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Note that in experimental fields it is not uncommon that an abstract is required to have "specific" unpublished results 9 months or so before the conference. The problem is if you are a theoretical/mathematical researcher in these lab based fields often your mathematical model and derivations are the crux of your research and a numerical exploration comes later. How do you write an abstract for these fields highlighting that you derived the model, proved a bunch of existence and uniqueness properties (that they likely don't care about) and have just started your exploration of numerical examples (likely the only thing they care about) without having anything definitive to say yet about your numerical examples.

The most definitive thing I could say about the numerical examples is, "We show that for a given set of parameter space we observe X and for another set of parameter space we observe Y. This is the consequence of X being true in contrast to Y being true in our field of application". To be clear I don't know anything about the structure of the parameter space that yield the two distinct X and Y scenarios yet, but I do know that both X and Y are possible given some preliminary simulations, and that the difference between X and Y is interesting.

One thing to note is this is not a conference that includes a proceedings. You have an abstract and a talk, but no paper comes out of it. Papers are strictly for peer reviewed journals in this field. The answers to this question How to write abstract for conference when you have no results yet? seem to be more geared towards fields where papers come out of the conference.

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    From experience: you just cannot simply publish without (numerical) results. Why? Applied people rely on those to qualitatively assess the value of your work. They have to compare it and the interested readers in those fields almost always judge a method by figures and numbers. They need to decide if that method is worth implementing, regardless of the approach's novelty constituents. Your one and only chance is to deliver a narrative (in the abstract) that clearly emphasizes why this method would surely beat state of the art alternatives. Otherwise, go for another conference.. – teodron Feb 19 '14 at 9:13
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    Both publishing and disseminating of a method require you convince the auditorium of the method's validity and quality. If it's an applied field crowd you'll be addressing, they'll cough asking for some sort of benchmarks. Sorry, but this is how these guys "roll". Pure mathematicians do not understand/do not care of how a method performs if it's novel enough (if you just show that one thing implies another thing or generalizes it, it's fine with them), whereas applied maths people will often care only about concrete gains and applicability. Alas, it also depends on the conference's reputation. – teodron Feb 19 '14 at 15:44
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    As a clear answer: present a proof or a narrative explaining clearly why your method improves upon a specific subject. That proof is valuable for both experimentalists and theorists, as it definitely decides upon the qualities of your method. Doing so, I see no point in why you won't be accepted to speak there :). You may also find some people keen on verifying your findings and thus producing the so-called results.. – teodron Feb 19 '14 at 15:53
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    Also, enunciating the obvious a bit: it sounds like you come from a more theoretical background (you might consider providing some professional information about yourself on your profile page; it can only help you get more appropriate answers, but from your other questions and answers I guess you are in a rather math-heavy branch of statistics) and you are finding the norms of speaking in this conference to be a bit awkward and outside of your comfort zone. Maybe then you can just attend the conference without giving a talk in it? – Pete L. Clark Mar 24 '14 at 0:12
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    @JeffE Some of my most productive collaborations have come from conferences that generated exactly this kind of problem. – Fomite May 29 '14 at 17:56
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Writing as a mathematical modeler in Epidemiology, and a regular submitter to conferences with these types of requirements, which are dominated by empirical research findings, this is something that's hard, if you approach it from the direction you have - with the numerical results coming at the "end" of your research.

It would be good to have a numerical result, because as has been mentioned, while you might not view these as the crux of your research, it may very well be the crux of why someone is interested in your research. Even as someone who does appreciate the theory side of things, I'm often rather more interested in the numerical results.

That being said, these conferences are mostly looking to avoid "Will be discussed" results, where there's no means to evaluate if you've done anything, or if it will be interesting. The latter is especially hard for deciding whether a presentation becomes an oral or poster presentation, because giving one of the precious oral slots to someone whose going to largely be discussing a slew of null results is (often) irksome.

You do however have results, and that should be enough to make it past the bar. If X and Y are both possible within the parameter space, and that means something for the field, then that is a specific result, and you should expand on why that's interesting.

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It does depend on the type and reputation of the conference, but in my experience most conferences that are not publishing their proceedings will accept all abstracts that are clearly written and have no overt language, logic, factual, or similar critical problems. Looking at the question you linked to, I think exactly the same advice that is posted there is relevant to conferences with no published proceedings. I say this because the goal of your abstract here is primarily to attract attention and get people to attend your talk. (But, does this conference publish its abstracts? Some do.)

Following the advice given in the answers to the linked question will achieve this goal without putting you in an ethical challenge or leading you to claim things that turn out to be untrue or, worse, so misguided or ambitious that it's embarrassing.

It's up to you to convince the reader of your abstract that you will have compelling numerical results by that time. This comes from explaining your methodology and approach in a way that will seem reasonable and so can be reasonably expected to lead to exciting, specific results. If you don't expect to, then maybe your project isn't well designed or well suited to this audience.

It never hurts to have a short abstract regardless of the conference rules on length. KISS! (Keep It Simple, Stupid) is appropriate here. If you are severely lacking anything interesting to say right now, it could be as straightforward as a paragraph version of: "We will present numerical results from a novel form of mathematical analysis of problem X, which will impact Y." If the audience is interested in topics X or Y then they might well show up regardless of their confidence in what new results you'll have.

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