15,508 research outputs found
Compressive Sensing DNA Microarrays
Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
In this paper, we propose an approach to controller synthesis for a class of
constrained nonlinear systems. It is based on the use of a hybridization, that
is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined
on a triangulation of the state-space where on each simplex of the
triangulation, the nonlinear dynamics is conservatively approximated by an
affine system subject to disturbances. Except for the disturbances, this
hybridization can be seen as a piecewise affine hybrid system on simplices for
which appealing control synthesis techniques have been developed in the past
decade. We extend these techniques to handle systems subject to disturbances by
synthesizing and coordinating local robust affine controllers defined on the
simplices of the triangulation. We show that the resulting hybrid controller
can be used to control successfully the original constrained nonlinear system.
Our approach, though conservative, can be fully automated and is
computationally tractable. To show its effectiveness in practical applications,
we apply our method to control a pendulum mounted on a cart
Real-time DNA microarray analysis
We present a quantification method for affinity-based
DNA microarrays which is based on the
real-time measurements of hybridization kinetics.
This method, i.e. real-time DNA microarrays,
enhances the detection dynamic range of conventional
systems by being impervious to probe
saturation in the capturing spots, washing
artifacts, microarray spot-to-spot variations, and
other signal amplitude-affecting non-idealities. We
demonstrate in both theory and practice that the
time-constant of target capturing in microarrays,
similar to all affinity-based biosensors, is inversely
proportional to the concentration of the target
analyte, which we subsequently use as the fundamental
parameter to estimate the concentration
of the analytes. Furthermore, to empirically
validate the capabilities of this method in practical
applications, we present a FRET-based assay which
enables the real-time detection in gene expression
DNA microarrays
Adjoint-Based Error Estimation and Mesh Adaptation for Hybridized Discontinuous Galerkin Methods
We present a robust and efficient target-based mesh adaptation methodology,
building on hybridized discontinuous Galerkin schemes for (nonlinear)
convection-diffusion problems, including the compressible Euler and
Navier-Stokes equations. Hybridization of finite element discretizations has
the main advantage, that the resulting set of algebraic equations has globally
coupled degrees of freedom only on the skeleton of the computational mesh.
Consequently, solving for these degrees of freedom involves the solution of a
potentially much smaller system. This not only reduces storage requirements,
but also allows for a faster solution with iterative solvers. The mesh
adaptation is driven by an error estimate obtained via a discrete adjoint
approach. Furthermore, the computed target functional can be corrected with
this error estimate to obtain an even more accurate value. The aim of this
paper is twofold: Firstly, to show the superiority of adjoint-based mesh
adaptation over uniform and residual-based mesh refinement, and secondly to
investigate the efficiency of the global error estimate
A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures
In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG)
method to numerically solve the Maxwell's equations coupled with the
hydrodynamic model for the conduction-band electrons in metals. By means of a
static condensation to eliminate the degrees of freedom of the approximate
solution defined in the elements, the HDG method yields a linear system in
terms of the degrees of freedom of the approximate trace defined on the element
boundaries. Furthermore, we propose to reorder these degrees of freedom so that
the linear system accommodates a second static condensation to eliminate a
large portion of the degrees of freedom of the approximate trace, thereby
yielding a much smaller linear system. For the particular metallic structures
considered in this paper, the resulting linear system obtained by means of
nested static condensations is a block tridiagonal system, which can be solved
efficiently. We apply the nested HDG method to compute the second harmonic
generation (SHG) on a triangular coaxial periodic nanogap structure. This
nonlinear optics phenomenon features rapid field variations and extreme
boundary-layer structures that span multiple length scales. Numerical results
show that the ability to identify structures which exhibit resonances at
and is paramount to excite the second harmonic response.Comment: 31 pages, 7 figure
Spectral Densities from Dynamic Density-Matrix Renormalization
Dynamic density-matrix renormalization provides valuable numerical
information on dynamic correlations by computing convolutions of the
corresponding spectral densities. Here we discuss and illustrate how and to
which extent such data can be deconvolved to retrieve the wanted spectral
densities. We advocate a nonlinear deconvolution scheme which minimizes the
bias in the ansatz for the spectral density. The procedure is illustrated for
the line shape and width of the Kondo peak (low energy feature) and for the
line shape of the Hubbard satellites (high energy feature) of the single
impurity Anderson model. It is found that the Hubbard satellites are strongly
asymmetric.Comment: RevTeX 4, 11 pages, 7 eps figures; published versio
Dynamical structure factor of a nonlinear Klein-Gordon lattice
The quantum modes of a nonlinear Klein-Gordon lattice have been computed
numerically [L. Proville, Phys. Rev. B 71, 104306 (2005)]. The on-site
nonlinearity has been found to lead to phonon bound states. In the present
paper, we compute numerically the dynamical structure factor so as to simulate
the coherent scattering cross section at low temperature. The inelastic
contribution is studied as a function of the on-site anharmonicity.
Interestingly, our numerical method is not limited to the weak anharmonicity
and permits one to study thoroughly the spectra of nonlinear phonons
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