Planar graphs are acyclically edge (Δ+5)(\Delta + 5)-colorable

An edge coloring of a graph $G$ is to color all the edges in the graph such that adjacent edges receive different colors. It is acyclic if each cycle in the graph receives at least three colors. Fiam{\v{c}}ik (1978) and Alon, Sudakov and Zaks (2001) conjectured that every simple graph with maximum degree $\Delta$ is acyclically edge $(\Delta + 2)$-colorable -- the well-known acyclic edge coloring conjecture (AECC). Despite many major breakthroughs and minor improvements, the conjecture remains open even for planar graphs. In this paper, we prove that planar graphs are acyclically edge $(\Delta + 5)$-colorable. Our proof has two main steps: Using discharging methods, we first show that every non-trivial planar graph must have one of the eight groups of well characterized local structures; and then acyclically edge color the graph using no more than $\Delta + 5$ colors by an induction on the number of edges.Comment: Full version with 120 page

Acyclic list edge coloring of outerplanar graphs

AbstractAn acyclic list edge coloring of a graph G is a proper list edge coloring such that no bichromatic cycles are produced. In this paper, we prove that an outerplanar graph G with maximum degree Δ≥5 has the acyclic list edge chromatic number equal to Δ

Pairwise Registration Algorithm for Large-Scale Planar Point Cloud Used in Flatness Measurement

In this paper, an optimized three-dimensional (3D) pairwise point cloud registration algorithm is proposed, which is used for flatness measurement based on a laser profilometer. The objective is to achieve a fast and accurate six-degrees-of-freedom (6-DoF) pose estimation of a large-scale planar point cloud to ensure that the flatness measurement is precise. To that end, the proposed algorithm extracts the boundary of the point cloud to obtain more effective feature descriptors of the keypoints. Then, it eliminates the invalid keypoints by neighborhood evaluation to obtain the initial matching point pairs. Thereafter, clustering combined with the geometric consistency constraints of correspondences is conducted to realize coarse registration. Finally, the iterative closest point (ICP) algorithm is used to complete fine registration based on the boundary point cloud. The experimental results demonstrate that the proposed algorithm is superior to the current algorithms in terms of boundary extraction and registration performance

Bimodal Imprint Chips for Peptide Screening: Integration of High-Throughput Sequencing by MS and Affinity Analyses by Surface Plasmon Resonance Imaging

Peptide probes and drugs have widespread applications in disease diagnostics and therapy. The demand for peptides ligands with high affinity and high specificity toward various targets has surged in the biomedical field in recent years. The traditional peptide screening procedure involves selection, sequencing, and characterization steps, and each step is manual and tedious. Herein, we developed a bimodal imprint microarray system to embrace the whole peptide screening process. Silver-sputtered silicon chip fabricated with microwell array can trap and pattern the candidate peptide beads in a one-well-one-bead manner. Peptides on beads were photocleaved <i>in situ</i>. A portion of the peptide in each well was transferred to a gold-coated chip to print the peptide array for high-throughput affinity analyses by surface plasmon resonance imaging (SPRi), and the peptide left in the silver-sputtered chip was ready for <i>in situ</i> single bead sequencing by matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF-MS). Using the bimodal imprint chip system, affinity peptides toward AHA were efficiently screened out from the 7 × 10⁴ peptide library. The method provides a solution for high efficiency peptide screening

Autophagy protects auditory hair cells against neomycin-induced damage

<p>Aminoglycosides are toxic to sensory hair cells (HCs). Macroautophagy/autophagy is an essential and highly conserved self-digestion pathway that plays important roles in the maintenance of cellular function and viability under stress. However, the role of autophagy in aminoglycoside-induced HC injury is unknown. Here, we first found that autophagy activity was significantly increased, including enhanced autophagosome-lysosome fusion, in both cochlear HCs and HEI-OC-1 cells after neomycin or gentamicin injury, suggesting that autophagy might be correlated with aminoglycoside-induced cell death. We then used rapamycin, an autophagy activator, to increase the autophagy activity and found that the ROS levels, apoptosis, and cell death were significantly decreased after neomycin or gentamicin injury. In contrast, treatment with the autophagy inhibitor 3-methyladenine (3-MA) or knockdown of autophagy-related (ATG) proteins resulted in reduced autophagy activity and significantly increased ROS levels, apoptosis, and cell death after neomycin or gentamicin injury. Finally, after neomycin injury, the antioxidant N-acetylcysteine could successfully prevent the increased apoptosis and HC loss induced by 3-MA treatment or ATG knockdown, suggesting that autophagy protects against neomycin-induced HC damage by inhibiting oxidative stress. We also found that the dysfunctional mitochondria were not eliminated by selective autophagy (mitophagy) in HEI-OC-1 cells after neomycin treatment, suggesting that autophagy might not directly target the damaged mitochondria for degradation. This study demonstrates that moderate ROS levels can promote autophagy to recycle damaged cellular constituents and maintain cellular homeostasis, while the induction of autophagy can inhibit apoptosis and protect the HCs by suppressing ROS accumulation after aminoglycoside injury.</p