Proximal Point Research Articles

Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques

In this work, in the context of Linear and convex Quadratic Programming, we consider Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is strongly supported by theoretical results concerning convergence and the rate of convergence, and can handle degenerate problems. Moreover, in the second part of this work, we analyse the interactions between the regularization parameters and the computational footprint of the linear algebra routines used to solve the Newton linear systems. In particular, when these systems are solved using an iterative Krylov method, we are able to show—using a new rearrangement of the Schur complement which exploits regularization—that general purposes preconditioners remain attractive for a series of subsequent IPM iterations. Indeed, if on the one hand a series of theoretical results underpin the fact that the approach here presented allows a better re-use of such computed preconditioners, on the other, we show experimentally that such (re)computations are needed only in a fraction of the total IPM iterations. The resulting regularized second order methods, for which low-frequency-update of the preconditioners are allowed, pave the path for an alternative class of second order methods characterized by reduced computational effort.

Some Best Proximity Point Results in the Orthogonal $$0$$-Complete $$b$$-Metric-Like Spaces

Some Best Proximity Point Results in the Orthogonal $$0$$-Complete $$b$$-Metric-Like Spaces

A marker-less assembly stage recognition method based on corner feature

Fast and robust product assembly stage recognition is a key step in human–machine cooperative assembly. To solve the recognition problem of similar adjacent assembly stages, a marker-less assembly stage recognition method is proposed based on corner feature between an assembling product and a digital model. Considering the geometric features of mechanical products, a corner identification method is proposed based on the circumferential angle difference (CADF). Then a corner matching method based on distance constraint is studied for ICP registration to realize the point cloud registration between the product and digital model. Based on the registration relationship, a similarity algorithm based on proximity point proportion is used to calculate the similarity between models and the input assembling product. The model with the greatest similarity is taken as the stage recognition result. In experiments on four group assembling products, the average stage recognition accuracy is 96.15%, which indicates that the proposed method can solve the stage recognition problem. The corner identification method based on the CADF outperforms the Harris-3D corner detection method in the efficiency of assembly stage recognition.

PROXIMAL POINT ALGORITHM FOR THE GENERALIZED P0 VARIATIONAL INEQUALITIES PROBLEMS

This paper studies the proximal point algorithm for the class of generalized variational inequalities. By using the upper semicontinuity result establishing the class of weakly univalent operators, we show that the iterative sequence generated by the algorithm is bounded, approaches to the solution set of the initial problem, and each of its accumulation points is a solution to the problem, provided that the solution set is bounded. We also give an example to show the necessity of boundedness.

Controlling Supratip Break and Tip Rotation and Projection with Preservation of the Pitanguy Ligament.

In this article, the author describes a new closed rhinoplasty technique in which the Pitanguy ligament was protected, ultimately resulting in better supratip break, tip projection, and tip rotation. Based on the inclusion and exclusion criteria, the records of 156 patients who underwent surgery with this "Pitanguy ligament protection and suturing" technique were evaluated retrospectively. In this novel technique, the Pitanguy ligament was dissected from the proximal and distal points with scissors in the lower third, and it was left intact. There was no need for revision operations in any patient. Twelve months after surgery, the Rhinoplasty Outcome Evaluation scores ranged between 80 and 100 points. The median score was 86.5 points. Patient satisfaction was excellent in 90% of the included cases. Protection of the Pitanguy ligament and attachment of this ligament to the nasal tip create better tip definition and generate several aesthetic and functional advantages. Therapeutic, IV.

A contribution to best proximity point theory and an application to partial differential equation

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem.

The Value of Interpersonal Network Continuity for College Students in Disruptive Times.

The COVID-19 pandemic-related social distancing practices that colleges implemented in Spring 2020 disrupted the typical mechanisms of propinquity (physical proximity) and homophily (shared characteristics) that physical institutions rely on to help students build and maintain relationships critical to learning and wellbeing. To explore how social distancing shaped students' academic and social networks and associated educational outcomes, we conceptualized it as a "network shock" and collected unique ego network data in April 2020. For participating students, maintaining interactions with the same set of individuals before and after social distancing was related to more positive outcomes across a range of self-reported wellbeing and learning indicators. On average, students experienced a loss of frequent academic contacts, while they maintained or replaced social interactions in their interpersonal networks after social distancing. Our investigation of the ways students experienced changes in their social and academic networks after a loss of physical proximity points to the role of interpersonal interaction network continuity for fostering wellbeing and learning in times of disruption, as well as the potential need for support in maintaining or rebuilding academic networks.

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.

A60 DOWN WITH THE SHP-1: CHRONIC HELMINTH INFECTION DISRUPTS BILE ACID HOMEOSTASIS AND SIGNALLING RECEPTOR ACTIVATION IN THE MURINE SMALL INTESTINE TO POTENTIALLY IMPACT GUT IMMUNITY

Abstract Background Helminths (parasitic worms) use immunomodulatory mechanisms to maintain their presence in the host intestines. Understanding how helminths reduce inflammation in the guts may lead to new therapeutic options for inflammatory bowel diseases. Our lab uses a helminth which infects the proximal small intestine of mice to identify new, potentially immunomodulatory molecules. In this project, we examined the impact of helminth infection on bile acids (BA)s; a class of metabolites that can function as immunomodulatory signalling molecules. To our knowledge, how helminth infection alters BA homeostasis, and the potential consequences for proximal small intestine immunity have not yet been reported. Purpose Our aims were to determine whether helminth infection alters (1) the intestinal BA pool, (2) expression of BA transporters in the small intestine, and (3) expression and/or activation of the Farnesoid X receptor (FXR), a BA signalling receptor. Method We used a murine model system to study the effects of the mouse-specific helminth Heligmosomoides polygyrus on BA homeostasis, BA transporter gene expression, and BA signalling receptors in the small intestine. Male and female littermate mice were used. Targeted metabolomics was used to assess the composition of the BA pool in the small intestine. Reverse transcription qPCR was used to quantify gene expression of BA transporters/signalling molecules in tissues. All data were segregated by sex of mice for data analysis. Result(s) We found that helminth infection disrupts the BA pool of mice, with consistent reductions in T-CDCA and T-αMCA during helminth infection. In the proximal small intestine, expression of the genes that encode the apical sodium dependant BA transporter (ASBT) and organic solute transporter alpha (OSTα) were unaffected during helminth infection, however expression of the organic solute transporter β (OSTβ) gene, which encodes half of the basal BA transporter, was decreased. Expression of Shp-1, an indicator of activation of BA receptor FXR, and expression of the Fxr gene were significantly decreased in both the proximal and distal small intestine. Lastly, expression of the gene encoding Gpbar1 trended upwards in the proximal and distal small intestine of female mice. Conclusion(s) Infection of mice with a proximal small intestine-dwelling helminth impacts BA homeostasis in the small intestine. Helminth infection decreases expression of a BA transporter in the proximal small intestine, although whether this contributes to or is caused by perturbations in the BA pool during infection remains to be seen. The downregulation of BA signalling we see during helminth infection in the proximal small intestine points to a potential functional impact on the host immune response which we now intend to explore. Understanding the immunomodulatory mechanisms used by helminths to dampen the host immune response could lead to further advancements in treating intestinal inflammatory disorders such as Crohn’s and Colitis. Disclosure of Interest None Declared

A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem

A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem

Some best approximation theorems and best proximity point theorems

A best approximation theorem for almost cyclic contractions has been proved in the recent article (Sadiq Basha in J. Fixed Point Theory Appl 23:32, 2021). The purpose of this note is to show that, with the same hypotheses as in the preceding best approximation theorem, the conclusion of the theorem can be strengthened to produce a best proximity point rather than a best approximation and hence a best proximity point theorem for almost cyclic contractions in the framework of a uniformly convex Banach space. Further, it is interesting to observe that such a best proximity point theorem for almost cyclic contractions generalizes/subsumes the well known best proximity point theorem, due to Eldred and Veeramani (J Math Anal Appl 323:1001–1006, 2006), for cyclic contractions in the framework of a uniformly convex Banach space. On the other hand, these best approximation theorems and best proximity point theorems for some types of contractions do not generalize the most elegant Banach’s contraction principle because of the underlying richer framework of a uniformly convex Banach space rather than a simpler framework like a complete metric space. Therefore, the purpose of this note is to bring forth the framework of utmost complete space and establish a best proximity point theorem for almost cyclic contractions in such a simpler framework, thereby generalizing the contraction principle.

Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT( k ) spaces

UDC 517.9 We propose a new modified proximal point algorithm in the setting of CAT(1) spaces, which can be used for solving the minimization problem and the common fixed-point problem. In addition, we prove several convergence results for the proposed algorithm under certain mild conditions. Further, we provide some applications for the convex minimization problem and the fixed point problem in the CAT( k ) spaces with a bounded positive real number k . In the process, several relevant results available in the existing literature are generalized and improved.

Breathing, Nostrils, and the Press: Rethinking the Hebrew–Yiddish Axis in the United States, 1870–1900

The early American Yiddish and Hebrew presses had various affinities and bonds. This essay seeks to examine the connections between newspapers written in the Hebrew alphabet in the United States between the 1870s and 1890s and highlight the parallel process of growth undergone by periodicals in both languages. Diverting from standard research in this area that treats the Yiddish and Hebrew presses in the United States as two separate entities, this essay emphasizes the points of contact and proximity between them. It reviews the interconnectedness of the Hebrew and Yiddish presses during its first two decades, emphasizing personalities and material culture, and situates the phenomenon against its broader cultural background. More specifically, it presents a case study—Hebrew and Yiddish periodicals published in Chicago in 1889—and compares the periodicals' content and form. The essay then traces the geographical and cultural bilingual heritage of the publications' founders. By analyzing the features and origins of these contacts, this essay offers a different and more nuanced consideration of the historical perception of Hebrew and Yiddish in the American context.

Intravascular ultrasound imaging for diagnosis and characterization of the popliteal compression syndrome.

Functional popliteal artery entrapment syndrome (fPAES) is a rare form of nonatherosclerotic claudication most often seen in young athletic patients. Diagnosis remains challenging, with various imaging modalities showing equivocal or subtle findings that may be missed. We sought to critically examine and quantitate the utility of intravascular ultrasound (IVUS) imaging, a common diagnostic tool for vascular compression syndromes, in diagnosis and characterization of fPAES. Patients presenting to a single tertiary care center between 2019 and 2022 with symptoms of PAES but without an anatomic etiology or equivocal workup were selected. Angiogram and IVUS with maneuvers were performed on affected extremities at rest, active plantarflexion/dorsiflexion, and plantarflexion/dorsiflexion against resistance. IVUS examination was recorded using a pull-back technique from the tibial vessels to the superficial femoral artery. The degree, length, and anatomic location of compression using the two imaging modalities were compared. Angiogram and IVUS with maneuvers were performed on 17 lower extremities (9 left, 8 right) in 15 patients (88% female; mean age, 21.2years). Evidence of arterial compression on angiography was noted in 88.2% (n= 15) of limbs (66.7% complete contrast cessation and 20% popliteal artery tapering); 13.3% (n= 2) only demonstrated sluggish flow as possible evidence of compression. Arterial compression was seen on IVUS imaging in 15 of 17 limbs, and all completely compressed around the IVUS catheter. The IVUS-measured mean length of compression was 10.5cm± 4.2 (median, 11cm; range, 4-23cm). Compression involved only the popliteal vessels in 86.7% (n= 13); one patient had both popliteal and tibioperoneal trunk compression, whereas another had tibioperoneal trunk and peroneal artery compression. Popliteal vein compression was 100%. The contrast cessation point on angiography and the proximal point of compression on IVUS imaging differed in 80% of cases (P< .05). The distal extent of compression was unable to be determined by angiogram findings but was clearly delineated by IVUS imaging in all cases. IVUS imaging is a more sensitive diagnostic and descriptive imaging modality compared with angiogram in patients with possible fPAES. IVUS and angiogram findings are greatly discordant; moreover, IVUS imaging can provide detailed information such as the precise extent and anatomic location of the arterial compression, which may be useful in aiding surgical planning. IVUS imaging should be considered the gold standard for diagnosing and characterizing fPAES before intervention planning.

Structural details of a Class B GPCR-arrestin complex revealed by genetically encoded crosslinkers in living cells

Understanding the molecular basis of arrestin-mediated regulation of GPCRs is critical for deciphering signaling mechanisms and designing functional selectivity. However, structural studies of GPCR-arrestin complexes are hampered by their highly dynamic nature. Here, we dissect the interaction of arrestin-2 (arr2) with the secretin-like parathyroid hormone 1 receptor PTH1R using genetically encoded crosslinking amino acids in live cells. We identify 136 intermolecular proximity points that guide the construction of energy-optimized molecular models for the PTH1R-arr2 complex. Our data reveal flexible receptor elements missing in existing structures, including intracellular loop 3 and the proximal C-tail, and suggest a functional role of a hitherto overlooked positively charged region at the arrestin N-edge. Unbiased MD simulations highlight the stability and dynamic nature of the complex. Our integrative approach yields structural insights into protein-protein complexes in a biologically relevant live-cell environment and provides information inaccessible to classical structural methods, while also revealing the dynamics of the system.

A New Best Proximity Point Results in Partial Metric Spaces Endowed with a Graph

For a given mapping f in the framework of different spaces, the fixed-point equations of the form fx=x can model several problems in different areas, such as differential equations, optimization, and computer science. In this work, the aim is to find the best proximity point and to prove its uniqueness on partial metric spaces where the symmetry condition is preserved for several types of contractive non-self mapping endowed with a graph. Our theorems generalize different results in the literature. In addition, we will illustrate the usability of our outcomes with some examples. The proposed model can be considered as a theoretical foundation for applications to real cases.

The advent of a pan-collagenous CLOVIS POINT for pathotropic targeting and cancer gene therapy, a retrospective.

The 'Clovis Point'-an enabling prehistoric gain-of-function in stone-age tool technologies which empowered the Paleoindian-Americans to hunt, to strike-deep, and to kill designated target megafauna more efficiently-was created biochemically by molecular-genetic bio-engineering. This Biomedical "Clovis Point" was crafted by adapting a broad-spectrum Pan-Collagen Binding Domain (Pan-Coll/CBD) found within the immature pre-pro-peptide segment of Von Willebrand Factor into a constructive series of advanced medical applications. Developed experimentally, preclinically, and clinically into a cutting-edge Biotechnology Platform, the Clovis Point is suitable for 1) solid-state binding of growth factors on collagenous scaffolds for improved orthopedic wound healing, 2) promoting regeneration of injured/diseased tissues; and 3) autologous stem cell capture, expansion, and gene-based therapies. Subsequent adaptations of the high-affinity Pan-Coll/CBD (exposed-collagen-seeking/surveillance function) for intravenous administration in humans, enabled the physiological delivery, aka Pathotropic Targeting to diseased tissues via the modified envelopes of gene vectors; enabling 4) precision tumor-targeting for cancer gene therapy and 5) adoptive/localized immunotherapies, demonstrating improved long-term survival value-thus pioneering a proximal and accessible cell cycle control point for cancer management-empowering modern medical oncologists to address persistent problems of chemotherapy resistance, recurrence, and occult progression of metastatic disease. Recent engineering adaptations have advanced the clinical utility to include the targeted delivery of small molecule APIs: including taxanes, mAbs, and RNA-based therapeutics.

An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.

General Hölder Smooth Convergence Rates Follow from Specialized Rates Assuming Growth Bounds

Often in the analysis of first-order methods for both smooth and nonsmooth optimization, assuming the existence of a growth/error bound or KL condition facilitates much stronger convergence analysis. Hence, separate analysis is typically needed for the general case and for the growth bounded cases. We give meta-theorems for deriving general convergence rates from those assuming a growth lower bound. Applying this simple but conceptually powerful tool to the proximal point, subgradient, bundle, dual averaging, gradient descent, Frank–Wolfe and universal accelerated methods immediately recovers their known convergence rates for general convex optimization problems from their specialized rates. New convergence results follow for bundle methods, dual averaging and Frank–Wolfe. Our results can lift any rate based on Hölder continuous gradients and Hölder growth bounds. Moreover, our theory provides simple proofs of optimal convergence lower bounds under Hölder growth from textbook examples without growth bounds.

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.