A graph G is called a pairwise compatibility graph (PCG, for short) if it admits a tuple (T,w, dmin, dmax) of a tree T whose leaf set is equal to the vertex set of G, a non-negative edge weight w, and two non-negative reals dmin ≤ dmax such that G has an edge between two vertices u, v ∈ V if and only if the distance between the two leaves u and v in the weighted tree (T, w) is in the interval [...

A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax, dmin ≤ dmax, such that each node u ∈ V is uniquely associated to a leaf of T and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dmax, where dT (u, v) is the sum of the weights of the edges on the unique path PT (u, v) from u to v in T...

Species vary in abundance and heterogeneity of spatial distribution, and the ecological and evolutionary consequences of such variability are poorly known. Evolutionary adaptation to heterogeneously distributed resources may arise from local adaptation with individuals of such locally adapted populations rarely dispersing long distances and hence having small populations and small overall range...

The MR imaging features of a paraganglioma of the cauda equina with associated spinal cord cysts are presented. MR imaging showed the tumor to be isointense with the spinal cord on all pulse sequences and to enhance homogeneously. The intramedullary cysts had increased signal intensity on proton density- and T2-weighted images, and involved the cervical and thoracic regions.

BACKGROUND AND PURPOSE Brain tumor cellularity has been assessed by using apparent diffusion coefficient (ADC). However, the ADC value might be influenced by both perfusion and true molecular diffusion, and the perfusion effect on ADC can limit the reliability of ADC in the characterization of tumor cellularity, especially, in hypervascular brain tumors. In contrast, the IVIM technique estimate...

A graph is called homogeneously traceable if every vertex an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for integer n≥9, there exists nonhamiltonian order n. The graphs they constructed are irregular. Thus it natural to consider the existence problem regular graphs. We prove two results: (1) For even n≥10, cubic n; (2) p≥18, 4-regular p circumference p−4. Unsol...

A graph G = (V,E) with a vertex set V and an edge set E is called a pairwise compatibility graph (PCG, for short) if there are a tree T whose leaf set is V , a non-negative edge weight w in T , and two non-negative reals dmin ≤ dmax such that G has an edge uv ∈ E if and only if the distance between u and v in the weighted tree (T,w) is in the interval [dmin, dmax]. PCG is a new graph class moti...

Using fractal noise images, we measured the dependence of Dmin and Dmax for stereo on the interocular differences of spatial frequency and contrast. Dmin exhibits a strong dependence on the highest spatial frequency contained in the image, while Dmax exhibits a weaker dependence on the lowest spatial frequency contained within the image. Neither relationship was found to be different when the f...

OBJECTIVE Discussing the effects of Ziyinqingre prescription on the level of airway resistance (Rrs), airway response threshold (Dmin), airway conductance (sGrs) and the level of inflammatory cytokines interleukin-4 (IL-4) and interferon-γ (IFN-γ) of the bronchial hyper-responsiveness (BHR) cough patients. METHOD 84 subjects diagnosed as BHR were randomly divided into 42 Chinese Traditional m...

Let T be an edge weighted tree and let dmin, dmax be two nonnegative real numbers. Then the pairwise compatibility graph (PCG) of T is a graph G such that each vertex of G corresponds to a distinct leaf of T and two vertices are adjacent inG if and only if the weighted distance between their corresponding leaves in T is in the interval [dmin, dmax]. Similarly, a given graph G is a PCG if there ...