Here are some thoughts but please feel free to exercise your own creativity!
Text: I would like the "i" in BiOS could be lower case. Perhaps the dot of the "i" could be a small geometrical figure? Perhaps this could be replicated for the "i" in institute? Maybe the words "BiOS Institute" could be written in legible way/font that resembles Sanskrit (the sacred language of the Vedas, see attached)? NOTE: the text should be graphically compatible with Arial Black, which is the font on the rest of the website.
Graphics: I like the complexity of yantras, particularly the sri yantra (see attached) as it pertains to the metaphysic of Indian architecture. Even if you just incorporated the words "BiOS Institute" with the Sri yantra, that may be perfect. Feel free to modify/simplify the sri yantra to make it more graphically pleasing. Other yantras or sacred geometries could be okay too but nothing to generic (i.e. golden rectangle).
Color: The logo should be monochrome, charcoal gray on a plain white background (see the attached snapshot from our website)
Other: Our logo will be engraved on a stainless stell business card. We have attached a couple of yantras on metal cards that we like. This is the vibe we are going for.
Format: vector-based file