159 research outputs found
Mesoscopic morphology and scaling law of stationary interfacial patterns for reaction diffusion systems
Visible fingerprint of X-ray images of epoxy resins using singular value decomposition of deep learning features
Although the process variables of epoxy resins alter their mechanical
properties, the visual identification of the characteristic features of X-ray
images of samples of these materials is challenging. To facilitate the
identification, we approximate the magnitude of the gradient of the intensity
field of the X-ray images of different kinds of epoxy resins and then we use
deep learning to discover the most representative features of the transformed
images. In this solution of the inverse problem to finding characteristic
features to discriminate samples of heterogeneous materials, we use the
eigenvectors obtained from the singular value decomposition of all the channels
of the feature maps of the early layers in a convolutional neural network.
While the strongest activated channel gives a visual representation of the
characteristic features, often these are not robust enough in some practical
settings. On the other hand, the left singular vectors of the matrix
decomposition of the feature maps, barely change when variables such as the
capacity of the network or network architecture change. High classification
accuracy and robustness of characteristic features are presented in this work.Comment: 43 pages, 16 figure
Arbitrarily weak head-on collision can induce annihilation -- The role of hidden instabilities
In this paper, we focus on annihilation dynamics for the head-on collision of
traveling patterns. A representative and well-known example of annihilation is
the one observed for 1-dimensional traveling pulses of the FitzHugh-Nagumo
equations. In this paper, we present a new and completely different type of
annihilation arising in a class of three-component reaction diffusion system.
It is even counterintuitive in the sense that the two traveling spots or pulses
come together very slowly but do not merge, keeping some separation, and then
they start to repel each other for a certain time. Finally, up and down
oscillatory instability emerges and grows enough for patterns to become extinct
eventually (see Figs. 1-3). There is a kind of hidden instability embedded in
the traveling patterns, which causes the above annihilation dynamics. The
hidden instability here turns out to be a codimension 2 singularity consisting
of drift and Hopf (DH) instabilities, and there is a parameter regime emanating
from the codimension 2 point in which a new type of annihilation is observed.
The above scenario can be proved analytically up to the onset of annihilation
by reducing it to a finite-dimensional system. Transition from preservation to
annihilation is also discussed in this framework.Comment: 38 pages, 14 figure
A giant plexiform schwannoma of the brachial plexus: case report
We report the case of a patient who noticed muscle weakness in his left arm 5 years earlier. On examination, a biloculate mass was observed in the left supraclavicular area, and Tinel's sign caused paresthesia in his left arm. Magnetic resonance imaging showed a continuous, multinodular, plexiform tumor from the left C5 to C7 nerve root along the course of the brachial plexus to the left brachia. Tumor excision was attempted. The median and musculocutaneous nerves were extremely enlarged by the tumor, which was approximately 40 cm in length, and showed no response to electric stimulation. We resected a part of the musculocutaneous nerve for biopsy and performed latissimus dorsi muscle transposition in order to repair elbow flexion. Morphologically, the tumor consisted of typical Antoni A areas, and immunohistochemistry revealed a Schwann cell origin of the tumor cells moreover, there was no sign of axon differentiation in the tumor. Therefore, the final diagnosis of plexiform Schwannoma was confirmed
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