Mathematics and Statistics

The subject of this investigation was spatial and spatio-temporal shark attack clusters occurring along California's coast between 1994 and 2010. Two hypotheses were postulated:(a) Shark attacks are proportionate to human beach activities.(b) No pronounced space-time relationship between human beach activity and shark attacks exists along this coast over time. The hypotheses were tested by using SaTScanTM version 9.1. 1, a spatial scan statistic program. The results show that well-defined high-and low-risk areas have ...

Shark attacks have historically been studied from a viewpoint of encounter number per region and so limited to the areas in which the attacks occurred. In this exploratory modeling study, the goal was to examine whether an area-specific cluster analysis algorithm undertaken with a modern cluster analysis tool (SaTScan™ 9.1. 0) could enhance our spatial and spatio-temporal understanding of attack patterns. The data used were from Florida's east coast between 1994 and 2009. The program suggests several high-and low ...

The trends of the world’s top ten countries relating to shark bite rates, defined as the ratio of the annual number of shark bites of a country and its resident human population, were analyzed for the period 2000-2016. A nonparametric permutation-based methodology was used to determine whether the slope of the regression line of a country remained constant over time or whether so-called joinpoints, a core feature of the statistical software Joinpoint, occurred, at which the slope changes and a better fit could be obtained by applying a straight-line model. More than 90% of all shark bite incidents occurred along the US, Australia, South Africa, and New Zealand coasts. Since three of these coasts showed a negative trend when transformed into bite rates, the overall global trend is decreasing. Potential reasons for this decrease in shark bite rates—besides an increase in the world’s human population, resulting in more beach going people, and a decrease of sharks due to overfishing—are...

Thyroid cancer is a common cancer in adolescents and young adults ranking 4th in frequency. Thyroid cancer has captured the interest of epidemiologists because of its strong association to environmental factors. The goal of this study is to identify thyroid cancer clusters in Florida for the period 2000-2008. This will guide further discovery of potential risk factors within areas of the cluster compared to areas not in cluster. Thyroid cancer cases for ages 15-39 were obtained from the Florida Cancer Data System. Next, using the purely spatial Poisson analysis function in SaTScan, the geographic distribution of thyroid cancer cases by county was assessed for clusters. The reference population was obtained from the Census Bureau 2010, which enabled controlling for population age, sex, and race. Two statistically significant clusters of thyroid cancer clusters were found in Florida: one in southern Florida (SF) (relative risk of 1.26; P value of <0.001) and the other in northweste...

This study's main goal was to develop a comprehensive Quality of Life (QoL) Index based on 31 demographic variables for the 3108 counties in the contiguous USA. Counties were ranked worst in QoL to best, and spatial cluster analysis is used to identify counties with significant low/high QoL clusters. GIS-based mapping was used to create informative heat maps with significant clusters shown. The rate of African Americans, diversity in a race within counties, and upward mobility were studied in a regression analysis in which QoL was predicted from these three covariates. The QoL Index was adjusted for the covariates, and a new spatial heat map with clusters is obtained. It was concluded that as the rate of African Americans increases in a county, the QoL decreases, while the QoL increases when diversity or upward mobility increases.

This study uses disease surveillance cluster analysis methods to identify clusters for the three most common pediatric cancers in Florida (brain tumors, leukemia, lymphoma). In addition to a univariate purely spatial analysis, a space-time analysis is done, followed by a nonparametric permutation test for space-time interaction. This is followed by a multivariate spatial analysis for the three pediatric cancer types together. The main findings include a significant spatial cluster for each of the three cancer types covered in this study, in addition to identifying two significant clusters for all pediatric cancer types combined.

While rape is a very serious crime and public health problem, no spatial mapping has been attempted for rape on the national scale. This article addresses the three research questions: (1) Are reported rape cases randomly distributed across the United States, after being adjusted for population density and age, or are there geographical clusters of reported rape cases? (2) Are the geographical clusters of reported rapes still present after adjusting for differences in poverty levels? (3) Are there geographical clusters where the proportion of reported rape cases that lead to an arrest is exceptionally low or exceptionally high? We studied the geographical variation of reported rape events (2003-2012) and rape arrests (2000-2012) in the 48 contiguous states of the USA. The disease surveillance software SaTScan TM with its spatial scan statistic is used to evaluate the spatial variation in rapes. The spatial scan statistic has been widely used as a geographical surveillance tool for diseases, and we used it to identify geographical areas with clusters of reported rape and clusters of arrest rates for rape. The spatial scan statistic was used to identify geographical areas with exceptionally high rates of reported rape. The analyses were adjusted for age, and in secondary analyses, for both age and poverty level. We also identified geographical areas with either a low or a high proportion of reported rapes leading to an arrest. We have identified geographical areas with exceptionally high (low) rates of reported rape. The geographical problem areas identified are prime candidates for more intensive preventive counseling and criminal prosecution efforts by public health, social service, and law enforcement agencies. Geographical clusters of high rates of reported rape are prime areas in need of expanded implementation of preventive measures, such as changing attitudes in our society toward rape crimes, in addition to having the criminal justice system play an even larger role in preventing rape.

Superfund sites are geographic locations selected by the U.S. Environmental Protection Agency as having extreme toxic chemical spills. In this article, we address three main research questions: (1) Are there geographical areas where the number (or density) of Superfund sites is significantly higher than in the rest of the USA? (2) Is there an association between cancer incidence and the number (or density) of Superfund sites? (3) Do counties with Superfund sites have higher proportions of minority populations than the rest of the USA? We study the geographic distribution of the overall cancer incidence rate (2007-2011) in addition to the geographic variation of Superfund sites for 2013. We used the disease surveillance software package SaTScan with its scan statistic to identify locations and relative risks of spatial clusters in cancer rates and in Superfund site count and density. We also used the surveillance software FlexScan to support and complement the results obtained with SaTScan. We find that geographic areas with Superfund sites tend to have elevated cancer risk, and also elevated proportions of minority populations.

Background COVID-19 is a new coronavirus that has spread from person to person throughout the world. Geographical disease surveillance is a powerful tool to monitor the spread of epidemics and pandemic, providing important information on the location of new hot-spots, assisting public health agencies to implement targeted approaches to minimize mortality. Methods County level data from January 22-April 28 was downloaded from USAfacts.org to create heat maps with ArcMapTM for diagnosed COVID-19 cases and mortality. The data was analyzed using spatial and space-time scan statistics and the SaTScanTM software, to detect geographical cluster with high incidence and mortality, adjusting for multiple testing. Analyses were adjusted for age. While the spatial clusters represent counties with unusually high counts of COVID-19 when averaged over the time period January 22-April 20, the space-time clusters allow us to identify groups of counties in which there exists a significant change over...

A standard cumulative sum (CUSUM) chart for controlling the process mean takes samples from the process at fixed-length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value. This article proposes a modification of the standard CUSUM scheme that varies the time intervals between samples depending on the value of the CUSUM control statistic. The variable sampling interval (VSI) CUSUM chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean. If the CUSUM statistic actually enters the signal region, then the VSI CUSUM chart signals in the same manner as the standard CUSUM chart. A Markov-chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal. Results show that the proposed VSI CUSUM chart is considerably more efficient than the standard CUSUM chart. Tables are provided to aid in the design of VSI CUSUM charts.

This study tested whether human body orientation can influence the behavior of bull sharks by examining sharks’ approach distances from a person positioned vertically or horizontally in the water. Results showed that bull sharks,Carcharhinus leucas, kept a significantly greater distance when the test subject was standing in chest-deep water with his head above water versus lying on the ocean floor. Furthermore, larger bull sharks in the immediate area withdrew when the subject entered the water.

Some experiments on human-computer interaction are aimed at evaluating hypotheses concerning cognitive work. Other experiments are intended to evaluate the software tools that shape the cognitive work. In both cases, effective experimentation is premised on the control and factorial analysis of sources of variability. This entails programmes of experimentation. However, sociotechnical systems are generally a 'moving target' in terms of the pace of change. The objective of this study was to create a general approach to experimental design and the measurement of cognitive work that can satisfy the requirements for experimentation and yet can also provide a 'fast track' to the evaluation of softwaresupported cognitive work. A measure called i-bar is presented, which is the inverse of the mid-range. The statistic is derived from data on trials-to-criterion in tasks that require practice and learning. This single measure is interpreted as a conjoint measurement scale, permitting: (a) evaluation of sensitivity of the principal performance measure (which is used to set the metric for trials to criterion); (b) evaluation of the learnability of the work method (i.e. the goodness of the software tool); (c) evaluation of the resilience of the work method. It is shown that it is possible to mathematically model such order statistics and derive methods for estimating likelihoods. This involves novel ways of thinking about statistical analysis for discrete non-Gaussian distributions. The idea and method presented herein should be applicable to the study of the effects of any training or intervention, including software interventions designed to improve legacy work methods and interventions that involve creating entirely new cognitive work systems.

The present study examines the potential capability of Caribbean reef sharks to perceive human body orientation, as well as discussing the sharks' swimming patterns in a person's vicinity. A standardized video method was used to record the scenario of single SCUBA divers kneeling in the sand and the approach patterns of sharks, combined with a control group of two divers kneeling back-to-back. When approaching a single testsubject, significantly more sharks preferred to swim outside the person's field of vision. The results suggest that these sharks are able to identify human body orientation, but the mechanisms used and factors affecting nearest distance of approach remain unclear.

This study examines the approach patterns of sharks in the vicinity of human divers, focusing on the diver's body orientation and a shark's distance from the sea bed when approaching the diver. A standardized video method was used to record the scenario of diver(s) kneeling in the sand while being approached by sharks. This showed that sharks had a preference to move in from outside a diver's field of vision while larger sharks stayed closer to the sea floor. This may simultaneously enhance camouflage while reducing potential escape routes for the approaching animal. This stealth behavior raises the question of how sharks may interpret humans when moving towards them.

One recurring factor seemingly causing an increase in shark attacks is lunar cycles, especially the full moon. However, the potential association between shark attacks and lunar cycles has never been verified. Our results show that a correlation between shark attacks and moon cycles does not statistically exist. With no correlation between shark attack rates―independent of people's activities―and lunar cycles found, we also applied the same statistical procedures to surfer incidents only. The reasoning for narrowing the attacks to those on surfers was as follows: (1) Surfers indicate the best conditions to surf exist during the full and new moon. (2) Surfers are more exposed to shark attacks than non-surfers. However, as with the initial results, shark attacks involving surfers did not show any correlation to lunar cycles, neither did those involving non-surfers. These results indicate that potential triggers for shark attacks need to be studied in a more pragmatic manner, using...

Sharksuckers, Echeneis naucrates, often attach themselves to sharks. Their presence 80 Raid Amin et al. likely affects sensory sensitive or hydrodynamic sensitive areas along a shark's body, which is thought to be the cause of a variety of behavioral patterns by the shark to remove the teleosts from their bodies. Here, we looked for clustered attachment locations of sharksuckers on free swimming lemon sharks, Negaprion brevirostris. A 3D model of a lemon shark created with Blender 2.66 was used to mark attachment positions, and analyzed using SatScan TM , a spatial scan statistic cluster analysis program. Several areas with high or low numbers of clusters were identified. Low cluster areas were interpreted to reflect high sensitivity areas, while high cluster areas were interpreted to be low sensitivity areas. One of these high cluster patches, for example, consists of the leading and trailing margins of the first dorsal fin, whereas pectoral fins reflect low cluster regions. This study is the first attempt to understand the distribution of sharksucker attachments on a shark's body under natural conditions with reference to the shark's hydrodynamics and sensory sensitivity.

Human encounters with sharks draw more attention than with any other marine creature [1] [2] [3]. This publicity refers to a time when sharks seemed to be little more than ferocious beasts that made getting away unharmed rather unlikely [4]. However, their true nature could not be further from their mainly infamous popularity driven by the media, which still fuels every thinkable broadcast outlet [5] [6] [7]. This media presentation stands in stark contrast to their bite statistics, which confirms that sharks are the least involved predators within the context of animal-human conflict [8] [9].

In this study, we aimed to identify spatial clusters of countries with high rates of cyber attacks directed at other countries. The cyber attack dataset was obtained from Canadian Institute for Cybersecurity, with over 110,000 Uniform Resource Locators (URLs), which were classified into one of 5 categories: benign, phishing, malware, spam, or defacement. The disease surveillance software SaTScanTM was used to perform a spatial analysis of the country of origin for each cyber attack. It allowed the identification of spatial and space-time clusters of locations with unusually high counts or rates of cyber attacks. Number of internet users per country obtained from the 2016 CIA World Factbook was used as the population baseline for computing rates and Poisson analysis in SaTScanTM. The clusters were tested for significance with a Monte Carlo study within SaTScanTM, where any cluster with p < 0.05 was designated as a significant cyber attack cluster. Results using the rate of the dif...