Fish oil fatty acids: EPA & DHA.
I’ve read that EPA tends to show slightly better results in outcomes related to mood, whereas DHA tends to be slightly better for cognition. Not mutually exclusive; probably a lot of overlap. This meta-analysis by Martins showed EPA fared better than DHA for depressive symptoms (2009); another one here, stressing the high %EPA relative to %DHA necessary for improvements (Sublette et al., 2011). Whereas the reverse is true for certain cognitive outcomes in this study by Sinn and colleagues (2012). Very few studies test EPA vs. DHA directly, and their effects on metabolism are relatively similar. They’re the ball bearings of fatty acids.
, 
, 
, 
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… all have one thing in common: some degree of carbohydrate restriction.
is an effective weight loss strategy for many. 
, on the other hand, is a pathological condition caused by insulin deficiency. The common theme is low insulin; however, in ketoacidosis, blood glucose levels are very high. Ketone levels are elevated in both states, although are 10-20x higher in ketoacidosis (~0.5-2 vs. > 20 mM). Nutritional ketosis and ketoacidosis should not be confused with one another, and a ketogenic diet doesn’t cause ketoacidosis.
(GOS) (
can help, too, if they’re administered with either prebiotics or fermented foods (they need something to nourish them in transit). 
was much higher in fat, and as such, increased the prevalence of a microbe involved in fat digestion. “Bilophila.” The article focused on this one and cited a 
increased the levels of Bacteroides and decreased Firmicutes. These are the two that brought the whole gut microbe-obesity connection into the spotlight. The microbiome in obese mice is characterized by low Bacteriodetes and high Firmicutes. Fecal transplants from obese mice to lean mice causes them to gain weight. Little is known about Bilophila relative to Bacteriodetes & Firmicutes, and I suspect the focus was on Bilophila because the authors wanted something negative to say about a meat-based, fiber-free ketogenic diet, and that 
condition. They were then given 4 eggs (~23 g protein) that were labeled with two stable isotopes (15N & 13C, derived from hens fed isotope-enriched diets!). Throughout the entire study duration, the subjects were infused with a third isotope, 2H-glucose. By collecting and analyzing the enrichment of isotopically-labeled metabolites like expired CO2, urea, and glucose, the researchers were able to determine the fate of those 23 grams of protein.
measure urinary acetoacetate (AcAc) and reflect the degree of ketosis in the blood probably about 2-4 hours ago. 
measure beta-hydroxybutyrate (bHB) right now. bHB fluctuates to a greater degree, eg, it plummets after a meal whereas AcAc takes longer to decline. AcAc/bHB is usually around 1, but increases after a meal (
et al., 1997)