The Effect of a Verbal Cognitive Task on Postural Sway Does Not Persist When the Task Is Over

Dual-task balance studies explore interference between balance and cognitive tasks. This study is a descriptive analysis of accelerometry balance metrics to determine if a verbal cognitive task influences postural control after the task ends. Fifty-two healthy older adults (75 ± 6 years old, 30 female) performed standing balance and cognitive dual-tasks. An accelerometer recorded movement from before, during, and after the task (reciting every other letter of the alphabet). Thirty-six balance metrics were calculated for each task condition. The effect of the cognitive task on postural control was determined by a generalized linear model. Twelve variables, including anterior–posterior centroid frequency, peak frequency and entropy rate, medial-later entropy rate and wavelet entropy, and bandwidth in all directions, exhibited significant differences between baseline and cognitive task periods, but not between baseline and post-task periods. These results indicate that the verbal cognitive task did alter balance, but did not bring about persistent effects after the task had ended. Traditional balance measurements, i.e., root mean square and normalized path length, notably lacked significance, highlighting the potential to use other accelerometer metrics for the early detection of balance problems. These novel insights into the temporal dynamics of dual-task balance support current dual-task paradigms to reduce fall risk in older adults.

Nonparametric inference of stochastic differential equations based on the relative entropy rate

The information detection of complex systems from data is currently undergoing a revolution,driven by the emergence of big data and machine learning methodology. Discovering governingequations and quantifying dynamical properties of complex systems are among central challenges. Inthis work, we devise a nonparametric approach to learn the relative entropy rate from observationsof stochastic differential equations with different drift functions. The estimator corresponding tothe relative entropy rate then is presented via the Gaussian process kernel theory. Meanwhile, thisapproach enables to extract the governing equations. We illustrate our approach in several examples.Numerical experiments show the proposed approach performs well for rational drift functions, notonly polynomial drift functions.

A Review of Shannon and Differential Entropy Rate Estimation

In this paper, we present a review of Shannon and differential entropy rate estimation techniques. Entropy rate, which measures the average information gain from a stochastic process, is a measure of uncertainty and complexity of a stochastic process. We discuss the estimation of entropy rate from empirical data, and review both parametric and non-parametric techniques. We look at many different assumptions on properties of the processes for parametric processes, in particular focussing on Markov and Gaussian assumptions. Non-parametric estimation relies on limit theorems which involve the entropy rate from observations, and to discuss these, we introduce some theory and the practical implementations of estimators of this type.

Sensitivity of the Spatial Distribution of Fixations to Variations in the Type of Task Demand and Its Relation to Visual Entropy

Ocular activity is known to be sensitive to variations in mental workload, and recent studies have successfully related the distribution of eye fixations to the mental load. This study aimed to verify the effectiveness of the spatial distribution of fixations as a measure of mental workload and its sensitivity to different types of demands imposed by the task: mental, temporal, and physical. To test the research hypothesis, two experimental studies were run: Experiment 1 evaluated the sensitivity of an index of spatial distribution (Nearest Neighbor Index; NNI) to changes in workload. A sample of 30 participants participated in a within-subject design with different types of task demands (mental, temporal, physical) applied to Tetris game; Experiment 2 investigated the accuracy of the index through the analysis of 1-min epochs during the execution of a visual-spatial task (the “spot the differences” puzzle game). Additionally, NNI was compared to a better-known ocular mental workload index, the entropy rate. The data analysis showed a relation between the NNI and the different workload levels imposed by the tasks. In particular: Experiment 1 demonstrated that increased difficulty, due to higher temporal demand, led to a more dispersed pattern with respect to the baseline, whereas the mental demand led to a more grouped pattern of fixations with respect to the baseline; Experiment 2 indicated that the entropy rate and the NNI show a similar pattern over time, indicating high mental workload after the first minute of activity. That suggests that NNI highlights the greater presence of fixation groups and, accordingly, the entropy indicates a more regular and orderly scanpath. Both indices are sensitive to changes in workload and they seem to anticipate the drop in performance. However, the entropy rate is limited by the use of the areas of interest, making it impossible to apply it in dynamic contexts. Conversely, NNI works with the entire scanpath and it shows sensitivity to different types of task demands. These results confirm the NNI as a measure applicable to different contexts and its potential use as a trigger in adaptive systems implemented in high-risk settings, such as control rooms and transportation systems.

Sensor-Based Entropy Source Analysis and Validation for Use in IoT Environments

The IoT market has grown significantly in recent years, and it is estimated that it will continue to do so. For this reason, the need to identify new solutions to ensure security is vital for the future development in this field. Inadequate sources of entropy are one of the factors that negatively influence security. In this study, inspired by NIST’s latest entropy estimation recommendations, we proposed a methodology for analyzing and validating a sensor-based entropy source, highlighted by an innovative experiment design. Moreover, the proposed solution is analyzed in terms of resistance to multiple types of attacks. Following an analysis of the influence of sensor characteristics and settings on the entropy rate, we obtain a maximum entropy value of 0.63 per bit, and a throughput of 3.12 Kb/s, even when no motion is applied on the sensors. Our results show that a stable and resistant entropy source can be built based on the data obtained from the sensors. Our assessment of the proposed entropy source also achieves a higher complexity than previous studies, in terms of the variety of approached situations and the types of the performed experiments.

An assessment of the mathematical model for estimating of entropy optimized viscous fluid flow towards a rotating cone surface

Entropy optimization in convective viscous fluids flow due to a rotating cone is explored. Heat expression with heat source/sink and dissipation is considered. Irreversibility with binary chemical reaction is also deliberated. Nonlinear system is reduced to ODEs by suitable variables. Newton built in shooting procedure is adopted for numerical solution. Salient features velocity filed, Bejan number, entropy rate, concentration and temperature are deliberated. Numerical outcomes for velocity gradient and mass and heat transfer rates are displayed through tables. Assessments between the current and previous published outcomes are in an excellent agreement. It is noted that velocity and temperature show contrasting behavior for larger variable viscosity parameter. Entropy rate and Bejan number have reverse effect against viscosity variable. For rising values of thermal conductivity variable both Bejan number and entropy optimization have similar effect.

Shannon Entropy Rate of Hidden Markov Processes

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge’s second part on structure.

Entropy Rates and Efficiency of Convecting-Radiating Fins

We present a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat. Starting from an analysis of the properties of the entropy rate of the steady state, we show how it is possible to assess the efficiency of such devices by looking at the amount of entropy produced in the heat transfer process. Our study concerns both purely convective fins and convection-radiant fins and takes advantage of explicit expressions for the distribution of heat along the fin. It is shown that, in a suitable limit, the standard definition of efficiency and the entropic definition coincide. The role of the fluid temperature is explicit in the new definition and in the purely convective case. An application to an aluminium fin is given. Analytical and numerical results are discussed.