No abstract

In this work we undertake the task of making a classification of the various existing paradigms used in the field of Artificial Neural Networks. Our critenon for classification is the degree of formalism of any of them, ranging from purely formal accounts like those of Hecht-Nielsen16 to models of purely physiological inspiration, such as the Darwin II network27. From our overview we can see that the field is far from being either homogeneous, organized or formal. From this we conclude that more work has to be made to find an unifying formalism. In its present state the field is nothing but a technology with many points of view, but not a Science.

UNIVEASIDCII) WTONOPlCI METROPOLIT~NCS-IZTFIPFILc)PFI J. Figuercla Nazuno UNIVERSIDCID IA SfiLLE Laboratorio d e Sistemas CcrmplejosRp. Postal 70-499, C.P. 64516 Mbxico, D.F. MEXICOPhysicists' irit erest in neural net works stems 1 argel y frctm the analogy between such networks and simple magnetic systems, such as t h e one studied by Sherrington arid Kirkpatrick. C111.Such analogy w a s first pointed out by Little and Shaw C53, and w a 5 developed by Hopfield C 4 3 , who pointed out the equivalence between t h e long-t ime behavior of n e t w u r k s with symmetric connections ar?d equilibrium properties of magnetic systems such a 5 s p i n glasses.Unfcwtunatel ly, this analogy has serious drawbacks. First, the connections in neural systems are not distributed in a random way, but have correlations that are formed both genetically, arid in the course o f learning and adaptation. another major differeurce is the asymmetry o f the c u n r e c t i ons : the pai rw i se i nt ev-act i cms bet ween neurons are, i n g e n e r a l , rrut reciprrrcal ly symmetric; hence, their dynamic prcrperties may be v e r y different f r o m those of equilibrium magnet ic systems. Finally, there i s no obvious genera', izat ion tcr the case of neurons with continuous valued st at 62s. The above arguments and t h e variety of neurocamputat iorral pr-ucedures inspired in physical ideas make evident that no global physical foundation exists for Neurwdynamic=.. The best caracterizak ions made are o f mathematical character, such a5 t h e high number o f degrees o f freedom, non-linearity arsd asyntotic stability; but this formalism h a s not y e t match a physical model as a paradigm f o r future research. Iri this paper w e proposse an stochastic physical model for a certain class o f neurocomputat ional architectures (for another type of foundations, 5ee C23). I n previous papers Cl, 0,9,101 w e proposed that certain formalism specially designed f o r t h e study o f Brownian Motion t6,121 could be applied t o t h e deduction of t h e neurudynamical equations currently used in feedback neural network models. That is, from equations ?such as (1) rt DtFI = iR-c)(t) -dr K(T)-FI(t-T) + Flt) w e r e deducted t h e neurodynamical equations corresponding t o the evolution o f N interacting neurons. They are given, for variuus Hopfield-type networks C4,73, by t h e following set 111 -573

Magnetic probes (also known as B-dot coil) are electromagnetic devices used to measure magneticeld variations in many frequency ranges. The measured magnetic eld frequency directly relates tothe elected method to make the B-dot coil calibration. This work presents a B-dot coil calibration ina frequency range from 6.16 kHz to 36.63 kHz. An inductor L (Helmholtz coil) connects in parallelwith a variable capacitor bank Cvar to form a coupled LCvar resonant circuit. The LCvar circuit isfed with a half bridge oscillator. The capacitance Cvar is varied until the circuit is in resonant stateat dierent frequencies. The resonant circuit produces sinusoidal oscillations in the aforementionfrequency band. The sensitivity is calculated by using voltage Vout of the B-dot coil and voltageVH measured from Helmholtz terminals.

A mis padres Guillenno y Lidia, que siempre rne impulsaron y apoglaron para salir adelante. A mi hermana Claudia, u.n apoyo curlstante aunque silencioso a lo largo de todos estos años. Al Dr. Eliezer Uraun, por la oportunidad de trabajar bajo su dirección y por proponerme un excelente proyecto de investigación.