Preliminary EoS for core-collapse supernova simulations with the QMC model

In this work we present the preliminary results of a complete equation of state (EoS) for core-collapse supernova simulations. We treat uniform matter made of nucleons using the the quark-meson coupling (QMC) model. We show a table with a variety of thermodynamic quantities, which covers the proton fraction range $Y_{p}=0-0.65$ with the linear grid spacing $\Delta Y_{p}=0.01$ ($66$ points) and the density range $\rho_{B}=10^{14}-10^{16}$g.cm$^{-3}$ with the logarithmic grid spacing $\Delta log_{10}(\rho_{B}/[$g.cm$^{-3}])=0.1$ ($21$ points). This preliminary study is performed at zero temperature and our results are compared with the widely used EoS already available in the literature

Lyndon Array Construction during Burrows-Wheeler Inversion

In this paper we present an algorithm to compute the Lyndon array of a string $T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler transform of $T$. Our algorithm runs in linear time using only a stack in addition to the data structures used for Burrows-Wheeler inversion. We compare our algorithm with two other linear-time algorithms for Lyndon array construction and show that computing the Burrows-Wheeler transform and then constructing the Lyndon array is competitive compared to the known approaches. We also propose a new balanced parenthesis representation for the Lyndon array that uses $2n+o(n)$ bits of space and supports constant time access. This representation can be built in linear time using $O(n)$ words of space, or in $O(n\log n/\log\log n)$ time using asymptotically the same space as $T$

Disease Localization in Multilayer Networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure

Correlation between Subjective Nasal Patency and Intranasal Airflow Distribution

Objectives (1) Analyze the relationship between intranasal airflow distribution and subjective nasal patency in healthy and nasal airway obstruction (NAO) cohorts using computational fluid dynamics (CFD). (2) Determine whether intranasal airflow distribution is an important objective measure of airflow sensation that should be considered in future NAO virtual surgery planning. Study Design Cross-sectional. Setting Academic tertiary medical center and academic dental clinic. Subjects and Methods Three-dimensional models of nasal anatomy were created based on computed tomography scans of 15 patients with NAO and 15 healthy subjects and used to run CFD simulations of nasal airflow and mucosal cooling. Subjective nasal patency was quantified with a visual analog scale (VAS) and the Nasal Obstruction Symptom Evaluation (NOSE). Regional distribution of nasal airflow (inferior, middle, and superior) was quantified in coronal cross sections in the narrowest nasal cavity. The Pearson correlation coefficient was used to quantify the correlation between subjective scores and regional airflows. Results Healthy subjects had significantly higher middle airflow than patients with NAO. Subjective nasal patency had no correlation with inferior and superior airflows but a high correlation with middle airflow (|r| = 0.64 and |r| = 0.76 for VAS and NOSE, respectively). Anterior septal deviations tended to shift airflow inferiorly, reducing middle airflow and reducing mucosal cooling in some patients with NAO. Conclusion Reduced middle airflow correlates with the sensation of nasal obstruction, possibly due to a reduction in mucosal cooling in this region. Further research is needed to elucidate the role of intranasal airflow distribution in the sensation of nasal airflow