Mathematical Exactitude Research Articles

PRM68 - Markov Models For Health Economic Evaluation Modelling In R With The Heemod Package

Most Markov models are built using basic spreadsheet software, which has drawbacks: analyses are hard to reproduce and lack of transparency, errors are difficult to spot, track and correct, and graphic capabilities are lacking. The R language can overcome these issues through script-based approaches, but programming models is not a simple matter, which has limited its use in this field. Our main objective was to develop a free and open-source R package for Markov models focused on reproducibility and ease of use. We developed an R package to compute the models described in the reference textbook “Decision Modelling for Health Economic Evaluation” by Briggs et al. We aimed to facilitate easy and transparent model writing that ensured security and reproducibility. To facilitate model building, a graphical user interface was developed, allowing output of model scripts for peer review. The finalized package, heemod, and the graphical user interface were made available for free on CRAN, the public and open-source R package repository. We reproduced in a concise and readable format all the results of the analyses described in “Decision Modelling for Health Economic Evaluation”, such as homogeneous and non-homogeneous (with time-varying properties) Markov models, as well as sensitivity and probabilistic uncertainty analysis (where it is possible to specify arbitrary distributions and correlation structures between parameters). This work shows that it is possible to develop complex Markov models easily in the R language without sacrificing transparency, reproducibility or mathematical exactitude. The free and open-source license facilitates code review and improvement of the package by third-party experts. We hope the availability of this package will facilitate the use of script-based approaches to health evaluation modelling and help improve the overall quality and reproducibility of studies in this domain.

Why Business Schools Need to Teach About the Blockchain

An overview of Cryptocurrency and Blockchain technology based business initiatives and models.Traditional in nature but revolutionary in its outlook, cryptocurrencies have often been mistrusted and discredited by critics due to their price volatility and fixed supply. In spite of these limitations, cryptocurrencies offer the possibility of rewiring the financial system based on the Blockchain, the underlying technology of all cryptocurrencies, which is heralded for its mathematical exactitude. In recent times, an increasing number of developers, mathematicians,entrepreneurs and academics have begun to leverage this technology, thus creating new business models and innovative ways in which value can be transferred without the use of traditional channels.As financial institutions, central banks and sovereign states begin to acknowledge these changes, formal research conducted by business schools is found lacking in this space. Thus, this report aims to explain the concept of the Blockchain and presents the reader with an explanation of the technical jargon in a nontechnical manner, without which it is difficult to comprehend these new business models. Having grasped these concepts, the report then delves into the new innovative companies using this technology and gauges the potential of these Blockchain-based businesses to change the economic structures and the rarefied services offered to its proponents in today’s digital age.

The Scientific Revolution—The Kidney and Nephrology in and about the Seventeenth Century (Part 1)

In the history of the evolution of the medical sciences, it is in the 17th century that the conscious, deliberate, and systematic study of the workings of the human body began. It was a product of the radical changing attitudes of this insurgent century when mathematical reasoning and mechanistic philosophy replaced the teleological outlook of earlier times. It was then that meticulous observation, reproducible quantification, experimental validation, and mathematical exactitude in the quest for truths launched the Scientific Revolution. The effect on medicine was a transformative change from a descriptive to an explanatory body of knowledge during the course of which rigorous anatomical dissections were used for the mechanical explanation of organ function, when morbid changes observed at postmortem began to be related to clinical features of disease, and when the secretive analytical methods of alchemy began to be refined for the study of chemical changes in living matter. Essentially what began with meticulous observations of anatomical features begat physiology and laid the foundations of pathology and chemistry. As a result, studies of organ structure, function, and changes in disease in general, and of the kidney in particular, were clarified and progressed at a rate never achieved theretofore.

Edmund Husserl: Idealisierung und Doxa

As its title indicates, our work deals with two motifs which, in the end, flow together. The first has to do with the confrontation (long a subject of philosophical discussion) between the Lebenswelt and its mathematization at the hands of the sciences. Mathematics, according to Husserl, is a science whose contents – axioms, laws, geometric solids – are ideas. Idealization, as practiced by Husserl, consists in adopting and adapting Kant’s interpretation of ‘the idea’, and in designating both mathematical exactitude and the thing in its totality as ‘ideas in the Kantian sense’. The second motif examines Husserl’s attempt to identify the Lebenswelt with Plato’s ‘mere opinion’ (doxa as opposed to episteme). Husserl mounts a defense of doxa, granting it a value as high as, or even higher than, that of episteme. We want to show what this higher value of doxa consists in. Thus, we enter into the problem of measurement, a phenomenon which, beginning as an estimative, pre-geometrical operation, leads to exactitude. In this context, we propose the following thesis: measurement, thanks to the idealization of ‘the thing’ which makes it possible, is the foundation of mathematical exactitude. However, things themselves are given only in gradations, fragments, sides – in other words, they are given perspectivally. Hence, propositions about them can at first only be subjective, private opinions (in the sense of doxa).

Tidal Effects on Rotating Gaseous Ellipsoids Revolving around a Central Massive Object

A computationally integrable set of ordinary differential equations is derived for a gaseous ellipsoid of uniform density orbiting in the gravitational potential of an extended massive object (represented by the logarithmic potential). Numerical integrations can be conducted in the same mathematical exactitude as in the classical theory of a homogeneous liquid ellipsoid in equilibrium. First, we obtain a series of equilibrium figures moving in a circular orbit and analyze their linear and nonlinear stability. The gaseous ellipsoids that are elongated toward the center are not realized within a critical radial distance from the extended massive object, whereas those elongated along the circular orbit are distributed in the full range of the radial distance. Then we consider the cases of a noncircular orbit around the center and examine the time-dependent tidal effects on the ellipsoid. No equilibrium figure exists, but excited nonlinear oscillation and disruption are numerically followed. The spin angular momentum of the ellipsoid is also shown to change rapidly at its pericenter passage when the tidal effect is strongest. When the angular momentum increases considerably, the ellipsoid is shown to elongate extremely and suffer tidal disruption. The condition for such tidal disruption is extensively examined. The results are applied to the apparent alignment of galaxies gathering densely around the central dominant object of a rich cluster of galaxies.

The Tyranny of the Clock

In no characteristic is existing society in theWest so sharply distinguished from the earlier societies, whether of Europe or the East, than in its conception of time. To the ancient Chinese or Greek, to the Arab herdsman or Mexican peon of today, time is represented in the cyclic processes of nature, the alternation of day and night, the passage from season to season. The nomads and farmers measured and still measure their day from sunrise to sunset, and their year in terms of the seedtime and harvest, of the falling leaf and the ice thawing on the lakes and rivers. The farmer worked according to the elements, the craftsman for so long as he felt it necessary to perfect his product. Time was seen in a process of natural change, and men were not concerned in its exact measurement. For this reason civilisations highly developed in other respects had the most primitive means of measuring time, the hour glass with it’s trickling sand or drippingwater, the sundial, useless on a dull day, and the candle or lamp whose unburnt remnant of oil or wax indicated the hours. All these devices where approximate and inexact, and were often rendered unreliable by the weather or the personal laziness of the tender. Nowhere in the ancient or medieval world were more than a tiny minority of men concerned with time in the terms of mathematical exactitude. Modern, Western man, however lives in a world which runs according to the mechanical and mathematical symbols of clock time. The clock dictates his movements and inhibits his actions. The clock turns time from a process of nature into a commodity that can be measured and bought and sold like soap or sultanas. And because, without some means of exact time keeping, industrial capitalism could never have developed and could not continue to exploit the workers, the clock represents an element of mechanical tyranny in the lives of modern men more potent than any individual exploiter or any other machine. It is valuable to trace the historical process by which the clock influenced the social development of modern European civilisation. It is a frequent circumstance of history that a culture or civilisation develops the device which will later be used for its destruction. The ancient Chinese, for example, invented gunpowder, which was developed by the military experts of the West and eventually led to the Chinese civilisation itself being destroyed by the high explosives of modern warfare. Similarly, the supreme achievement of the ingenuity of the craftsmen in the medieval cities of Europe was the invention of the mechanical clock, which, with it’s revolutionary alteration of the concept of time, materially assisted the growth of exploiting capitalism and the destruction of medieval culture. There is a tradition that the clock appeared in the eleventh century, as a device for ringing bells at regular intervals in the monasteries which, with the regimented life they imposed on their inmates, were the closest social approximation in themiddle ages to the factory of today.The first authenticated

Modeling Theory and Composing Process Models

In 1914, near the beginning of World War I, philosopher Pierre Duhem expressed a profound disdain for scientists who used models as conceptual aids. In Duhem's view, models were a kind of mental crutch, needed only by those poor souls who were burdened with an English mind-a mind that was careless, unexacting, and unable to manage complex systems of abstract representation. The French mind, on the other hand, which was characterized by straitness, clarity, and method, did not require the clumsy simplifications provided by models in order to apprehend reality (68-73). Intricate formulae were its daily fare, if not its raison d'ttre. This ability of the mind to handle complex representational systems without the assistance of mechanical or graphic aids was, to Duhem's way of thinking, not only a requisite for true thought but also another clear testament to the superiority of the race over that of the English. Duhem's argument, developed in The Aim and Structure ofPhysical Theory, is interesting for a variety of reasons, not merely because it manages to combine philosophy with a rather quaint form of Frankish nationalism. It is also noteworthy for the contrast it provides to current critiques of writing process models and their underlying epistemologies. To Duhem, meaningful understanding was intimately linked to rigor, mathematical exactitude, and representational precision; since models were simplifications, their descriptions were unreliable and their utility questionable at best. In an age when positivism had not yet been supplanted as the dominant ideology guiding inquiry, Duhem criticized models for their failure to be positivistic enough. To a number of present-day composition scholars such as Patricia Bizzell, Marilyn Cooper and Michael Holzman (Talking, Reply), and William Irmscher, this view of models-in light of poststructuralist epistemology and reflexive methodological criticism-seems naive, a relic of a past age when scientific subjectivism masked itself as objectivity. In their critiques of cognitive writing process models, notably those models offered by John Hayes and Linda Flower (Identifying, Writing), Robert de Beaugrande, and Marlene Scardamalia and Carl Bereiter, these scholars suggest that the epistemological

Caricature and Photography in Second Empire Paris

In 1841, two years after the announcement of Daguerre's invention, the Swiss writer and cartoonist Rodolphe Topffer published an essay in response to claims that painting, and art in general, would soon be outmoded by the miraculous silver image. Faced with the mathematical exactitude and material fidelity of the daguerrian plate, Topffer argued that imitation was a means but not an end of art and that “resemblance” had very little to do with “identity.” A simple sketch of four legs, long ears, a body, and a skinny tail is immediately recognizable as a donkey; the reproduction of every hair on the beast in no way adds to that resemblance. The marks on the page are symbols acting on the mind that recall the viewer's idea of an object rather than its physical form. Therefore, Topffer concluded, the daguerreotype poses no threat to the artist, since a machine cannot translate our ideas of the world or evoke the same impressions, dreams, and feelings that the canvases of a Claude or Poussin inspire.

Mathematical methodology in the thought of charles S, Peirce

It is fitting that the celebration of Peirce's New Elements of Mathematics should be taking place in New York City, where Peirce was often to be found attending mathematical meetings at Columbia University and where he consulted the resources of the old Astor Library for the production of many of his writings. This paper considers Peirce—a lifelong student of logic—as he examined scientific and mathematical methodology on all levels, in ages past as well as in the then-contemporary literature. Peirce hoped to create an exact philosophy by applying the ideas of modern mathematical exactitude. He developed a semiotic pattern of mathematical procedure with which to test validity in all areas of investigation.

What Will Be the Instruments of Latin-American Advancement?

What are the elements that Latin America needs in order to achieve economic development? The process of economic development is an extremely complex one, calling for means and procedures which cannot be specified with mathematical exactitude. Examination of important and well-known points of view on the subject indicates that these elements include international co-operation, which really embraces all the others; agrarian reform, to increase and diversify agricultural output, train the farmers, and build and improve penetration roads to transport crops; rational development of natural resources such as forests; encouragement of industrialization by means of stabilized international markets and more equitable trade policies on the part of the more developed countries —especially the West European countries; and external co-operation by other nations in the form of public and private investment and technological assistance. The economic integration of Latin America would also be an effective means of furthering economic development. The Alliance for Progress is highly useful in helping the Latin-American countries to combine these elements to bring about the emergence of economic development, for example, by undertaking surveys of the needs of Latin-American countries, by evaluation of development projects and external financing, and by channeling the funds for implementation of programs.—Ed.

West Indian Volcanic Eruptions

AS a panacea for much ignorance, the subtle fluid of Franklin stands next to superstition. If you cannot explain the angry workings of a volcano by a Pluto, a Vulcan or the strug-glings of the damned, tell the man in the street that it is due to electricity and he is happy. At the present moment, in seventeen columns of the Revue Scientifique of September 6, M. Arthur Tarquin offers to the world an electrical theory of volcanic action which, to a great extent, is novel. At the outset we are told that the earth is entirely governed by the sun, and as its energy varies so will various activities on the earth vary. In establishing such a connection for volcanic activity, M, Tarquin, however, poses as a special pleader. In Tokio, for example, he says that earthquakes (sic) are most numerous about the times when sun-spots are at a maximum and at a minimum. Dr. E. Naumann, who examined the earthquake registers of Japan, however, failed to find such a connection/ and others who have worked with materials relating to other countries have arrived at similar conclusions. As another example of incompleteness in statement, we are told that at the “moment prdcis” of the eruption in Martinique, with a mathematical exactitude magnetic needles at observatories throughout the world were violently disturbed. Even if we admit this to have been the case, we fail to see why similar phenomena were not observed with the more violent eruption which took place the day previously in St. Vincent.