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Search Results (251)

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15 pages, 28225 KB  
Article
CBCT-Based Epidemiological Study of Root and Root Canal Anatomy in Mandibular Second Molars in an Italian Clinical Cohort
by Katia Greco, Riccardo Federico Visconti, Gaetano Paolone, Maria Teresa Sberna, Enrico Felice Gherlone and Giuseppe Cantatore
J. Clin. Med. 2026, 15(10), 3688; https://doi.org/10.3390/jcm15103688 - 11 May 2026
Viewed by 63
Abstract
Background: Mandibular second molars show notable variability in root canal structures and C-shaped morphology, with possible differences among populations. Methods: This retrospective cross-sectional CBCT study included 500 patients attending the Department of Dentistry at IRCCS Ospedale San Raffaele (Milan, Italy) with [...] Read more.
Background: Mandibular second molars show notable variability in root canal structures and C-shaped morphology, with possible differences among populations. Methods: This retrospective cross-sectional CBCT study included 500 patients attending the Department of Dentistry at IRCCS Ospedale San Raffaele (Milan, Italy) with bilateral mandibular second molars and was reported according to STROBE guidelines. CBCT scans (Hyperion X5; voxel size 0.125 mm) were assessed by two endodontists using standardized criteria. Root-based canal configurations were classified according to Vertucci in cases with complete bilateral coding of homologous mesial and distal roots; C-shaped morphology was classified using Fan’s system and analyzed separately because Vertucci coding is not applicable to C-shaped systems. Categorical variables were analyzed using χ2 or Fisher’s exact test, continuous variables with parametric or non-parametric tests, and right–left comparisons with paired-sample tests (p < 0.05). Results: Complete bilateral Vertucci coding was feasible in 494/500 patients (98.8%), yielding 988 mesial and 988 distal roots for analysis. C-shaped canal configuration was detected in 1.2% of patients (6/500; 95% CI 0.44–2.59%); females showed a higher proportion than males (2.0% vs. 0.4%), with no evidence of a sex association (Fisher’s exact test, p = 0.216). Fan subtype annotation was available for 5/6 patients and 7 teeth; C1, C3, and C4 patterns were observed. In the Vertucci dataset, mesial roots most frequently exhibited Types II (52.0%) and IV (26.5%), whereas distal roots were predominantly Type I (62.4%), followed by Type III (29.8%). Contralateral symmetry was observed in 27.3% of mesial roots (135/494; 95% CI 23.4–31.5%) and 59.1% of distal roots (292/494; 95% CI 54.6–63.5%). Mean pulp chamber roof-to-floor distance was 2.623 ± 0.263 mm on the right and 2.567 ± 0.343 mm on the left (paired p < 0.001; mean difference 0.056 mm; 95% CI 0.023–0.089 mm). Conclusions: In this cohort, C-shaped morphology was rare, and no evidence of a sex association was found, although the small number of cases limits statistical power. Mesial roots showed more variability than distal roots, and contralateral symmetry was moderate and greater for distal roots than for mesial roots, supporting contralateral anatomy as a helpful—rather than predictive—clinical reference. Full article
(This article belongs to the Section Dentistry, Oral Surgery and Oral Medicine)
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14 pages, 1122 KB  
Article
The Big Nose Pattern at the Second Upper Molar—A Retrospective CBCT Study
by Carol Antonio Dandoczi, Mugurel Constantin Rusu, Răzvan Costin Tudose and Mihail Silviu Tudosie
Dent. J. 2026, 14(5), 280; https://doi.org/10.3390/dj14050280 - 8 May 2026
Viewed by 149
Abstract
Background/Objectives: A marked anteroposterior gradient of nasal fossa pneumatisation over the posterior maxillary alveolar base has been documented at the second premolar level, yet whether this gradient extends to the second upper molar (M2)—the primary site for posterior implant rehabilitation—remains uncharacterised. We [...] Read more.
Background/Objectives: A marked anteroposterior gradient of nasal fossa pneumatisation over the posterior maxillary alveolar base has been documented at the second premolar level, yet whether this gradient extends to the second upper molar (M2)—the primary site for posterior implant rehabilitation—remains uncharacterised. We aimed to quantify this gradient by classifying pneumatisation patterns above the maxillary alveolar base at M2 (Type 1: pure antral; Type 2: antral with palatine recess; Type 3: Big Nose pattern with combined antral and nasal involvement), assess bilateral symmetry and sex distribution, and compare findings with published second premolar data. Methods: A retrospective study was conducted on 165 cone-beam computed tomography scans (330 sides) from a Romanian population. Patterns were classified as Type 1 (pure antral), Type 2 (antral with palatine recess), or Type 3 (Big Nose pattern). Bilateral symmetry was assessed using Cohen’s kappa, and sex differences using Fisher’s exact test. Results: Type 1 was observed in 93.3% of sides, Type 2 in 4.2%, and Type 3 in 2.4%. Bilateral symmetry was 98.8% (kappa = 0.904), with all Type 3 cases occurring bilaterally. No significant sex difference was found (p = 0.363), although Type 3 showed a non-significant male predominance (OR = 4.55; p = 0.305). The Big Nose pattern was 6.8-fold less prevalent at M2 than at the second premolar level. Conclusions: A 6.8-fold reduction in Big Nose prevalence from the second premolar (16.2%) to M2 (2.4%) confirms a pronounced anteroposterior gradient in nasal fossa involvement over the posterior maxillary alveolar base—the central finding of this study. At M2, the maxillary sinus dominates exclusively in 97.6% of sides, rendering standard sinus floor elevation highly predictable. The invariable bilaterality of the Big Nose pattern at M2 supports contralaterally symmetrical surgical planning. These findings provide a gradient-based clinical framework: nasal-floor-aware augmentation planning is essential anteriorly (premolar region), whereas standard sinus augmentation protocols are reliably applicable at M2. Full article
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15 pages, 1222 KB  
Article
Longitudinal Ultrasound Assessment of Achilles and Patellar Tendon Morphology in National Collegiate Athletic Association Division 1 Female Gymnasts
by Phillip Hartog, Lee J. Hinkle, Ulrike H. Mitchell and A. Wayne Johnson
J. Funct. Morphol. Kinesiol. 2026, 11(2), 185; https://doi.org/10.3390/jfmk11020185 - 5 May 2026
Viewed by 140
Abstract
Background: Collegiate gymnastics imposes high repetitive loads on the lower extremities, particularly the Achilles and patellar tendons, yet longitudinal data describing tendon adaptation across a competitive season remain limited. Objectives: To examine seasonal changes in Achilles and patellar tendon morphology (thickness, [...] Read more.
Background: Collegiate gymnastics imposes high repetitive loads on the lower extremities, particularly the Achilles and patellar tendons, yet longitudinal data describing tendon adaptation across a competitive season remain limited. Objectives: To examine seasonal changes in Achilles and patellar tendon morphology (thickness, cross-sectional area [CSA], echogenicity, vascularity, and symmetry) across a twelve-month competitive cycle in Division I female gymnasts and to explore relationships with pain. Methods: This longitudinal observational study included twenty-five Division I female gymnasts (age: 20.0 ± 1.6 years; height: 159.5 ± 6.2 cm; weight: 57.8 ± 5.7 kg). Bilateral ultrasound assessments of the Achilles and patellar tendons were performed at three time points (post-summer, preseason, and postseason). Tendon thickness, CSA, echogenicity, and vascularity were evaluated using standardized imaging protocols. Symmetry indices were calculated, and pain was assessed using validated scales. Normality was assessed using appropriate statistical tests. Parametric data were expressed as mean ± standard deviation (SD), and non-parametric data as median and interquartile range. Paired comparisons were conducted using paired t-tests or Wilcoxon signed-rank tests, with Holm correction applied for multiple comparisons. Results: Achilles tendon thickness increased from summer to postseason (p < 0.05), with no significant changes in CSA after adjustment. Echogenicity and vascularity remained unchanged. Patellar tendon morphology was largely stable; however, left proximal thickness decreased from summer to preseason and remained reduced at postseason (p < 0.01), with no other consistent regional changes. Pain prevalence increased modestly across the season without a clear lateralized pattern or association with symmetry indices. Conclusions: Achilles tendon thickness appears to be a sensitive marker of seasonal adaptation in female collegiate gymnasts, whereas patellar tendon morphology remains stable. These findings support the use of longitudinal ultrasound monitoring for athlete screening and load management. Full article
25 pages, 1081 KB  
Article
Emergence and Stabilization of Hemispheric Specialization Under Symmetric Developmental Conditions: A Minimal Evolutionary Model
by Nobuchika Yamaki and Tenna Churiki
Symmetry 2026, 18(5), 783; https://doi.org/10.3390/sym18050783 - 2 May 2026
Viewed by 269
Abstract
Hemispheric specialization is a widespread feature of vertebrate nervous systems, but the minimal conditions under which bilateral systems differentiate, acquire polarity, and retain asymmetric states remain unclear. Here, we examined these issues using a minimal evolutionary model with two initially equivalent processing channels. [...] Read more.
Hemispheric specialization is a widespread feature of vertebrate nervous systems, but the minimal conditions under which bilateral systems differentiate, acquire polarity, and retain asymmetric states remain unclear. Here, we examined these issues using a minimal evolutionary model with two initially equivalent processing channels. Each channel evolved a spatial integration width while receiving the same input, and fitness rewarded the magnitude of a bilateral mismatch-separation signal rather than explicit anomaly localization. Under exact developmental symmetry, 40 lineages evolved robust left–right differences in integration width without significant directional fixation (median |Δa| = 2.511; 22 right-wider, 18 left-wider). Weak developmental gain asymmetry biased polarity selection in a graded manner, shifting outcomes toward right-wider or left-wider solutions depending on bias direction. Forced-symmetry, shared-parameter, and single-channel controls showed that high performance depended on allowing differentiated bilateral processing. After biased solutions were reseeded under restored symmetry, differentiation was retained and amplified (median |Δa| > 6.6), consistent with history-dependent persistence within the sampled fitness landscape. Structured backgrounds increased differentiation magnitude but imposed greater decision-time costs. These results distinguish differentiation, polarity bias, and persistence as separable components of minimal hemispheric specialization. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Computational Biology)
12 pages, 1154 KB  
Article
Three-Dimensional CBCT Analysis of Second Mesiobuccal Canal Anatomy in Maxillary Molars
by Hanadi Sabban, Maysoon Albahiti and Suha S. Maddah
Diagnostics 2026, 16(9), 1299; https://doi.org/10.3390/diagnostics16091299 - 27 Apr 2026
Viewed by 303
Abstract
Background: This study aimed to evaluate the prevalence, morphology, and influencing factors of the second mesiobuccal (MB2) canal in maxillary molars and the middle-mesial canal in mandibular molars using cone-beam computed tomography (CBCT). Methods: A total of 146 CBCT scans acquired [...] Read more.
Background: This study aimed to evaluate the prevalence, morphology, and influencing factors of the second mesiobuccal (MB2) canal in maxillary molars and the middle-mesial canal in mandibular molars using cone-beam computed tomography (CBCT). Methods: A total of 146 CBCT scans acquired between 2023 and 2025 were retrospectively analyzed at the Oral Radiology Division, King Abdulaziz University Dental Hospital. Canal prevalence, morphometric dimensions, symmetry, and Vertucci configurations were recorded and correlated with age, sex, and voxel size. Results: MB2 canals were detected in 64.4% of maxillary first molars and 29.6% of second molars, while middle-mesial canals were found in 17.8% of mandibular first molars and 6.4% of second molars. Detection rates declined with increasing voxel size and patient age (p < 0.05). Bilateral symmetry was strong for MB2 (κ = 0.78) but moderate for mandibular canals (κ = 0.29). Vertucci Type I and II were most common in maxillary roots, and Type IV predominated in mandibular mesial roots. Conclusions: These findings confirm CBCT as a reliable tool for identifying complex canal systems and emphasize the importance of voxel resolution and anatomical understanding in enhancing endodontic diagnosis and treatment success. Full article
(This article belongs to the Special Issue Advances in Oral and Maxillofacial Imaging)
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15 pages, 2598 KB  
Article
Volume Change of Masticatory Muscles by Skeletal Class III Orthognathic Surgery with and Without Facial Asymmetry: A Cross-Sectional and Longitudinal Study
by Hidehito Arima, Chie Tachiki, Takashi Takaki, Keiichi Nishikawa, Tazuko K. Goto, Kenji Sueishi and Yasushi Nishii
J. Clin. Med. 2026, 15(9), 3308; https://doi.org/10.3390/jcm15093308 - 26 Apr 2026
Viewed by 207
Abstract
Objectives: This study aimed to analyze longitudinal changes in masticatory muscle volume at pretreatment and after orthognathic surgery in skeletal Class III patients with and without facial asymmetry. Methods: Patients were divided into symmetry and asymmetry groups (n = 30, each; male: [...] Read more.
Objectives: This study aimed to analyze longitudinal changes in masticatory muscle volume at pretreatment and after orthognathic surgery in skeletal Class III patients with and without facial asymmetry. Methods: Patients were divided into symmetry and asymmetry groups (n = 30, each; male: female ratio 1: 1, for both groups; age at T1: asymmetry group 25.4 ± 8.1, symmetry group 22.9 ± 7.7). Computed tomography images were obtained at pretreatment (T1), one month after surgery (T2), and at 22 months postoperatively (T3). Three-dimensional reconstruction software was used to measure the volumes of the masseter, temporalis, medial pterygoid, and lateral pterygoid muscles. Results: At T1, the asymmetry group exhibited significantly smaller masseter and temporalis muscle volumes on the deviated side. These differences tended to decrease at T3. No significant bilateral differences were observed in the medial or lateral pterygoid muscles at each point. Longitudinal analyses showed that temporalis and lateral pterygoid muscle volumes decreased from T1 to T2 and increased from T2 to T3, whereas masseter muscle volume did not have a significantly longitudinal difference and the medial pterygoid muscle volume decreased significantly at T3. Conclusions: In Class III patients with facial asymmetry, pretreatment asymmetry of the masseter and temporalis muscle volumes tended to improve postoperatively as bilateral muscle volume increased. Full article
(This article belongs to the Section Dentistry, Oral Surgery and Oral Medicine)
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29 pages, 4549 KB  
Article
Smart Sensor-Driven Gait Rehabilitation Walker Using Machine Learning for Predictive Home-Based Therapy
by Gokul Manavalan, Yuval Arnon, A. N. Nithyaa and Shlomi Arnon
Sensors 2026, 26(8), 2547; https://doi.org/10.3390/s26082547 - 21 Apr 2026
Viewed by 510
Abstract
Abnormal gait associated with neuromuscular and musculoskeletal disorders represents a growing clinical burden, particularly in aging populations. This study presents a modular, low-cost Smart Rehabilitation Walker (SRW) that integrates multimodal sensing and real-time haptic feedback to enable simultaneous gait monitoring and corrective intervention [...] Read more.
Abnormal gait associated with neuromuscular and musculoskeletal disorders represents a growing clinical burden, particularly in aging populations. This study presents a modular, low-cost Smart Rehabilitation Walker (SRW) that integrates multimodal sensing and real-time haptic feedback to enable simultaneous gait monitoring and corrective intervention in both clinical and home environments. The system combines force-sensing resistors for bilateral load symmetry assessment, inertial measurement units for fall detection, and surface electromyography (sEMG) for neuromuscular activity monitoring within a closed-loop assistive feedback architecture. A 15-day pilot study involving ten individuals with rheumatoid arthritis and clinically observed neurological gait abnormalities demonstrated measurable improvements in gait biomechanics. The Force Symmetry Index (FSI), calculated using the Robinson symmetry metric, decreased from an average of 0.9691 to 0.2019, corresponding to a 79.26% average reduction in inter-limb load asymmetry. Concurrently, sEMG measurements showed a substantial increase in neuromuscular activation (ΔEMG = 4.28), with statistical analysis confirming a significant improvement across participants (paired t-test: t(9) = 13.58, p < 0.001). To model rehabilitation trajectories, a nonlinear predictive framework based on Gaussian Process Regression achieved high predictive accuracy (R2 ≈ 0.9, with a mean RMSE of 0.0385), while providing uncertainty-aware trend estimation. Validation using an independent amyotrophic lateral sclerosis gait dataset further demonstrated the transferability of the analytical pipeline. These results highlight the potential of sensor-enabled assistive walkers as scalable platforms for quantitative gait rehabilitation, adaptive feedback, and long-term mobility monitoring. Full article
(This article belongs to the Special Issue Novel Optical Biosensors in Biomechanics and Physiology)
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14 pages, 715 KB  
Article
The Nerve-Sparing Quality (NSQ) Score: A Novel Intraoperative Scoring System for Assessing Nerve-Sparing Quality During Robot-Assisted Radical Prostatectomy—A Concept and Feasibility Study
by Jakub Kempisty, Krzysztof Balawender, Oskar Dąbrowski and Karol Burdziak
J. Clin. Med. 2026, 15(8), 2979; https://doi.org/10.3390/jcm15082979 - 14 Apr 2026
Viewed by 389
Abstract
Introduction: Nerve-sparing (NS) during robot-assisted radical prostatectomy (RARP) plays a critical role in postoperative functional recovery, particularly urinary continence and erectile function. Despite the importance of precise neurovascular bundle (NVB) preservation, intraoperative assessment of NS quality remains largely subjective and lacks standardized [...] Read more.
Introduction: Nerve-sparing (NS) during robot-assisted radical prostatectomy (RARP) plays a critical role in postoperative functional recovery, particularly urinary continence and erectile function. Despite the importance of precise neurovascular bundle (NVB) preservation, intraoperative assessment of NS quality remains largely subjective and lacks standardized evaluation tools. The aim of this study was to develop and preliminarily evaluate a structured intraoperative scoring system designed specifically for assessing NS quality during RARP. Methods: A novel 10-point intraoperative NS scoring system (NSQ Score) based on five domains was developed: dissection plane, bleeding control, bundle manipulation, continuity of dissection, and symmetry. Each parameter was rated on a 0–2 scale. Thirty robot-assisted radical prostatectomy (RARP) procedures performed in 2024 were randomly selected from a prospectively maintained institutional surgical video archive. Cases were not pre-filtered based on tumor stage, surgical difficulty, or intraoperative complexity. High-definition video recordings of the nerve-sparing phase were anonymized and independently evaluated by three experienced observers blinded to patient outcomes and to each other’s assessments. Inter-rater agreement was analyzed using weighted Cohen’s kappa statistics with quadratic weights, complemented by exact and near-agreement proportions. Cluster bootstrap resampling was applied to account for bilateral observations. Results: A total of 48 evaluable observations were analyzed. The overall inter-rater agreement demonstrated a weighted kappa of 0.41 (95% CI 0.36–0.48), indicating fair-to-moderate agreement among reviewers. Exact agreement occurred in 43% of observations, while near-agreement (allowing one ordinal level difference) reached 98%. Among individual parameters, symmetry demonstrated the highest reliability with substantial agreement (κ = 0.70; 95% CI 0.58–0.81). Other domains showed fair agreement, including intraoperative bleeding (κ = 0.36), continuity of dissection (κ = 0.39), bundle manipulation (κ = 0.34), and dissection plane (κ = 0.27). Agreement levels were comparable between left- and right-sided dissections. Conclusions: We propose a novel structured intraoperative scoring system for evaluating nerve-sparing quality during RARP. The scale is simple, procedure-specific, and feasible for structured postoperative or video-based assessment. Preliminary results demonstrate fair-to-moderate inter-rater reliability with very high near-agreement, supporting the feasibility of this tool for clinical use. The proposed scoring system may facilitate standardized training, objective performance assessment, and future studies correlating intraoperative NS quality with functional outcomes. Full article
(This article belongs to the Special Issue Robotic Urologic Surgery: Clinical Applications and Advances)
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17 pages, 1898 KB  
Article
Side-Dependent Trunk Muscle Modulation During Sit-to-Stand After Stroke: An Exploratory EMG and Kinematic Study
by Grazia Cravero, Alice De Luca, Beatrice Lagomarsino, Carmelo Lentino, Giorgia Marchesi, Debora Siri, Camilla Pierella and Maura Casadio
Sensors 2026, 26(8), 2353; https://doi.org/10.3390/s26082353 - 10 Apr 2026
Viewed by 469
Abstract
Sit-to-stand (STS) is a fundamental functional task frequently impaired after stroke and widely used in rehabilitation to assess motor control and balance. While lower-limb kinematic and muscular asymmetries during STS have been documented, the contribution of trunk muscle coordination to compensatory strategies has [...] Read more.
Sit-to-stand (STS) is a fundamental functional task frequently impaired after stroke and widely used in rehabilitation to assess motor control and balance. While lower-limb kinematic and muscular asymmetries during STS have been documented, the contribution of trunk muscle coordination to compensatory strategies has received limited attention. We investigated STS performance in seven individuals with chronic right-sided hemiparesis under two conditions (free arms and crossed arms) to characterize phase-dependent kinematic asymmetries and side-dependent trunk muscle modulation relevant to rehabilitation practice. Optoelectronic motion capture was synchronized with bilateral surface electromyography, providing time-aligned kinematic and neuromuscular signals for sensor-based assessment of STS. Participants exhibited prolonged and highly variable STS durations, along with ankle asymmetries during the rising and lowering phases and hip asymmetries during upright standing, indicating increased reliance on the less impaired limb. Electromyography revealed side-dependent modulation of trunk muscles, notably latissimus dorsi, erector spinae longissimus, and multifidus, characterized by a prolonged relative contribution on the more impaired side. These findings suggest that altered trunk muscle modulation contributes to compensatory STS strategies after stroke and highlight the importance of trunk-focused neuromuscular assessment to guide individualized rehabilitation interventions aimed at improving symmetry, postural stability, and movement efficiency. Full article
(This article belongs to the Special Issue Sensor-Based Rehabilitation in Neurological Diseases)
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18 pages, 1379 KB  
Article
Gaussian Topology Refinement and Multi-Scale Shift Graph Convolution for Efficient Real-Time Sports Action Recognition
by Longying Wang, Hongyang Liu and Xinyi Jin
Symmetry 2026, 18(4), 639; https://doi.org/10.3390/sym18040639 - 10 Apr 2026
Viewed by 251
Abstract
Skeleton-based action recognition is a critical technology for intelligent sports analysis. Although the human skeletal structure exhibits inherent bilateral symmetry, sensor noise on resource-constrained edge devices frequently induces geometric distortion and topological asymmetry. Consequently, achieving a balance between high accuracy and real-time performance [...] Read more.
Skeleton-based action recognition is a critical technology for intelligent sports analysis. Although the human skeletal structure exhibits inherent bilateral symmetry, sensor noise on resource-constrained edge devices frequently induces geometric distortion and topological asymmetry. Consequently, achieving a balance between high accuracy and real-time performance remains a significant challenge. To this end, we propose EMS-GCN, an Efficient Multi-scale Shift Graph Convolutional Network that integrates geometric priors. Specifically, we design a Gaussian kernel-driven topology refinement module to mitigate structural noise inherent in sensor data. By leveraging geometric symmetry and Gaussian distances among nodes, this module dynamically constrains graph topology learning, thereby effectively rectifying the structural asymmetry and ambiguity induced by noise. Furthermore, we construct a Multi-scale Shift Linear Attention (MSLA) module to replace computationally intensive temporal convolutions. Leveraging temporal shift invariance, this module captures multi-scale contexts via parameter-free shift operations. Furthermore, we introduce a linear temporal attention mechanism to model global temporal dependencies with linear complexity, effectively resolving the information asymmetry inherent in long-range interactions. Finally, EMS-GCN incorporates a dual-branch attention structure to adaptively calibrate feature responses. Extensive experiments demonstrate that our model maintains high recognition accuracy with only 0.56 M parameters, representing a reduction of over 60% compared to mainstream baselines. These results validate the efficacy of leveraging geometric and temporal symmetries to enhance real-time sports analysis. Full article
(This article belongs to the Section Computer)
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28 pages, 2486 KB  
Article
Sharpness Estimation of Hankel Determinants and Logarithmic Coefficients for a Family of Analytic Functions Related to a Lung-Shaped Domain
by Mohamed A. Mamon, Shams Alyusof, Rabab Alyusof and Alaa H. El-Qadeem
Mathematics 2026, 14(8), 1240; https://doi.org/10.3390/math14081240 - 8 Apr 2026
Viewed by 404
Abstract
This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of [...] Read more.
This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of orders two and three, determine bounds for the first four logarithmic coefficients, and derive the bounds of some Zalcman functionals. The lung-shaped domain is characterized by the subordination condition involving a secant-based function, which maps the unit disk onto a geometrically distinctive region exhibiting bilateral symmetry. All obtained bounds are demonstrated to be sharp through the construction of specific extreme functions. Full article
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23 pages, 737 KB  
Article
Symmetric and Asymmetric J-Curve Effects of the Real Exchange Rate on the Manufacturing Trade Balance Between Türkiye and Germany
by Derya Hekim
Economies 2026, 14(4), 117; https://doi.org/10.3390/economies14040117 - 4 Apr 2026
Viewed by 571
Abstract
This study investigates whether fluctuations in the real exchange rate give rise to symmetric or asymmetric J-curve effects in manufacturing trade between Türkiye and Germany, thereby positioning the analysis within and contributing to the broader scholarly discourse on exchange rate–trade balance dynamics. Using [...] Read more.
This study investigates whether fluctuations in the real exchange rate give rise to symmetric or asymmetric J-curve effects in manufacturing trade between Türkiye and Germany, thereby positioning the analysis within and contributing to the broader scholarly discourse on exchange rate–trade balance dynamics. Using monthly data for the period 2013M01–2025M07, the paper first estimates a linear Autoregressive Distributed Lag (ARDL) model for the bilateral manufacturing trade balance and subsequently extends the framework to a nonlinear ARDL (NARDL) specification, which explicitly incorporates symmetry and asymmetry by decomposing real exchange rate changes into positive (depreciation) and negative (appreciation) partial sums. The linear ARDL results provide no evidence of a conventional J-curve and suggest that the aggregate impact of the real exchange rate is weak and often statistically insignificant. In contrast, the NARDL estimates uncover pronounced long-run and cumulative short-run asymmetries: real depreciations of the Turkish lira are associated with a persistent improvement in the bilateral manufacturing trade balance, whereas appreciations exert weak and statistically insignificant effects, a finding that remains robust when a real effective exchange rate measure is employed. Overall, the evidence indicates that Türkiye–Germany manufacturing trade does not conform to the standard J-curve pattern. These findings suggest that trade policy should adopt an asymmetric stance toward exchange rate movements: since depreciations yield persistent trade balance improvements while appreciations produce negligible effects, policies designed to support export competitiveness should prioritize the management of depreciation episodes rather than assuming symmetric adjustment dynamics. Full article
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17 pages, 1622 KB  
Article
Comparison of Limb Symmetry Index Values Across Different Knee Flexor Strength Testing Conditions in Healthy Male Recreational Athletes
by Natalia Urban and Aleksandra Królikowska
Appl. Sci. 2026, 16(7), 3440; https://doi.org/10.3390/app16073440 - 1 Apr 2026
Viewed by 648
Abstract
Background/Objectives: Restoring lower-limb strength and symmetry is crucial after ACL injury and reconstruction. The limb symmetry index (LSI) is often used to assess strength symmetry for return-to-sport decisions, but various assessment methods can influence outcomes. This study aimed to compare LSI across [...] Read more.
Background/Objectives: Restoring lower-limb strength and symmetry is crucial after ACL injury and reconstruction. The limb symmetry index (LSI) is often used to assess strength symmetry for return-to-sport decisions, but various assessment methods can influence outcomes. This study aimed to compare LSI across common knee flexor testing methods in healthy male athletes and to examine associations between absolute strength outcomes, thereby establishing baseline reference values for LSI in a healthy population. Methods: Twenty-two healthy recreationally active males participated in this prospective cross-sectional study. Knee flexor strength was assessed bilaterally using three force plate isometric tests, a static dynamometer-based test (isometric), and isokinetic dynamometer-based tests. Absolute strength values were normalized to body mass. LSI values were calculated for each testing condition. Differences in LSI across modalities were analyzed with repeated-measures ANOVA, and associations between normalized strength outcomes were assessed using Pearson correlation coefficients. Results: LSI values ranged from 96.69 to 101.83 across the testing conditions, with no significant differences observed between measures. Normalized absolute strength outcomes demonstrated very strong correlations within the same measurement category (r = 0.86–0.94 for force plate tests and r = 0.88–0.96 for isokinetic tests). In contrast, correlations between isometric and isokinetic strength outcomes were moderate (r = 0.41–0.67). Conclusions: LSI values were consistent across knee flexor strength testing modalities, suggesting that symmetry assessment was relatively consistent across different measurement methods in the studied group. In contrast, normalized absolute strength outcomes showed only moderate and variable associations across modalities, indicating that different testing approaches assess related but not interchangeable aspects of muscle strength. Full article
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21 pages, 2668 KB  
Article
Two-Dimensional Sagittal-Plane Gait Evaluation and Similarity Analysis in Parkinson’s Disease Under ON and OFF Conditions: A Pilot Study
by Jocabed Mendoza-Martínez, Fiacro Jiménez-Ponce, Karla Nayelli Silva-Garcés, Sergio Rodrigo Méndez García, Adolfo Angel Casarez Duran and Christopher René Torres-SanMiguel
Brain Sci. 2026, 16(4), 385; https://doi.org/10.3390/brainsci16040385 - 31 Mar 2026
Viewed by 447
Abstract
Background/Objectives: Freezing of gait (FoG) is a disabling motor manifestation of Parkinson’s disease (PD) associated with impaired neural control of locomotion and increased gait variability. Quantitative characterization of gait kinematics may provide biomechanical insight into FoG-related instability, particularly under different dopaminergic states. Methods: [...] Read more.
Background/Objectives: Freezing of gait (FoG) is a disabling motor manifestation of Parkinson’s disease (PD) associated with impaired neural control of locomotion and increased gait variability. Quantitative characterization of gait kinematics may provide biomechanical insight into FoG-related instability, particularly under different dopaminergic states. Methods: This pilot study evaluated sagittal-plane knee kinematics in healthy individuals (n = 27) and patients with PD. (n = 8) under OFF and ON dopaminergic medication conditions using two-dimensional videogrammetry (Kinovea®). Knee flexion–extension trajectories were time-normalized to 0–100% of the gait cycle, and group ensemble profiles (mean ± SD) were computed. Results: Phase-specific range of motion (ROM), within-subject variability, and interlimb coordination were quantified. Interlimb coordination was assessed using Pearson’s correlation coefficients (r) and cross-correlation lag analysis computed per subject and summarized statistically across groups. Compared with healthy participants, PD patients in the OFF state exhibited significantly reduced knee ROM during stance and swing (p < 0.05), accompanied by increased kinematic variability and disrupted temporal coordination. Interlimb correlation was significantly lower in PD OFF compared to healthy gait groups (p = 0.010), with larger temporal lags, indicating impaired bilateral synchronization. Following medication intake (ON state), knee excursion increased and interlimb coordination partially improved; however, correlation values and timing symmetry did not fully normalize to healthy levels. Conclusions: These findings demonstrate that sagittal-plane knee kinematics and interlimb coordination metrics derived from low-cost 2D videogrammetry are sensitive to the dopaminergic state and reveal persistent neuromotor deficits in PD. The proposed framework provides an interpretable and accessible approach for characterizing gait organization in Parkinson’s disease and supports future integration with clinical assessment and longitudinal monitoring. Full article
(This article belongs to the Special Issue Advances in Parkinson's Disease and Movement Disorders)
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13 pages, 256 KB  
Article
Relationship Between Quadriceps Muscle Strength Asymmetry and Lower Limb Biomechanical Asymmetry During Running in Patients Who Underwent Anterior Cruciate Ligament Reconstruction
by Xialin Ge, Mingxuan Gao, Yiming Tao, Longting Suo, Shuang Ren and Yingfang Ao
Bioengineering 2026, 13(4), 400; https://doi.org/10.3390/bioengineering13040400 - 30 Mar 2026
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Abstract
(1) Background: Postoperative anterior cruciate ligament reconstruction often involves quadriceps strength asymmetry, leading to abnormal lower limb biomechanics during running. While previous studies have examined the relationship between isokinetic strength and walking or jumping, the association between running, a key criterion for return [...] Read more.
(1) Background: Postoperative anterior cruciate ligament reconstruction often involves quadriceps strength asymmetry, leading to abnormal lower limb biomechanics during running. While previous studies have examined the relationship between isokinetic strength and walking or jumping, the association between running, a key criterion for return to sport, and lower limb biomechanics remains unclear, particularly regarding isokinetic strength asymmetry at different angular velocities. (2) Methods: Isokinetic quadriceps strength, running kinematic, and kinetic data were collected from 39 ACLR individuals. Paired t-tests compared bilateral differences, and Pearson correlation analysis assessed associations between biomechanical parameters and muscle strength. (3) Results: The injured leg showed significantly weaker Qc at 60°/s, 180°/s, and 300°/s (p < 0.05). Compared to the uninjured leg, the injured leg demonstrated a significantly greater hip flexion angle at initial contact (p < 0.05); the injured leg exhibited significantly reduced knee flexion angle at the time of peak vertical ground reaction force and peak knee flexion angle (p < 0.05); the injured leg exhibited significantly reduced knee flexion moment at PVGRF, peak knee flexion moment, peak knee extension moment (p < 0.05). Both the 60°/s Qc and Qe showed moderate negative correlations with knee flexion angles, and 180°/s Qc correlated with knee flexion moment at PVGRF (p < 0.05). (4) Conclusions: ACLR patients show quadriceps strength asymmetry and abnormal sagittal knee and hip biomechanics during running. Strength symmetry moderately correlates with knee kinematics and kinetics in a velocity-dependent manner. Rehabilitation should focus on multi-speed and eccentric training with neuromuscular and hip–knee coordination exercises to optimize movement and support safe return to sports. Full article
(This article belongs to the Section Biomechanics and Sports Medicine)
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