Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes

The median function on graphs with bounded profiles

The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.

Shoulder Muscular Activity During Isometric Three-Point Kneeling Exercise on Stable and Unstable Surfaces

The purpose of this study was to determine if performing isometric 3-point kneeling exercises on a Swiss ball influenced the isometric force output and EMG activities of the shoulder muscles when compared with performing the same exercises on a stable base of support. Twenty healthy adults performed the isometric 3-point kneeling exercises with the hand placed either on a stable surface or on a Swiss ball. Surface EMG was recorded from the posterior deltoid, pectoralis major, biceps brachii, triceps brachii, upper trapezius, and serratus anterior muscles using surface differential electrodes. All EMG data were reported as percentages of the average root mean square (RMS) values obtained in maximum voluntary contractions for each muscle studied. The highest load value was obtained during exercise on a stable surface. A significant increase was observed in the activation of glenohumeral muscles during exercises on a Swiss ball. However, there were no differences in EMG activities of the scapulothoracic muscles. These results suggest that exercises performed on unstable surfaces may provide muscular activity levels similar to those performed on stable surfaces, without the need to apply greater external loads to the musculoskeletal system. Therefore, exercises on unstable surfaces may be useful during the process of tissue regeneration.

Characterization of subgraph relationships and distribution in complex networks

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel approach which extends from single nodes to the whole network level by considering non-overlapping subgraphs (i.e. connected components) and their interrelationships and distribution through the network. Though such subgraphs can be completely general, our methodology focuses on the cases in which the nodes of these subgraphs share some special feature, such as being critical for the proper operation of the network. The methodology of subgraph characterization involves two main aspects: (i) the generation of histograms of subgraph sizes and distances between subgraphs and (ii) a merging algorithm, developed to assess the relevance of nodes outside subgraphs by progressively merging subgraphs until the whole network is covered. The latter procedure complements the histograms by taking into account the nodes lying between subgraphs, as well as the relevance of these nodes to the overall subgraph interconnectivity. Experiments were carried out using four types of network models and five instances of real-world networks, in order to illustrate how subgraph characterization can help complementing complex network-based studies.

A Levinson algorithm based on an isometric transformation of Durbin`s

Starting from the Durbin algorithm in polynomial space with an inner product defined by the signal autocorrelation matrix, an isometric transformation is defined that maps this vector space into another one where the Levinson algorithm is performed. Alternatively, for iterative algorithms such as discrete all-pole (DAP), an efficient implementation of a Gohberg-Semencul (GS) relation is developed for the inversion of the autocorrelation matrix which considers its centrosymmetry. In the solution of the autocorrelation equations, the Levinson algorithm is found to be less complex operationally than the procedures based on GS inversion for up to a minimum of five iterations at various linear prediction (LP) orders.

Activation of Selected Shoulder Muscles During Unilateral Wall and Bench Press Tasks Under Submaximal Isometric Effort

STUDY DESIGN: Controlled laboratory study. OBJECTIVE: To assess the activation of 7 shoulder muscles under 2 closed kinetic chain (CKC) tasks for the upper extremity using submaximal isometric effort, thus providing relative quantification of muscular isometric effort for these muscles across the CKC exercises, which may be applied to rehabilitation protocols for individuals with shoulder weakness. BACKGROUND: CKC exercises favor joint congruence, reduce shear load, and promote joint dynamic stability. Additionally, knowledge about glenohumeral and periscapular muscle activity elicited during CKC exercises may help clinicians to design protocols for shoulder rehabilitation. METHODS: Using surface electromyography, activation level was measured across 7 shoulder muscles in 20 healthy males, during the performance of a submaximal isometric wall press and bench press. Signals were normalized to the maximal voluntary isometric contraction, and, using paired t tests, data were analyzed between the exercises for each muscle. RESULTS: Compared to the wall press, the bench press elicited higher activity for most muscles, except for the upper trapezius. Levels of activity were usually low but were above 20% maximal voluntary isometric contraction for the serratus anterior on both tasks, and for the long head triceps brachii on the bench press. CONCLUSIONS: Both the bench press and wall press, as performed in this study, led to relatively low EMG activation levels for the muscles measured and may be considered for use in the early phases of rehabilitation. J Ort hop Sports Phys Ther 2011;41(7):520-525, Epub 2 February 2011. doi:10.2519/jospt.2011.3418

Standardization of the Electromyographic Signal Through the Maximum Isometric Voluntary Contraction

The objective of this study was to analyze the electromyographic (EMG) data, before and after normalization. One hundred (100) normal subjects (with no signs and symptoms of temporomandibular disorders) participated in this study. A surface EMG of the masticatory muscles was performed. Two different tests were performed: maximum voluntary clench (MVC) on cotton rolls and MVC in intercuspal position. The normalization was done using the mean value of the EMG signal of the first examination. The coefficient of variation CV showed lower values for the standardized data. The standardization was effective in reducing the differences between records from the same subject and in different subjects.

Functional roles of abdominal and back muscles during isometric axial rotation of the trunk

Electromyographic (EMG) studies have shown that a large number of trunk muscles are recruited during axial rotation. The functional roles of these trunk muscles in axial rotation are multiple and have not been well investigated. In addition, there is no information on the coupling torque at different exertion levels during axial rotation. The aim of the study was to investigate the functional roles of rectus abdominis. external oblique. internal oblique, latissimus dorsi, iliocostalis lumborum and multifidus during isometric right and left axial rotation at 100%, 70%, 50% and 30% maximum voluntary contractions (MVC) in a standing position. The coupling torques in sagittal and coronal planes were measured during axial rotation to examine the coupling nature of torque at different levels of exertions. Results showed that the coupled sagittal torque switches from nil to flexion at maximum exertion of axial rotation. Generally, higher EMG activities were shown at higher exertion levels for all the trunk muscles. Significant differences in activity between the right and left axial rotation exertions were demonstrated in external oblique, internal oblique, latissimus dorsi and iliocostalis lumborum while no difference was shown in rectus abdominis and multifidus. These results demonstrated the different functional roles of trunk muscles during axial rotation. This is important considering that the abdominal and back muscles not only produce torque but also maintain the spinal posture and stability during axial rotation exertions. The changing coupling torque direction in the sagittal plane when submaximal to maximal exertions were compared may indicate the complex nature of the kinetic coupling of trunk muscles. (C) 2001 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.

Repeatability of maximal voluntary force and of surface EMG variables during voluntary isometric contraction of quadriceps muscles in healthy subjects

The repeatability of initial values and rate of change of EMG signal mean spectral frequency (MNF), average rectified values (ARV), muscle fiber conduction velocity (CV) and maximal voluntary contraction (MVC) was investigated in the vastus medialis obliquus (VMO) and vastus lateralis (VL) muscles of both legs of nine healthy male subjects during voluntary, isometric contractions sustained for 50 s at 50% MVC. The values of MVC were recorded for both legs three times on each day and for three subsequent days, while the EMG signals have been recorded twice a day for three subsequent days. The degree of repeatability was investigated using the Fisher test based upon the ANalysis Of VAriance (ANOVA), the Standard Error of the Mean (SEM) and the Intraclass Correlation Coefficient (ICC). Data collected showed a high level of repeatability of MVC measurement (normalized SEM from 1.1% to 6.4% of the mean). MNF and ARV initial values also showed a high level of repeatability (ICC > 70% for all muscles and legs except right VMO). At 50% MVC level no relevant pattern of fatigue was observed for the VMO and VL muscles, suggesting that other portions of the quadriceps might have contributed to the generated effort. These observations seem to suggest that in the investigation of muscles belonging to a multi-muscular group at submaximal level, the more selective electrically elicited contractions should be preferred to voluntary contractions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fatigue-related changes in torque output and electromyographic parameters of trunk muscles during isometric axial rotation exertion - An investigation in patients with back pain and in healthy subjects

Study Design. A cross-sectional case-control study. Objectives. To examine the effect of fatigue on torque output as well as electromyographic frequency and amplitude values of trunk muscles during isometric axial rotation exertion in back pain patients and to compare the results with a matched control group. Summary of Background Data. Back pain patients exhibited different activation strategies in trunk muscles during the axial rotation exertions. Fatigue changes of abdominal and back muscles during axial rotation exertion have not been examined in patients with back pain. Methods. Twelve back pain patients and 12 matched controls performed isometric fatiguing axial rotation to both sides at 80% maximum voluntary contraction in a standing position. During the fatiguing exertion, electromyographic changes of rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum, and multifidus were recorded bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were also measured. Results. No difference in the endurance capacity was found between back pain and control groups. At the initial period of the exertion, back pain patients demonstrated a statistical trend (P = 0.058) of greater sagittal coupling torque as well as lower activity of rectus abdominis and multifidus and higher activity in external oblique. During the fatigue process similar changes of coupling torque were demonstrated in both sagittal and coronal planes, but a smaller fatigue rate for right external oblique, increase in median frequency for latissimus dorsi, and lesser increase in activity for back muscles were found in the back pain group compared with the control group. Conclusions. Alterations in electromyographic activation and fatigue rates of abdominal and back muscles demonstrated during the fatigue process provide insights into the muscle dysfunctions in back pain and may help clinicians to devise more rational treatment strategies.

EMG activity of trunk muscles and torque output during isometric axial rotation exertion: a comparison between back pain patients and matched controls

Abnormal patterns of trunk muscle activity could affect the biomechanics of spinal movements and result in back pain. The present study aimed to examine electromyographic (EMG) activity of abdominal and back muscles as well as triaxial torque output during isometric axial rotation at different exertion levels in back pain patients and matched controls. Twelve back pain patients and 12 matched controls performed isometric right and left axial rotation at 100%, 70%, 50%, and 30% maximum voluntary contractions in a standing position. Surface EMG activity of rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum and multifidus were recorded bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were measured. Results showed that there was a trend (P = 0.08) of higher flexion coupling torque during left axial rotation exertion in back pain patients. Higher activity for external oblique and lower activity for multifidus was shown during left axial rotation exertion in back pain group when compared to the control group. In right axial rotation, back pain patients exhibited lesser activity of rectus abdominis at higher levels of exertion when compared with matched controls. These findings demonstrated that decreased activation of one muscle may be compensated by overactivity in other muscles. The reduced levels of activity of the multifidus muscle during axial rotation exertion in back pain patients may indicate that spinal stability could be compromised. Future studies should consider these alternations in recruitment patterns in terms of spinal stability and internal loading. The findings also indicate the importance of training for coordination besides the strengthening of trunk muscles during rehabilitation process. (C) 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.

Effect of fatigue on torque output and electromyographic measures of trunk muscles during isometric axial rotation

Objectives: To examine the changes in torque output resulting from fatigue, as well as changes in electromyographic measures of trunk muscles during isometric axial rotation and to compare these changes between directions of axial rotation. Design: Subjects performed fatiguing right and left isometric axial rotation of the trunk at 80% of maximum voluntary contraction while standing upright. Setting: A rehabilitation center. Participants: Twenty-three men with no history of back pain. Interventions: Not applicable. Main Outcome Measures: Surface electromyographic Signals were recorded from 6 trunk muscles bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were also measured. Results: During the fatiguing axial rotation contraction, coupling torques of both sagittal and coronal planes were slightly decreased and no difference was found between directions of axial rotation. Decreasing median frequency and an increase in electromyographic amplitude were also found in trunk muscles with different degrees of changes in individual muscles. There were significant differences (P

Reliability of electromyographic and torque measures during isometric axial rotation exertions of the trunk

Objective: The aim of the present study was to investigate the between-days reliability of electromyographic (EMG) measurement of 6 bilateral trunk muscles and also the torque output in 3 planes during isometric right and left axial rotation at different exertion levels. Methods: Ten healthy subjects performed isometric right and left axial rotation at 100, 70, 50 and 30% maximum voluntary contractions in two testing sessions at least 7 days apart. EMG amplitude and frequency analyses of the recorded surface EMG signals were performed for rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum and multifidus bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were measured. Results: For both EMG amplitude and frequency values, good (intraclass correlation coefficient, ICC = 0.75-0.89) to excellent (ICC greater than or equal to 0.90) reliability was found in the 6 trunk muscles at different exertion levels during axial rotation. The reliability of both maximal isometric axial rotation torque and coupling torques in sagittal and coronal planes were found to be excellent (ICC greater than or equal to 0.93). Conclusions: Good to excellent reliability of EMG measures of trunk muscles and torque measurements during isometric axial rotation was demonstrated. This provides further confidence of using EMG and triaxial torque assessment as outcome measures in rehabilitation and in the evaluation of the human performance in the work place. (C) 2003 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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