Open Problems and Future Directions

Major problems facing an investigator who wants to prepare data for analysis or neural network modeling concern what input data features are to be used and how the information will be encoded before presentation to the model. Another issue to be faced concerns discovery of biological rules and features from the data, after analysis or modeling-e.g., what do the results mean Interpretation of weights after training, for example, is a particularly difficult problem. 

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When setting up such a model, two building blocks are available which come from different modeling fields, namely, the Stefan Maxwell equations describing the flow of a gas mixture through a porous medium and the equations of multiphase flow in a porous medium. We will shortly describe both of them. After that, we make an attempt to join both of them into a combined model. The discussion of open problems and future directions concludes the section. 

We open with a brief report of the early discovery of the occurrence and isolation of these proteins and the elucidation of their function and homology, followed by a brief discussion of some problems in their isolation and the determination of their activity. We then consider various aspects of their three-dimensional structures and their significance. We summarize studies on the implications of their sequence similarities, and also on the binding of metal ions, especially calcium(H), and consider their implications. Then follows a brief discussion of lactose synthase, an enzyme of which a-lactalbumin and galactosyltransferase are essential components. We then examine the evidence concerning the evolution of the two proteins, about which there are conflicting views (see Section X,B). Some conclusions and predictions of future directions are made. 

The earliest research in a field builds on past work and this always makes it difficult to ascribe priority to important discoveries that lead to new directions or paradigms for future research. Certainly, there were many early investigations that used computer simulation of Newton s equations of motion to tackle important open problems. For instance, Hirschfelder et al. [2] studied the dynamics of the gas phase H + H2 reaction on a model potential surface to determine the reaction rate. In later years this investigation spawned the field of gas phase molecular dynamics. The paper by Fermi et al. [3] on the simulation of the dynamics of a model one-dimensional solid was influential in the field of non-linear dynamics. Neither these papers nor the body of work they stimulated had an immediate important impact on statistical mechanics [4]. 

The important open question is precisely what happens just after the first bond is fused or broken. There is no precise answer, and it seems that the efforts in the future will be concentrated in this direction. We reported that the current belief is that in the lattice models, after the failure of the first bond, a cascading effect occurs and the failure propagates, even when the current or the voltage across the sample is kept constant at the first failure value. However, this dynamic problem has not been solved yet. Very recently of course Zapperi et al. (1997) have confirmed the critical divergence of breadown susceptibility x the breakdown point in the random fuse some other models, as discussed in the section 2.3.7(b). They also argued that this divergence of % = / nP n)dn " suggests... 

The chapter presents some of the significant recent developments and indicates the direction of future developments in oil spill fingerprinting and remote sensing. Widespread adoption of uniform practices in oil identification will benefit all who are concerned with the problem of identifying sources of oil pollution. Airborne remote sensing is, at present, the only practical way to maintain pollution surveillance over wide areas of open sea. 

These obvious advantages suggest that other applications will be presented in the future. For example, preliminary work has shown that LCT can be applied to problems in quantum computing [51]. Here, the present approach could open new perspectives. Also, it is interesting to address the question of how the scheme can be realized experimentally. We are optimistic that there are many more interesting problems that can be treated using the local control scheme, and we hope that the present compilation of work will stimulate research in that direction. 

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