Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions in Operational Risk   In this paper we explore the functional correlation approach to operational
risk. We consider networks with heterogeneous a-priori conditional and
unconditional failure probability. In the limit of sparse connectivity,
self-consistent expressions for the dynamical evolution of order parameters are
obtained. Under equilibrium conditions, expressions for the stationary states
are also obtained. The consequences of the analytical theory developed are
analyzed using phase diagrams. We find co-existence of operational and
non-operational phases, much as in liquid-gas systems. Such systems are
susceptible to discontinuous phase transitions from the operational to
non-operational phase via catastrophic breakdown. We find this feature to be
robust against variation of the microscopic modelling assumptions.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph