I had the same thought as elgado about the Omega, but I'd say regarding the spartan logo, a downward V or arrow is the symbol used by the ancient greek city-state which they take their name from. The university's Logo is not crescents but if you look carefully the bottom is attached and hinged, it's forceps of some kind (representing a tool of research)
The forceps around the atom is an interesting observation. Perhaps it is because the atom by itself does not lead to knowledge and enlightenment, but rather through observations made possible by use of each side to grasp it.
So, the question is what does the color duality represent? Quantitative and Qualitative analysis?
The Gaians is a thorned stem surrounding a flower. The flower represents reproduction and the perfection of natural processes, while the thorned stem clearly indicates their will to safegaurd it. While Environmentalism does have pacifist tendencies, any Ecologist knows that nature can be violent and ruthless.
As for the Hive, recall that Yang is quoted in the Mono-Polar magnets tech saying that 'Yin-Yang Dualism can be over-come', with sufficent enlightenment. Thusly is half covered in blue, that half is overcome with enlightenment. The other half, if I were to really reach I would guess is three layered. The first layer, white, is the purity and nobility of their motives. The second layer, black, is the harsh road of adversity it requires. The third layer, white in the center, is the enlightenment attained though acting towards their 'greater good'. Along with that, of course, it's a Ying Yang which has significance in and of itself.