Termination Criterion Research Articles

Termination of trastuzumab in HER2-positive metastatic breast cancer patients who received trastuzumab beyond progression

The purpose of the study was to assess the prognosis of HER2-positive metastatic breast cancer patients who received trastuzumab beyond progression and investigate the predictors of complete response. HER2-positive metastatic breast cancer patients who received long-term trastuzumab were included in the study. Predictors of complete response were analyzed with binary regression analysis. The prognosis of patients who had their trastuzumab-based treatment terminated was assessed. Eighty patients were involved in the study. The patients were received with trastuzumab for a median of 62 months (12–191). A complete response was observed in 60 (75%) patients. The median duration to development of complete response was found as 14.8 months (2.4–55). In logistic regression analysis: using endocrine therapy with trastuzumab (p = 0.04), menopausal status (p = 0.03), and the number of metastatic sites (p = 0.01) were found to be statistically significant factors for a complete response. Trastuzumab-based therapy of fifteen patients was terminated, six (40%) patients continued to receive an aromatase inhibitor, and nine (60%) patients were followed up without treatment. After termination of trastuzumab, at a median follow-up of 32 months (11–66), recurrence was detected in two (13.3%) patients. We detected that menopausal status, the number of metastatic sites, and using endocrine therapy with trastuzumab were predictors of complete response in HER2-positive metastatic breast cancer patients who received long-term trastuzumab-based therapy. We observed that HER2-positive metastatic breast cancer patients may be completely cured with trastuzumab-based therapy. There are no defined criteria for termination of trastuzumab treatment in this selected patient group. It is necessary to confirm our data with multicenter studies involving a large number of patients.

Systematic identification of low voltage-high frequency electrogram zones at sites of left atrial reentrant tachycardia termination

Abstract Funding Acknowledgements Type of funding sources: Private company. Main funding source(s): Abbott Laboratories Background Localization of the critical isthmus of conduction of LAMRT circuits within scar tissue is challenging (Panel A). Low voltage (LV) has been used as a marker for the arrhythmic substrate. However, voltage amplitudes due to near field (NF) vs. far-field (FF) electrogram (EGM) components are not clearly differentiated. The peak frequency (PF) associated with bipolar EGM’s is a novel parameter which may distinguish them (Panel B). Purpose To compare the ability of LV vs. LVHF to discriminate the LAMRT termination region Methods Bipolar voltage and activation maps were generated with a 16-pole grid catheter (Advisor HD Grid) during LAMRT (Panels A,C). Peak frequency maps were retrospectively computed (Panels B,D). LAMRT’s were included if acute termination could be achieved by focal RF lesion set restricted to a boundary <1.5cm diameter. The left atrial (LA) mapped surface was sub-regioned into the termination (T-ZONE) and non-termination (NT-ZONE) zones. The T-ZONE surface was centered about the site of termination and was allowed to extend to a rectangular kernel >0.5cm and <1.5cm across perpendicular axes, with the NT-ZONE encompassing the remainder of the mapped surface area (SA). Sensitivity (SE) and specificity (SP) of discrimination of the T-ZONE vs. NT-ZONE was measured according to the %T-ZONE vs. %NT-ZONE SA occupied at LV thresholds ranging from 0.1-1.0mV in increments of 0.1mV (Panel E). In addition to LV, LVHF at peak frequency cutoffs of 150Hz (LVHF150), 200Hz (LVHF200), 250Hz (LVHF250) and 300Hz (LVHF300) were also assessed for T-ZONE discrimination (Panels F,G). Results Of 16 consecutive patients with 24 ATs prospectively enrolled, 13 LAMRT’s from 13 patients met the termination criteria for inclusion. LAMRT termination consisted of a mean of 2.85±2.82 focal RF lesions. The T-ZONE occupied a mean SA of 0.82±0.30cm2 (41±19 EGM points) vs. 158.6±42.2cm2 (2967±1227 points) for the NT-ZONE. While the mean voltage from the T-ZONE was significantly lower vs. the NT-Zone (0.12±0.05mV vs. 0.60±0.28mV respectively), mean T-ZONE peak frequency of the was significantly higher vs. the NT-ZONE (345±76Hz vs. 255±34Hz). The maximum EGM duration in the T-ZONE was 172±63ms. ROC discrimination of the T-ZONE resulted in AUC’s of 0.69- LV, 0.76- LVHF150, 0.80- LVHF200, 0.81- LVHF250 and 0.76- LVHF300. LVHF200 and LVHF250 yielded the best improvements in AUC vs. LV unconstrained by high PF (11.3% and 12.2% respectively)(Panel G). LVHF200 with a cutoff of 0.2mV yielded a balanced SE/SP of 0.86/0.83 respectively, while LVHF250 with a cutoff of 0.3mV yielded a balanced SE/SP of 0.85/0.84. Conclusion During AT, systematic identification of EGM regions of high frequency within low voltage can significantly improve discrimination of the site of AT. termination, beyond.

Synthesis of PET-Magnesium Oxide-Chitosan Nanocomposite Membranes for the Dehydration of Natural Gas

Flat thin-film magnesium oxide-chitosan nanocomposite membranes were synthesized with polyethylene terephthalate (PET) and employed for natural gas dehydration. The water vapor permeation was most pronounced with a nanocomposite membrane doped with 0.9 g MgO nanoparticles (NP) as a result of a significant upsurge in the permeability of water vapor in the membrane (0.87). With the increase in MgO NP, large macro-voids are created, substratum pore size, and thickness together with the water vapor permeation were upsurged. The dehydration of natural gas performance of magnesium oxide-chitosan nanocomposite membranes synthesized with PET was enhanced with the increase in MgO NP embedded in the membrane. Though water vapor permeation was restricted by the polyester non-woven material used as a support for the nano composite membranes, as the three membranes did not reach the permeation coefficient of 1. However, the permeation coefficient increased with an increased MgO NP, with three mambrane samples (M1, M2 and M3) having permeation coefficient of 0.763, 0.77 and 0.87 respectively. The gas reduced with an increase MgO NP, with M1, M2 and M3 having 3.46×10−2, 3.17×10−2 and 3.88×10−3 kg/m3 respectively. From the adsorption study, the discrepancy observed between CH4 and vapor with isotherm models was ascribed to the different adsorption behavior of CH4 and vapor on the membrane-active area. The cost of making the membrane cannot be considered as a terminal criterion because most of the cost-effective option is not always the optimum one. The membranes confirmed their suitability for the dehydration of natural gas.

Biomechanical comparative study of midline cortical vs. traditional pedicle screw trajectory in osteoporotic bone

IntroductionIn lumbar spinal stabilization pedicle screws are used as standard. However, especially in osteoporosis, screw anchorage is a problem. Cortical bone trajectory (CBT) is an alternative technique designed to increase stability without the use of cement. In this regard, comparative studies showed biomechanical superiority of the MC (midline cortical bone trajectory) technique with longer cortical progression over the CBT technique. The aim of this biomechanical study was to comparatively investigate the MC technique against the not cemented pedicle screws (TT) in terms of their pullout forces and anchorage properties during sagittal cyclic loading according to the ASTM F1717 test.MethodsFive cadavers (L1 to L5), whose mean age was 83.3 ± 9.9 years and mean T Score of -3.92 ± 0.38, were dissected and the vertebral bodies embedded in polyurethane casting resin. Then, one screw was randomly inserted into each vertebra using a template according to the MC technique and a second one was inserted by freehand technique with traditional trajectory (TT). The screws were quasi-static extracted from vertebrae L1 and L3, while for L2, L4 and L5 they were first tested dynamically according to ASTM standard F1717 (10,000 cycles at 1 Hz between 10 and 110 N) and then quasi-static extracted. In order to determine possible screw loosening, there movements were recorded during the dynamic tests using an optical measurement system.ResultsThe pull-out tests show a higher pull-out strength for the MC technique of 555.4 ± 237.0 N compared to the TT technique 448.8 ± 303.2 N. During the dynamic tests (L2, L4, L5), 8 out of the 15 TT screws became loose before completing 10,000 cycles. In contrast, all 15 MC screws did not exceed the termination criterion and were thus able to complete the full test procedure. For the runners, the optical measurement showed greater relative movement of the TT variant compared to the MC variant. The pull-out tests also revealed that the MC variant had a higher pull-out strength, measuring at766.7 ± 385.4 N, while the TT variant measured 637.4 ± 435.6 N.ConclusionThe highest pullout forces were achieved by the MC technique. The main difference between the techniques was observed in the dynamic measurements, where the MC technique exhibited superior primary stability compared to the conventional technique in terms of primary stability. Overall, the MC technique in combination with template-guided insertion represents the best alternative for anchoring screws in osteoporotic bone without cement.

High-intensity exercise does not protect against orthostatic intolerance following bedrest in 55- to 65-yr-old men and women.

Prolonged bedrest provokes orthostatic hypotension and intolerance of upright posture. Limited data are available on the cardiovascular responses of older adults to head-up tilt following bedrest, with no studies examining the potential benefits of exercise to mitigate intolerance in this age group. This randomized controlled trial of head-down bedrest (HDBR) in 55- to 65-yr-old men and women investigated if exercise could avert post-HDBR orthostatic intolerance. Twenty-two healthy older adults (11 female) underwent a strict 14-day HDBR and were assigned to either an exercise (EX) or control (CON) group. The exercise intervention included high-intensity, aerobic, and resistance exercises. Head-up tilt-testing to a maximum of 15 minutes was performed at baseline (Pre-Bedrest) and immediately after HDBR (R1), as well as 6 days (R6) and 4 weeks (R4wk) later. At Pre-Bedrest, three participants did not complete the full 15 minutes of tilt. At R1, 18 did not finish, with no difference in tilt end time between CON (422 ± 287 s) and EX (409 ± 346 s). No differences between CON and EX were observed at R6 or R4wk. At R1, just 1 participant self-terminated the test with symptoms, while 12 others reported symptoms only after physiological test termination criteria were reached. Finishers on R1 protected arterial pressure with higher total peripheral resistance relative to Pre-Bedrest. Cerebral blood velocity decreased linearly with reductions in arterial pressure, end-tidal CO2, and cardiac output. High-intensity interval exercise did not benefit post-HDBR orthostatic tolerance in older adults. Multiple factors were associated with the reduction in cerebral blood velocity leading to intolerance.

Application of Lightweight Deflectometer to Assess Structural Competency of Nontraditional Airfield Pavements During Contingency Aircraft Operations

This paper discusses the use of the heavy and light weight deflectometer devices, hereafter referred to as HWD and LWD, respectively, to monitor the structural condition of airfield pavements during aircraft operations at contingency environments. Four airfield pavements like those encountered at contingency environments, referred to as nontraditional airfield pavements, were selected to conduct accelerated pavement traffic testing with simulated C-17 and C-130 aircraft. Pavement rut development was monitored, and both HWD and LWD tests were also conducted at selected traffic intervals. Both HWD and LWD were capable of tracking the pavement deterioration under accelerated traffic testing, which indicates that the LWD could be considered a potential rapid and practical pavement evaluation tool for nontraditional pavements during contingency aircraft operations. Based on current rutting failure threshold, a termination criterion in relation to a reduction in the stiffness parameter from the LWD test could be preliminarily used to aid in expediently determining acceptable aircraft operations on nontraditional airfield pavements. The influence of key operational parameters such as base plate dimension, the depth of influence from the impact force, and pavement rut formation must be further investigated to improve the effectiveness and applicability of the LWD test for nontraditional airfield pavements. The results from this study could be of interest to other low-volume road applications such as in agriculture, oilfield, large construction sites, and mining where pavement evaluation and management practices could be improved with the use of practical tools such as the LWD during the operations of heavy equipment or machinery.

The value of a machine learning algorithm to predict adverse short-term outcome during resuscitation of patients with in-hospital cardiac arrest: a retrospective study.

Background and importance Guidelines recommend that hospital emergency teams locally validate criteria for termination of cardiopulmonary resuscitation in patients with in-hospital cardiac arrest (IHCA). Objective To determine the value of a machine learning algorithm to predict failure to achieve return of spontaneous circulation (ROSC) and unfavourable functional outcome from IHCA using only data readily available at emergency team arrival. Design Retrospective cohort study. Setting and participants Adults who experienced an IHCA were attended to by the emergency team. Outcome measures and analysis Demographic and clinical data typically available at the arrival of the emergency team were extracted from the institutional IHCA database. In addition, outcome data including the Cerebral Performance Category (CPC) score count at hospital discharge were collected. A model selection procedure for random forests with a hyperparameter search was employed to develop two classification algorithms to predict failure to achieve ROSC and unfavourable (CPC 3-5) functional outcomes. Main results Six hundred thirty patients were included, of which 390 failed to achieve ROSC (61.9%). The final classification model to predict failure to achieve ROSC had an area under the receiver operating characteristic curve of 0.9 [95% confidence interval (CI), 0.89-0.9], a balanced accuracy of 0.77 (95% CI, 0.75-0.79), an F1-score of 0.78 (95% CI, 0.76-0.79), a positive predictive value of 0.88 (0.86-0.91), a negative predictive value of 0.61 (0.6-0.63), a sensitivity of 0.69 (0.66-0.72), and a specificity of 0.84 (0.8-0.88). Five hundred fifty-nine subjects experienced an unfavourable outcome (88.7%). The final classification model to predict unfavourable functional outcomes from IHCA at hospital discharge had an area under the receiver operating characteristic curve of 0.93 (95% CI, 0.92-0.93), a balanced accuracy of 0.59 (95% CI, 0.57-0.61), an F1-score of 0.94 (95% CI, 0.94-0.95), a positive predictive value of 0.91 (0.9-0.91), a negative predictive value of 0.57 (0.48-0.66), a sensitivity of 0.98 (0.97-0.99), and a specificity of 0.2 (0.16-0.24). Conclusion Using data readily available at emergency team arrival, machine learning algorithms had a high predictive power to forecast failure to achieve ROSC and unfavourable functional outcomes from IHCA while cardiopulmonary resuscitation was still ongoing; however, the positive predictive value of both models was not high enough to allow for early termination of resuscitation efforts.

A New Stopping Criterion for Krylov Solvers Applied in Interior Point Methods

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is applied as a black box with a standard termination criterion which asks for a sufficient reduction of the residual in the linear system. Such an approach often leads to an unnecessary 'oversolving' of linear equations. In this paper, an IPM that relies on an inner termination criterion not based on the residual of the linear system is introduced and analyzed. Moreover, new indicators for the early termination of the inner iterations are derived from a deep understanding of IPM needs. The new technique has been adapted to the Conjugate Gradient (CG) and to the Minimum Residual method (MINRES) applied in the IPM context. The new criterion has been tested on a set of quadratic optimization problems including compressed sensing, image processing and instances with partial differential equation constraints, and it has been compared to standard residual tests with variable tolerance. Evidence gathered from these computational experiments shows that the new technique delivers significant improvements in terms of inner (linear) iterations and those translate into significant savings of the IPM solution time.

Automated testing and interactive construction of unavoidable sets for graph classes of small path‐width

AbstractLet be a class of graphs with a membership test, , and let be the class of graphs in of path‐width at most . We present an interactive framework that finds an unavoidable set for , which is a set of graphs such that any graph in contains an isomorphic copy of a graph in . At the core of our framework is an algorithm that verifies whether a set of graphs is, indeed, unavoidable for . While obstruction sets are well‐studied, so far there is no general theory or algorithm for finding unavoidable sets. In general, it is undecidable whether a finite set of graphs is unavoidable for a given graph class. However, we give a criterion for termination: our algorithm terminates whenever is locally checkable of bounded maximum degree and is a finite set of connected graphs. For example, ‐regular graphs, ‐colourable graphs, and ‐free graphs are locally checkable classes. We put special emphasis on the case that is the class of cubic graphs and tailor the algorithm to this case. In particular, we introduce the new concept of high‐degree‐first path‐decompositions, which enables highly efficient pruning techniques. We exploit our framework to prove a new lower bound on the path‐width of cubic graphs. Moreover, we determine the extremal girth values of cubic graphs of path‐width for all and all smallest graphs which take on these extremal girth values. Further, we present a new constructive characterisation of the extremal cubic graphs of path‐width 3 and girth 4.

Physical Activity in Neurological Disorders: A Narrative Review

Physical activity levels of people with chronic neurological disorders are lower than those of healthy people. Problems in neurological disorders, including gait abnormalities, muscle weakness/loss of strength, spasticity, tremor, fatigue, balance disorder, and incontinence, results in lower physical activity level. After determining the situations that are contraindicated for physical activity, the patients should be evaluated by physiotherapists, and possible risks that may occur should be determined. Many studies have demonstrated that physical activity significantly reduces mortality and morbidity, increases community participation, and improves health-related quality of life. These benefits show that increased physical activity and exercise should be part of the standard management of neurological disorders. In these patients, physical activity programs should be structured individually by providing appropriate environmental conditions and safety, following the assessment of the functional status and severity of the disease. The duration, intensity, and type of planned physical activity should be adjusted individually; Appropriate rest intervals should be given during the activity, and termination criteria should be determined according to individual tolerance. This literature review aims to provide an up-to-date overview of physical activity recommendations for individuals with chronic neurological disorders.

On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)

In this paper, we study the non-asymptotic convergence rate of the DCA (difference-of-convex algorithm), also known as the convex–concave procedure, with two different termination criteria that are suitable for smooth and non-smooth decompositions, respectively. The DCA is a popular algorithm for difference-of-convex (DC) problems and known to converge to a stationary point of the objective under some assumptions. We derive a worst-case convergence rate of O(1/N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(1/\\sqrt{N})$$\\end{document} after N iterations of the objective gradient norm for certain classes of DC problems, without assuming strong convexity in the DC decomposition and give an example which shows the convergence rate is exact. We also provide a new convergence rate of O(1/N) for the DCA with the second termination criterion. Moreover, we derive a new linear convergence rate result for the DCA under the assumption of the Polyak–Łojasiewicz inequality. The novel aspect of our analysis is that it employs semidefinite programming performance estimation.

Doubly iteratively reweighted algorithm for constrained compressed sensing models

We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and nonconvex loss functions such as the Cauchy loss function and the Tukey biweight loss function in the constraint. Our framework employs iteratively reweighted $$\ell _1$$ and $$\ell _2$$ schemes to construct subproblems that can be efficiently solved by well-developed solvers for basis pursuit denoising such as SPGL1 by van den Berg and Friedlander (SIAM J Sci Comput 31:890-912, 2008). We propose a new termination criterion for the subproblem solvers that allows them to return an infeasible solution, with a suitably constructed feasible point satisfying a descent condition. The feasible point construction step is the key for establishing the well-definedness of our proposed algorithm, and we also prove that any accumulation point of this sequence of feasible points is a stationary point of the constrained compressed sensing model, under suitable assumptions. Finally, we compare numerically our algorithm (with subproblems solved by SPGL1 or the alternating direction method of multipliers) against the SCP $$_\textrm{ls}$$ in Yu et al. (SIAM J Optim 31: 2024-2054, 2021) on solving constrained compressed sensing models with the log-penalty function as the objective and the Cauchy loss function in the constraint, for badly scaled measurement matrices. Our computational results show that our approaches return solutions with better recovery errors, and are always faster.

Hyperparameter Optimization of a Convolutional Neural Network Model for Pipe Burst Location in Water Distribution Networks

The current paper presents a hyper parameterization optimization process for a convolutional neural network (CNN) applied to pipe burst locations in water distribution networks (WDN). The hyper parameterization process of the CNN includes the early stopping termination criteria, dataset size, dataset normalization, training set batch size, optimizer learning rate regularization, and model structure. The study was applied using a case study of a real WDN. Obtained results indicate that the ideal model parameters consist of a CNN with a convolutional 1D layer (using 32 filters, a kernel size of 3 and strides equal to 1) for a maximum of 5000 epochs using a total of 250 datasets (using data normalization between 0 and 1 and tolerance equal to max noise) and a batch size of 500 samples per epoch step, optimized with Adam using learning rate regularization. This model was evaluated for distinct measurement noise levels and pipe burst locations. Results indicate that the parameterized model can provide a pipe burst search area with more or less dispersion depending on both the proximity of pressure sensors to the burst or the noise measurement level.

Optimization of Gradient Descent Parameters in Attitude Estimation Algorithms.

Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment of the algorithm parameters, which is often overlooked in the literature. Here, we present the effects of the step size, the maximum number of iterations, and the initial quaternion, as well as different propagation methods on the quality of the estimation in noiseless and noisy conditions. A novel figure of merit and termination criterion that defines the algorithm's accuracy is proposed. Furthermore, the guidelines for selecting the optimal set of parameters in order to achieve the highest accuracy of the estimate using the fewest iterations are proposed and verified in simulations and experimentally based on the measurements acquired from an in-house developed model of a satellite attitude determination and control system. The proposed attitude estimation method based on the gradient descent algorithm and complementary filter automatically adjusts the number of iterations with the average below 0.5, reducing the demand on the processing power and energy consumption and causing it to be suitable for low-power applications.

Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

We present a solution framework for general alternating current optimal power flow (AC OPF) problems that include discrete decisions. The latter occur, for instance, in the context of the curtailment of renewables or the switching of power-generation units and transmission lines. Our approach delivers globally optimal solutions and is provably convergent. We model AC OPF problems with discrete decisions as mixed-integer nonlinear programs (MINLPs). The solution method starts from a known framework that uses piecewise linear relaxations. These relaxations are modeled as mixed-integer linear programs and adaptively refined until some termination criterion is fulfilled. In this work, we extend and complement this approach by problem-specific as well as very general algorithmic enhancements. In particular, these are mixed-integer second order cone programs as well as primal and dual cutting planes. For example, objective and no-good cuts help to compute good feasible solutions in which outer approximation constraints tighten the relaxations. We present extensive numerical results for various AC OPF problems in which discrete decisions play a major role. Even for hard instances with a large proportion of discrete decisions, the method is able to generate high-quality solutions efficiently. Furthermore, we compare our approach with state-of-the-art MINLP solvers. Our method outperforms all other algorithms. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This research has been funded by the Federal Ministry of Education and Research of Germany [Grant 05M18WEB]. This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The authors thank the Deutsche Forschungsgemeinschaft for support within projects A05, B06, B07, and B10 of the Sonderforschungsbereich/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks.” This work has been supported by the Federal Ministry for Economic Affairs and Energy, Germany [Grant 03El1036A]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1270 .

A Fast-Converging Particle Swarm Optimization through Targeted, Position-Mutated, Elitism (PSO-TPME)

We improve convergence speed by two orders of magnitude and the global exploration capabilities of particle swarm optimization (PSO) through targeted position-mutated elitism (TPME). The proposed fast-converging TPME operator requires a fitness-based classification technique to categorize the particles. The introduced classification is motivated by its simplicity, low memory requirements, and automated termination criteria based on convergence. The three key innovations address particle classification, elitism, and mutation in the cognitive and social model. PSO-TPME is benchmarked against five popular PSO variants for multi-dimensional functions, which are extensively adopted in the optimization field, In particular, the convergence accuracy, convergence speed, and the capability to find global minima are investigated. The statistical error is assessed by numerous repetitions. The simulations confirmed that in ten of the thirteen investigated functions, the proposed PSO variant outperforms other variants in terms of convergence rate and accuracy by at least two orders of magnitude. On the other hand, the simulations demonstrated the early exploration capabilities of PSO-TPME in all tested functions. In the first ten iterations, PSO-TPME outperformed all the investigated PSO variants by at least two orders of magnitude.

NeuralMinimizer: A Novel Method for Global Optimization

The problem of finding the global minimum of multidimensional functions is often applied to a wide range of problems. An innovative method of finding the global minimum of multidimensional functions is presented here. This method first generates an approximation of the objective function using only a few real samples from it. These samples construct the approach using a machine learning model. Next, the required sampling is performed by the approximation function. Furthermore, the approach is improved on each sample by using found local minima as samples for the training set of the machine learning model. In addition, as a termination criterion, the proposed technique uses a widely used criterion from the relevant literature which in fact evaluates it after each execution of the local minimization. The proposed technique was applied to a number of well-known problems from the relevant literature, and the comparative results with respect to modern global minimization techniques are shown to be extremely promising.

A novel numerical optimality technique to find the optimal results of Volterra integral equation of the second kind with discontinuous kernel

In this study we consider linear and nonlinear Volterra integral equations (VIEs) of the second kind with discontinuous kernel. A novel iterative method using floating point arithmetic (FPA) is presented to solve the problem. Also a convergence theorem and error analysis of the method are presented. The main novelty of this study is to validate the results using the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method which is based on stochastic arithmetic (SA). Moreover instead of applying usual mathematical softwares we use the CADNA (Control of Accuracy and Debugging for Numerical Applications) library which must be done on Linux operating system using C, C++ or Fortran codes. Applying the method and the library we will be able to find the optimal results such as optimal error, optimal iteration of the method and optimal approximation. Proving the main theorem of the CESTAC method we show the equality between the number of common significant digits (NCSDs) of two successive iterations with the exact and approximate solutions. Thus it can help us to apply a new termination criterion instead of absolute error to show the accuracy and efficiency of the method.

Adaptive mesh refinements for analyses of 2D linear elasticity problems using the Kriging-based finite element method

Finite element analyses of irregular structures require adaptive mesh refinement to achieve more accurate results in an efficient manner. This is also true for a non-conventional finite element method with Kriging interpolation, called the Kriging-based finite element method (K-FEM). This paper presents a study of automatic adaptive meshing procedures for analyses of two-dimensional linear elasticity problems using the K-FEM. The Matlab Partial Differential Equation Toolbox was utilized for generating meshes with Delaunay triangulation. Three error indicators, namely, the strain energy error, the gradient of effective stresses, and the element-free Galerkin strain energy error, were employed for estimating the element errors. To find the most effective error indicator, the resulting total number of elements and configurations of the final meshes were compared. The results show that the resulting final meshes were affected by the initial mesh configurations, the refinement criteria, and the termination criteria. The gradient of effective stresses indicator was found to be the most effective error indicator for the K-FEM, as it can accurately estimate the element errors.

Shape optimization of a meniscus-adherent nanotip.

A soluble tip can dissolve into a tip with curvature when partially immersed in a liquid. This process has been used in the manufacture of sophisticated tips. However, it is difficult to observe the dissolution process in the laboratory, and the dissolution mechanisms at the nanoscale still need to be better understood. Here we utilize molecular dynamics simulations to study the dissolution process of a meniscus-adherent nanotip. The tip apex curvature radius reaches its minimum in the intermediate state. The shape of this state is defined as the optimized shape, which can be used as the termination criterion in applications. In addition, the shape of one optimized tip can be well-fitted to a double-Boltzmann function. The upper Boltzmann curve of this function forms via the competition between the chemical potential influence and the intermolecular forces, while the formation of the lower Boltzmann curve is controlled by the chemical potential influence. The parameters of the double-Boltzmann function are strongly correlated with the nanotip's initial configuration and dissolubility. A shape factor ξ is proposed to characterize the sharpness of optimized tips. Theory and simulations show that optimized tips possess a greater ability to shield the capillary effect than common tips. Our findings elucidate the meniscus-adherent nanotip's dissolution process and provide theoretical support for nano-instrument manufacture.