Constructing low-dimensional ordinary differential equations from chaotic time series of high- or infinite-dimensional systems using radial-function-based regression.

In our previous study [N. Tsutsumi, K. Nakai, and Y. Saiki, Chaos 32, 091101 (2022)1054-150010.1063/5.0100166] we proposed a method of constructing a system of ordinary differential equations of chaotic behavior only from observable deterministic time series, which we will call the radial-function-based regression (RfR) method. The RfR method employs a regression using Gaussian radial basis functions together with polynomial terms to facilitate the robust modeling of chaotic behavior. In this paper, we apply the RfR method to several example time series of high- or infinite-dimensional deterministic systems, and we construct a system of relatively low-dimensional ordinary differential equations with a large number of terms. The examples include time series generated from a partial differential equation, a delay differential equation, a turbulence model, and intermittent dynamics. The case when the observation includes noise is also tested. We have effectively constructed a system of differential equations for each of these examples, which is assessed from the point of view of time series forecast, reconstruction of invariant sets, and invariant densities. We find that in some of the models, an appropriate trajectory is realized on the chaotic saddle and is identified by the stagger-and-step method.

Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics.

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and statistical properties as well as to infer short time-series. Our successful modeling relies on the introduction of a set of Gaussian radial basis functions to capture local structures. The proposed method is used to construct a system of ordinary differential equations whose orbit reconstructs a time-series of a variable of the well-known Lorenz system as a simple but typical example. A system for a macroscopic fluid variable is also constructed.

Dynamical system analysis of a data-driven model constructed by reservoir computing.

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical characteristics can be reconstructed much more precisely by a data-driven model than by computing directly from training data. With this idea, we predict the laminar lasting time distribution of a particular macroscopic variable of chaotic fluid flow, which cannot be calculated from a direct numerical simulation of the Navier-Stokes equation because of its high computational cost.

Immediate effect of neuromuscular electrical stimulation on the abductor hallucis muscle: A randomized controlled trial.

Hallux valgus (HV) is a foot deformity with deviation of the greater toe and the first metatarsal. There is little evidence on training the abductor hallucis muscle (AbdH) to treat HV because of the difficulty in implementing the necessary interventions. Although neuromuscular electrical stimulation (NMES) has been used to induce voluntary exercise, there is currently no study on NMES for AbdH. We aimed to verify the immediate effect of NMES on the AbdH muscle function. For the NMES group (n = 15), electrical stimulation was applied for 20 min. In the sham group (n = 15), the stimulating device was set but not turned on. Electromyogram, HV angle (HVA) at rest and during abduction of the big toe, and strength of the AbdH were evaluated. Analysis of covariance was used to investigate differences within groups using the baseline as the covariate. NMES significantly improved the maximal voluntary isometric contractions (%MVIC), HVA at exercise, and muscle strength (%MVIC: p = .00, HVA exercise: p = .00, AbdH strength: p = .00). HVA at rest showed no change (p = .12). Application of NMES on the AbdH muscle immediately improved its activity output, muscle strength, and HVA during exercise.

Effects of deep thermotherapy on chest wall mobility of healthy elderly women.

Chest wall mobility decreases with age in community-dwelling women aged 65 years or older. Thermotherapy is used to improve soft-tissue extensibility. However, its effects on chest wall mobility are unclear. This study aimed to examine the effect of thermotherapy on chest wall mobility in healthy elderly women. Twenty-eight elderly women participated in this study. Chest wall mobility at three levels (axillary, xiphoid, and tenth rib), respiratory function (forced vital capacity and forced expiratory volume), and tissue temperature (skin temperature (ST)) and deep temperature (DT) with 10 mm and 20 mm depth from the skin (10 mm DT and 20 mm DT)) were measured before and after 15 minutes of thermotherapy. The subjects randomly received one of the three interventions (capacitive and resistive electric transfer (CRet), hot pack (HP), and sham CRet (sham)). Chest wall mobility at all levels significantly increased after CRet intervention. Hot pack significantly increased tenth rib excursion; it also significantly increased ST, 10 mm DT, and 20 mm DT, whereas CRet significantly increased 10 mm DT and 20 mm DT. There were significant differences between CRet, HP, and sham in ST, 10 mm DT, and 20 mm DT. Furthermore, 20 mm DT had increased more in CRet than in HP. CRet improved chest wall mobility at all levels and HP improved at the tenth rib level. This implies that CRet can be one of the approaches to improve chest wall mobility.

Detailed analysis of the transverse arch of hallux valgus feet with and without pain using weightbearing ultrasound imaging and precise force sensors.

BACKGROUND: Hallux valgus is the most common forefoot deformity and affects the transverse arch structure and its force loading patterns. This study aims to clarify the differences in the transverse arch structure and the force under the metatarsal heads individually, between normal feet and hallux valgus feet, and between hallux valgus feet with pain and without pain. We further test the association between the parameters of the transverse arch and hallux valgus angle and between the parameters and pain in hallux valgus. METHODS: Women's feet (105 feet) were divided into normal group (NORM) and hallux valgus group (HVG); and further into subgroups: hallux valgus without pain (HV Pain (-)) and hallux valgus with pain (HV Pain (+)). Transverse arch height and metatarsal heads height were measured using weight-bearing ultrasound imaging. Force under the metatarsal heads was measured using force sensors attached directly on the skin surface of the metatarsal heads. The measurements were taken in three loading positions: sitting, quiet standing and 90% weight shift on the tested foot. Differences between the groups were compared using Student t-test and Wilcoxon Exact test. Multivariate logistic analysis with adjustment for physical characteristics was also conducted. RESULTS: Transverse arch height was significantly higher in HVG than in NORM in all positions; there were no significant differences between HV Pain (+) and HV pain (-). Lateral sesamoid was significantly higher in HVG and HV Pain (+) than in NORM and HV Pain (-) respectively when bearing 90% of the body weight unilaterally. There was a trend of higher forces under the medial forefoot without significant difference. Transverse arch height and lateral sesamoid height were associated with the hallux valgus angle, while lateral sesamoid height was associated with forefoot pain in hallux valgus deformity. CONCLUSIONS: This study shows the differences in the transverse arch structure between normal feet and feet with hallux valgus, and between hallux valgus feet with and without pain. This finding is noteworthy when considering future treatments of painful feet, notably the height of the lateral sesamoid which seems to play a role in forefoot pain.

Risk factors of low back pain and the relationship with sagittal vertebral alignment in Tanzania.

BACKGROUND: LBP is a common and serious problem affecting vast populations of the world. However, only few studies on LBP in sub-Saharan Africa have been conducted. Studies report that LBP and pelvic angle are interrelated, and African residents have a high pelvic tilt. The strategy to prevent LBP should focus on activities that promote holistic health. For that purpose, it is important to grasp the state of LBP and how it affects people's lifestyle in Tanzania to clarify the direction of implementation of physiotherapy treatment and reduce the incidences of LBP among adults. This study aimed to investigate the prevalence and presentation of low back pain (LBP) and the relationship between anthropometric measurements and LBP among people in Moshi city, Kilimanjaro region Tanzania. METHODS: Following signing consent forms, participants were given questionnaires regarding LBP and then grouped accordingly into either asymptomatic or symptomatic cohorts. Anthropometric measurements of participants' height, weight, curvature of the spine, and pelvic angle were obtained. RESULTS: A Mann-Whitney U test analysis showed a significant difference in pelvic angle, body mass index (BMI), and thoracic kyphosis angle between the asymptomatic group and the symptomatic group. No significant differences in lumbar lordosis angle or abdominal muscle strength were found between the two groups. CONCLUSIONS: A person with symptomatic LBP in Tanzania has a large anteversion of the pelvic tilt and a thoracic kyphotic posture. This study shows a relationship between sagittal spinal alignment and LBP in Tanzania, which could allow for prospective identification of subjects prone to developing LBP in the future.

Relationship between forefoot structure, including the transverse arch, and forefoot pain in patients with hallux valgus.

[Purpose] Hallux valgus occurs in the forefoot where the transverse arch is located and may be a factor involved in forefoot pain. The relationship between forefoot pain and forefoot structure is unknown. This study aimed to analyze the relationship between forefoot pain and the transverse arch in patients with hallux valgus. [Participants and Methods] In this study, 122 (197 feet) adult females (46 to 86 years old) with hallux valgus were studied. By using questionnaires, the females were divided into two groups depending on whether or not they had forefoot pain (a group with forefoot pain [P group] and a group without forefoot pain [NP group]). The hallux valgus angle was measured using a goniometer, and the transverse arch was measured using a weight-bearing plantar ultrasonography imaging device. The transverse arch measurements included the transverse arch height and length. [Results] Only the transverse arch length, even after adjustment, was significantly greater in the P group. No significant difference was found between the hallux valgus angle and the transverse arch height. [Conclusion] The greater transverse arch length in the P group was possibly due to the collapsing transverse arch support muscles. Increased width probably caused inadequate impact absorption which in turn led to forefoot pain.

Acute effects of capacitive and resistive electric transfer (CRet) on the Achilles tendon.

This study aimed to investigate the acute effects of capacitive and resistive electric transfer (CRet) on Achilles tendon elongation during muscle contraction, as well as the circulation in the peritendinous region. Sixteen healthy men participated in this study. All 16 participants underwent 2 interventions: (1) CRet trial and (2) CRet without power (sham trial). Tendon elongation was measured four times. Using near-infrared spectroscopy, the blood circulation (volume of total-hemoglobin (Hb), oxygenated hemoglobin (oxy-Hb), and deoxygenated hemoglobin (deoxy-Hb)) was measured for 5 min before the intervention and for 30 min after the intervention. The differences between the measurements obtained before and after intervention were compared between the two interventions. The changes in tendon elongation and deoxy-Hb were not significantly different between the interventions. Total- and oxy-Hb were significantly increased in the CRet trial compared with the sham trial. In addition, the increases in total-Hb and oxy-Hb lasted for 30 min after the CRet intervention (CRet vs. sham: oxy-Hb: F = 8.063, p = 0.001, total-Hb: F = 4.564, p = 0.011). In conclusion, CRet significantly improved blood circulation in the peritendinous region.

Home exercise therapy to improve muscle strength and joint flexibility effectively treats pre-radiographic knee OA in community-dwelling elderly: a randomized controlled trial.

To compare the efficacy and adherence rates of two parallel home exercise therapy programs-multiple exercise (training and stretching the knee and hip muscles) and control (training the quadriceps muscles)-on knee pain, physical function, and knee extension strength in community-dwelling elderly individuals with pre-radiographic knee osteoarthritis (OA). One hundred patients with medial knee pain were randomly allocated to one of two 4-week home exercise programs. Individuals with a Kellgren/Lawrence (K/L) grade 0 or 1 OA (pre-radiographic knee OA) in the medial compartment were enrolled. Primary outcomes were knee pain (visual analog scale), self-reported physical function (Japanese Knee Osteoarthritis Measure [JKOM]), and isometric maximum muscle strength of the knee extensor measured using a hand-held dynamometer. A total of 52 patients (28 [53.8%] in the multiple exercise group, 24 [46.2%] in the control group) completed the trial. The JKOM activities of daily living and general health conditions outcomes improved significantly in the multiple exercise group compared to the control group (JKOM activities of daily living, beta = - 0.76; 95% confidence interval [CI], - 1.39 to - 0.13; p = 0.01; JKOM general health conditions, beta = - 0.25; 95% CI, - 0.48 to - 0.01; p = 0.03). The home exercise compliance rates of the multiple exercise and control groups were 96.6 and 100%, respectively. When targeting pre-radiographic knee OA in community-dwelling elderly, it is important to implement home exercise programs that aim to improve muscle strength and joint flexibility rather than knee extension muscle power only.

Machine-learning inference of fluid variables from data using reservoir computing.

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the complex behavior: the first, called partial inference, requires continued knowledge of partial time-series data during the inference as well as past time-series data, while the second, called full inference, requires only past time-series data as training data. For the first case, we are able to infer long-time motion of microscopic fluid variables. For the second case, we show that the reservoir dynamics constructed from only past data of energy functions can infer the future behavior of energy functions and reproduce the energy spectrum. It is also shown that we can infer time-series data from only one measurement by using the delay coordinates. This implies that the obtained reservoir systems constructed without the knowledge of microscopic data are equivalent to the dynamical systems describing the macroscopic behavior of energy functions.

Development of a questionnaire survey to evaluate lower limb function of patients with knee osteoarthritis.

This study aimed to develop a self-questionnaire index relevant to lower limb functional assessment reflecting clinical symptoms and activity restrictions associated with activities of daily living (ADL) for patients with knee osteoarthritis. This cross-sectional study enrolled patients with knee osteoarthritis (Kellgren/Lawrence grade ≥ 1). Participants evaluated clinical symptoms and activity restrictions using self-reported questionnaires. Radiographic evaluation, knee joint range of motion (ROM), and lower limb muscle strength were assessed. Associations between clinical symptoms, activity restrictions, and knee and hip joint function were evaluated using multiple and logistic regression analysis. Overall, 142 participants were included in the final analysis. Patients with knee pain while rising from a chair had lower knee and hip extension strength (knee extension ß = - 0.28; 95% confidence interval (CI), - 0.41 to - 0.14; P < 0.0001; hip extension ß = - 0.26; 95% CI, - 0.42 to - 0.08; P = 0.0034), and restricted knee extension ROM (odds ratio [OR] = 2.17; 95% CI, 1.02-4.63; P = 0.041). Patients with knee pain during stair climbing, turning or who were unable to stand on one leg without external support had reduced hip abduction muscle strength (ß = - 0.17; 95% CI, - 0.27 to - 0.07; P = 0.0008). Patients with knee pain while rising from a chair or stepping showed more severe knee joint degeneration on radiographic evaluation (OR = 3.26; 95% CI, 1.11-10.91; P = 0.03). The self-questionnaire index reflected clinical symptoms and activity restrictions associated with ADL and was significantly associated with lower limb function in individuals with knee osteoarthritis.

Effect of Capacitive and Resistive electric transfer on changes in muscle flexibility and lumbopelvic alignment after fatiguing exercise.

[Purpose] This study aimed to clarify the effects of Capacitive and Resistive electric transfer (CRet) on changes in muscle flexibility and lumbopelvic alignment after fatiguing exercise. [Subjects and Methods] Twenty-two healthy males were assigned into either the CRet (n=11) or control (n=11) group. Fatiguing exercise and CRet intervention were applied at the quadriceps muscle of the participants' dominant legs. The Ely test, pelvic tilt, lumbar lordosis, and superficial temperature were measured before and after exercise and for 30 minutes after intervention. Statistical analysis was performed using one-way analysis of variance, with Tukey's post-hoc multiple comparison test to clarify within-group changes and Student's t-test to clarify between-group differences. [Results] The Ely test and pelvic tilt were significantly different in both groups after exercise, but there was no difference in the CRet group after intervention. Superficial temperature significantly increased in the CRet group for 30 minutes after intervention, in contrast to after the exercise and intervention in the control group. There was no significant between-group difference at any timepoint, except in superficial temperature. [Conclusion] CRet could effectively improve muscle flexibility and lumbopelvic alignment after fatiguing exercise.

Relationship between transverse arch height and foot muscles evaluated by ultrasound imaging device.

[Purpose] Few studies on the transverse arch (TA) in the forefoot have been conducted. The forefoot is where pains occur most frequently and is related to walking and balance; hence, paying attention to TA is vital. However, the relationship between TA and foot muscles has not been investigated. Therefore, this study aims to investigate muscles related to TA. [Subjects and Methods] Nineteen healthy young males were included. Measurements of their feet, excluding one foot with recent foot pain (n=37), were obtained. The height of TA (TAH) was measured in two ways: during 10% and 90% loading of body weight. The cross-sectional area and thickness of five muscles were measured: flexor digitorum longus, peroneus longus and brevis, flexor hallucis brevis, flexor digitorum brevis (FDB) and abductor hallucis (ABH). All measurements were performed with an ultrasound device. [Results] FDB and ABH were correlated with TAH during 10% and 90% loading after removing the effect of body mass index and age. The greater FDB and ABH, the higher TAH. [Conclusion] As FDB becomes larger, the second, third and fourth metatarsal heads are raised more. Furthermore, the height of the first metatarsal head is lowered by a larger ABH. These mechanisms may increase TAH.

Relationship between agility and lower limb muscle strength, targeting university badminton players.

[Purpose] Targeting university badminton players, this study investigated the relationship between agility, which is associated with performance in badminton, and lower limb muscle strength, and examined which muscles influence agility. [Subjects and Methods] A total of 23 male university badminton players were evaluated for side-shuffle test scores and lower limb strength. The relationships between agility, lower limb strength, and duration of experience playing badminton were evaluated using a correlation analysis. Moreover, the relationship between agility and lower limb strength was evaluated by partial correlation analysis, adjusting for the effects of experience of each badminton player. [Results] The agility score correlated with hip extension and ankle plantar flexion strength, with adjustment for badminton experience. [Conclusion] This study suggests that hip extension training and improvement in ankle plantar flexion strength may improve agility.

Demequina salsinemoris sp. nov., isolated on agar media supplemented with ascorbic acid or rutin.

Three strains, KV-810(T), KV-811 and KV-816, were isolated from mangrove soil from a southern island in Japan on media supplemented with ascorbic acid or rutin. These strains contained l-ornithine as the diagnostic diamino acid in the cell-wall peptidoglycan and DMK-9(H(4)) as the predominant menaquinone. The G+C content of the DNA was 70-72 mol%. These characteristics in combination with 16S rRNA gene sequence analysis revealed that the novel strains belonged to the genus Demequina. The DNA-DNA hybridization values showed that the three new strains belonged to the same species, a novel species of the genus Demequina. Therefore strains KV-810(T), KV-811 and KV-816 are proposed as representing a novel species, Demequina salsinemoris sp. nov. The type strain is KV-810(T) (=DSM 22060(T)=NBRC 105323(T)).