Intrinsic degree-correlations in static model of scale-free networks

We calculate the mean neighboring degree function $\bar k_{\rm{nn}}(k)$ and the mean clustering function $C(k)$ of vertices with degree $k$ as a function of $k$ in finite scale-free random networks through the static model. While both are independent of $k$ when the degree exponent $\gamma \geq 3$, they show the crossover behavior for $2 < \gamma < 3$ from $k$-independent behavior for small $k$ to $k$-dependent behavior for large $k$. The $k$-dependent behavior is analytically derived. Such a behavior arises from the prevention of self-loops and multiple edges between each pair of vertices. The analytic results are confirmed by numerical simulations. We also compare our results with those obtained from a growing network model, finding that they behave differently from each other.Comment: 8 page

Nephrectomy for a case of intrarenal dermoid cyst: was it an appropriate decision?

Dermoid cyst in a kidney is rarely seen. We report a case of intrarenal dermoid cyst which mimics malignant renal tumour and discuss the dilemma in managing this disease

Validation of the English and Chinese versions of the Quick-FLIC quality of life questionnaire.

A useful measure of quality of life should be easy and quick to complete. Recently, we reported the development and validation of a shortened Chinese version of the Functional Living Index-Cancer (FLIC), which we called the Quick-FLIC. In the present study of 327 English-speaking and 221 Chinese-speaking cancer patients, we validated the English version of the Quick-FLIC and further assessed the Chinese version. The 11 Quick-FLIC items were administered alongside the 11 remaining items of the full FLIC, but there appeared to be little context effect. Validity of the English version of the Quick-FLIC was attested by its strong correlation with two other measures of quality of life, and its ability to detect differences between patients with different performance status and treatment status (each P<0.001). Its internal consistency (alpha=0.86) and test-retest reliability (intraclass correlation=0.76) were also satisfactory. The measure was responsive to changes in performance status (P<0.001). The Chinese version showed similar characteristics. The Quick-FLIC behaved in ways that are highly comparable with the FLIC, even though the Quick-FLIC comprised only 11 items whereas the FLIC comprised 22. Further research is required to see whether the use of shorter instruments can improve data quality and response rates, but the fact that shorter instruments place less burden on the patients is itself inherently important

Sandpile avalanche dynamics on scale-free networks

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-\eta}$ with $0\leq\eta<1$, where $k_i$ is the degree of node $i$. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents $\tau$ and $\delta$, respectively. They are given as $\tau=(\gamma-2 \eta)/(\gamma-1-\eta)$ and $\delta=(\gamma-1-\eta)/(\gamma-2)$ for $\gamma<3-\eta$, 3/2 and 2 for $\gamma>3-\eta$, respectively. The power-law distributions are modified by a logarithmic correction at $\gamma=3-\eta$.Comment: 8 pages, elsart styl

Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint

We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a sufficient condition for its local convergence. We exhibit an example that illustrates the theory.Comment: arXiv admin note: substantial text overlap with arXiv:1411.171

A box-covering algorithm for fractal scaling in scale-free networks

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box, and thereby, vertices in preassigned boxes can divide subsequent boxes into more than one pieces, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap and thereby, vertices can belong to more than one box. Then, the number of distinct boxes a vertex belongs to is distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.Comment: 12 pages, 11 figures, a proceedings of the conference, "Optimization in complex networks." held in Los Alamo