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Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming. The prevalence of such datasets has consistently driven the demand for new tools and methods that exploit the…
We study the question of constructive approximation of the harmonic measure $\omega_x^\Omega$ of a connected bounded domain $\Omega$ with respect to a point $x\in\Omega$. In particular, using a new notion of computable harmonic…
We recall the main concepts of the Le Cam theory of statistical experiments , especially the notion of Le Cam distance and its properties. We also review classical tools for bounding such a distance before presenting some examples. A proof…
Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods…
For a transcendental entire function $f$ of finite order in the Eremenko-Lyubich class $\mathcal{B}$, we give conditions under which the Lebesgue measure of the escaping set $\mathcal{I}(f)$ of $f$ is zero. This is inspired by the recent…
The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function $\mathcal{T}$, and further to investigate its relations to the Hardy-Littlewood maximal…
During the past sixty years, a lot of effort has been made regarding the productive efficiency. Such endeavours provided an extensive bibliography on this subject, culminating in two main methods, named the Stochastic Frontier Analysis…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue's dominated convergence theorem and some other results related to this theorem.…
This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…
Percentage thinking, i.e., assessing quantities as parts per hundred, spread from Roman tax ledgers to modern algorithms. Building on Simon Stevin's La Thiende (1585) and the 19th-century metrication that institutionalized base-10…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
Quantum measurement is universal for quantum computation. Two models for performing measurement-based quantum computation exist: the one-way quantum computer was introduced by Briegel and Raussendorf, and quantum computation via projective…
In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyperbolic system. We show that (i) locally these manifolds can…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
This paper discovers a new phenomenon about the Duffin-Schaeffer conjecture, which claims that $\lambda(\cap_{m=1}^{\infty}\cup_{n=m}^{\infty}{\mathcal E}_n)=1$ if and only if $\sum_n\lambda({\mathcal E}_n)=\infty$, where $\lambda$ denotes…