Assessing the impact of educational campaigns on controlling HCV among women in prison settings

Prior studies have shown that imprisonment is a major risk factor for hepatitis C infection, with the risk of infection directly proportional to the length of incarceration. Women are at least twice as likely as men to contract HCV as they have limited access to information, health services and safe intravenous drug injecting equipments. We develop a mathematical model to assess the impact of educational campaigns on controlling HCV among women in prison settings. Equilibria for the model are determined and their stability are examined. Population-level effects of increased educational campaigns to encourage safe injecting practices among women in prison are evaluated through numerical simulations. The results suggest that educating women prisoners about abstaining from intravenous drug misuse may significantly reduce HCV prevalence among women in prison settings. Targeted education campaigns, which are effective at stopping transmission of HCV more than 80% of the time, will be highly effective at controlling the disease among women in prisons.     

融合多变量主成份与因子分析算法的犯罪率研究

基于犯罪过程的不确定性结构,融合多变量主成份分析与因子分析算法,分析了影响犯罪率的城市化率、失业率、客运量、人均GDP、城市基尼系数、农村基尼系数等多个相关变量因素,由MATLAB仿真建立了犯罪率的多元回归模型,并采用MINITAB数学软件对浙江省1988-2007二十年样本数据进行了实测,获取了影响犯罪率的潜在因子与方差贡献率,讨论了多元回归模型的统计检验及相对误差,解决了犯罪率各相关变量的权重分布及信息相互重叠问题.     

On Greenberg's Two-Step Model of Criminal Recidivism

With more than two million people currently incarcerated in U.S. prisons and jails, many of them repeat offenders, there is widespread agreement that criminal recidivism is a serious and costly problem in both human and economic terms. In this article, a stochastic model, which is a somewhat simplified version of a model first proposed by Greenberg, is discussed. An argument for the model is made based on recent theoretical and empirical studies that demonstrate the importance of social bonds in both the commission of and the abstinence from crime. This argument provides a stronger theoretical basis for the model, since it suggests that the model's trichotomization of a cohort of released prisoners reflects truly discrete differences and not just a convenient simplification imposed on a continuous variable. The model is shown to fit trial data sets very well, enabling the measurement of asymptotic recidivism—the ultimate percentage of a release cohort who will recidivate.     

连续犯罪预测的区域覆盖加权模型(AOWM)

2010年MCM(美国大学生数学建模竞赛)B题-Criminology要求建立连续犯罪的预测模型用于抓捕案犯.利用统计学、犯罪心理学相关知识,建立了区域覆盖加权模型(Area Overlap Weighted Model,简称AOWM).AOWM操作便利,在分析真实案例时的正确率能达到80%以上,因此具有较好的应用前景.     

Demand estimation with failure and capacity constraints: An application to prisons

A stochastic model for projecting demand for a population-driven, input-output facility that incorporates demographic changes, facility returns representing “failures”, and capacity constraints is proposed and demonstrated. The model is applied to the problem of prison population projection. The approach models the flow of inmates through the prison system, exploits the differences in the incarceration hazard rates of individuals in the general population and those who have been incarcerated previously, and explicitly considers the impact of constrained prison capacity on release policy and future admissions. First-time arrivals to prison are modeled as a Poisson process arising from the general population; recidivist arrivals are modeled using a failure model, where the reincarceration hazard rate is a function of age and race. The model is demonstrated for the State of North Carolina. The effect of limited prison capacity on the average time served is shown. Further, the results demonstrate that an early release policy will generate an increase in prison admissions through t'he return to prison of former inmates. The implications for current “get tough” sentencing policy initiatives relative to the prison crowding problem, the length of stay for offenders not included in the new policies, and the recursive effect of these policies on the input-output dynamics are considered. The results suggest the tradeoffs that exist between early release policies and capacity limitations.     

对警力与犯罪相互关系的实证研究

文章利用江苏省"十五"期间的面板数据对警力与犯罪问题进行实证研究。与以往文献不同,我们把一线民警从整体警力中剥离出来,认为一线民警的数量与犯罪率存在双向因果关系。通过对联立方程组进行三阶段最小二乘估计(3SLS),我们发现,刑事案件以及治安案件案发数对一线民警比重没有显著的影响;增加一线民警比重能够显著减少刑事案件相对数,而对治安案件却没有显著影响;此外,警察总量对刑事案件以及治安案件的发生都没有显著影响。进一步研究发现,在经济社会环境不同的地区(例如苏南、苏北),尽管案发绝对数存在显著差异,但是警力与犯罪的相互关系并没有表现出显著的差异。     

ORGANIZED CRIMES AGAINST NATURE: ELEPHANTS IN SOUTHERN AFRICA

Poaching of elephants in Southern Africa is now dominated by international groups following a model of organized crime. This shift, from poaching conducted by small, local groups; with limited mobility, weapons, and technology, to individuals who organize, finance, equip, and transport well‐armed poaching units to previously scouted locations, has made the protection of elephants in Southern Africa much more difficult and dangerous. This paper develops a model of high‐tech criminal poaching. A poaching organization makes a decision on the number of “planned poaching expeditions.” If a poaching unit is intercepted the entire organization is destroyed, but is replaced by a new organization in the next year. The operating life of a poaching organization is a stochastic process, which in turn induces a stochastic evolution in the elephant population. Under plausible conditions, the number of planned poaching expeditions is highly sensitive to the probability of interception by anti‐poaching patrols, but is nonresponsive to reductions in the black‐market ivory price. Thereby it might be better to focus conservation efforts on increasing the probability of intercepting poaching units rather than trying to control black market ivory prices. A benchmark value of poaching expeditions is identified—above which elephants may slowly decline to extinction.     

Using the Viable Systems Model to examine multi-agency arrangements for combatting transnational organised crime

Traditionally, most operational research applications in the area of law enforcement and criminal justice have used quantitative techniques to forecast patterns and levels of offending and to optimise various police, judicial and prison processes. This paper seeks to examine the role that more qualitative modelling approaches might contribute in this important application area. Specifically, the paper examines the role that cybernetic theory and viable systems modelling can contribute in helping government bodies and law enforcement agencies to think through how, organisationally, they can best respond to the increasingly complex problem of transnational organised crime. Focussing on new multi-agency collaborative arrangements, the paper argues that there is a need for more informed debate that can account for the complexity of the challenge and point towards more holistic and integrated solutions. Against this background, the paper argues that the viable systems modelling approach has much to offer because it is theoretically grounded in the management of complexity; because its flexibility allows it to accommodate the trend for law enforcement agencies to work more closely with partner agencies, and to do so at multiple organisational levels; and because its user-friendly annotated diagramming conventions allow stakeholders to focus discussion and work towards outcomes that make sense in particular settings.     

Criminal careers of young adult offenders after release

This longitudinal study examined stability and change of delinquency among young offenders after their release. The sample consists of male Germans (N = 2405) who were incarcerated in five juvenile prisons in different federal states. Standardized interviews were repeatedly conducted with the prisoners during imprisonment and after release to gather information about personal and social risk as well as protective factors. Based on official criminal records, delinquency was registered up to eight years after the first incarceration. The time interval between release and recidivism, severity of offending and the kind of punishment was observed. Applying of Trajectory Analysis according to Nagin (2005) three distinct developmental trajectories can be identified differing in both level of and change in offending over time: Occasional offenders, high level offenders and age-limited offenders. The groups differ in personal and social factors. Results are discussed with regard to offender treatment and prison aftercare.     

The social impact in a high-risk community: A cellular automata model

This research examines the spread of criminal behavior and hard drug consumption using a mathematical approach called cellular automata (CA). This CA model is based on two behavioral concepts. Firstly, peer association impacts criminal involvement. Secondly, addiction can heighten criminal activity. The model incorporates four types of actors who interact in a high-risk social community and one intervention method. The actors exert a social influence on each other by encouraging or discouraging drug use and criminal behavior. The intervention method called Incapacitation has a probabilistic impact on the individuals in the model. The results identify the threshold where positive influences on a population reduce the number of high-rate offenders in the community. These results are discussed to further the knowledge about the social influences in a high-risk community and how these influences can effect decisions on offender management.     

Preservice Secondary Mathematics Teachers' Conceptualizations of Equity: Access and Power as Seen Through Vignette Responses

Attention to equity in the mathematics education field has been growing in recent years. We have evidence that many novice secondary mathematics teachers do not feel prepared to teach in regards to diverse populations. We need to know more about how secondary preservice mathematics teachers (PSMTs) conceptualize equitable environments. This study investigates 30 secondary PSMTs' proposed responses to two hypothetical vignettes from mathematics department conversations regarding calculator usage and mathematical discourse, respectively, utilizing two of Gutiérrez's four dimensions of equity: Access and Power. Results suggest these PSMTs considered equity, equality, and creating a classroom that invites participation among other factors when thinking of an equitable approach with respect to calculator usage. When considering mathematical discourse, PSMTs cited the need to “model” proper use of mathematical language as well as to allow students to themselves verbalize it. Implications mathematics education and teacher education more broadly are to integrate equity and equality discussions in methods courses and to include strategies to facilitate productive discourse.     

MODELING THE EFFECT OF RARITY VALUE ON THE EXPLOITATION OF A WILDLIFE SPECIES SUBJECTED TO THE ALLEE EFFECT

The overexploitation of wildlife species is a serious problem in the field of biodiversity conservation. The species subjected to natural Allee effects are even more threatened by exploitation. Moreover, for many wildlife species, their rarity can fuel their exploitation by making them disproportionately desirable and consequently increasing their market price. In this paper, a mathematical model is proposed and analyzed to study how the value that consumers place on rarity can threaten the survival of a species subjected to natural Allee effects. It is assumed that the value of a species increases as its density declines. The analysis of model shows that the increase in the consumers' response to rarity can drive the system to admit Hopf‐bifurcation and heteroclinic bifurcation. The occurrence of the heteroclinic cycle indicates that the increase in consumers' response to rarity can cause the extinction of the species. It is found that an increase in the Allee threshold causes a decrease in the threshold value of consumers' response below which extinction is inevitable.     

An historical example of mathematical modelling: the trajectory of a cannonball

Classroom considerations of the concept and processes of mathematical modelling can do much to strengthen students’ problem solving skills. A systematic exposure to the techniques of mathematical modelling helps students formulate problems, re‐think those problems in mathematical terms, appreciate possible solution constraints and seek solutions that are realistic within the scope and conditions of the problem. While many mathematical modelling situations can be found in today's world, there are special pedagogical values in examining existing mathematical models that have an historical basis. Such an examination should reveal the mechanics of a modelling situation and how a model evolves or is refined to meet ever increasing human demands for accuracy or practicality. The trajectory of a cannonball provides such a modelling example. This topic captures the imagination of students and supplies the basis for a variety of classroom discussions and problem solving encounters.     

Well‐posedness for the Navier Slip Thin‐Film equation in the case of partial wetting

Consider a viscous liquid droplet spreading on a surface. The classical slip condition at the liquid‐solid interface is the no‐slip condition. However, this condition yields infinite dissipation rate when the contact line moves (“no‐slip paradox”). For this reason other slip conditions such as the Navier slip condition have been proposed. We prove well‐posedness for a reduced 1‐D fluid model related to Navier slip. It turns out that the profile of the droplet cannot be described by a smooth function (not even for an initially smooth profile). However, existence and uniqueness can be proved in larger classes of spaces that allow for certain classes of singular expansions at the moving contact point. © 2011 Wiley Periodicals, Inc.     

Explicitly Solvable Nonlocal Eigenvalue Problems and the Stability of Localized Stripes in Reaction‐Diffusion Systems

The transverse stability of localized stripe patterns for certain singularly perturbed two‐component reaction‐diffusion (RD) systems in the asymptotic limit of a large diffusivity ratio is analyzed. In this semi‐strong interaction regime, the cross‐sectional profile of the stripe is well‐approximated by a homoclinic pulse solution of the corresponding 1‐D problem. The linear instability of such homoclinic stripes to transverse perturbations is well known from numerical simulations to be a key mechanism for the creation of localized spot patterns. However, in general, owing to the difficulty in analyzing the associated nonlocal and nonself‐adjoint spectral problem governing stripe stability for these systems, it has not previously been possible to provide an explicit analytical characterization of these instabilities, including determining the growth rate and the most unstable mode within the band of unstable transverse wave numbers. Our focus is to show that such an explicit characterization of the transverse instability of a homoclinic stripe is possible for a subclass of RD system for which the analysis of the underlying spectral problem reduces to the study of a rather simple algebraic equation in the eigenvalue parameter. Although our simplified theory for stripe stability can be applied to a class of RD system, it is illustrated only for homoclinic stripe and ring solutions for a subclass of the Gierer–Meinhardt model and for a three‐component RD system modeling patterns of criminal activity in urban crime.     

A note on the production of matroid minors

The circuits containing some fixed element of a connected matroid (such a collection is called a port) provide a matroid generalization of the “path collections” of graphs. In this note we show how to translate forbidden minor theorems in matroid theory into results about ports — and we find that many theorems are strengthened by such translation. Those collections of sets which are “path collections” of graphs may then be characterized.     

A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.     

Quasistatic frictional thermo‐piezoelectric contact problem

We consider here a mathematical model describing the bilateral frictional contact between a thermo‐piezoelectric body and a thermally conductive foundation. We model the behavior of the material with a linear thermo‐electro‐elastic constitutive law. The process is assumed to be quasistatic and the contact is modeled with a nonlocal version of Coulomb's dry friction law, in which the frictional heat generated in the process, is taken into account. We drive a variational formulation of the problem and establish the existence of its weak solution.     

Making Connections: Elementary Teachers' Construction of Division Word Problems and Representations

If teachers make few connections among multiple representations of division, supporting students in using representations to develop operation sense demanded by national standards will not occur. Studies have investigated how prospective and practicing teachers use representations to develop knowledge of fraction division. However, few studies examined primary (K‐3) teachers' learning of contextual division problems, making connections among representations of division, and resolving the ambiguity of representing quotients with remainders. A written post‐course assessment provided evidence that most teachers created partitive division word problems, used a set model without splitting the remainder, and wrote equations with limited success. Post‐course written reflections demonstrated that many teachers developed pedagogical knowledge for helping students make connections among multiple representations, and mathematical knowledge of unit fractions. These findings suggest two areas that have implications for mathematics teacher educators who design professional development courses to facilitate teachers' learning of mathematical content and pedagogical knowledge of division and fraction relationships.