65,786 research outputs found
Derived categories of graded gentle one-cycle algebras
Let be a graded algebra. It is shown that the derived category of dg
modules over (viewed as a dg algebra with trivial differential) is a
triangulated hull of a certain orbit category of the derived category of graded
-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
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