60 research outputs found
Projecting social contact matrices to populations stratified by binary attributes with known homophily
Contact networks are heterogeneous. People with similar characteristics are
more likely to interact, a phenomenon called assortative mixing or homophily.
While age-assortativity is well-established and social contact matrices for
populations stratified by age have been derived through extensive survey work,
we lack empirical studies that describe contact patterns of a population
stratified by other attributes such as gender, sexual orientation, ethnicity,
etc. Accounting for heterogeneities with respect to these attributes can have a
profound effect on the dynamics of epidemiological forecasting models.
Here, we introduce a new methodology to expand a given e.g. age-based contact
matrix to populations stratified by binary attributes with a known level of
homophily. We describe a set of linear conditions any meaningful social contact
matrix must satisfy and find the optimal matrix by solving a non-linear
optimization problem. We show the effect homophily can have on disease dynamics
and conclude by briefly describing more complicated extensions.
The available Python source code enables any modeler to account for the
presence of homophily with respect to binary attributes in contact patterns,
ultimately yielding more accurate predictive models.Comment: 20 pages, 3 figures, 4 table
Canalization reduces the nonlinearity of regulation in biological networks
Biological networks such as gene regulatory networks possess desirable
properties. They are more robust and controllable than random networks. This
motivates the search for structural and dynamical features that evolution has
incorporated in biological networks. A recent meta-analysis of published,
expert-curated Boolean biological network models has revealed several such
features, often referred to as design principles. Among others, the biological
networks are enriched for certain recurring network motifs, the dynamic update
rules are more redundant, more biased and more canalizing than expected, and
the dynamics of biological networks are better approximable by linear and
lower-order approximations than those of comparable random networks. Since most
of these features are interrelated, it is paramount to disentangle cause and
effect, that is, to understand which features evolution actively selects for,
and thus truly constitute evolutionary design principles. Here, we show that
approximability is strongly dependent on the dynamical robustness of a network,
and that increased canalization in biological networks can almost completely
explain their recently postulated high approximability.Comment: 21 pages, 8 figure
Collectively canalizing Boolean functions
This paper studies the mathematical properties of collectively canalizing
Boolean functions, a class of functions that has arisen from applications in
systems biology. Boolean networks are an increasingly popular modeling
framework for regulatory networks, and the class of functions studied here
captures a key feature of biological network dynamics, namely that a subset of
one or more variables, under certain conditions, can dominate the value of a
Boolean function, to the exclusion of all others. These functions have rich
mathematical properties to be explored. The paper shows how the number and type
of such sets influence a function's behavior and define a new measure for the
canalizing strength of any Boolean function. We further connect the concept of
collective canalization with the well-studied concept of the average
sensitivity of a Boolean function. The relationship between Boolean functions
and the dynamics of the networks they form is important in a wide range of
applications beyond biology, such as computer science, and has been studied
with statistical and simulation-based methods. But the rich relationship
between structure and dynamics remains largely unexplored, and this paper is
intended as a contribution to its mathematical foundation.Comment: 15 pages, 2 figure
Revealing the canalizing structure of Boolean functions: Algorithms and applications
Boolean functions can be represented in many ways including logical forms,
truth tables, and polynomials. Additionally, Boolean functions have different
canonical representations such as minimal disjunctive normal forms. Other
canonical representation is based on the polynomial representation of Boolean
functions where they can be written as a nested product of canalizing layers
and a polynomial that contains the noncanalizing variables. In this paper we
study the problem of identifying the canalizing layers format of Boolean
functions. First, we show that the problem of finding the canalizing layers is
NP-hard. Second, we present several algorithms for finding the canalizing
layers of a Boolean function, discuss their complexities, and compare their
performances. Third, we show applications where the computation of canalizing
layers can be used for finding a disjunctive normal form of a nested canalizing
function. Another application deals with the reverse engineering of Boolean
networks with a prescribed layering format. Finally, implementations of our
algorithms in Python and in the computer algebra system Macaulay2 are available
at https://github.com/ckadelka/BooleanCanalization.Comment: 13 pages, 1 figur
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