Signal propagation

The signal propagation in the MLF networks is similar to that of the perceptron-like networks, described in Section 44.4.1. For each object, each unit in the input layer is fed with one variable of the X matrix and each unit in the output layer is intended to provide one variable of the Y table. The values of the input units are passed unchanged to each unit of the hidden layer. The propagation of the signal from there on can be summarized in three steps. 

Each hidden unit,y, receives the signals from the p units of the previous layer, the input layer. From these signals the net input is calculated  

The net input, NET, is then passed to the transfer function that transforms it into the output signal of the unit. Different transfer functions may be used, the most common non-linear one being the sigmoidal function (Fig. 44.5b). 

The output units receive the weighted output signals of the h hidden units. The weighted sums are calculated and passed through the transfer function to yield the final output of the network. 

---

Frustrated Loops. The period of a loop depends on whether or not it is frustrated . Consider the parity of the number of value inversions contained in a loop. If it is odd, the loop is said to be frustrated. In this case, a signal propagating around the loop has to go around twice before the loop returns to its initial state. Letting I be the number of site in a loop, the period of the loop is therefore equal to 2 X i for configurations with no symmetries, or an odd factor of 21 for certain special cases. In particular, a frustrated loop cannot have fixed points. 

Since, as we have continually been reminded throughout this book, the capacity for some kind of signal propagation is critical for being able to perform arbitrary computational processes, it should come as no surprise that there is a finite intersection between both context-sensitive and unrestricted Chomsky languages - the latter, of which, we recall require the class of universal computers as their accept-... 

Fig. 44.10. An example of signal propagation in an MLF network with transfer function ...

Quantitative imaging of lateral ErbBl receptor signalling propagation in the plasma membrane. Science 290, 1567-70. 

Reynolds, A. R., Tischer, C., Verveer, P. J., Rocks, O. and Bastiaens, P. I. H. (2003). EGFR activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation. Nat. Cell. Biol. 

Ananthanarayanan, B., Ni, Q. and Zhang, J. (2005). Signal propagation from membrane messengers to nuclear effectors revealed by reporters of phosphoinositide dynamics and Akt activity. Proc. Natl. Acad. Sci. USA 102, 15081-6. 

Lee, J., Owens, J.T., Hwang, I., Meares, C., and Kustu, S. (2000) Phosphorylation-induced signal propagation in the response regulator NtrC. J. Bacteriol. 182, 5188-5195. 

T. C. Ni and M. A. Savageau, Application of biochemical systems theory to metabolism in human red blood cells. Signal propagation and accuracy of representation. J. Biol. Chem. 271... 

Nikolaev, V. O., Bunemann, M., Hein, L., Hannawacker, A., and Lohse, M. J. (2004). Novel single chain cAMP sensors for receptor-induced signal propagation. J. Biol. Chem. 279, 37215-37218. 

Csordas, G., Madesh, M., Antonsson, B., and Hajnoczky, G., 2002, tcBid promotes Ca2+ signal propagation to the mitochondria control of Ca2+ permeation through the outer mitochondrial membrane, EMBO J. 21, pp. 2198-2206... 

---