After two years doctors finally were able to figure out why an 8-year-old Australian boy had high concentrations of lead in his body. It started when the unnamed boy complained of a stomachache severe enough to warrant a doctor visit. Doctors then found over 50 lead pellets trapped inside the boy's appendix--with no explanation for how the pellets got there from the digestive tract. However, the physicians didn't suspect this unusual location right away, according to a LiveScience report. After identifying foreign objects inside what looked like the boy's stomach, doctors flushed his digestive system out--but the objects remained unchanged.
A key challenge in sequential decision problems is to determine how many samples are needed for an agent to make reliable decisions with good probabilistic guarantees. We introduce Hoeffding-like concentration inequalities that hold for a random, adaptively chosen number of samples. Our inequalities are tight under natural assumptions and can greatly simplify the analysis of common sequential decision problems. In particular, we apply them to sequential hypothesis testing, best arm identification, and sorting. The resulting algorithms rival or exceed the state of the art both theoretically and empirically.
Reviewing statistics from the final quarter of 2016, Tauer discovered among Jackson County workers 65 and older there was a higher concentration in retail trade; professional, scientific and technical services; real estate, rental and leasing; and other services when compared with overall figures. He added differences were only between 1 and 3.4 percentage points. Not surprisingly, there was less concentration in physically demanding construction and manufacturing sectors.
The historical result of concentration of measure theory was obtained on the uniform distribution on the sphere by Lévy Lévy (1951) and later formalized by Milman and Gromov Gromov and Milman (1983) who extended the approach to other families of distributions, notably involving isoperimetric inequalities and the Ricci curvature. To present the simplest picture possible, we admit for the moment that what we call "concentrated vectors" (or "Lipschitz concentrated vectors") are transformations X F(Z) R
U.S. Vice President Mike Pence arrives to the gate of former German Nazi concentration camp in Dachau near Munich, Germany February 19, 2017. DACHAU, Germany -- U.S. Vice President Mike Pence paid a somber visit to the site of the Dachau concentration camp on Sunday, walking along the grounds where tens of thousands of people were killed during World War II. Pence was joined by his wife, Karen Pence, and the couple's 23-year-old daughter, Charlotte, as they toured the exhibits at the former concentration camp that was established by the Nazis in 1933 near Munich. The vice president was accompanied by Abba Naor, a survivor of the camp, and other dignitaries as he passed through the wrought iron gate bearing the inscription, "Arbeit macht frei," or "Work sets you free." The Pences placed a wreath beneath the International Memorial at the center of the camp, toured the barracks and viewed the ovens inside the crematorium.