel Plate Cutting Path Optimisation Problem Based on Euler's Theorem and Greedy Algorithm

Steel plate cutting as one of the key technologies in the field of machining, planning the optimal path and reducing the air distance can improve the cutting efficiency of the steel plate, and improving the cutting efficiency is the most critical step in the machining process. In this paper, we analyze the main reasons for the generation of empty paths and make the assumption of cutting the whole part at once while cutting the part. On this basis, Euler's theorem and greedy algorithm are used to find the proximal point of the cutting path from the outer contour to the inner contour, and to plan the optimal path and the resulting shortest air distance for a given cutting of the outer contour of the serrated steel plate as well as the cutting of different shapes of parts in the inner part of the serrated steel plate. The resulting shortest air travel distance is 31.5536 by matlab.

A novel highly efficient alternating direction method of multipliers for large-scale trimmed concave SVM

Support vector machine (SVM) is widely utilized for classification in diverse fields thanks to its superior performance. However, when tackling large-scale SVM problems, it encounters high computational complexity. To address this issue, we develop a novel trimmed concave loss SVM model called Ltri-SVM, which achieves sparsity and robustness simultaneously. The new optimality theory for the nonconvex and nonsmooth Ltri-SVM is developed by our new constructed proximal stationary point. Based on which, a new fast alternating direction method of multipliers (ADMM) with working set and low computational complexity is established for addressing Ltri-SVM. Based on our new established optimality theory, our proposed algorithm will divides the training dataset into two distinct categories: the non-working and the working sets. In every training iteration, the algorithm modifies the parameters associated with the working set, while ensuring that the parameters belonging to the non-working set remain unchanged. This algorithm enables the updating of parameters on smaller datasets, which in turn decreases computational complexity and improves the efficiency of runtime. Further, we prove that our algorithm is global convergence. Numerical experiments have confirmed the excellent performance of our algorithm in terms of accuracy in classification, number of support vector and computational speed, surpassing nine other leading solvers. For instance, when solving the real dataset with over 107 samples, our algorithm is able to complete the task in just 18.92 s, which is much faster than other solvers that take at least 650.4 s.

Best approximation theorems via relatively u-continuous and Jaggi nonexpansive mappings

In this paper, we introduced a new type of cyclic (noncyclic) mappings, called Jaggi relatively nonexpansive mappings and use to investigate the existence of best proximity points (pairs) in the framework of reflexive (strictly convex) Banach spaces by using a geometric concept of proximal normal structure. We also present a best proximity version of Schauder’s fixed point problem for non-self mappings. Finally, we prove the existence of a common best proximity point for an arbitrary family of cyclic relatively u-continuous mappings which are compact and then we obtain a generalization of Markov-Kakutani’s theorem.

Some Iterations of Best Proximity Point

The aim of this paper is to investigate the convergence of two types of iterative methods , that is Manna and Ishikawa to the optimal proximity points for cyclic Kannan and Chatterjee mappings defined on Banach spaces .

The Closest Point Theorem in CAT p (0) Metric Spaces

In this work, we investigate the closest point theorem in complete CAT p ( 0 ) metric spaces for p ≥ 2 . As an application, an extension of the Banach Contraction Principle for best proximity points is obtained.

Approximate proximal methods for variational inequalities on Hadamard manifolds

ABSTRACT In this paper, we present an approximate proximal point method for addressing the variational inequality problem on Hadamard manifolds, and we analyse its convergence properties. The proposed algorithm exhibits inexactness in two aspects. Firstly, each proximal subproblem is approximated by utilizing the enlargement of the vector field under consideration, and subsequently, the next iteration is obtained by solving this subproblem while allowing for a suitable error tolerance. As an illustrative application, we develop an approximate proximal point method for nonlinear optimization problems on Hadamard manifolds.

Etiology of craniofacial and cardiac malformations in a mouse model of SF3B4-related syndromes

Pathogenic variants in SF3B4, a component of the U2 snRNP complex important for branchpoint sequence recognition and splicing, are responsible for the acrofacial disorders Nager and Rodriguez Syndrome, also known as SF3B4-related syndromes. Patients exhibit malformations in the head, face, limbs, vertebrae as well as the heart. To uncover the etiology of craniofacial malformations found in SF3B4-related syndromes, mutant mouse lines with homozygous deletion of Sf3b4 in neural crest cells (NCC) were generated. Like in human patients, these embryos had craniofacial and cardiac malformations with variable expressivity and penetrance. The severity and survival of Sf3b4 NCC mutants was modified by the level of Sf3b4 in neighboring non-NCC. RNA sequencing analysis of heads of embryos prior to morphological abnormalities revealed significant changes in expression of genes forming the NCC regulatory network, as well as an increase in exon skipping. Additionally, several key histone modifiers involved in craniofacial and cardiac development showed increased exon skipping. Increased exon skipping was also associated with use of a more proximal branch point, as well as an enrichment in thymidine bases in the 50 bp around the branch points. We propose that decrease in Sf3b4 causes changes in the expression and splicing of transcripts required for proper craniofacial and cardiac development, leading to abnormalities.

Morphometric and anatomic characteristics of pronator quadratus muscle

PurposeIn surgical procedures commonly employed for the management of scaphoid and distal radial fractures, the incision and dissection of the pronator quadratus muscle play a pivotal role. Nevertheless, comprehensive investigations into the anatomical intricacies of the pronator quadratus muscle have been relatively scarce within the clinical community. In light of this, our study endeavors to make a substantive contribution to the medical literature by conducting a meticulous examination of the morphology and morphometry of this muscle. MethodsThis study is a cross-sectional observational study conducted on 22 cadaveric upper extremities (44 sides) preserved between January 2005 and December 2018 at Istanbul University. The study included specimens with intact dissection areas and no prior surgical intervention. Observations focused on the morphometry of the pronator quadratus muscle and related anatomical structures. Statistical analysis was performed using SPSS v23.0, employing Student's t-test and paired t-test, with significance set at p < 0.05. ResultsSignificant differences were found in the morphometric measurements of the pronator quadratus muscle between the right and left upper extremities, particularly in the vertical distance between the proximal and distal attachment points of the pronator quadratus to the radius (p = 0.008). Additionally, significant differences were observed between male and female samples for radius length (p < 0.001), ulna length (p < 0.001), pronator quadratus width (p < 0.001), and the vertical distance between pronator quadratus attachment points on both the radius (p = 0.001) and ulna (p = 0.001). Furthermore, significant correlations were identified between radius length and parameters such as the vertical distance between pronator quadratus attachment points on both the radius (p = 0.002) and pronator quadratus width (p = 0.03), and between ulna length and parameters including the vertical distances on the radius (p = 0.001) and ulna (p = 0.024). ConclusionIn light of our comprehensive analysis, which encompasses not only the anatomical features of the pronator quadratus muscle but also its vascular supply and the organization of its neurovascular structures, we posit that our study holds significant implications for the field of orthopedic surgery. We anticipate that this research will furnish valuable insights that can inform and enhance orthopedic procedures.

Inertial proximal point algorithm for sum of two monotone vector fields in Hadamard manifold

Inertial proximal point algorithm for sum of two monotone vector fields in Hadamard manifold

A Bregman proximal point algorithm without convexity in Banach spaces

ABSTRACT In this paper, we first introduce a Bregman prox-convexity notion as the generalization of the convexity for Bregman prox-convexity in Banach spaces. We verify the single-valudeness and Bregman firm nonexpansiveness of the Bregman proximity operator of the functions and provide examples of the notion. Using this notion, we show that the Bregman proximal point scheme remains convergent under appropriate conditions on the functions to be minimized in the setting of Banach spaces.

Variance Reduction Techniques for Stochastic Proximal Point Algorithms

AbstractIn the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties. Stochastic proximal point algorithms have been studied as an alternative to stochastic gradient algorithms since they are more stable with respect to the choice of the step size. However, their variance-reduced versions are not as well studied as the gradient ones. In this work, we propose the first unified study of variance reduction techniques for stochastic proximal point algorithms. We introduce a generic stochastic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. For this algorithm, in the smooth setting, we provide several convergence rates for the iterates and the objective function values, which are faster than those of the vanilla stochastic proximal point algorithm. More specifically, for convex functions, we prove a sublinear convergence rate of O(1/k). In addition, under the Polyak-łojasiewicz condition, we obtain linear convergence rates. Finally, our numerical experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts in terms of the stability with respect to the choice of the step size in most cases, especially for difficult problems.

An Intraoperative Technique to Assess Tissue Tension and Leg Length When Aligning the Hip Centre of Rotation With the Acetabulum in Hip Arthroplasties.

Hip arthroplasties are cost-effective procedures; however, instability and leg length discrepancy are common complications that can lead to higher revision rates and patient dissatisfaction. Preoperative planning aids surgeons in choosing the right offset and neck length before surgery. Nonetheless, intraoperative measures are still necessary due to the differences dictated by the surgical procedure. Several hip trials might be needed to reach the optimum choice of implants. We have introduced a technique that utilizes the trunnion as a reference point to the hip centre of rotation, matching it with the acetabulum centre of rotation after applying the necessary soft tissue tension. This serves as a proximal reference point. Using the trunnion, as opposed to the trial head, allows for a better assessment of tissue tension within the acetabular void, avoiding constraints imposed by the applied trial head. Additionally, determining the acetabulum's centre of rotation is challenging if obscured by the trial head. Matching the two tibial tuberosities indicates the correct leg length, serving as the distal reference point. Both reference points should be considered together to select the right neck length and offset for optimal tissue tension. This technique has been tested on hip arthroplasty patients over five years. All hip surgeons who used this technique agree that it gives a better representation of the tissue tension, easing the challenges when preparing the acetabulum as well as reducing the need for multiple trials.

CLINICAL PERFORMANCE OF EQUIA FORTE FILL. GAENIAL POSTERIOR, CENTION N IN CLASS II CAVITY IN PRIMARY TEETH- AN IN VIVO STUDY

Context: Aims:The aim of this study is to compare clinical performance of EQUIA Forte Fill. G-Aenial Posterior, Cention N in class II cavity in primary teeth- An In vivo study Setting and design:The study was conducted at Himachal Institute of dental sciences, Department of Pediatrics and Preventive dentistry, Paonta Sahib, Himachal Pradesh Subject and methods:In total 45 class II restorations were performed in patients aged 4-9 years using three different restorative materials: EQUIA Forte Fill [EF], GAenial Posterior [GP], Cention N [CN]. The restorations were evaluated using method USPHS criteria in terms of anatomic form, secondary caries, color match, retention, marginal adaptation, polishability, surface staining, pre and post operative sensitivity, soft tissue health, proximal contact point. The data was analized using chi-square test, McNemars test, marginal homogeneity test. Statistical analysis used: The statistical analysis was done using Statistical Package for Social Sciences (SPSS for Windows, Version 19.0). Descriptive statistics were calculated as frequency and percentage. The comparison of study parameters at various time periods among the three study groups was done using chi-square test. Comparison of change in study parameters at various time periods was assessed using McNemars test and marginal homogeneity test. The level of significance for the present study was fixed at a p-value of less than 0.05. Result:The clinical performance of GAenial Posterior was superior to EQUIA Forte Fill and Cention N Conclusion:GAenial Posterior is a promising user-friendly restorative material that can be used to restore carious primary teeth. It offers a better restorative properties like aesthetics, improved radiopacities and can be manipulated with ease by the clinicians.

Best Proximity Point Results for Fuzzy Proximal Quasi Contractions with Applications

In this work, we introduce a new type of multivalued fuzzy proximal quasi-contraction. These are generalized contractions which are a hybrid of H-contractive mappings and quasi-contractions. Furthermore, we establish the best proximity point results for newly introduced fuzzy contractions in the context of fuzzy b-metric spaces. Fuzzy b-metric spaces are more general than fuzzy metric spaces and are linked with the cosine distance, which is used in various contexts of artificial intelligence to measure the similarity between elements of a vector space.

A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming

A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming

Integral Equations: New Solutions via Generalized Best Proximity Methods

This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond.