1,589 research outputs found
Bayesian networks for enterprise risk assessment
According to different typologies of activity and priority, risks can assume
diverse meanings and it can be assessed in different ways. In general risk is
measured in terms of a probability combination of an event (frequency) and its
consequence (impact). To estimate the frequency and the impact (severity)
historical data or expert opinions (either qualitative or quantitative data)
are used. Moreover qualitative data must be converted in numerical values to be
used in the model. In the case of enterprise risk assessment the considered
risks are, for instance, strategic, operational, legal and of image, which many
times are difficult to be quantified. So in most cases only expert data,
gathered by scorecard approaches, are available for risk analysis. The Bayesian
Network is a useful tool to integrate different information and in particular
to study the risk's joint distribution by using data collected from experts. In
this paper we want to show a possible approach for building a Bayesian networks
in the particular case in which only prior probabilities of node states and
marginal correlations between nodes are available, and when the variables have
only two states
Basic and degenerate pregeometries
We study pairs , where is a 'Buekenhout-Tits'
pregeometry with all rank 2 truncations connected, and is transitive on the set of elements of each type. The family of such
pairs is closed under forming quotients with respect to -invariant
type-refining partitions of the element set of . We identify the
'basic' pairs (those that admit no non-degenerate quotients), and show, by
studying quotients and direct decompositions, that the study of basic
pregeometries reduces to examining those where the group is faithful and
primitive on the set of elements of each type. We also study the special case
of normal quotients, where we take quotients with respect to the orbits of a
normal subgroup of . There is a similar reduction for normal-basic
pregeometries to those where is faithful and quasiprimitive on the set of
elements of each type
A characterisation of weakly locally projective amalgams related to and the sporadic simple groups and
A simple undirected graph is weakly -locally projective, for a group of
automorphisms , if for each vertex , the stabiliser induces on the
set of vertices adjacent to a doubly transitive action with socle the
projective group for an integer and a prime power .
It is -locally projective if in addition is vertex transitive. A theorem
of Trofimov reduces the classification of the -locally projective graphs to
the case where the distance factors are as in one of the known examples.
Although an analogue of Trofimov's result is not yet available for weakly
locally projective graphs, we would like to begin a program of characterising
some of the remarkable examples. We show that if a graph is weakly locally
projective with each and or , and if the distance factors
are as in the examples arising from the rank 3 tilde geometries of the groups
and , then up to isomorphism there are exactly two possible
amalgams. Moreover, we consider an infinite family of amalgams of type
(where each and ) and prove that if
there is a unique amalgam of type and it is
unfaithful, whereas if then there are exactly four amalgams of type
, precisely two of which are faithful, namely the ones related
to and , and one other which has faithful completion
Locally -distance transitive graphs
We give a unified approach to analysing, for each positive integer , a
class of finite connected graphs that contains all the distance transitive
graphs as well as the locally -arc transitive graphs of diameter at least
. A graph is in the class if it is connected and if, for each vertex ,
the subgroup of automorphisms fixing acts transitively on the set of
vertices at distance from , for each from 1 to . We prove that
this class is closed under forming normal quotients. Several graphs in the
class are designated as degenerate, and a nondegenerate graph in the class is
called basic if all its nontrivial normal quotients are degenerate. We prove
that, for , a nondegenerate, nonbasic graph in the class is either a
complete multipartite graph, or a normal cover of a basic graph. We prove
further that, apart from the complete bipartite graphs, each basic graph admits
a faithful quasiprimitive action on each of its (1 or 2) vertex orbits, or a
biquasiprimitive action. These results invite detailed additional analysis of
the basic graphs using the theory of quasiprimitive permutation groups.Comment: Revised after referee report
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