Calculating effective gun policies

Following recent shootings in the USA, a debate has erupted, one side favoring stricter gun control, the other promoting protection through more weapons. We provide a scientific foundation to inform this debate, based on mathematical, epidemiological models that quantify the dependence of firearm-related death rates of people on gun policies. We assume a shooter attacking a single individual or a crowd. Two strategies can minimize deaths in the model, depending on parameters: either a ban of private firearms possession, or a policy allowing the general population to carry guns. In particular, the outcome depends on the fraction of offenders that illegally possess a gun, on the degree of protection provided by gun ownership, and on the fraction of the population who take up their right to own a gun and carry it with them when attacked, parameters that can be estimated from statistical data. With the measured parameters, the model suggests that if the gun law is enforced at a level similar to that in the United Kingdom, gun-related deaths are minimized if private possession of firearms is banned. If such a policy is not practical or possible due to constitutional or cultural constraints, the model and parameter estimation indicate that a partial reduction in firearm availability can lead to a reduction in gun-induced death rates, even if they are not minimized. Most importantly, our analysis identifies the crucial parameters that determine which policy reduces the death rates, providing guidance for future statistical studies that will be necessary for more refined quantitative predictions

Nonlinear dynamics of sand banks and sand waves

Sand banks and sand waves are two types of sand structures that are commonly observed on an off-shore sea bed. We describe the formation of these features using the equations of the fluid motion coupled with the mass conservation law for the sediment transport. The bottom features are a result of an instability due to tide–bottom interactions. There are at least two mechanisms responsible for the growth of sand banks and sand waves. One is linear instability, and the other is nonlinear coupling between long sand banks and short sand waves. One novel feature of this work is the suggestion that the latter is more important for the generation of sand banks. We derive nonlinear amplitude equations governing the coupled dynamics of sand waves and sand banks. Based on these equations, we estimate characteristic features for sand banks and find that the estimates are consistent with measurements

Техніка та технологія дезінтеграції й гравітаційного збагачення рідкіснометалічних руд

On the base of the analysis of centrifugal concentrators designs there has been justified the selection of apparatus for the rare-metal ores beneficiation. Process of pyrochlore ore grinding in mills of different types has been investigated and the expediency of use of impact centrifugal action mills to ensure selectivity of minerals disclosure has been founded. Efficient technical and technological parameters of the centrifugal action mills have been justified on the base of active experimental method. The influence of disintegration methods on technological indication of rare-metal ore beneficiation of Mazurovske deposits in centrifugal Nelson concentrator has been analyzed.На основі аналізу конструкцій відцентрових концентраторів обґрунтовано вибір апарату для збагачення рідкіснометалічних руд. Виконано дослідження процесу подрібнення пірохлорової руди в млинах різного типу та встановлено доцільність застосування млинів ударно-відцентової дії для забезпечення селективності розкриття мінералів. Методом активного експерименту обґрунтовано раціональні технічні та технологічні параметри млина ударно-відцентрової дії. Проаналізовано вплив способів дезінтеграції на технологічні показники збагачення рідкіснометалевої руди Мазурівського родовища у відцентровому концентраторі Нельсона

Admission predictors for success in a mathematics graduate program

There are many factors that can influence the outcome for students in a mathematics PhD program: bachelor's GPA (BGPA), bachelor's major, GRE scores, gender, Under-Represented Minority (URM) status, institution tier, etc. Are these variables equally important predictors of a student's likelihood of succeeding in a math PhD program? In this paper, we present and analyze admission data of students from different groups entering a math PhD program at a southern California university. We observe that some factors correlate with success in the PhD program (defined as obtaining a PhD degree within a time-limit). According to our analysis, GRE scores correlate with success, but interestingly, the verbal part of the GRE score has a higher predictive power compared to the quantitative part. Further, we observe that undergraduate student GPA does not correlate with success (there is even a slight negative slope in the relationship between GPA and the probability of success). This counterintuitive observation is explained once undergraduate institutions are separated by tiers: students from "higher tiers" have undergone a more rigorous training program; they on average have a slightly lower GPA but run a slightly higher probability to succeed. Finally, a gender gap is observed in the probability to succeed with female students having a lower probability to finish with a PhD despite the same undergraduate performance, compared to males. This gap is reversed if we only consider foreign graduate students. It is our hope that this study will encourage other universities to perform similar analyses, in order to design better admission and retention strategies for Math PhD programs.Comment: 13 pages, 11 figures, 4 table

Signal Response Sensitivity in the Yeast Mitogen-Activated Protein Kinase Cascade

The yeast pheromone response pathway is a canonical three-step mitogen activated protein kinase (MAPK) cascade which requires a scaffold protein for proper signal transduction. Recent experimental studies into the role the scaffold plays in modulating the character of the transduced signal, show that the presence of the scaffold increases the biphasic nature of the signal response. This runs contrary to prior theoretical investigations into how scaffolds function. We describe a mathematical model of the yeast MAPK cascade specifically designed to capture the experimental conditions and results of these empirical studies. We demonstrate how the system can exhibit either graded or ultrasensitive (biphasic) response dynamics based on the binding kinetics of enzymes to the scaffold. At the basis of our theory is an analytical result that weak interactions make the response biphasic while tight interactions lead to a graded response. We then show via an analysis of the kinetic binding rate constants how the results of experimental manipulations, modeled as changes to certain of these binding constants, lead to predictions of pathway output consistent with experimental observations. We demonstrate how the results of these experimental manipulations are consistent within the framework of our theoretical treatment of this scaffold-dependent MAPK cascades, and how future efforts in this style of systems biology can be used to interpret the results of other signal transduction observations

Kraichnan model of passive scalar advection

A simple model of a passive scalar quantity advected by a Gaussian non-solenoidal ("compressible") velocity field is considered. Large order asymptotes of quantum-field expansions are investigated by instanton approach. The existence of finite convergence radius of the series is proved, a position and a type of the corresponding singularity of the series in the regularization parameter are determined. Anomalous exponents of the main contributions to the structural functions are resummed using new information about the series convergence and two known orders of the expansion.Comment: 21 page

Success probability for selectively neutral invading species in the line model with a random fitness landscape

We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for non-mutants. This model is similar to those considered in Farhang-Sardroodi et al. [PLOS Comput. Biol., 13(11), 2017; J. R. Soc. Interface, 16(157), 2019]. We show that the probability of mutant fixation in a population of size $N$, starting from a single mutant, is greater than $1/N$, which would be the case if there were no variation in fitness whatsoever. In the small variation regime, we recover precise asymptotics for the success probability of the mutant. This demonstrates that the introduction of randomness provides an advantage to minority mutations in this model, and shows that the advantage increases with the system size. We further demonstrate that the mutants have an advantage in this setting only because they are better at exploiting unusually favorable environments when they arise, and not because they are any better at exploiting pockets of favorability in an environment that is selectively neutral overall.Comment: 25 pages, 4 figure