Continuity of the Explosive Percolation Transition

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent $\tau = 2.06(2)$, followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to $N=2^{37}$ collapse perfectly onto a scaling curve characterized solely by the single exponent $\tau$. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as $N\rightarrow\infty$. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely-spread belief of its discontinuity.Comment: Some corrections during the revie

Scaling of cluster heterogeneity in percolation transitions

We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability $p$ increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that $H$ diverges algebraically approaching the percolation critical point $p_c$ as $H\sim |p-p_c|^{-1/\sigma}$ with the critical exponent $\sigma$ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent $\nu_H = (1+d_f/d)\nu$ where $d_f$ is the fractal dimension of the critical percolating cluster and $\nu$ is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.Comment: 4 pages, 4 figure

Inelastic scattering in a monolayer graphene sheet; a weak-localization study

Charge carriers in a graphene sheet, a single layer of graphite, exhibit much distinctive characteristics to those in other two-dimensional electronic systems because of their chiral nature. In this report, we focus on the observation of weak localization in a graphene sheet exfoliated from a piece of natural graphite and nano-patterned into a Hall-bar geometry. Much stronger chiral-symmetry-breaking elastic intervalley scattering in our graphene sheet restores the conventional weak localization. The resulting carrier-density and temperature dependence of the phase coherence length reveal that the electron-electron interaction including a direct Coulomb interaction is the main inelastic scattering factor while electron-hole puddles enhance the inelastic scattering near the Dirac point.Comment: 12 pages, 3 figures, submitted to PR

Automatic 3D Registration of Dental CBCT and Face Scan Data using 2D Projection images

This paper presents a fully automatic registration method of dental cone-beam computed tomography (CBCT) and face scan data. It can be used for a digital platform of 3D jaw-teeth-face models in a variety of applications, including 3D digital treatment planning and orthognathic surgery. Difficulties in accurately merging facial scans and CBCT images are due to the different image acquisition methods and limited area of correspondence between the two facial surfaces. In addition, it is difficult to use machine learning techniques because they use face-related 3D medical data with radiation exposure, which are difficult to obtain for training. The proposed method addresses these problems by reusing an existing machine-learning-based 2D landmark detection algorithm in an open-source library and developing a novel mathematical algorithm that identifies paired 3D landmarks from knowledge of the corresponding 2D landmarks. A main contribution of this study is that the proposed method does not require annotated training data of facial landmarks because it uses a pre-trained facial landmark detection algorithm that is known to be robust and generalized to various 2D face image models. Note that this reduces a 3D landmark detection problem to a 2D problem of identifying the corresponding landmarks on two 2D projection images generated from two different projection angles. Here, the 3D landmarks for registration were selected from the sub-surfaces with the least geometric change under the CBCT and face scan environments. For the final fine-tuning of the registration, the Iterative Closest Point method was applied, which utilizes geometrical information around the 3D landmarks. The experimental results show that the proposed method achieved an averaged surface distance error of 0.74 mm for three pairs of CBCT and face scan datasets.Comment: 8 pages, 6 figures, 2 table

Development of a Perirenal Hematoma after Hula-Hooping

The development of a perirenal hematoma is rare and primarily the result of trauma, malignancy, or a connective tissue disease. Infrequently, a continuous or even mild trauma can cause a perirenal hematoma. Here, we report a case involving the development of a perirenal hematoma after excessive hula-hooping in the absence of a major trauma history

Elevated intracellular cAMP exacerbates vulnerability to oxidative stress in optic nerve head astrocytes.

Glaucoma is characterized by a progressive loss of retinal ganglion cells and their axons, but the underlying biological basis for the accompanying neurodegeneration is not known. Accumulating evidence indicates that structural and functional abnormalities of astrocytes within the optic nerve head (ONH) have a role. However, whether the activation of cyclic adenosine 3',5'-monophosphate (cAMP) signaling pathway is associated with astrocyte dysfunction in the ONH remains unknown. We report here that the cAMP/protein kinase A (PKA) pathway is critical to ONH astrocyte dysfunction, leading to caspase-3 activation and cell death via the AKT/Bim/Bax signaling pathway. Furthermore, elevated intracellular cAMP exacerbates vulnerability to oxidative stress in ONH astrocytes, and this may contribute to axonal damage in glaucomatous neurodegeneration. Inhibition of intracellular cAMP/PKA signaling activation protects ONH astrocytes by increasing AKT phosphorylation against oxidative stress. These results strongly indicate that activation of cAMP/PKA pathway has an important role in astrocyte dysfunction, and suggest that modulating cAMP/PKA pathway has therapeutic potential for glaucomatous ONH degeneration