The present document is devoted to structural properties of neural population dynamics and especially their differential flatness. Several applications of differential flatness in the present context can be envisioned, among which: trajectory tracking, feedforward to feedback switching, cyclic character, positivity and boundedness.

We survey two approaches to flatness necessary and sufficient conditions and compare them on examples.

We propose a scenario in which the cosmological domain wall and monopole problems are solved without any fine tuning of the initial conditions or parameters in the Lagrangian of an underlying filed theory. In this scenario domain walls sweep out (unwind) the monopoles from the early universe, then the fast primordial black holes perforate the domain walls, change their topology and destroy them...

This paper describes the application of diierential atness techniques from nonlinear control theory to mechanical (La-grangian) systems. Systems which are diierentially at have several useful properties which can be exploited to generate eeective control strategies for nonlinear systems. For the special case of mechanical control systems, much more geometric information is present and the purpo...

We characterize those small categories with the property that flat (contravariant) functors on them are coherently axiomatized in the language of presheaves on them. They are exactly the categories with the property that every finite diagram into them has a finite set of (weakly) initial cocones.

The average concentration of a passive scalar advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness (kurtosis) is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum d...

Modulated metasurface (MTS) antennas can provide a broadside pencil beam at the frequency where cylindrical surface wave (SW) wavelength matches period of impedance modulation. For modulations with constant period, mismatch between SW and imposes limitation on gain-bandwidth product. However, this be overcome by shaping local as function radial distance. Doing so, we generate an annular active ...

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector...

A full authority helicopter control design based on differential flatness is presented. The concept of outer flatness is deployed for the design. The position dynamics and attitude dynamics are treated as the outer and inner systems respectively. The proposed design is based on an approximate model which is differentially flat, and then modified for the exact model. Given a desired trajectory i...

In this paper, we present an approach to incorporate discriminative weight training into a statistical model-based voice activity detection (VAD) method. In our approach, the VAD decision rule is derived from the optimally weighted likelihood ratios (LRs) using a minimum classification error (MCE) method. An adaptive online means of selecting two kinds of weights based on a power spectral flatn...