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I am in a bit of a situation. Basically, the research on which I was basing my PhD was carried out by a former post-doc in our group. After one year and a half not being able to replicate his results, I exploited my admin privileges on our cluster to download his codes. I discovered that the algorithms he used in his publication are different from the ones used in the experiments, as the ones he claims he is using are not really applicable and the ones he is using do not have the claimed complexity. He even went so far to provide made up (theoretical) timings to cover this up.

My supervisor knows about this issue from me and he also knows that the post-doc has stopped responding to my mails trying to replicated his work. My supervisor is very hands-off and I don't believe that he has any fault in this but his name is on the publication. Moreover, I feel he is disappointed in the post-doc and feels guilty. So, it seems to me that pressing the issue does no good for me and I have stopped mentioning the topic to my supervisor. (I am still quite angry about this issue as this has cost me about a year and a half of my PhD)

I have been able to salvage the original idea of the publication and come up with an algorithm which has the correct complexity and we are now writing the paper. To the reader these two publications might appear extremely similar and I would like to include a sentence in the introduction that the previous publication is not a working algorithm. What is a good, diplomatic way of doing this?

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    There isn’t a diplomatic way to expose someone as having committed academic fraud. You either expose him undiplomatically and face the shitstorm that is likely to follow, or give up the idea of insinuating that his algorithm doesn’t work as claimed.
    – Dan Romik
    Apr 26 at 15:51
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    @DanRomik While I fully agree that in case of fraud, there is no nice way to resolve the issue, I would give first give the benefit of doubt to the people involved. Being sloppy, making wrong assumptions, or making errors, even when they are serious is not the same as committing academic fraud.
    – Greg
    Apr 27 at 3:18
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    @Greg did you read the question? Academic fraud is what the question is about, and I don’t see a point in questioning OP’s premise, which seems based on very clear evidence.
    – Dan Romik
    Apr 27 at 3:39
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    @DanRomik It's quite possible that the OP has missed or misinterpreted some of the post-docs work, especially when they haven't even been able to talk to them about it. It seems safer to approach it as improving/making corrections to prior work than to approach it with big accusations. Apr 27 at 19:32
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    I exploited my admin privileges on our cluster to download his codes → I suffer by just reading this part. Besides your actual problem, you should have your admin rights revoked after such a thing (at a minimum). Depending on the jurisdiction this can be theft, exposition of private data, and other monstruosities.
    – WoJ
    Apr 29 at 13:47
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There are lots of ways to go about this.

Since your advisor is a co-author on the previous paper, this may be difficult, since they are invested in the existing paper and have some credibility at stake. Theoretically, they should be happy to retract/rewrite the older paper, but we are human. You are probably correct that they feel guilty- everyone with their name on the paper is ultimately responsible for all of the content.

At the same time, this can make some things easier for you. Finding an error in previously published work opens some new avenues for publication. Now, instead of a simple sentence, you can issuing a comment or a correction on a previous paper - many journals will allow you to publish a correction or remark on their previous articles, particularly if you can demonstrate a major problem or flaw.

Critically, do not be a jerk about this process. Simply state that there has been an oversight or error in the work by XYZ. Do not speculate as to why it went wrong or how. Even with evidence that their results do not match their data, there could be numerous reasons for it. Journals don't want to be told they did a bad job, neither does your advisor- but everyone would prefer you correct an error softly and with tact rather than letting someone else do it loudly and disruptively.

Edit: I am not sure your evidence is legally obtained, nor am I fully confident from this post that the evidence is conclusive that they were fraudulent. Until both of those conditions are met, I wouldn't recommend making accusations of data fabrication - publicly or privately. You will have, in all likelihood, a legal battle - for which I am not a lawyer. But you can conclusively say, as another commenter mentioned: "We were not able to reproduce the results."

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    That's right, as he couldn't reproduce the result of the previous paper, and he has a working, thus probably different algorithm now, he just has to write: "A similar algorithm was presented in [X], but we were unable to reproduce the result. Our algorithm is novel because of [reasons], and is able to produce the excepted result." Not being able to reproduce something is a pretty big deal already. (This may be complicated by the authorship of the supervisor again, though.) @rptr5
    – Neinstein
    Apr 27 at 6:47
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    If anything I'd consider a research more credible if in a later paper they openly re-analyze their previous approach and correct their findings. I can understand though that this can be hard for some people.
    – user116079
    Apr 27 at 11:35
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    @Hakaishin It might vary based on the fields, but in my field (CS), the phrase "unable to reproduce prior work" doesn't have negative connotation. It simply means there could be some details that were omitted, or there could be a mistake in the original paper, or the author could not get the same data set/split, and many other reasons. So it's still reasonable to say.
    – justhalf
    Apr 27 at 16:06
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    @justhalf - that's great for CS especially in the light of this paper: Producing wrong data without doing anything obviously wrong! (Mytkowicz, Diwan, Hauswirth, Sweeney, 2009)
    – davidbak
    Apr 27 at 18:05
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    It seems patently implausible (in my field anyway) that an introduction as bare of details as "We could not reproduce [results from our own group], so we [redid it without further analysis]" would ever get past peer-review. I would expect to be asked aggressively about this in the review, and I might even expect that some reviewers would sound the alarm about it.
    – nben
    Apr 28 at 15:47
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If your advisor knows that the paper was published with fake claims/data and is not willing to take action, I would sincerely consider working under someone else's supervision. This should be something that keeps him up at night for one or two days, but after accepting the hit that his career will take for this mistake, it is absolutely fundamental that he takes action - even if the action goes against his own reputation.

If your advisor is also an author of the paper, this matter is also interesting for another reason: It exposes how little some of the authors know what the hell is going on behind a paper with their names...

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    "Gift authorship" is pretty common in a lot of stem fields. Often it is people's advisors who are receiving the authorship for merely providing funding to their group members.
    – Taw
    Apr 27 at 5:16
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    @Taw yes, I know. What do you think of this? Personally, I find it a very bad model. Apr 27 at 6:09
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    Convincing funding agencies that an idea is worth exploring and to get you money for it is non trivial. You should try it some times. Apr 27 at 13:22
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    Authorship is more complex than some people think. Many papers in stem fields require a variety of skills. I work a lot with biologists and doctors. I hope I'm not expected to check their cultures or observe them while they visit patients. And I'm sure nobody expects them to check my models and my code.
    – Luca Citi
    Apr 27 at 20:20
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    @LucaCiti it doesn't matter. After malpractice is discovered, the person in charge is expected to take action Apr 27 at 20:40
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Most universities should have a research integrity officer. You could contact them to ask what you should do next. We had to go through ethical research training, and the training said that you could even ask them a question "hypothetically" to explore your options without having to jump into accusations.

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If the previous paper is just sloppy, you can write something of the sort "We present an improved analysis of..." and then explain in your paper the advantages of your technique.

If there is scientific misconduct in the previous paper, ideally your supervisor would have it retracted. Also depends to a certain extent if the former postdoc is still in the same field.

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    I would like to second the retraction suggestion, but in principle, an erratum might be sufficient, if, as the topicstarter says, "To the reader these two publications might appear extremely similar".
    – sleepy
    Apr 26 at 16:52
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    This is not enough imho. I would add "We were not able to replicate the previous results."
    – PatrickT
    Apr 27 at 1:58
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Have a sit-down with your supervisor and speak openly and frankly about this. Prepare carefully how you are going to put this into words. Ask him how he would like to address the problem, but ultimately accept his decision, whether he bravely faces it or shrugs it off, because you have little to gain in dragging him down.

Write up a "Corrigendum" in which, with your supervisor's consent, you make references to the fact that you were unable to replicate the previous results. If your supervisor wishes, he can allege a "spreadsheet" error in the previous study, otherwise just leave it vague.

Hopefully no-one was seriously injured in the process: The time you spent attempting to replicate a fraudulent result is not entirely wasted, I'm sure. Whatever evidence you have uncovered about the fraud would not stand in a court of law. You have learned a valuable lesson: academia does have its fair share of incompetence and fraud.

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