4,928 research outputs found
Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes
Parameter estimation for nonlinear dynamic system models, represented by
ordinary differential equations (ODEs), using noisy and sparse data is a vital
task in many fields. We propose a fast and accurate method, MAGI
(MAnifold-constrained Gaussian process Inference), for this task. MAGI uses a
Gaussian process model over time-series data, explicitly conditioned on the
manifold constraint that derivatives of the Gaussian process must satisfy the
ODE system. By doing so, we completely bypass the need for numerical
integration and achieve substantial savings in computational time. MAGI is also
suitable for inference with unobserved system components, which often occur in
real experiments. MAGI is distinct from existing approaches as we provide a
principled statistical construction under a Bayesian framework, which
incorporates the ODE system through the manifold constraint. We demonstrate the
accuracy and speed of MAGI using realistic examples based on physical
experiments
Color Capable Sub-Pixel Resolving Optofluidic Microscope and Its Application to Blood Cell Imaging for Malaria Diagnosis
Miniaturization of imaging systems can significantly benefit clinical diagnosis in challenging environments, where access to physicians and good equipment can be limited. Sub-pixel resolving optofluidic microscope (SROFM) offers high-resolution imaging in the form of an on-chip device, with the combination of microfluidics and inexpensive CMOS image sensors. In this work, we report on the implementation of color SROFM prototypes with a demonstrated optical resolution of 0.66 µm at their highest acuity. We applied the prototypes to perform color imaging of red blood cells (RBCs) infected with Plasmodium falciparum, a particularly harmful type of malaria parasites and one of the major causes of death in the developing world
An efficient basis set representation for calculating electrons in molecules
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004)
is generalized to obtain a straightforward, surprisingly accurate, and scalable
numerical representation for calculating the electronic wave functions of
molecules. It uses a basis set of product sinc functions arrayed on a Cartesian
grid, and yields 1 kcal/mol precision for valence transition energies with a
grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are
replaced with matrix elements obtained from the kinetic energy operator. A
resolution-of-the-identity approximation renders the primitive one- and
two-electron matrix elements diagonal; in other words, the Coulomb operator is
local with respect to the grid indices. The calculation of contracted
two-electron matrix elements among orbitals requires only O(N log(N))
multiplication operations, not O(N^4), where N is the number of basis
functions; N = n^3 on cubic grids. The representation not only is numerically
expedient, but also produces energies and properties superior to those
calculated variationally. Absolute energies, absorption cross sections,
transition energies, and ionization potentials are reported for one- (He^+,
H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.Comment: Submitted to JC
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