The Basic Problem of Systematics

The central tenets of the falsificationist philosophy of Karl R. Popper are reviewed in detail, and the way they do or do not apply to systematics and phylogeny reconstruction is analyzed. Cladistic analysis, cast in either maximum parsimony or in maximum likelihood approaches, is not compatible with Popperian falsificationism. The main reasons are the absence of a deductive link between a hypothesis of phylogenetic relationships and character distribution on a tree, which translates into the absence of the basic asymmetry of falsification versus verification. This sets Popper s philosophy of science apart from inductive systems. In cladistic analysis, falsification (disconfirmation) is symmetrical to verification (confirmation), which reveals an inductive and hence probabilistic background. The basic problem of systematics as an empirical science resides in character conceptualization and its critical evaluation. 

Stagnant debates in contemporary systematics will remain so if systematics does not solve its basic problem. Ever more and faster algorithms can be devised to generate hypotheses of relationships and ever more statistical measures can be used to place confidence limits on those hypotheses. These do not, however, solve the basic problem of systematics, which is the nature of character hypotheses, and the problem of their critical discussion. 

A survey over the area of stiff-chain polyelectrolytes has been given. Such rod-like polyelectrolytes can be realized by use of the poly(p-phenylene) backbone [9-13]. The PPP-polyelectrolytes present stable systems that can be studied under a wide variety of conditions. Moreover, electric birefringence demonstrates that these macroions form molecularly disperse solution in water [49]. The rod-like conformation of these macroions allows the direct comparison with the predictions of the Poisson-Boltzmann cell model [27-30] which has been shown to be a rather good approximation for monovalent counterions but which becomes an increasingly poor approximation for higher valent counterions [29]. Here it was shown in Sect. 2.2 that the basic problem of the PB model, namely the neglect of correlations, can be remedied in a systematic fashion. 

These problems indicate that in order to further investigate the nature of testability in systematics, we have to expand our discussion of the basic problems of empiricism to the problem of basic statements. 

It should be emphasized at this point that the basic requirements of compatibility and consistency of finite elements used in the discretization of the domain in a field problem cannot be arbitrarily violated. Therefore, application of the previously described classes of computational grids requires systematic data transfomiation procedures across interfaces involving discontinuity or overlapping. For example, by the use of specially designed mortar elements necessary communication between incompatible sections of a finite element grid can be established (Maday et ah, 1989). 

Chapter 1 deals with the basic concepts of modelling, and the formulation of mass and energy balance relationships. In combination with other forms of relationship, these are shown to lead to a systematic development of models. Though the concepts are simple, they can be applied to very complex problems. 

Whereas many scientists shared Mulliken s initial skepticism regarding the practical role of theory in solving problems in chemistry and physics, the work of London (6) on dispersion forces in 1930 and Hbckel s 7t-electron theory in 1931 (7) continued to attract the interest of many, including a young scientist named Frank Westheimer who, drawing on the physics of internal motions as detailed by Pitzer (8), first applied the basic concepts of what is now called molecular mechanics to compute the rates of the racemization of ortho-dibromobiphenyls. The 1946 publication (9) of these results would lay the foundation for Westheimer s own systematic conformational analysis studies (10) as well as for many others, eg, Hendrickson s (11) and Allinger s (12). These scientists would utilize basic Newtonian mechanics coupled with concepts from spectroscopy (13,14) to develop nonquantum mechanical models of structures, energies, and reactivity. 

The use of dyes is so large and the literature of dye chemistry is so correspondingly large that numerous efforts have been made to classify dyes in a systematic manner. The basic problem is of course the immense variety available in the realm of organic chemistry. Most organic molecules of even nominal molecular weight can be analyzed from multiple points of view—and even named based on these points of view. There was a natural division between natural and man-made dyes but it is now only of historical significance. 

On the basis of AEP alone we can tackle the problem where 1/y is not much smaller than T. It is possible, indeed, to evaluate in a fairly systematic way correction of orders higher than 1/y. However, we are in a position to assert that the basic structure of Eq. (13) would be left unchanged, so that no relevant changes from the picture of Section III may be expected. 

Further aspects, pros and cons of WPPF, are discussed in Chapter 5. Here it is important to underline the fact that the validity of profile fitting is limited by the basic assumption of using an a priori selected profile function without any sound hypothesis that the specific functional form is appropriate to the case of study. The consequence of this arbitrary assumption can be quite different. For example, in most practical cases, profile fitting can provide reliable values of peak position and area, whereas the effects on the profile parameters are less known and rarely considered. The arbitrary choice of a profile function tends to introduce systematic errors in the width and shape parameters, which invariably introduce a bias in a following LPA, whose consequences can hardly be evaluated. It is therefore a natural tendency, for complex problems and to obtain more reliable results, to remove the a priori selected profile functions - leading to the following section dedicated to Whole Powder Pattern Modelling methods. 

Another significant class of problems, whose waveguiding properties require a systematic study, is the PCBs that constitute the basic parts of many contemporary telecommunication or computer devices. A general PCB configuration is shown in Figure 7.16. Most components... 

The basic problem in nonlinear least squares is finding the values of 0 that minimizes the residual sum of squares which is essentially a problem in optimization. Because the objective functions used in pharmacokinetic pharmacodynamic modeling are of a quadratic nature (notice that Eq. (3.13) is raised to the power 2), they have a convex or curved structure that can be exploited to find an estimate of 0. For example, consider the data shown in Fig. 3.1. Using a 1-compartment model with parameters 0 = (V, CL, volume of distribution (V) can be systematically varied from 100 to 200 L and clearance (CL) can be systematically varied from 2 to 60 L/h. With each parameter combination, the residual sum of squares can be calculated and plotted... 

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