The sustainability of stock price fluctuations: Explanation from a recursive dynamic model.

The sustainability of stock price fluctuations indicated by many empirical studies hardly reconciles with the existing models in standard financial theories. This paper proposes a recursive dynamic asset pricing model based on the comprehensive impact of the sentiment investor, the information trader and the noise trader. The dynamic process of the asset price is characterized and a numerical simulation of the model is provided. The model captures the features of the actual stock price that are consistent with the empirical evidence on the sustainability of stock price fluctuations. It also offers a partial explanation for other financial anomalies, for example, asset price's overreaction, asset bubble and the financial crisis. The major finding is that investor sentiment is the key factor to understand the sustainability of stock price fluctuations.

Numerical reconstruction of turbid slab optical properties using global optimization algorithms.

The detection and reconstruction of the optical properties within turbid slabs/plate parallel mediums have been widely investigated for its applications in medical diagnosis, atmosphere detection, etc., where the scattering of light would be expected. Although the scattering signal can be utilized for diagnostics purposes, the multiple scattering in the intermediate scattering regime (with an optical depth ~ 2-9) has posed a remarkable challenge. Existing optical tomography methods usually only reconstruct the reduced scattering coefficient to investigate the properties of the scattering target, while reconstruction efforts in analyzing the exact scattering phase function are rare. Solving such issues can provide much more information for proper interpretation of the characteristics of the turbid slab. This work demonstrates an inversion method based on optimization algorithms and the angular distribution of the transmitted light at the entrance plane and the exit plane of the sought medium. Candidate phase functions were pre-calculated and the optimization algorithm is able to reconstruct the phase function spatial distribution of the turbid slab with a satisfactory computational cost. Parametric studies were also performed to analyze the performance of each optimization algorithm used and the sensitivity of this Markov reconstruction scheme to noise.

Evaluating different epidemiological models with the identical basic reproduction number ℛ0.

Epidemiological models with the identical basic reproduction number R0 may behave differently on both short time scale and long time scale. In this paper, we compare the predicted final sizes for several deterministic epidemic models and estimate the probabilities of a minor/major outbreak for continuous-time Markov chain (CTMC) models, all epidemic models have the identical R0 . It is proved that the final size predicted by the epidemic model with homogeneous mixing is larger than with heterogeneous mixing. For CTMC models with heterogeneous mixing, the probabilities of a minor outbreak initiated by superspreaders and non-superspreaders are calculated and compared. For both deterministic modelling and stochastic modelling, numerical simulations are performed to support the mathematical analysis.

Risk literacy assessment of general practitioners and medical students using the Berlin Numeracy Test.

BACKGROUND: The responsibility for helping patients understand potential health benefits and risks, especially regarding screening tests, falls largely to general practitioners (GPs). The Berlin Numeracy Test (BNT) specifically measures risk literacy (i.e., the ability to understand different aspects of statistical numeracy associated with accurate interpretation of information about risks). This study explored the association between risk literacy levels and clinical experience in GPs vs. medical students. Additionally, the effect of GP risk literacy on evaluation of the predictive value of screening tests was examined. METHODS: The participants were 84 GPs and 92 third-year medical students who completed the BNT (total score range 0-4 points). The GPs received an additional case scenario on mammography screening as a simple measure of performance in applying numeracy skills. RESULTS: Despite having an average of 25.9 years of clinical experience, GPs scored no better than medical students on risk literacy (GPs: 2.33 points, 95% confidence interval [CI] 2.08-2.59; students: 2.34, 95% CI 2.07-2.61; P = .983). Of all GPs, 71.6% (n = 58) greatly overestimated the real predictive value. CONCLUSIONS: In this study, we found no difference in risk literacy between current students and current GPs. GPs lack risk literacy and consequently do not fully understand numeric estimates of probability in routine screening procedures.

Analog Site Experiment in the High Andes-Atacama Region: Surface Energy Budget Components on Ojos del Salado from Field Measurements and WRF Simulations.

Remote sensing data are abundant, whereas surface in situ verification of atmospheric conditions is rare on Mars. Earth-based analogs could help gain an understanding of soil and atmospheric processes on Mars and refine existing models. In this work, we evaluate the applicability of the Weather Research and Forecasting (WRF) model against measurements from the Mars analog High Andes-Atacama Desert. Validation focuses on the surface conditions and on the surface energy budget. Measurements show that the average daily net radiation, global radiation, and latent heat flux amount to 131, 273, and about 10 W/m2, respectively, indicating extremely dry atmospheric conditions. Dynamically, the effect of topography is also well simulated. One of the main modeling problems is the inaccurate initial soil and surface conditions in the area. Correction of soil moisture based on in situ and satellite soil moisture measurements, as well as the removal of snow coverage, reduced the surface skin temperature root mean square error from 9.8°C to 4.3°C. The model, however, has shortcomings when soil condition modeling is considered. Sensible heat flux estimations are on par with the measurements (daily maxima around 500 W/m2), but surface soil heat flux is greatly overestimated (by 150-500 W/m2). Soil temperature and soil moisture diurnal variations are inconsistent with the measurements, partially due to the lack of water vapor representation in soil calculations.

A latent topic model with Markov transition for process data.

We propose a latent topic model with a Markov transition for process data, which consists of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem-solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem-solving item in the 2012 version of the Programme for International Student Assessment (PISA).

Assessment of the shock adsorption properties of bike helmets: a numerical/experimental approach.

In this paper, a numerical and experimental study of the shock absorption properties of bike helmets is presented. Laboratory compression and tensile tests were carried out on samples of expanded polystyrene (EPS) and polycarbonate (PC), respectively constituting the internal shock absorption layer and the external hard shell of composite helmets. The measured responses of the two materials were then exploited to calibrate the relevant elasto-plastic constitutive models, adopted in full-scale finite element analyses of a helmet subject to standardized impacts. The simulations allowed assessing the time evolution of the acceleration measured inside the headform (according e.g., to EN 1078) and the failure mechanisms of the helmet, if any, as induced by the localization of plastic deformations.

Experimental and Numerical Simulation of Biodegradable Stents with Different Strut Geometries.

OBJECTIVE: Biodegradable stents represent a new technological development in the field of cardiovascular angioplasty. The stent geometry plays a crucial role in determining stent performance. METHODS: This study describes four stent models with various strut geometries (circular, triangular, hexagonal, and spline) and identical links. The performance of the various stents is assessed by modeling the processes of compression and balloon expansion using experimental and numerical techniques. RESULTS: Four adjustable variables related to radial strength, foreshortening rate, maximum expanded diameter and coverage are considered in this studies. The maximum stress distributions from our numerical analysis are in agreement with the experimental fracture measurements. CONCLUSION: Analysis of the stent parameters indicates that the hexagonal geometry is a relatively good stent strut design. The results described in this paper will be useful in further optimization studies and for the development of stents with a higher radial strength and increased fracture resistance.

Time-dependent diffusion in undulating thin fibers: Impact on axon diameter estimation.

Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modeling axons as straight cylinders. Axons do not, however, propagate in straight trajectories, and so far the impact of the axonal trajectory on diameter estimation has been insufficiently investigated. Here, we employ a toy model of axons, which we refer to as the undulating thin fiber model, to analyze the impact of undulating trajectories on the time dependence of diffusion. We study time-dependent diffusion in the frequency domain and characterize the diffusion spectrum by its height, width, and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin fibers is the main parameter that determines the characteristics of the diffusion spectra. At lower frequencies (longer diffusion times), straight cylinders and undulating thin fibers can have virtually identical spectra. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and microscopic orientation dispersion of the fibers. At higher frequencies (shorter diffusion times), spectra from cylinders and undulating thin fibers differ. The low-frequency behavior of the spectra from the undulating thin fibers may also differ from that of cylinders, because the power law exponent of undulating fibers can reach values below 2 for experimentally relevant frequency ranges. In conclusion, we argue that the non-straight nature of axonal trajectories should not be overlooked when analyzing and interpreting diffusion MRI data.

Computational modeling of therapy on pancreatic cancer in its early stages.

More than eighty percent of pancreatic cancer involves ductal adenocarcinoma with an abundant desmoplastic extracellular matrix surrounding the solid tumor entity. This aberrant tumor microenvironment facilitates a strong resistance of pancreatic cancer to medication. Although various therapeutic strategies have been reported to be effective in mice with pancreatic cancer, they still need to be tested quantitatively in wider animal-based experiments before being applied as therapies. To aid the design of experiments, we develop a cell-based mathematical model to describe cancer progression under therapy with a specific application to pancreatic cancer. The displacement of cells is simulated by solving a large system of stochastic differential equations with the Euler-Maruyama method. We consider treatment with the PEGylated drug PEGPH20 that breaks down hyaluronan in desmoplastic stroma followed by administration of the chemotherapy drug gemcitabine to inhibit the proliferation of cancer cells. Modeling the effects of PEGPH20 + gemcitabine concentrations is based on Green's fundamental solutions of the reaction-diffusion equation. Moreover, Monte Carlo simulations are performed to quantitatively investigate uncertainties in the input parameters as well as predictions for the likelihood of success of cancer therapy. Our simplified model is able to simulate cancer progression and evaluate treatments to inhibit the progression of cancer.

Correlations between stochastic endemic infection in multiple interacting subpopulations.

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

CardioFAN: open source platform for noninvasive assessment of pulse transit time and pulsatile flow in hyperelastic vascular networks.

A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid-structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax-Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics.

Combination of "quadratic adaptive algorithm" and "hybrid operator splitting" or uniformization algorithms for stability against acceleration in the Markov model of sodium ion channels in the ventricular cell model.

The Markovian model has generally been used for cardiac electrophysiological simulations. However, the Markovian model is so stiff that speeding up the computation of the algorithms with variable time-steps always results in simulation instability. In particular, the unstable simulations always occur at a low voltage rate or current change, while transition rates in the Markovian model are changing markedly. The uniformization (UNI) method allows for a Markovian model simulation with high stability but also a high computation cost. To save computation costs with variable time-steps, we propose a speed increasing idea that is a compromise to the trade-off between stability and acceleration by combining Chen-Chen-Luo's "quadratic adaptive algorithm" (CCL) method with "hybrid operator splitting" (HOS) into the solver (CCL + HOS solver). The computation cost of this CCL + HOS solver is approximately 24 times lower than the CCL + UNI solver, and the CCL + HOS solver can function 295 times faster in comparison to the HOS solver with a fixed time-step (DT). The suggested optimal solver should be CCL + HOS solver with a maximum time-step at 0.1 ms due to its high speed with low error. Additionally, the CCL method has much better performance and stability than the hybrid method in this single-cell model simulation.

Numerical assessment of the human body response to a ground-level explosion.

This paper presents the results of a numerical analysis of the behaviour of a human body after a ground-level explosion. The explosions were generated by condensed charges for different stand-off distances and various masses of explosive. The detonations points were located at distances of 1.0 and 2.0 meters from the dummy (human model) obstacle. The different masses of spherically-shaped TNT charges (0.4-1.0 kg) were initiated centrally. The blast wave propagation was generated using a coupled numerical design, which included Eulerian and Lagrangian descriptions for different domains, i.e. the dummy, air, and explosive domains. The main objective of this work was to present the actual pressures and accelerations around the dummy and the body motion caused by the rapid shock of the pressure action. Reaction forces and moments of anatomical joints were provided. Furthermore, the safety criteria presented in the official standards were compared to the simulation results. In this research, different positions against the loading masses were analysed. In each analysis the same standing human model was used. The dummy geometry was based on a medium size male (1.79 m, 84.8 kg). The human body was modelled as consisting of separate, rigid parts (with adequate masses and inertia moments) connected by joints exhibiting nonlinear behaviour. Anatomical ranges of motion were taken into consideration, and a dedicated numerical technique was proposed to model the resistance moment vs. the range of motion relations for the most important human body joints.

Computational Models of Laryngeal Aerodynamics: Potentials and Numerical Costs.

Human phonation is based on the interaction between tracheal airflow and laryngeal dynamics. This fluid-structure interaction is based on the energy exchange between airflow and vocal folds. Major challenges in analyzing the phonatory process in-vivo are the small dimensions and the poor accessibility of the region of interest. For improved analysis of the phonatory process, numerical simulations of the airflow and the vocal fold dynamics have been suggested. Even though most of the models reproduced the phonatory process fairly well, development of comprehensive larynx models is still a subject of research. In the context of clinical application, physiological accuracy and computational model efficiency are of great interest. In this study, a simple numerical larynx model is introduced that incorporates the laryngeal fluid flow. It is based on a synthetic experimental model with silicone vocal folds. The degree of realism was successively increased in separate computational models and each model was simulated for 10 oscillation cycles. Results show that relevant features of the laryngeal flow field, such as glottal jet deflection, develop even when applying rather simple static models with oscillating flow rates. Including further phonatory components such as vocal fold motion, mucosal wave propagation, and ventricular folds, the simulations show phonatory key features like intraglottal flow separation and increased flow rate in presence of ventricular folds. The simulation time on 100 CPU cores ranged between 25 and 290 hours, currently restricting clinical application of these models. Nevertheless, results show high potential of numerical simulations for better understanding of phonatory process.

Asymptotic and exact interval estimators of the common odds ratio under the sequential parallel comparison design.

When studying treatments for psychiatric or mental diseases in a placebo-controlled trial, we may consider use of the sequential parallel comparison design to reduce the number of patients needed through the reduction of the high placebo response rate. Under the assumption that the odds ratio of responses is constant between phases in the sequential parallel comparison design, we derive the conditional maximum likelihood estimator for the odds ratio. On the basis of the conditional likelihood, we further derive three asymptotic interval and an exact interval estimators for the odds ratio of responses. We employ Monte Carlo simulation to evaluate the performance of these interval estimators in a variety of situations. We find that the asymptotic interval and exact interval estimators developed here can all perform well. We use the double-blind, placebo-controlled study assessing the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy for treating patients with major depressive disorder to illustrate the use of these estimators.

Uncertainty Quantification for Non-invasive Assessment of Pressure Drop Across a Coarctation of the Aorta Using CFD.

PURPOSE: Numerical assessment of the pressure drop across an aortic coarctation using CFD is a promising approach to replace invasive catheter-based measurements. The aim of this study was to investigate and quantify the uncertainty of numerical calculation of the pressure drop introduced during two essential steps of medical image processing: segmentation of the patient-specific geometry and measurement of patient-specific flow rates from 4D-flow-MRI. METHODS: Based on the baseline segmentation, geometries with different stenosis diameters were generated for a sample of ten patients. The pressure drop generated by these geometries was calculated for different volume flow rates using computational fluid dynamics. Based on these simulations, a second order polynomial fit was calculated. Based on these polynomial fits an uncertainty of pressure drop calculation was quantified. RESULTS: The calculated pressure drop values varied strongly between the patients. In four patients, pressure drops above and below the clinical threshold of 20 mmHg were found. The median standard deviation of the pressure drop was 2.3 mmHg. The sensitivity of the pressure drop toward changes in the volume flow rate or the stenosis geometry varied between patients. CONCLUSION: The uncertainty of numerical pressure drop calculation introduced by uncertainties during image segmentation and measurement of volume flow rates was comparable to the uncertainty of pressure drop measurements using invasive catheterization. However, in some patients this uncertainty would have led to different treatment decision. Therefore, patient-specific uncertainty assessment might help to better understand the reliability of a numerically calculated biomarker as the pressure drop across an aortic coarctation.

Stochastic differential game for management of non-renewable fishery resource under model ambiguity.

A new bio-economic model for managing population of non-renewable inland fishery resource in uncertain environment is presented. Population dynamics of the resource is described with stochastic differential equations (SDEs) having ambiguous growth and mortality rates. The performance index to be maximized by the manager of the resource while minimized by nature is presented in the context of differential game theory. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation that governs the optimal resource management strategy under the ambiguity. The main contribution of this paper is a series of theoretical analysis on the reduced HJBI equation for non-renewable fishery resources in a broad sense, indicating that the ambiguity critically affects the resulting optimal controls. Practical implications of the theoretical analysis results are also presented focusing on artificially hatched Plecoglossus altivelis (Ayu), an important inland fishery resource in Japan.

Uncertainty Quantification of a Multiscale Model for In-Stent Restenosis.

PURPOSE: Coronary artery stenosis, or abnormal narrowing, is a widespread and potentially fatal cardiac disease. After treatment by balloon angioplasty and stenting, restenosis may occur inside the stent due to excessive neointima formation. Simulations of in-stent restenosis can provide new insight into this process. However, uncertainties due to variability in patient-specific parameters must be taken into account. METHODS: We performed an uncertainty quantification (UQ) study on a complex two-dimensional in-stent restenosis model. We used a quasi-Monte Carlo method for UQ of the neointimal area, and the Sobol sensitivity analysis (SA) to estimate the proportions of aleatory and epistemic uncertainties and to determine the most important input parameters. RESULTS: We observe approximately 30% uncertainty in the mean neointimal area as simulated by the model. Depending on whether a fast initial endothelium recovery occurs, the proportion of the model variance due to natural variability ranges from 15 to 35%. The endothelium regeneration time is identified as the most influential model parameter. CONCLUSION: The model output contains a moderate quantity of uncertainty, and the model precision can be increased by obtaining a more certain value on the endothelium regeneration time. We conclude that the quasi-Monte Carlo UQ and the Sobol SA are reliable methods for estimating uncertainties in the response of complicated multiscale cardiovascular models.

Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions.

We propose a reduced ODE model for the mechanical activation of cardiac myofilaments, which is based on explicit spatial representation of nearest-neighbour interactions. Our model is derived from the cooperative Markov Chain model of Washio et al. (Cell Mol Bioeng 5(1):113-126, 2012), under the assumption of conditional independence of specific sets of events. This physically motivated assumption allows to drastically reduce the number of degrees of freedom, thus resulting in a significantly large computational saving. Indeed, the original Markov Chain model involves a huge number of degrees of freedom (order of [Formula: see text]) and is solved by means of the Monte Carlo method, which notoriously reaches statistical convergence in a slow fashion. With our reduced model, instead, numerical simulations can be carried out by solving a system of ODEs, reducing the computational time by more than 10, 000 times. Moreover, the reduced model is accurate with respect to the original Markov Chain model. We show that the reduced model is capable of reproducing physiological steady-state force-calcium and force-length relationships with the observed asymmetry in apparent cooperativity near the calcium level producing half activation. Finally, we also report good qualitative and quantitative agreement with experimental measurements under dynamic conditions.