# 7.1 Probabilistic boolean and bayesian networks

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This course is a short series of lectures on Statistical Bioinformatics. Topics covered are listed in the Table of Contents. The notes were preparedby Ewa Paszek, Lukasz Wita and Marek Kimmel. The development of this course has been supported by NSF 0203396 grant.

## Probabilistic boolean networks

In a Boolean network, each (target) gene is ‘predicted’ by several other genes by means of a Boolean function (predictor). Thus, after having inferred such a function from gene expression data, it could be concluded that if we observe the values of the predictive genes, we know, with full certainty, the value of the target gene. Conceptually, such an inherent determinism seems problematic as it assumes an environment with no uncertainty. However, the data that used for the inference exhibits uncertainty on several levels.

Another class model called Probabilistic Boolean Networks (PBNs) (Shmulevich et al., 2002) shares the appealing properties of Boolean networks, but is able to cope with uncertainty, both in the data and the model selection. A model incorporates only a partial description of a physical system. This means that a Boolean function giving the next state of a variable is likely to be only partially accurate.

The basic idea is to extend the Boolean network to accommodate more than one possible function for each node. Thus, to every node xi . , their corresponds a set Fi={ fj },j=1,..., l(i) , Where each fj is a possible function determining the value of gene xi and l(i) is the number of possible functions for gene xi . A realization of the PBN at a given instant of time is determined by a vector of Boolean functions, where the ith element of that vector contains the predictor selected at that instant for gene xi . In other words, the vector function fk:{0,1}^n mapps to {0,1}^n acts as a transition function (mapping) representing a possible realization of the entire PBN. Such functions are commonly referred to as multiple-output Boolean functions Each of the N possible realizations can be thought of as a standardBoolean network operates for one time step. In other words, at every state x(t) belongs to {0,1}^n , one of the N Boolean networks is chosen and used to make the transition to the next state x(t+1) belongs to {0,1}^n . The probability Pi that the ith (Boolean) network or realization is selected can be easily expressed in terms of the individual selection probabilities Cj see (Shmulevich et al., 2002). The dynamics of the PBN are essentially the same as for Boolean networks, but at any given point in time, the value of each node is determined by one of the possible predictors, chosen according to its corresponding probability.This can be interpreted by saying that at any point in time, we have one out of N possible networks. The basic building block of a PBN is shown in the Figure1.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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