Stabilization of heterodimensional cycles

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.Comment: 31 pages, 9 figure

Auto-tuning control systems for improved operation of continuous fluidized bed spray granulation processes with external product classification

AbstractIn this contribution control of continuous fluidized bed spray granulation processes with external product classification is studied. From a practical point of view control schemes being easy to implement and maintain using standard process control systems are preferable. Hence, the focus will be on standard PI control structures. In order to account for variations and uncertainties in the process an additional tuning procedure should be included. Here, an optimization based online controller adaptation scheme called iterative feedback tuning (ITF) will be investigated

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

Transient glutathione depletion determines terminal differentiation in HL-60 cells

To better define the role of glutathione (GSH) in cell differentiation, the present study measured GSH concentrations during terminal HL-60 cell differentiation, in the presence and absence of differentiation-inducing agents, and in the presence and absence of GSH altering agents. Interestingly, there was a small transient increase in intracellular GSH levels during dimethyl sulfoxide (DMSO) or 1α,25-dihydroxyvitamin D3 (VD3) induced differentiation. This increase coincided with an increase in nitroblue tetrazolium (NBT) reduction capacity, a measure of superoxide anion production, but there was no apparent change in the GSH/glutathione disulfide (GSSG) ratio. Surprisingly, treatment of cells with low doses of 1-chloro-2,4-dinitrobenzene (CDNB; 5 µM) or diethylmaleate (DEM; 0.5 mM), which transiently deplete GSH levels to about 40% of control levels, resulted in enhanced differentiation of HL-60 cells exposed to VD3 or all-trans-retinoic acid (ATRA), as well as under un-induced conditions (i.e., spontaneous differentiation). Enhanced differentiation occurred when cells were treated with the GSH-depleting agents 4 hours after treatment with differentiation inducers. These findings indicate that intracellular GSH levels are regulated in a complex fashion during HL-60 cell differentiation, and that transient GSH depletion using low doses of CDNB and DEM enhances the differentiation process

Persistent Chaos in High Dimensions

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.Comment: 4 pages, 3 figures; Changes in response to referee comment