Pencils and rulers out, everyone, math lesson begins! Your teacher today is a Dr Smut Clyde, afterwards there will be an oral exam about the Atangana-Baleanu fractional operator. Thus, listen up and take notice. Those who fail to pay attention will have to come up front to the black board and tell the rest of the class what they think is so funny.

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A Critique of Pure Reason

(Divers weights, and divers measures, both of them are alike abomination to the LORD)

By Smut Clyde

Alfred Nobel never endowed a Nobel Prize for Mathematics, forcing us to invent other means to recognise mathematicians for their contributions and excellence. There is an Abel Prize, and a Fields Medal, but the rarest, most sought-after token of recognition is when the Chen brothers steal your identity to use as a fictive co-author on one of their plagiarism gallimaufreys.* For instance, “Bunnitru Daleanu” was based on (and memorialises) the nonpareil Rumanian mathematician Dumitru Baleanu – now resident in Turkey and ensconced in Çankaya University.

UPDATE: Baleanu relocated to Lebanon and has a new primary affiliation, at Lebanese American University. Çankaya University will have to fend for themselves.

A second form of acclaim is to inspire a clause in the Problematic Paper Screener (Cabanac et al. 2022), flagging references to your work and casting shade upon any other paper that cites it. For instance, "partial administrator AND (Baleanu OR Riemann)".

Now D. Baleanu has already featured (twice) in For Better Science, though that is not such an exclusive honour. He is a very productive mathematician indeed. Many of his 2000+ papers address applications of “fractional calculus” where he shares his input with Abdon Atangata.

A science journalist for New Scientist lavishes uncritical praise on that contribution and provides some background, in the November 2021 issue:

“It isn’t just drug delivery that could see concrete benefits – it could help us solve all manner of problems, from detecting cancer to preventing the spread of pollution to making more efficient batteries. “I can’t count the number of ways in which this can be applied,” says Abdon Atangana at the University of the Free State in Bloemfontein, South Africa, who discovered some of the key maths behind the breakthrough. […]

He worked out his own fractional operator in 2015 and sent the result to Dumitru Baleanu at Çankaya University in Ankara, Turkey, to be checked. Baleanu was impressed. “When he read it, he said to me, ‘you have opened the doors of heaven’,” says Atangana. The reason for the excitement was that Baleanu could see that the Atangana-Baleanu operator, as it is now known, would prove remarkably useful across a wide range of applications. He wasn’t wrong. […]

“Nature is full of things that exhibit crossover,” says Atangana. Mathematicians looking to model the spread of disease, for instance, have turned to his operator in droves. In 2018, Baleanu and colleagues from Turkey, Nigeria and Pakistan showed that the new operator was able to give solutions to a previously insoluble problem: how best to vaccinate when an epidemic involves two strains of a pathogen wreaking havoc on a population. […]

Baleanu and his colleagues put this success down to the fact that fractional operators, including the Atangana-Baleanu operator, can model something akin to memory.”

This would be the obvious point to diglain about Fractional Differentials (“diglain” is a word I made up just now, combining the best parts of “digress” and “explain”). In the interests of burying the lede, though, it’s time for a different tangent.

The Matthew Principle tells us that to those who have, shall be given. It holds sway over the realms of academia, on account of the policies for remuneration and career advancement that currently apply there, whereby authors whose papers are frequently cited are rewarded with $$$ that they can use to buy even more citations. This is how we got citational billionaires.

The Matthew Principle applies even to Mathematics. The field has an image of ivory-towered unworldly theorists for whom the concepts of ‘practicality’ and ‘applications’ are alien… but when not converting coffee into theorems, even mathematicians are aware that for large enough X and Y it is good when X many of their papers are cited by Y other authors. Concerns have been growing for years that certain countries and institutions have adopted citation shenanigans as official policy, to the extent that the bibliometric company Clarivate finally disqualified mathematicians from their tendentious “Highly Cited Researcher” scoreboard, which in turn triggered Michele Catanzaro to write about the scandal for Science.

Alas, Catanzaro did not single out specific individuals or journals who might have dominated this surge in productivity, and no “citation cartel” is described in detail despite the attention-grabbing title. In lieu of that, my anonymous coauthor performed a bibliometric cluster analysis of the patterns of international collaboration among highly-cited mathematicians.** It turns out that maths is no longer a single, unified world of discourse. Institutions have specialised, diverging into distinct hubs of collegiality and cooperation:

• 1. A mathematical ‘first world’ of Europe, the US, Korea, Australia and others.
• 2. A BRICS hub: China, with India, and also South America (and Scandinavia).
• 3. An Islamic hub, centred on the financially flush though intellectually bankrupt universities of Saudi Arabia, plus client institutions in Pakistan and Turkey, extending through Saharan Africa and South-East Asia – though also into Rumania.
• 4. russia, Egypt, Morocco, South Africa.

I also received this plot where the citational productivity of highly-cited mathematicians (by country) is plotted against productivity for all mathematicians. Evidently there are countries where the citational elite dominate the whole citation economy. Notably Taiwan, Saudi Arabia and Turkey, but also China, up in the upper-right corner. Ideally, Clarivate or some other bibliometric specialist would calculate the Gini Coefficient of citation inequality, so we could compare the distributions for different countries and mathematical establishments.

But first: Baleanu and Atangana’s specialty, the Fractional Calculus.

In boring vanilla calculus, differentiation and integration operate in integer steps. If (say) location is a function of time, its first differential is velocity. Differentiate velocity in turn and it becomes acceleration, while integration transforms it back into location. But mathematicians are constitutionally incapable of seeing a family of integer-stepped functions without trying to fill in the gaps by defining fractional-order differential and integration operators. This is in line with the fine old maths tradition of tackling problems by making them more difficult.

The question has a trivial answer for sine and cosine functions. Thus it is equally easy for a cyclic repeating function of time (which can be treated as a sum of sinusoid contributions). Things become harder for non-periodic behavior. While integral differentials are local, calculable for any value of t in isolation, the real-number equivalents are non-local with definitions that drag in the entire function. So boundary conditions must be defined. It is no surprise to see our old friend the Gamma function – familiar from the question of generalising the factorial operator and defining it for real numbers as well as for integers.

More generally, there is a choice of fractional-calculus approaches using different kernels. They have real-world applications, for modelling disease spread and signal processing and fluid dynamics… situations with lags and inertia where the past and future of a function are important, so the non-locality of fractional differentials is an asset. Even when the equations are resistant to rigorous analytical solution, numerical methods (approximations) can give results.

In practice “disease spread” means COVID-19. A whole separate scoreboard at Retraction Watch, keeping track of depublished COVID-related papers, bears witness to the opportunities that the pandemic urgency created for publishing shite research.***

Atangana-Baleanu operators aspire to be part of this choice while improving on their predecessors. Sadly, the consensus among mathematicians and engineers is that Atangana’s “fractional differential” operator is not all that (but really a low-pass filter), and that the attempts to define boundary conditions in Atangana-Baleanu papers are nothing but fiddle-faddle and malarkey, leading to “solutions” that are not even numerically correct. So retractions rained down like the Hammer of Thor.

• Atangana (2016), “Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus“. Retracted October 2016). The author blamed the journal for introducing all the errors and omissions, and linked to an earlier arXived version that contained the same errors and omissions.
• Gnitchogna & Atangana (2018), “New two step Laplace Adam‐Bashforth method for integer a noninteger order partial differential equations“. Retracted March 2023
• Gómez-Aguilar & Atangana (2019), “Power and exponentials laws: Theory and application“. Retracted July 2019.
• Bonyah et al (2019), “A fractional model for predator-prey with omnivore“. Retracted July 2020
• Owolabi & Atangana (2019), “On the formulation of Adams-Bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems“. Retracted December 2021. Both appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science, as part of a Special Issue on “Fractional Differential Operators with Non-singular Kernels and their Applications in Nonlinear Systems”, edited by Atangana and Owolabi. Though after a flurry of peer-review-related retractions, the journal sent the Special issue down the memory hole and pretended that Atangana had never sat on the Advisory Board.
• Atangana & Araz (2020), “New numerical method for ordinary differential equations: Newton polynomial“. Retracted July 2020.
• Khan (2019), “Neglecting nonlocality leads to unrealistic numerical scheme for fractional differential equation: Fake and manipulated results“. Retracted in May 2019, see Retraction Watch coverage. A volley of unfounded fraud accusations launched against R. Garrappa (in response to Garrappa’s 2019 critique of Atangana’s work) and published in that Atangana-edited Special Issue of Chaos that no longer exists. Purportedly written not by Atangana, but rather by his frequent coauthor M.A Khan, yeah right.

Atangana does not handle criticism gracefully, resorting to salty language and accusing his critics of colonial sockpuppetry.

Judging from his contributions to a PubPeer comment thread, Atangana harbours some non-orthodox opinions on COVID, and we find him explaining that he was forced to make up his own (eight) “sadistical” data points to model using his mathemagic, because the official disease-prevalence statistics are all distorted by the Elders of Zion or someone.

It may be that the same conspiracy robbed Atangana of his Editorial-Board status at Results in Physics. On the other hand, he remains persona grata at Chaos, Solitons & Fractals (despite the disappearance of Baleanu from the latter).

Atangana is also gone from the editors of Alexandria Engineering Journal. That may be related to the Special Issue he edited there, on “New trends of numerical and analytical methods for engineering problems“; and a particular paper “A bibliometric analysis of Atangana-Baleanu operators in fractional calculus“, now retracted because the nominal author ‘Alexander Templeton’ doesn’t exist. We are left to wonder who would use a false name and a burner email account to write literature reviews, so as to receive no credit for it… apart from pseudonymous PubPeer contributors and guest-bloggers at For Better Science, of course.

Speaking of Advances in Difference Equations (ADE), this no longer exists. In a stroke of magic and an undated Announcement from Springer it became Advances in Continuous and Discrete Models – a journal with different aims and a completely different Atangana- and Baleanu-free slate of editors. The stub of the ADE website is still extant at the time of writing but acknowledges none of these developments. It may be that Springer left it in place, rather than inform the old editors, to leave them happy in the illusion that they still have their journal.

We must cling to that illusion ourselves for the moment. The productivity of highly-cited mathematicians is plotted again below at left, but grouped by journal rather than by country, and the calculations predate ADE‘s transformation. A fondness for ADE among the highly-cited elite had raised that journal so high that it didn’t see the others all the way down there.

While at right, the prominence of specific authors. The raw data were drawn from maths journals, while Atangana prefers engineering or interdisciplinary or physics journals, which is (I am advised) why he doesn’t show up. Second place is occupied instead by T. Abdeljawad, a frequent Baleanu collaborator.

A ribbon plot emphasises the importance of ADE in Baleanu’s output (and Abdeljawad’s). Perhaps this answers the questions that Catanzaro didn’t ask in Science. These Highly-Cited Mathematicians all have multiple affiliations, hence the Country column in the plot.

But I must bid farewell to Abdon for the moment (and to his equally implausible epidemiologist spouse Ernestine Atangana), before they entice my mind from another subject of almost equal importance. For further reading on the Atangana-Baleanu Fractional Calculus I comment readers to Diethelm et al (2020a), “Why fractional derivatives with nonsingular kernels should not be used“, and Diethelm et al (2020b), “Good (and Not So Good) Practices in Computational Methods for Fractional Calculus“. Back to Baleanu now!

In January 2022 a Turkish journalist described Baleanu’s prodigious productivity in tones of polite raised-eyebrows incredulity that bordered on accusations of shenanigans. She focused on his cosmopolitan collaborations; and on his role in the rising profile of Çankaya University during its three decades of existence, dragging it singlehandedly into the purview of the Top University rankings from Times Higher Education.

PorP, “Publish or Perish”, is a potent force. It drives a “para-scholarship” economy in which there are multiple markets, and spawned multiple phenomena of junk science. Conveniently, Baleanu illustrates them all! He also provides opportunities to boost the profile of For Better Science with a series of self-citations.

However, the appearance of a manuscript on the auction block is no guarantee of its cromulence. Nor is it a guarantee that any of the actual writers want to be associated with it, to the extent of including their own names among the ostensible author list. In operational terms, the main difference from the papermill business model is that here the workers retain control of the product of their labour. Power to the workers!

(A) Readers should all be familiar with the existence of papermills. In a closely-related phenomenon, authorship slots on a provisionally-accepted manuscript are auctioned off in return for financial aid toward the journal’s publication fees. An international, cross-disciplinary collaboration behind a paper can be one indicator of an authorship-bazaar provenance.

Muhammad Naveed, Dumitru Baleanu, Ali Raza , Muhammad Rafiq , Atif Hassan Soori , Muhammad Mohsin Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters Advances in difference equations (2021) doi: 10.1186/s13662-021-03618-z 

(B) Ghostwriting invites ‘hidden self-citation’, providing the true authors of a for-sale manuscript with an opportunity to show off their own plumage. The citation trade has progressed from the days of excessive self-citation or mutual back-scratching among the members of a cartel, or citational coercion from corrupt editors and reviewers. In the present dispensation, researchers can pay a broker to promote their work through transactional citations (unhindered by the absence of context or relevance in the papers where these appear, or by the abject absurdity of the results). Brokers and papermills work together, the latter selling the Reference sections of their products as a secondary advertising-slot income stream; papers can be marked as fraudulent by Reference sections that resemble Incan architecture, assembled from great pre-hewn cyclopean slabs – paper-lists that recur across constructions.

• Hui-Hui Guo , Mohd Yazid Bajuri , Hussam Alrabaiah , Taseer Muhammad , S. Mohammad Sajadi , Ferial Ghaemi , Dumitru Baleanu, Arash Karimipour The investigation of energy management and atomic interaction between coronavirus structure in the vicinity of aqueous environment of HO molecules via molecular dynamics approach Journal of molecular liquids (2021) doi: 10.1016/j.molliq.2021.117430 
• Awatef Abidi , Zahra Jokar , Seyedmahmoodreza Allahyari , Fereshteh Kolahi Sadigh , S. Mohammad Sajadi , Payam Firouzi , Dumitru Baleanu, Ferial Ghaemi , Arash Karimipour Improve thermal performance of Simulated-Body-Fluid as a solution with an ion concentration close to human blood plasma, by additive Zinc Oxide and its composites: ZnO/Carbon Nanotube and ZnO/Hydroxyapatite Journal of molecular liquids (2021) doi: 10.1016/j.molliq.2021.117457 

When citation plantations go horribly wrong: a papermiller forgot to fill in all the gaps in the template being used.

Feng Li Incorporating fractional operators into interaction dynamics of a chaotic biological model Results in physics (2023) doi: 10.1016/j.rinp.2023.107052 

Fortunately for citation purchasers, when a dumpster-dived citation delivery vehicle is retracted from the literature after recognition of its nature, the beneficiaries’ citation indices are not affected. This is not optimal, but the bibliometry companies that calculate and license these index values are subsidiaries of large academic publishers who are doing very well out of the PorP paradigm, so I do not expect any sudden change in the formulae they use.

(C) The Vickers Curse is where a glitch in G**gle Scholar unmasked a thousand citation-delivery vehicles as ghost-written garbage, because their Reference Sections – composed of bogus, paid-for citations – were cobbled together in such careless haste that they defaulted to a not-entirely-relevant paper on insect pheromones. Consulting PubPeer, we find that Baleanu fell victim to it.

A.I.K. Butt, W. Ahmad , M. Rafiq, D. Baleanu Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic Alexandria Engineering Journal (2022) doi: 10.1016/j.aej.2021.12.042 

(D) “Tortured phrases” are another hint of a papermill / auction provenance. After assembly of the text, the paragraphs are fed through ‘SpinBot’ Rogetifying software to mask the extent of plagiarism by replacing words with near-synonyms. Hilarity often ensues.

Shabir Ahmad, Aman Ullah , Ali Akgül , Dumitru Baleanu Theoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels Alexandria Engineering Journal (2022) doi: 10.1016/j.aej.2021.10.065

Below, the Atangana-Baleanu “fractional operator” became “partial administrator“. This engarblement happened often enough that a clause in the Problematic Paper Screener looks for it specifically:

Muhammad Farman , Ali Akgül, Dumitru Baleanu, Sumaiyah Imtiaz , Aqeel Ahmad Analysis of Fractional Order Chaotic Financial Model with Minimum Interest Rate Impact Fractal and Fractional (2020) doi: 10.3390/fractalfract4030043 

The motive force of PorP has generated (at least) three entire subgenres of mockademia, all refreshingly free from genuine research. Each is a cloistered playground for charlatans and mountebanks, with its own private language and its own write-only / cite-only journals. Papers in each Glass-Bead Game seemingly present ‘applications’, but none of the methods they discuss are used outside the hortus conclusus of para-scholarship so they are safe from the danger of disproof or falsification from a hostile encounter against reality.

1. Nanofluid convection simulations of fluid flow. The range of conceivable geometries and nanoparticles, combined with temperature boundary conditions and magnetic complications, place few constraints on the number of potential papers. No mathematics is required: only the computer time to run well-established finite-element software that’s so old that the source-code is probably written in Fortran, plus the sheer brass neck to send the results off to some complaisant editor to be published as a significant advance for Science.

Bagh Ali, Ghulam Rasool, Sajjad Hussain, Dumitru Baleanu, Sehrish Bano Finite Element Study of Magnetohydrodynamics (MHD) and Activation Energy in Darcy–Forchheimer Rotating Flow of Casson Carreau Nanofluid Processes (2020) doi: 10.3390/pr8091185 

More tortured phrases:

Umair Khan , Anum Shafiq , A. Zaib, Dumitru Baleanu Hybrid nanofluid on mixed convective radiative flow from an irregular variably thick moving surface with convex and concave effects Case Studies in Thermal Engineering (2020) doi: 10.1016/j.csite.2020.100660 

Umair Aurang Zaib, Sakhinah Abu Bakar, Anuar Ishak, Dumitru Baleanu, El-Sayed M Sherif Computational simulation of cross-flow of Williamson fluid over a porous shrinking/stretching surface comprising hybrid nanofluid and thermal radiation AIMS Mathematics (2022) doi: 10.3934/math.2022362

2. In generalised fluffy logic, the central conceit or axiom is that guesstimates data of dubious quality can be pooled with others to inform policy decisions as long as each rectally-sourced data stream is paired with a rectally-sourced rating of its reliability as they go into the sausage machine. That is, the curse of GIGO is lifted by using additional streams of garbage to modulate the main stream of garbage.

A multitude of meta-fuzzy procedures abound, but this is no obstacle to the invention of new sausage machines because none of the competing ones is anywhere in use. Regular contributor Rhipidura albiventris works that side of the street over at PubPeer.

• Samayan Narayanamoorthy, L. Ramya, Dumitru Baleanu, Joseph Varghese Kureethara, V. Annapoorani Application of normal wiggly dual hesitant fuzzy sets to site selection for hydrogen underground storage International Journal of Hydrogen Energy (2019) doi: 10.1016/j.ijhydene.2019.09.103 
• Samayan Narayanamoorthy, Lakshmanaraj Ramya, Daekook Kang, Dumitru Baleanu, Joseph Varghese Kureethara, Veerappan Annapoorani A new extension of hesitant fuzzy set: An application to an offshore wind turbine technology selection process IET Renewable Power Generation (2021) doi: 10.1049/rpg2.12168. “Energy is derived from the panchabhutas or the five classical elements (𝜎𝜏𝜔𝜄𝜒𝜖𝜄𝜔) that includes water, land, air, sky and fire.”
• Selvaraj Geetha, Samayan Narayanamoorthy, Joseph Varghese Kureethara, Dumitru Baleanu, Daekook Kang The hesitant Pythagorean fuzzy ELECTRE III: An adaptable recycling method for plastic materials Journal of Cleaner Production (2021) doi: 10.1016/j.jclepro.2020.125281 

As it happens, Geetha et al. did respond to the PubPeer queries – though to the journal editors rather than to PubPeer – and internal sources provided me with a copy. In essence they argue that the proliferation of tortured phrases was not torture at all, but merely a Bondage-&-Discipline sex-dungeon in which the phrases were consenting participants. Don’t kink-shame. Also, when they defined the weighting factors λ_k as adding to a total of 1, and then gave a worked example in which λ_k do not add up to 1, this was merely a typo which does not affect the validity of the worked example. The Assistant Editor at Journal of Cleaner Production is hopelessly out of depth with all this, and is inclined to let the authors off with a Correction.

3. Animal-themed / swarm-intelligence heuristics. By mimicking animal survival strategies we are tapping into the timeless wisdom of Evolution itself!

Each addition to this field invokes the ‘No Free Lunch’ theorem (i.e. no single optimisation algorithm is best for solving all classes of optimisation problem) as an excuse for augmenting the existing over-stocked bestiary with yet another animal-themed algorithm. Each new arrival is presented as an improvement, as some existing heuristic can always be implemented so that it performs even worse on one or other cherry-picked benchmark problems, of which a veritable orchard exists (though let’s be honest – no actual numerical-performance tests occur and the figures are just made up). Authors never mention the No-Free-Lunch corollary: there is no way of telling which algorithm is best for a specific class of problem, except by trying them all (including the latest one).

• Asiyeh Ebrahimzadeh, Raheleh Khanduzi, Samaneh P A Beik, and Dumitru Baleanu Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation Journal of Vibration Control (2021) doi: 10.1177/10775463211051447
• Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Dumitru Baleanu & Juan L. G. Guirao Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model Soft Computing (2022) doi: 10.1007/s00500-022-07359-3
• Juan L. G. Guirao, Zulqurnain Sabir, Muhammad Asif Zahoor Raja & Dumitru Baleanu Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model. Eur. Phys. J. Plus (2022). doi: 10.1140/epjp/s13360-022-02421-3

History does not repeat, but it rhymes. Unless it follows the alliteration rules of Old Norse poetry. Plagiarising an expert here:

“Self-contained, self-citing networks of mathematical fiddle-faddle are nothing new. In the most celebrated case, one Mohamed El Naschie founded the journal Chaos Fractals & Solitons, then remained Editor-in-Chief when ownership passed to Elsevier, allowing him to foist paper after paper of pure bafflegab upon an uncomprehending world. He employed his own notation, his own unique rules for ratiocination, and a small army of sockpuppet pseudonyms to defend his theories. [Wikipedia]”

“El Naschie’s largest contributions to science were perhaps to help discredit Elsevier publishing ethics, and the use of Impact-Factor citations-index metrics for rating journals and institutions. Archived copies are still available for much of the no-longer-extant ‘El Naschie Watch‘ blog.”

What eventually robbed El Naschie of his Editorial role at Chaos Fractals & Solitons was his penchant for bumptious lawsuits against people who questioned the integrity of peer review there, or the validity of his “fractal Cantorian space-time” numerology. The bad publicity – especially the negative verdicts – were undermining Elsevier’s investment in the journal. Still he deserves credit for showing that a sufficiently grandiose style of bullshit, and a coterie of coat-tail-riding mutually-supportive fans (the E-infinity Brotherhood), are all that a charlatan needs to rise to the pinnacle of mathematical eminence and influence.

COVID CODA

“Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?” (Atangana 2020) appeared in Chaos Solitons & Fractals, as part of a Special Issue devoted to COVID-19 and mathematical models. The Special Issue was also edited by Abdon Atangana so readers should not expect the text to bear evidence of heavy-handed editing for coherence or plausibility.

The paper begins with commendable modesty: “Our paper does not claim to have found the cure for COVID-19“. Atangana did stake out his claim to be the first person to think of fitting a mathematical model to the spread of COVID-19.

Atangana’s model certainly had original aspects, such as allowing for the possibility that COVID-fatality corpses remained infectious. He posited that the number of dead infectious corpses C(t) is initially positive, as the basis for proving that C(t) > 0 for all t. Which is to say, the mathematical model was nonsense.

More to the point, if dead but infectious corpses are recovering, you are in a case nightmare purple Zombie Apocalypse scenario and mass mortality from a respiratory / vascular infection is the least of your worries.

Atangana informs us that “In this paper, using data from Italy, we presented some basic statistical figures to give an indication of the spread profile.” In fact the analysis consists of numerical simulations of the spread of some hypothetical non-COVID disease under various implausible conditions; it does not draw upon the Italian data at any point. As if to make up for this neglect, the author plots the irrelevant Italian numbers twice – as line graphs and as bar charts.

Perhaps the best part of this bizarre paper-shaped paroxysm is the lengthy introductory diatribe, which is all THERE ARE SOME THINGS MAN WAS NOT MEANT TO KNOW, and is best imagined as a title card from a silent movie starring Rudolf Klein-Rogge.

No, wait, the even bester part is the discovery that this hot-garbage dumpster fire has been cited 393 times by other authors who chose it to support their own COVID-19 dumpster fires. That is how fast the wordmills are churning out wordwooze into the scientific literature. Or 451 citations by the more liberal count of G**gle Scholar.

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* The judges would also have accepted “plagiarism slumgullion”.

** My colleague began with Ioannidis’ list of highly cited researchers in 2019, and filtered out 349 researchers who were working in applied mathematics; then searched Web-of-Science, finding 1027 papers published by these authors in the year 2020. Then these papers from high-performing mathemagicians were compared with all the 2020 papers in the applied-mathematics field.

*** Orchestes quercus wondered whether a series of preposterous COVID-19 papers with similar phrasing were the work of a specialised papermill.

• Aliakbar Karimipour, Ali Amini , Mohammad Nouri , Annunziata D’Orazio, Roozbeh Sabetvand, Maboud Hekmatifar , Azam Marjani, Quang-vu Bach Molecular dynamics performance for coronavirus simulation by C, N, O, and S atoms implementation dreiding force field: drug delivery atomic interaction in contact with metallic Fe, Al, and steel Computational particle mechanics (2021) doi: 10.1007/s40571-020-00367-w 
• Omid Malekahmadi , Akbar Zarei , Mohammad Behzad Botlani Esfahani , Maboud Hekmatifar , Roozbeh Sabetvand, Azam Marjani , Quang-Vu Bach Thermal and hydrodynamic properties of coronavirus at various temperature and pressure via molecular dynamics approach Journal of Thermal Analysis and Calorimetry (2021) doi: 10.1007/s10973-020-10353-2 
• Amirhosein Hadian , Somaye Yaghoubi , Aliakbar Karimipour , HPM Viet Investigating the effect of SiO2 nanoparticle addition and thickness of face-coverings on COVID-19 protection using molecular dynamics approach Engineering analysis with boundary elements (2023) doi: 10.1016/j.enganabound.2023.09.015 

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