Racial Bias in Motor Vehicle Searches: Additional Theory and Evidence

Knowles, Persico, and Todd (2001) develop a model of police search and offender behavior. Their model implies that if police are unprejudiced the rate of guilt should not vary across groups. Using data from Interstate 95 in Maryland, they find equal guilt rates for African-Americans and whites and conclude that the data is not consistent with racial prejudice against African-Americans. This paper generalizes the model of Knowles, Persico, and Todd by accounting for the fact that potential offenders are frequently not observed by the police and by including two different levels of offense severity. The paper shows that for African-American males the data is consistent with prejudice against African-American males, no prejudice, and reverse discrimination depending on the form of equilibria that exists in the economy. Additional analyses based on stratification by type of vehicle and time of day were conducted, but did not shed any light on the form of equilibria that best represents the situation in Maryland during the sample period.

From Theory to Practice: Improving the Impact of Health Services Research.

BACKGROUND: While significant strides have been made in health research, the incorporation of research evidence into healthcare decision-making has been marginal. The purpose of this paper is to provide an overview of how the utility of health services research can be improved through the use of theory. Integrating theory into health services research can improve research methodology and encourage stronger collaboration with decision-makers. DISCUSSION: Recognizing the importance of theory calls for new expectations in the practice of health services research. These include: the formation of interdisciplinary research teams; broadening the training for those who will practice health services research; and supportive organizational conditions that promote collaboration between researchers and decision makers. Further, funding bodies can provide a significant role in guiding and supporting the use of theory in the practice of health services research. SUMMARY: Institutions and researchers should incorporate the use of theory if health services research is to fulfill its potential for improving the delivery of health care.

The Devil’s Calculus: Mathematical Models of Civil War

In spite of the movement to turn political science into a real science, various mathematical methods that are now the staples of physics, biology, and even economics are thoroughly uncommon in political science, especially the study of civil war. This study seeks to apply such methods - specifically, ordinary differential equations (ODEs) - to model civil war based on what one might dub the capabilities school of thought, which roughly states that civil wars end only when one side’s ability to make war falls far enough to make peace truly attractive. I construct several different ODE-based models and then test them all to see which best predicts the instantaneous capabilities of both sides of the Sri Lankan civil war in the period from 1990 to 1994 given parameters and initial conditions. The model that the tests declare most accurate gives very accurate predictions of state military capabilities and reasonable short term predictions of cumulative deaths. Analysis of the model reveals the scale of the importance of rebel finances to the sustainability of insurgency, most notably that the number of troops required to put down the Tamil Tigers is reduced by nearly a full order of magnitude when Tiger foreign funding is stopped. The study thus demonstrates that accurate foresight may come of relatively simple dynamical models, and implies the great potential of advanced and currently unconventional non-statistical mathematical methods in political science.

THE POTENTIAL EFFECTS OF A COMMUNITY DEVELOPMENT PROGRAM ON DEMOGRAPHIC VARIABLES IN HIMALAYAN INDIAN VILLAGES

A community development program operating in the mountains of North India was studied to assess its potential effects on mortality, fertility and migration patterns in the community which it served. The development program operated in Jaunpur Block, Tehri-Garhwal District, Uttar Pradesh State. Two comparable villages in the district were studied. The development program had been working in one for two years, and the other was completely untouched by the program.^ Since not enough time had elapsed since the beginning of the development program's work for any effects on demographic patterns to be visable in Jaunpur Block, this study looked to attitudes of village residents as indicators of future demographic trends. Existing demographic patterns and their interrelationship with socio-religious customs were examined in the test village. A questionnaire was then administered to ascertain attitudinal differences between the residents of the test village and the control village.^ The primary work of the community development program was to train women as village health workers. The results of the attitudinal comparison of the residents of the two villages showed a marked difference in attitudes relating to the position of women in society. The data showed a higher esteem for women in the test village than in the control village, and it is argued that this difference may be attributable to the work of the development program.^ Predicting future demographic trends in Jaunpur Block on the basis of the observed difference in villagers' attitudes toward the status of women is speculatory. Jaunpur Block appears to be in the demographic stage of pre-transition, maintaining relatively high rates of both mortality and fertility. Based on demographic transition theory the next significant change in demographic patterns in Jaunpur is predicted to be a decline in mortality, and an increase in the status of women is unrelated to this prediction.^ The community development program which was studied terminated unexpectedly during the time of this study. A case study of the program's final months is presented, and speculation on the future course of demographic trends in Jaunpur Block is related to the possible alternatives for future development in the area. ^

Potential REST Targets in Neural Stem Cells and Glioblastoma-Derived Stem Cells

Glioblastoma multiforme (GBM) tumors are the most common malignant primary brain tumors in adults. The current theory is that these tumors are caused by self-renewing glioblastoma-derived stem cells (GSCs). At the current time, the mechanisms that regulate self-renewal and other oncogenic properties of GSCs remain unknown. Recently, we found transcriptional repressor REST maintains self-renewal in neural stem cells (NSCs) and in GSCs. REST also regulates other oncogenic properties, such as apoptosis, invasion and proliferation. However, the mechanisms by which REST regulates these oncogenic properties are unknown. In an attempt to determine these mechanisms, we performed loss and gain-of-function experiments and genome-wide mRNA expression analysis in GSCs, and we were able to identify REST-regulated genes in GSCs. This was accomplished, after screening concordantly regulated genes in NSCs and GSCs, utilizing two RE1 databases, and setting two-fold expression as filters on the resulting genes. These results received further validation by qRT-PCR. Ingenuity Pathway Analysis (IPA) analysis further revealed the top REST target genes in GSCs were downstream targets of REST and/or involved in other cancers in other cell lines. IPA also revealed that many of the differentially-regulated genes identified in this study are involved in oncogenic properties seen in GBM, and which we believe are related to REST expression.

Potential connections (least-cost paths) between existing and potential bison habitat patches in the Carpathian Mountains

Habitat connectivity is important for the survival of species that occupy habitat patches too small to sustain an isolated population. A prominent example of such a species is the European bison (Bison bonasus), occurring only in small, isolated herds, and whose survival will depend on establishing larger, well-connected populations. Our goal here was to assess habitat connectivity of European bison in the Carpathians. We used an existing bison habitat suitability map and data on dispersal barriers to derive cost surfaces, representing the ability of bison to move across the landscape, and to delineate potential connections (as least-cost paths) between currently occupied and potential habitat patches. Graph theory tools were then employed to evaluate the connectivity of all potential habitat patches and their relative importance in the network. Our analysis showed that existing bison herds in Ukraine are isolated. However, we identified several groups of well-connected habitat patches in the Carpathians which could host a large population of European bison. Our analysis also located important dispersal corridors connecting existing herds, and several promising locations for future reintroductions (especially in the Eastern Carpathians) that should have a high priority for conservation efforts. In general, our approach indicates the most important elements within a landscape mosaic for providing and maintaining the overall connectivity of different habitat networks and thus offers a robust and powerful tool for conservation planning.

A Mathematical Representation of "Excitement" in Games: A Contribution to the Theory of Game Systems

Researchers have long believed the concept of "excitement" in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures the concept from the viewpoint of an audience and from that of a player. One of the key aspects of the index is the differential of the probability of "winning" before and after one specific "play" in a given game. The index makes a large contribution to the study of games and enables researchers to compare and analyze the “excitement” of various games. It may be applied in many fields, especially the area of welfare economics, and applications may range from those related to allocative efficiency to axioms of justice and equity.

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Online games for the teaching of mathematics

In this article we present a didactic experience developed by the GIE (Group of Educational Innovation) “Pensamiento Matemático” of the Polytechnics University of Madrid (UPM), in order to bring secondary students and university students closer to Mathematics. It deals with the development of a virtual board game called Mate-trivial. The mechanics of the game is to win points by going around the board which consists of four types of squares identified by colours: “Statistics and Probability”, “Calculus and Analysis”, “Algebra and Geometry” and “Arithmetic and Number Theory ”. When landing on a square, a question of its category is set out: a correct answer wins 200 points, if wrong it loses 100 points, and not answering causes no effect on the points, but all the same, two minutes out of the 20 minutes that each game lasts are lost. For the game to be over it is necessary, before those 20 minutes run out, to reach the central square and succeed in the final task: four chained questions, one of each type, which must be all answered correctly. It is possible to choose between two levels to play: Level 1, for pre-university students and Level 2 for university students. A prototype of the game is available at the website “Aula de Pensamiento Matemático” developed by the GIE: http://innovacioneducativa.upm.es/pensamientomatematico/. This activity lies within a set of didactic actions which the GIE is developing in the framework of the project “Collaborative Strategies between University and Secondary School Education for the teaching and learning of Mathematics: An Application to solve problems while playing”, a transversal project financed by the UPM.

Bare-tether sheath and current: comparison of asymptotic theory and kinetic simulations in stationary plasma

Analytical expressions for current to a cylindrical Langmuir probe at rest in unmagnetized plasma are compared with results from both steady-state Vlasov and particle-in-cell simulations. Probe bias potentials that are much greater than plasma temperature (assumed equal for ions and electrons), as of interest for bare conductive tethers, are considered. At a very high bias, both the electric potential and the attracted-species density exhibit complex radial profiles; in particular, the density exhibits a minimum well within the plasma sheath and a maximum closer to the probe. Excellent agreement is found between analytical and numerical results for values of the probe radiusR close to the maximum radius Rmax for orbital-motion-limited (OML) collection at a particular bias in the following number of profile features: the values and positions of density minimum and maximum, position of sheath boundary, and value of a radius characterizing the no-space-charge behavior of a potential near the high-bias probe. Good agreement between the theory and simulations is also found for parametric laws jointly covering the following three characteristic R ranges: sheath radius versus probe radius and bias for Rmax; density minimum versus probe bias for Rmax; and (weakly bias-dependent) current drop below the OML value versus the probe radius for R > Rmax.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

A theory of electron collection by a grid sphere

Use of a spherical grid as electron collector at the anodic end of a tether, as recently proposed, is considered. The standard analysis of space-charge limited current to a solid sphere (with neither magnetic nor plasma-motion effects), which has been shown to best fit TSS1R in-orbit results at very high bias, is used to determine effects from grid transparency on current collected; the analysis is first reformulated in the formalism recently introduced in the two-dimensional analysis of bare-tethers. A discussion of the electric potential created by a spherical grid in vacuum is then carried out; it is shown that each grid-wire collects current well below its maximum OML current, the effective grid transparency being close to its optical value. Formulae for the current to a spherical grid, showing the effects of grid transparency, is determined. A fully consistent analysis of electric potential and electron density, outside and inside the grid, is completed.

Categorical Structures in Non-Commutative Measure Theory.

In this paper, we investigate effect algebras and base normed spaces from the categorical point of view. We prove that the category of effect algebras is complete and cocomplete as well as the category of base normed spaces is complete, and discuss the contravariant functor from the category of effect algebras to the category of base normed spaces.

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.