554 research outputs found
Fixed Boundary Flows
We consider the fixed boundary flow with canonical interpretability as
principal components extended on the non-linear Riemannian manifolds. We aim to
find a flow with fixed starting and ending point for multivariate datasets
lying on an embedded non-linear Riemannian manifold, differing from the
principal flow that starts from the center of the data cloud. Both points are
given in advance, using the intrinsic metric on the manifolds. From the
perspective of geometry, the fixed boundary flow is defined as an optimal curve
that moves in the data cloud. At any point on the flow, it maximizes the inner
product of the vector field, which is calculated locally, and the tangent
vector of the flow. We call the new flow the fixed boundary flow. The rigorous
definition is given by means of an Euler-Lagrange problem, and its solution is
reduced to that of a Differential Algebraic Equation (DAE). A high level
algorithm is created to numerically compute the fixed boundary. We show that
the fixed boundary flow yields a concatenate of three segments, one of which
coincides with the usual principal flow when the manifold is reduced to the
Euclidean space. We illustrate how the fixed boundary flow can be used and
interpreted, and its application in real data
Manifold Fitting under Unbounded Noise
There has been an emerging trend in non-Euclidean dimension reduction of
aiming to recover a low dimensional structure, namely a manifold, underlying
the high dimensional data. Recovering the manifold requires the noise to be of
certain concentration. Existing methods address this problem by constructing an
output manifold based on the tangent space estimation at each sample point.
Although theoretical convergence for these methods is guaranteed, either the
samples are noiseless or the noise is bounded. However, if the noise is
unbounded, which is a common scenario, the tangent space estimation of the
noisy samples will be blurred, thereby breaking the manifold fitting. In this
paper, we introduce a new manifold-fitting method, by which the output manifold
is constructed by directly estimating the tangent spaces at the projected
points on the underlying manifold, rather than at the sample points, to
decrease the error caused by the noise. Our new method provides theoretical
convergence, in terms of the upper bound on the Hausdorff distance between the
output and underlying manifold and the lower bound on the reach of the output
manifold, when the noise is unbounded. Numerical simulations are provided to
validate our theoretical findings and demonstrate the advantages of our method
over other relevant methods. Finally, our method is applied to real data
examples
Utilization of Molecular Simulation Software Gaussian 03 to Design Absorbent for CO2 Capture
AbstractA preliminary study on the interaction between molecules of absorbent for CO2 absorption was undertaken using Gaussian 03 molecular simulation software. The results indicate that the molecular interaction energy has strong correlations with Henry's constant. The lower interaction energy between molecules, solvent molecules form an “associated complex” more stability, and therefore the worse the effect of CO2 absorption
Unconventional Flatband Line States in Photonic Lieb Lattices
Flatband systems typically host "compact localized states"(CLS) due to
destructive interference and macroscopic degeneracy of Bloch wave functions
associated with a dispersionless energy band. Using a photonic Lieb
lattice(LL), we show that conventional localized flatband states are inherently
incomplete, with the missing modes manifested as extended line states which
form non-contractible loops winding around the entire lattice. Experimentally,
we develop a continuous-wave laser writing technique to establish a
finite-sized photonic LL with specially-tailored boundaries, thereby directly
observe the unusually extended flatband line states.Such unconventional line
states cannot be expressed as a linear combination of the previously observed
CLS but rather arise from the nontrivial real-space topology.The robustness of
the line states to imperfect excitation conditions is discussed, and their
potential applications are illustrated
A routing protocol for multisink wireless sensor networks in underground coalmine tunnels
Traditional underground coalmine monitoring systems are mainly based on the use of wired transmission. However, when cables are damaged during an accident, it is difficult to obtain relevant data on environmental parameters and the emergency situation underground. To address this problem, the use of wireless sensor networks (WSNs) has been proposed. However, the shape of coalmine tunnels is not conducive to the deployment of WSNs as they are long and narrow. Therefore, issues with the network arise, such as extremely large energy consumption, very weak connectivity, long time delays, and a short lifetime. To solve these problems, in this study, a new routing protocol algorithm for multisink WSNs based on transmission power control is proposed. First, a transmission power control algorithm is used to negotiate the optimal communication radius and transmission power of each sink. Second, the non-uniform clustering idea is adopted to optimize the cluster head selection. Simulation results are subsequently compared to the Centroid of the Nodes in a Partition (CNP) strategy and show that the new algorithm delivers a good performance: Power efficiency is increased by approximately 70%, connectivity is increased by approximately 15%, the cluster interference is diminished by approximately 50%, the network lifetime is increased by approximately 6%, and the delay is reduced with an increase in the number of sinks
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