‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2013) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predictors are computed using a finite number B of bootstrap replicates, and worki...

Consider the minimal weights of paths between two points in a complete graph K n with random weights on the edges, the weights being e.g. uniformly distributed. It is shown that, asymptotically, this is log n=n for two given points, that the maximum if one point is xed and the other varies is 2 log n=n, and that the maximum over all pairs of points is 3 log n=n. Some further related results are...

G02BSF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02BSF computes Kendall and/or Spearman non-parametric rank correlation coefficients for a set of data omitting cases with missing values from only those calculations involving the variables for whi...

The elliptic-matrix quantum Olshanetsky-Perelomov problem is introduced for arbitrary root systems by means of an elliptic generalization of the Dunkl operators. Its equivalence with the double aane generalization of the Knizhnik-Zamolodchikov equation (in the induced representations) is established. We generalize the aane the Knizhnik-Zamolodchikov equation from Ch1,2,3] replacing the correspo...

Four (1,-1, 0)-matrices of order m, X = (x ij), Y = (y ij), Z = (z ij), U = (u ij) satisfying will be called semi Williamson type matrices of order m. In this paper we prove that if there exist Williamson type matrices of order n 1 ;: :: ;n k then there exist semi Williamson type matrices of order N = Q k j=1 n rj j , where r j are non-negative integers. As an application, we obtain a W(4N;2N)....

Let G = (V; E) be a directed graph with n vertices. For each e 2 E there is an associated reward r e ; the n n matrix A = a ij ] is deened by a ij = r ij if ij 2 E and a ij = ?1 if ij 6 2 E. The max-algebra system of equations y(k) = y(k?1) A is a deterministic dynamic programming recursion for the maximum total reward y i (k) when the system is in state i at stage k and the one-stage transitio...

Given a graph G = ([n], E) and w ∈ R , consider the integer program maxx∈{±1}n ∑ ij∈E wijxixj and its canonical semidefinite programming relaxation max ∑ ij∈E wijv T i vj , where the maximum is taken over all unit vectors vi ∈ R. The integrality gap of this relaxation is known as the Grothendieck constant κ(G) of G. We present a closed-form formula for the Grothendieck constant of K5-minor free...

We visualized synchronous dynamic brain networks by using prewhitened (stationary) magnetoencephalography signals. Data were acquired from 248 axial gradiometers while 10 subjects fixated on a spot of light for 45 s. After fitting an autoregressive integrative moving average model and taking the residuals, all pairwise, zero-lag, partial cross-correlations (PCC(ij)(0)) between the i and j senso...