We study the energy landscape of a model single particle on random potential, that is, we investigate topology level sets smooth fields $${\mathbb {R}}^{N}$$ form $$X_N(x) +\frac{\mu }{2} \Vert x\Vert ^2,$$ where $$X_{N}$$ is Gaussian process with isotropic increments. derive asymptotic formulas for mean number critical points values in an open set as dimension N goes to infinity. In companion ...

We study the deep relation existing between differential logical relations and incremental computing by showing how self-differences in former precisely correspond to derivatives latter. The byproduct of such a relationship is twofold: on one hand, we show can be seen as powerful meta-theoretical tool analysis computations, enabling an easy proof soundness differentiation. On other generalize s...