#Bayesian Analysis

[crimsonpublishers-oabb]

Adapting Hartigan & Wong K-Means for the Efficient Clustering of Sets1

This paper proposes an algorithm, named HWK-Sets, based on K-Means, suited for clustering data which are variable-sized sets of elementary items. An example of such data occurs in the analysis of medical diagnosis, where the goal is to detect human subjects who share common diseases so as to predict future illnesses from previous medical history possibly. Clustering sets is difficult because data objects do not have numerical attributes and therefore it is not possible to use the classical Euclidean distance upon which K-Means is normally based. An adaptation of the Jaccard distance between sets is used, which exploits application-sensitive information. More in particular, the Hartigan and Wong variation of K-Means is adopted, which can favor the fast attainment of a careful solution. The HWK-Sets algorithm can flexibly use various stochastic seeding techniques. Since the difficulty of calculating a mean among the sets of a cluster, the concept of a medoid is employed as a cluster representative (centroid), which always remains a data object of the application. The paper describes the HWK-Sets clustering algorithm and outlines its current implementation in Java based on parallel streams. After that, the efficiency and accuracy of the proposed algorithm are demonstrated by applying it to 15 benchmark datasets.

Read More About This Article: https://crimsonpublishers.com/oabb/fulltext/OABB.000564.php

Read More About Crimson Publishers: https://crimsonpublishers.com/oabb/index.php

[raffaellopalandri]

Statistical Tools

Daily writing promptWhat was the last thing you searched for online? Why were you looking for it?View all responses Checking which has been my most recent search on Google, I found that I asked for papers, published in the last 5 years, that used a Montecarlo method to check the reliability of a mathematical method to calculate a team’s efficacy. Photo by Andrea Piacquadio on Pexels.com I was…

[dorianbrightmusic]

*sigh*

one of the most important skills that is utterly drilled into you in academia is critical thinking. In an arts degree, you must learn to dissect an argument – if you cannot analyse effectively, you won't get through. In a science degree, you will be taught not only how to read papers, but how to critique them. Science is defined by the scientific method – and as tedious as it may sound, there is no skill more important than being able to scientific method your way through life.

The most important part of research is knowing how to do research – how do you find high-quality papers? What is high-quality evidence? Is it actually appropriate? What does 'significant' actually mean? The media loooves to deploy these terms without having a clue what the scientific meaning is – and as a result, the public get fooled. If you do not know how to do research, you will not find good information by doing your own research.

For example – members of the public who do their own 'research' into trans healthcare might come across the Cass Review, and see that it doesn't find much 'high-quality evidence' for gender-affirming care. They might think 'okay, guess trans healthcare is bad/experimental'. But if you've done academia, you'll know that 'high-quality' is just a synonym for 'randomised control trial' (RCT). For most research, RCTs are the gold standard. But RCTs require that people be unable to tell which condition they're in – that is, if they're receiving a placebo, they won't be able to tell. But with gender-affirming care, you can't exactly conceal the effects of hormones or surgery from a participant – after all, growing boobs/having a voice break/getting facial hair/altered sexual function is kinda hard to not notice. So, an RCT would actually be a completely inappropriate study design. Ergo ‘high-quality’ evidence is a misnomer, since it’d be really poor evidence for whether the treatment is helpful. As such, we know that so-called low-quality evidence is both more appropriate and perfectly sufficient. Academia is crucial to learning to debunk bad research.

And before y’all claim ‘but the papers being cited are all the ones that are getting funding – it’s just corrupt’ – you do realise being taught to spot bad science means that we get explicitly told how to spot corruption? Often, we can learn to tell when papers’ results are dodgy. Academia is about learning not to accept status or fame as a good enough reason to trust something. While I agree there are massive problems with some fields getting underfunded, or with science deprioritising certain social groups, abolishing science will only make this worse.

So. In conclusion, academia may be flawed, but it’s by far the best thing we have for learning to think critically. Anti-intellectualism is a blight on society, and horribly dangerous - it gets folks killed.

[skylobster]

The ancient Greek craftsmen achieved a machining precision of 0.001 inches - a truly mind-boggling accomplishment for the era!

[darkmaga-returns]

A groundbreaking new peer-reviewed study involving a staggering 85 million people has confirmed that Covid “vaccines” have caused sudden deaths, strokes, heart attacks, coronary artery disease, and other deadly chronic conditions to skyrocket to epidemic levels.

The study, one of the largest published reviews to date, found that mRNA and viral vector Covid “vaccines” are responsible for surging reports of deadly cardiovascular events.

During the large-scale analysis, the study confirmed that Covid mRNA and viral vector injections caused the following spikes around the world:

Strokes increased 240%

Heart attacks +286%

Coronary artery disease +244%

Arrhythmia +199%

The study was led by Raheleh Karimi from the Department of Biostatistics and Epidemiology at the Isfahan University of Medical Sciences in Iran.

During the major study, Karimi coordinated a team of international researchers, including leading scientists in Spain and Portugal.

The study’s paper was published in the latest editions of the prestigious International Journal of Preventive Medicine.

This comprehensive Bayesian multivariate meta-analysis included 15 studies.

[typhlonectes]

Implications for Snake Evolution:

Morphology and systematics of a new fossil snake from the early Rupelian (Oligocene) White River Formation, Wyoming 

Jasmine A Croghan, Alessandro Palci, Silvio Onary, Michael S Y Lee, Michael W Caldwell

Abstract

Extinct snake taxa are recognized primarily from isolated vertebrae. A new specimen from the early Oligocene of Wyoming provides a rare opportunity to examine four nearly complete and articulated fossil snakes.

Informally assigned previously to the ‘erycine’ vertebral form taxa Ogmophis and Calamagras, a detailed comparison reveals that this fossil snake exhibits vertebral differences from both taxa and is, furthermore, a new taxon, Hibernophis breithaupti gen. et sp. nov., based on a combination of apomorphies such as absence of basal tubera, low subrectangular prootic, low parasphenoid wings obscuring the anterior opening of the Vidian canal, and foramen for the mandibular branch of the trigeminal nerve posteriorly displaced inside the adductor fossa of the compound.

Parsimony and Bayesian phylogenetic analysis of combined morphological and molecular data from a broad selection of snakes places Hibernophis breithaupti as sister taxon to all other booids, distant from both Old and New World ‘erycines’.

However, an alternative position close to New World ‘erycines’ and ungaliophiines cannot be rejected.

Read more: https://academic.oup.com/zoolinnean/advance-article-abstract/doi/10.1093/zoolinnean/zlae073/7696309

[max1461]

Regarding the culture on here (and twitter) being overly concept-centric; people having a tendency to view particular things as being mere instantiations of concepts as opposed to concepts emerging from the particulars of life:

It's like, whether it's therapy jargon or Bayesian reasoning or Marxist analysis, people on here really seem to love analyzing everything through some kind of established frame. Often the frame is constantly rotating. When social justice was tumblr's épistémè it used to constantly pick up new frameworks, and still the rationalists are always picking up on some new framework (or rolling their own). There's always a new framework du jour.

Nobody just looks at shit and decides independently what they think of it. Nobody just has specific, isolated, personal opinions about this or that particular topic. It's all tied into some established body of theory. Or at least, when people do just look at shit and come to an independent opinion, they feel the need to articulate it in reference to some established body of theory.

I hate this! I can't express how wrong I think this is in terms of like, being a productive way to engage with the world. Like, this kind of social theorizing... whether Marxist, rationalist, or psychiatric... it should be secondary. It should be something you put in an essay or research paper, and not something you live your life by. Why? Well there are a lot of reasons. Models, even accurate models, are necessarily simplifications of reality. In your actual lived experience you have the kind of direct knowledge of a situation that makes this sort of theorizing superfluous. And more humanistically, subordinating the actuality of your life, your human interactions, etc. to like... static, lifeless ideas... it sucks! Why would you do this!

There are epistemic problems with social theorizing in general too, but that's not even the point, that's beside the point.

Before anyone is a proletarian, an autistic narcissist, a Bayesian agent... they are an individual, they are the person in front of me, right? Before any of my actions are elements of any system or pattern, they are my specific actions, taken in some moment to some specific end. All the concepts are secondary. The real world is actual.

Right? Right?

This is not really a fact claim so much as an... emotional claim? I am claiming the correctness of some specific outlook or way of relating to the world, not some specific set of facts. And actually I think there's a lot of value in the concept-first way of relating. I certainly don't want to embody it, to me it seems awful, sterile, frightening and lonely. But some people don't feel that way, they love it, and that's great on its own, and beyond that: through their way of engaging with the world they clearly produce all sorts of concepts that I and others like me would never think to produce, and some of those concepts are bound to turn out to be nonsense but some will turn out to be worthwhile, and there you go. There is value in being a uh... a conceptualist, I'm going to call this worldsense "conceptualism". But I don't want to be one. Or be expected to act like one, as is the implicit expectation on here. I want to be an actualist. I am an actualist.

See look. Even here I'm framing things in terms of concepts. I'm behaving now as a conceptualist. I don't do this naturally. But it's impossible not to write for your audience. It's impossible not to speak to your audience. Some people can do it but not me. Speech, for me, inherently involves a model of the other, and I cannot speak but specifically to the other I model. And on here, the other is conceptualist, so I behave as a conceptualist.

[barbrububble]

I am SO GLAD I am not working in education bc after a story of how students use chatgpt in university my blood was booooiling. Using it for text is bad enough (the point is the process and doing it yourself!!) but one guy "did Bayesian analysis" by telling chatgpt to do it!! How do you even know if it calculated anything using which parameters or just pretended to and gave you a fake text-predicted answer?

I would murder fr I'm so relieved I don't have to deal with this bs

[covid-safer-hotties]

Impact of vaccination on SARS-CoV-2 transmission in the UK: a modelling study - Preprint Posted Sept 7, 2024

An interesting preprint. TL;DR: Vaccination for covid in-and-of itself does little to halt the spread. We must take further measures such as masking, testing, distancing when ill, and improving ventilation/air quality indoors.

Abstract Background Efficacy and effectiveness of vaccines against SARS-CoV-2 infection, severe disease and death have been widely assessed. However, the impact of vaccination against SARS-CoV-2 transmission is far less well-characterized, and has major implications for public health, because it informs the indirect effects of vaccination in addition to its direct effects. Analysing the effects of SARS-CoV-2 vaccination on transmission is challenging, because they must be considered in tandem with the time-varying reproduction number (Rt), while also accounting for regional variability, for example due to the presence of more transmissible variants.

Methods We fitted a Bayesian hierarchical model to previously obtained estimates of Rt to estimate the effectiveness of vaccination with one, two and three doses on SARS-CoV-2 transmission in the UK during 2021. Vaccine effectiveness is defined as the proportional reduction in the time-varying reproduction number Rt. The model accounts for transmission at national and Lower Tier Local Authority (LTLA)-level, and uses vaccination data provided by the UK Health Security Agency (UKHSA), detailing the LTLA-specific proportions of people who have received doses one, two and three. The model also incorporates data on the proportion of wild-type, Alpha and Delta SARS-CoV-2 variants over time in each LTLA, obtained from UKHSA and the COVID-19 Genomics UK (COG-UK) Consortium.

Results We find that vaccination had moderate-to-large effectiveness against transmission for dose 1 (39.30%, 95% CrI 26.64% - 48.07%), and for dose 3 (48.69%, 95% CrI 27.97% - 71.30%), but negligible effects on dose 2, likely attributable to the coincident importation and dominance of the Delta variant in the UK. Nationally, our model fitted the previously estimated values of time-series of Rt values well, largely reproducing the reproduction number averaged across LTLAs for each timepoint. This lends support to our hypothesis that the extent of vaccination (or lack thereof) was a major determinant of transmission intensity. Our model fits further reproduced well the reproduction numbers at regional level, although outliers were less well captured, implying some degree of variation that is not explained by our model.

Conclusions To our knowledge, our analysis is the first evidence of the effectiveness of SARS-CoV-2 vaccination against its transmission at population level. We find that vaccination is an effective tool for the control of SARS-CoV-2 transmission, in addition to its well-documented effects on disease burden and mortality. Our results allow future assessment of the impact of vaccination accounting for several circulating variants and sociodemographic factors.

[vanity-complex]

Brb, flirting with a man on tinder by referencing Bayesian style statistical analysis.

[eccentric-nucleus]

like it is funny to think about the initial google bayesian spam filter that was so good it seemed magical -- it uses statistical analysis to detect spam that differs, statistically, from non-spam!! -- and how ultimately the thing polluting the web now is oh yeah we invented a generator that creates text that's statistically identical to human-generated text. whoops!

[compneuropapers]

Interesting Reviews for Week 40, 2024

What Role Does Striatal Dopamine Play in Goal-directed Action? Hart, G., Burton, T. J., & Balleine, B. W. (2024). Neuroscience, 546, 20–32.

Bayesian reinforcement learning: A basic overview. Kang, P., Tobler, P. N., & Dayan, P. (2024). Neurobiology of Learning and Memory, 211, 107924.

Is there selective retroactive memory enhancement in humans?: a meta-analysis. Koevoet, D., & Postma, A. (2024). Psychonomic Bulletin & Review, 31(2), 531–540.

Prägnanz in visual perception. Van Geert, E., & Wagemans, J. (2024). Psychonomic Bulletin & Review, 31(2), 541–567.

[raffaellopalandri]

Advanced Methodologies for Algorithmic Bias Detection and Correction

I continue today the description of Algorithmic Bias detection. Photo by Google DeepMind on Pexels.com The pursuit of fairness in algorithmic systems necessitates a deep dive into the mathematical and statistical intricacies of bias. This post will provide just a small glimpse of some of the techniques everyone can use, drawing on concepts from statistical inference, optimization theory, and…

[malbecmusings]

Even before al the bodies have been recovered, the blame game is in full swing over Perini Navi's 55m Bayesian that went down in a storm off Porticello, Sicily. I read this morning the chief of the group that owns Perini Navi came out swinging, putting the blame squarely on the crew.

There's a good technical analysis from designer Chris Feers below the cut.

TL;Don't want to read: Monohulls of all stripes are designed to survive a knockdown; Perini's engineering is some of he best in the world. Bayesian had a retractable keel which could shorten her 32' draft to 12'. With the keel extended, meaning she had full use her counterweight, she would have been able to right herself in a full knockdown. Even if her mast were below the waterline, even if she lost her mast, maybe more so if she lost her mast, assuming she was watertight, her design would allow her to self recover. With the keel retracted tho, her righting moment would be dramatically less. If she wasn't watertight, a knockdown would be unrecoverable and she would, as she did, quickly end up on the bottom of the ocean.

I have so many questions. We won't know the full story for a bit but seven people losing their lives should have been an avoidable outcome.

This is a one in a million tragedy but we should examine the facts and learn from them. Bayesian boasts the second highest mast in the world at 75 metres on a length of 56m. She has a lifting keel to enable her to get into shallow areas. Fully down it gives a draft of 9.83m and raised a draft of 4m. A sailing yacht has a keel to counter the heeling moment generated by the power of her sail plan. I’m sorry to say that size matters to a superyacht owner and naval architects are seduced into providing solutions. As yacht size increases the resistance of the hull reduces in proportion, so less sail area is required to adequately power longer yachts. But these floating fashion items are driven by appearance and bragging rights - and you lose prestige if someone has a bigger mast than you. Always the status pecking order questions are – how big – how fast – what cost – and is it black? If you designed Bayesian with a reasonable sail area and a ‘normal’ mast she would not look impressiive – which is what superyachts have to be.

The stability of a yacht has to be sufficient to counter the power of the rig but, as mast heights increase, the keels can often become so deep that the places of interest are restricted hence the lifting keel solution. Stability comes from two factors – the hull form and the ballast keel which acts like a pendulum. As the yacht heels the volume of the immersed hull section produce a buoyancy force which resists heeling. Initially the keel gives little force but as the angle of heel increases ‘physics’ makes the keel contribution significant (leverage). The greater the keel length, the greater the effect. The combination of the hull buoyancy on the heeled side and the keel on the ‘windward’ side produces the force necessary to keep the yacht from capsize. If the keel of Bayesian was retracted it would lose a significant six meters of moment arm or leverage from its probable 200 tons of keel bulb. When we design yachts we calculate the stability, or righting lever, as a function of heeled ‘bouyancy’ force and the ballast moment arm combined. (the GZ) This can be plotted on a graph to show the stability at any heel angle and identifies the angle at which stability becomes negative causing the yacht to capsize.

Normally an ocean yacht will experience a negative point at about 120 degrees of heel. With a lifting keel this point is greatly reduced maybe to less than 90 degrees. If Bayesian was at anchor with the keel raised and no sail up the crew would have every confidence that she could remain safe in most normal wind conditions. Every captain at this level has passed an exam on stability and would be aware of his vessels stability graph.

Many years ago I sat at Cremorne and watched a spiralling williwaw race across Sydney harbour and pass through Mosman. This twister was only about 30 metres wide but it destroyed houses and overturned cars in its path. A few feet away nothing was harmed.

The power of a twister is intense and powerful with the wind is coming from every direction. This was what hit Bayesian. The problem of large rigs is windage, even with no sails. But this yacht had three furling sails forward and a big boom with the weight of a furled mainsail inside all above the centre of gravity. Also there were a few communication domes on the spreaders.

We use a wind pressure coefficient to measure the force of the wind on the rig and sails. Even without sails the WPC for Bayesian must have been pretty large when hit by a wind force of varying direction with a local velocity way above the norm. Once she was knocked down beyond her stability limit with the keel up she stood no chance and, laying flat to the water, her deck openings would have allowed a flood of water aboard and she would founder. This would happen in a couple of minutes.

The observation of a lightning strike can be discounted because these vessels are grounded and any damage from a strike would have caused a slow sinking at worst – not a capsize and founder.

The individuals within a professional crew with sailing experience may have sensed the wind and motion of the vessel and quickly reacted to instinctively save themselves in the seconds they had. My guess is that some were already on deck alarmed by the general conditions.The guests would have found themselves totally disoriented in flooding cabins, in darkness with the walls, doors and passageways at ninety degrees to the norm. They had practically no chance because it would be completely beyond their experience. The crew would have been unable to be of any help due to the speed of the unexpected event.

I have been a professional yacht designer and builder for fifty years specialising in lifting keel yachts. My son, a professional navigator, was Third Officer on a ketch superyacht with masts 100m tall; a yacht so big, at 88metres, that it was almost beyond human handling even with the machinery on board. But of course it is the biggest and most expensive’ etc etc. What we have here is a one off accident which is a wake up call to an industry where common sense has departed as yachts get more silly in size and design.

In summary Bayesian was caught in the wrong place at the wrong time. A freak accident which the designers and crew would have little chance to predict.

If the keel had been down she would have probably survived the knock down. But without sails up the crew would have experience of her basic stability for normal conditions which would have felt adequate. Any enquiry must examine the design factors such as the stability vanishing point in the condition she was at the time of the accident; keel up, tank loadings and rig factors for windage (WPC) and centre of gravity etc. And a calculation of the wind force required to heel the boat to 90 degrees in the condition at the time of the accident.

All forms of transport have had these unpredictable one off events leading to changes of regulations and professional practice. Titanic, Boeing, 1955 Le Mans, the 1952 Farnborough crash, the 1979 Fastnet – all have made a difference and these events all came unpredicted and out of the blue often at a time of complacency.

Chris Freer – yacht designer – August 2024

[frithwontdie]

Are Ashkenazi Jews white? Short answer, No!

Ashkenazi Jews may appear white, but are not. Some identify as white and some don't. Even many jewish news articles claim their not white.

But what do the facts say?

Ashkenazi Jews are a genetically and culturally Middle Eastern people, who only began to “integrate” into European society after the rise of Liberalism in the 17th or 18th Century. Their history in Europe has been full of conflict. Being continually massacred, and expelled from every single European country that they have ever inhabited. It was clear that white Europeans considered jews to be categorically separate race from them. (plus the Jews also considered themselves separate from white Europeans as well). Plus the overwhelming majority have distinctly non-European phenotypes that are obviously Middle Eastern in origin.

Plus, the claim that they're white, is not supported by scientific, genetic evidence.

Despite their long-term residence in different countries and isolation from one another, most Jewish populations were not significantly different from one another at the genetic level.

Admixture estimates suggested low levels of European Y-chromosome gene flow into Ashkenazi and Roman Jewish communities.  Jewish and Middle Eastern non-Jewish populations were not statistically different. The results support the hypothesis that the paternal gene pools of Jewish communities from Europe, North Africa, and the Middle East descended from a common Middle Eastern ancestral population, and suggest that most Jewish communities have remained relatively isolated from neighboring non-Jewish communities during and after the Diaspora.”

The m values based on haplotypes Med and 1L were ~13% ± 10%, suggesting a rather small European contribution to the Ashkenazi paternal gene pool. When all haplotypes were included in the analysis, m increased to 23% ± 7%. This value was similar to the estimated Italian contribution to the Roman Jewish paternal gene pool.

About 80 Sephardim, 80 Ashkenazim and 100 Czechoslovaks were examined for the Yspecific RFLPs revealed by the probes p12f2 and p40a,f on TaqI DNA digests. The aim of the study was to investigate the origin of the Ashkenazi gene pool through the analysis of markers which, having an exclusively holoandric transmission, are useful to estimate paternal gene flow. The comparison of the two groups of Jews with each other and with Czechoslovaks (which have been taken as a representative source of foreign Y-chromosomes for Ashkenazim) shows a great similarity between Sephardim and Ashkenazim who are very different from Czechoslovaks. On the other hand both groups of Jews appear to be closely related to Lebanese. A preliminary evaluation suggests that the contribution of foreign males to the Ashkenazi gene pool has been very low (1 % or less per generation).

Jewish populations show a high level of genetic similarity to each other, clustering together in several types of analysis of population structure. These results support the view that the Jewish populations largely share a common Middle Eastern ancestry and that over their history they have undergone varying degrees of admixture with non-Jewish populations of European descent. We find that the Jewish populations show a high level of genetic similarity to each other, clustering together in several types of analysis of population structure. Further, Bayesian clustering, neighbor-joining trees, and multidimensional scaling place the Jewish populations as intermediate between the non-Jewish Middle Eastern and European populations. These results support the view that the Jewish populations largely share a common Middle Eastern ancestry and that over their history they have undergone varying degrees of admixture with non-Jewish populations of European descent.

A sample of 526 Y chromosomes representing six Middle Eastern populations (Ashkenazi, Sephardic, and Kurdish Jews from Israel; Muslim Kurds; Muslim Arabs from Israel and the Palestinian Authority Area; and Bedouin from the Negev) was analyzed for 13 binary polymorphisms and six microsatellite loci. The investigation of the genetic relationship among three Jewish communities revealed that Kurdish and Sephardic Jews were indistinguishable from one another, whereas both differed slightly, yet significantly, from Ashkenazi Jews. The differences among Ashkenazim may be a result of low-level gene flow from European populations and/or genetic drift during isolation.

Archaeologic and genetic data support that both Jews and Palestinians came from the ancient Canaanites, who extensively mixed with Egyptians, Mesopotamian and Anatolian peoples in ancient times. Thus, Palestinian-Jewish rivalry is based in cultural and religious, but not in genetic, differences.

One study 2010 study stated that Both Ashkenazi Jews and Sephardic jews share only 30% European DNA with the rest being of middle east decent. And by a recent 2020 study on remains from Bronze Age (over 3000 years ago) southern Levantine (Canaanite) populations suggests Ashkenazi Jews derive more than half of their ancestry from Bronze Age Levantine populations with the remaining 41% of their ancestry being European and 50% being Middle Eastern.

[darkmaga-returns]

There will be much more to this story as it unfolds but the Informed Consent Action Network (ICAN) has finally obtained the VAERS safety information produced by the FDA themselves.

During the pandemic, FDA conducted analyses of COVID-19 vaccine adverse events and tried to hide the results from the public. After two years of FOIA requests and lawsuits, FDA finally produced a portion of its “Empirical Bayesian (EB) data mining” reports. This type of analysis was designed to detect COVID-19 vaccine safety signals using VAERS reports. The data should be very revealing as far as what issues FDA was seeing during the vaccine rollout—especially given the agency has kept this data secret for years. This is the first time this critical data has been released to the public. An initial review of the records produced has revealed a long list of adverse events that far surpassed FDA’s “standard alert threshold”—meaning, there is (or should have been) great concern on the part of federal health authorities who were privy to this data. As just one example, ICAN discovered that “heavy menstrual bleeding” and “menstruation irregular” began showing up on the reports as early as April 2021!

I have only done a cursory review of the reported signals but what immediately caught my attention is that by 4th March, 2022, by their own metrics, all three US “vaccines” appear to be signalling serious adverse events, including

death (Janssen)

exposure via breast milk (Moderna, Pfizer)

suspected COVID-19 (Janssen); and

ineffectiveness (Pfizer).

If a product is ineffective, surely everything else is moot?! If that “ineffective” product is fatal in some cases, well…

No wonder they tried so shared to stop it being “shared more broadly”?