Stability of the gauge equivalent classes in stationary transport

For anisotropic attenuating media, the albedo operator determines the scattering and the attenuation coefficients up to a gauge transformation. We show that such a determination is stable

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data

We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. We give a detailed convergence proof by focusing to a large extent on the dual problem. This leads naturally to the alternating split Bregman algorithm. The dual problem also turns out to yield a novel method to recover the full vector field $J$ from knowledge of its magnitude, and of the voltage $f$ on the boundary. We then present several numerical experiments that illustrate the convergence behavior of the proposed algorithm

Results of the COVID-19 mental health international for the general population (COMET-G) study.

INTRODUCTION: There are few published empirical data on the effects of COVID-19 on mental health, and until now, there is no large international study. MATERIAL AND METHODS: During the COVID-19 pandemic, an online questionnaire gathered data from 55,589 participants from 40 countries (64.85% females aged 35.80 ± 13.61; 34.05% males aged 34.90±13.29 and 1.10% other aged 31.64±13.15). Distress and probable depression were identified with the use of a previously developed cut-off and algorithm respectively. STATISTICAL ANALYSIS: Descriptive statistics were calculated. Chi-square tests, multiple forward stepwise linear regression analyses and Factorial Analysis of Variance (ANOVA) tested relations among variables. RESULTS: Probable depression was detected in 17.80% and distress in 16.71%. A significant percentage reported a deterioration in mental state, family dynamics and everyday lifestyle. Persons with a history of mental disorders had higher rates of current depression (31.82% vs. 13.07%). At least half of participants were accepting (at least to a moderate degree) a non-bizarre conspiracy. The highest Relative Risk (RR) to develop depression was associated with history of Bipolar disorder and self-harm/attempts (RR = 5.88). Suicidality was not increased in persons without a history of any mental disorder. Based on these results a model was developed. CONCLUSIONS: The final model revealed multiple vulnerabilities and an interplay leading from simple anxiety to probable depression and suicidality through distress. This could be of practical utility since many of these factors are modifiable. Future research and interventions should specifically focus on them

Coupled Physics Electrical Conductivity Imaging

Coupled physics electrical conductivity imaging utilizes interactions between the electric and some other fields, thereby providing useful interior functionals. Combining the interior and boundary data, such couplings are aimed to overcome low resolution inherent to the traditional electrical impedance tomography. In this paper we present a brief overview of some physical and mathematical aspects of coupled physics electrical conductivity imaging

History, practical aspects and contemporary research on witness and victim interviewing in France

International audienc