text:
Page 1
Selection Policy-Induced Reduction Mappings for
Boolean Networks
Ivan Ivanov, Plamen Simeonov, Noushin Ghaffari, Xiaoning Qian, and Edward R. Dougherty
Abstract—Developing computational models paves the way to
understanding, predicting, and influencing the long-term behavior
of genomic regulatory systems. However, several major challenges
have to be addressed before such models are successfully applied
in practice. Their inherent high complexity requires strategies for
complexity reduction. Reducing the complexity of the model by re-
moving genes and interpreting them as latent variablesleads to the
problem of selecting which states and their corresponding transi-
tions best account for the presence of such latent variables. We use
the Boolean network (BN) model to develop the general framework
for selection and reduction of the model's complexity via desig-
nating some of the model's variables as latent ones. We also study
the effects of the selection policies on the steady-state distribution
and the controllability of the model.
Index Terms—Compression, control, gene regulatory networks,
selection policy.
eficially altering the dynamic behavior of the underlying bio-
logical system [1]. Owing to the inherent computational burden
of optimal control methods [2], the extreme complexity, which
grows exponentially with network size, creates an impediment
for the design of optimal control policies for large gene regu-
latory networks. The computational burden can be mitigated in
different ways, for instance, by using an approximation to the
optimal policy [3] or designing greedy algorithms that do not
approximation and greedy-control methods can only work with
networks that are still relatively small. Another approach, the
one considered here, is to reduce the network.
and study intervention strategies for the purpose of ben-
Manuscript received September 15, 2009; accepted April 23, 2010. Date of
publication May 17, 2010; date of current version August 11, 2010. The as-
sociate editor coordinating the review of this manuscript and approving it for
publication was Dr. Yufei Huang. The work presented in the paper was partially
supported by the NSF Grant CCF-0514644.
I. Ivanov is with the Department of Veterinary Physiology and Pharma-
cology, Texas A&M University, College Station, TX 77843 USA (e-mail:
P. Simeonov is with the Department of Mathematics, University of Houston-
Downtown, Houston, TX 77002 USA (e-mail: firstname.lastname@example.com.).
N. Ghaffari is with the Department of Electrical and Computer Engineering,
and the Department of Statistics, Texas A&M University, College Station, TX
77843 USA (e-mail: firstname.lastname@example.com.).
X. Qian is with the Department of Computer Science and Engineering, Uni-
versity of South Florida, Tampa, FL 33620 USA (e-mail: firstname.lastname@example.com.).
E. R. Dougherty is with the Department of Electrical and Computer Engi-
neering, Texas A&M University, College Station, TX 77843 USA. He is also
with the Translational Genomics Research Institute (TGEN), Phoenix, AZ
85004 USA (e-mail: email@example.com.).
Digital Object Identifier 10.1109/TSP.2010.2050314
The Boolean network (BN) model [6] and the probabilistic
Boolean network (PBN) model [7] which in its binary form is
essentiallycomposedof acollectionof constituentBoolean net-
works connected via a probability structure, have played key
roles in the study of gene regulatory systems, in particular, with
regard to regulatory intervention. These models are especially
useful when there is evidence of switch-like behavior. In ad-
dition, the dynamical behavior of the PBN model is described
by the well developed theory of Markov chains and their asso-
ciated transition probability matrices, which allows for a rig-
orous mathematical treatment of optimal regulatory interven-
tion. To address the issue of changing the long-run behavior,
stochastic control has been employed to find stationary con-
trol policies that affect the steady-state distribution of a PBN
[8]; however, the algorithms used to find these solutions have
complexity which increases exponentially with the number of
genes in the network. Hence, there is a need for size reducing
mappings that produce more tractable models whose dynamical
behavior and stationary control policies are "close" to those of
the original model, the key issue here being closeness, whatever
way in which that is characterized.
ping of this kind was introduced in [9]. It preserves the proba-
exponentiallycompared to theoriginal PBN, thereby increasing
complexity of a different kind and making the biological inter-
pretation of the reduced PBN problematic.
The reduction mapping proposed in [10] addresses this
issue by mapping a given PBN onto a set of candidate PBNs
without increasing the number of constituent networks in the
original model. The removed gene is considered as a latent
variable which induces a specific "collapsing" of pairs of
states from the state space of the original PBN and induces a
selection of their successive states based on the steady-state
distribution of the network. The "collapsing" procedure
represents a situation in which a gene is not observable,
which implies that states of the regulatory system that differ
only in the expression of that gene become identical and
thus "collapse" into each other. The notion of collapsing is
both natural and general. If
network that differ only in the value of gene
is to be deleted, then these states will be identified as
in the reduced network and the
question becomes how to treat them within the functional
structure of the network.
This paper introduces a general framework for the construc-
tion of reduction mappings based on the "collapsing" heuristic
are two states in the
, and gene
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Page 2
control, in particular, the mean-first-passage-time (MFPT) con-
trol policy [4]. Since a binary PBN is a collection of Boolean
networks with perturbation, we treat selection policies within
the framework of Boolean networks with perturbation
By reducing each constituent BN for the same gene, in effect,
we reduce the PBN.
A. Boolean and Probabilistic Boolean Networks
A BN with perturbation ,
defined by a set of nodes
Boolean functions
represents the expression level of gene , with 1 representing
high and 0 representing low expression. The vector
of a gene
is predicted by the values of a set,
at the previous time step, based on the regulatory function
The set of genes
set and the function
is called the predictor function of
state of the
is a vector
the state space of the
is the collection
network. The perturbation parameter
gene mutations, i.e., at each time point there is a probability
of any gene changing its value uniformly randomly. Since there
genes, the probability of a random perturbation occurring
at any time point is
. At any time point , the state of
the network is given by
is called a gene activity profile (GAP). The dynamics of a
are completely described by its
of the underlying Markov chain undergoing the transition from
the state
to the state. The perturbation probability
the chain ergodic and therefore it possesses a steady-state prob-
ability distribution
Computing the elements of
present it here because of its importance in the subsequent con-
siderations. When computing the transition probabilities for a
one has to realize that at every time step one of the two
mutually exclusive events happens: either the chain transitions
accordingtotheregulatoryrules oraperturbationoccurs.This
interpretation implies that when no perturbation occurs the net-
in computing
for every given state
is when
is a singleton attractor, i.e.,
, where
sitions where the binary representations of
each other. The second case is when
In this case,
. The transition
the regulatory rules
with a probability of
turbation with a probability of
, on
and a vector of
genes is
. The variable
, of genes
is called the predictor
, and
of all states of the
models random
, and
transition probability
is the probability
is straightforward. We elect to
. The first case
. In this case,
is the number of the po-
, where
differ from
, for any
can happen by either applying
or by per-
. In summary
is the indicator function that takes value 1 if
according to the truth table and is equal to 0 other-
A probabilistic Boolean network (PBN) consists of a set
of nodes/genes
, and a set of vector valued network functions,
, governing the state transitions of the genes, each
network function being of the form
[7] In most applications, the discretization is either binary or
ternary. Here we use binary
random decision is made as to whether to switch the network
function for the next transition, with the probability
switch being a system parameter. If a decision is made to
switch the network function, then a new function is chosen
from among
, with the probability of choosing
being the selection probability
not conditioned by the current network and the current network
can be selected). Each network function
the individual BNs being called the contexts of the PBN. The
PBN behaves as a fixed BN until a random decision (with
) is made to switch contexts according to the
from among
then the PBN is said to be instantaneously random; if
[11], then the PBN is said to be context-sensitive. Our interest is
with context-sensitive PBNs with perturbation, meaning that at
each time point there is a probability
value uniformly randomly. Excluding the selection-probability
structure, a context-sensitive PBN is a collection of
the contexts of the PBN. It is in this sense that by considering
reduction mappings for
reduction mappings for PBNs.
. At each time point a
of a
(note that network selection is
determines a BN,
. If,
of any gene flipping its
we are ipso facto considering
B. Effect of Rank-One Perturbations on the Steady-State
When studying the network reduction, we will need to char-
acterize the changes in the steady-state distribution resulting
rank-one perturbations (not to be confused with the notion of
in the framework of structural intervention in gene regulatory
networks [12] and more generally in the framework of Markov
chain perturbation theory [13].
and denote the transition probability matrix
and steady-state distribution for the perturbed
and , where
lytical expressions for the steady-state distribution change can
be obtained using the fundamental matrix, which exists for any
ergodic Markov chain and is given by
is a column vector whose components are all unity
[14]. Letting
, the steady-state distribution change
For a rank-one perturbation, the perturbed Markov chain has
the transition probability matrix
two arbitrary vectors satisfying
, we have
denotes transpose. Ana-
, whereare
, and represents a
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IVANOV et al.: SELECTION POLICY-INDUCED REDUCTION MAPPINGS4873
rank-one perturbation of the original transition probability ma-
. In this case, it can be shown that [12]
An important special case occurs when the transition mecha-
nisms before and after perturbation differ only in one state, say
th state. Then
th row, whereis the coordinate vector with a 1 in the
position and 0s elsewhere. Substituting this into (2) yields
has nonzero values only in its
the respective vectors. For the th state
, and,are the th coordinates of
The results for these special cases can be extended to arbi-
trary types of perturbations so that it is possible to compute
the steady-state distributions of arbitrarily perturbed Markov
chains in an iterative fashion [12].
C. MFPT Control Policy
The problem of optimal intervention is usually formulated as
an optimal stochastic control problem [2]. We focus on treat-
ments that specify the intervention on a single control gene . A
control policy
based on
for each time step . The values 0/1 are
interpreted as off/on for the application of the control.
MFPTs of a state
and its flipped (with respect to ) state
[4]. When considering therapeutic intervention, the state space
can be partitioned into desirable
according to the expression values of a given set
For simplicity we will assume that
gene determines the partition. The intuition behind the MFPT
algorithmisthat,giventhecontrolgene ,whenadesirablestate
reacheson average faster than
control and start the next network transition from
and are reversed when
one can assumethatthe gene
is theleftmost gene in thestate's
binary representation, i.e.,
the desirable states correspond to the value
assumption, the probability transition matrix
chain can be written as
is a sequence of decision
and undesirable states
of genes.
, i.e., only one
, it is reasonable to apply
. The roles
. Without loss of generality
and, and
. With this
of the Markov
Using this representation one can compute the mean first-pas-
sage times
and by solving the following system of
linear equations [15]:
MFPT algorithm designs stationary(time independent) control
for each gene
by comparing the coordinate differences
to , a tuning parameter that can be set to
a higher value when the ratio of the cost of control to the cost
of the undesirable states is higher, the intent being to apply the
control less frequently.
denotes a unit vector of the appropriate length. The
andcontain the MFPTs from each state in
,andfromeachstatein totheset
in the network
To motivate the definition of a selection policy, we consider
a specific reduction mapping designed using information about
the steady-state distribution of the network [10]. That mapping
is constructed assuming that the gene
the network. For every state
that differs from
only in the value of gene . Next, for every
such pair
and, we consider their successor states
, and. Following deletion,
variable and, under the reduction mapping, the states
'collapse' to a state in the reduced network. The state
tained from either or
by removing their th coordinate. The
reduction mapping, denoted by
of the reduced network by selecting the transition
or , otherwise. This particular type of re-
duction is a special case of a reduction mapping
by a selection policy
, which we define next.
Definition 1: A selection policy
deleted gene
is a dimensional vector,
indexed by the states of and having components equal to 1 at
exactly one of the positions corresponding to each pair
For each gene
there are
Using this definition, one can consider the reduction mapping
corresponding to the selection policy
the truth table of the reduced network by selecting the transition
if or, otherwise. Greater reduction of
iterativemanner following the approach outlined inthis section.
Each selection policy is obtained by the action of a corre-
sponding selection matrix
column unit vector ,
is to be 'deleted' from
, let denote the state
becomes a latent
is ob-
, constructs the truth table
corresponding to the
different selection policies.
. constructs
of dimension on the
placing the rows corresponding to the 0 entries in the selection
with zero rows. The selection matrix serves as a right
, to the
is obtained from the identity matrix by re-
matrix obtained
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Page 4
from the selection matrix by deleting its zero rows. In what fol-
lows, we will focus on the selection policies that correspond to
the case
. This could be achieved by permuting the gene
indexes and does not restrict the generality of our considera-
tions. For example, in the case of BNs on 3 genes, one of the
matrixes has the following format:
posing and then by setting for each column ,
above example of the matrix
matrix is obtained from by first trans-
, . The
We define the companion matrix
for the reduction map-
The companion matrix
closely related to the dynamics of the reduced network
Its importance can be seen from the following theorem, which
states that
is asymptotically equal to the transition proba-
bility matrix
Theorem 1: For every selection policy
defines a Markov chain that is
denotes the maximum element of the respective
Proof: Without loss of generality we set
definition, each row of the companion matrix
as follows. First, the appropriate rows from
cording to the selection policy
and the columns in the resulting
pairsindexedbythepairsofflippedstates and
companion matrix. Because the elements of
the matrices
andare indexed with the states
compare them element-wise. Note that only rows in the orig-
inal probability transition matrix
contribute in the formation of both
.Thus, for eachstate,
to consider:
In this case considerations similar to the one in Section II
show that
. By the
is obtained
are selected ac-
. The other rows are discarded
matrix are added in
, we
indexed by statesfor
, thereare severalcases
which equals to
. When or
we haveand
. Thus
enough to notice that
is the Hamming distance between the states
, e.g., the definition ofin Section II. Now, it is
but , whereis defined similarly to
In this caseand
which gives
For the rest of the states the verification that
can be done as in case 1.
In this case, while
. Computations, similar to the previous two
cases show that
Finally, for states
as in the previous case and show that
The above considerations show that each row of the com-
couldpossiblydiffer fromthecorresponding
row in the transition probability matrix
one of them perturbed by a term that equals to
the other one by a term that equals to
tities tend to 0 as
. The norm of the matrix difference
from the statement of the theorem is proportional to the larger
of these two numbers, and thus we obtain the conclusion of the
An immediate corollary of the theorem is that, if all of the
states in a
are either singleton attractors or part of at-
tractor cycles of the type
bility matrix
for the reduced network is identical to the com-
panion matrix for every reduction mapping induced by a selec-
tion policy. The salient observation following from the theorem
is that for large networks
probability of perturbation,
very small perturbation, identical to
In the next two sections, we use the companion matrix
to study the effects of selection-policy-induced reduction
mappings on both the steady-state distribution of the original
network and a specific type of stationary control policy, the
MFPT control policy. The issue of the effects of a reduction
,the computations are the same
in only two entries,
. Both quan-
, then the transition proba-
or for networks with a high
is, up to a
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IVANOV et al.: SELECTION POLICY-INDUCED REDUCTION MAPPINGS4875
on the steady-state distribution is different from the issue of its
effects on a stationary control policy for the network; however,
the reduction effects on the steady-state distribution and the
control policy can both be used as measures for the goodness
of reduction mappings.
In this section we use the companion matrix
reduction mapping
turbation theory to study the effects of the reduction on the
steady-state distribution of the
section, one can assume without loss of generality that the gene
determines the partition
, andis the gene to be 'deleted' from the network.
(1), all the entries in P have two terms
. We note that the first term is the multi-
plication of the probability of no random flipping
the indicator
determined by the Boolean functions
of the. We denote
is determined by the perturbation parameter
ming distance between
. Hence,
for any entry in the transition matrix
as given in the text. Each entry in
corresponds to and each entry in
. Obviously,is the same for all
number of genes and the same value for the perturbation param-
eter , and
is determined by the regulatory rules or Boolean
given in the.
For a given selection policy
by replacing the rows in
that correspond to
the rows where
or by leaving them unchanged if
. Similarly to, the probability transition matrix
for this new Markov chain can be decomposed as
for the
and results from Markov chain per-
. Similarly to the previous
of the state space
. The second term
and the Ham-
. We denote it by
. Thus, we can
corresponds to
with the same
, define a new Markov chain
the assumption
fora on3genesunder
The so introduced new Markov chain is obtained from the orig-
inal Markov chain representing the
rank-one perturbations. Thus, following [12], one can
compute the total change in the steady-state distribution caused
by those perturbations. By the definition of the steady-state
. For each state , we have
by performing at most
have the similar form
denotes the th column of . For the state , we
Note that
neighboring odd and even columns. Now, for every such pair of
flipped states we compute
andare flipped states and and are
Recall that
neighboring odd and even rows in
example of
. We have
and, when
are identical, see the above
, the
Based on the definition of
is straightforward to see that
, and using Hamming distances, it
Theneighboring oddand evenrowsin
fact that for an arbitrary pair of neighboring odd and even states
and the Hamming distances between , and ,
to each other gives us
areidenticaland the
are equal
We denote
lowed here leads to the steady-state distribution for the com-
panion matrix
. Thus
for all . The procedure fol-
This observation when combined with the Markov chain per-
tion policy
on the steady-state distribution of a given
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Page 6
can be estimated approximately by comparing the
sional vector with coordinates equal to the appropriate sums
andto the steady-state distribution for the com-
panion matrix
. Indeed, according to Theorem 1 the steady-
state distribution
of the Markov chain described by the com-
of the reduced network. At the same time, this
probability distribution can be obtained via the relation
from the steady-state distribution
is obtained from the probability transition matrix of the original
by means of at most
discussion in Section II-B and (4) in particular, show how one
one of these perturbations. The total effect on the steady-state
distribution produced by all of the perturbations that lead to the
can be computed by iteratively applying (4). Thus,
for every state
in the original
turbation effect on the sums
proper collapsing of the steady-state of the original network if
one considers the deleted gene
cussion shows that the differences
distribution of the original
of the Markov
rank-one perturbations. The
one can compute the per-
which represent the
as a latent variable. This dis-
In this section we study the effects of the selection-policy-
induced reduction mappings on control policies designed for a
mathematical formulation can be related to selection policies.
As we will see, this requirement is met by the MFPT control
For a selection policy
and its corresponding reduction
we can consider the MFPT stationary control
policy on the reduced network. In this regard we assume
without loss of generality that
gene and
is the gene to be deleted from the network.
Interpreting the deletion of gene
non-observable, variable, it is desirable that the MFPT control
for the reduced network
sible to the one designed for the original network when both
control policies have the same parameter
can achieve similar control actions for every state
its corresponding reduced state . Obviously, this is achieved
only if
. Thus, we arrive at the following
definition which is formulated for the general case of stationary
control policies.
,, is the control
as creation of a latent, or
is as close as pos-
. In this way, one
Definition 2: Given a stationary control policy
to be deleted from the
sistent at the state
is called-inconsistent. The ratio
-inconsistent states
is called the -relative inconsistency of the control policy
The pairs of
-inconsistent states in the original network
present us with two possible options for defining the control
action for the states in the reduced network obtained by col-
lapsing those pairs into their respective reduced states. Thus,
one should measure the effects of a selection policy-induced
reduction mapping by comparing the control actions for the
of states that are not
control actions for their corresponding reduced states in the
reduced network
. The next definition provides a relative
measure of those effects.
Definition 3: Given a stationary control policy
at the state
if and only if the control action for the
reduced state
is different from
to the total number of states in
the selection policy
on the control policy
Because there is only a finite number of selection policies
, there exists a selection policy
among the all possible selection policies
given stationary control policy
Recall that the MFPT control policy
on the comparisons between
to. Thus, one can achieve the desired similarity be-
tween the MFPT control policies by minimizing the differences
and betweentherespectivevectorsofmean
first-passage times for the states in the original and the reduced
the dimension of
and is
subtract the vectors of mean first-passage times for the reduced
network from their counterparts for the original network.
This problem can be circumvented by using the companion
matrix. Because the sets of desirable and undesirable states are
the same for the Markov chain corresponding to the reduced
network and the one corresponding to
equations similar to (6) and (7), namely
and a gene
, the policy
if and only if
is called -incon-
. The
of the number of
to the total number of states in
-inconsistent to the
and a gene
. The ratio of the
is called the relative effect of
that minimizes the relative
on any
designed for a.
is designed based
, and one cannot simply
, one can consider
Consider a state
and (12), one gets (14), shown at the bottom of the page. where
the index
describes the coordinates of the vector
collapse to the state
such that. Then, from (6)
and the
. The right hand
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IVANOV et al.: SELECTION POLICY-INDUCED REDUCTION MAPPINGS4877
side suggests that the proper vector to subtract from
vector defined by the action of the matrix
, where, referringto(6),
submatrix ofand
with identical elements for each pair of positions indexed by a
pair of flipped states
. Thus, if one pairs every equation of
type (14) with an artificially introduced identity corresponding
to the state
that was not selected by the policy
is the
on the vector
is theupper left
has dimension
then one gets a linear system of
can be represented in a matrix format as
equations. That system
where the matrix
(6) and (7), by replacing the rows corresponding to 0 entries in
the selection policy
with the appropriate unit basis vectors
. Similar considerations lead to
is obtained from the matrix , e.g.,
where the matrix
(6) and (7), by replacing the rows corresponding to 0 entries in
the selection policy
with the appropriate unit basis vectors
, andwith
sub-matrix of
that the differences
corresponding to the eigenvalue of 1 for the matrices
, respectively.
Recall that there exists a selection policy
with regard to minimizing the relative effect
the all possible selection policies
control policy
. Whereas for every candidate for deletion
gene there is an optimal selection policy to reduce the network,
finding that optimal selection policy requires finding the MFPT
control policy for each one of the
networks. This procedure is highly complex because it requires
finding the respective transition probability matrixes for all of
the reduced networks, then solving the corresponding systems
of linear equations, e.g., (6) and (7), to find the vectors of mean
first-passage times, and finally, executing the algorithm that
determines the control policy for the reduced network.
minimize the differences
lection policy
that ensures close to 0 coordinates for these
vectors at the positions that correspond to the places where its
coordinates equals to 1 is asymptotically (as
and Theorem 1 shows that the convergence is fast. The relations
given by (16) and (17) show that the differences
belong to the linear subspaces spanned by the eigen-
vectors corresponding to the eigenvalue of 1 for their respec-
tive matrixes
and. Our interest is in finding the ele-
ments of those subspaces that have small coordinates at the po-
sitions that correspond to the places where the selection policy
equals to 1.
subspaces based on the structure of a given selection policy, we
is obtained from the matrix, e.g.,
being the lower left
. Equations (16) and (17) show
are eigenvectors
that is optimal
on the stationary MFPT
possible reduced
, every se-and
) optimal
provide two theorems concerning estimating the probability of
finding vectors that belong to the subspaces and have a certain
growth condition imposed on their coordinates. These probabil-
ities are proportional to either the surface area or the volume of
certainportionsofthe -ballin
or metric.Thus,weareinterestedinthesets
, where, . By
adjusting the parameters
having the vectors of MFPT
to each other at the coordinates where the selection policy
equals to 1. Here we only state the theorems, leaving the proofs
in the Appendix.
Theorem 2: Consider the set
, one can estimate the probability of
and( and) close
. Then
Theorem 3: Consider the sets and . Then
functions of the respective sets,
onto the subspace spanned by the coordinate vectors
,and are the characteristic
is the projection of
describe the area of the projec-
tion of the intersection between the positive coordinate cone in
and the surface of the -ball in
topology respectively. The projections are onto the subspace
spanned by the coordinate vectors
Similarly, the quantity
-dimensional volume of the set
portion of the
-ball in the
endowed with the and
describes the
, the volume of the
space that is bounded by the
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Page 8
Fig. 1. 4-gene ?? has 256 possible selection policies. All of these selection policies and their SSD shift toward Desirable states are shown in this figure. 16 out
of 256 selection policies produce the maximum shift toward Desirable states and are identified by a circle around them. Out heuristic selection policy is one of
these 16 optimal selection policies.
on the positive coordinate cone in
hand: estimating the closeness of the vectors
andin either
of the possible permutations of the coordinate vectors, one can
see that the probability of finding vectors with the structure
described in the statements of the theorems is proportional
in thecase, and to
case. These two quantities rapidly tend to zero if some of
the numbers
tend to zero. It is important to notice that the
minimum in either
ornorm of the coordinates of interest
of the vectors
and the selection policy
relative effect
of the selection policy
depends on the choice of the parameter
is related to the cost of control [4]. Smaller values of
that control is applied more often, larger size of the set
a potential increase of
. Smaller values for
that a brute force search for vectors
enough to the MFPT vectors
Thus, there is a need for heuristic approaches that identify
both a gene for deletion and a selection policy which has small
relative effect on the control policy. It is also desirable that the
reduced network shares similar controllability properties as the
original one, where the controllability is understood in terms of
the shift of the steady-state distribution towards the desirable
states after the application of MFPT control policy. The control
lectionpolicyinthefollowing scenario:(i) a geneis selectedfor
and the positive coordinate cone in. We focus
because of the task at
and or
or norm. Taking into account all
in the
depends only on the
. At the same time, the
on the control
, and
also imply
that are close and
is a hard problem.and
deletion by a procedure involving the Coefficient of Determina-
chosen selection policy is applied; (iii) steps (i) and (ii) are used
iteratively until a network of a predetermined (computationally
feasible) size is achieved, (iv) the MFPT control policy is de-
rived for the reduced network; and (v) a control policy is in-
duced on the original network from the policy derived for the
reduced network.
We performed simulation studies to illustrate the new con-
cepts developed in this paper. Specifically, we study the rela-
tionship between the relative effect of the selection policy on
the MFPT control policy and the shift of the steady-state distri-
bution of the network towards the desirable states.
The key concept in this paper is that of the selection policy
which determines the reduction mapping, and subsequently
the structure of the reduced network. Given the large number
of possible selection policies, it is not feasible to exhaustively
search for the optimal selection policy. The optimal selection
policy; therefore, if that stationary control policy is changed,
then the optimal selection policy could change as well. Thus, it
is important to develop heuristics for determining suboptimal
selection policies. The algorithm CoD-Reduce outlined in [16]
designs such a policy. Fig. 1 shows the performance of that
algorithm using a 4-gene network as an example: the designed
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Page 9
IVANOV et al.: SELECTION POLICY-INDUCED REDUCTION MAPPINGS4879
Fig. 2. The average SSD shift toward Desirable states and the relative effects on the control policies of successive reductions of 2 sets of 100 ?? . Each set has
randomly generated attractors which constrained to be evenly distributed between the Desirable and Undesirable states. At each step the MFPT control policy is
designed and applied on the network. As the figure shows the SSD shift is similar in the original and reduced networks by applying their own control policies.
Also, SSD shift and relative effect curves follow inverse patterns. (a) 9 genes. (b) 10 genes.
suboptimal selection policy is among the several optimal selec-
tion policies. In our simulation study, we use CoD-Reduce to
design the selection policy.
We have generated several sets, 100 networks each, of
using the algorithm developed in [18] for different numbers of
constraint on their attractors: half of them are among the desir-
able states of the respective network. For each randomly gen-
erated network, also referred to as the original network in the
trol policy. Then we compute the difference between the total
mass of the desirable states in the SSD of the network before
and after applying the MFPT control policy. We refer to this
difference as the SSD shift (toward the desirable states). It is
clear that more efficient stationary control policies will produce
larger SSD shifts. For the next step in the simulations, we use
CoD-Reduce and delete one gene from the network and find the
the relative effect of the selection policy on the MFPT control
policy for the original network by comparing that control policy
to the MFPT control policy for the reduced network. The reduc-
tion step and the calculation of the relative effect on the MFPT
control policy ares repeated iteratively using the reduced net-
work from the previous step as the "original" network for the
new reduction step.
Fig. 2 illustrates our findings: CoD-Reduce does not have a
significant effect (on average) on the amount of SSD shift if
a single gene is removed from the model. Similarly, there is a
small change (on average) in the relative effect of the selection
to its reduced version. Thus on average, our heuristic for per-
forming selection policy-based reduction does not have much
of an impact on the controllability of the network when a single
gene is removed from it. However, the effects of reduction tend
to accumulate with the removal of more genes, and ultimately
the reduction mappings produce poor results when a very few
genes remain in the network.
In general, the SSD shift and the relative effect tend to follow
actions for the states on the larger network and their respective
reduced states in the smaller network which could ultimately
lead to a significant difference in the shifts induced by those
control policies in the steady-state distributions of the models.
A. Gastrointestinal Cancer Network Application
We have considered the effects of the reduction on a real-
world,experiment-drivennetwork generatedusing thegastroin-
testinal cancer data set from [19]. Before applying reduction,
we must infer the gene regulatory network from the gene ex-
pression data and obtain the
the gene expression data are normalized, filtered and binarized
using the methods from [20]. For the inference, we use the pro-
cedure used by [16] which is a modified version of the seed al-
gorithm proposed by Hashimoto et al. [21]. The algorithm is
initialized by the C9orf65 gene as the seed gene and the gene
CXCL12 is chosen as the control gene. The seed gene is se-
lected based on the fact that it is one of two genes composing
the best classifier in [19] and the control gene selection is based
on the strong CoD [17] connection to the seed gene. The coef-
ficient of determination (CoD) measures how a set of random
variables improves the prediction of a target variable, relative to
the best prediction in the absence of any conditioning observa-
tion [17]. Let
binary random variables,
a binary target variable, and
Boolean function such that
error of
as a predictor of
. Let
of thebest estimate of
without any predictors. TheCoD is de-
fined as
. In the preprocessing step,
be a vector of predictor
is the expected squared dif-
be the minimum MSE
. The mean-square
The network is grown by adding one gene at a time; at each
iterative step the gene having the strongest connectivity, mea-
sured by the CoD, to one of the genes from the current network
is added to the network. Then, the network is rewired taking
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Page 10
into account that a new gene in the network can change the
way genes influence each other. The total number of the genes
in the final network is 17: C9orf65, CXCL12, TK1, SOCS2,
RPS11, THC2210612, THC2161967, IER2 and LAMP1. This
has a very large state space of size
computation of its SSD is infeasible. Thus the SSD is estimated
by first running the network for a long time and then using the
Kolmogorov-Smirnov test to decide if the network has reached
its steady state. Initially the best gene for deletion is selected
using CoD-Reduce [16] and the network is reduced by deleting
one gene, then CoD-Reduce is applied consecutively to reduce
the network down to 10 genes: C9orf65, CXCL12, RPS18,
RPS13, THC2199344, SNX26, RPL26, SLC20A1, RPS11 and
THC2210612. After reducing the original network down to
10 genes, the MFPT control policy for the reduced network
is designed and then induced back on the original 17-gene
network. The induction of the control policy is a necessary
step since the control policy designed on the reduced network
is of smaller dimension compared to the original one. We use
the method outlined in [16] for inducing the control policy de-
signed on the 10-gene network to the original 17-gene network.
After deleting one gene, each state in the reduced network
corresponds to two states, referred to here as "parent" states,
in the original network that collapsed together. After designing
the contol policy and assigning the control actions to the states
of the reduced network, in the induction procedure, the control
action of each state in the reduced network will be duplicated
as the control actions for its parent states.
Table I shows the total probability mass of the desirable and
undesirable states before and after applying the induced control
policy. As the table illustrates, there is about 13% shift in the
steady-state distribution of the network toward more desirable
. Exact
This paper presents a general compression strategy for
Boolean network models of genomic regulation. The strategy is
based on the concept of a selection policy, and the complexity
of the model is reduced by consecutively removing genes from
the network. The removed genes are treated as latent or non-ob-
servable variables, and the truth tables for the reduced models
are constructed based on the particular selection policy. The
effects of the compression on both the dynamical behavior of
the model and on the MFPT control policy are discussed using
the companion to the selection policy matrix. It is important to
emphasizethatwhilethereis always an optimalselection policy
which minimizes the effects of compression on the stationary
control policy the problem of finding it is a hard one. Thus,
there is a need to develop suboptimal compression algorithms
based on heuristical approaches.
Proof (Theorem 2): The integral evaluation is easily veri-
fied by induction with respect to
In the case
direct integral evaluation shows that
. Next, assuming that thestatement of the the-
orem is true for
, one can compute
as follows:
This completes the proof of Theorem 2.
Proof (Theorem 3): We use induction with respect to
First we establish the case
. In this case,
. We obtain , thus
From the definition of it is clear that
For every
we have (with the empty sum being
where. Thus, (with
Then, we should have
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Page 11
IVANOV et al.: SELECTION POLICY-INDUCED REDUCTION MAPPINGS4881
which is true since
by (19) and (20). Now we handle the general case. Let
and define
Definition (22) clearly implies (with
a relevant induction hypothesis is
This hypothesis is verified using (24). We set
We obtain
The last expression gives the right-hand side of (25) after a
simple evaluation of the integral. The first formula of the the-
orem follows from (23) and (25).
It remains to evaluate
inition of
and (21) we have
. From the def-
By the above definition, we obtain the recurrence relation
Furthermore, the
provides the following hypothesis
evaluation of
To verify (31), again we set
(30) yields (32) at the bottom of the page.
Now (31) follows from (26) and (32). From (28) and (31) we
get the second formula in the statement of the theorem. This
completes the proof of Theorem 3.
,. Then,
The authors want to thank B. Shekhtman for the inspiring
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Page 12
[1] A. Datta, R. Pal, A. Choudhary, and E. R. Dougherty, "Control
approaches for probabilistic gene regulatory networks," IEEE Signal
Process. Mag., vol. 24, no. 1, pp. 54–63, 2007.
[2] D. P. Bertsekas, Dynamic Programming and Optimal Control, 3rd
ed.Belmont, MA: Athena Scientific, 2005.
[3] B. Faryabi, A. Datta, and E. R. Dougherty, "On approximate stochastic
control in genetic regulatory networks," IET Syst. Biol., vol. 1, no. 6,
pp. 361–368, 2007.
[4] G. Vahedi, B. Faryabi, J.-F. Chamberland, A. Data, and E. R.
Dougherty, "Intervention in gene regulatory networks via a stationary
mean-first-passage-time control policy," IEEE Trans. Biomed. Eng.,
pp. 2319–2331, Oct. 2008.
[5] X. Qian, I. Ivanov, N. Ghaffari, and E. R. Dougherty, "Intervention in
behavior," BMC Syst. Biol., 2009.
[6] S. A. Kauffman, "Metabolic stability and epigenesis in randomly con-
structed genetic nets," J. Theoret. Biol., vol. 22, pp. 437–467, 1969.
[7] I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, "Probabilistic
boolean networks: A rule-based uncertainty model for gene regulatory
networks," Bioinform., vol. 18, no. 2, pp. 261–274, 2002.
[8] R. Pal, A. Datta, and E. R. Dougherty, "Robust intervention in proba-
bilistic Boolean networks," IEEE Trans. Signal Process., vol. 56, no.
3, pp. 1280–1294, 2008.
[9] E. R. Dougherty and I. Shmulevich, "Mappings between probabilistic
Boolean networks," Signal Process., vol. 83, no. 4, pp. 799–809, 2003.
[10] I. Ivanov and E. R. Dougherty, "Reduction mappings between proba-
bilistic boolean networks," EURASIP J. Acoust. Signal Process., vol.
1, no. 1, pp. 125–131, 2004.
[11] M. Brun, E. R. Dougherty, and I. Shmulevich, "Steady-state probabil-
ities for attractors in probabilistic Boolean networks," Signal Process.,
vol. 85, no. 10, pp. 1993–2013, 2005.
[12] X. Qian and E. R. Dougherty, "On the long-run sensitivity of proba-
bilistic Boolean networks," J. Theoret. Biol., pp. 560–577, 2009.
[13] J. J. Hunter, "Stationary distributions and mean first passage times
of perturbed Markov chains," Linear Algebra Appl., vol. 410, pp.
217–243, 2005.
[14] P. J. Schweitzer, "Perturbation theory and finite Markov chains," J.
Appl. Probab., vol. 5, pp. 401–413, 1968.
[15] J. Norris, Markov Chains.Cambridge, U.K.: Cambridge Univ. Press,
[16] N.Ghaffari,I.Ivanov,X.Qian,andE.R.Dougherty,"ACoD-basedre-
duction algorithm for designing stationary control policies on Boolean
networks," Bioinformatics, vol. 26, pp. 1556–1563, 2010.
[17] E. R. Dougherty, S. Kim, and Y. Chen, "Coeffcient of determination in
nonlinear signal processing," Signal Process., vol. 80, pp. 2219–2235,
[18] R. Pal, I. Ivanov, A. Datta, and E. R. Dougherty, "Generating Boolean
no. 21, pp. 4021–4025, Nov. 2005.
[19] N. D. Price, J. Trent, A. K. El-Naggar, D. Cogdell, E. Taylor, K. K.
Hunt, R. E. Pollock, L. Hood, I. Shmulevich, and W. Zhang, "Highly
accurate two-gene classifier for differentiating gastrointestinal stromal
tumors and leiomyosarcomas," Proc. Nat. Acad. Sci., vol. 104, no. 9,
pp. 3414–3419, 2007.
[20] I. Shmulevich and W. Zhang, "Binary analysis and optimization-based
normalization of gene expression data," Bioinform., vol. 18, no. 4, pp.
555–565, 2002.
[21] R. Hashimoto, S. Kim, I. Shmulevich, W. Zhang, M. L. Bittner, and E.
R. Dougherty, "A directed-graph algorithm to grow genetic regulatory
subnetworks from seed genes based on strength of connection," Bioin-
form., vol. 20, no. 8, pp. 1241–1247, 2004.
Ivan Ivanov received the Ph.D. degree in mathe-
matics from the University of South Florida, Tampa.
He is an Assistant Professor with the Department
of Veterinary Physiology and Pharmacology, Texas
A&M University, College Station, TX. His current
research is focused on genomic signal processing,
and, in particular, on modeling the genomic regu-
latory mechanisms and on mappings reducing the
complexity of the models of genomic regulatory
Plamen Simeonov received the Ph.D. degree in
mathematics from the University of South Florida,
He is an Associate Professor of mathematics with
the Department of Computer and Mathematical Sci-
ences, University of Houston-Downtown, Houston,
TX. His current research interests are in the areas
of analysis, approximation theory, potential theory,
orthogonal polynomials and special functions, com-
puter-aided geometric design, and biostatistics.
Noushin Ghaffari received the M.Sc. degree in
computer information systems from the University
of Houston—Clear Lake, TX, in 2006.
Currently, she is pursuing the Ph.D. degree with
the Department of Electrical and Computer Engi-
neering, Texas A&M University, College Station.
Her research interests include: genomic signal
processing, systems biology, and computational
biology; especially complexity reduction and control
of Genetic Regulatory Networks.
Xiaoning Qian received the Ph.D. degree in elec-
trical engineering from Yale University, New Haven,
CT, in 2005.
Currently, he is an Assistant Professor with the
Department of Computer Science and Engineering,
University of South Florida, Tampa. He was with
the Bioinformatics Training Program, Texas A&M
University, College Station. His current research
interests include computational biology, genomic
signal processing, and biomedical image analysis.
Edward R. Dougherty received the M.S. degree
in computer science from Stevens Institute of
Technology, Hoboken, NJ, the Ph.D. degree in math-
ematics from Rutgers University, New Brunswick,
NJ, and the Doctor Honoris Causa by the Tampere
University of Technology, Finland.
and Computer Engineering, Texas A&M Univer-
sity, College Station, where he holds the Robert
M. Kennedy '26 Chair in Electrical Engineering
and is Director of the Genomic Signal Processing
Laboratory. He is also co-Director of the Computational Biology Division of
the Translational Genomics Research Institute, Phoenix, AZ, and is an Adjunct
Professor with the Department of Bioinformatics and Computational Biology,
University of Texas M. D. Anderson Cancer Center, Houston. He is author
of 15 books, editor of five others, and author of 250 journal papers. He has
contributed extensively to the statistical design of nonlinear operators for image
processing and the consequent application of pattern recognition theory to
nonlinear image processing. His current research in genomic signal processing
is aimed at diagnosis and prognosis based on genetic signatures and using gene
regulatory networks to develop therapies based on the disruption or mitigation
of aberrant gene function contributing to the pathology of a disease.
Dr. Dougherty is a fellow of SPIE, has received the SPIE President's Award,
and served as the editor of the SPIE/IS&T Journal of Electronic Imaging. At
Texas A&M University received the Association of Former Students Distin-
guished Achievement Award in Research, been named Fellow of the Texas En-
gineering Experiment Station, and named Halliburton Professor of the Dwight
Look College of Engineering.
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|May 17, 2012, 11:21 AM
cheap glue caddy by fourmost http://www.hobbylinc.com/htm/for/for158.htm I have always wanted to buy a fourmost angle cutter/sander ,i have a builder buddy that swears by them .http://www.hobbylinc.com/Fourmost_Hand_Tools
Last edited by cracksmeup; May 17, 2012 at 11:28 AM.
|May 17, 2012, 11:22 AM
No Its Dangerous if you Do it Wrong...
|May 17, 2012, 11:29 AM
I fogged on a coat of clear finish for now.
What's really surprising is that mine looks just like the manufactured ones,when finished.
Go for it.
|May 17, 2012, 12:16 PM
Here is an example of my balsa scratch building "creds": My Beriev Be-200 was built starting with a scale three view and was done in 100% balsa, ply and light ply: no plastic, no fiberglass, no carbon fiber, no laser cut parts and almost no plans...
I personally think that it makes much more sense to group models by type than by construction material. I would rather find all scale projects in one spot, than have to look in several forums....ditto on sailplanes, ditto on sport models, and so forth.
If all the most feverent devotees to balsa scratch building go off and create their own forum and post everything in there, I think it will lessen the exposure that the typical "new" modeler gets to these great techniques. What will happen to cross pollenation of techniques in various model media and the education of new builders?
I think too many forums overly fragments the content on R/C groups. Perhaps differentiation of projects within a forum could be done with the type of tags currently applied at the start of the thread...discussion, mini how-to, etc. Perhaps a tag for balsa scratch builds/kits, a tag for arfs, a tag for in each special interest forum could be part of the solution, especially if the fourms could be made searchable by the tags. Would that not solve the problem?
I thnik a very nice scale scratch build/own design project might be posted in this new balsa forum and get overlooked by the other members interested in scale models that do not frequent the new forum.
Are we going to end up subdividing the new balsa forum into frums covering balsa models covered in heat shrink covering, vs models fiberglassed and painted, or covered in fabric and dope? Where does it end?
I find it interesting that cracksmeup thinks a no vote comes only from a "drive by low life". Please be advised that I gave this matter thoughtful consideration, previously mentioned my thoughts on one the several threads discussing this new forum. Your assumptions are completely invalid and quite frankly, insulting.
I stand by my no vote and hope others vote no as well.
Last edited by Thomas B; May 17, 2012 at 12:31 PM.
|May 17, 2012, 01:49 PM
Joined Nov 2011
89 Posts
Thomas, very well spoken. Where can a guy post a balsa scratch build, not of a scale, not sport, not trainer, not a wing, own design, high wing pusher prop, motor mounted up behind the wing, camer plane, it may look like a sailplane but it's just not, weighing 8 pounds and cruises 50 mph. The plane is for purpose not pretty. I was waiting to post in the new balsa scratch build fourm, but you make some pretty good points.
|May 17, 2012, 02:35 PM
And of course ,when the OP gets the 50 required votes,having met the rules of merit,you will have the option of checking in on occasion,to see if the intent is failing.
The desire of the OP as I see it,is to scratch build from plans of no particular aircraft style...The build option is by the person who follows the suggestions laid down by contributors, who offer differing ways to do it.
It doesn't matter what type aircraft model is being represented,the thread will show the neophyte how to get started....beginning with 3-views,ending with workable plans.
Generic plans will show what is involved in building your own design,which is what the OP desired to accomplish.....sort of a wide range view of a narrow road . -How to do it,not WHAT to build.
We're offering the talents of many accomplished modelers ,wishing to extend their experience to those unfortunate enough to not know how to take the first step to bringing a dream to reality.
We appreciate your input,however,since that enables us to address reticent views.
I believe we're actually narrowing down a search area,to balsa scratch building,encompassing a variety of views.
Last edited by epoxyearl; May 17, 2012 at 02:42 PM.
|May 17, 2012, 03:08 PM
Joined Nov 2011
89 Posts
|May 17, 2012, 03:32 PM
Scallopking-you are the idea behind what we are trying to accomplish- an aircraft that fits nowhere comfortably,but will be at home here,because it,s a scratch-built generic airplane.-nuff said.
An unnamed niche-ne;"tag"
|May 18, 2012, 05:27 AM
Hi. What are your interests? What do you build,or what would you like to build?
|May 18, 2012, 05:50 AM
|May 18, 2012, 06:09 AM
Prop tests
So ,this morning,all motivated to test my homemade prop,I removed and cleaned the fuel tank in the old Telemaster ,which had sat idle since October.
I installed new lines and a filter,a new glow plug and tightened the prop one more time.
I filled the tank with new fuel,installed the glow driver,which I had charged all night,and tried to start the OS91.-Not a pop ! Nothing !
I took a new Glow plug and tried it in the driver....nada.-Apparently the battery has given up,although the indicater light had been on,showing a connection.
So it's off to the LHS at 10,to get a new Glowdriver. Darn darn darn.
|May 18, 2012, 08:06 AM
As for being a pessimist, I've always tried to help people on RC Groups and learn from other people's advice. I gave my reasons for why I didn't consider the thread to be a good idea and I was subject to a temper tantrum from the OP so I figured to leave well alone.
In answer to your question, I've been a balsa builder for over 30 years. Probably built well over 200 planes, mainly R/C but many vintage free flighters, plus I have a couple of ARTFs.
BTW - Putting lol at the end of a character assasination doesn't make you any less of an a***hole for saying it!
|May 18, 2012, 08:27 AM
I nailed that one -didn't I?
And you're the one who told me not to be so sensitive about remarks made on here.
The difference is,I accept my role in life.
Character assassination? Where? I don't see where anybody called you an axx hole...just pointed out you have a unique way of presenting yourself,emphasing my faults,and minimising your own.
And I can take it without going to the moderators and reporting you,although if they see it and point you,I won't disagree. I Yam what I Yam.
Last edited by epoxyearl; May 18, 2012 at 08:41 AM.
|May 18, 2012, 08:48 AM
OK - so we've obviously wound each other up. You're the only person who's taken issue with me since I've been a member of RC Groups, and I've clearly annoyed you as well, so let's agree to play nice in future
We've probably got much more in common than our differences - deal?
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Drama Ghost Isode 13 Raw
Hyosung shares her thought on her first drama 'Ghost-Seeing Detective'
In a recent interview, Secret's Hyosung shared her thoughts on her first drama "Ghost-Seeing Detective".
In this OCN's drama, Hyosung portrayed a ghost girl who helped the detective to solve mysterious cases. The drama came to an end on the 7th.. ... Read more
Hyosung Transforms into High School Girl for New Drama "Ghost-Seeing Detective Cheo Yong"
Secret's Hyosung has recently updated her Instagram with several photos of herself transforming into a high school student for her new drama "Ghost-Seeing Detective Cheo Yong." . ... Read more
SECRET's Hyosung handwrites a letter analyzing her character in OCN drama 'Ghost-Seeing Detective'
SECRET"s Hyosung showed her passion and immersion into acting for the upcoming OCN drama "Ghost-Seeing Detective". The production team revealed on February 4, "Hyosung sent us a handwritten letter analyzing her character, high school ghost Han Na Young." . ... Read more
More pictures revealed of SECRET's Hyosung for drama 'Ghost-Seeing Detective'
And the supernatural dramas continue in 2014 with upcoming OCN drama "Ghost-Seeing Detective," starring SECRET"s Hyosung as the helpful spirit of a high school student.
More pictures of Hyosung on set were revealed, showing her wearing her cute high school uniform while showing a variety of facial expressions. . ... Read more
Changmin to act out the tender feelings of a first love on Mnet's new ghost drama 'Mimi'
TVXQ"s Changmin will showcase his acting skills as the lead star in Mnet"s new ghost drama "Mimi"!
An Mnet rep stated on the 22nd, "Changmin will star as the male lead in the four-part ghost romance drama "Mimi"." . ... Read more
Hyosung perches on top of a traffic signal for drama 'Ghost-Seeing Detective'
SECRET"s Hyosung tried out acting with wires for the OCN drama "Ghost-Seeing Detective"!
The drama "Ghost-Seeing Detective" is about (drumroll please…) a ghost-seeing detective, his rookie partner, and a high school ghost who helps them out. Hyosung plays the high school ghost, and she pulled off filming her first series of scenes perfectly through her bright attitude. . ... Read more
Korean drama of the week "Ghost - Drama"
Korean drama of the week "Ghost – Drama" (2012)
Directed by Kim Hyeong-sik, Park Shin-woo
Written by Kim Eun-hee-I. ... Read more
"Ghost - Drama" Song Ha-yoon to come back with KBS
Actress Song Ha-yoon who is known as the reporter Choi Seung-hyeon from the drama "Ghost – Drama", has been cast for a short drama in KBS. . ... Read more
"Drama Special - Mother's Island", everyone in ghost make over
Summer evening feature KBS 2TV "Drama Special – Mother's Island" is being filmed in Baekam-ri in Yeong-gwang. This place well known for "Mapado". The crew and cast of this drama worked hard under the flaming hot sun and in the mud flat. . ... Read more
Upcoming Korean drama "Ghost Seeing Detective Cheo Yong"
Added the upcoming Korean drama "Ghost Seeing Detective Cheo Yong"'s page to HanCinema database
"Ghost Seeing Detective Cheo Yong" (2013). ... Read more


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Sequestration, Fiscal Cliff -What's the Deal?
I don't completely understand this, but I think the ball is in Prez. Obama's court. I mean I think he could make the Republican house members sweat and get a good deal.
So are they going to delay it or work it out? And what's so bad about taking away the Bush tax cuts anyway? Or is it the Defense budget cuts that would hurt jobs in California- causing a new recession in San Diego?
Inquiring minds want to know. Really. I get this was a special poison pill that allowed the debt limit to get raised. And that the Republicans refused to play ball and allow either the Bush tax cuts to go away or any tax on the rich in the meantime. And Obama said it's not going to happen, that some compromise or delay will take place....
But what if it did happen? What's so bad about lowering Federal discretionary spending 10% and putting taxes back where they were? I'm not in love with making more bombs...am I being naive??? Please tell me your thoughts and share your knowledge..
alexr, I am not sure about the rules and terms of outdoor games but I will venture to say "Ball in Play!"
Sequestration is a very big deal in terms of it's potential impact on the economy as well as the fact the cuts are mandatory and totally indiscriminate. 8-10 % cuts to all domestic and defense programmes, no exceptions except for medicare and SS . That is no way to run a country. Cuts are needed but they also need to be made wisely and in the right places or there will be serious economic and social consequences.
The time out on the tax cuts are not part of sequestration , just so happens that they expire Dec 31st at the same time sequestration kicks in. Removing that much money from the economy, at the same time as the cuts, will result in almost certain recession, boarding on depression.
It is the job of Congress to deal with budgets in a sane and rational way not wholesale cuts. president Obama has got to lead on this one. He needs to help broker a deal that involves BOTH revenues increases, without raising taxes on the middle class, coupled with cuts that help reduce the debt without throwing the country into total chaos. No time to play the bully but he must be firm and he needs to ensure a balanced approach.
I don't know that it will cause a recession that will be felt too much. Remember that the last recession had quite a kick because the housing market was in turmoil at the same time.
Canada went through it's own round of tax hikes and budgetary cuts years ago and yes, while some felt the cuts, it was a necessary measure that ultimately left us in much better financial shape. Chase is speaking from experience in her post.
Just remember, the longer you leave it, the worse it will be.
I read the article in the link back in October. It was and still is fascinating. Obviously, it was written before the election, so it talks about what might happen in each scenario (Romney winning and Obama winning).
Now that we know the outcome of the election, I read the Obama winning part again. Very interesting.
I do not remember how I came across this article in October. It's very likely it was posted on a thread here. If it was, I don't remember who posted it. But, if you posted it back then, please claim credit. It is a fascinating look at what Obama might/could do about that fiscal cliff.
Here is a link that might be useful: NY Mag Article
The time out on the tax cuts are not part of sequestration , just so happens that they expire Dec 31st at the same time sequestration kicks in. Removing that much money from the economy, at the same time as the cuts, will result in almost certain recession, boarding on depression.
Really waiting for our more learned members to weigh in on this, but it seems to me (and lord knows I can be wrong:) that the republicans "might" have set themselves up with the "sequestration" part of this non-compromise with Obama. In fact I wonder if the democrats knew this would come to pass? .. shrug
I'm not quite on board with taxes 'removing the money from the economy'. Given that the gvt turns around and spends it very quickly in the same economy paying salaries, buying fighter jets, and so on.
Point being reinforced that a major hit to the economy comes from reduced gvt spending. If they stop funding new fighter planes from General Dynamics, a lot of people lose their jobs.
A followup yesterday from the same author in the link.
I agree, ohiomom. Hoping to get some thoughts from some here that know a lot more about this than I do.
I read something several years ago about Obama. It was early in his first term and I was honestly unhappy with some of the things he wasn't doing. I'll never find the article, but the author basically said to be patient. That Obama was playing chess, while the rest of us were playing checkers. I thought that was a bit over the top, but perhaps he was right.
Here is a link that might be useful: Followup
"Obama was playing chess"
.....me thinks a lot of people have made the mistake of underestimating this president, and may have even taken kindness/compassion for weakness.
This may play out as successful as their campaign strategy.
Interesting days ahead...
snip" To recap, the basic situation is this. Back when George W. Bush was in office, he wanted to cut taxes. And he wanted to disguise the cost of his tax cuts. So he had his allies on Capitol Hill write the legislation so that the tax cuts would automatically expire at the end of a 10-year window.
That window closed at the end of 2010. But during the 2010 lame-duck session, Republicans were riding high on electoral victory and the Obama administration was concerned that tax hikes would hurt the economy. So they cut a deal to extend the Bush tax cuts two more years into the 2012 lame-duck session. It was a smart idea for everyone concerned. With the economy weak, there really was no case for a short-term tax increase, and this way the presidential election would resolve everything. If Obama lost, his GOP opponent would surely sign a permanent extension of the Bush tax cuts. But if Obama won, then he'd block any extension.
But Republicans didn't create permanent cuts when they had the chance in 2002. Their daring strategy raised the stakes, but they didn't get the cards they need. Game over.
Yet the conservative movement, Boehner, the media, and- most amazingly of all, many leaders in the Democratic Party -are still playing. Boehner delivered a post-election speech calling for tax reform that would put the top marginal income tax rate even lower than it is today. Sen. Chuck Schumer says Democrats will work with the business community to persuade Boehner to change his mind.
The conceit here is the frankly bizarre idea that since Obama wants to extend the Bush tax cuts for the middle class, he needs to engage in some kind of bargaining process. But this is silly. The Senate already passed a plan to extend the middle-class tax cuts. Now the choice before the House of Representatives is whether they want to vote to pass that plan before the new year or after the new year. Grover Norquist, the conservative Solon on taxes, appears to have made a metaphysical ruling that a vote for partial extension (before the new year) is a vote for higher taxes. That's silly, but the dictates of holy writ are often a bit arbitrary. All Republicans need to do is wait until the Bush tax cuts have already expired. At that point, a vote for a tax cut that Obama will sign-i.e., the middle-class tax cuts only-would clearly be a vote to cut taxes rather than raise them.
To take the bargaining process seriously at this point you have to believe that come 2013, House Republicans would actually refuse to cut taxes on the grounds that the president's tax-cut proposal doesn't cut taxes enough. Then they would blame the economic drag and middle-class pain that their own refusal to cut taxes had caused on the Democrats. But that doesn't pass the laugh test as a political argument. It ignores the fact that the GOP quite genuinely wants to see rich people pay lower taxes. And since rich people have lots of income that falls below the top bracket cutoff, they actually benefit massively from the middle-class tax cuts Obama favors.- snip
Here is a link that might be useful: limk
Speaking conversationally here, you know how many people I meet that don't understand the following- (maybe we should blame the media)-(from David's link above):
"And since rich people have lots of income that falls below the top bracket cutoff, they actually benefit massively from the middle-class tax cuts Obama favors."
I'll be half way through a conversation when it dawns on me that the other side thinks a tax raise is on their entire earnings. And they'll feel sorry for the rich, "Golly, they paid 90% tax in 1960?"
I get a similar sinking feeling when someone says Social Security needs to be cut or the age requirement need to be raised because it's bankrupting us...etc. When actually only a tiny tweak is needed to get through the baby boom. And I do blame the media for some of this hysteria.
I'll be half way through a conversation when it dawns on me that the other side thinks a tax raise is on their entire earnings.
We've seen the same thing here. People constantly saying that if the tax rate goes up, people will stop earning money. Puhleeeeassse! They make it sound like the more they earn the less they take home. Clearly do not understand how the tax code works.
Clearly, the more one earns, the higher the tax rate, and the more in total taxes are paid.
There will be--trust me--people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington.
There will be--trust me--people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington.
Ah, the people you hang out with are amazing.
They think Washington cares, or what? And if they don't want to exploit a market - make more money - then I imagine someone else will be happy to do so.
Why, it might even be somebody grateful for what the government has done for them - you know, immigrants, student loan recipients, ex-welfare moms, and so on - so happy to be making enough salary/profit now to pay federal income taxes.
Imagine that - giving back to your country, instead of me, mine, me mine.
There will be--trust me--people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington.
They may be a few, but I've seen more planning regarding capital expenditures, sales of assets, taking a bonus in a subsequent rather than current year, etc. in light of changes in the tax code than those intentionally reducing personal income for extended periods to spite someone else. No prudent business person that I have ever known what pass up an opportunity to make money. Laying low risks yielding market share, missing investment opportunities, losing professional standing, gaps in resume, etc.
There will be others who will gratefully fill the gap created by the resentful slackers.
Ridiculous. And laughable.
Like anyone would say oh, no, I'm not goint to make more money. I'm not going to put myself into that higher bracket. They are only charged the higher rate on the amount over the line where the tax rate goes up. But, of course you, demi, understand that (at least I think you do). I'm at a loss for words to describe how ridiculous that statement is.
"people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington.
That is one of the most ridiculous things I have read here."
I have known 1 person who did this and 1 who was considering it. The first was a person living in a Scandinavian country where, when his tax rate hit 65% during the year, he just stopped working because it was no longer profitable for him to work.
I knew another person 2 or 3 years ago who was considering to refuse a raise that would put him just over the threshold and into another tax bracket. I don't know how that turned out.
When/if tax rates get too high they do discourage productivity, as in the first case above. You don't want the talented and productive people sitting on the sidelines because it's too expensive for them to work. In the case of a 65% bracket, yes, that's way too high.
A 20% increase in taxes might be enough to alter behavior if a wage earner and their family are sensitive to swings in tax rates. For example, if the tax rates increase on the middle class, I intend to increase the amount of 401K contributions, and maybe throw a bit more in the tax deductible health savings account. It could actually cause me to pay less in taxes than I did last year, even though my salary is 3% higher.
So tax rates can have consequences, in that they change financial behaviors of people who are sensitive to tax increases. Ever wonder why all those ugly strip malls started springing up in the 50s? Tax shelters.
lionheart - I cannot speak about your 1st case since I know nothing about tax laws in other countries, nor does it apply here.
For the 2nd case, you do understand that the higher tax rate will only apply to the income above the threshold, right? So, you will still take home more money, not less money. Assuming you understand that, please explain why in the world anyone would refuse a raise that will let them bring home MORE MONEY and instead stay at their current level and bring home LESS MONEY.
I'm sorry, but I find it impossible to believe that anyone in their right mind would do this. It makes absolutely no sense since it is impossible to take home less money.
Think what you wish, what I said is true.
Like Lionheart, I know people that are willing to put their money where their mouths are.
Obama and the Democrats can go ahead and raise taxes on the higher earners, it still won't be anywhere near enough, and there will be numbers of earners will just not contribute to the economy, won't risk the money and who will just let the government not get what it's depending on by not exceeding the limit to put them in the higher tax bracket.
It doesn't sound silly to someone who does not worship money.
that is why liberals don't get conservatives, liberals worship taking other peoples money from taxes and the power they get from it. just the liberal forget the the 60's since business can do the same thing protester did then.
the doctors in Canada do it. when they reach the limit of money they make reach there cost. they shut for rest season.
As long as we're dragging out anecdotal evidence, here is mine: I know a business owner who donated $10,000 to the Romney campaign and who is currently searching for ways to increase business income -- as in new customers, updating products, etc.
"There will be--trust me--people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington."
Yes people will throw temper tantrums & say I won't earn & you can't make me! I won't invest if capital gains taxes are 25%.
That can't be what your saying or is it more I will maximize every loophole possibles so it appears I have no income or I have deferred income.
people who INTENTIONALLY will not make as much money as they can--in order to send a message to Washington.
Most of us who own businesses are far more interested in making sure that they continue to thrive than in sending messages to anyone. If competitors in my sector want to get carried away with emotionalism and make less money, that's fine with me. Voids to fill mean more customers and more money for me. Taxes a part of doing business, I plan for them and get on with it.
I won't invest if capital gains taxes are 25%.
That can't be what your saying or is it more I will maximize every loophole possibles so it appears I have no income or I have deferred income.
No, it means there are people that will not invest if capital gains tax rates are increased too much, or they will control their investments so as not to earn over a certain amount.
I won't invest if capital gains taxes are 25%.
Depends on how long you are looking to hold the asset(s). A long-term investment may well extend beyond President Obama's second term in office. Who knows what the rate will be then. The one you're hurting most could be your portfolio.
I won't invest if capital gains taxes are 25%.
All investments carry risks, so I understand how an investor might decide that the potential net return with a higher tax rate wasn't worth the risk. The earlier comments were about "send[ing] a message to Washington," not a risk/ROI assessment.
Beyond a reasonable cushion of liquidity, I don't have like "lazy money" that isn't working for me, but investment goals and strategies differ.
What's the figgin' "Death tax" exemption these days? 5 million? I remember just a dozen years ago it was only $675,000 - we used to call it "Inheritance Tax" and before that it was called an "Estate Tax". Maybe if the rich think that the exemption will be lowered to 1 million they'll just decide to die first. Of course the people who inherit it pay 0 (zero) capital gains. anyway....
I don't like comparing various years of tax rates because the tiers are different and so are the deductions, deferments etc.. Marginal versus Effective. It is confusing.
At least some people know that in 1960 the top tax bracket rate was 90% on income. Those were the good years.
Capital gains tax has been higher too- for many years of the 1970's it was 35%- those were good years too...Many of Reagan's years Long Term Capital gains were well over 25% and a few years close to 33%- and that was the result of the Tax Reform Act of 1986- a law championed by Reagan! I guess that makes Reagan a Communist ...(although he did reduce the rate on the higher income tax brackets.)
The link below is from a short article in Mother Jones- there is another link there to a CRS report if you care to wade through it.
Here is a link that might be useful: Charts- How The Rich get Richer
Capital Gains tax only matters if you are selling so I guess what you really mean is that you will hold on to the investments you have and not sell them regardless of the gains you may make. Sounds like cutting off your nose to spite your face to me.
In preparation for a boost to capital gains are you going to liquidate all your assets now or will you hold them in the hopes the if rates go up they are lowered some day? That could be a bit risky....
There is no way that there will be an income tax hike but even Romney said he would consider revenue increases by the closing of loopholes and increasing revenue streams to those earning over 250K. It's not a position held only by Democrats. Revenue increases would have happened under the Republicans as well...because there is no choice if you are to get yourself out of this mess in a responsible fashion.
Everyone says the deficit is a huge concern to them and it should be. New spending is pretty much a non starter and programm cuts are inevitable.
The cuts and the revenue increases are all aimed at reducing the deficit not additional spending ......isn't that the goal?
Everyone contributed to the financial mess and everyone has an obligation to contribute to the solution. It can't happen another way.
Posted by alexr (My Page) on
Mon, Nov 12, 12 at 1:49
What's the figgin' "Death tax" exemption these days? 5 million? I remember just a dozen years ago it was only $675,000 - we used to call it "Inheritance Tax" and before that it was called an "Estate Tax". Maybe if the rich think that the exemption will be lowered to 1 million they'll just decide to die first. Of course the people who inherit it pay 0 (zero) capital gains. anyway....
As of January 1, 2013, just weeks away, the exemption reverts back to the 2001 and 2002 rates, which is only one million and a 55% TAX RATE.
So I guess those older folks with an estate worth much more than $5 million have only a few more weeks to die- maybe at the hands of their relatives! But Congress may yet bail them out,(them being the 'Nobles') we'll just have to wait and see... might be a few unnatural deaths of the rich before New Years...
Oh by the way, what's the 'Gift Tax' exemption now?
Here's a big talker changing his tune:
NEW YORK (CNNMoney) -- David Siegel, the CEO who had warned his employees they'd face layoffs if President Obama was re-elected, gave everyone a 5% raise last week instead.
Siegel isn't backing off his gloomy predictions for the economy under Obama's second term. But he said his company, Westgate Resorts, had record profitability this year and he wanted to share the success with employees, most of whom had not gotten a raise the year before.
The CEO said he believes his employees will need higher wages to deal with increased costs he expects everyone will face under Obama. And he's not backing off his prediction that developments like Obamacare and the Dodd-Frank financial regulations will hurt the economy in the years ahead -- and could lead him to make staff cuts eventually.
"I never told anyone if Obama got elected, I was firing anybody. That just got twisted by the media," said Siegel in a phone interview on Monday.
Before the election, he said that if Obama was re-elected, he might retire and even halt work on the 90,000-square foot home he now has under construction, which many believe will be the largest private home in the United States. But he said he's going to keep working, and building the home, "as long as I enjoy going to work and there are not more obstacles thrown in my way."
Here is a link that might be useful: source
That home put a lot of food on a lot of tables and kept a lot of people off of food stamps.
Gee. If the same resources had gone into building 90 x 1,000 sq foot homes, you would have the same economic benefits, and there would be 90 families with homes, instead of one. Thats a whole neighborhood, and they'd all pay property taxes, fund a school, build a community, etc. You know, that whole support the middle class thing that Obama talks about.
But keep on defending that 0.001%, pretending that building mega-mansions is what makes this country strong. I just hope he put in car elevators. Keepin' up with the Romneys.
People who build houses they can afford don't need defending by me, they don't need to defend or justify ANYTHING to ANYONE.
Who do you care what other people do with their money?
Assuming people paid their owed taxes, it's none of your business to speculate about how you think they COULD have spent their money.
None of your business.
Of course, your right to spend your time doing that.
I hope they did put in an elevator.
It helps people that work for OTIS or Kryssenthupp.
Its pretty much a joke around here, where one neighborhood of 20 meg-mansions in Telluride or Aspen burns as much natural gas and uses as much electricity as an entire town, what with each one having a heated swimming pool, 300 feet of heated driveway, etc.
Having money means you can kiss off conservation and environmental considerations. Who gives a rip about global warming when you can crank up the AC in your 90,000 sq foot home?
Good citizens all. Job Creators, worthy of our awe and worship.
How someone spends there money is their business but that does not mean that it is socially responsible. We all have an obligation to our environment and our fellow man.
For example, I was taken aback last year while in Florida with the numbers of HUGE gas/diesel driven yachts in the water. The water had a visible oil slick on it. That is just plain irresponsible and unnecessary but of course it is their "right" to spend their money as they wish even if it costs our environment.


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Here's the news on County Road 42
With summer in full swing, people may be wondering why the construction project on County Road 42 hasn't started yet.
According to Dave Robley, Douglas County Public Works director, it's because the public spoke and public works listened.
Last summer - during most of the season - the County Road 42 project was in full swing. It began early and concluded at the end of August.
Are you a newspaper subscriber but you don't have a Digital Access account yet? https://secure.forumcomm.com/?publisher_ID=40&event=subscriber/lookup.
You will need your subscription account number and phone number. Not sure if you have an account? Email us at email@example.com and we can help you.


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North East
Regional Campaigns Officer, North East:
Lucy Dixon
RNIB, Parkside House
Elton Street East
Telephone: 0191 234 5409
Email: email@example.com
Get involved
Want to make a difference in your region? Fed up of feeling excluded from local services?
Join RNIB campaigns in the North East to push for change in the local authority decisions that impact lives every day. Contact RNIB campaigns team on 020 7391 2123 or at firstname.lastname@example.com.
Or contact Lucy directly on 0191 234 5409 or at firstname.lastname@example.com.


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Find commute times to your work, school, gym and more.
Willowbrook Place
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Free Rent Until 4/1/15 on ALL Homes in Inventory, $ 199 Deposit, $ 199 Closing Fee, No App Fee
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On public transit line. Close to all college campuses - MUO, UT, Lourdes. Centrally located with easy access to I80-90.
Willowbrook Place in Toledo, OH offers a quality community setting that is only minutes from the city. We're only a short distance from I-475 and the Ohio Turnpike, giving you access to everything you need. At Willowbrook Place, we pride ourselves on offering residents the best community possible. Our clubhouse is perfect for events, our swimming pool and playscape are lovely, our on-site customer service team is ready to assist with any questions and we take pride in our community. So if you are looking for a new home in the Toledo area, consider Willowbrook Place. You won't find anything else like it!
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Lease Terms Offered: 12 mos. dogs and cats permitted. Full security deposit required with pets. 1 pet per home. An additional rent charge of $25/month applies. Noisy, unruly or dangerous pets are not permitted, including Rottweilers, Dobermans, Pit Bulls and Wolf Breeds. Contact management office with any questions regarding pet policy.
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Very peaceful and clean community. The grounds are always kept up nice and litter free. The residents seem t Read Moreo be friendly and the office staff (management) has always been friendly and helpful.
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The time we were renting there they went through 4 different managers who changed rules every time. We had and Read More ok to paint my daughters bedroom by the time we moved out we got charged for it because new manager did not approve. On top of that there maintenance man quiet leaving us without a person to fix anything for almost a month. We had a leaking shower that leaked through the wall that was not fixed due to this issue. Instead of finding a sub they ignored all our requests.
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Nixon Tours Stalactite-Infested Basement of State Capitol
Gov. Jay Nixon took a handful of Missouri lawmakers and reporters on a tour of the muddy, stalactite infested basement of the state Capitol to show what repairs need to be made to the nearing century old building.
Woman Shocked While Recusing Cat From Flooding
A woman is was shocked while saving a cat from a flooded basement.
Frail Mo. Teen Found Cuffed In Parents' Basement
Authorities found a frail 17-year-old boy handcuffed to a pole in his parents' Kansas City basement, where he said he'd been kept since his father withdrew him from school in September.
Woman's Body Found In Burning Alton Home
Fire has been labelled as "suspicious".
MSD Can't Buy Out Residents with Water Damage
Some South St. Louis residents are looking for a buy-out after a storm caused water damage.


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Flame Resistant Overalls
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How can I cause a Clojure macro to act as a function, so I can pass it as an argument for example? I would expect to have to wrap it somehow.
I would not expect the wrapped version to behave exactly the same as the original macro (differences of call by name vs call by value), but it would be useful in a few cases where this wasn't important.


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The Gist
From Our Editors
Rather than relying on microwave ovens, heat lamps, and deep fryers, chef Kathy Christopher and her culinary team craft all of Hilltop Ale House's pub favorites right on the grill. Cooks create each item on her weekly menu entirely by hand, roasting cashews dusted with curry spices and stacking Reuben sandwiches with Boar's Head corned beef braised in Blackthorn hard cider. Meanwhile, barkeeps work the taps, helping wash down meals with a selection of wine, ports, bubbly, spirits, and more than 15 microbrews including a rotating selection of handcrafted suds from small, local breweries and cask-conditioned beers in kegs powered by hand-pulled engines that use no CO2. A 55-inch high-definition LCD television bathes diners in the light of major-league matchups, while the English-style pub's back room–adorned with French doors and windows looking out over a garden–sets the stage for special lunches, dinners, and paintball matches.