A generalization of a result of Häggkvist and Nicoghossian

Using a variation of the Bondy-Chvátal closure theorem the following result is proved: If G is a 2-connected graph with n vertices and connectivity κ such that d(x) + d(y) + d(z) ≥ n + κ for any triple of independent vertices x, y, z, then G is hamiltonian

Isomorphisms and traversability of directed path graphs

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph \forw P_k(D) of a digraph $D$ is obtained by representing the directed paths on $k$ vertices of $D$ by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in $D$ form a directed path on $k+1$ vertices or form a directed cycle on $k$ vertices in $D$. In this introductory paper several properties of \forw P_3(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs $D$ with \forw P_3(D)\cong D, we show that \forw P_3(D_1)\cong\forw P_3(D_2) ``almost always'' implies $D_1\cong D_2$, and we characterize all digraphs with Eulerian or Hamiltonian \forw P_3-graphs

On "the matching polynomial of a polygraph"

In this note we give an explanation for two phenomena mentioned in the concluding remarks of “The matching polynomial of a polygraph” by Babić et al. The following results are obtained: \ud 1.\ud Although three matrices for given polygraphs defined in the above article in general have different orders, they determine the same recurrence relations for the matching polynomial of these polygraghs.\ud 2.\ud Under certain symmetry conditions, the order of the recurrence relations can be reduced by almost a half

Heavy paths and cycles in weighted graphs

A weighted graph is a graph in which each edge e is assigned a non-negative\ud number $w(e)$, called the weight of $e$. In this paper, some theorems on the\ud existence of long paths and cycles in unweighted graphs are generalized to heavy\ud paths and cycles in weighted graphs

Directed paths with few or many colors in colored directed graphs

Given a graph $D=(V(D),A(D))$ and a coloring of $D$, not necessarily a proper coloring of either the arcs or the vertices of $D$, we consider the complexity of finding a path of $D$ from a given vertex $s$ to another given vertex $t$ with as few different colors as possible, and of finding one with as many different colors as possible. We show that the first problem is polynomial-time solvable, and that the second problem is NP-hard. \u

Noise Issues of Modal Identification using Eigensystem Realization Algorithm

AbstractThe eigensystem realization algorithm (ERA) is one of the most popular methods in civil engineering applications for estimating the modal parameters, including complex-valued modal frequencies and modal vectors, of dynamic systems. In dealing with noisy measurement data, the ERA partitions the realized model into principal (signal) and perturbational (noise) portions so that the noise portion can be disregarded. During the separation of signal and noise, a critical issue is the determination for the dimensions of the block Hankel matrix which is built from noisy measurement data. We show that the signal and noise matrices can be better separated when the number of blockrows and number of block-columns of the corresponding block Hankel matrix are chosen to be close to each other. We introduce the concept of using the Frobenius norm (L2-norm) of the signal and noise matrices to quantify the signal to noise ratio in the global sense (involving multiple signals). We also propose a verification procedure to justify that the estimated modal parameters are noise insensitive and thus indeed associated with the true system. The procedure involves artificially injecting random noise into the measured signals (which are noisy signals) to create noisy-noisy signals, then comparing the identification results obtained respectively from the measured and noisynoisy signals. Using experimental data collected from a test plate, we demonstrate that if signal and noise portions have been properly separated while using the measured data, then the artificial noise would almost completely accumulate to the noise portion. Therefore, the modal estimation based on the signal portion only would remain the same by using either the measured or the noisy-noisy signals

Human gait recognition with matrix representation

Human gait is an important biometric feature. It can be perceived from a great distance and has recently attracted greater attention in video-surveillance-related applications, such as closed-circuit television. We explore gait recognition based on a matrix representation in this paper. First, binary silhouettes over one gait cycle are averaged. As a result, each gait video sequence, containing a number of gait cycles, is represented by a series of gray-level averaged images. Then, a matrix-based unsupervised algorithm, namely coupled subspace analysis (CSA), is employed as a preprocessing step to remove noise and retain the most representative information. Finally, a supervised algorithm, namely discriminant analysis with tensor representation, is applied to further improve classification ability. This matrix-based scheme demonstrates a much better gait recognition performance than state-of-the-art algorithms on the standard USF HumanID Gait database

Reduction behavior of tin-containing phase in tin-bearing iron concentrates under CO-CO2 mixed gases

The main purpose of this study was to ascertain the reduction behavior of tin phase (SnO2) in tin-bearing iron concentrates at the respective temperature of 1273 and 1373 K in diverse CO-CO2 mixed gases using chemical analysis, XRD, and SEMEDS analysis. The results show that the reduction behavior of SnO2 depends on the roasting temperature and CO content. At 1273 K, the SnO2 will be reduced to Sn (l) with the CO content being higher than 17.26 vol%, and there is no formation of SnO(s). With the temperature increased to 1373 K, the SnO2 is reduced stepwise in the order to form SnO2 ? SnO (l) ? Sn(l) with CO content over 15.75 vol%. The kinetic study shows that activation energy of the reaction SnO2(s)+CO(g)=Sn(l)+ CO2(g) is 144.75 kJ/mol at 1073-1223 K, being far lower than the one in the reduction of SnO2(s) into SnO(g) at 1273-1323 K, which leads to a conclusion that the tin in tin-bearing iron concentrates could be removed effectively after the Sn(l) sulfurated into SnS at relatively lower temperatures (1073-1223 K) using the sulfidation roasting method

Identification and mapping of quantitative resistance to late blight (Phytophthora infestans) in Solanum habrochaites LA1777

Late blight (Phytophthora infestans) can have devastating effects on tomato production over the whole world. Most of the commercial cultivars of tomato, Solanum lycopersicum, are susceptible. Qualitative and quantitative resistance has been described in wild relatives of tomato. In general qualitative resistance can more easily be overcome by newly evolved isolates. Screening of three S. habrochaites accessions (LA1033, LA2099 and LA1777) through a whole plant assay showed that accession LA1777 had a good level of resistance to several isolates of P. infestans. To explore the potential in this wild species, an introgression line (IL) population of S. habrochaites LA1777 was used to screen individual chromosome regions of the wild species by a detached leaf assay. Two major isolates (T1,2 and T1,2,4) were used and two parameters were measured: lesion size (LS), and disease incidence (DI). Substantial variation was observed between the individual lines. QTLs were identified for LS but not for DI. The presence of five QTLs derived from LA1777 (Rlbq4a, Rlbq4b, Rlbq7, Rlbq8 and Rlbq12) results in unambiguous higher levels of resistance. All QTLs co-localized with previously described QTLs from S. habrochaites LA2099 except QTL Rlbq4b, which is therefore a novel QT