# Idriss J. Aberkane's research while affiliated with Centro de Estudios y Experimentación de Obras Públicas and other places

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## Publications (12)

The algebraic topology of Collatz attractors (or “Collatz Feathers”) remains very poorly understood. In particular, when pushed to infinity, is their set of branches discrete or continuous? Here, we introduce a fundamental theorem proving that the latter is true. For any odd x, we first define Axn as the set of all odd numbers with Syr(x) in their...

This paper investigates the behavior of rotating binaries. A rotation by r digits to the left of a binary number B exhibits in particular cases the divisibility l∣N1(B)·r+1, where l is the bit-length of B and N1(B) is the Hamming weight of B, that is the number of ones in B. The integer r is called the left-rotational distance. We investigate the c...

The Collatz dynamic is known to generate a complex quiver of sequences over natural
numbers for which the inflation propensity remains so unpredictable it could be used to generate reliable proof-of-work algorithms for the cryptocurrency industry; it has so far resisted every attempt at linearizing its behavior. Here, we establish an ad hoc equival...

This paper investigates the behaviour of rotating binaries. A rotation by $r$ digits to the left of a binary number $B$ exhibits in particular cases the divisibility $l\mid N_1(B)\cdot r+1$, where $l$ is the bit-length of $B$ and $N_1(B)$ is the Hamming weight of $B$, that is the number of ones in $B$. The integer $r$ is called the left-rotational...

The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers which inflation propensity remains so unpredictable it could be used to generate reliable proof of work algorithms for the cryptocurrency industry. Here we establish an ad hoc equivalent of modular arithmetic for Collatz sequences to automatically demonstrat...

Introduced by Gunter Pauli, the Blue Economy, namely bio-inspired industrial ecology or self-profitable circular economy, is a remarkable example of the way the knowledge flow can fundamentally alter micro-, meso- and macroeconomics, and be converted into cash flow. Its reception is also a case of limited rationality in management and economics, an...

The human noosphere and its inner dynamic are forming a fascinating yet poorly understood multiscale complex system, in which one may represent the interaction of individual knowledge holders and their collective dynamic. Here I propose a simple, improvable paradigm for noodynamics (the study of knowledge flows) and nooconomics at large (the econom...

Let us consider the industrial and economic impact of genetic programming and its generic availability to the masses. Is the interaction between genetic programming and the so-called “cognitariat” the beginning of a “genetic revolution” in the industrial sense ? Can we theorise a genetic marketplace, based on the dynamic of bids and asks for geneti...

Could we flow knowledge faster and better? Why is this a problem in the first place? How can we tackle it technologically? What could be a prototype solution? This work unifies these questions in the outline of a single, refutable paradigm of noodynamics - the study of knowledge flows - and nooconomics, the economy of knowledge. This paradigm will...

Let us suppose that any media is the outsourcing of a mental function ; writing, then, is the outsourcing of working memory. For Dehaene and others, writing is a neural recycling by which populations specialized in form recognition are associated with sounds, thus forming a simple grapheme-phoneme association. Could there be other forms of writing...

We aim to develop a new way of teaching mathematics by diverting some best-sold video games to stimulate the students. A cognitive approach of motivation and rule acquisition can lead us to some new results about pedagogy. Our study is deeply based on these words of mathematician David Hilbert: "mathematics is a game played according to certain sim...

## Citations

... For example, Bocart 2018 [1] demonstrated that it could be successfully used to develop a readily applicable proof-of-work algorithm independent of large prime numbers for the cryptocurrency industry. In a previous publication [2], we studied and exhibited the particular geometry of the Collatz basins of attraction (hereunder, "attractors") and connected it to the also difficult Furstenberg conjecture, of which the entire complexity lies in that "base 2 and base 3 representations share no common structure" (Furstenberg 1960 [3] and 1967 [4], and Shmerkin 2021 [5]). Collatz attractors, also known as "Collatz feathers" [6] or "Collatz seaweeds", are forming complex quivers among natural numbers, but very little is still known of their particular geometry and topological properties. ...

Reference: Collatz Attractors Are Space-Filling

... In other words, the disruptive potential of digital technologies should be unleashed to turn waste into a resource, leveraging data as an essential raw material from which information and knowledge can be derived to generate sustainable value [77]. Finally, we sought to provide promising research directions to advance research on the smart circular economy paradigm (see Table 4) regarding the need to: (i) develop the research objectives from exploratory and descriptive to confirmatory and prescriptive purposes, relying on a wide spectrum of research methodologies; (ii) move the focus from single organizations to the entire ecosystem of stakeholders; (iii) combine different enabling digital technologies; and (iv) assess the environmental impact of digital technologies to prevent rebound effects. ...

... Ces nouvelles formes d'apprentissage, qu'elles soient de l'ordre du cognitif (Greenfield & Zeitlin, 1994 ;Philippette, 2014), du social (Taylor, 2006 ;Berry, 2012) ou propres à la pratique du jeu (Aberkane, 2005 ;Amato, 2006), renvoient forcément à la question du pédagogique. Berry (2011) explique que la notion d'apprentissage par le jeu remonte à l'Antiquité et que l'histoire de la pédagogie révèle de nombreuses tentatives d'exploiter des matériaux ludiques pour faire apprendre (aujourd'hui, des entreprises sont spécialisées à cet effet). ...