Prediction interval is awidely used tool in industrial applications to predict the distribution of future observations. The exact minimum coverage probability and the average coverage probability of the conventional prediction interval for a discrete random variable have not been accurately derived in the literature. In this paper, procedures to compute the exact minimumconfidence levels and th...

Abstract. A lower bound on the misclassification probability for a finite number of classes is obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. This bound, which is shown to be exact in a certain rather strong sense, is based on an exact upper bound on the difference between the maximum and the mean of a finite set of real numbers...

A short, and definitely not a complete representation of η production processes on hadrons is given. First of all, the different ways of obtaining the πN → ηN and πN → ηN amplitudes are presented. After that, an overview of results obtained using these amplitudes as input for calculating processes like: N N → ηN N , pd → η 3 He, πd → ηN N and ηd, η 3 He and η 4 He as well as η-light nuclei bond...

The high energy limit of QCD is investigated in the generalized leading logarithmic approximation. We study unitarity corrections to the BFKL Pomeron containing t-channel states with up to six gluons. Special attention is given to the field theory structure of the corresponding multi–gluon amplitudes. We discuss the transition from two to six gluons in the t-channel.

We present the implementation of the dipole subtraction formalism for the real radiation contributions to any next-to-leading order QCD process in the MadGraph/MadEvent framework. Both massless and massive dipoles are considered. Starting from a specific (n+1)-particle process the package provides a Fortran code for all possible dipoles to all Born processes that constitute the subtraction term...

We investigate the radiation amplitude zeros exhibited by many Standard Model amplitudes for triple weak gauge boson production processes. We show thatWZγ production amplitudes have especially rich structure in terms of zeros, these amplitudes have zeros originating from several different sources. It is also shown that TYPE I current null zone is the special case of the equality of the specific...

The kinematical constraints of helicity amplitudes are studied using the general ideas of Jackson and Hite. The helicity amplitudes are expressed in terms of a Taylor ser ies expansion from which all constraints at threshold and pseudothreshold can be tr ivial ly found. The simplicity of this approach is i l lustrated by deriving all of the constraints for 7rp --* N~ and ~rp --* AN.

The natural interpretation of deep inelastic scattering is in terms of hard scattering on QCD constituents of the target. We examine the relation between amplitudes measured in exclusive lepto-production and the quark content of the nucleon. We show that in the Bjorken limit, the natural interpretation of amplitudes measured in these hard exclusive processes is in terms of the quark content of ...

We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Høyer, and Tapp, and imply an N3/4 logN quantum upper bound for the element distinctness problem (contrasting with N logN classical complexity). We also give an algorithm to finding a triangle in a graph more efficient...

In this article, I show that a recent family of quantum algorithms, based on the quantum amplitude amplification algorithm, can be used to describe a cognitive heuristic called availability bias. The amplitude amplification algorithm is used to define quantitatively the ease of a memory task, while the quantum amplitude estimation and the quantum counting algorithms to describe cognitive tasks ...