In this study, the incomplete gamma function, an exponential function, a mixed-log function and a polynomial function were evaluated to describe the lactation curve in Moroccan Holstein-Friesian dairy cows. Data from 1990 to 1999, comprising 77130 monthly milk yields of 6029 dairy cows in 280 dairy herds, were used. Edits were carried out by considering the lactation length (5 d and

We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...

The classification performance of nearest prototype classifiers largely relies on the prototype learning algorithm. The minimum classification error (MCE) method and the soft nearest prototype classifier (SNPC) method are two important algorithms using misclassification loss. This paper proposes a new prototype learning algorithm based on the conditional log-likelihood loss (CLL), which is base...

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function $$\alpha (t)\in (0,1)$$ , develop an exponential-sum-approximation (ESA) technique to approach Caputo fractional derivative. The ESA keeps both quadrature exponents and number of exponentials in summation unchanged at different time level. Approximating parameters are properly selected achieve...

We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction strategies, called experts. By using a general loss function, we generalize previous work on univer...

This paper addresses selection of the loss function for regression problems with finite data. It is well-known (under standard regression formulation) that for a known noise density there exist an optimal loss function under an asymptotic setting (large number of samples), i.e. squared loss is optimal for Gaussian noise density. However, in real-life applications the noise density is unknown an...

We carefully study how well minimizing convex surrogate loss functions corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. We consider the agnostic setting, and investigate guarantees on the misclassification error of the loss-minimizer in terms of the margin error rate of the best predictor. We show that, aiming for such a...

We show that for any Boolean function f : {0, 1} → {0, 1}, the bounded-error quantum communication complexity Q (f ◦ ⊕) of XOR functions f(x ⊕ y) satisfies that Q (f ◦ ⊕) = O ( 2 ( log ‖f̂‖1, + log n ) log(1/ ) ) , where d = deg2(f) is the F2-degree of f , and ‖f̂‖1, = ming:‖f−g‖∞≤ ‖ĝ‖1. This implies that the previous lower bound Q (f ◦ ⊕) = Ω(log ‖f̂‖1, ) by Lee and Shraibman [LS09] is tight for ...

Learning a classifier from positive and unlabeled data is an important class of classification problems that are conceivable in many practical applications. In this paper, we first show that this problem can be solved by cost-sensitive learning between positive and unlabeled data. We then show that convex surrogate loss functions such as the hinge loss may lead to a wrong classification boundar...