The plumber ran the dishwasher and ran water in the kitchen sink. There was no water leaking out onto the floor, so it was obvious that the problem was coming from the neighboring apartment. However, no one was at home next door, so he could only offer a temporary solution until he makes an appointment to see the neighbors. Since I do not use the dishwasher (I have always been a "wash the dishes by hand kind of guy") he disconnected the dishwasher and plugged up the connection. I gave the plumber my email address so that he could inform me when he returns to see the neighbors.
Just in case the "temporary fix" doesn't work, I have thrown into the washer the towels and rags that the cleaning lady used to create a "dam" around the affected area. After they come out of the dryer I will put the "dam" back in place.
We will see what happens next!