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.

Use of calculus of variations to determine the shape of hovering rotors of minimum power and its application to micro air vehicles

In this paper, calculus of variations and combined blade element and momentum theory (BEMT) are used to demonstrate that, in hover, when neither root nor tip losses are considered; the rotor, which minimizes the total power (MPR), generates an induced velocity that varies linearly along the blade span. The angle of attack of every blade element is constant and equal to its optimum value. The traditional ideal twist (ITR) and optimum (OR) rotors are revisited in the context of this variational framework. Two more optimum rotors are obtained considering root and tip losses, the ORL, and the MPRL. A comparison between these five rotors is presented and discussed. The MPR and MPRL present a remarkable saving of power for low values of both thrust coefficient and maximum aerodynamic efficiency. The result obtained can be exploited to improve the aerodynamic behaviour of rotary wing micro air vehicles (MAV). A comparison with experimental results obtained from the literature is presented.

Calculus of the uncertainty in acoustic field measurements: comparative study between the uncertainty propagation method and the distribution propagation method

The new Spanish Regulation in Building Acoustic establishes values and limits for the different acoustic magnitudes whose fulfillment can be verify by means field measurements. In this sense, an essential aspect of a field measurement is to give the measured magnitude and the uncertainty associated to such a magnitude. In the calculus of the uncertainty it is very usual to follow the uncertainty propagation method as described in the Guide to the expression of Uncertainty in Measurements (GUM). Other option is the numerical calculus based on the distribution propagation method by means of Monte Carlo simulation. In fact, at this stage, it is possible to find several publications developing this last method by using different software programs. In the present work, we used Excel for the Monte Carlo simulation for the calculus of the uncertainty associated to the different magnitudes derived from the field measurements following ISO 140-4, 140-5 and 140-7. We compare the results with the ones obtained by the uncertainty propagation method. Although both methods give similar values, some small differences have been observed. Some arguments to explain such differences are the asymmetry of the probability distributions associated to the entry magnitudes,the overestimation of the uncertainty following the GUM

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Bacterial diversity within the human subgingival crevice

Molecular, sequence-based environmental surveys of microorganisms have revealed a large degree of previously uncharacterized diversity. However, nearly all studies of the human endogenous bacterial flora have relied on cultivation and biochemical characterization of the resident organisms. We used molecular methods to characterize the breadth of bacterial diversity within the human subgingival crevice by comparing 264 small subunit rDNA sequences from 21 clone libraries created with products amplified directly from subgingival plaque, with sequences obtained from bacteria that were cultivated from the same specimen, as well as with sequences available in public databases. The majority (52.5%) of the directly amplified 16S rRNA sequences were <99% identical to sequences within public databases. In contrast, only 21.4% of the sequences recovered from cultivated bacteria showed this degree of variability. The 16S rDNA sequences recovered by direct amplification were also more deeply divergent; 13.5% of the amplified sequences were more than 5% nonidentical to any known sequence, a level of dissimilarity that is often found between members of different genera. None of the cultivated sequences exhibited this degree of sequence dissimilarity. Finally, direct amplification of 16S rDNA yielded a more diverse view of the subgingival bacterial flora than did cultivation. Our data suggest that a significant proportion of the resident human bacterial flora remain poorly characterized, even within this well studied and familiar microbial environment.

Calculus of variations. Supplementary notes and exercises to 1945-1946 notes, at New York University.

Reproduced from typewritten copy.

Calculus of variations 1945-1946,

Bibliography: leaf 169.

The calculus,

Preface to revised edition signed: W. C. Brenke and E. R. Hedrick.

Aspects of the calculus of variations /

Reproduced from type-written copy.

Calculus, a modern approach.

Bibliography: p. xxi.

Calculus, a modern approach.

Mode of access: Internet.

Introduction to the calculus,

"A revision of the author's A first course in the differential and integral calculus."--Pref.

Introduction to the calculus,

"A revision of the author's A first course in the differential and integral calculus."--Pref.