"its common for those on lowcarb diets to end up suffering from depression, absent mindedness and other related problems"
out of curiousity, do you have a resource you could post for that statement?
Your next statement is partially incorrect. The brain certainly uses glucose from dietary carbohydrate for energy, but through gluconeogenesis, it's certainly capable of converting protein to glucose, your body does it all the time.
Not to mention that the precursor to serotonin (and niacin) is tryptophan, an amino acid, not a carbohydrate, though found in some carbohydrate-rich, it's not the primary source for our bodies. Glucose is used to fuel neurons, but astrocytes can use glucose from gluconeogenesis as well as ketone bodies for fuel, too.
Depression also isn't soley based on serotonin levels as is evidenced by the wide range of problems with depression...it also involves dopamine and norepinephrine in most cases. So the correlation between eating few carbohydrates and depression isn't likely the case. Blood sugar spikes can certainly make a person temporarily feel better after noshing on a candy bar if they're hungry, but alternatively, your body isn't necessarily going to go into depression when eating carbohydrates from vegetables as opposed to sugar (the basis of low-carb diets).