Quantifying the risk of mass shootings at specific locations.

Mass shootings are horrific events that annually take scores of innocent lives in the United States. Federal, state, and local governments as well as educational, religious, and private-sector organizations propose and enact polices and strategies to protect people from and during active shooter situations. A probabilistic risk assessment of a mass shooting for a specific organization, jurisdiction, or location can be the first step toward evaluating the effectiveness of risk mitigation strategies and determining which strategies might be most appropriate for a location. This article proposes a novel hierarchical method to assess the probability of a mass shooting at specific locations based on available historical data. First, the method generates a probability distribution over the annual number of mass shootings in the United States. Second, the article uses this national number of mass shootings to determine the risk for each state. Third, the state risk assessment is decomposed to calculate the probability of a mass shooting in a specific location such as a school. Multiple ways to assess the risk are presented, leading to slightly different probability assessments for a location. Results indicate that annual probability of a mass shooting in the largest high school in California is on the order of 10 - 6 - 10 - 5 $10^{-6}-10^{-5}$ , and the annual probability of a mass shooting in the largest high school in Iowa is about half as likely as in the California school.

Allocating Resources to Enhance Resilience, with Application to Superstorm Sandy and an Electric Utility.

This article constructs a framework to help a decisionmaker allocate resources to increase his or her organization's resilience to a system disruption, where resilience is measured as a function of the average loss per unit time and the time needed to recover full functionality. Enhancing resilience prior to a disruption involves allocating resources from a fixed budget to reduce the value of one or both of these characteristics. We first look at characterizing the optimal resource allocations associated with several standard allocation functions. Because the resources are being allocated before the disruption, however, the initial loss and recovery time may not be known with certainty. We thus also apply the optimal resource allocation model for resilience to three models of uncertain disruptions: (1) independent probabilities, (2) dependent probabilities, and (3) unknown probabilities. The optimization model is applied to an example of increasing the resilience of an electric power network following Superstorm Sandy.

Summarizing risk using risk measures and risk indices.

Our society is fascinated with risk in many different areas and disciplines. One of the main ways to describe and communicate the level of risk is through risk indices, which summarize risk using numbers or categories such as words, letters, or colors. These indices are used to communicate risks to the public, understand how risk is changing over time, compare among different risks, and support decision making. Given the different methods to construct risk indices, including flawed methods such as risk matrices, this article develops specific steps that analysts can follow to create a risk index. This article emphasizes the importance of describing risk with a probability distribution, developing a numerical risk measure that summarizes the probability distribution, and finally translating the risk measure to an index. Measuring the risk is the most difficult part and requires the analyst to summarize a probability distribution into one or possibly a few numbers. The risk measure can then be transformed to a numerical or categorical index. I apply the method outlined in this article to construct a risk index that compares the risk of fatalities in aviation and highway transportation.

Comparing different models to forecast the number of mass shootings in the United States: An application of forecasting rare event time series data.

The number of mass shootings in the United States has increased in the recent decades. Understanding the future risk of the mass shootings is critical for designing strategies to mitigate the risk of mass shootings, and part of understanding the future risk is to forecast the frequency or number of mass shootings in the future. Despite the increasing trend in mass shootings, they thankfully remain rare events with fewer than 10 mass shootings occurring in a single year. Limited historical data with substantial annual variability poses challenges to accurately forecasting rare events such as the number of mass shootings in the United States. Different forecasting models can be deployed to tackle this challenge. This article compares three forecasting models, a change-point model, a time series model, and a hybrid of a time series model with an artificial neural network model. Each model is applied to forecast the frequency of mass shootings. Comparing among results from these models reveals advantages and disadvantages of each model when forecasting rare events such as mass shootings. The hybrid ARIMA-ANN model can be tuned to follow variation in the data, but the pattern of the variation may not continue into the future. The mean of the change-point model and the ARIMA model exhibit much more less annual variation and are not influenced as much by the inclusion of a single data point. The insights generated from the comparison are beneficial for selecting the best model and accurately estimating the risk of mass shootings in the United States.

Investigating the relationship of porcine reproductive and respiratory syndrome virus RNA detection between adult/sow farm and wean-to-market age categories.

Porcine reproductive and respiratory syndrome (PRRS) is a disease caused by the PRRS virus (PRRSV) that has spread globally in the last 30 years and causes huge economic losses every year. This research aims to 1) investigate the relationship between the PRRSV detection in two age categories (wean-to-market and adult/sow farm), and 2) examine the extent to which the wean-to-market PRRSV positive rate forecasts the adult/sow farm PRRSV positive rate. The data we used are the PRRSV RNA detection results between 2007 and 2019 integrated by the US Swine Disease Reporting System project that represent 95% of all porcine submissions tested in the US National Animal Health Network. We first use statistical tools to investigate to what extent the increase in PRRSV positive submissions in the wean-to-market is related to the PRRSV increase in adult/sow farms. The statistical analysis confirms that an increase in the PRRSV positive rate of wean-to-market precedes the increase in the adult/sow farms to a large extent. Then we create the dynamic exponentially weighted moving average control charts to identify out-of-control points (i.e., signals) in the PRRSV rates for both wean-to-market and adult/sow farms. This control-chart-based analysis finds that 78% of PRRSV signals in the wean-to-market are followed by a PRRSV rate signal in the adult/sow farms within eight weeks. We expect that our findings will help the producers and veterinarians to justify and reinforce the implementation of bio-security and bio-contaminant practices to curb disease spread across farms.

Ranaspumin-2: structure and function of a surfactant protein from the foam nests of a tropical frog.

Ranaspumin-2 (Rsn-2) is a monomeric, 11 kDa surfactant protein identified as one of the major foam nest components of the túngara frog (Engystomops pustulosus), with an amino acid sequence unlike any other protein described so far. We report here on its structure in solution as determined by high-resolution NMR analysis, together with investigations of its conformation and packing at the air-water interface using a combination of infrared and neutron reflectivity techniques. Despite the lack of any significant sequence similarity, Rsn-2 in solution adopts a compact globular fold characteristic of the cystatin family, comprising a single helix over a four-stranded sheet, in a motif not previously associated with surfactant activity. The NMR structure of Rsn-2 shows no obvious amphiphilicity that might be anticipated for a surfactant protein. This suggests that it must undergo a significant conformational change when incorporated into the air-water interface that may involve a hinge-bending, clamshell opening of the separate helix and sheet segments to expose hydrophobic faces to air while maintaining the highly polar surfaces in contact with the underlying water layer. This model is supported by direct observation of the relative orientations of secondary structure elements at the interface by infrared reflection absorption spectroscopy, and by protein packing densities determined from neutron reflectivity profiles.

Foam nest components of the túngara frog: a cocktail of proteins conferring physical and biological resilience.

The foam nests of the túngara frog (Engystomops pustulosus) form a biocompatible incubation medium for eggs and sperm while resisting considerable environmental and microbiological assault. We have shown that much of this behaviour can be attributed to a cocktail of six proteins, designated ranaspumins (Rsn-1 to Rsn-6), which predominate in the foam. These fall into two discernable classes based on sequence analysis and biophysical properties. Rsn-2, with an amphiphilic amino acid sequence unlike any hitherto reported, exhibits substantial detergent-like surfactant activity necessary for production of foam, yet is harmless to the membranes of eggs and spermatozoa. A further four (Rsn-3 to Rsn-6) are lectins, three of which are similar to fucolectins found in teleosts but not previously identified in a land vertebrate, though with a carbohydrate binding specificity different from previously described fucolectins. The sixth, Rsn-1, is structurally similar to proteinase inhibitors of the cystatin class, but does not itself appear to exhibit any such activity. The nest foam itself, however, does exhibit potent cystatin activity. Rsn-encoding genes are transcribed in many tissues of the adult frogs, but the full cocktail is present only in oviduct glands. Combinations of lectins and cystatins have known roles in plants and animals for defence against microbial colonization and insect attack. Túngara nest foam displays a novel synergy of selected elements of innate defence plus a specialized surfactant protein, comprising a previously unreported strategy for protection of unattended reproductive stages of animals.

Incorporation of N-heterocyclic cations into proteins with a highly directed chemical modification.

N-Heterocyclic cations are incorporated into proteins using 5-(2-bromoethyl)phenanthridinium bromide, which selectively reacts with either cysteine or lysine residues, resulting in ethylphenanthridinium (Phen) or highly stable cyclised dihydro-imidazo-phenanthridinium (DIP) adducts respectively; these modifications have been found to manipulate the observed structure of lysozyme and bovine serum albumin by AFM.