On generalized semi-infinite optimization and bilevel optimization

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newton-type methods for solving the problems. We show by a structural analysis that for (GSIP)-problems the regularity assumptions for the reduction approach can be expected to hold generically at a solution but for general (BL)-problems not. The genericity behavior of (BL) and (GSIP) is in particular studied for linear problems

Inflation in anisotropic scalar-tensor theories

The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest

Continuous detonation reaction engine

Reaction engine operates on the principles of a controlled condensed detonation rather than on the principles of gas expansion. The detonation results in reaction products that are expelled at a much higher velocity

Development of detonation reaction engine

Reaction engine operates on the principle of a controlled condensed detonation. In this engine the gas products that are expelled from the engine to produce thrust are generated by the condensed detonation reaction. The engine is constructed of two basic sections consisting of a detonation wave generator section and a condensed detonation reaction section

Photonic band mixing in linear chains of optically coupled micro-spheres

The paper deals with optical excitations arising in a one-dimensional chain of identical spheres due optical coupling of whispering gallery modes (WGM). The band structure of these excitations depends significantly on the inter-mixing between WGMs characterized by different values of angular quantum number, $l$. We develop a general theory of the photonic band structure of these excitations taking these effects into account and applied it to several cases of recent experimental interest. In the case of bands originating from WQMs with the angular quantum number of the same parity, the calculated dispersion laws are in good qualitative agreement with recent experiment results. Bands resulting from hybridization of excitations resulting from whispering gallery modes with different parity of $l$ exhibits anomalous dispersion properties characterized by a gap in the allowed values of \emph{wave numbers} and divergence of group velocity.Comment: RevTex, 28 pages, 7 Figure

A warped kernel improving robustness in Bayesian optimization via random embeddings

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6

XIV. Syphilis of the Ear

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