Original Math Notes
All Seasons
Season 5
Episode 503: Blowback
Assembly of a graphene sheet from random carbon rings
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 16:
          Exactly.  My aggregation model will
          filter through the characteristics
          of the victims searching for the
          strongest attributes in order to
          determine their most likely choice
          of seat.

Random Tree Aggregation »

In random tree aggregation, a new branch can be added anywhere. Each new branch placement is selected randomly from among the nodes already present.
Scene 20:
          -- speaking of rearranging
          molecules... did you see where
          Professor Eric Kolokoff has
          developed a new kind of graphene-
          based digital paper...

They back against the table. Larry stares at the screen.

Rolling Up a Sheet of Graphene »

A planar hexagonal lattice is rolled up into a cylinder. This can be an illustration of how a graphene sheet forms a nanotube of "armchair" geometry.
Scene 46:
          My program analyzed the DVD's...
          We're cool, it's all legit.  I'm
          under instructions from the LAPD to
          info share with the FBI.
          I got results by using a Hidden
          Markov Model...

Finite-State, Discrete-Time Markov Chains »

Consider a system that is always in one of n states, numbered 1 through n. Every time a clock ticks, the system updates itself according to an n×n matrix of transition probabilities, the (i,j)th entry of which gives the probability that the system moves from state i to state j at any clock tick. A Markov chain is a system like this, in which the next state depends only on the current state and not on previous states. Powers of the transition matrix approach a matrix with constant columns as the power increases. The number to which the entries in the ith column converge is the asymptotic fraction of time the system spends in state i.
Scene 46:
                    CHARLIE (cont'd)
          -- similarly, the data you
          presented appears to be an average
          distribution of police work.

ON SCREEN - data appears...

                    CHARLIE (cont'd)
          Until, like the stereogram, you
          continue to stare or look at the
          same data over and over again...
            (data changes)
          And a hidden pattern emerges.

Floating Disk Stereogram »

When this stereogram is stereo-viewed, a disk floats above or below a background rectangle.
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