We study the number and distribution of limit cycles a planar vector field whose component functions are random polynomials. prove lower bound on average when polynomials sampled from Kostlan-Shub-Smale ensemble. Investigating problem introduced by Brudnyi [Ann. Math. (2) 154 (2001), pp. 227–243] we also consider special local setting counting near randomly perturbed center focus, perturbation ...

Traditional computers work numerically only with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this lecture, a new computational methodology (that is not related to non-standard analysis approaches) is described. It is based on the principle ‘The part is less than the whole’ applied to all quantities (finite, ...

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values $\varepsilon=4-d$. Exploiting recent navigator method in conjunction with extremal functional method, test various qualitative quantitative features $\varepsilon$-expansion. We follow scaling dimensions numerous operators perturbatively control...

The sensitivity of time averages in a chaotic system to an infinitesimal parameter perturbation grows exponentially with the averaging time. However, long-term or ensemble statistics often vary differentiably parameters. Ruelle's response theory gives rigorous formula for these parametric derivatives linear response. But direct evaluation this is ill-conditioned, and hence downstream applicatio...

Psychological games aim to represent situations in which players may have belief-dependent motivations. In this setting, utility functions are directly dependent on the entire hierarchy of beliefs each player. On other hand, literature strategic ambiguity classical highlights that ambiguous (or imprecise) about opponents’ strategy choices. paper, we look at issue framework simultaneous psycholo...