Computational modelling of structural integrity following mass loss in polymeric charred cellular solids

A novel computational technique is presented for embedding mass-loss due to burning into the ANSYS finite element modelling code. The approaches employ a range of computational modelling methods in order to provide more complete theoretical treatment of thermoelasticity absent from the literature for over six decades. Techniques are employed to evaluate structural integrity (namely, elastic moduli, Poisson’s ratios, and compressive brittle strength) of honeycomb systems known to approximate three-dimensional cellular chars. That is, reducing the mass of diagonal ribs and both diagonal-plus-vertical ribs simultaneously show rapid decreases in the structural integrity of both conventional and re-entrant (auxetic, i.e., possessing a negative Poisson’s ratio) honeycombs. On the other hand, reducing only the vertical ribs shows initially modest reductions in such properties, followed by catastrophic failure of the material system. Calculations of thermal stress distributions indicate that in all cases the total stress is reduced in re-entrant (auxetic) cellular solids. This indicates that conventional cellular solids are expected to fail before their auxetic counterparts. Furthermore, both analytical and FE modelling predictions of the brittle crush strength of both auxetic and conventional cellular solids show a relationship with structural stiffness

Investigating the relationship between the diversity index and frequency of offending

Purpose Recent work has suggested that specialization is correlated with frequency of offending, but this observed relationship may actually depend on the measuring instrument used. The diversity index is a common method of measuring specialization in such studies, and this paper investigates whether this observed correlation is due in part to the mathematical form of the diversity index itself. The criminological question as to whether specialization increases or decreases with offense frequency cannot be answered until the behavior of the diversity index is better understood. We use simulations to investigate the behavior of the diversity index where the number of crimes is small (the small sample problem), simulating from known distributions of offending. Two of the distributions used in the simulation are defined to be unspecialized. The first uses an equiprobable distribution of offenses across offense categories. The second uses the distribution of offenses in the British population. The third distribution is from a specialist distribution, and assumes that different offenders have different probabilities of choosing particular offenses. We report these simulations for both three and ten crime categories. To set the simulated results in context, we use an extract from the UK Police National Computer to investigate the criminological question as to whether specialization increases with offense frequency. For all three simulation schemes, the diversity index $D$ increases steeply with the frequency of offending $N$ at low frequencies, with the increase slowing around $N=20$, and becoming flat when the number of offenses $N$ reaches 500. This relationship is observed for both three crime categories and ten crime categories. The observed relationship of D with N can be used to correct the diversity index to allow the true relationship of specialization with offense frequency to be investigated. We recommend that the diversity index be used with caution when there are small numbers of crimes over fixed time periods. Any increase or decrease of the diversity index over the criminal career life course may reflect the behavior of the measurement tool with the number of offenses, rather than any change in specialization itself. Applying one of the suggested suitable correction methods to $D$ will mitigate this problem

Cross-sensory correspondences:heaviness is dark and low-pitched

Everyday language reveals how stimuli encoded in one sensory feature domain can possess qualities normally associated with a different domain (e.g., higher pitch sounds are bright, light in weight, sharp, and thin). Such cross-sensory associations appear to reflect crosstalk among aligned (corresponding) feature dimensions, including brightness, heaviness, and sharpness. Evidence for heaviness being one such dimension is very limited, with heaviness appearing primarily as a verbal associate of other feature contrasts (e.g., darker objects and lower pitch sounds are heavier than their opposites). Given the presumed bi-directionality of the crosstalk between corresponding dimensions, heaviness should itself induce the cross-sensory associations observed elsewhere, including with brightness and pitch. Taking care to dissociate effects arising from the size and mass of an object this is confirmed. When hidden objects varying independently in size and mass are lifted, objects that feel heavier are judged to be darker and to make lower pitch sounds than objects feeling less heavy. These judgements track the changes in perceived heaviness induced by the size-weight illusion. The potential involvement of language, natural scene statistics, and Bayesian processes in correspondences, and the effects they induce, is considered

Smoothing group-based trajectory models through B-splines

Purpose This paper investigates the use of B-spline smoothers as an alternative to polynomials in time when estimating trajectory shape in group-based trajectory models. The use of polynomials in these models can cause undesirable curve shapes, such as uplifts at the end of the trajectory, which may not be present in the data. Moreover, polynomial curves are global, meaning that a data point at one end of the trajectory can affect the shape of the curve at the end. Methods We use the UK Offenders Index 1963 birth cohort to investigate the use of B-splines. The models are fitted using Latent Gold, and two information criteria (BIC and ICL-BIC are used to estimate the number of knots of the B-spline, as well as the number of groups. A small simulation study is also presented. Results A three-group solution was chosen. It is shown that B-splines can provide a better fit to the observed data than cubic polynomials. The offending trajectory groups correspond to the classic groups of adolescent-limited, low-rate chronic and high-rate chronic which were proposed by Moffitt. However ,the shapes of the two chronic trajectory curves are more consistent with the life-course persistent nature of chronic offending than the traditional cubic polynomial curves. The simulation shows improved performance of the B-spline over cubic polynomials. Conclusions The use of B-splines is recommended when fitting group-based trajectory models. Some software products need further development to include such facilities, and we encourage this development

Math Students help their Community develop Balanced Refuse Collection Routes

In fall of 2017, the Superintendent of Public Works for Kutztown Borough approached Kutztown University’s Department of Mathematics seeking help in “re-balancing” refuse collection routes in the Borough of Kutztown.  Historically, refuse was collected two days a week on the south side (Mondays and Thursdays) of Main Street and two days a week on the north side (Tuesdays and Fridays) of Main Street.  Wednesdays were used for recycling collection.  Over the years, new housing development was primarily on the north side of Main Street.  As a result of this development, refuse collection time had become “unbalanced”; requiring more time for the north side collection.  During the spring semester 2018, several math majors in their last semester at Kutztown University developed a new refuse collection strategy.  This strategy balanced collection times over the four collection days and just as importantly, minimized the modifications to the existing routes.  Additionally, a minimum number of residents were impacted while accounting for future housing development.  Their strategy has been successfully used in the Borough of Kutztown since August 2018

Statistical modelling of a terrorist network

This paper investigates the group structure in a terrorist network through the latent class model and a Bayesian model comparison method for the number of latent classes. The analysis of the terrorist network is sensitive to the model specification. Under one model it clearly identifies a group containing the leaders and organisers, and the group structure suggests a hierarchy of leaders, trainers and “footsoldiers” who carry out the attacks

Gambling harm and crime careers

Incarcerated populations across the world have been found to be consistently and significantly more vulnerable to problem gambling than general populations in the same countries. In an effort to gain a more specific understanding of this vulnerability the present study applied latent class analysis and criminal career theory to gambling data collected from a sample of English and Scottish, male and female prisoners (N=1057). The analysis found six clusters measured by responses to the Problem Gambling Severity Index (PGSI), primarily distinguished by loss chasing behaviour. Longitudinal offending data drawn from the Police National Computer database found four criminal career types, distinguished by frequency and persistence over time. A significant association was found between higher level loss chasing and high rate offending in criminal careers. High rate offenders whose offending peaked in their mid 20’s were 5.3 times more likely to be higher level loss chasers and high rate chronic persistent offenders 3.7 times more likely than other criminal career types. Theories that link gambling, offending and impulse control are discussed and targeted interventions are proposed

Aqueous Angiography with Fluorescein and Indocyanine Green in Bovine Eyes.

PurposeWe characterize aqueous angiography as a real-time aqueous humor outflow imaging (AHO) modality in cow eyes with two tracers of different molecular characteristics.MethodsCow enucleated eyes (n = 31) were obtained and perfused with balanced salt solution via a Lewicky AC maintainer through a 1-mm side-port. Fluorescein (2.5%) or indocyanine green (ICG; 0.4%) were introduced intracamerally at 10 mm Hg individually or sequentially. With an angiographer, infrared and fluorescent images were acquired. Concurrent anterior segment optical coherence tomography (OCT) was performed, and fixable fluorescent dextrans were introduced into the eye for histologic analysis of angiographically positive and negative areas.ResultsAqueous angiography in cow eyes with fluorescein and ICG yielded high-quality images with segmental patterns. Over time, ICG maintained a better intraluminal presence. Angiographically positive, but not negative, areas demonstrated intrascleral lumens with anterior segment OCT. Aqueous angiography with fluorescent dextrans led to their trapping in AHO pathways. Sequential aqueous angiography with ICG followed by fluorescein in cow eyes demonstrated similar patterns.ConclusionsAqueous angiography in model cow eyes demonstrated segmental angiographic outflow patterns with either fluorescein or ICG as a tracer.Translational relevanceFurther characterization of segmental AHO with aqueous angiography may allow for intelligent placement of trabecular bypass minimally invasive glaucoma surgeries for improved surgical results

Changing crime-mix patterns of offending over the life course:a comparative study in England & Wales and the Netherlands.

This chapter presents a comparative analysis of England and Wales and the Netherlands through examining criminal lifestyles through conviction data and how they change with age. The analysis has used latent Markov modelling to jointly estimate the crime mix patterns (different offenders have different selections of offences) and the transition probabilities (offenders move from one pattern to another or desist as they age). We discuss issues relating to comparing the two datasets, including definitions of offences in the two jurisdictions and the year of birth distribution of the two samples. We investigate whether some crime mix patterns are more specialized than others in terms of their long term patterns, and whether offenders belonging to some crime patterns are likely to desist earlier than others

Intraocular pressure and medication changes associated with Xen gel stent: A systematic review of the literature

The Xen gel stent (Allergan Inc, an AbbVie company; Dublin, Ireland) was conceived as an option for patients requiring modest IOP reduction but for whom trabeculectomy was not yet indicated. As with any glaucoma surgery, establishing criteria for patient selection and identifying factors that contribute to a high likelihood of success are important. To help guide clinical decision-making, a systematic review of published studies on the gel stent was performed, with the goal of understanding postoperative outcomes based on clinical and patient factors. Results were organized around a series of pertinent clinical questions based on scenarios encountered in clinical practice. Criteria for including studies were intentionally broad, with the objective of simulating the diverse population of glaucoma patients encountered in real-world practice. Outcomes for IOP and medication reduction postoperatively were assessed in various analyses, including in eyes with various glaucoma types and severity; in eyes naïve to surgery as well as those with a history of prior incisional glaucoma surgery; and when surgery was performed as a standalone procedure or at the time of cataract surgery. The results of each of the various analyses were consistent in demonstrating that successful gel stent surgery achieved a postoperative IOP of approximately 14.0 mm Hg and reduction to fewer than 1 glaucoma medication. Additional data are shown on outcomes by method of implant (ab interno vs ab externo); intraoperative use of antifibrotics; and rates of needling in published studies