Deep learning has become the method of choice in many application domains of machine learning in recent years, especially for multi-class classification tasks. The most common loss function used in this context is the cross-entropy loss, which reduces to the log loss in the typical case when there is a single correct response label. While this loss is insensitive to the identity of the assigned...

Online propagation of untrue information has been and is becoming an increasing problem. Understanding modeling the diffusion on Social Networks (OSN's) voluminous data prime concern. The paper provides history epidemic spread its analogy with information. This a review online social networks methods detection based epidemiological models. Open research challenges potential future directions ar...

We show that Kummer's conjectured asymptotic estimate for the size of the rst factor of the class number of a cyclotomic eld is untrue under the assumption of two well-known and widely believed conjectures of analytic number theory.

This paper is a corrigendum to the article ``On ideal theorem for number fields''. The main result of this proves be untrue and replaced by an estimate weighted sum with improved error term.

Null hypothesis significance testing is the typical statistical approach in search of the truthfulness of hypotheses. This method does not formally consider the prior credence in the hypothesis, which affects the chances of reaching correct conclusions. When scientifically implausible or empirically weakly supported hypotheses are tested, there is an increased risk that a positive finding in a ...