(1) Suppose that w belongs to a C d , d r. The total number of leaves in C 0 ; : : :; C d?1 is P d?1 j=0 2 j = 2 d ? 1. Therefore, 2 d ? 1 < i. Since w belongs to C d , i P d j=0 2 j = 2 d+1 ? 1. Thus, 2 d i < 2 d+1 , implying that d = blog ic. Consider the path from the root of T r to w. The path has length 2d + 1: d edges on the path from the root of T r to v d , one edge connecting v d and t...

In this paper, we investigate the maximally parallel attribute of P Systems. Some properties of P Systems are abstracted, which are the filter property and the enumeration property. They are applied to solve the sorting problem and the Hamilton cycle problem, respectively.

Our main result is that the Steiner point removal (SPR) problem can always be solved with polylogarithmic distortion, which answers in the affirmative a question posed by Chan, Xia, Konjevod, and Richa in 2006. Specifically, we prove that for every edge-weighted graph G = (V, E,w) and a subset of terminals T ⊆ V , there is a graph G′ = (T, E′, w′) that is isomorphic to a minor of G such that fo...

Blood samples from 182 patients presenting at the out-patient clinic in Richard-Toll, Senegal were analysed by Thick smear microscopy, the QBC, PCR and the new dipstick PATH Malaria® assay which detects the histidine rich protein II antigen of Plasmodium falciparum. Thick smear microscopy was used as the reference method. Sensitivity, specificity, predictive positive and negative values were 10...

For a spanning tree T in a nontrivial connected graph G and for vertices u and v inG, there exists a unique u−v path u = u0, u1, u2, . . ., uk = v in T . A u− v T -path in G is a u− v path u = v0, v1, . . . , vl = v in G that is a subsequence of the sequence u = u0, u1, u2, . . . , uk = v. A u− v T -path of minimum length is a u− v T -geodesic in G. The T distance dG|T (u, v) from u to v in G i...

By classical and path-integral molecular dynamics simulations, we study the pressure-temperature ($P$-$T$) phase diagram of LaH$_{10}$ to clarify impact temperature atomic zero-point motions. We calculate XRD pattern analyze space group crystal structures. For 125 GPa $\leq P\leq$ 150 $T=300$ K, show that a highly symmetric $Fm\bar{3}m$ structure, for which superconductivity is particularly fav...

This paper presents an approximation algorithm for finding a shortest path between two points s and t in a weighted planar subdivision P . Each face f of P is associated with a weight wf , and the cost of travel along a line segment on f is wf multiplied by the Euclidean norm of that line segment. The cost of a path which traverses across several faces of the subdivision is the sum of the costs...

1, Path calibration using the aftershock The calibration is obtained by convolving the mainshock data with the 1D synthetic of the aftershock and then deconvolving with the data of the aftershock. We have applied a 1Hz low-pass filter to the calibrated data because the effect of 3D slab structure in the source region cannot be ignored at higher frequency (>1Hz) (Fig.S1). The mechanism of the af...

We denote by Bp,T (Rd) the Banach space which consists of continuous paths starting at 0 with finite p-variation norm ‖ ‖p. The 1-variation norm of x is the same as the total variation of x. The p-variation norm defines a weaker topology of the C1-path space with x0 = 0. Actually it is proved that I0,T (x) is a continuous functional of x in the p-variation topology for any 1 ≤ p < 2. However it...