On ABC spectral radius of uniform hypergraphs

Given a $k$-uniform hypergraph $G$ with vertex set $[n]$ and edge set $E(G)$, the ABC tensor $\mathcal{ABC}(G)$ of $G$ is the $k$-order $n$-dimensional tensor with \mathcal{ABC}(G)_{i_1, \dots, i_k}= \begin{cases} \dfrac{1}{(k-1)!}\sqrt[k]{\dfrac{\sum_{i\in e}d_{i}-k}{\prod_{i\in e}d_{i}}} & \mbox{if $e\in E(G)$} 0 & \mbox{otherwise} \end{cases} for $i_j\in [n]$ with $j\in [k]$, where $d_i$ is the degree of vertex $i$ in $G$. The ABC spectral radius of a uniform hypergraph is the spectral radius of its ABC tensor. We give tight lower and upper bounds for the ABC spectra radius, and determine the maximum ABC spectral radii of uniform hypertrees, uniform non-hyperstar hypertrees and uniform non-power hypertrees of given size, as well as the maximum ABC spectral radii of unicyclic uniform hypergraphs and linear unicyclic uniform hypergraphs of given size, respectively. We also characterize those uniform hypergraphs for which the maxima for the ABC spectral radii are actually attained in all cases

Accelerated hardware video object segmentation: From foreground detection to connected components labelling

This is the preprint version of the Article - Copyright @ 2010 ElsevierThis paper demonstrates the use of a single-chip FPGA for the segmentation of moving objects in a video sequence. The system maintains highly accurate background models, and integrates the detection of foreground pixels with the labelling of objects using a connected components algorithm. The background models are based on 24-bit RGB values and 8-bit gray scale intensity values. A multimodal background differencing algorithm is presented, using a single FPGA chip and four blocks of RAM. The real-time connected component labelling algorithm, also designed for FPGA implementation, run-length encodes the output of the background subtraction, and performs connected component analysis on this representation. The run-length encoding, together with other parts of the algorithm, is performed in parallel; sequential operations are minimized as the number of run-lengths are typically less than the number of pixels. The two algorithms are pipelined together for maximum efficiency

Wounding triggers MIRO-1 dependent mitochondrial fragmentation that accelerates epidermal wound closure through oxidative signaling.

Organisms respond to tissue damage through the upregulation of protective responses which restore tissue structure and metabolic function. Mitochondria are key sources of intracellular oxidative metabolic signals that maintain cellular homeostasis. Here we report that tissue and cellular wounding triggers rapid and reversible mitochondrial fragmentation. Elevated mitochondrial fragmentation either in fzo-1 fusion-defective mutants or after acute drug treatment accelerates actin-based wound closure. Wounding triggered mitochondrial fragmentation is independent of the GTPase DRP-1 but acts via the mitochondrial Rho GTPase MIRO-1 and cytosolic Ca2+. The fragmented mitochondria and accelerated wound closure of fzo-1 mutants are dependent on MIRO-1 function. Genetic and transcriptomic analyzes show that enhanced mitochondrial fragmentation accelerates wound closure via the upregulation of mtROS and Cytochrome P450. Our results reveal how mitochondrial dynamics respond to cellular and tissue injury and promote tissue repair