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I'm just curious to know what are the most important requirements for filling up Ph.D. application, generally. is job resumes important if available? Or for example GRE, Publications or Research interest? What is more important?

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Acceptance into a doctoral program isn't a matter of accounting and counting chits. Someone, or a group, needs to make the assessment that you are highly likely to be successful. To that end your GPA is relevant, but so is everything you write or say as part of the process. If you are considered to be a serious candidate with a fairly easily predictable good future, you will be considered.

After that, it can be a matter of competition. There will be a lot of other candidates that have excellent records and they are also being "weighed".

But certainly, anything that shows past success in the kinds of things that doctoral students actually do (pubs, research) is a big plus. But don't neglect your SOP, where you talk about your envisioned future.

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Recommendation Letters and Research Experience

The PhD admissions committee wants to know if an applicant will be a successful researcher. That is a nebulous quality. GPA, GRE, and other numerical scores only give a partial picture, since coursework and exam-taking are very different from open-ended research.

The best indicator of research ability is prior research experience and how well that went. How well your prior research went is best indicated by the recommendation letters of the people who worked with you.

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Taking a graduate student is a big investment for a PI. That person will consume financial resources, affect lab culture, and will be responsible for forwarding the PIs own agenda and reputation. And, grad students stick around a long time, so personality/fit is important.

Aside from test scores, most PIs want someone who

  1. Has demonstrated interest and capability in the field (demonstrated through publications, manuscripts, or personal conversations)
  2. An understanding of what they’re getting themselves into (demonstrated through undergrad research, conference attendance, etc)
  3. Passion to work hard and grow intellectually and professionally (demonstrated through personal conversations and letters of recommendation)

I would say these points weigh equally if not more than raw test scores. I have no shortage of examples of highly successful students with less than stellar test scores (though institutions also have their own bar for that).

Most important is that you pursue a personal approach. Call the PI personally and express your limitless interest and excitement.

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Or for example GRE, Publications or Research interest? What is more important?

Previous publications can be a very strong indicator of ability to do well in a PhD program, particularly if they are well written and in reasonable journals. When a student applies for a PhD program with published papers already under their belt, this can be a strong factor.

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The ability to conduct high-quality independent research is probably one of the most important aspects most advisors (PIs) look for in potential candidates. Of course, there are several ways to gauge that aspect; for example, prior research experience, publications, the ability to formulate research problems, etc. After all, your PhD success will depend on how good you are as a researcher. I should also add that the answer will probably be field-dependent.

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