Statistical inference and string theory

In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an [Formula: see text]-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a [Formula: see text]-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in [Formula: see text] dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature space–times.

On the theory of one-sided models in spaces with arbitrary cones

The paper presents a way of constructing quasimonotone nonautonomous systems ensuring x-stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U-stability on the set of non wandering points is proved to imply u-stability of quasimonotone nonlinear system and exponential u-stability on minimal attraction center provides u-stability of the total systems Examples are available.