10,324 research outputs found
Quasi-Random Influences of Boolean Functions
We examine a hierarchy of equivalence classes of quasi-random properties of
Boolean Functions. In particular, we prove an equivalence between a number of
properties including balanced influences, spectral discrepancy, local strong
regularity, homomorphism enumerations of colored or weighted graphs and
hypergraphs associated with Boolean functions as well as the th-order strict
avalanche criterion amongst others. We further construct families of
quasi-random boolean functions which exhibit the properties of our equivalence
theorem and separate the levels of our hierarchy.Comment: 27 pages, 6 figure
Join-irreducible Boolean functions
This paper is a contribution to the study of a quasi-order on the set
of Boolean functions, the \emph{simple minor} quasi-order. We look at
the join-irreducible members of the resulting poset . Using a
two-way correspondence between Boolean functions and hypergraphs,
join-irreducibility translates into a combinatorial property of hypergraphs. We
observe that among Steiner systems, those which yield join-irreducible members
of are the -2-monomorphic Steiner systems. We also describe
the graphs which correspond to join-irreducible members of .Comment: The current manuscript constitutes an extension to the paper
"Irreducible Boolean Functions" (arXiv:0801.2939v1
Cell fate reprogramming by control of intracellular network dynamics
Identifying control strategies for biological networks is paramount for
practical applications that involve reprogramming a cell's fate, such as
disease therapeutics and stem cell reprogramming. Here we develop a novel
network control framework that integrates the structural and functional
information available for intracellular networks to predict control targets.
Formulated in a logical dynamic scheme, our approach drives any initial state
to the target state with 100% effectiveness and needs to be applied only
transiently for the network to reach and stay in the desired state. We
illustrate our method's potential to find intervention targets for cancer
treatment and cell differentiation by applying it to a leukemia signaling
network and to the network controlling the differentiation of helper T cells.
We find that the predicted control targets are effective in a broad dynamic
framework. Moreover, several of the predicted interventions are supported by
experiments.Comment: 61 pages (main text, 15 pages; supporting information, 46 pages) and
12 figures (main text, 6 figures; supporting information, 6 figures). In
revie
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