Theoretical Motivation

A brief review of the existing empirical evidence on the relationship between R D intensity and concentration indicates that the results are at best mixed. Indeed, it seems that no solid empirical regularities can be detected in the data. On the theoretical side, we are faced with a set of models, each representing a specific situation, with each model providing a different, sometimes unique, equilibrium. 

According to Sutton ((1991), (1998)), a single model may be adequate, but only for a narrow subset of R D intensive industries. By contrast, the bounds approach does not require the identification of a unique equilibrium. Rather, it focuses on the whole set of outcomes that could form part of the equilibrium. This method proceeds by eliminating the set of realisations that cannot belong to any equilibrium given a sensible set of assumptions. 

Clearly, there exist various ways to model each stage the difficulty lies in the fact that there is no adequate discrimination process across models since the particulars of firms decision process are not observable. Thus, the objective of 

Notice that sunk costs are independent of market size, but profits derived fi om them are growing with market size, since firms following this policy set higher prices and obtain a larger market share. Thus, if firms face a large number of competitors, i.e., have a very small market share, then it will be profitable for some firm to outspend its rivals sunk costs and capture a larger 

Low substitution will imply that in spite of the effectiveness of R D expenditures, concentration may be low. This happens when there are many products associated to different R D trajectories (low K). In this case, escalation does not lead to higher profitability, since market share is constrained to a single group of products. In such cases, a proliferation strategy is more effective in attaining a large market share. 

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The theoretical motivating ideas for the photochemical and spectroscopic studies are illustrated by the simplified energy level diagram drawn below. 

Coccaro EF, Siever LJ, Klar HM, Maurer G, Cochrane K, et al. 1989. Serotonergic studies in patients with affective and personality disorders Correlates with suicidal and impulsive aggressive behavior. Arch Gen Psychiatry 46 587-599. Cohen JD, Barch DM, Carter C, Servan-Schreiber D. 1999a. Context-processing deficits in schizophrenia Converging evidence from three theoretically motivated cognitive tasks. JAbnorm Psychol 108 120-133. 

Cohen JD, Barch DM, Carter C, Servan-Schreiber D. 1999b. Context-processing deficits in schizophrenia Converging evidence from three theoretically motivated cognitive tasks. JAbnorm Psychol 108 120-133. 

In some sitrrations, no theoretically motivated analytic form y = fix) is apparent, and low-order series approximations do not provide a good fit. Yon should then be cautious about using high-order empirical series fitting forms, since they may yield very poor... 

Tlie ultimate test of new, theoretically motivated protocols for materials discovery is, of course, experimental. To motivate such experimentation, the effectiveness of these protocols is demonstrated by combinatorial chemistry experiments where the experimental screening step is replaced by hgures of merit returned by the random-phase volume model. The random phase volume model is not fundamental to the protocols it is introduced as a simple way to test, parameterize, and validate the various searching methods,... 

C. P. Robert, The Bayesian choice a decision-theoretic motivation. Springer, New York, (1994). 

Winfree, E. 2000. Algorithmic/self-assembly of DNA theoretical motivation and 2D assembly experiments. Journal of Biomolecular Structure and Dynamics 11 263-270. 

Such practical and theoretical motivations drive the need for automatic methods that can reduce the dimensionality of a dataset in an intelligent way. Spectral dimensionality reduction is one such family of methods. Spectral dimensionality reduction seeks to transform the high-dimensional data into a lower dimensional space that retains certain properties of the subspace or sub manifold upon which the data lies. This transformation is achieved via the spectral decomposition of a square symmetric... 

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