Skill Differences in a Discrete Motor Task Emerging From the Environmental Perception Phase

Because of the challenges associated with measuring human perception and strategy, the process of human performance from perception to motion to results is not fully understood. Therefore, this study clarifies the phase at which errors occur and how differences in skill level manifest in a motor task requiring an accurate environmental perception and fine movement control. We assigned a golf putting task and comprehensively examined various errors committed in five phases of execution. Twelve tour professionals and twelve intermediate amateur golfers performed the putting task on two surface conditions: flat and a 0.4-degree incline. The participants were instructed to describe the topographical characteristics of the green before starting the trials on each surface (environmental perception phase). Before each attempt, the participants used the reflective markers to indicate their aim point from which the ball would be launched (decision-making phase). We measured the clubface angle and impact velocity to highlight the pre-motion and motion errors (pre-motion and motion phase). In addition, mistakes in the final ball position were analyzed as result errors (post-performance phase). Our results showed that more than half of the amateurs committed visual–somatosensory errors in the perception phase. Moreover, their aiming angles in the decision-making phase differed significantly from the professionals, with no significant differences between slope conditions. In addition, alignment errors, as reported in previous studies, occurred in the pre-motion phase regardless of skill level (i.e., increased in the 0.4-degree condition). In the motion phase, the intermediate-level amateurs could not adjust their clubhead velocity control to the appropriate level, and the clubhead velocity and clubface angle control were less reproducible than those of the professionals. To understand the amateur result errors in those who misperceived the slopes, we checked the individual results focusing on the final ball position. We found that most of these participants had poor performance, especially in the 0.4-degree condition. Our results suggest that the amateurs’ pre-motion and strategy errors depended on their visual–somatosensory errors.

Some degree conditions for P≥k-factor covered graphs

A spanning subgraph of a graph $G$ is called a path-factor of $G$ if its each component is a path. A path-factor is called a $\mathcal{P}_{\geq k}$-factor of $G$ if its each component admits at least $k$ vertices, where $k\geq2$. Zhang and Zhou [\emph{Discrete Mathematics}, \textbf{309}, 2067-2076 (2009)] defined the concept of $\mathcal{P}_{\geq k}$-factor covered graphs, i.e., $G$ is called a $\mathcal{P}_{\geq k}$-factor covered graph if it has a $\mathcal{P}_{\geq k}$-factor covering $e$ for any $e\in E(G)$. In this paper, we firstly obtain a minimum degree condition for a planar graph being a $\mathcal{P}_{\geq 2}$-factor and $\mathcal{P}_{\geq 3}$-factor covered graph, respectively. Secondly, we investigate the relationship between the maximum degree of any pairs of non-adjacent vertices and $\mathcal{P}_{\geq k}$-factor covered graphs, and obtain a sufficient condition for the existence of $\mathcal{P}_{\geq2}$-factor and $\mathcal{P}_{\geq 3}$-factor covered graphs, respectively.

Sharp Minimum Degree Conditions for the Existence of Disjoint Theta Graphs

In 1963, Corrádi and Hajnal showed that if $G$ is an $n$-vertex graph with $n \ge 3k$ and $\delta(G) \ge 2k$, then $G$ will contain $k$ disjoint cycles; furthermore, this result is best possible, both in terms of the number of vertices as well as the minimum degree. In this paper we focus on an analogue of this result for theta graphs. Results from Kawarabayashi and Chiba et al. showed that if $n = 4k$ and $\delta(G) \ge \lceil \frac{5}{2}k \rceil$, or if $n$ is large with respect to $k$ and $\delta(G) \ge 2k+1$, respectively, then $G$ contains $k$ disjoint theta graphs. While the minimum degree condition in both results are sharp for the number of vertices considered, this leaves a gap in which no sufficient minimum degree condition is known. Our main result in this paper resolves this by showing if $n \ge 4k$ and $\delta(G) \ge \lceil \frac{5}{2}k\rceil$, then $G$ contains $k$ disjoint theta graphs. Furthermore, we show this minimum degree condition is sharp for more than just $n = 4k$, and we discuss how and when the sharp minimum degree condition may transition from $\lceil \frac{5}{2}k\rceil$ to $2k+1$.

Monochromatic paths and cycles in 2-edge-coloured graphs with large minimum degree

A graph G arrows a graph H if in every 2-edge-colouring of G there exists a monochromatic copy of H. Schelp had the idea that if the complete graph $K_n$ arrows a small graph H, then every ‘dense’ subgraph of $K_n$ also arrows H, and he outlined some problems in this direction. Our main result is in this spirit. We prove that for every sufficiently large n, if $n = 3t+r$ where $r \in \{0,1,2\}$ and G is an n-vertex graph with $\delta(G) \ge (3n-1)/4$ , then for every 2-edge-colouring of G, either there are cycles of every length $\{3, 4, 5, \dots, 2t+r\}$ of the same colour, or there are cycles of every even length $\{4, 6, 8, \dots, 2t+2\}$ of the samecolour. Our result is tight in the sense that no longer cycles (of length $>2t+r$ ) can be guaranteed and the minimum degree condition cannot be reduced. It also implies the conjecture of Schelp that for every sufficiently large n, every $(3t-1)$ -vertex graph G with minimum degree larger than $3|V(G)|/4$ arrows the path $P_{2n}$ with 2n vertices. Moreover, it implies for sufficiently large n the conjecture by Benevides, Łuczak, Scott, Skokan and White that for $n=3t+r$ where $r \in \{0,1,2\}$ and every n-vertex graph G with $\delta(G) \ge 3n/4$ , in each 2-edge-colouring of G there exists a monochromatic cycle of length at least $2t+r$ .

Tamanho de amostra para avaliação do grau de multicolinearidade em caracteres produtivos de centeio

The objectives of this work were to determine the sample size (number of plants) necessary to estimate the indicators of the of multicollinearity degree - condition number (CN), determinant of the correlation matrix (DET), and variance inflation factor (VIF) - in productive traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively, and seven productive traits were evaluated in 780 plants. Twenty-one cases were obtained from seven traits, combined five to five. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling were performed, with replacement. For each resample the CN, DET and FIV were determined and the average among 2,000 estimates of each indicator of the multicollinearity degree was calculated. Then, for each case and indicator, the sample size was determined through three models: models of maximum modified curvature, segmented linear with plateau response, and segmented quadratic with plateau response. There was superiority the quadratic model segmented with plateau in adjusting the degree of multicollinearity according to the sample size for all indicators. There is a need greater sample size to detect multicollinearity when diagnosed by DET and for sizes larger than 101, 258 and 102 plants when diagnosing for the number of conditions, determinant and inflation factor performed, respectively.

A note on the degree conjecture for separability of multipartite quantum states

The degree conjecture for bipartite quantum states which are normalized graph Laplacians was first put forward by Braunstein et al. [Phys. Rev. A 73 (2006) 012320]. The degree criterion, which is equivalent to PPT criterion, is simpler and more efficient to detect the separability of quantum states associated with graphs. Hassan et al. settled the degree conjecture for the separability of multipartite quantum states in [J. Math. Phys. 49 (2008) 0121105]. It is proved that the conjecture is true for pure multipartite quantum states. However, the degree condition is only necessary for separability of a class of quantum mixed states. It does not apply to all mixed states. In this paper, we show that the degree conjecture holds for the mixed quantum states of nearest point graph. As a byproduct, the degree criterion is necessary and sufficient for multipartite separability of [Formula: see text]-qubit quantum states associated with graphs.