Mirror Diffusion of Cosmic Rays in Highly Compressible Turbulence Near Supernova Remnants

Recent gamma-ray observations have revealed inhomogeneous diffusion of cosmic rays (CRs) in the interstellar medium (ISM). This is expected, as the diffusion of CRs depends on the properties of turbulence, which can vary widely in the multiphase ISM. We focus on the mirror diffusion arising in highly compressible turbulence in molecular clouds (MCs) around supernova remnants (SNRs), where the magnetic mirroring effect results in significant suppression of diffusion of CRs near CR sources. Significant energy loss via proton–proton interactions due to slow diffusion flattens the low-energy CR spectrum, while the high-energy CR spectrum is steepened due to the strong dependence of mirror diffusion on CR energy. The resulting broken power-law spectrum of CRs matches well the gamma-ray spectrum observed from SNR/MC systems, e.g., IC443 and W44.

On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

Objectives : Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state groups that are especially vulnerable to cross-border firearm violence. Methods : Incidence of firearm violence (2000 to 2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results : Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant. Conclusion : The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence : Source states, Transitive states, Destination states, Isolated issue states and Stable . It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighbouring Source and Transitive States.

On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

Objectives – Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state-groups that are especially vulnerable to cross-border firearm violence.Methods – Incidence of firearm violence (2000-2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results – Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant.Conclusion – The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence – Source states, Transitive states, Destination states, Isolated issue states and Stable states. It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighboring Source and Transitive States.

On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes

General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance are included in the considered class. For these processes, the transition probability density function is explicitly determined. Moreover, simulation procedures are applied to the diffusion processes obtained starting from Wiener and Ornstein–Uhlenbeck processes. Specific examples in which the infinitesimal moments include periodic functions are discussed.

Estimating the extent of glioblastoma invasion

Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection–diffusion–reaction equations. The patient-wise parametrization of these models, and their validation via experimental data has been found to be difficult, as time sequence measurements are mostly missing. Also the clinical interest lies in the actual (invisible) tumor extent for a particular MRI/DTI scan and not in a predictive estimate. Therefore we propose a stationalized approach to estimate the extent of glioblastoma (GBM) invasion at the time of a given MRI/DTI scan. The underlying dynamics can be derived from an instationary GBM model, falling into the wide class of advection-diffusion-reaction equations. The stationalization is introduced via an analytic solution of the Fisher-KPP equation, the simplest model in the considered model class. We investigate the applicability in 1D and 2D, in the presence of inhomogeneous diffusion coefficients and on a real 3D DTI-dataset.

WHY DOES A HUMAN DIE? A STRUCTURAL APPROACH TO COHORT-WISE MORTALITY PREDICTION UNDER SURVIVAL ENERGY HYPOTHESIS

We propose a new approach to mortality prediction under survival energy hypothesis (SEH). We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero. This study assumes that SE follows a time-inhomogeneous diffusion process and defines the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is a fictitious construct, we illustrate that this assumption has the potential to yield a good parametric family of cumulative probability of death, and the parametric family yields surprisingly good predictions for future mortality rates.