This supplement contains our reworking of Neyman's calculations. It is important to note that, although our proofs may not be technically elegant, they are designed to reveal explicitly the errors of Neyman (1935). A.1 Randomized Complete Block Designs Consider N blocks and T treatments, with each block having T experimental units, and treatments randomized to experimental units independently a...

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

The infection behavior of Steinernema carpocapsae infective juveniles (IJ) was investigated in the presence and absence of S. glaseri. Mixed inoculation of S. carpocapsae with S. glaseri IJ significantly raised the nictation rates of S. carpocapsae IJ. Significantly more S. carpocapsae IJ migrated to the host insect in the mixed inoculation with S. glaseri IJ on agar plates. More S. carpocapsae...

Rouse model is the basic molecular for unentangled linear polymer chains in melts. Recent studies suggest that parameters characterizing melts, spring strength κ , segmental friction coefficient ζ, and mean-square Brownian force intensity B, change under fast flow thereby providing significant rheological nonlinearities with those melts (Matsumiya et al., Macromolecules, 51, 9710 (2018)). This ...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

Differences in activity between infective juveniles (IJ) of the entomopathogenic nematode Steinernema carpocapsae that emerged directly from cadavers onto either a sand or agar substrate compared with those emerging from a cadaver into water and then being placed on the same substrate are known to occur. Differences between S. carpocapsae IJ that emerged directly from a cadaver vs. those that e...

In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method. Keywords—FCM algorithm, Principal Components Analysis, ClusI. FUZZY SET THEORETIC SIMILARITY MEASURES ONE of the most important ...

Abstract We study the statistical estimation problem of orthogonal group synchronization and rotation synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$ where $W_{ij}$ a Gaussian random matrix $Z_i^*$ either an or matrix, each $Y_{ij}$ observed independently with probability $p$. analyze iterative polar decomposition algorithm for $Z^*$ show it ha...

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

Estimation in binary longitudinal data by using generalized estimating equation (GEE) becomes complicated in the presence of missing data because standard GEEs are only valid under the restrictive missing completely at random assumption. Weighted GEE has therefore been proposed to allow the validity of GEE's under the weaker missing at random assumption. Multiple imputation offers an attractive...