Derived categories of graded gentle one-cycle algebras

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules. This is applied to study derived categories of graded gentle one-cycle algebras.Comment: To appear in JPA

Partial Hyperbolicity and Homoclinic Tangencies

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure

Ultra-compact branchless plasmonic interferometers

Miniaturization of functional optical devices and circuits is a key prerequisite for a myriad of applications ranging from biosensing to quantum information processing. This development has considerably been spurred by rapid developments within plasmonics exploiting its unprecedented ability to squeeze light into subwavelength scale. In this study, we investigate on-chip plasmonic systems allowing for synchronous excitation of multiple inputs and examine the interference between two adjacent excited channels. We present a branchless interferometer consisting of two parallel plasmonic waveguides that can be either selectively or coherently excited via ultra-compact antenna couplers. The total coupling efficiency is quantitatively characterized in a systematic manner and shown to exceed 15% for small waveguide separations, with the power distribution between the two waveguides being efficiently and dynamically shaped by adjusting the incident beam position. The presented design principle can readily be extended to other configurations, giving new perspectives for highly dense integrated plasmonic circuitry, optoelectronic devices, and sensing applications.Comment: 15 pages, 6 figure

Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining if parameters associated with correlated predictors should be shrunk together or kept apart. Under suitable conditions, we prove that this empirical Bayes posterior concentrates around the true sparse parameter at the optimal rate asymptotically. A simplified version of a shotgun stochastic search algorithm is employed to implement the variable selection procedure, and we show, via simulation experiments across different settings and a real-data application, the favorable performance of the proposed method compared to existing methods.Comment: 25 pages, 4 figures, 2 table