Kemeny's constant and Wiener index on trees

On trees of fixed order, we show a direct relation between Kemeny's constant and Wiener index, and provide a new formula of Kemeny's constant from the relation with a combinatorial interpretation. Moreover, the relation simplifies proofs of several known results for extremal trees in terms of Kemeny's constant for random walks on trees. Finally, we provide various families of co-Kemeny's mates, which are two non-isomorphic connected graphs with the same Kemeny's constant, and we also give a necessary condition for a tree to attain maximum Kemeny's constant for trees with fixed diameter

Kemeny's constant and enumerating Braess edges in trees

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees

Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem

We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. We prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ for various families of graphs. In particular, we show that if the maximum degree of a graph $G$ on $n$ vertices is $n-O(1)$ or $n-\Omega(n)$, then $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ is at most $O(n)$

Fiedler vectors with unbalanced sign patterns

summary:In spectral bisection, a Fielder vector is used for partitioning a graph into two connected subgraphs according to its sign pattern. We investigate graphs having Fiedler vectors with unbalanced sign patterns such that a partition can result in two connected subgraphs that are distinctly different in size. We present a characterization of graphs having a Fiedler vector with exactly one negative component, and discuss some classes of such graphs. We also establish an analogous result for regular graphs with a Fiedler vector with exactly two negative components. In particular, we examine the circumstances under which any Fiedler vector has unbalanced sign pattern according to the number of vertices with minimum degree

Vision Sensor Based Fuzzy System for Intelligent Vehicles

Those in the automotive industry and many researchers have become interested in the development of pedestrian protection systems in recent years. In particular, vision-based methods for predicting pedestrian intentions are now being actively studied to improve the performance of pedestrian protection systems. In this paper, we propose a vision-based system that can detect pedestrians using an on-dash camera in the car, and can then analyze their movements to determine the probability of collision. Information about pedestrians, including position, distance, movement direction, and magnitude are extracted using computer vision technologies and, using this information, a fuzzy rule-based system makes a judgement on the pedestrian’s risk level. To verify the function of the proposed system, we built several test datasets, collected by ourselves, in high-density regions where vehicles and pedestrians mix closely. The true positive rate of the experimental results was about 86%, which shows the validity of the proposed system

On the effectiveness of random walks for modeling epidemics on networks.

Random walks on graphs are often used to analyse and predict epidemic spreads and to investigate possible control actions to mitigate them. In this study, we first show that models based on random walks with a single stochastic agent (such as Google's popular PageRank) may provide a poor description of certain features of epidemic spread: most notably, spreading times. Then, we discuss another Markov chain based method that does reflect the correct mean infection times for the disease to spread between individuals in a network, and we determine a procedure that allows one to compute them efficiently via a sampling strategy. Finally, we present a novel centrality measure based on infection times, and we compare its node ranking properties with other centrality measures based on random walks. Our results are provided for a simple SI model for epidemic spreading

On the effectiveness of random walks for modeling epidemics on networks

Random walks on graphs are often used to analyse and predict epidemic spreads and to investigate possible control actions to mitigate them. In this study, we first show that models based on random walks with a single stochastic agent (such as Google’s popular PageRank) may provide a poor description of certain features of epidemic spread: most notably, spreading times. Then, we discuss another Markov chain based method that does reflect the correct mean infection times for the disease to spread between individuals in a network, and we determine a procedure that allows one to compute them efficiently via a sampling strategy. Finally, we present a novel centrality measure based on infection times, and we compare its node ranking properties with other centrality measures based on random walks. Our results are provided for a simple SI model for epidemic spreading

Immunomodulatory Effects of an Aqueous Extract of Black Radish on Mouse Macrophages via the TLR2/4-Mediated Signaling Pathway

Here, we determined the immunostimulatory effects of black radish (Raphanus sativus ver niger) hot water extract (BRHE) on a mouse macrophage cell line (RAW 264.7) and mouse peritoneal macrophages. We found that BRHE treatment increased cell proliferation, phagocytic activity, nitric oxide (NO) levels, cytokine production, and reactive oxygen species synthesis. Moreover, BRHE increased the expression of the following immunomodulators in RAW 264.7 cells and peritoneal macrophages: pro-inflammatory cytokines (IL-1β, IL-6, and TNF-α), iNOS, and COX-2. BRHE treatment significantly up-regulated the phosphorylation of components of the mitogen-activated protein kinase (MAPK), nuclear factor-κB (NF-κB), Akt, and STAT3 signaling pathways. Further, the effects of BRHE on macrophages were significantly diminished after the cells were treated with the TLR2 antagonist C29 or the TLR4 antagonist TAK-242. Therefore, BRHE-induced immunostimulatory phenotypes in mouse macrophages were reversed by multiple inhibitors, such as TLR antagonist, MAPK inhibitor, and Akt inhibitor indicating that BRHE induced macrophage activation through the TLR2/4–MAPK–NFκB–Akt–STAT3 signaling pathway. These results indicate that BRHE may serve as a potential immunomodulatory factor or functional food and provide the scientific basis for the comprehensive utilization and evaluation of black radish in future applications