I don't think that's as simple as the article tries to make it out to be.
As poorer people start moving into a neighborhood, the richer people will flee away en masse. It seems to me that rich people will pay any amount of money just to make sure they're living where other rich people are, even if that means moving somewhere less convenient.
As the poorer people start taking over a hood due to prices going down for whatever reason (e.g. building more "affordable" accommodation), it begins to deteriorate such that in a decade or two, it becomes a "rough" place with badly maintained houses, dirty streets, broken street lamps, youngster gangs roaming around and so on.
That's not the default of the poor people themselves only, I think, but a combination of them naturally having lower standards (so they complain less about broken things to the local government - not sure I can accept that poorer areas are less maintained because there's no people living there who are in government), less money to keep up with maintenance (so houses deteriorate and stop looking cute), higher tendency of the youngsters in getting involved in gangs and crime (simply because many of them have far fewer opportunities in life, and they become aware of that very early) and so on.
Where I live is not a rough hood by any means, but it's more "affordable" than many other places... and I can see at least some of these things happening here... the government doesn't keep the vegetation on public places nearly as well trimmed as in the rich areas, there's definitely less care with the quality of the street pavement, houses are not completely deteriorated but most are not in perfect shape either... I just need to walk around 20 mins to get into an area where everything changes and houses are all of a sudden perfectly well kept, the public areas are beautiful, even the people look "prettier".
This segregation seems to happen naturally with humans everywhere.