Kinematic Variables Research Articles

Correlated variables and changes in fascial stiffness and pelvic mobility following the myofascial induction method utilizing the crossed hands technique

BackgroundMyofascial Induction Therapy (MIT) is a physiotherapeutic (PT) intervention addressing musculoskeletal disorders. Standardizing MIT as a manual PT intervention ensures consistency and replicability. AimTo describe correlated variables and changes in fascial stiffness and pelvic mobility after applying the Crossed Hands Technique based on MIT. MethodsA quasi-experimental study involved 15 PTs trained in myofascial induction and 15 healthy individuals. Environmental (ambient temperature, stretcher height, width), patient (subscapular fatty fold, BMI, height, chest length, lumbopelvic mobility, fascial stiffness), and PT variables (pressure, traction, hand temperature, kinematic changes) were assessed during lumbodorsal hands-cross at 1-min intervals for 5 min. Pelvic mobility was measured using kinovea photogrammetry and dorsolumbar stiffness using a durometer. Descriptive analysis and correlations were applied. ResultsPTs had a mean 5.3 years of MIT experience. The average force was 5.5 N, traction force 0.39 N. Post-technique, individuals showed 4° increased pelvic mobility, minimal stiffness changes at T7 and L4 levels. Kinematic variables for the PTs revealed an average shoulder flexion of 40° and bilateral elbow flexion of 18°. Following the application of the technique, individuals who received MIT experienced a 4° increase in pelvic mobility, with only minor changes in stiffness observed at both the T7 and L4 levels. ConclusionsThe Crossed Hands Technique involves key variables like force and traction, varying over time. Clinical outcomes are influenced by patient and environmental factors. Notably, the physiotherapist's hand temperature, right shoulder internal rotation, right foot abduction, and fourth finger opening show significant correlations with tissue stiffness changes.

The geometry of interpersonal synchrony in human dance

Collective synchronized behavior has powerful social-communicative functions observed across several animal taxa.1,2,3,4,5,6,7 Operationally, synchronized behavior can be explained by individuals responding to shared external cues (e.g., light, sound, or food) as well as by inter-individual adaptation.3,8,9,10,11 We contrasted these accounts in the context of a universal human practice-collective dance-by recording full-body kinematics from dyads of laypersons freely dancing to music in a "silent disco" setting. We orthogonally manipulated musical input (whether participants were dancing to the same, synchronous music) and visual contact (whether participants could see their dancing partner). Using a data-driven method, we decomposed full-body kinematics of 70 participants into 15 principal movement patterns, reminiscent of common dance moves, explaining over 95% of kinematic variance. We find that both music and partners drive synchrony, but through distinct dance moves. This leads to distinct kinds of synchrony that occur in parallel by virtue of a geometric organization: anteroposterior movements such as head bobs synchronize through music, while hand gestures and full-body lateral movements synchronize through visual contact. One specific dance move-vertical bounce-emerged as a supramodal pacesetter of coordination, synchronizing through both music and visual contact, and at the pace of the musical beat. These findings reveal that synchrony in human dance is independently supported by shared musical input and inter-individual adaptation. The independence between these drivers of synchrony hinges on a geometric organization, enabling dancers to synchronize to music and partners simultaneously by allocating distinct synchronies to distinct spatial axes and body parts.

Analysis of Kinematic Variables According to Menstrual Cycle Phase and Running Intensity: Implications for Training Female Athletes

Depending on the phase of the menstrual cycle, different values of running kinematic variables can be obtained. The aim of this study is to analyze whether there are changes in the kinematic variables in running throughout the menstrual cycle and to relate them to running performance and injury prevention. Eight regular female runners and triathletes performed a maximal treadmill test, as well as a submaximal test (6′ stages at 50%, 60% and 80% of maximal aerobic speed) in each of the phases of the menstrual cycle: menstruation phase (day 2.4 ± 0.7), follicular phase (day 10.4 ± 2.2) and luteal phase (day 21.8 ± 2.1). Running dynamics were measured using RunScribe. For parametric data, a general linear model of repeated measures was applied, with two intrasubject independent variables, menstrual cycle phases (with three levels: Menstruation, Follicular, and Luteal) and running intensity (with four levels relative to the maximum speed reached in the test: 100%, 80%, 60%, and 50%). For variables with non-normal distributions, Friedman tests were performed with Wilcoxon post-tests adjusted for significance according to Bonferroni. The maximum stance velocity from foot strike to the point of maximum pronation (°/s) was higher in the menstruation phase than in the follicular and luteal phases (p = 0.008), the step rate (s/min) was higher in the follicular phase than in the menstruation and luteal phases (p = 0.049), the vertical velocity (m/s) was lower in the follicular phase than in the menstruation (p = 0.004) and luteal phases (p = 0.003), and the contact time (ms) was lower in the luteal phase than in the menstruation and follicular phases. These results suggest that training at high intensities could be a factor in greater risk of injury in female athletes, especially in the menstruation phase, finding in the luteal phase and at an intensity of 80% a greater efficiency in the running.

Evaluation of forelimb gait variation overground at a walk in sound and lame dogs using a combination of diagnostic techniques

BackgroundKinetic and kinematic gait analysis is increasingly practised as a part of lameness evaluation in dogs. The aim of this study was to examine the normal short- and long-term variation in forelimb gait in sound control dogs (CD) at a walk using seven selected variables of objective kinetic and kinematic gait analyses. Also, to compare the findings in CD to a group of forelimb lame dogs with elbow osteoarthritis (OAD). An additional aim was to test a kinetic based graphic method for lameness detection; symmetry squares (SS). A prospective longitudinal study was carried out on client owned CD and OAD. Clinical and orthopaedic evaluations were performed to ensure soundness and detect and grade lameness. Seven kinetic and kinematic variables and SS were tested for lameness evaluation. The CD were divided into two subgroups, CD1 and CD2, and examined twice: CD1 with two months interval and CD2 with 3–4 h interval. The OAD group was evaluated once and compared to the CD groups’ first examination.ResultsThirteen CD and 19 OAD were included. For CD1 and CD2, there were no significant differences in any examined variable between examination occasions. Total peak force/impulse symmetry and fore-hind peak force/impulse symmetry differed significantly between OAD and CD. Symmetry squares had a 74% agreement to subjective orthopaedic evaluations.ConclusionsIn CD, no difference in the examined variables was seen between examination occasions. Four out of seven objective variables differed significantly between CD and OAD. The graphic SS method might have diagnostic potential for lameness detection, making it possible to detect a shift from lame to non-lame limbs. Potentially, this might be especially helpful in bilaterally lame dogs, which often represent a clinical challenge in lameness evaluation.

Predicting pedalling metrics based on lower limb joint kinematics

This study aimed to predict the index of effectiveness (IE) and positive impulse proportion (PIP) to assess the cyclist’s pedalling technique from lower limb kinematic variables. Several wrapped feature selection techniques were applied to select the best predictors. To predict IE and PIP two multiple linear regressions (MLR) composed of 11 predictors (R² = 0.81 ± 0.12, R² = 0.81 ± 0.05) and two artificial neural networks (ANN) composed of 21 and 28 predictors (R² = 0.95 ± 0.01, R² = 0.92 ± 0.02) were developed. The ANN predicts with accuracy, and the MLR shows the influence of each predictor.

Consistency of sex-based differences between treadmill and overground running using an inertial measurement unit (IMU)

Differences in running gait between treadmill and overground running has been subject of study, while consistency of group differences between running surfaces has not been previously analysed. This study examined both the differences between running surfaces and the consistency of sex-based differences between surfaces in some spatiotemporal and kinematic variables measured by an inertial measurement unit fastened over the lumbar spine. Thirty-two (sixteen females) endurance runners firstly performed overground and then treadmill (1 % inclination) runs at speeds between 9–21 km∙h−1. Males showed lower flight time (FT) [moderate effect size (ES)] during treadmill running compared to overground, while females showed greater stride frequency (SF) (moderate ES), lower stride length (SL) (moderate ES), FT (moderate ES), and vertical (VT) trunk displacement (moderate ES), as well as greater medio-lateral (ML) trunk displacement (moderate ES). No differences in CT between surfaces were found (trivial to small). Furthermore, all the sex-differences were consistent between treadmill and overground running: Males showed lower SF (large and moderate ES, respectively), greater SL (large and moderate ES) and CT (moderate and large ES), lower FT (large ES), greater VT displacement (moderate to large ES), and lower ML displacement (moderate ES) than females. These results may be of interest to carefully transfer the running gait analyses between surfaces depending on sex.

Sports Performance Analysis of Wheelchair Basketball Players Considering Functional Classification

Wheelchair basketball (WB) is a sport modality adapted for people with disabilities who present functional classification (FC) according to their mobility, from 1.0 for players with lesser functional capacity up to 4.5 for great mobility and trunk control players. This study aimed to analyze and compare the external load (EL) and the internal load (IL) of the WB players according to their FC in 5 × 5 simulation game tasks. The main objective of this task was to develop a simulated game in which two teams of five players faced each other to resemble the physical demands of an official match. The development of these tasks allowed for the players to learn the different systems of play, and to improve tactical skills. To conduct the study, 12 (male) national professional WB players (years: 30.7 ± 4.82 and WB experience: 5 ± 1.43) participated in the study and were grouped according to FC. WIMU PROTM devices monitored the EL manufactured by RealTrack Systems in Almería, Spain, and to measure the player’s IL, GarminTM Heart Rate (HR) bands were used (GarminTM in Olathe, KS, USA). The EL variables were divided as kinematic (distance, explosive distance, acc, dec, max. acc, max. dec, average speed, max. speed) and neuromuscular (player load, impact). The IL variables were average HR, max. HR and %max. HR. The main results show that players with greater functional capacity (FC = 4.0) developed higher values in the IL and neuromuscular variables analyzed (p < 0.05), as well as in some kinematic variables like distance, dec and average speed (p < 0.05). This information is relevant because it helps to personalize the training load based on competitive demands and create a gradual and adaptable training program. This information helps athletes to develop better performance during training and prevent injuries caused by overexertion.

Sensitivity of principal component analysis outcomes to data pre-processing conditions when quantifying trial-to-trial variability in whole-body kinematics

This study investigated whether modes of variance in trial-to-trial whole-body kinematic variability identified by principal component analysis (PCA) were consistent across data pre-processing conditions generated from a common dataset. Comparisons made included 1) when trajectory data was expressed in a global vs. local reference frame; 2) when the number of landmarks used to represent whole-body motion differed, and; 3) whether input trajectory data were normalized to participant stature. Varying data pre-processing conditions prior to PCA does not bias the total variance identified. However, it can influence how modes of variance are dispersed across PCs, which in turn, can influence interpretation.

Preliminary Virtual Constraint-Based Control Evaluation on a Pediatric Lower-Limb Exoskeleton.

Pediatric gait rehabilitation and guidance strategies using robotic exoskeletons require a controller that encourages user volitional control and participation while guiding the wearer towards a stable gait cycle. Virtual constraint-based controllers have created stable gait cycles in bipedal robotic systems and have seen recent use in assistive exoskeletons. This paper evaluates a virtual constraint-based controller for pediatric gait guidance through comparison with a traditional time-dependent position tracking controller on a newly developed exoskeleton system. Walking experiments were performed with a healthy child subject wearing the exoskeleton under proportional-derivative control, virtual constraint-based control, and while unpowered. The participant questionnaires assessed the perceived exertion and controller usability measures, while sensors provided kinematic, control torque, and muscle activation data. The virtual constraint-based controller resulted in a gait similar to the proportional-derivative controlled gait but reduced the variability in the gait kinematics by 36.72% and 16.28% relative to unassisted gait in the hips and knees, respectively. The virtual constraint-based controller also used 35.89% and 4.44% less rms torque per gait cycle in the hips and knees, respectively. The user feedback indicated that the virtual constraint-based controller was intuitive and easy to utilize relative to the proportional-derivative controller. These results indicate that virtual constraint-based control has favorable characteristics for robot-assisted gait guidance.

A comparison study of myoelectric regression performances when estimating different types of joint kinematic data

Myoelectric control is used in assistive devices such as powered prostheses or exoskeletons, and advances in this area could greatly improve the quality of life for individuals with motor disabilities. Regression machine learning models have been studied to provide a more natural and intuitive control of these devices. Such models have often been applied to estimate joint kinematic variables like angles, angular velocities, and accelerations, with the former receiving considerably more attention in the literature. Despite this prevailing focus, we proposed that employing velocities or accelerations as the target variable of myoelectric regressors instead of angles could lead to better regression performances. To investigate this, our study compares the performance of electromyogram (EMG) regressors in predicting each of these three joint kinematic variables. A comprehensive comparison was conducted, including different regression models, feature extraction methods, conditions, joints, and performance metrics. Overall, the performances of models estimating joint angular velocities or accelerations were consistently superior to those estimating angles. However, the differences between angular velocities and accelerations often were small and lacked statistical significance. These results were observed for most models, features, and conditions, not just the best-performing ones (which were: models = convolutional neural networks; features = waveform length, difference absolute mean value, and Willison amplitude; and conditions = wider and faster movements). Several factors were proposed to explain these findings in the context of current literature, including aspects of the EMG-kinematic signals relationships, kinematic waveform properties, studied movements, and the process for obtaining kinematic variables. Based on the results and discussion, recommendations for future works were made, and areas for further research were suggested, both aiming at improving myoelectric assistive technologies.

Accuracy, Validity, and Reliability of Markerless Camera-Based 3D Motion Capture Systems versus Marker-Based 3D Motion Capture Systems in Gait Analysis: A Systematic Review and Meta-Analysis.

(1) Background: Marker-based 3D motion capture systems (MBS) are considered the gold standard in gait analysis. However, they have limitations for which markerless camera-based 3D motion capture systems (MCBS) could provide a solution. The aim of this systematic review and meta-analysis is to compare the accuracy, validity, and reliability of MCBS and MBS. (2) Methods: A total of 2047 papers were systematically searched according to PRISMA guidelines on 7 February 2024, in two different databases: Pubmed (1339) and WoS (708). The COSMIN-tool and EBRO guidelines were used to assess risk of bias and level of evidence. (3) Results: After full text screening, 22 papers were included. Spatiotemporal parameters showed overall good to excellent accuracy, validity, and reliability. For kinematic variables, hip and knee showed moderate to excellent agreement between the systems, while for the ankle joint, poor concurrent validity and reliability were measured. The accuracy and concurrent validity of walking speed were considered excellent in all cases, with only a small bias. The meta-analysis of the inter-rater reliability and concurrent validity of walking speed, step time, and step length resulted in a good-to-excellent intraclass correlation coefficient (ICC) (0.81; 0.98). (4) Discussion and conclusions: MCBS are comparable in terms of accuracy, concurrent validity, and reliability to MBS in spatiotemporal parameters. Additionally, kinematic parameters for hip and knee in the sagittal plane are considered most valid and reliable but lack valid and accurate measurement outcomes in transverse and frontal planes. Customization and standardization of methodological procedures are necessary for future research to adequately compare protocols in clinical settings, with more attention to patient populations.

Head Kinematics and Injury Analysis in Elite Bobsleigh Athletes Throughout a World Cup Tour.

The neurocognitive health effects of repetitive head impacts have been examined in many sports. However, characterizations of head impacts for sliding-sport athletes are lacking. To describe head impact kinematics and injury epidemiology in elite athletes during the 2021-2022 Bobsleigh World Cup season. Cross-sectional study. On-track training and competitions during the Bobsleigh World Cup season. Twelve elite bobsleigh athletes (3 pilots [1 female], 9 push athletes [5 females]; age = 30 ± 5 years; female height and weight = 173 ± 8 cm and 75 ± 5 kg, respectively; male height and weight = 183 ± 5 cm and 101 ± 5 kg, respectively). Athletes wore an accelerometer-enabled mouthguard to quantify 6-degrees-of-freedom head impact kinematics. Isometric absolute and relative neck strength, number of head acceleration events (HAEs), workload (J), peak linear velocity (m·s-1), peak angular velocity (rad·s-1), peak linear acceleration (g), and peak angular acceleration (rad·s-2) were derived from mouthguard manufacturer algorithms. Linear mixed-effect models tested the effects of sex (male versus female), setting (training versus competition), and position (pilot versus push athlete) on the kinematic variables. A total of 1900 HAEs were recorded over 48 training and 53 competition days. No differences were found between the number of HAEs per run per athlete by sex (incidence rate ratio [IRR] = 0.82, P = .741), setting (IRR = 0.94, P = .325), or position (IRR = 1.64, P = .463). No sex differences were observed for workload (mean ± SD: males = 3.3 ± 2.2 J, females = 3.1 ± 1.9 J; P = .646), peak linear velocity (males = 1.1 ± 0.3 m·s-1, females = 1.1 ± 0.3 m·s-1; P = .706), peak angular velocity (males = 4.2 ± 2.1 rad·s-1, females = 4.7 ± 2.5 rad·s-1; P = .220), peak linear acceleration (male = 12.4 ± 3.9g, females = 11.9 ± 3.5g; P = .772), or peak angular acceleration (males = 610 ± 353 rad·s-2, females = 680 ± 423 rad·s-2; P = .547). Also, no effects of setting or position on any kinematic variables were seen. Male athletes had greater peak neck strength than female athletes for all neck movements, aside from right-side flexion (P = .085), but no sex differences were noted in relative neck strength. We provide a foundational understanding of the repetitive HAEs that occur in bobsleigh athletes. Future authors should determine the effects of repetitive head impacts on neurocognitive function and mental health.

The effect of ballistic exercises on some kinematic variables and the development of special physical characteristics for the front straight punch skill for karate juniors

The effect of ballistic exercises on some kinematic variables and the development of special physical characteristics for the front straight punch skill for karate juniors

Machine Learning Investigation of Downburst-Prone Environments in Canada

Abstract Thunderstorms are recognized as one of the most disastrous weather threats in Canada because of their power to cause substantial damage to human-made structures and even result in fatalities. It is therefore essential for operational forecasting to diagnose thunderstorms that generate damaging downdrafts of negatively buoyant air, known as downbursts. This study develops several machine learning models to identify environments supportive of downbursts in Canada. The models are trained and evaluated using 38 convective parameters calculated based on ERA5 reanalysis vertical profiles prior to thunderstorms with (306 cases) and without (19 132 cases) downbursts across Canada. Various resampling techniques are implemented to adjust data imbalance. An increase in the performance of the random forest (RF) model is observed when the support vector machine synthetic minority oversampling technique is utilized. The RF model outperforms other tested models, as indicated by model performance metrics and calibration. Several model interpretability methods highlight that the RF model has learned physical trends and patterns from the input variables. Moreover, the thermodynamic parameters are deemed to have higher impacts on the model outcomes compared to parcel, kinematic, and composite variables. For example, a considerable rise in the downburst probability is detected with an increase in cold pool strength. This study serves as one of the earliest attempts toward the fledgling field of machine learning applications in weather forecasting systems in Canada. The findings suggest that the developed model has the potential to enhance the effectiveness of issuing severe thunderstorm warnings in Canada, although further assessment with operational meteorologists is needed to validate its practical application. Significance Statement Severe thunderstorms demand particular attention in forecasting as their outflow can pose a serious threat to both structures and human life. This study uses machine learning techniques to predict whether or not a thunderstorm generates a damaging outflow in Canada. Atmospheric conditions that could trigger a severe thunderstorm are identified and discussed. Results show that the models have the potential to assist forecasters in better analyzing and predicting thunderstorms that generate destructive winds. Consequently, taking advantage of promising machine learning tools can yield more reliable forecasts of damaging thunderstorms, thereby mitigating the economic and societal burdens of these storms on Canadian communities.

Evaluating the Repeatability of Musculoskeletal Modelling Force Outcomes in Gait among Chronic Stroke Survivors: Implications for Contemporary Clinical Practice

This study aims to evaluate the consistency of musculoskeletal modelling outcomes during walking in chronic post-stroke patients, focusing on both affected and unaffected sides. Understanding the specific muscle forces involved is crucial for designing targeted rehabilitation strategies to improve balance and mobility after a stroke. Musculoskeletal modelling provides valuable insights into muscle and joint loading, aiding clinicians in analysing essential biomarkers and enhancing patients’ functional outcomes. However, the repeatability of these modelling outcomes in stroke gait has not been thoroughly explored until now. Twelve post-stroke, hemiparetic survivors were included in the study, which consisted of a gait analysis protocol to capture kinematic and kinetic variables. Two generic full body MSK models—Hamner (Ham) and Rajagopal (Raj)—were used to compute joint angles and muscle forces during walking, with combinations of two muscle force estimation algorithms (Static Optimisation (SO) and Computed Muscle Control (CMC)) and different joint degrees-of-freedoms (DOF). The multiple correlation coefficient (MCCoef) was used to compute repeatability for all forces, grouped based on anatomical function. Regardless of models and DOFs, the mean minimum (0.75) and maximum (0.94) MCCoefs denote moderate-to-excellent repeatability for all muscle groups. The combination of the Ham model and SO provided the most repeatable muscle force estimations of all the muscle groups except for the hip flexors, adductors and internal rotators. DOF configuration did not generally affect muscle force repeatability in the Ham–SO case, although the 311 seemed to relate to the highest values. Lastly, the DOF setting had a significant effect on some muscle groups’ force output, with the highest magnitudes reported for the 321 and 322 of non-paretic and paretic hip adductors and extensors, knee flexors and ankle dorsiflexors and paretic knee flexors. The primary findings of our study can assist users in selecting the most suitable modelling workflow and encourage the widespread adoption of MSK modelling in clinical practice.

CSP2023: 414 - Spinal kinematic variability is increased in people with chronic low back pain

CSP2023: 414 - Spinal kinematic variability is increased in people with chronic low back pain

Peridynamic differential operator for stress analysis of imperfect functionally graded porous sandwich beams based on refined zigzag theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

Space and players' number constrains the external and internal load demands in youth futsal.

The aim of this study was to analyze the effects of space and number of players manipulation on the external and internal load demands of youth futsal athletes. Forty-two male U17 players (age = 15.62 ± 0.58 years) from three futsal teams participated in the study. In this cross-sectional study that lasted 8-week, the player's sample practiced six futsal tasks (T1-T6) and a futsal game played under the official rules (T7). From T1-T6, two task constraints were manipulated: (i) the number of players and, (ii) the space of play. The WIMU PRO™ Ultra-Wideband (UWB) tracking system was used to measure the external and internal load during the futsal tasks. External load was quantified using kinematic and mechanical variables extracted from positional data and, the internal load was quantified using Heart rate (HR) and rating of perceived exertion (RPE). Repeated measures ANOVA was used for comparison purposes. In general, the results showed high external (total distance, distance 18.1-21, above 21 Km/h, and high intensity acceleration and deceleration, p < 0.001) and internal load (heart rate average and rating of perceived exertion, p < 0.001) in the tasks with low number of players and high area. In relation to the match, the tasks with small relative area per player (GK + 2 vs. 2 + GK and GK + 3 vs. 3 + GK in 20 × 20 m) promoted low external load. It was concluded that increasing the relative area by reducing the number of players involved in the tasks in the form of small-sided games (GK + 2 vs. 2 + GK and GK + 3 vs. 3 + GK), in relation to the futsal game (GK + 4 vs. 4 + GK), can be considered a pedagogical strategy to increase the external and internal load demands of young futsal players.

FIRE 6.5: Feynman integral reduction with new simplification library

FIRE is a program which performs integration-by-parts (IBP) reductions of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an upgrade of FIRE which incorporates a new library FUEL initially described in a separate publication, which enables a flexible choice of third-party computer algebra systems as simplifiers, as well as efficient communications with some of the simplifiers as C++ libraries rather than through Unix pipes. We achieve significant speedups for IBP reductions of Feynman integrals involving many kinematic variables, when using an open source backend based on FLINT newly added in this work, or the Symbolica backend developed by Ben Ruijl as a potential successor of FORM. Program summaryProgram title: FIRE, version 6.5 (FIRE 6.5)CPC Library link to program files:https://doi.org/10.17632/cy6k69pb3y.2Developer's repository link:https://gitlab.com/feynmanintegrals/fire.gitLicensing provisions: GPLv2Programming language:Wolfram Mathematica 8.0 or higher, C++17Supplementary material: See linked repository for installation instructions.Journal reference of previous version: Comput. Phys. Commun. 247 (2020) 106877Does the new version supersede the previous version?: Yes.Reasons for the new version: The new version no longer relies on a single computer algebra system, Fermat [1], but instead allows a flexible choice of several systems, some of which offer higher performance, especially when the number of variables is large.Summary of revisions: A new library FUEL [2] is used as a core component of the new version of FIRE to access different computer algebra systems as simplifiers of rational function expressions. Since the first release of FUEL described elsewhere, FUEL version 1.0 here has been enhanced with a new backend based on the open source library FLINT [3] that provides highly performant simplification of rational functions.Nature of problem: Feynman integrals of a given family are reduced to a finite set of master integrals, by solving linear equations arising from integration by parts, using Gaussian elimination. The coefficients of the linear equations are generally rational functions in kinematic variables and the spacetime dimension, and the simplification of such rational functions during Gaussian elimination is a key task that is improved in this upgrade of FIRE.Solution method: Computer algebra systems with state-of-the-art capabilities for polynomial GCD computations are used as simplification backends, or simplifiers in short. Due to the design of FIRE, text strings are used as the exchange format for rational functions before and after simplification. A fast C++ parser is written to parse strings into the internal format of an external simplifer, FLINT [3], with state-of-the-art performance for multivariate polynomial calculations. Similarly, the simplifier Symbolica [4] has high performance in both GCD computations and parsing, and has been integrated into FIRE.

Measurement of associated J/ψ-ψ(2S) production cross-section in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV

The cross-section of associated J/ψ-ψ(2S) production in proton-proton collisions at a centre-of-mass energy of s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV is measured using a data sample corresponding to an integrated luminosity of 4.2 fb−1, collected by the LHCb experiment. The measurement is performed for both J/ψ and ψ(2S) mesons having transverse momentum pT< 14 GeV/c and rapidity 2.0 < y < 4.5, assuming negligible polarisation of the J/ψ and ψ(2S) mesons. The production cross-section is measured to be 4.5 ± 0.7 ± 0.3 nb, where the first uncertainty is statistical and the second systematic. The differential cross-sections are measured as functions of several kinematic variables of the J/ψ-ψ(2S) candidates. The results are combined with a measurement of J/ψ-J/ψ production, giving a cross-section ratio between J/ψ-ψ(2S) and J/ψ-J/ψ production of 0.274 ± 0.044 ± 0.008, where the first uncertainty is statistical and the second systematic.