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Purpose: The purpose of this study was to identify how generalized fatigue along with hormonal changes throughout the menstrual cycle affects trunk variability and local dynamic stability during gait. Methods: General fatigue was induced by an incremental test on a treadmill, and the menstrual cycle was divided into three phases: follicular, ovulatory, and luteal. Twenty-six healthy, young volunteers (aged 18 to 28 years) who did not use oral contraceptives or other hormonal drugs with a regular menstrual cycle participated in the study. They walked on the treadmill for 4 min at the preferred speed, before the incremental test, followed by four sets of 4 min alternating between walking, also at preferred speed, and resting. From trunk kinematic data, the following were extracted: the mean of the standard deviation along strides, as a measure of variability, and the maximum Lyapunov exponent, as a measure of local dynamic stability (LDS). Results: After the incremental test, variability increased, and LDS decreased. However, they showed a tendency to return to the initial value faster in women compared to previous results for men. In the follicular phase, which has less hormonal release, the volunteers had an almost complete recovery in LDS soon after the first rest interval, suggesting that female hormones can interfere with fatigue recovery. Nevertheless, concerning the LDS, it was significantly lower in the luteal phase than in the follicular phase. Conclusion: Women that are not taking oral contraceptives should be aware that they are susceptible to increased gait instabilities in the pre-menstrual phase after strenuous activities.

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The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

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Muscle fatigue negatively affects gait, and the changes in gait pattern due to muscle fatigue is influenced by which muscles are fatigued and pre-existing physical activity levels. However, how these factors alter gait stability and variability, measures related to risk of fall, remains unclear. To explore how muscular fatigue affects linear and nonlinear gait features in young adults, the effects of triceps surae fatigue and weight training level on gait variability and local stability, as well as a 12-min recovery time of post-fatigue period, were evaluated in young adults (trained and untrained groups). Some features were estimated, i.e., (i) step length (SL) and step frequency (SF), (ii) average standard deviation of trunk acceleration along strides (VAR), and (iii) local dynamic stability (LDS; maximum Lyapunov exponent). LDS presented a significant increase in the anterior-posterior direction with recovery to trained group. SL and SF changed immediately post-fatigue and recovered for both groups, while VAR increased significantly in all directions, with a recovery in the vertical direction for both groups and in the medial-lateral direction for trained group. Localized fatigue affected the analyzed gait variables independent of the participant's training condition, and an interval of 12 min does not seem to be enough for a complete recovery, suggesting a longer recovery period after tasks involving localized triceps surae fatigue to guarantee basal levels of gait variability and local stability. Graphical abstract Flow chart of the experimental protocol. A) Pre-fatigue: 4 min walking at PWS. B) Post-fatigue: first 4 min walking after fatigue protocol. C) Post-fatigue: second 4 min walking after fatigue protocol. D) Post-fatigue: third 4 min walking after fatigue protocol (PWS, preferred walking speed; AP, anterior-posterior; V, vertical; ML, medial-lateral).

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Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh-Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan-Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh-Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.

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This study aims to analyze gait variability and stability of individuals with amputation walking on upward (8%), horizontal (0%), and downward (- 8%) inclines, by using linear and nonlinear descriptors. Trunk linear variability and gait spatiotemporal parameters were evaluated. Nonlinear variability (local dynamic stability-LDS), was estimated by the maximum Lyapunov exponent (λ) computed from a trunk marker velocity. The gait descriptors were compared among three distinct groups (N participants): unilateral transtibial amputees (TTA, N = 12); unilateral transfemoral amputees (TFA, N = 13); control group (CT, N = 15). For step width and support phase, the effect of inclination was greater for TFA group, especially in the DOWN condition. Linear variability was higher for amputees (TFA and TTA) especially in the UP condition in the medial-lateral and anterior-posterior directions. TTA and TFA groups presented greater λ values than CT group in medial-lateral direction indicating decreased LDS, but TFA group presented smaller λ values than TTA and CT groups in the V direction. Our findings showed that inclination introduced significant changes in the estimated parameters for all groups, with greater changes for amputee groups. Furthermore, the level of amputation directly affects the analyzed gait parameters being the TFA group the one which presents greater changes. Graphical abstract The objective of this study was to analyze gait variability of individuals with amputation walking on (A) upward (+ 8%), (B) horizontal (0%), and (C) downward (- 8%) inclines, by using linear and nonlinear biomechanical descriptors. Linear measures of variability, such trunk variability and gait spatiotemporal parameters were evaluated. Nonlinear variability was estimated by the exponent of divergence (maximum Lyapunov exponent) of the velocity of a marker fixed in the subject's trunk while walking on inclined surfaces.

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Considering the numerous possibilities of having suitable thermoelectric energy conversion at nano-scale level, especially for molecular systems, in the present work we put forward a new proposal along this using a flat DNA segment as a functional element. It is modeled by coupling two chains to a form a two-stranded ladder like geometry, with interactions to first neighbors, within the tight-binding prescription. We critically investigate electrical and thermal properties of DNA molecule depending on the length of the system, temperature, molecule-to-lead coupling and the degree of (correlated) disorder. Our analysis might be helpful in analyzing thermoelectric signatures of correlated and uncorrelated disordered systems, and can be verified in laboratory.

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The objective of this study was to assess gait variability after anterior cruciate ligament reconstruction (ACLR), as an indicative of possible altered gait pattern and a measure of recovery compared to control subjects. Forty subjects (32 male), divided into 4 groups of 10 participants, were enrolled in the study: a control group (CG), and observational groups OG-I (90 days), OG-II (180 days), and OG-III (360 days) after ACLR. All subjects underwent the same rehabilitation program for six months. For kinematic recording, each subject walked on a treadmill for 4 min at a preferred walking speed. Linear gait variability was assessed using average standard deviation (VAR) and normalized root mean square of medial-lateral (ML) trunk acceleration (RMSratio). Gait stability was assessed using the margin of stability (MoS) and local dynamic stability (LDS), and nonlinear variability was assessed using sample entropy (SEn). Compared to the CG, the VAR ML increased significantly in the OG-I group and decreased incrementally in OG-II and OG-III. MoS increased significantly in the OG-I group and tends to maintain in OG-II and OG-III, while LDS was greater in the CG and decreased incrementally in the OG groups. The SEn was higher in the OG groups than in the CG and increased in OG-II and OG-III. The results indicated that ACL reconstruction was followed by a progressive increase in stability and a progressive increase in variability over the postoperative rehabilitation period. In terms of stability and gait variability, six months of physiotherapy for rehabilitation after ACL reconstruction appears to be effective, but it is insufficient for a complete recovery as compared to healthy individuals.

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Overloaded backpacks can cause changes in posture and gait dynamic balance. Therefore, the aim of this study was to assess gait regularity and local dynamic stability in young adults as they carried a backpack in different positions, and with different loads. Twenty-one healthy young adults participated in the study, carrying a backpack that was loaded with 10 and 20% of their body weight (BW). The participants walked on a level treadmill at their preferred walking speeds for 4 min under different conditions of backpack load and position (i.e. with backpack positioned back bilaterally, back unilaterally, frontally or without a backpack). Results indicate that backpack load and positioning significantly influence gait stability and regularity, with the exception of the 10% BW bilateral back position. Therefore, the recommended safe load for school-age children and adolescents (10% of BW) should also be considered for young adults. Practitioner summary: Increase in load results in changes in posture, muscle activity and gait parameters, so we investigated the gait adaptations related to regularity and stability. Conditions with high backpack loads significantly influenced gait stability and regularity in a position-dependent manner, except for 10% body weight bilateral back position.

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This study evaluated linear and nonlinear gait features in healthy older adults walking on inclined surfaces at different speeds. Thirty-seven active older adults (experimental group) and fifty young adults (control group) walked on a treadmill at 100% and ±20% of their preferred walking speed for 4 min under horizontal (0%), upward (UP) (+8%), and downward (DOWN) (-8%) conditions. Linear gait variability was assessed using the average standard deviation of trunk acceleration between strides (VAR). Gait stability was assessed using the margin of stability (MoS). Nonlinear gait features were assessed by using the maximum Lyapunov exponent, as a measure of local dynamic stability (LDS), and sample entropy (SEn), as a measure of regularity. VAR increased for all conditions, but the interaction effects between treadmill inclination and age, and speed and age were higher for young adults. DOWN conditions showed the lowest stability in the medial-lateral MoS, but not in LDS. LDS was smaller in UP conditions. However, there were no effects of age for either MoS or LDS. The values of SEn decreased almost linearly from the DOWN to the UP conditions, with significant interaction effects of age for anterior-posterior SEn. The overall results supported the hypothesis that inclined surfaces modulate nonlinear gait features and alter linear gait variability, particularly in UP conditions, but there were no significant effects of age for active older adults.

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