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Without adequate rest, the brain's ability to function quickly deteriorates. The brain works harder to counteract sleep deprivation effects, but operates less effectively: concentration levels drop, and memory becomes impaired.
Similarly, the brain's ability to problem solve is greatly impaired. Decision-making abilities are compromised, and the brain falls into rigid thought patterns that make it difficult to generate new problem-solving ideas. Insufficient rest can also cause people to have hallucinations. Other typical effects of sleep deprivation include:

depression
heart disease
hypertension
irritability
slower reaction times
slurred speech
tremors