Inference of Median Subjective Threshold in Psychophysical Experiments

We consider the response of a test subject upon a skin area being heated with an electromagnetic wave or a contact surface. When the specifications of the electromagnetic beam are fixed, the stimulus is solely described by the heating duration. The binary response of a subject, escape or no escape, is determined by the stimulus and a subjective threshold that varies among test realizations. We study four methods for inferring the median subjective threshold in psychophysical experiments: 1) sample median, 2) maximum likelihood estimation (MLE) with 2 variables, 3) MLE with 1 variable, and 4) adaptive Bayesian method. While methods 1 - 3 require samples of time to escape measured in the method of limits, method 4 utilizes binary outcomes observed in the method of constant stimuli. We find that a) the adaptive Bayesian method converges and is as efficient as the sample median even when the assumed model distribution is incorrect;b) this robust convergence is lost if we infer the mean instead of the median;c) for the optimal performance in an uncertain situation, it is best to use a wide model distribution;d) the predicted error from the posterior standard deviation is unreliable, dominated by the assumed model distribution.

Non-Dimensional Analysis of Thermal Effect on Skin Exposure to an Electromagnetic Beam

We consider the problem of inducing withdrawal reflex on a test subject by exposing the subject’s skin to an electromagnetic beam. Heat-sensitive nociceptors in the skin are activated wherever the temperature is above the activation temperature. Withdrawal reflex occurs when the activated volume reaches a threshold. We non-dimensionalize the problem to write the temperature as the product of a parameter-free function of non-dimensional variables and a function of beam parameters. This formulation allows studying beam parameters without knowing skin material parameters. We examine the effects of spot size, total power and distribution type of the electromagnetic beam on 3 quantities at reflex: 1) the time to reflex, 2) the maximum temperature increase, and 3) the total energy consumption. We find that the flat-top beam is the best, with the lowest energy consumption and the smallest maximum temperature increase. The Super-Gaussian beam is only slightly inferior to the flat-top. The Gaussian beam has by far the worst performance among these three.

Born of a Natural Disaster, 50 Years Later Bangladesh Faces More Environmental Challenges

Rural-to-urban migration and globalized trade are swelling cities worldwide,but these forces are perhaps more powerfully concentrated in Dhaka,Bangladesh,than anywhere on earth.Born of a natural disaster 50 years ago,the world’s most densely-populated country faces multiple environmental challenges.Water,with seasonal monsoons,is both a blessing and a curse.A one meter rise in sea level,for example,would displace as many as 25 million Bangladeshis,and cause the largest mass migration in history.Each drought,flood,or cyclone drives scores of environmental refugees from rural areas to the capital city of Dhaka,where air and water pollution run rampant.Recent rapprochement with India over decades-long boundary disputes offers hope that environmental cooperation in the vulnerable Bay of Bengal can follow.

Effect of Depth-Dependent Nociceptor Density on the Heat-Induced Withdrawal Reflex

Previously we introduced a concise dose-response model for the heat-induced withdrawal reflex caused by millimeter wave radiation. The model predicts the occurrence of withdrawal reflex from the given spatial temperature profile. It was formulated on the assumption that the density of nociceptors in skin is uniform, independent of the depth. The model has only two parameters: the activation temperature of heat-sensitive nociceptors and the critical threshold on the activated volume for triggering withdrawal reflex. In this study, we consider the case of depth-dependent nociceptor density in skin. We use a general parametric form with a scaling parameter in the depth direction to represent the nociceptor density. We analyze system behaviors for four density types of this form. Based on the theoretical results, we develop a methodology for 1) identifying from test data the density form of nociceptors distribution, 2) finding from test data the scaling parameter in the density form, and 3) determining from test data the activation temperature of nociceptors.

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power;then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.

A Two-Parameter Description for the Injury Risk of Flash Bangs with Uncertainty

We study the random injury outcome caused by multiple flash bang submunitions on a crowd. We are particularly interested in the fluctuations in injury outcome among individual realizations. Previously, to simulate the distribution of the actual number of injured, we developed a comprehensive Monte Carlo model. While the full computational model is important for thorough theoretical investigations, in practical operations, it is desirable to characterize the phenomenological behavior of injury outcome using a concise model with only one or two parameters. Conventionally, the injury outcome is indicated by the average fraction of injured, which is called the risk of significant injury (RSI). The single metric RSI description fails to capture fluctuations in the injury outcome. The number of injured in the crowd is influenced by many random factors: the aiming error of flash bang mortar, the dispersion of submunitions after mortar burst, the amount of acoustic dose reaching individual subjects, and the biovariability of individual subjects’ reactions to a given acoustic dose. We aim to include these random factors properly and concisely. In this study, we represent the random injury outcome as a compound binomial model, in which the hidden injury probability is drawn from a two-parameter model distribution. We formulate and examine six model distributions for the injury probability. The best performer is a mixture of uniform and triangle distributions, parameterized by (RSI, dp) where dp is the standard deviation of the hidden injury probability. This mixture model predicts the behavior of injury outcome with uncertainty, based solely on the two parameters (RSI, dp) in the flash bang description. For example, we can predict the probability of the injury outcome not exceeding a prescribed tolerance. We advocate the adoption of this two-parameter characterization for flash bangs to replace the single-parameter RSI description. Whenever we need to give a high level coarse description of a flash bang situation, we state that the injury risk is represented by (RSI, dp).

Extracting Human Reaction Time from Observations in the Method of Constant Stimuli

We consider the psychophysical experiments in which the test subject’s binary reaction is determined by the prescribed exposure duration to a stimulus and a random variable subjective threshold. For example, when a subject is exposed to a millimeter wave beam for a prescribed duration, the occurrence of flight action is binary (yes or no). In experiments, in addition to the binary outcome, the actuation time of flight action is also recorded if it occurs;the delay from the initiation time to the actuation time of flight action is the human reaction time, which is not measurable. In this study, we model the random subjective threshold as a Weibull distribution and formulate an inference method for estimating the human reaction time, from data of prescribed exposure durations, binary outcomes and actuation times of flight action collected in a sequence of tests. Numerical simulations demonstrate that the inference of human reaction time based on the Weibull distribution converges to the correct value even when the underlying true model deviates from the inference model. This robustness of the inference method makes it applicable to real experimental data where the underlying true model is unknown.

Promoting physical activity in a public health context

In this special issue of the Journal of Sport and Health Science entitled Physical Activity and Public Health,5 papers,1 commentary,and 1 research highlight discuss efforts using public health approaches to increase physical activity(PA)in global settings.Such efforts are warranted based on the prevalence of adults(23%)worldwide who are insufficiently active at levels recommended by the World Health Organization(WHO).

Integrating Test Data and ATBM Simulations into Dose Propagation Uncertainty Formulation for Bone Fracture Risk Assessment

We consider the problem of assessing bone fracture risk for a subject hit by a blunt impact projectile. We aim at constructing a framework for integrating test data and Advanced Total Body Model (ATBM) simulations into the risk assessment. The ATBM is a finite element model managed by the Joint Non-Lethal Weapons Directorate for the purpose of assessing the risk of injury caused by blunt impacts from non-lethal weapons. In ATBM simulations, the quantity that determines arm bone fracture is the calculated maximum strain in the bone. The main obstacle to accurate prediction is that the calculated strain is incompatible with the measured strain. The fracture strain measured in bending tests of real bones is affected by random inhomogeneity in bones and uncertainty in measurement gauge attachment location/orientation. In contrast, the strain calculated in ATBM simulations is based on the assumption that all bones are perfectly elastic with homogeneous material properties and no measurement uncertainty. To connect test data and ATBM simulations in a proper and meaningful setting, we introduce the concept of elasticity-homogenized strain. We interpret test data in terms of the homogenized strain, and build an empirical dose-injury model with the homogenized strain as the input dose for predicting injury. The maximum strain calculated by ATBM has randomness due to uncertainty in specifications of ATBM setup parameters. The dose propagation uncertainty formulation accommodates this uncertainty efficiently by simply updating the shape parameters in the dose-injury model, avoiding the high computational cost of sampling this uncertainty via multiple ATBM runs.

Dose-Injury Relation as a Model for Uncertainty Propagation from Input Dose to Target Dose

We study a general framework for assessing the injury probability corresponding to an input dose quantity. In many applications, the true value of input dose may not be directly measurable. Instead, the input dose is estimated from measurable/controllable quantities via numerical simulations using assumed representative parameter values. We aim at developing a simple modeling framework for accommodating all uncertainties, including the discrepancy between the estimated input dose and the true input dose. We first interpret the widely used logistic dose-injury model as the result of dose propagation uncertainty from input dose to target dose at the active site for injury where the binary outcome is completely determined by the target dose. We specify the symmetric logistic dose-injury function using two shape parameters: the median injury dose and the 10 - 90 percentile width. We relate the two shape parameters of injury function to the mean and standard deviation of the dose propagation uncertainty. We find 1) a larger total uncertainty will spread more the dose-response function, increasing the 10 - 90 percentile width and 2) a systematic over-estimate of the input dose will shift the injury probability toward the right along the estimated input dose. This framework provides a way of revising an established injury model for a particular test population to predict the injury model for a new population with different distributions of parameters that affect the dose propagation and dose estimation. In addition to modeling dose propagation uncertainty, we propose a new 3-parameter model to include the skewness of injury function. The proposed 3-parameter function form is based on shifted log-normal distribution of dose propagation uncertainty and is approximately invariant when other uncertainties are added. The proposed 3-parameter function form provides a framework for extending skewed injury model from a test population to a target population in application.

天降奇兵

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