Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prediction, Retrodiction, and The Amount of Information Stored in the
  Present   We introduce an ambidextrous view of stochastic dynamical systems, comparing
their forward-time and reverse-time representations and then integrating them
into a single time-symmetric representation. The perspective is useful
theoretically, computationally, and conceptually. Mathematically, we prove that
the excess entropy--a familiar measure of organization in complex systems--is
the mutual information not only between the past and future, but also between
the predictive and retrodictive causal states. Practically, we exploit the
connection between prediction and retrodiction to directly calculate the excess
entropy. Conceptually, these lead one to discover new system invariants for
stochastic dynamical systems: crypticity (information accessibility) and causal
irreversibility. Ultimately, we introduce a time-symmetric representation that
unifies all these quantities, compressing the two directional representations
into one. The resulting compression offers a new conception of the amount of
information stored in the present.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org