Gait speed or gait variability, which one to use as a marker of risk to develop Alzheimer disease? A pilot study

BACKGROUND

Previous literature demonstrates the interest of gait analysis to predict cognitive decline in old people.

AIMS

This pilot study aims to determine if gait speed or gait variability is a marker able to early identify, among mild cognitive impairment (MCI) subjects, those at risk to develop Alzheimer's disease (AD) in the future.

METHODS

13 MCI subjects were included in 2007. Their gait parameters (walking speed, stride length and gait frequency, regularity and symmetry) were measured in 2007 and 2008 in simple task (ST) and in dual task (DT) using a triaxial accelerometer (Locometrix(®)). Among the 13 MCI subjects included in 2007, 10 were assessed in 2008. So, 23 (13 in 2007 + 10 in 2008) gait tests were collected. In 2011, MCI people were considered as "MCI+" when they developed AD (between baseline and 2011) and as "MCI-" if they did not. Among the 23 gait tests, 15 were from MCI+ (9 gait tests in 2007 and 6 in 2008) and 8 from MCI- (4 gait tests in 2007 and 4 gait tests in 2008). Mann-Whitney non-parametric U test was used to compare gait parameters of MCI+ and MCI-.

RESULTS

Gait speed, symmetry and regularity were lower in MCI+ than in MCI-.

DISCUSSION

Despite the small sample size, the results presented in this original pilot study are in line as the infrequent previous literature related to this topic. The authors discuss lacks and strengths of this work.

CONCLUSIONS

These results suggest that both gait speed and gait variability could be markers to early identify MCI at risk to develop AD.

Interpreting response time effects in functional imaging studies

It has been suggested that differential neural activity in imaging studies is most informative if it is independent of response time (RT) differences. However, others view RT as a behavioural index of key cognitive processes, which is likely linked to underlying neural activity. Here, we reconcile these views using the effort and engagement framework developed by Taylor, Rastle, and Davis (2013) and data from the domain of reading aloud. We propose that differences in neural engagement should be independent of RT, whereas, differences in neural effort should co-vary with RT. We illustrate these different mechanisms using data from an fMRI study of neural activity during reading aloud of regular words, irregular words, and pseudowords. In line with our proposals, activation revealed by contrasts designed to tap differences in neural engagement (e.g., words are meaningful and therefore engage semantic representations more than pseudowords) survived correction for RT, whereas activation for contrasts designed to tap differences in neural effort (e.g., it is more difficult to generate the pronunciation of pseudowords than words) correlated with RT. However, even for contrasts designed to tap neural effort, activity remained after factoring out the RT–BOLD response correlation. This may reveal unpredicted differences in neural engagement (e.g., learning phonological forms for pseudowords > words) that could further the development of cognitive models of reading aloud. Our framework provides a theoretically well-grounded and easily implemented method for analysing and interpreting RT effects in neuroimaging studies of cognitive processes.

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We propose a way to interpret correlations between activity and RT in fMRI studies.

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Activity for contrasts tapping neural engagement should be independent of RT.

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Activity for contrasts tapping neural effort should correlate with RT.

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RT correlated activity during pseudo and irregular word naming supports our proposal.

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Additional engagement for pseudo and irregular words requires further investigation.

Quantification and reliability of center of pressure movement during balance tasks of varying difficulty

Postural control is often assessed by quantifying the magnitude of the center of pressure (COP) movement. However, these measures usually focus on the gross amount of movement and ignore the temporal structure of the COP signal. A novel non-linear analysis technique was recently developed to characterize the temporal structure of the COP signal with an output termed the entropic half-life [E(1/2)]. The E(1/2) reflects how much of the previous postural position is used to determine the current postural control strategy (memory effect). The purpose of this study was to quantify the E(1/2) and four COP movement magnitude measurements (medio-lateral and anterior-posterior excursion, path length, 95% ellipse area) for balance tasks increasing in sensory difficulty, as well as the test-retest reliability of each measure. Twenty-seven healthy young adults completed single limb stance tasks varying in sensory difficulty (rigid surface eyes open, rigid surface eyes closed, foam surface eyes open) on two separate occasions. Relative reliability was assessed using an intraclass correlation coefficient (ICC3,3). Absolute reliability was assessed using the standard error of the measurement (SEM) and the sensitivity of the measurement to true changes was assessed using the minimal detectable change (MDC95). The E(1/2) was found to have excellent reliability for all tasks tested (ICC range 0.82-0.91, SEM range 3.5-14.1 mm, MCD95 range 9.7-39.2 mm). The high reliability of the E(1/2) was comparable to that of movement magnitude measurements. This may be used in order to better understand the underlying motor control system.

Wearable sensors can reliably quantify gait alterations associated with disability in people with progressive multiple sclerosis in a clinical setting

Gait disability in people with progressive multiple sclerosis (MS) is difficult to quantify using existing clinical tools. This study aims to identify reliable and objective gait-based biomarkers to monitor progressive multiple sclerosis (MS) in clinical settings. During routine clinical visits, 57 people with secondary progressive MS and 24 healthy controls walked for 6 minutes wearing three inertial motion sensors. Fifteen gait measures were computed from the sensor data and tested for between-session reliability, for differences between controls and people with moderate and severe MS disability, and for correlation with Expanded Disability Status Scale (EDSS) scores. The majority of gait measures showed good to excellent between-session reliability when assessed in a subgroup of 23 healthy controls and 25 people with MS. These measures showed that people with MS walked with significantly longer step and stride durations, reduced step and stride regularity, and experienced difficulties in controlling and maintaining a stable walk when compared to controls. These abnormalities significantly increased in people with a higher level of disability and correlated with their EDSS scores. Reliable and objective gait-based biomarkers using wearable sensors have been identified. These biomarkers may allow clinicians to quantify clinically relevant alterations in gait in people with progressive MS within the context of regular clinical visits.

Spatiotemporal gait analysis of older persons in clinical practice and research : Which parameters are relevant?

For older persons walking is a basic activity of daily life which characterizes the person's functional mobility. Therefore, the improvement of walking performance is a major clinical outcome during geriatric rehabilitation. Furthermore, walking performance is relevant for several geriatric research issues. Quantitative gait analysis can describe walking performance in detail. Besides gait speed, various qualitative parameters related to different aspects of walking performance, such as symmetry, regularity, coordination, dynamic balance and foot movement during the swing phase, can serve as outcome parameters in geriatric research and in clinical practice. Clinicians and researchers have to decide which parameters are appropriate to be used as relevant outcome parameters in the investigated person or group of persons.

Entropy Analysis in Gait Research: Methodological Considerations and Recommendations

The usage of entropy analysis in gait research has grown considerably the last two decades. The present paper reviews the application of different entropy analyses in gait research and provides recommendations for future studies. While single-scale entropy analysis such as approximate and sample entropy can be used to quantify regularity/predictability/probability, they do not capture the structural richness and component entanglement characterized by a complex system operating across multiple spatial and temporal scales. Thus, for quantification of complexity, either multiscale entropy or refined composite multiscale entropy is recommended. For both single- and multiscale-scale entropy analyses, care should be made when selecting the input parameters of tolerance window r, vector length m, time series length N and number of scales. This selection should be based on the proposed research question and the type of data collected and not copied from previous studies. Parameter consistency should be investigated and published along with the main results to ensure transparency and enable comparisons between studies. Furthermore, since the interpretation of the absolute size of both single- and multiscale entropy analyses outcomes is not straightforward, comparisons should always be made with a control condition or group.

Effect of parameter selection on entropy calculation for long walking trials

It is sometimes difficult to obtain uninterrupted data sets that are long enough to perform nonlinear analysis, especially in pathological populations. It is currently unclear as to how many data points are needed for reliable entropy analysis. The aims of this study were to determine the effect of changing parameter values of m, r, and N on entropy calculations for long gait data sets using two different modes of walking (i.e., overground versus treadmill). Fourteen young adults walked overground and on a treadmill at their preferred walking speed for one-hour while step time was collected via heel switches. Approximate (ApEn) and sample entropy (SampEn) were calculated using multiple parameter combinations of m, N, and r. Further, r was tested under two cases r*standard deviation and r constant. ApEn differed depending on the combination of r, m, and N. ApEn demonstrated relative consistency except when m=2 and the smallest r values used (rSD=0.015*SD, 0.20*SD; rConstant=0 and 0.003). For SampEn, as r increased, SampEn decreased. When r was constant, SampEn demonstrated excellent relative consistency for all combinations of r, m, and N. When r constant was used, overground walking was more regular than treadmill. However, treadmill walking was found to be more regular when using rSD for both ApEn and SampEn. For greatest relative consistency of step time data, it was best to use a constant r value and SampEn. When using entropy, several r values must be examined and reported to ensure that results are not an artifact of parameter choice.

Association between physical activity and conversion from mild cognitive impairment to dementia

Background

Physical activity has been suggested to prevent the conversion of mild cognitive impairment (MCI) to dementia in patients. We investigated the association between the continuance and regularity of physical activity and the risk of developing dementia in patients with MCI.

Methods

We analyzed 6-year followed up data for 247,149 individuals in the National Health Insurance Service (NHIS) cohort of Korea who were enrolled between January 1, 2009, and December 31, 2015. The patients were divided into four groups: those who did not engage in physical activity consistently (Never-PA group), those who initiated physical activity (Initiation-PA group), those who ceased physical activity (Withdrawal-PA group), and those who performed physical activity consistently (Maintenance-PA group). We also divided the patients into two groups: those who engaged in physical activity irregularly (Irregular-PA) and those who undertook physical activity regularly (Regular-PA).

Results

When the risk for the Never-PA group was set as the benchmark (ref = 1), the Maintenance-PA group had the lowest incidence of dementia of the Alzheimer type (DAT) compared to the other groups (HR = 0.82, 95% CI 0.79–0.86). The DAT risk of the Initiation-PA group (HR = 0.89, 95% CI 0.85–0.93) was lower than the Never-PA group. In addition, compared to the Irregular-PA group, the Regular-PA group had a 15% reduced risk for developing DAT.

Conclusions

Although no causal inference could be made, continued regular physical activity in patients with MCI is associated with a protective effect against developing DAT. Moreover, ceasing physical activity could halt this protective effect.

Supplementary information

Supplementary information accompanies this paper at 10.1186/s13195-020-00707-1.

Prediction error and regularity detection underlie two dissociable mechanisms for computing the sense of agency

The sense of agency refers to the subjective feeling of controlling one's own actions, and through them, events in the outside world. According to computational motor control models, the prediction errors from comparison between the predicted sensory feedback and actual sensory feedback determine whether people feel agency over the corresponding outcome event, or not. This mechanism requires a model of the relation between action and outcome. However, in a novel environment, where this model has not yet been learned, the sense of agency must emerge during exploratory behaviours. In the present study, we designed a novel control detection task, in which participants explored the extent to which they could control the movement of three dots with a computer mouse, and then identified the dot that they felt they could control. Pre-recorded motions were applied for two dots, and the participants' real-time motion only influenced one dot's motion (i.e. the target dot). We disturbed participants' control over the motion of the target dot in one of two ways. In one case, we applied a fixed angular bias transformation between participant's movements and dot movements. In another condition, we mixed the participant's current movement with replay of another movement, and used the resulting hybrid signal to drive visual dot position. The former intervention changes the match between motor action and visual outcome, but maintains a regular relation between the two. In contrast, the latter alters both matching and motor-visual correlation. Crucially, we carefully selected the strength of these two perturbations so that they caused the same magnitude of impairment of motor performance in a simple reaching task, suggesting that both interventions produced comparable prediction errors. However, we found the visuomotor transformation had much less effect on the ability to detect which dot was under one's own control than did the nonlinear disturbance. This suggests a specific role of a correlation-like mechanism that detects ongoing visual-motor regularity in the human sense of agency. These regularity-detection mechanisms would remain intact under the linear, but not the nonlinear transformation. Human sense of agency may depend on monitoring ongoing motor-visual regularities, as well as on detecting prediction errors.

Sampling frequency influences sample entropy of kinematics during walking

Sample entropy (SaEn) has been used to assess the regularity of lower limb joint angles during walking. However, changing sampling frequency and the number of included strides can potentially affect the outcome. The present study investigated the effect of sample frequency and the number of included strides on the calculations of SaEn in joint angle signals recorded during treadmill walking. Eleven subjects walked at their preferred walking speed for 10 min, and SaEn was calculated on sagittal plane hip, knee, and ankle angle signals extracted from 50, 100, 200, 300, and 400 strides at sampling frequencies of 60, 120, 240, and 480 Hz. Increase in sampling frequency decreased the SaEn significantly for the three joints. The number of included strides had no effect on the SaEn calculated on the hip joint angle and only limited effect on the SaEn calculated on the knee and ankle joint signals. The present study suggests that the number of data points within each stride to a greater extent determines the size of the SaEn compared to the number of strides and emphasizes the use of a fixed number of data points within each stride when applying SaEn to lower limb joint angles during walking. Graphical abstract Sampling frequency influences sample entropy of kinematics during walking.

Differences in pattern of variability for lower extremity kinematics between walking and running

This study characterizes walking and running patterns in healthy individuals using linear and nonlinear methods Seventeen individuals (12 males, 5 females) volunteered for the study. 3D kinematic data during walking (WA) and running (RU) on a motorized treadmill were captured using reflective markers placed on lower body (200Hz). A single 25s trial (5000 data points) was collected for each gait task. WA speed was 1.39±0.12m/s, whereas RU speed was 2.56±0.27m/s. Variables of interest included ankle plantar/dorsi flexion, knee flexion/extension, knee abduction/adduction, hip flexion/extension, and hip abduction/adduction angles. For linear analysis, standard deviation (SD) and coefficient of variation (CV) were calculated for the entire time series for both conditions. Nonlinear analysis included assessing pattern of regularity of respective kinematic time series using approximate entropy (ApEn). Inferential analyses were conducted using MANOVA to compare selected dependent measures (p<0.05). SD for knee flexion/extension angle (WA=23.34±4.17, RU=27.51±5.25) and ankle plantar/dorsi flexion angle (WA=9.24±2.37, RU=12.88±2.00) were both greater during running. For all other variables, there were no significant differences in degree of variability between walking and running (p's>0.05). Running ApEn values were greater than walking ApEn values for knee flexion/extension (WA=0.14±0.02, RU=0.23±0.04), knee abduction/adduction (WA=0.18±0.07, RU=0.24±0.07), hip flexion/extension (WA=0.09±0.02, RU=0.17±0.04), and hip abduction/adduction (WA=0.12±0.03, RU=0.21±0.05). Greater variability was demonstrated during running across all joints compared to walking. This suggests that ApEn is more sensitive to detecting changes between different gait conditions than standard discrete measures of variability (SD).

Examining the role of imageability and regularity in word reading accuracy and learning efficiency among first and second graders at risk for reading disabilities

This study explored word reading accuracy and word learning efficiency in first- and second-grade students (N = 125). In two experiments, students participated in a short training exposing them to words that varied on orthographic regularity and imageability. In Experiment 1 the form of word feedback was manipulated (phonemic vs. whole word), whereas in Experiment 2 pretraining exposure was manipulated (training on meaning vs. imageability). Crossed random effects models were used to explore child- and item-level predictors related to number of exposures to mastery, posttest word reading performance, and maintenance performance after 1 week. Results from Experiment 1 indicate that imageability plays a role in irregular word learning. Results from Experiment 2 suggest that students who received imageability training required fewer exposures to reach mastery. There was a significant interaction between initial word reading skill and condition, with students with low word reading skills requiring fewer exposures for mastery if they were in the imageability condition. Overall, these findings suggest that word imageability significantly affects both word reading accuracy and rate of word learning.

Knowledge of sequence structure prevents auditory distraction: an ERP study

Infrequent, salient stimuli often capture attention despite their task-irrelevancy, and disrupt on-going goal-directed behavior. A number of studies show that presenting cues signaling forthcoming deviants reduces distraction, which may be a "by-product" of cue-processing interference or the result of direct preparatory processes for the forthcoming distracter. In the present study, instead of "bursts" of cue information, information on the temporal structure of the stimulus sequence was provided. Young adults performed a spatial discrimination task where complex tones moving left or right were presented. In the predictable condition, every 7th tone was a pitch-deviant, while in the random condition the position of deviants was random with a probability of 1/7. Whereas the early event-related potential correlates of deviance-processing (N1 and MMN) were unaffected by predictability, P3a amplitude was significantly reduced in the predictable condition, indicating that prevention of distraction was based on the knowledge about the temporal structure of the stimulus sequence.

Temporal dynamics of contingency extraction from tonal and verbal auditory sequences

Consecutive sound events are often to some degree predictive of each other. Here we investigated the brain's capacity to detect contingencies between consecutive sounds by means of electroencephalography (EEG) during passive listening. Contingencies were embedded either within tonal or verbal stimuli. Contingency extraction was measured indirectly via the elicitation of the mismatch negativity (MMN) component of the event-related potential (ERP) by contingency violations. MMN results indicate that structurally identical forms of predictability can be extracted from both tonal and verbal stimuli. We also found similar generators to underlie the processing of contingency violations across stimulus types, as well as similar performance in an active-listening follow-up test. However, the process of passive contingency extraction was considerably slower (twice as many rule exemplars were needed) for verbal than for tonal stimuli These results suggest caution in transferring findings on complex predictive regularity processing obtained with tonal stimuli directly to the speech domain.

Towards better diagnostic criteria for periodic fever, aphthous stomatitis, pharyngitis and adenitis syndrome

AIM

Periodic fever, aphthous stomatitis, pharyngitis and cervical adenitis (PFAPA) syndrome is the most common cause of a periodic fever in childhood. The exact pathogenesis and the aetiology of PFAPA are still unknown.

METHODS

We conducted a non-systematic review of published articles about PFAPA syndrome and summarised the evidence for diagnostic criteria and treatment options for PFAPA.

RESULTS

The first proposed diagnostic criteria for PFAPA, in addition to periodic fever, included aphthous stomatitis, pharyngitis or cervical lymphadenitis in children younger than five years at the beginning of the symptoms. C-reactive protein (CRP) levels and leucocyte counts increase in most patients during episodes. Recent research reveals that tonsillectomy provides an immediate and long-lasting cure for PFAPA, even in the absence of classic criteria of aphthous stomatitis, pharyngitis or cervical adenitis and in children older than five years.

CONCLUSION

We suggest that PFAPA can be diagnosed in children with at least five regularly occurring fever episodes without any other explanation, even in the absence of aphthous stomatitis, pharyngitis or cervical lymphadenitis and also in children older than five years.

Spatiotemporal variation in travel regularity through transit user profiling

New smart card datasets are providing new opportunities to explore travel behaviour in much greater depth than anything accomplished hitherto. Part of this quest involves measuring the great array of regular patterns within such data and explaining these relative to less regular patterns which have often been treated in the past as noise. Here we use a simple method called DBSCAN to identify clusters of travel events associated with particular individuals whose behaviour over space and time is captured by smart card data. Our dataset is a sequence of three months of data recording when and where individual travellers start and end rail and bus travel in Greater London. This dataset contains some 640 million transactions during the period of analysis we have chosen and it enables us to begin a search for regularities at the most basic level. We first define measures of regularity in terms of the proportions of events associated with temporal, modal (rail and bus), and service regularity clusters, revealing that the frequency distributions of these clusters follow skewed distributions with different means and variances. The analysis then continues to examine how regularity relative to irregular travel across space, demonstrating high regularities in the origins of trips in the suburbs contrasted with high regularities in the destinations in central London. This analysis sets the agenda for future research into how we capture and measure the differences between regular and irregular travel which we discuss by way of conclusion.

Upper body accelerations during walking are altered in adults with ACL reconstruction

This study was designed to assess and compare the pattern of acceleration from the lower trunk, neck and head regions for individuals with reconstructed ACL compared to healthy controls during walking. Participants with unilateral ACL reconstruction and matched control persons participated in the study. Accelerations were collected using three triaxial accelerometers attached to the head, neck, and lower trunk. Measures of amplitude and signal regularity of the acceleration data were performed. Similarities were seen between both groups with regards to the general acceleration patterns in all three axes. However, the results also revealed that the individuals with ACL reconstruction had significantly greater peak power in the AP direction at higher frequencies, indicating a reduced ability to attenuate frequency signals. Further, the ACL group had a reduced ability to control head motion during gait, as indicated by reduced regularity in VT. Both groups demonstrated a similar pattern of gait-related oscillations across the head, neck and trunk segments. However, adults with a reconstructed ACL demonstrated a reduced capacity to compensate for the higher frequency components of the gait signal, which may have led to a decline in head control. Overall, these findings indicate that previous damage to the ACL is not simply localized to the knee joint, but influences upper body control, too.

Altered movement strategy of chronic ankle instability individuals with postural instability classified based on Nyquist and Bode analyses

BACKGROUND

The aim of the current study was to assess movement strategies during a single leg balance in chronic ankle instability individuals with unstable postural control strategy identified by Nyquist and Bode analyses in conjunction with sample entropy.

METHODS

Thirty-three participants with self-reported chronic ankle instability and 22 healthy controls performed single-leg eyes closed static balance trials. The sagittal and frontal plane kinematics in the lower extremity and trunk as well as center of pressure trajectories were recorded during three, 20-second trials. The Nyquist and Bode stability analyses, which classify center of pressure waveforms as stable based on the resulting gain and phase margins, were performed to identify the presence of postural control deficits. Sample entropy was implemented to analyze movement strategies during the task.

FINDINGS

Based on the Nyquist and Bode stability analyses, we included 19 out of 33 chronic ankle instability participants with unstable postural control strategy and 16 out of 22 controls with stable postural control strategy in the final analyses. Chronic ankle instability participants demonstrated a significantly lower sample entropy value in sagittal and frontal plane trunk kinematics and sagittal plane hip kinematics compared to the controls. No between-group differences existed in other kinematic measures.

INTERPRETATION

The lower sample entropy values in participants with chronic ankle instability indicates that those with postural control deficits may increase reliance on the trunk and hip joint contributions to the maintenance of postural control, reflecting changes in the sensorimotor constraints on movement patterns during the task.

The influence of ion concentrations on the dynamic behavior of the Hodgkin-Huxley model-based cortical network

Action potentials (APs) in the form of very short pulses arise when the cell is excited by any internal or external stimulus exceeding the critical threshold of the membrane. During AP generation, the membrane potential completes its natural cycle through typical phases that can be formatted by ion channels, gates and ion concentrations, as well as the synaptic excitation rate. On the basis of the Hodgkin-Huxley cell model, a cortical network consistent with the real anatomic structure is realized with randomly interrelated small population of neurons to simulate a cerebral cortex segment. Using this model, we investigated the effects of Na(+) and K(+) ion concentrations on the outcome of this network in terms of regularity, phase locking, and synchronization. The results suggested that Na(+) concentration does slightly affect the amplitude but not considerably affects the other parameters specified by depolarization and repolarization. K(+) concentration significantly influences the form, regularity, and synchrony of the network-generated APs. No previous study dealing directly with the effects of both Na(+) and K(+) ion concentrations on regularity and synchronization of the simulated cortical network-generated APs, allowing for the comparison of results obtained using our methods, was encountered in the literature. The results, however, were consistent with those obtained through studies concerning resonance and synchronization from another perspective and with the information revealed through physiological and pharmacological experiments concerning changing ion concentrations or blocking ion channels. Our results demonstrated that the regularity and reliability of brain functions have a strong relationship with cellular ion concentrations, and suggested the management of the dynamic behavior of the cellular network with ion concentrations.

Lexique-Infra: grapheme-phoneme, phoneme-grapheme regularity, consistency, and other sublexical statistics for 137,717 polysyllabic French words

Psycholinguistic research has shown that both the regularity and consistency of the grapheme-phoneme and phoneme-grapheme correspondences impact word processing. Lexique-Infra is a new database providing infra-lexical statistics for 137,717 French words. The frequencies of the grapheme-phoneme and phoneme-grapheme correspondences as well as other indicators (consistency, regularity, letter frequencies, bigrams, trigrams, phonemes, biphones, and syllables, etc.) are proposed and have been computed from the corpus of subtitles in Lexique 3.83. The aim of this new database is to propose numerous infra-lexical variables based on adult frequencies for a large number of words.

An approach to decision-making via picture fuzzy soft graphs

Fuzzy soft graphs are effective mathematical tools that are used to model the vagueness of the real world. A fuzzy soft graph is a fusion of the fuzzy soft set and the graph model and is widely used across different fields. In this current research, the concept of picture fuzzy soft graphs is presented by combining the theory of picture soft sets with graphs. The introduction of this new picture fuzzy soft graphs is an emerging concept that can be rather developed into various graph theoretical concepts. Since soft sets are most usable in real-life applications, the newly combined concepts of the picture and fuzzy soft sets will lead to many possible applications in the fuzzy set theoretical area by adding extra fuzziness in analyzing. The notions of picture soft graphs, strong and complete picture soft fuzzy graphs, a few types of product picture fuzzy soft graphs, and regular, totally regular picture fuzzy soft graphs are discussed and validated using real-world scenarios. In addition, an application of decision-making for medical diagnosis in the current COVID scenario using the picture fuzzy soft graph has been illustrated.

Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

Gait regularity assessed by wearable sensors: Comparison between accelerometer and gyroscope data for different sensor locations and walking speeds in healthy subjects

Inertial measurement units (IMU), including accelerometers and gyroscopes, can support the assessment of gait regularity, relevant for an effective walking. Gait regularity is typically quantified by an autocorrelation analysis of trunk/pelvis accelerations. A methodological upgrade fosters a multi-sensor approach including upper and lower limbs. Very few studies dealt with gait regularity using gyroscope data and no comparison between the two inertial sensors has been published. Therefore, this study compares gait regularity assessment by autocorrelation analyses performed on accelerometer and gyroscope data simultaneously acquired. Twenty-five adult healthy subjects walked steady-state on treadmill at three speeds (3.6, 5.0, 6.4 km/h), with rest between. Four IMUs were firmly attached on the trunk, pelvis, wrist and ankle. The autocorrelation method was applied to time-windows of the signal vector magnitude and resulted, on average for each trial, in its regularity index (RI) and periodicity index (PI), i.e. the stride time. Results showed that both sensors identified the same PI (Spearman correlation coefficient = 0.999), and evidenced that, for matched sensor locations and gait speeds, the accelerometer-based RI was larger/equal to the gyroscope-based RI on 86.3% of all conditions (overall median of gyroscope-to-accelerometer RI ratio was 91.1%). The two sensors gave always statistically different RI, with the exception of the ankle at the lowest speed and wrist at higher speeds. Such results help remove potential confounders from analyses performed with different sensors and support the use of accelerometers for gait regularity assessment, not excluding that gyroscopes may be more suitable for other human movements.

When sounds look right and images sound correct: cross-modal coherence enhances claims of pattern presence

How do people decide whether a stimulus contains a pattern? One possibility is that they rely on a global, non-specific signal of coherence. Interestingly, this signal might reflect a combination of different stimulus sources. Consequently, the coherence of one stimulus might influence decisions about coherence of a second, unrelated stimulus. We explored this possibility in three experiments in which participants judged the presence of a pattern in targets from one sensory modality, while being exposed in the background to incidental coherent and incoherent stimuli in a different modality (visual→auditory, auditory→visual). Across all three experiments, using a variety of judgments, coherence of incidental background cross-modal patterns enhanced claims of pattern presence. These findings advance our understanding of how people judge order in the structured as well as in the unstructured world.

Fluctuations of observed breeding Rough-legged Hawks and Gyrfalcons: regularity reconsidered

We recently assessed regularity in fluctuation of annual numbers of breeding pairs observed for several raptor species, and found no indication of reputed regular or cyclic fluctuations in our Colville River, Alaska sample for Gyrfalcons (Falco rusticolus) or Rough-legged Hawks (Buteo lagopus) (Mindell et al. 1987). Discussions with colleagues have prompted us to expand our analysis and clarify key points. We present time series analyses, using the Colville River sample size and interval (13 surveys during a 27 year period) for a data set on lynx (Lynx canadensis) (Elton and Nicholson 1942) and for a hypothetical Gyrfalcon population. Indication of regular 10-year fluctuations (P<0.05) in these analyses supports the adequacy of our Colville River sample size and interval in assessing a possible 10-year cycle for Gyrfalcons. We provide dates and methods used for the annual Colville River surveys in discussing applications and limitations of the survey findings. We use the annual Colville River surveys as an index of fluctuation in actual numbers of Gyrfalcons and Rough-legged Hawks present in the study area at the time, based on similarity in timing of surveys between years, use of boat surveys in 12 of 13 years, evidence indicating similarity in sampling error between years, and demonstration of the adequacy of the sample interval. Whether or not numbers of breeding Gyrfalcons and Rough-legged Hawks fluctuate regularly remains an open question. We have provided a first assessment of regularity in fluctuation of observed numbers of breeding pairs, and find regularity for this parameter unsupported considering the Colville River study area as a whole. If other researchersare stirred to test "conventional wisdom" presuming regularity, our study will have served its purpose.