A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions

Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.

Modeling Solid Waste Minimization Performance at Source in Dar es Salaam City, Tanzania

Municipal solid waste generation is strongly linked to rising human population and expanding urban areas, with significant implications on urban metabolism as well as space and place values redefinition. Effective management performance of municipal solid waste management underscores the interdisciplinarity strategies. Such knowledge and skills are paramount to uncover the sources of waste generation as well as means of waste storage, collection, recycling, transportation, handling/treatment, disposal, and monitoring. This study was conducted in Dar es Salaam city. Driven by the curiosity model of the solid waste minimization performance at source, study data was collected using focus group discussion techniques to ward-level local government officers, which was triangulated with literature and documentary review. The main themes of the FGD were situational factors (SFA) and local government by-laws (LGBY). In the FGD session, sub-themes of SFA tricked to understand how MSW minimization is related to the presence and effect of services such as land use planning, availability of landfills, solid waste transfer stations, material recovery facilities, incinerators, solid waste collection bins, solid waste trucks, solid waste management budget and solid waste collection agents. Similarly, FGD on LGBY was extended by sub-themes such as contents of the by-law, community awareness of the by-law, and by-law enforcement mechanisms. While data preparation applied an analytical hierarchy process, data analysis applied an ordinary least square (OLS) regression model for sub-criteria that explain SFA and LGBY;and OLS standard residues as variables into geographically weighted regression with a resolution of 241 × 241 meter in ArcMap v10.5. Results showed that situational factors and local government by-laws have a strong relationship with the rate of minimizing solid waste dumping in water bodies (local R square = 0.94).

Energy Minimization for Heterogenous Traffic Coexistence with Puncturing in Mobile Edge Computing-Based Industrial Internet of Things

Puncturing has been recognized as a promising technology to cope with the coexistence problem of enhanced mobile broadband(eMBB) and ultra-reliable low latency communications(URLLC)traffic. However, the steady performance of eMBB traffic while meeting the requirements of URLLC traffic with puncturing is a major challenge in some realistic scenarios. In this paper, we pay attention to the timely and energy-efficient processing for eMBB traffic in the industrial Internet of Things(IIoT), where mobile edge computing(MEC) is employed for data processing. Specifically, the performance of eMBB traffic and URLLC traffic in a MEC-based IIoT system is ensured by setting the threshold of tolerable delay and outage probability, respectively. Furthermore,considering the limited energy supply, an energy minimization problem of eMBB device is formulated under the above constraints, by jointly optimizing the resource blocks(RBs) punctured by URLLC traffic, data offloading and transmit power of eMBB device. With Markov's inequality, the problem is reformulated by transforming the probabilistic outage constraint into a deterministic constraint. Meanwhile, an iterative energy minimization algorithm(IEMA) is proposed.Simulation results demonstrate that our algorithm has a significant reduction in the energy consumption for eMBB device and achieves a better overall effect compared to several benchmarks.

基于两步正则化Gauss-Newton迭代算法的ECT图像重建

电容层析成像(ECT)技术求解图像重建问题属于非线性问题,并且存在严重的不适定性。为提高图像重建精度,提出了一种基于两步正则化Gauss-Newton迭代算法的ECT图像重建方法。针对标准正则化Gauss-Newton迭代算法在图像重建中存在的不收敛问题,引入了两步迭代方法;改进了正则化矩阵,提高了解估计的精确度;考虑到Gauss-Newton算法对迭代初值的依赖性,加入了同伦算法。最后,进行仿真和静态实验,并与线性反投影(LBP)算法、Landweber算法、Tikhonov正则化算法进行对比。结果表明,该方法可有效提高图像重建精度。

New direction for surgery:Super minimally invasive surgery

The top goal of modern medicine is treating disease without destroying organ structures and making patients as healthy as they were before their sickness.Minimally invasive surgery(MIS)has dominated the surgical realm because of its lesser invasiveness.However,changes in anatomical structures of the body and reconstruction of internal organs or different organs are common after traditional surgery or MIS,decreasing the quality of life of patients post-operation.Thus,I propose a new treatment mode,super MIS(SMIS),which is defined as“curing a disease or lesion which used to be treated by MIS while preserving the integrity of the organs”.In this study,I describe the origin,definition,operative channels,advantages,and future perspectives of SMIS.

Minimization of Electric Power Losses on 132 kV and 220 kV Uganda Electricity Transmission Lines

The classical minimization of power losses in transmission lines is dominated by artificial intelligence techniques, which do not guarantee global optimum amidst local minima. Revolutionary and evolutionary techniques are encumbered with sophisticated transformations, which weaken the techniques. Power loss minimization is crucial to the efficient design and operation of power transmission lines. Minimization of losses is one way to meet steady grid supply, especially at peak demand. Thus, this paper has presented a gradient technique to obtain optimal variables and values from the power loss model, which efficiently minimizes power losses by modifying the traditional power loss model that combines Ohm and Corona losses. Optimality tests showed that the unmodified model does not support the minimization of power losses on transmission lines as the Hessian matrix portrayed the maximization of power losses. However, the modified model is consistent with the gradient method of optimization, which yielded optimum variables and values from the power loss model developed in this study. The unmodified (modified) models for Bujagali-Kawanda 220 kV and Masaka West-Mbarara North 132 kV transmission lines in Uganda showed maximum power losses of 0.406 (0.391) and 0.452 (0.446) kW/km/phase respectively. These results indicate that the modified model is superior to the unmodified model in minimizing power losses in the transmission lines and should be implemented for the efficient design and operation of power transmission lines within and outside Uganda for the same transmission voltages.

Modified MMS: Minimization Approach for Model Subset Selection

Considering the recent developments in the digital environment,ensuring a higher level of security for networking systems is imperative.Many security approaches are being constantly developed to protect against evolving threats.An ensemble model for the intrusion classification system yielded promising results based on the knowledge of many prior studies.This research work aimed to create a more diverse and effective ensemble model.To this end,selected six classification models,Logistic Regression(LR),Naive Bayes(NB),K-Nearest Neighbor(KNN),Decision Tree(DT),Support Vector Machine(SVM),and Random Forest(RF)from existing study to run as independent models.Once the individual models were trained,a Correlation-Based Diversity Matrix(CDM)was created by determining their closeness.The models for the ensemble were chosen by the proposed Modified Minimization Approach for Model Subset Selection(Modified-MMS)from Lower triangular-CDM(L-CDM)as input.The proposed algorithm performance was assessed using the Network Security Laboratory—Knowledge Discovery in Databases(NSL-KDD)dataset,and several performance metrics,including accuracy,precision,recall,and F1-score.By selecting a diverse set of models,the proposed system enhances the performance of an ensemble by reducing overfitting and increasing prediction accuracy.The proposed work achieved an impressive accuracy of 99.26%,using only two classification models in an ensemble,which surpasses the performance of a larger ensemble that employs six classification models.

Feasibility and safety of minimally invasive multivisceral resection for T4b rectal cancer:A 9-year review

BACKGROUND Colorectal cancer is the third most common cancer and the second highest cause of cancer-related mortality worldwide.About 5%-10%of patients are diagnosed with locally advanced rectal cancer(LARC)on presentation.For LARC invading into other structures(i.e.T4b),multivisceral resection(MVR)and/or pelvic ex-enteration(PE)remains the only potential curative surgical treatment.MVR and/or PE is a major and complex surgery with high post-operative morbidity.Minimally invasive surgery(MIS)has been shown to improve short-term post-operative outcomes in other gastrointestinal malignancies,but there is little evi-dence on its use in MVR,especially so for robotic MVR.This is a single-center retrospective cohort study from 1st January 2015 to 31st March 2023.Inclusion criteria were patients diagnosed with cT4b rectal cancer and underwent MVR,or stage 4 disease with resectable systemic metastases.Pa-tients who underwent curative MVR for locally recurrent rectal cancer,or me-tachronous rectal cancer were also included.Exclusion criteria were patients with systemic metastases with non-resectable disease.All patients planned for elective surgery were enrolled into the standard enhanced recovery after surgery pathway with standard peri-operative management for colorectal surgery.Complex sur-gery was defined based on technical difficulty of surgery(i.e.total PE,bladder-sparing prostatectomy,pelvic lymph node dissection or need for flap creation).Our primary outcomes were the margin status,and complication rates.Cate-gorical values were described as percentages and analysed by the chi-square test.Continuous variables were expressed as median(range)and analysed by Mann-Whitney U test.Cumulative overall survival(OS)and recurrence-free survival(RFS)were analysed using Kaplan-Meier estimates with life table analysis.Log-rank test was performed to determine statistical significance between cumulative estimates.Statistical significance was defined as P<0.05.Meier estimates with life table analysis.Log-rank test was performed to determine statistical significance between cumulative estimates.Statistical significance was defined as P<0.05.RESULTS A total of 46 patients were included in this study[open MVR(oMVR):12(26.1%),miMVR:36(73.9%)].Patients’American Society of Anesthesiologists score,body mass index and co-morbidities were comparable between oMVR and miMVR.There is an increasing trend towards robotic MVR from 2015 to 2023.MiMVR was associated with lower estimated blood loss(EBL)(median 450 vs 1200 mL,P=0.008),major morbidity(14.7%vs 50.0%,P=0.014),post-operative intra-abdominal collections(11.8%vs 50.0%,P=0.006),post-operative ileus(32.4%vs 66.7%,P=0.04)and surgical site infection(11.8%vs 50.0%,P=0.006)compared with oMVR.Length of stay was also shorter for miMVR compared with oMVR(median 10 vs 30 d,P=0.001).Oncological outcomes-R0 resection,recurrence,OS and RFS were comparable between miMVR and oMVR.There was no 30-d mortality.More patients underwent robotic compared with laparoscopic MVR for complex cases(robotic 57.1%vs laparoscopic 7.7%,P=0.004).The operating time was longer for robotic compared with laparoscopic MVR[robotic:602(400-900)min,laparoscopic:Median 455(275-675)min,P<0.001].Incidence of R0 resection was similar(laparoscopic:84.6%vs robotic:76.2%,P=0.555).Overall complication rates,major morbidity rates and 30-d readmission rates were similar between la-paroscopic and robotic MVR.Interestingly,3-year OS(robotic 83.1%vs 58.6%,P=0.008)and RFS(robotic 72.9%vs 34.3%,P=0.002)was superior for robotic compared with laparoscopic MVR.CONCLUSION MiMVR had lower post-operative complications compared to oMVR.Robotic MVR was also safe,with acceptable post-operative complication rates.Prospective studies should be conducted to compare short-term and long-term outcomes between robotic vs laparoscopic MVR.

An Optimized Test Case Minimization Technique Using Genetic Algorithm for Regression Testing

Regression testing is a widely used approach to confirm the correct functionality of the software in incremental development.The use of test cases makes it easier to test the ripple effect of changed requirements.Rigorous testingmay help in meeting the quality criteria that is based on the conformance to the requirements as given by the intended stakeholders.However,a minimized and prioritized set of test cases may reduce the efforts and time required for testingwhile focusing on the timely delivery of the software application.In this research,a technique named Test Reduce has been presented to get a minimal set of test cases based on high priority to ensure that the web applicationmeets the required quality criteria.A new technique TestReduce is proposed with a blend of genetic algorithm to find an optimized and minimal set of test cases.The ultimate objective associated with this study is to provide a technique that may solve the minimization problem of regression test cases in the case of linked requirements.In this research,the 100-Dollar prioritization approach is used to define the priority of the new requirements.

A Note on Sharp Affine Poincaré-Sobolev Inequalities and Exact in Minimization of Zhang’s Energy on Bounded Variation and Exactness

As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.

Low-complexity iterative equalization for OTFS based on alternating minimization

To achieve robust communication in high mobility scenarios,an iterative equalization algorithm based on alternating minimization(AM)is proposed for the orthogonal time frequency space(OTFS)system.The algorithm approximates the equalization problem to a convex function optimization problem in the real-valued domain and solves the problem iteratively using the AM algorithm.In the iterative process,the complexity of the proposed algorithm is reduced further based on the study of the cyclic structure and sparse property of the OTFS channel matrix in the delay-Doppler(DD)domain.The new method for OTFS is simulated and verified in a high-speed mobile scenario and the results show that the proposed equalization algorithm has excellent bit error rate performance with low complexity.

Optimal Placement and Sizing of Distributed Generations for Power Losses Minimization Using PSO-Based Deep Learning Techniques

The integration of distributed generations (DGs) into distribution systems (DSs) is increasingly becoming a solution for compensating for isolated local energy systems (ILESs). Additionally, distributed generations are used for self-consumption with excess energy injected into centralized grids (CGs). However, the improper sizing of renewable energy systems (RESs) exposes the entire system to power losses. This work presents an optimization of a system consisting of distributed generations. Firstly, PSO algorithms evaluate the size of the entire system on the IEEE bus 14 test standard. Secondly, the size of the system is allocated using improved Particles Swarm Optimization (IPSO). The convergence speed of the objective function enables a conjecture to be made about the robustness of the proposed system. The power and voltage profile on the IEEE 14-bus standard displays a decrease in power losses and an appropriate response to energy demands (EDs), validating the proposed method.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Exploring the landscape of minimally invasive pancreatic surgery: Progress, challenges, and future directions

Minimally invasive surgery(MI)has become the standard of care for many surgical procedures aimed at reducing the burden on patients.However,its adoption in pancreatic surgery(PS)has been limited by the pancreas’s unique location and the complexity of the dissection and reconstruction phases.These factors continue to contribute to PS having one of the highest morbidity and mortality rates in general surgery.Despite a rough start,MIPS has gained widespread acceptance in clinical practice recently.Robust evidence supports MI distal pancreatectomy safety,even in oncological cases,indicating its potential superiority over open surgery.However,definitive evidence of MI pancre-aticoduodenectomy(MIPD)feasibility and safety,particularly for malignant lesions,is still lacking.Nonetheless,reports from high-volume centers are emer-ging,suggesting outcomes comparable to those of the open approach.The robotic PS increasing adoption,facilitated by the wider availability of robotic platforms,may further facilitate the transition to MIPD by overcoming the technical con-straints associated with laparoscopy and accelerating the learning curve.Alth-ough the MIPS implementation process cannot be stopped in this evolving world,ensuring patient safety through strict outcome monitoring is critical.Investing in younger surgeons with structured and recognized training programs can promote safe expansion.

Outcomes following minimally invasive dorsal cheilectomy for hallux rigidus:A systematic review

BACKGROUND Cheilectomy of the 1^(st)metatarsophalangeal joint(MTPJ)is one of the most common procedures for the management of hallux rigidus.However,there is no consensus regarding outcomes following minimally invasive dorsal cheilectomy(MIDC)for the management of hallux rigidus.AIM To evaluate outcomes following MIDC for the management of hallux rigidus.METHODS During November 2023,the PubMed,EMBASE and Cochrane Library databases were systematically reviewed to identify clinical studies examining outcomes following MIDC for the management of hallux rigidus.RESULTS Six studies were included.In total,348 patients(370 feet)underwent MIDC for hallux rigidus at a weighted mean follow-up of 37.9±16.5 months.The distribution of patients by Coughlin and Shurna's classification was recorded in 4 studies as follows:Ⅰ(58 patients,27.1%),Ⅱ(112 patients,52.3%),Ⅲ(44 patients,20.6%).Three studies performed an additional 1^(st)MTPJ arthroscopy and debridement following MIDC.Retained intra-articular bone debris was observed in 100%of patients in 1 study.The weighted mean American orthopedic foot and ankle society score improved from a preoperative score of 68.9±3.2 to a postoperative score of 87.1.The complication rate was 8.4%,the most common of which was persistent joint pain and stiffness.Thirty-two failures(8.7%)were observed.Thirty-three secondary procedures(8.9%)were performed at a weighted mean time of 8.6±3.2 months following the index procedure.CONCLUSION This systematic review demonstrated improvements in subjective clinical outcomes together with a moderate complication rate following MIDC for the management of hallux rigidus at short-term follow-up.A moderate reoperation rate at short-term follow-up was recorded.The marked heterogeneity between included studies and paucity of high quality comparative studies limits the generation of any robust conclusions.

Application Research of PETD Combined with MRI Nerve Root Water Imaging in the Minimally Invasive Treatment of LDH

Objective: This study aims to evaluate the safety and efficacy of PETD combined with nerve root water imaging of MRI for the treatment of lumbar disc herniation. Methods: A retrospective review was performed on 62 patients with lumbar disc herniation from March 2019 to March 2021. The study included an experimental group of 30 patients and a control group of 32 patients. The experimental group underwent PETD combined with nerve root water imaging of MRI, while the control group received traditional PETD treatment. The visual analogue scoring method (VAS score), and JOA lumbar spine function score before and after surgery were compared between the two groups, and efficacy was assessed and compared using the MacNab score. Results: The mean operation time was significantly reduced in the experimental group (56.43 &#177;10.40 minutes) compared to the control group (65.69 &#177;14.12 minutes). The VAS score was compared between the two groups with preoperative (p = 0.624), one month after surgery (p = 0.325), three months after surgery (p = 0.676), one year after surgery (p = 0.341);The JOA score was compared between the two groups with preoperative (p = 0.961), one month after the surgery (p = 0.266), three months after surgery (p = 0.185), one year after surgery (p = 0.870), they were no significant statistical difference;The efficacy evaluation of the last follow-up Macnab showed that all the 30 patients in the experimental group were excellent, 31 of 32 patients in the control group were excellent, 1 case was good;There was no statistical difference in the comparison between the two groups (p > 0.05). Conclusion: The study concludes that the combined approach of PETD with nerve root water imaging of MRI is a safe, effective, and more efficient alternative to conventional PETD for treating lumbar disc herniation.

Potential value of detection of minimal residual disease in colorectal cancer following radical resection

Although there has been significant advancement in the identification and management of colorectal cancer(CRC)in recent years,there is still room for improvement in the current standard treatment regimen.One area of concern is the lack of reliable tumor markers to predict treatment efficacy and guide tailored care.Due to its dynamic,effective,and non-invasive benefits over tissue biopsy,the detection of minimal or molecular residual lesions(MRD)based on circulating tumor DNA(ctDNA)is beneficial to the clinical development of drugs for patients with CRC after radical treatment,as well as for continuous monitoring of tumor recurrence and malignancy molecular gene evolution.The detection of ctDNA can currently be used to guide individual postoperative auxiliary treatment decisions(upgrade or downgrade treatment)in CRC,stratify the risk of clinical recurrence more precisely,and predict the risk of recurrence in advance of imaging examination,according to a large number of observational or prospective clinical studies.With increasing clarity comes the possibility of selecting a regimen of treatment based on postoperative ctDNA,which also improves the accuracy of clinical recurrence risk assessment for CRC.Therefore,it is anticipated that the identification of ctDNA would alter the current framework for dealing with CRC and lead to individualized,stratified precision therapy;however,additional confirmation will require subsequent high-quality,prospective,large-scale randomized controlled studies.This article will provide an overview of the definition and clinical significance of MRD,the primary indications and technological challenges for MRD detection,along with the advancement in clinical research about ctDNA detection following radical resection of the CRC.

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Symmetry of upper eyelid after unilateral blepharoptosis repair with minimally invasive conjoint fascial sheath suspension technique

AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective study of patients who underwent unilateral minimally invasive CFS suspension surgery between January 2018 and December 2021.Inclusion criteria included unilateral mild and moderate ptosis,good levator muscle function(>9 mm)and follow-up of at least 6mo.Pre-and post-operative symmetry was graded subjectively for marginal reflex distance 1(MRD1),tarsal platform show(TPS)and eyebrow fat span(BFS).A t-test was used to evaluate MRD1,TPS and BFS asymmetry by calculating delta values.The Bézier curve tool of the Image J software was used to extract the upper eyelid contours,where the symmetry was measured by the percentage of overlapping curvatures(POC).RESULTS:Totally 105 patients(105 eyelids)were included(mild group,n=84;moderate group,n=21).Postoperatively,all patients increased MRD1 and decreased TPS in the ptotic eye while maintaining unchanged BFS.The asymmetric delta value for MRD1 was measured to be 1.48±0.86 preoperatively,and it decreased to 0.58±0.67 postoperatively in all cases(P=0.0004).In patients with mild ptosis,the asymmetry value of TPS fell significantly from 1.15±0.62 to 0.68±0.38(P=0.0187).The symmetry of the upper eyelid contour increased in all subgroups of patients,with a POC of 59.39%±13.45%preoperatively and POC of 78.29%±13.80%postoperatively.CONCLUSION:Minimally invasive CFS suspension is proved to be an effective means of improving the symmetry of unilateral ptosis in terms of MRD1(all subgroups),POC(all subgroups)and TPS(only mild group),whereas BFS is unaffected.

The clinical application and advancement of robot-assisted McKeown minimally invasive esophagectomy for esophageal cancer

Robotic surgery systems,as emerging minimally invasive approaches,have been increasingly applied for the treatment of esophageal cancer because they provide a high-definition three-dimensional surgical view and mechanical rotating arms that surpass the limitations of human hands,greatly enhancing the accuracy and flexibility of surgical methods.Robot-assisted McKeown esophagectomy(RAME),a common type of robotic esophagectomy,has been gradually implemented with the aim of reducing postoperative complications,improving postoperative recovery and achieving better long-term survival.Multiple centers worldwide have reported and summarized their experiences with the RAME,and some have also discussed and analyzed its perioperative effects and survival prognosis compared with those of video-assisted minimally invasive esophagectomy.Compared to traditional surgery,the RAME has significant advantages in terms of lymph node dissection although there seems to be no difference in overall survival or disease-free survival.With the continuous advancement of technology and the development of robotic technology,further development and innovation are expected in the RAME field.This review elaborates on the prospects of the application and advancement of the RAME to provide a useful reference for clinical practice.