The socionics functions are defined in a somewhat vague, inconsistent fashion (I've seen awareness of essences ascribed to both Ne and Ni, being a good judge of character ascribed to both Fi and Fe, etc.), and none of the socionics types are entirely good descriptions of my personality, so I've had difficulty settling on a type and quadra for myself. The types that I've eliminated as possibilities are INTp and INFj, because my experiences with ESFjs and ESTps make it clear that they're not my Conflictors. I also have doubts that I'm an INTj, another of the types that would initially seem plausible, because, while I haven't interacted much with ESFps, the profile I read for that type on Wikisocion described what sounded to me like an awesome person. I'm also disinclined to think that I'm someone who, like an INTj, is looking for a Caregiver, because I tend to feel uncomfortable when people take care of me, and my physical, Si-oriented needs seem to be something that I'm at least as capable of handling as anyone else would be.
Getting more in-depth on functions, and putting the focus more on specifically quadra-oriented matters. The one thing that is immediately clear to me is that I'm more Fe+Ti than Fi+Te. I enjoy outward emotional expressiveness, and if someone possesses it, that, to me, is one of the strongest points that they could have in their favor. Another point against socionics Fi is that it tends to strike me as being intrusive; Fi-valuers are especially prone to expect you to conform to their personal morals, and when you don't, they can be over-willing to express their disapproval and drag down a good social atmosphere. Also, perhaps by its nature, Fi is prone to have scruples about the kinds of things that seem, to me, to be largely irrelevant to anyone except the Fi-valuer himself. I do not enjoy being held to someone else's standards when there's no clear external benefit to being in that position.
As far as Ti vs. Te, I do value practicality, like a Te-valuer, and I'm generally a methodical person, but at the same, I'm prone to disregard the facts, laws, and statistics of physical reality, viewing them as shallow and frequently deceptive. On the other hand, there's not really much I could say against socionics Ti--it's something that I clearly use and value, and being good at it is important for my self-esteem--except that I have limited patience for internal logic as an end unto itself. The beauty of numbers, grammar or a musical tuning system are meaningless to me unless I think familiarizing myself with them will help me to achieve a goal dependent on an understanding of them. It could be argued that that is a case of Ti working at the service of Te, but since it's clear that I value Fe, and all of the more plausible Te-valuing types have been eliminated as possibilities, it may as well be considered as clear evidence that I value Ti.
As far as Ni+Se vs. Ne+Si, I'm not nearly as sure which of them I value. The difference between Ni and Ne, and what each of them means independently, is not especially clear to me; many of the key traits ascribed to one are elsewhere ascribed to the other, and reading about one of them by itself does not leave me with a very cohesive impression (I could say the same thing about a few of the other socionics functions, like Fi, which seems like an awkward marriage of MBTI Fe and Fi). I'm slightly more confident about placing myself on the Se vs. Si spectrum. If I were to look at Si by itself, it would be difficult for me to decide whether I value it or not. In favor of valuing it, I'm slightly health-nuttish, I have limited tolerance for unpleasant sensory experiences, and my self-esteem is largely based on my appearance. But I often ignore Si-related things; I let myself go cold and hungry and thirsty, while other people express their concern over my physical comfort, to which I respond with assurances that I'm fine, rather than with the enthusiasm that would be expected of an Si-valuer. This contradicts what I said--that I have little tolerance for unpleasant sensory experiences--but it's true. I explain that by saying that my awareness of Si is very off-and-on. Whether Si is more positive or negative to me is difficult to say. I find it to be a cause of great stress, to have a body that is subject to ugliness, pain and ruin; my body is really my Achilles' heel. On the other hand, I do love sensory beauty, on occasion, although I often ignore it. As for my feelings toward Se, they're less ambiguous, and I'm prone to say that I value the function. The people who are active, confident, and strong-willed are the ones whom I tend to admire the most. And the thing I want more than anything else is to be powerful.
If I value Se over Si, it follows that I value Ni over Ne. If I also value Ti and Fe over Fi and Te, it follows that I'm in Beta Quadra, which is a conclusion that I'll gladly accept. Delta Quadra seems a little boring to me; Gamma Quadra seems a bit unfriendly and slightly too serious; Alpha Quadra is somewhat more child-like than where I would feel at home; and Beta Quadra strikes me as being full of cool and exciting people.