NEURONAL DYNAMICS I:ACTIVATIONS AND SIGNALS BIOLOGICAL ACTIVATIONS AND SIGNALS Competitive Neuronal Signal The neuron "wins"at time t if S(x())=1,"loses"if S(x())=1 and otherwise possesses a fuzzy win-loss status between 0 an 1. a.Binary signal functions [0,1] b.Bipolar signal functions:[-1,1] McCulloch-Pitts (M-P)neurons logical signal function Binary Bipolar S(x)= 12
12 BIOLOGICAL ACTIVATIONS AND SIGNALS Competitive Neuronal Signal 1 1 2 1 1 − + = + = −cx −cx e S x e S(x) ( ) logical signal function ( Binary Bipolar ) The neuron “wins” at time t if , “loses” if and otherwise possesses a fuzzy win-loss status between 0 an 1. a. Binary signal functions : [0,1] b. Bipolar signal functions : [-1,1] McCulloch—Pitts (M—P) neurons NEURONAL DYNAMICS Ⅰ: ACTIVATIONS AND SIGNALS S(x(t)) =1 S(x(t)) =1
NEURONAL DYNAMICS I:ACTIVATIONS AND SIGNALS NEURON FIELDS Neurons within a field are topologically ordered,often by proximity. zeroth-order topology lack of topological structure Denotation:Fx→F→Fz,{Fx,F},{Fx,F,Fz} Fx→F f:R”→RP neural system samples the function m times to generate the associated pairs (,),...,( The overall neural network behaves as an adaptive filter and sample data changed network parameters. 13
13 NEURON FIELDS Neurons within a field are topologically ordered, often by proximity. zeroth-order topology : lack of topological structure Denotation: , , neural system samples the function m times to generate the associated pairs , ... , The overall neural network behaves as an adaptive filter and sample data changed network parameters. FX → FY → FZ { , } FX FY { , , } FX FY FZ ( , ) m m ( , ) x y 1 1 x y NEURONAL DYNAMICS Ⅰ: ACTIVATIONS AND SIGNALS n p f : R → R FX → FY f