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