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The set of time series of spikes is expanded into a vector space, V , by taking all linear combinations. A definition is then given for an inner product on this vector space. This gives a definition of norm, of distance between time series, and of orthogonality. This also allows us to compute the best approximation to a given time series which can be formed… (More)

We give an algorithm to compute asymptotic expansions of exp-log functions. This algorithm automatically computes the necessary asymptotic scale and does not suffer from problems of indefinite cancellation. In particular, an asymptotic equivalent can always be computed for a given exp-log function.

The elementary numbers are the complex numbers which can be implicitly or explicitly defined by starting with the rationals and using addition, subtraction, multiplication and exponentiation. More explicitly, an ele. mentary point is a non-singular solution of n equations, involving exponential polynomials, in n unknowns; and an elementary number is… (More)

Non algebraic cylindrical decompositions are discussed. False derivatives and local Sturm sequences are defimed as tools for computing them. The crucial fact in the algebraic case is that we can chacterize the number of distinct real roots of a polynomial p(y) by a condition on the coefficients. An attempt is made to obtain an analogous chacterizat ion for… (More)

Numerical quantities can be represented as phase differences between equiperiodic oscillating subsystems in a spiking neural net. It is then possible to represent integer variables, and the increment and decrement operations, X := X + 1, X := X − 1. It is possible to represent the if construction, the while construction, and some other programming language… (More)