Fixed-Time Consensus-Based Nash Equilibrium Seeking

Dear Editor,This letter examines the fixed-time stability of the Nash equilibrium(NE)in non-cooperative games.We propose a consensus-based NE seeking algorithm for situations where players do not have perfect information and communicate via a topology graph.The proposed algorithm can achieve NE in a fixed time that does not depend on initial conditions and can be adjusted in advance.

Secure Tracking Control via Fixed-Time Convergent Reinforcement Learning for a UAV CPS

Dear Editor,This letter is concerned with the secure tracking control problem in the unmanned aerial vehicle(UAV) system by fixed-time convergent reinforcement learning(RL). By virtue of the zero-sum game,the false data injection(FDI) attacker and secure controller are viewed as game players.

Additive manufactured osseointegrated screws with hierarchical design

Bone screws are devices used to fix implants or bones to bones.However,conventional screws are mechanically fixed with thread and often face long-term failure due to poor osseointegration.To improve osseointegration,screws are evolving from solid and smooth to porous and rough.Additive manufacturing(AM)offers a high degree of manufacturing freedom,enabling the preparation of predesigned screws that are porous and rough.This paper provides an overview of the problems currently faced by bone screws:long-term loosening and screw breakage.Next,advances in osseointegrated screws are summarized hierarchically(sub-micro,micro,and macro).At the sub-microscale level,we describe surface-modification techniques for enhancing osseointegration.At the micro level,we summarize the micro-design parameters that affect the mechanical and biological properties of porous osseointegrated screws,including porosity,pore size,and pore shape.In addition,we highlight three promising pore shapes:triply periodic minimal surface,auxetic structure with negative Poisson ratio,and the Voronoi structure.At the macro level,we outline the strategies of graded design,gradient design,and topology optimization design to improve the mechanical strength of porous osseointegrated screws.Simultaneously,this paper outlines advances in AM technology for enhancing the mechanical properties of porous osseointegrated screws.AM osseointegrated screws with hierarchical design are expected to provide excellent long-term fixation and the required mechanical strength.

Biomechanical effects of posterior lumbar interbody fusion with vertical placement of pedicle screws compared to traditional placement

BACKGROUND The pedicle screw technique is widely employed for vertebral body fixation in the treatment of spinal disorders.However,traditional screw placement methods require the dissection of paraspinal muscles and the insertion of pedicle screws at specific transverse section angles(TSA).Larger TSA angles require more force to pull the muscle tissue,which can increase the risk of surgical trauma and ischemic injury to the lumbar muscles.AIM To study the feasibility of zero-degree TSA vertical pedicle screw technique in the lumbosacral segment.METHODS Finite element models of vertebral bodies and pedicle screw-rod systems were established for the L4-S1 spinal segments.A standard axial load of 500 N and a rotational torque of 10 N/m were applied.Simulated screw pull-out experiment was conducted to observe pedicle screw resistance to pull-out,maximum stress,load-displacement ratio,maximum stress in vertebral bodies,load-displacement ratio in vertebral bodies,and the stress distribution in pedicle screws and vertebral bodies.Differences between the 0-degree and 17-degree TSA were compared.RESULTS At 0-degree TSA,the screw pull-out force decreased by 11.35%compared to that at 17-degree TSA(P<0.05).At 0-degree and 17-degree TSA,the stress range in the screw-rod system was 335.1-657.5 MPa and 242.8-648.5 MPa,separately,which were below the fracture threshold for the screw-rod system(924 MPa).At 0-degree and 17-degree TSA,the stress range in the vertebral bodies was 68.45-78.91 MPa and 39.08-72.73 MPa,separately,which were below the typical bone yield stress range for vertebral bodies(110-125 MPa).At 0-degree TSA,the load-displacement ratio for the vertebral bodies and pedicle screws was slightly lower compared to that at 17-degree TSA,indicating slightly lower stability(P<0.05).CONCLUSION The safety and stability of 0-degree TSA are slightly lower,but the risks of screw-rod system fracture,vertebral body fracture,and rupture are within acceptable limits.

Revised in-depth meta-analysis on the efficacy of robot-assisted versus traditional free-hand pedicle screw insertion

Objective:Robot-assisted pedicle screw insertion has recently emerged as an alternative to the traditional free-hand technique.However,discrepancies in the accuracy of screw placement between the 2 methods have been highlighted by some comparative studies.This meta-analysis was conducted to synthesize evidence comparing these techniques.Methods:Searches were conducted in 5 electronic databases adhering to specific eligibility criteria for randomized and observational studies.The data were analyzed using RevMan software and the results are presented as odds ratios(ORs),mean differences,or standard mean differences(SMDs)with 95%confidence intervals(CIs).Our analysis included 12 studies(7 randomized trials and 5 observational studies,involving 883 patients and 4903 screws).Results:The results demonstrated a higher rate of Grade A Gertzbein and Robbins pedicle placement score(OR:1.77;95%CI:1.10e2.87),a lower rate of revision surgeries(OR:0.21;95%CI:0.09e0.52),and a shorter radiation exposure duration(SMD?1.38,95%CI:2.32 to0.44)in the robot-assisted group compared with the free-hand group.Nonetheless,the length of hospital stay,volume of intraoperative blood loss,postoperative visual analogue scale scores for back pain,and rate of wound infection were similar between the 2 groups.Significant heterogeneity was observed in some outcomes.Conclusion:Compared with the free-hand method,the robot-assisted technique provides greater accuracy and reduced radiation exposure.The efficacy of the robot-assisted technique is expected to improve further as experience with its use in surgery grows.

A Bioequivalence Study of Empagliflozin/Metformin Fixed-Dose Combination in Healthy Subjects under Fasting Conditions

Background: This study evaluated the bioequivalence of empagliflozin 12.5 mg/metformin 1000 mg tablets compared to Synjardy® (Empagliflozin 12.5 mg/metformin 1000 mg) tablets in healthy male subjects under fasting conditions. Methods: This was a phase I, randomized, single-dose, two-period, two-sequence, crossover study to evaluate the bioequivalence (BE) profiles of two fixed-dose combinations (FDCs) of empagliflozin/metformin. Cmax, AUC0-t and AUC0-∞ from test and reference formulations were evaluated to access BE. The plasma concentrations were measured using a validated liquid chromatography-mass spectrometry (LC-MS/MS) method. Of the 24 subjects enrolled, 23 completed both periods of the study. The two formulations test and reference were considered bioequivalent if 90% confidence interval (CI) fell within 80.00% - 125.00% for Cmax, AUC0-t and AUC0-∞. Tolerability and safety were assessed throughout the study. Results: The pharmacokinetic (PK) parameters were similar between the test product (T) and reference product (R) Synjardy®. The 90% CI of the test/reference ratios of log-transformed PK parameters point estimates was Cmax: 89.87% (85.68% - 94.27%), AUC0-t: 87.91% (83.65% - 92.39%) and AUC0-∞: 87.16% (82.80% - 91.75%) to empagliflozin and Cmax: 92.19% (87.95% - 96.65%), AUC0-t: 91.38% (84.42% - 98.91%) and AUC0-∞: 93.78% (83.82% - 104.93%) to metformin respectively (90% CI for all PK parameters fell within 80.00% - 125.00%). Conclusion: Our results demonstrated BE between the test and reference formulations of oral tablets of empagliflozin 12.5 mg/metformin 1000 mg (FDC) in healthy male subjects under fasting conditions.

Effect of the Particle Packing Configuration on Fixed Bed Performance

Fixed-bed reactors are generally considered the optimal choice for numerous multi-phase catalytic reactions due to their excellent performance and stability.However,conventional fixed beds often encounter challenges related to inadequate mass transfer and a high pressure drop caused by the non-uniform void fraction distribution.To enhance the overall performance of fixed beds,the impact of different packing configurations on performance was investigated.Experimental and simulation methods were used to investigate the fluid flow and mass transfer performances of various packed beds under different flow rates.It was found that structured beds exhibited a significantly lower pressure drop per unit length than conventional packed beds.Furthermore,the packing configurations had a critical role in improving the overall performance of fixed beds.Specifically,structured packed beds,particularly the H-2 packing configuration,effectively reduced the pressure drop per unit length and improved the mass transfer efficiency.The H-2 packing configuration consisted of two parallel strips of particles in each layer,with strips arranged perpendicularly between adjacent layers,and the spacing between the strips varied from layer to layer.

Comparative efficacy of proximal femoral nail vs dynamic condylar screw in treating unstable intertrochanteric fractures

BACKGROUND Among the most frequent hip fractures are trochanteric fractures,which usually occur from low-energy trauma like minor falls,especially in older people with osteoporotic bones.AIM To evaluate the treatment efficacy of dynamic condylar screws(DCS)and proximal femoral nails(PFN)for unstable intertrochanteric fractures.METHODS To find pertinent randomized controlled trials and retrospective observational studies comparing PFN with DCS for the management of unstable femoral intertrochanteric fractures,a thorough search was carried out.For research studies published between January 1996 and April 2024,PubMed,EMBASE,Scopus,Web of Science,Cochrane Library,and Google Scholar were all searched.The complete texts of the papers were retrieved,vetted,and independently examined by two investigators.Disputes were settled by consensus,and any disagreements that persisted were arbitrated by a third author.RESULTS This study included six articles,comprising a total of 173 patients.Compared to the DCS,the PFN had a shorter operation time[mean difference(MD):-41.7 min,95%confidence interval(95%CI):-63.04 to-20.35,P=0.0001],higher success rates with closed reduction techniques[risk ratio(RR):34.05,95%CI:11.12-104.31,P<0.00001],and required less intraoperative blood transfusion(MD:-1.4 units,95%CI:-1.80 to-1.00,P<0.00001).Additionally,the PFN showed shorter fracture union time(MD:-6.92 wk,95%CI:-10.27 to-3.57,P<0.0001)and a lower incidence of reoperation(RR:0.37,95%CI:0.17-0.82,P=0.01).However,there was no discernible variation regarding hospital stay,implant-related complications,and infections.CONCLUSION Compared to DCS,PFN offers shorter operative times,reduces the blood transfusions requirements,achieves higher closed reduction success,enables faster fracture healing,and lowers reoperation incidence.

Roller Screw and Threaded Chain Speed Reducer: An Experimental Evaluation

We are developing a speed reducer that can be considered a transformation of a worm gear reducer: the worm is replaced by an inverted roller screw, and the gear is replaced by a threaded chain drive. This configuration lessens wear, increases load capacity, and improves efficiency. The threaded chain consists of nut-shaped links. This paper presents the results of tests carried out on a prototype with a reduction ratio of 46.

Simultaneous Adsorption of Aqueous Pb2+, Cu2+, Zn2+, and Cd2+ Using Surfactant-Modified and Unmodified Activated Carbon in a Fixed Bed Column

The goal of this work is to improve the simultaneous removal of Pb2+, Cu2+, Zn2+, and Cd2+ ions from synthetic wastewater in a fixed bed column by incorporating sodium dodecyl sulfate (SDS) onto the surface of activated carbon made from coconut shells. The activated carbons were characterized using Fourier transform infrared spectroscopy (FT-IR) and scanning electron microscopy-energy dispersive x-ray (SEM-EDX). The adsorption column dynamics were studied by varying the flow rates (5, 10 and 15 mL/min), bed heights (10, 15 and 20 cm), and initial concentrations (50, 150, and 250 mg/L). The activated carbon has a pore volume of 0.715 cm3/g and a BET-specific surface area of 1410 m2/g. Sodium dodecyl sulfate (SDS) surfactant incorporation onto the surface of the activated carbon enhances its capacity for simultaneous adsorption of Pb2+, Cu2+, Zn2+, and Cd2+ from the aqueous medium. The affinity of the heavy metals to both unmodified (AC) and modified (AC-SDS) activated carbons followed the order of Pb2+ > Cu2+ > Zn2+ > Cd2+. The dynamic adsorption of the column depends on the flow rate, bed height, initial metal concentration, and SDS surface modification. With a 5 mL/min flow rate, a 20 cm bed height, and a 50 mg/L initial metal concentration, a maximum break-through time of 150 minutes for the unmodified activated carbon (AC) and 180 minutes for the SDS-modified activated carbon (AC-SDS) was reached.

A Study on the Internal Control and Countermeasures of Fixed Assets in Private Universities:A Case Study of N College

Fixed assets in universities occupy an important position in university management due to their wide coverage and large amount of money.Due to insufficient funding supply,private universities mainly focus on the allocation and utilization of fixed assets,which reflects the overall characteristics of cautious allocation,maximum utilization,and delayed elimination in the actual management of fixed assets.This article aims to conduct research and analysis on the entire lifecycle process of the allocation,use,and disposal of fixed assets in private universities,summarize the problems existing in the internal control of fixed assets in private universities,and propose corresponding countermeasures and suggestions in a targeted manner.

Clinical Effectiveness of the Plate Screw Internal Fixation Technique in the Treatment of Patients with Traumatic Fractures of Long Bones in the Lower Extremities

Objective: To investigate the effectiveness of the plate screw internal fixation technique on the clinical outcomes of patients with traumatic fractures of long bones in the lower extremities. Methods: From January 2022 to December 2023, 70 patients with traumatic fractures of long bones in the lower extremities were admitted to the hospital and randomly divided into two groups: the control group and the observation group, each consisting of 35 cases. The control group underwent traditional closed interlocking intramedullary nailing, while the observation group received internal fixation with steel plates and screws. Relevant surgical indicators, treatment effectiveness, and postoperative complication rates were compared between the two groups. Results: The observation group exhibited significantly short surgical duration (80.65 ± 5.01 vs. 88.36 ± 5.26 minutes), fracture healing time (13.27 ± 0.32 vs. 15.52 ± 0.48 weeks), and hospitalization days (10.49 ± 1.13 vs. 16.57 ± 1.15 days) compared to the control group (P = 0.000). The effective treatment rate was significantly higher in the observation group (29/82.86%) than in the control group (21/60.00%), with a significant difference observed (χ2 = 4.480, P = 0.034). Additionally, the complication rate in the observation group (2/5.71%) was significantly lower than that in the control group (8/22.86%), with a correlated difference (χ2 = 4.200, P = 0.040). Conclusion: The plate screw internal fixation technique demonstrates significant clinical efficacy in treating traumatic fractures of long bones in the lower extremities. It improves the healing rate, reduces complications, and represents a safe and effective treatment strategy worthy of widespread use and application.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

Vision-Based Fixed-Time Uncooperative Aerial Target Tracking for UAV

Dear Editor,In this letter,a vision-based fixed-time control is proposed for an unmanned aerial vehicle(UAV)with actuator saturation to track an uncooperative target.The fixed-time control is designed in backstepping framework.The relative states between UAV and the target are not directly measured,and are estimated by an onboard monocular camera.

The Effects of Bone Screw Configurations on the Interfragmentary Movement in a Long Bone Fixed by a Limited Contact Locking Compression Plate

The locking compression plates (LCP) are efficient tools in open reduction and internal fixation (ORIF), especially in osteoporotic bones. Two important factors of screw density and screw position can affect the functionality of the bone plate. Several studies have assessed the influence of the screw configurations on the bone-plate stiffness, but the effects of screw positions on the interfragmentary strain, εIF of LCP construct have not been investigated yet. In this study, finite element method was used to investigate the influence of screws number and position on the interfragmentary strain of LCP-femur system for a mid-shaft fracture. Results of this study showed that by insertion of screws closer to the fracture site, εIF decreases by 2nd degree polynomial function versus screw position, but by adding the screws from the ends of the plate, or by moving and placing the screws towards the fracture site, the reduction of εIF will be linear. Results of this study were compared and are in agreement with some studies in the literature, even though their scope was mostly stability of the bone-implant system, whereas our scope was focused on the interfragmentary strain.

Effect of screw position on bone tissue differentiation within a fixed femoral fracture

Plate and screw constructs are routinely used in the treatment of long bone fractures. Despite considerable advancements in technology and techniques, there can still be complications in the healing of long bone fractures. Non-unions, delayed unions, and hardware failures are common complications observed in clinical practice following open reduction and internal fixation of fractures [1]. Potential causes of these adverse clinical effects may be disruptive to the periosteal and endosteal blood supply, stress shielding effects, and inadequate mechanical stability. The goal of the present study was to explore the effect of screw position on the fracture healing and formation of new bone tissue with mechanoregulatory algorithms in a computational model. An idealized poroelastic 3D finite element (FE) model of a femur with a 5 mm fracture gap, including a plate-screw construct was developed. Nineteen different plate-screw combinations, created by varying the number and position of screws within the plate, were created to identify a construct with the most favourable attributes for fracture healing. The first phase of the study evaluated constructs through mechanical stress analyses to identify those constructs with high loadsupport capability. The second phase of the study evaluated healing and bone formation with a biphasic mechanoregulatory algorithm to simulate tissue differentiation for fixation within selected constructs. The results of our analysis demonstrated a 4-screw symmetrical construct with the largest distance between screws to provide the most favourable balance of stability and optimized conditions to promote fracture healing.

Relay-Switching-Based Fixed-Time Tracking Controller for Nonholonomic State-Constrained Systems:Design and Experiment

Dear Editor,This letter investigates the fixed-time trajectory tracking controller design for nonholonomic chained systems with static state constraints.Firstly,a fixed-time tracking control law is given to carry out relay switching,which divides the controller development process into two stages.

Fatigue Life Analysis of Fixed Structure of Posterior Thoracolumbar Pedicle Screw

In order to analyze the fatigue life of the posterior thoracolumbar fixed structure, a loading model was established in accordance with the anti-fatigue test requirements specified by ASTM Standard F1717-04. Two three-dimensional Models of the fixed structure with two bars and four bars were built by 3D software (UG), and imported into ANSYS software for static analysis. The maximum and minimum stresses of risk nodes under different loads and moments were obtained. The fatigue life was then calculated using relevant mathematical formula of S-N curve and Goodman curve. It was found that the stress at the middle of the crossbeam between the two bars is larger than the surroundings and is liable to suffer from fatigue.

Distal clavicle fractures treated by anteroinferior plating with a single screw: Two case reports

BACKGROUND For the treatment of distal clavicle fractures,each treatment method has its own advantages and disadvantages,and there is no optimal surgical solution.CASE SUMMARY Based on this,we report 2 cases of distal clavicle fractures treated utilizing an anterior inferior plate with a single screw placed in the distal,in anticipation of providing a better surgical approach to distal clavicle fracture treatment.Two patients were admitted to the hospital after trauma with a diagnosis of distal clavicle fracture,and were admitted to the hospital for internal fixation of clavicle fracture by incision and reduction,with good postoperative functional recovery.CONCLUSION With solid postoperative fixation and satisfactory prognostic functional recovery,this technique has been shown to be simple,easy to perform and effective.

Multitrack and multianchor point screw technique combined with the Wiltse approach for lesion debridement for lumbar tuberculosis

BACKGROUND The incidence of lumbar tuberculosis is high worldwide,and effective treatment is a continuing problem.AIM To study the safety and efficacy of the multitrack and multianchor point screw technique combined with the contralateral Wiltse approach for lesion debridement to treat lumbar tuberculosis.METHODS The C-reactive protein(CRP)level,erythrocyte sedimentation rate(ESR),visual analogue scale(VAS)score,oswestry disability index(ODI)and American Spinal Injury Association(ASIA)grade were recorded and analysed pre-and postoperatively.RESULTS The CRP level and ESR returned to normal,and the VAS score and ODI were decreased at 3 mo postoperatively,with significant differences compared with the preoperative values(P<0.01).Neurological dysfunction was relieved,and the ASIA grade increased,with no adverse events.CONCLUSION The multitrack,multianchor point screw fixation technique combined with the contralateral Wiltse approach for debridement is an effective and safe method for the treatment of lumbar tuberculosis.