Supercloseness and asymptotic analysis of the Crouzeix-Raviart and enriched Crouzeix-Raviart elements for the Stokes problem

For the Crouzeix-Raviart and enriched Crouzeix-Raviart elements, asymptotic expansions of eigenvalues of the Stokes operator are derived by establishing two pseudostress interpolations, which admit a full one-order supercloseness with respect to the numerical velocity and the pressure, respectively. The design of these interpolations overcomes the difficulty caused by the lack of supercloseness of the canonical interpolations for the two nonconforming elements, and leads to an intrinsic and concise asymptotic analysis of numerical eigenvalues, which proves an optimal superconvergence of eigenvalues by the extrapolation algorithm. Meanwhile, an optimal superconvergence of postprocessed approximations for the Stokes equation is proved by use of this supercloseness. Finally, numerical experiments are tested to verify the theoretical results

A Program Logic for Verifying Secure Routing Protocols

The Internet, as it stands today, is highly vulnerable to attacks. However, little has been done to understand and verify the formal security guarantees of proposed secure inter-domain routing protocols, such as Secure BGP (S-BGP). In this paper, we develop a sound program logic for SANDLog-a declarative specification language for secure routing protocols for verifying properties of these protocols. We prove invariant properties of SANDLog programs that run in an adversarial environment. As a step towards automated verification, we implement a verification condition generator (VCGen) to automatically extract proof obligations. VCGen is integrated into a compiler for SANDLog that can generate executable protocol implementations; and thus, both verification and empirical evaluation of secure routing protocols can be carried out in this unified framework. To validate our framework, we encoded several proposed secure routing mechanisms in SANDLog, verified variants of path authenticity properties by manually discharging the generated verification conditions in Coq, and generated executable code based on SANDLog specification and ran the code in simulation

Intraflagellar transport delivers tubulin isotypes to sensory cilium middle and distal segments.

Sensory cilia are assembled and maintained by kinesin-2-dependent intraflagellar transport (IFT). We investigated whether two Caenorhabditis elegans α- and β-tubulin isotypes, identified through mutants that lack their cilium distal segments, are delivered to their assembly sites by IFT. Mutations in conserved residues in both tubulins destabilize distal singlet microtubules. One isotype, TBB-4, assembles into microtubules at the tips of the axoneme core and distal segments, where the microtubule tip tracker EB1 is found, and localizes all along the cilium, whereas the other, TBA-5, concentrates in distal singlets. IFT assays, fluorescence recovery after photobleaching analysis and modelling indicate that the continual transport of sub-stoichiometric numbers of these tubulin subunits by the IFT machinery can maintain sensory cilia at their steady-state length

Comprehensive analysis of gene expression patterns of hedgehog-related genes

BACKGROUND: The Caenorhabditis elegans genome encodes ten proteins that share sequence similarity with the Hedgehog signaling molecule through their C-terminal autoprocessing Hint/Hog domain. These proteins contain novel N-terminal domains, and C. elegans encodes dozens of additional proteins containing only these N-terminal domains. These gene families are called warthog, groundhog, ground-like and quahog, collectively called hedgehog (hh)-related genes. Previously, the expression pattern of seventeen genes was examined, which showed that they are primarily expressed in the ectoderm. RESULTS: With the completion of the C. elegans genome sequence in November 2002, we reexamined and identified 61 hh-related ORFs. Further, we identified 49 hh-related ORFs in C. briggsae. ORF analysis revealed that 30% of the genes still had errors in their predictions and we improved these predictions here. We performed a comprehensive expression analysis using GFP fusions of the putative intergenic regulatory sequence with one or two transgenic lines for most genes. The hh-related genes are expressed in one or a few of the following tissues: hypodermis, seam cells, excretory duct and pore cells, vulval epithelial cells, rectal epithelial cells, pharyngeal muscle or marginal cells, arcade cells, support cells of sensory organs, and neuronal cells. Using time-lapse recordings, we discovered that some hh-related genes are expressed in a cyclical fashion in phase with molting during larval development. We also generated several translational GFP fusions, but they did not show any subcellular localization. In addition, we also studied the expression patterns of two genes with similarity to Drosophila frizzled, T23D8.1 and F27E11.3A, and the ortholog of the Drosophila gene dally-like, gpn-1, which is a heparan sulfate proteoglycan. The two frizzled homologs are expressed in a few neurons in the head, and gpn-1 is expressed in the pharynx. Finally, we compare the efficacy of our GFP expression effort with EST, OST and SAGE data. CONCLUSION: No bona-fide Hh signaling pathway is present in C. elegans. Given that the hh-related gene products have a predicted signal peptide for secretion, it is possible that they constitute components of the extracellular matrix (ECM). They might be associated with the cuticle or be present in soluble form in the body cavity. They might interact with the Patched or the Patched-related proteins in a manner similar to the interaction of Hedgehog with its receptor Patched

Data-efficient Event Camera Pre-training via Disentangled Masked Modeling

In this paper, we present a new data-efficient voxel-based self-supervised learning method for event cameras. Our pre-training overcomes the limitations of previous methods, which either sacrifice temporal information by converting event sequences into 2D images for utilizing pre-trained image models or directly employ paired image data for knowledge distillation to enhance the learning of event streams. In order to make our pre-training data-efficient, we first design a semantic-uniform masking method to address the learning imbalance caused by the varying reconstruction difficulties of different regions in non-uniform data when using random masking. In addition, we ease the traditional hybrid masked modeling process by explicitly decomposing it into two branches, namely local spatio-temporal reconstruction and global semantic reconstruction to encourage the encoder to capture local correlations and global semantics, respectively. This decomposition allows our selfsupervised learning method to converge faster with minimal pre-training data. Compared to previous approaches, our self-supervised learning method does not rely on paired RGB images, yet enables simultaneous exploration of spatial and temporal cues in multiple scales. It exhibits excellent generalization performance and demonstrates significant improvements across various tasks with fewer parameters and lower computational costs

Effective Image Restorations Using a Novel Spatial Adaptive Prior

Bayesian or Maximum a posteriori (MAP) approaches can effectively overcome the ill-posed problems of image restoration or deconvolution through incorporating a priori image information. Many restoration methods, such as nonquadratic prior Bayesian restoration and total variation regularization, have been proposed with edge-preserving and noise-removing properties. However, these methods are often inefficient in restoring continuous variation region and suppressing block artifacts. To handle this, this paper proposes a Bayesian restoration approach with a novel spatial adaptive (SA) prior. Through selectively and adaptively incorporating the nonlocal image information into the SA prior model, the proposed method effectively suppress the negative disturbance from irrelevant neighbor pixels, and utilizes the positive regularization from the relevant ones. A two-step restoration algorithm for the proposed approach is also given. Comparative experimentation and analysis demonstrate that, bearing high-quality edge-preserving and noise-removing properties, the proposed restoration also has good deblocking property

Gravity Theory-Based Affinity Propagation Clustering Algorithm and Its Applications

The original Affinity Propagation clustering algorithm (AP) only used the Euclidean distance of data sample as the only standard for similarity calculation. This method of calculation had great limitations for data with high dimension and sparsity when the original algorithm was running. Due to the single calculation method of similarity, the convergence and clustering accuracy of the algorithm were greatly affected. On the other hand, in the universe, we can consider the formation of galaxies is a clustering process. In addition, the interaction between different celestial bodies are achieved through universal gravitation. This paper introduced the Density Peak clustering algorithm (DP) and gravitational thought into the AP algorithm, and constructed the density property to calculate the similarity, put forward the Affinity Propagation clustering algorithm based on Gravity (GAP). The proposed algorithm was more accurate to calculate similarity of simple points through the local density of corresponding points, and then used the gravity formula to update the similarity matrix. The data clustering process could be seen as the sample points spontaneously attract each other based on ‘gravitation’. Experimental results showed that the convergence performance of GAP algorithm is obviously improved over the AP algorithm, and the clustering effect was better