Rossmo's formula
Rossmo's formula is a geographic profiling formula to predict where a serial criminal lives. It relies upon the tendency of criminals to not commit crimes near places where they might be recognized, but also to not travel excessively long distances. The formula was developed and patented in 1996 by criminologist Kim Rossmo and integrated into a specialized crime analysis software product called Rigel. The Rigel product is developed by the software company Environmental Criminology Research Inc. (ECRI), which Rossmo co-founded. Formula. Imagine a map with an overlaying grid of little squares named sectors. If this  map is a raster image file on a computer, these sectors are pixels. A sector formula_1 is the square on row "i" and column "j", located at coordinates formula_2. The following function gives the probability formula_3 of the position of the serial criminal residing within a specific sector (or point) formula_2: formula_5 where: formula_6 Here the summation is over past crimes located at coordinates formula_7. formula_8 is a characteristic function that returns 0 when a point formula_2 is an element of the buffer zone B (the neighborhood of a criminal residence that is swept out by a radius of B  from its center). formula_8 allows "p" to switch between the two terms. If a crime occurs within the buffer zone, then formula_11 and, thus, the first term does not contribute to the overall result. This is a prerogative for defining the first term in the case when the distance between a point (or pixel) becomes equal to zero. When formula_12, the 1st term is used to calculate formula_3. formula_14 is the Manhattan distance between a point formula_2 and the "n"-th crime site formula_7. Explanation. The summation in the formula consists of two terms. The first term describes the idea of  decreasing probability with increasing distance. The second term deals with the concept of a "buffer zone". The variable formula_17 is used to put more weight on one of the two ideas. The variable formula_18 describes the radius of the buffer zone. The constant formula_19 is empirically determined. The main idea of the formula is that the probability of crimes first increases as one moves through the buffer zone away from the "hotzone", but decreases afterwards. The variable formula_20 can be chosen so that it works best on data of past crimes. The same idea goes for the variable formula_21. The  distance is calculated with the Manhattan distance formula. Applications. The formula has been applied to fields other than forensics. Because of the buffer zone idea, the formula works well for studies concerning predatory animals such as white sharks. This formula and math behind it were used in crime detecting in the Pilot episode of the TV series "Numb3rs" and in the 100th episode of the same show, called "Disturbed".