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In this review, we examine the recent progress in saliency prediction and proposed several avenues for future research. In spite of tremendous efforts and huge progress, there is still room for improvement in terms finer-grained analysis of…

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

The ability of a classifier to take on new information and classes by evolving the classifier without it having to be fully retrained is known as incremental learning. Incremental learning has been successfully applied to many…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…

Recent developments in the field of high precision calculations in the Standard Model are illustrated with particular emphasis on the evidence for radiative corrections and on the estimate of the theoretical error in perturbative…

The purpose of the paper, of which this is part II, is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. Part II provides…

Remarks on mathematical proof and the practice of mathematics.

This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…

We propose a survey of the research contributions on the field of Educational Timetabling with a specific focus on "standard" formulations and the corresponding benchmark instances. We identify six of such formulations and we discuss their…

In this lecture I will review some recent progress in improving the accuracy of the calculation of density perturbations resulting from inflation.

Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…

Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called…

Comment on ``Boosting Algorithms: Regularization, Prediction and Model Fitting'' [arXiv:0804.2752]

We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

We survey recent developments on the Restriction conjecture.

A methodology that seeks to enhance model prediction performance is presented. The method involves generating multiple auxiliary models that capture relationships between attributes as a function of each other. Such information serves to…

This note provides truncated formulae with explicit error terms to compute Euler products over primes in arithmetic progressions of rational fractions. It further provides such a formula for the product of terms of the shape $F(1/p, 1/p^s)$…

Comment on "Classical Simulations Including Electron Correlations for Sequential Double Ionization" [arXiv:1204.3956]