Non-standard Definitions Research Articles

Cap-Weighted Indexing Revisited

The author first observes that arguments that indexing is a momentum strategy, a large cap strategy, or even a style of investing that is sometimes in fashion and sometimes out of fashion are misleading. He then counters these arguments with a careful, non-standard definition of cap-weighted indexing, which distinguishes between the amount of the company being purchased and the amount of money that this purchase costs. He concludes that the argument that cap-weighted indexing is a momentum play is false, as it fails to distinguish between the amount of the company being purchased and the cost of this purchase. It also fails to distinguish between a bet that a portfolio is making relative to the market, and one that is made by the market as a whole. Thus, by defining indexing as the purchase of the same fractional amount of each company, it becomes apparent that indexing is not a momentum play, a size play, nor a style play.

Therapeutic options in obstructive sleep apnoea: have we made enough progress?

Obstructive sleep apnoea/hypopnoea syndrome not to OSA/H. These cost estimations, however, did not take into account the possible medical (OSA/H) has a high prevalence. According to most epidemiological studies (despite some limitations consequences of apnoea-related road traffic accidents. due to non-standard definition criteria), OSA/H involves 1–4% of the middle-aged symptomatic Numerous studies have reported on the relationship between sleepiness, as a consequence of population, even more if we consider non-symptomatic people or patients above 60 years, although sleep disruption due to OSA/H, and automobile acccidents or near-missed accidents. The relative in this population the clinical symptoms and consequences are less clear [1]. In addition, high blood risk to have an accident lies between 2.3 and 7.3, but here, unlike what is seen in the studies on pressure and coronary heart disease, with their high burden of morbidity and mortality are definitively cardiovascular complications of OSA/H, there is generally no close correlation between this risk and recognized as major complications of OSA/H independently of associated obesity, alcohol intake, the severity of OSA/H. The sleep medical community has taken this sex and age [2–4]. Obstructive sleep apnoea/ hypopnoea affects mainly middle-aged, prodisease seriously, and has developed a number of therapeutic modalities such as weight loss, befessionally active patients, which implies high health care costs and loss of working days. havioural modifications, tracheostomy, naso-pharyngeal tube, uvulopalatopharyngoplasty (UPPP), The medical cost of undiagnosed sleep apnoea has been evaluated in a case–control study group nasal surgery, nasal dilators, electric stimulation of pharyngeal muscles, continuous positive airway of 358 US obese patients with moderate OSA/H (mean apnoea–hypopnoea index 37) [5]. In the year pressure (CPAP), oral appliances (OAs) and maxillofacial surgery. Continuous positive airway presprior to the diagnosis, mean annual medical costs were US$2720 for cases, compared with US$1384 sure and OAs are the most studied and used modalities. for controls. The difference was statistically significant (P<0.01). The severity of sleep-disordered This year, we celebrate the 20th anniversay of the publication by Sullivan et al. [6] on the efficacy breathing was correlated to the magnitude of medical costs. The additional cost estimation for the of CPAP for OSA/H. Since that time, CPAP remains a well-proven treatment. Nevertheless until recently entire USA was calculated at $3.4 billion each year. It should be mentioned that there was no matching there remained a need to demonstrate its efficacy in the improvement of morbidity, mortality and between cases and controls for body weight, so that the cost differences could be due to obesity and quality of life with randomized placebo-controlled studies as noted in the disturbing paper of Wright et al. in 1997 [7]. In this issue of Sleep Medicine Reviews, Drs William Beninati and Mark Sanders Correspondence should be addressed to: Daniel Rodenstein, give us a summary of the efficacy studies published Cliniques Saint-Luc, Av. Hippocrate 10, 1200 Brussels, Belgium. Fax: 32 2 764 28 31; E-mail:rodenstein@pneu.ucl.ac.be in the last 3 years [8]. With them we can clearly

Thermostatistics of extensive and non-extensive systems using generalized entropies

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short- and long-range interactions. The first method is quite general and it is based on the numerical evaluation of the density of states with a given energy. The second method is more specific for Tsallis thermostatistics and it is based on a standard Monte Carlo Metropolis algorithm along with a numerical integration procedure. We show here that both methods are robust and efficient. We present results of the application of the methods to the one-dimensional Ising model both in a short-range and in a long-range (non-extensive) case. We show that the thermodynamic potentials for different values of the system size N and different values of the non-extensivity parameter q can be described by scaling relations which are an extension of the ones holding for the Boltzmann–Gibbs statistics ( q=1). Finally, we discuss the differences in using standard or non-standard mean value definitions in the Tsallis thermostatistics formalism and present a microcanonical ensemble calculation approach of the averages.

Are data on the prevalence and duration of breastfeeding reliable? The case of Italy

Many countries produce data on the prevalence and duration of breastfeeding, but are they reliable? We reviewed 16 studies on breastfeeding in Italy published after 1990. They report a prevalence of breastfeeding at and around birth ranging from 66% to 91%, decreasing to 17–52% at 4 mo and 28–36% at 6 mo. Most studies refer to a non‐representative sample of the Italian population. Two studies used standard definitions of breastfeeding, but their results are difficult to interpret or cannot be generalized. Five other studies used non‐standard definitions that undermine the interpretation of results. The remaining nine studies used no definition at all. All studies used a recall period different from 24 h, or from the whole hospital stay for breastfeeding at discharge, making the interpretation of results even more difficult. We conclude that the published information gives an inaccurate picture of the prevalence and duration of breastfeeding in Italy, leading to unjustified optimism and inaction. The actual figures may be lower, as shown by preliminary data from a small Italian region: using standard definitions and methods during a 9‐mo monitoring period, exclusive breastfeeding averaged 35% at discharge and 23% at about 4 mo of age.

Mechanizing Nonstandard Real Analysis

AbstractThis paper first describes the construction and use of the hyperreals in the theorem-prover Isabelle within the framework of higher-order logic (HOL). The theory, which includes infinitesimals and infinite numbers, is based on the hyperreal number system developed by Abraham Robinson in his nonstandard analysis (NSA). The construction of the hyperreal number system has been carried out strictly through the use of definitions to ensure that the foundations of NSA in Isabelle are sound. Mechanizing the construction has required that various number systems including the rationals and the reals be built up first. Moreover, to construct the hyperreals from the reals has required developing a theory of filters and ultrafilters and proving Zorn's lemma, an equivalent form of the axiom of choice.This paper also describes the use of the new types of numbers and new relations on them to formalize familiar concepts from analysis. The current work provides both standard and nonstandard definitions for the various notions, and proves their equivalence in each case. To achieve this aim, systematic methods, through which sets and functions are extended to the hyperreals, are developed in the framework. The merits of the nonstandard approach with respect to the practice of analysis and mechanical theorem-proving are highlighted throughout the exposition.

A Daniell integral approach to nonstandard Kurzweil-Henstock integral

A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from [9]. The theory is recovered together with a few new results.

An Introduction to History Dependent Automata

Automata (or labeled transition systems) are widely used as operational models in the field of process description languages like CCS [13]. There are however classes of formalisms that are not modelled adequately by the automata. This is the case, for instance, of the π-calculus [15,14], an extension of CCS where channels can be used as values in the communications and new channels can be created dynamically. Due to the necessity to represent the creation of new channels infinite automata are obtained in this case also for very simple agents and a non-standard definition of bisimulation is required.In this paper we present an enhanced version of automata, called history dependent automata, that are adequate to represent the operational semantics of π-calculus and of other history dependent formalisms. We also define a bisimulation equivalence on history dependent automata, that captures π-calculus bisimulation. The results presented here are discussed in more detail in [21].

My route to arithmetization

I had the pleasure of renewing my acquaintance with Per Lindstrom at the meeting of the Seventh Scandinavian Logic Symposium, held in Uppsala in August 1996. There at lunch one day, Per said he had long been curious about the development of some of the ideas in my paper [1960] on the arithmetization of metamathematics. In particular, I had used the construction of a non-standard definition !* of the set of axioms of P (Peano Arithmetic) to

What is a solution of an ODE?

This article will introduce a nonstandard definition of the 'solution' of an ordinary differential equation (ODE). I hope that this article will start some discussion; further, I hope that this article will have some effect on the ambitious European CATHODE project, which is attempting to provide tools in computer algebra for handling ordinary differential equations.

Characterizing classes of functions computable by quantum parallelism

Computation by quantum parallelism involves associating a quantum state v(f) to each function f : Z m → Z n . v(f) is formed from superpositions of states labelled by the values of f , the standard choice being an equally weighted superposition of all the values of f . A joint property G(f) of the values f (0),..., f ( m –1) is called computable by quantum parallelism (QPC) if there is an observable g which will reveal the value G(f) , with non-zero probability, when applied to v(f) , and will never show a false value. It is shown that the problem of deciding which G s are QPC can be formulated entirely in terms of the linear relations which exist among the v(f) s. In the case of f : Z m → Z 2 , G :( Z 2 ) m → Z 2 we explicitly describe all properties which are QPC and show that this includes only m 2 + m + 2 of the 2 2 m such properties. By using a suitable nonstandard definition for v(f) this number can be increased to 2 2 m — 2 m+1 (for m &gt; 1).

Numerical study of initially expanding mixmaster universes

Numerical studies by Burd et al. (1989) and Hobill et al. (1989) indicate that the mixmaster universe is not chaotic since the Liapunov exponents computed from its dynamics by the standard formula vanish. Burd et al. use a non-standard short-time definition of the exponents to indicate that mixing is still present. Here it is found that mixmaster universes regarded as trajectories in a minisuperspace exhibit a quasichaos if the trajectory passes through a maximum of expansion despite the vanishing Liapunov exponents. It is shown that the frequency of bounces off the minisuperspace potential and the importance of the potential corners increase near the maximum of expansion. Trajectories with small but finite differences in their initial conditions exhibit qualitatively distinct evolutions in the direction of the big crunch. This phenomenon is not found for initially collapsing universes.

Simultaneity, conventialism, general covariance, and the special theory of relativity

In a recent article, De Ritis and Guccioni claimed to give an easy way of falsifying the conventionalist interpretation of the definition of simultaneity of distant events within an inertial system. For a particular closed light path, they derived a necessary condition and claimed that it could be violated by a nonstandard choice of the definition of simultaneity. It is pointed out here that (as shown by many authors) the possibility of a nonstandard definition is implicitly contained in a generally covariant formulation of the special theory of relativity, and it is shown that conditions such as the one they derived are satisfied automatically. The most general position-independent definition of simultaneity is given, and an example of a position- as well as direction-dependent definition is exhibited in an Appendix. A number of objections against the possibility of a nonstandard definition of simultaneity raised by various authors are discussed and are found to lack any physical or mathematical justification.

Chiral order parameter of the Wilson fermion formulation in a lattice CPN-1 model.

We study the Wilson formulation of fermions in the CP/sup N/-1 model by means of a nonstandard definition of the vacuum. We discuss the results.

Why Data Bases Should Not Replace Randomized Clinical Trials

Advances in computer technology have made it possible to store large amounts of observational data concerning treatment of patients for medical disorders. It has been suggested that these data banks might replace randomized clinical trials as a means of evaluating the efficacy of therapies. A review of the methodological problems likely to arise in analyzing such data for the purpose of comparing treatments suggests that sound inferences would not generally be possible because of difficulties with bias in treatment assignment, nonstandard definitions, definitions changing in time, specification of groups to be compared, missing data, and multiple comparisons.

Computer Applications of Petroleum Data System: ABSTRACT

The Petroleum Data System, a collection of general field and reservoir information, has been available for public use for approximately 3 years. Data have been used in a variety of studies by oil companies, consultants, and government agencies. In particular, many studies have been done in an effort to determine the potential of specific basins for future exploration and drilling, the feasibility of certain types of enhanced recovery techniques, and future reserves from existing fields. The different types of output are histograms, scatterplots, bargraphs, correlations, simple listings, and summary reports obtained by manipulation of the data in the file. These examples illustrate problems that have to be faced in working with large data bases, such as End_Page 542------------------------------ missing data, conflicting data, and fuzzy or nonstandard data definitions. End_of_Article - Last_Page 543------------

Universal conventionalism and space-time

Geo-chronometric conventionalism (GC) is shown to be part of a more general thesis, universal conventionalism, stating that coordinative definitions are needed in order to compare two measurements of any physical quantity at different space-time points. Two fully elaborated examples of the use of non-standard coordinative definitions in physics are given, demonstrating that the use of these definitions can actually simplify the physical formalism.

Diophantine Correct Non-Standard Models in the Isols

Dedekind introduced a non-standard definition of finiteness as follows. A set a is Dedekind finite if there is no 1-1 function f, defined on a, which maps a onto a proper subset of a. (In the absence of the axiom of choice, there can be Dedekind finite sets which are not finite in the usual inductive sense.) Dekker [1] introduced a relativised notion of Dedekind finiteness, where sets a are subsets of the set E -{O, 1, 2, .. . } of non-negative integers, and 1-1 functions f are 1-1 partial recursive functions. A subset a of E is called isolated if there is no 1-1 partial recursive function f, defined on a, such that f(a) ; a. This gave rise to an effective analogue of the theory of cardinals of Dedekind finite sets, the theory of isols. Sets a, 18 c E are called recursively equivalent if there is a 1-1 partial recursive function p, at least defined on a, such that p(a) 1 8. The equivalence class of an isolated set a is an isol, and A is the set of isols. Operations of addition and multiplication for isols are given by