Van Gelder’s specification of the dynamical hypothesis does not improve on previous notions. All three key attributes of dynamical systems apply to Turing machines and are hence too general. However, when a more restricted definition of a dynamical system is adopted, it becomes clear that the dynamical hypothesis is too underspecified to constitute an interesting cognitive claim. Van Gelder cla...

We decribe a general result on the approximation of fixed points of operators between Banach spaces allowing an explicit estimation of the error. This result is particularly suited for the approximation of invariant measures in dynamical systems and in particular by the Ulam method. We apply this result to implement an algorithm for the rigorous computation of invariant densities of piecewise e...

Dynamic textures are sequences of images that exhibit some form of temporal stationarity, such as waves, steam, and foliage. We pose the problem of recognizing and classifying dynamic textures in the space of dynamical systems where each dynamic texture is uniquely represented. Since the space is non-linear, a distance between models must be defined. We examine three different distances in the ...

We investigate experimentally and theoretically the dynamics of a semiconductor laser subject to filtered optical feedback. Depending on the feedback strength we find dynamical regimes with different dependence on the feedback phase. In particular, the influence of the feedback phase on cw emission and on frequency oscillations is characterized experimentally. We also measure the dependence of ...

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by incorporating the well-documented dependence of connection probability on distance. Spatially extended spiking networks exhibit symmetry-breaking bifurcations and gener...

It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schrödinger (NLS) equation is upper-bounded by logp1` SNRq with SNR “ P0{σ pzq, where P0 is the average input signal power and σpzq is the total noise power up to distance z. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dyn...

We use a statistical mechanical model to study nonthermal denaturation of DNA in the presence of protein-mediated loops. We find that looping proteins which randomly link DNA bases located at a distance along the chain could cause a first-order phase transition. We estimate the denaturation transition time near the phase transition, which can be compared with experimental data. The model descri...

Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of “how good” and “for how long” the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities t...

We discuss the signature of a peculiar constellation of very massive stars at a projected distance of 2-3 pc around R136a. We discuss various scenarios for its possible origin, such as independent clusters, triggered star formation, supernovae, and ejections via dynamical interactions. If the latter scenario were the correct one this would have significant implications on the way to probe the c...