Equality-constrained minimization of polynomial functions

This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.

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.

LIMITED MEMORY QUASI-NEWTON METHOD FOR LARGE-SCALE LINEARLY EQUALITY-CONSTRAINED MINIMIZATION

In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem is solved by using the scaled conjugate gradient method. A truncated solution of the subproblem is determined so that computation is decreased. The technique of limited memory is used to update the approximated inverse Hessian matrix of the Lagrangian function. Hence, the new method is able to handle large dense problems. The convergence of the method is analyzed and numerical results are reported.

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.

Efficacy and safety of minimally invasive laparoscopic surgery under general anesthesia for ovarian cancer

BACKGROUND Ovarian cancer is one of the most common malignant tumors in female reproductive system in the world,and the choice of its treatment is very important for the survival rate and prognosis of patients.Traditional open surgery is the main treatment for ovarian cancer,but it has the disadvantages of big trauma and slow recovery.With the continuous development of minimally invasive technology,minimally invasive laparoscopic surgery under general anesthesia has been gradually applied to the treatment of ovarian cancer because of its advantages of less trauma and quick recovery.However,the efficacy and safety of minimally invasive laparoscopic surgery under general anesthesia in the treatment of ovarian cancer are still controversial.AIM To explore the efficacy and safety of general anesthesia minimally invasive surgery in the treatment of ovarian cancer.METHODS The clinical data of 90 patients with early ovarian cancer in our hospital were analyzed retrospectively.According to the different surgical treatment methods,patients were divided into study group and control group(45 cases in each group).The study group received minimally invasive laparoscopic surgery under general anesthesia for ovarian cancer,while the control group received traditional open surgery for ovarian cancer.The European Organization for Research and Treatment of Cancer Quality of Life Questionnaire(EORTC QLQ-C30),clinical efficacy and safety of the two groups were compared.RESULTS The intraoperative blood loss,length of hospital stay,postoperative gas evacuation time,and postoperative EORTC QLQ-C30 score of the study group were significantly better than those of the control group(P<0.05).The incidence of postoperative complications in the study group was significantly lower than in the control group(P<0.05).The two groups had no significant differences in the preoperative adrenocorticotropic hormone(ACTH),androstenedione(AD),cortisol(Cor),cluster of differentiation 3 positive(CD3+),and cluster of differentiation 4 positive(CD4+)indexes(P>0.05).In contrast,postoperatively,the study group's ACTH,AD,and Cor indexes were lower,and the CD3+and CD4+indexes were higher than those in the control group(P<0.05).CONCLUSION Minimally invasive laparoscopic surgery under general anesthesia in patients with early ovarian cancer can significantly improve the efficacy and safety,improve the short-term prognosis and quality of life of patients,and is worth popularizing.

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.

Minimally invasive reconstruction of extensive mid-lower ureteral strictures using a bilateral Boari flap

Objective:To describe and evaluate the technique using bilateral Boari flap ureteroneocystostomy(BBFUNC)for bilateral mid-lower ureteral strictures.Methods:We retrospectively reviewed five patients who underwent minimally invasive BBFUNC in our institution(Union Hospital,Wuhan,China)between July 2019 and December 2021.The bilateral ureters were mobilized and transected above the stenotic segments.The bladder was isolated and incised longitudinally from the middle of the anterior wall.Then,an inverted U-shaped bladder flap was created on both sides,fixed onto the psoas tendon,and anastomosed to the ipsilateral distal normal ureter.Following double-J stenting,the Boari flaps were tubularized,and the bladder was closed with continuous sutures.The patients’perioperative data and follow-up outcomes were collected,and a descriptive statistical analysis was performed.Results:No case converted to open surgery,and no intraoperative complication occurred.The median surgical time was 230(range 203-294)min.The median length of the bladder flaps was 6.2(range 4.3-10.0)cm on the left and 5.5(range 4.7-10.5)cm on the right side.All patients had not developed recurrent ureteral stenosis during the median follow-up time of 17(range 16-45)months and had a normal maximum flow rate after surgery.The median post-void residual was 7(range 0-19)mL.The maximal bladder capacity was decreased in one(20%)patient.Conclusion:The present study demonstrates that minimally invasive BBFUNC is feasible and safe in treating is limited.

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.