Well-Posed Initial-Boundary Value Problem for a Constrained Evolution System and Radiation-Controlling Constraint-Preserving Boundary Conditions

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system evolving the constraint quantity statically, i.e., the second time derivative of the constraint quantity is zero. A new set of radiation-controlling constraint-preserving boundary conditions is constructed for the free evolution problem. Comparison between the new conditions and the standard constraint-preserving boundary conditions is made using the Fourier-Laplace analysis and the power series decomposition in time. The new boundary conditions satisfy the Kreiss condition and are free from the ill-posed modes growing polynomially in time.Comment: To appear in the Journal of Hyperbolic Differential Equations. In response to the reviewers request, a theorem on well-posedness of the free evolution problem has been added, definitions clarified in Sections 4 and 5, as well as a typo was removed from Section

Controlling Chimeras

Coupled phase oscillators model a variety of dynamical phenomena in nature and technological applications. Non-local coupling gives rise to chimera states which are characterized by a distinct part of phase-synchronized oscillators while the remaining ones move incoherently. Here, we apply the idea of control to chimera states: using gradient dynamics to exploit drift of a chimera, it will attain any desired target position. Through control, chimera states become functionally relevant; for example, the controlled position of localized synchrony may encode information and perform computations. Since functional aspects are crucial in (neuro-)biology and technology, the localized synchronization of a chimera state becomes accessible to develop novel applications. Based on gradient dynamics, our control strategy applies to any suitable observable and can be generalized to arbitrary dimensions. Thus, the applicability of chimera control goes beyond chimera states in non-locally coupled systems

Controlling Patent Prosecution History

[Excerpt] “One of the most salient effects of patent prosecution history arises in the context of the doctrine of equivalents. Under that doctrine, although patent claims may be found to be broader than their literal scope, territory surrendered during prosecution cannot be encompassed as equivalent. Nor can territory forfeited by initial failure to claim be captured under the doctrine of equivalents. Most attorneys who prosecute applications are apt to be aware of such problems and to take measures to avoid them.

Controlling Quantum State Reduction

Every measurement leaves the object in a family of states indexed by the possible outcomes. This family, called the posterior states, is usually a family of the eigenstates of the measured observable, but it can be an arbitrary family of states by controlling the object-apparatus interaction. A potentially realizable object-apparatus interaction measures position in such a way that the posterior states are the translations of an arbitrary wave function. In particular, position can be measured without perturbing the object in a momentum eigenstate.Comment: 9 pages, REVTe

Controlling secretion to limit chemoresistance

The tumor microenvironment influences cancer progression and therapy outcome by mechanisms not yet fully understood. In this issue, Bent et al. (2016) show how chemotherapy causes endothelial senescence. Interestingly, senescent endothelial cells do not mount a typical senescence-associated secretory phenotype but instead acutely secrete IL-6, promoting chemoresistance. This study unveils a physiological switch involving PI3K/AKT/mTOR signaling that restrains the senescence secretory responses to limit the detrimental consequences of persistent inflammation