We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log β(m,n) + k2); for planar graphs this bound can be improved to O(n+ k2). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k2n + n log n, k2 + kn log(n/k))). The k best orth...

Consider the Lie algebras Lr,t : [K1,K2] = sK3, [K3,K1] = rK1, [K3,K2] = −rK2, [K3,K4] = 0, [K4,K1] = −tK1, and [K4,K2] = tK2, subject to the physical conditions, K3 and K4 are real diagonal operators representing energy, K2 = K † 1, and the Hamiltonian H = ω1K3 + (ω1 + ω2)K4 + λ(t)(K1e−iφ +K2e) is a Hermitian operator. Matrix representations are discussed and faithful representations of least ...

Bayesian learning of belief networks (BLN) is a method for automatically constructing belief networks (ENs) from data using search and Bayesian scoring techniques. K2 is a particular instantiation of the method that implements a greedy search strategy. To evaluate the accuracy of K2, we randomly generated a number of BNs and for each of those we simulated data sets. K2 was then used to induce t...

Let K1,K2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a ∈ K1, b ∈ K2}. We show that the set K1K2 is star-shaped if K1 is a line segment or a circular disk. Examples for K1 and K2 are given so that K1 and K2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product num...

Three types of auscultatory gaps, called G1, G2, and G3, that occur during blood pressure measurement have been identified by using wideband external pulse recording. We have previously shown that the wideband external pulse recorded during cuff deflation can be separated into three components (K1, K2, and K3), one of which (K2) is closely related to the Korotkoff sound. G1 occurs with cuff pre...

Vitamin K2 has been demonstrated to promote the osteogenic differentiation of mesenchymal stem cells; however, the mechanisms underlying this effect remain unclear. As microRNA (miR)‑133a has been identified as a negative regulator of osteogenic differentiation, the present study hypothesized that vitamin K2 promoted osteogenesis by inhibiting miR‑133a. Using human bone marrow stromal cells (hB...

We isolated PCR, RNA ligase-mediated rapid amplification of cDNA ends (RLM-RACE-PCR)-, and RT-PCR-generated clones from mouse kininogen family transcripts. DNA sequencing indicated that the clones were from two distinct genes. One set (K1) is from the previously reported mouse kininogen gene. The second set (K2) has an open reading frame, is 93% identical to K1 in the overlapping nucleotide seq...

Approximate Hammett reaction constants rho calculated from k2/K8 values of several phenyl esters of N-acetyl-L-phenylalanine, hippuric acid, and beta-phenylpropionic acid are 0.0, 0.4, and 1.0 respectively. To determine whether the lack of substituent effect of k2/K8 with the N-acetyl-L-phenylalanine esters is a result of substituent-insensitive k2 or rate-limiting association of enzyme and sub...

A method of ultrasonic leaching has been developed for the destructive analysis of magmatic rock samples. This method was applied to determine three new elements, Ca, Mg and Al, in magmatic rock samples. The accuracy of the ultrasonic leaching method (CULM) was tested using standard reference materials (SRMs) and the recovery ratio as K1 = CULM/CSRM was defined. Another recovery ratio, K2, was ...

We perform a homogeneous search for and analysis of optical occultations phase variations the most favorable ultra-short-period (USP) ($P<1$~d) sub-Neptunes ($R_{p}<4 R_{\oplus}$) observed by $\textit{Kepler}$ K2, with aim better understanding their nature. first selected 16 K2 USP sub-Neptunes, based on expected occultation signal. filtered out stellar variability in light curves, using slidin...