882 research outputs found
Efficient Localization of Discontinuities in Complex Computational Simulations
Surrogate models for computational simulations are input-output
approximations that allow computationally intensive analyses, such as
uncertainty propagation and inference, to be performed efficiently. When a
simulation output does not depend smoothly on its inputs, the error and
convergence rate of many approximation methods deteriorate substantially. This
paper details a method for efficiently localizing discontinuities in the input
parameter domain, so that the model output can be approximated as a piecewise
smooth function. The approach comprises an initialization phase, which uses
polynomial annihilation to assign function values to different regions and thus
seed an automated labeling procedure, followed by a refinement phase that
adaptively updates a kernel support vector machine representation of the
separating surface via active learning. The overall approach avoids structured
grids and exploits any available simplicity in the geometry of the separating
surface, thus reducing the number of model evaluations required to localize the
discontinuity. The method is illustrated on examples of up to eleven
dimensions, including algebraic models and ODE/PDE systems, and demonstrates
improved scaling and efficiency over other discontinuity localization
approaches
A continuous analogue of the tensor-train decomposition
We develop new approximation algorithms and data structures for representing
and computing with multivariate functions using the functional tensor-train
(FT), a continuous extension of the tensor-train (TT) decomposition. The FT
represents functions using a tensor-train ansatz by replacing the
three-dimensional TT cores with univariate matrix-valued functions. The main
contribution of this paper is a framework to compute the FT that employs
adaptive approximations of univariate fibers, and that is not tied to any
tensorized discretization. The algorithm can be coupled with any univariate
linear or nonlinear approximation procedure. We demonstrate that this approach
can generate multivariate function approximations that are several orders of
magnitude more accurate, for the same cost, than those based on the
conventional approach of compressing the coefficient tensor of a tensor-product
basis. Our approach is in the spirit of other continuous computation packages
such as Chebfun, and yields an algorithm which requires the computation of
"continuous" matrix factorizations such as the LU and QR decompositions of
vector-valued functions. To support these developments, we describe continuous
versions of an approximate maximum-volume cross approximation algorithm and of
a rounding algorithm that re-approximates an FT by one of lower ranks. We
demonstrate that our technique improves accuracy and robustness, compared to TT
and quantics-TT approaches with fixed parameterizations, of high-dimensional
integration, differentiation, and approximation of functions with local
features such as discontinuities and other nonlinearities
AN INVESTIGATION OF ON-CHIP ANTENNA CHARACTERISTICS RELATED TO ENERGY HARVESTING APPLICATIONS
The way a certain antenna operates is highly dependent on the dielectric medium in which it is placed. Dielectric media can be characterized by their dielectric constant, which is also called relative permittivity. When no electric field is applied, the positive and negative charges of the dielectric molecules are evenly distributed. Application of an electric field disrupts this balance and results in the creation of dipoles. The number of dipoles that are created is proportional to the permittivity of the dielectric. Permittivity is a measure of the sensitivity of the material to an applied electric field. Stated another way, permittivity is a measure of how much energy can be stored in the electric field.This thesis reports the research on several types of on-the-chip antennas such as a rectangular spiral and a rectangular patch. The characteristics of these antennas that are useful to Energy Harvesting are analyzed and the effects of permittivity changes in the dielectrics surrounding the antenna are studied
DNA-Mediated Electrochemistry
The base pair stack of DNA has been demonstrated as a medium for long-range charge transport chemistry both in solution and at DNA-modified surfaces. This chemistry is exquisitely sensitive to structural perturbations in the base pair stack as occur with lesions, single base mismatches, and protein binding. We have exploited this sensitivity for the development of reliable electrochemical assays based on DNA charge transport at self-assembled DNA monolayers. Here, we discuss the characteristic features, applications, and advantages of DNA-mediated electrochemistry
Functionalized hyperbranched polymers via olefin metathesis
Hyperbranched polymers are highly branched, three-dimensional
macromolecules which are closely related to dendrimers
and are typically prepared via a one-pot polycondensation of
AB_(n≥2) monomers.^1 Although hyperbranched macromolecules
lack the uniformity of monodisperse dendrimers, they still
possess many attractive dendritic features such as good solubility,
low solution viscosity, globular structure, and multiple end
groups.^1-3 Furthermore, the usually inexpensive, one-pot synthesis
of these polymers makes them particularly desirable
candidates for bulk-material and specialty applications. Toward
this end, hyperbranched polymers have been investigated as both
rheology-modifying additives to conventional polymers and as
substrate-carrying supports or multifunctional macroinitiators,
where a large number of functional sites within a compact space
becomes beneficial
Multiplexed DNA-Modified Electrodes
We report the use of silicon chips with 16 DNA-modified electrodes (DME chips) utilizing DNA-mediated charge transport for multiplexed detection of DNA and DNA-binding protein targets. Four DNA sequences were simultaneously distinguished on a single DME chip with 4-fold redundancy, including one incorporating a single base mismatch. These chips also enabled investigation of the sequence-specific activity of the restriction enzyme Alu1. DME chips supported dense DNA monolayer formation with high reproducibility, as confirmed by statistical comparison to commercially available rod electrodes. The working electrode areas on the chips were reduced to 10 μm in diameter, revealing microelectrode behavior that is beneficial for high sensitivity and rapid kinetic analysis. These results illustrate how DME chips facilitate sensitive and selective detection of DNA and DNA-binding protein targets in a robust and internally standardized multiplexed format
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