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What does the highlighted parts mean in the following passage?

Light striking your eyes is the most influential zeitgeber. When researchers invited volunteers into the laboratory and exposed them to light at intervals that were at odds with the outside world, the participants unconsciously reset their biological clocks to match the new light input. The circadian rhythm disturbances and sleep problems that affect up to 90% of blind people demonstrate the importance of light to sleep/wake patterns.

At intervals means occasionally but we don't know if all exposed durations are long equally.

"At odds with something" means "in disagreement" so volunteers exposed to light in nights but did not expose to light in daytime, it is kind of contrary to light outside.

Is this right?

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At intervals means that there was time in between. If you wanted to express that the periods of light exposure were equally spaced (though not necessarily equal in duration) you could say at regular intervals, which is a common phrase.

at intervals

  1. With time between; not continuously:
    the light flashed at intervals

Oxford Dictionaries

In this context, to be at odds with means to differ from:

at odds

  1. appearing not to correspond or match
    the silvery hair was at odds with her youthful shape

Collins Dictionary

Put together, it means that the participants were exposed to light/dark cycles, but that those cycles were different from the day/night cycles of the outside world. This doesn't mean that the cycles were the opposite, as it sounds like you have guessed. It just means that they were not the same. Most likely, since it was an experiment, they varied the times of the artificial "day" and "night" to check that the participants were syncing to that and not to the outside world.

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