text:
FCC takes aim at annoying telemarketing calls
Federal Communications Commission circulated a proposal designed to close loopholes, reaffirm current rules
FCC takes aim at annoying telemarketing calls Federal Communications Commission circulated a proposal designed to close loopholes, reaffirm current rules Check out this story on detroitnews.com: http://detne.ws/1HMm0X5
AP Published 5:37 p.m. ET May 27, 2015
Washington— Those automated phone calls during the dinner hour, late at night or to your wireless phone can be so frustrating — and the government is taking note.
The head of the Federal Communications Commission circulated a proposal Wednesday designed to close loopholes, reaffirm current anti-robocall rules, and encourage wireless and wireline carriers to do more to fight against unwanted telemarketing calls and spam text messages to consumers.
A key part of the plan: clearing up any confusion over whether the phone carriers can offer blocking services — so-called robo-blocking technology that could help people stop the unwanted calls.
"We are giving the green light for robocall-blocking technology," FCC Chairman Tom Wheeler wrote in a blog-post on the commission website.
Phone companies have said that they worry that automatic call-blocking might run afoul of laws requiring them to connect phone calls.
In his blog post, Wheeler said the technology can be offered without violating the rules. "The FCC wants to make it clear: telephone companies can — and in fact should — offer consumers robocall-blocking tools," he said.
Another part of the plan aims to make it easier for consumers to say "no" to robocalls and texts. People would simply be able to say "stop" and cannot be told that they need to fill out a form and mail it in to get the calls to cease. And for people who switch phones and inherit a new phone number, the Wheeler proposal says they should not be subjected to unwanted calls that the previous owner consented to.
Unwanted robocalls, robotexts, and telemarketing calls are the biggest source of consumer complaints at the FCC, with the agency receiving more than 215,000 complaints last year alone.
Consumer groups praised the Wheeler plan, which the commission will vote on at its June 18 meeting.
"This should clear the way for companies to offer the call-blocking tools that people want to stop robocalls from invading their homes morning, noon and night," said Delara Derakhshani, policy counsel for Consumers Union.
An industry group, US Telecom, said it was studying Wheeler's proposal. "USTelecom supports the FCC's efforts to provide consumers with options to mitigate unwanted phone calls, and to take strong enforcement actions against illegal robocallers," spokeswoman Anne Veigle said.
She declined to say specifically whether the group supports Wheeler's plan to allow or encourage the phone companies to offer the blocking technologies to consumers.
A spokeswoman for AT&T referred a reporter to US Telecom for comment. Representatives of Verizon, Sprint and T-Mobile didn't immediately have a comment.
Some lawmakers questioned parts of the proposal.
Sen. Edward Markey, D-Mass., a member of the Commerce, Science and Transportation Committee, expressed concern about an exception in the proposal that would allow free calls or texts in some circumstances, such as to alert a consumer to possible fraud on a bank account or to remind a person about an important prescription refill.
The proposed exemptions, he said, "will result in an increase in unwanted calls and texts to consumers without their consent."
The commission had received more than 20 petitions from companies —including bankers, debt collectors, app developers, retail stores, and others — seeking clarity on rules pertaining to robocalls. Dozens of state attorneys general also had asked the FCC to weigh in on whether blocking robocalls might violate any telecommunications statutes.
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\section{Introduction}

\noindent Threshold models have been used to theoretically describe
processes of contagion in social, financial, and infrastructure
networks
\cite{granovetter1978threshold,morris2000contagion,guilbeault2018complex,kempe2003maximizing}.
Unlike the classic or simple epidemic models used to describe the
spread of infectious diseases, threshold models require a node to have
multiple transmissions from neighbors before changing from an
inactive-susceptible-dysfunctional state to an
active-infected-functional state, or vice versa.  These processes
exhibit propagation of states as cascades that lead to a first-order
transition of differing magnitudes
\cite{Watts,lee2014threshold,bizhani2012discontinuous,cellai2013critical}.
We can use these models to describe the spread of innovation,
information, and behavior among nodes because they tend to change
their state or behavior after interacting with not one, but a group of
other nodes
\cite{kempe2003maximizing,wang2016dynamics,monsted2017evidence}.  For
example, Centola showed in an online social network experiment that an
individual tends to adopt a behavior after several neighbors exhibit
the same behavior \cite{centola2010spread}. A threshold model is an
activation process when the number of active nodes increases with time
and a deactivation process when it decreases.

K-core percolation is one of the simplest threshold models used to study
the deactivation process \cite{dorogovtsev2006k}. In k-core percolation
all nodes are initially active. A fraction $1-p$ of nodes then becomes
inactive or dysfunctional. The fraction of active nodes after the initial failure, $p$, is the control parameter of the model. Then a recursive rule is applied: if an
active node $i$ has fewer than $k_{c}^\ast$ active neighbors, it becomes
inactive. If $k_c^\ast$ is the same for all nodes, then the process is called
homogeneous k-core percolation, if not, then it is called heterogeneous
k-core percolation \cite{cellai2011tricritical}.  In the k-core process,
when all nodes have a number of active nodes greater than or equal to
the threshold $k_{c}^\ast$, the process reaches a steady state. At this
stage the order parameter of k-core is the fraction of active nodes or
the fraction of nodes that belong to the largest connected cluster or
giant component (GC).

Dorogovtsev {\it et al}.~\cite{dorogovtsev2006k} demonstrated that in the
homogeneous k-core process the giant component equals the fraction of
active nodes, and that it exhibits a first-order transition when
computed for several values of initial failure $p$. In addition, Baxter
{\it et al}.~\cite{Bax_2011} found that for heterogeneous k-core there are
finite clusters of active nodes at the steady state, indicating that the
fraction of nodes belonging to the GC is lower than the total fraction
of active nodes. They also found that for the same set of parameters the
process can exhibit simultaneously a continuous and a discontinuous
transition not observed in homogeneous k-core.

Bootstrap percolation is a simple threshold model often used to study
activation processes \cite{adler1988diffusion,Bax_2010}. In this model
all nodes are initially inactive, except for a fraction $f$ of nodes
that activate spontaneously. Then each inactive node becomes active if
it has at least $k_{b}^\ast$ active neighbors. Analogous to k-core,
when $k_b^\ast$ is the same for all nodes the process is homogeneous
bootstrap percolation, and when it is not, the process is heterogeneous bootstrap
percolation. This activation process continues recursively until a
steady state is reached. Baxter {\it et al}.  \cite{Bax_2010,Bax_2011} found
that the total fraction of active nodes $S_b$ exhibit a first-order
transition at a critical value $f_{c1}$. Using a generating function
formalism \cite{Cal_01,New_01,New_02,Bra_01} they also proposed
equations for computing the fraction of active nodes belonging to the
GC, $P_{\infty,b}$, as a function of $f$, but they did not compare
their results with those of stochastic simulations. We perform
simulations of the bootstrap percolation process, and find that the
equations in Ref.~\cite{Bax_2010,Bax_2011} underestimate the fraction
of nodes that belong to the giant component. Using the generating
function formalism, we find the correct solution for $P_{\infty b}$
and show that Refs.~\cite{Bax_2010,Bax_2011}
disregard some activation events when the giant component is
computed.

Although there are several variants for activation and deactivation
models, such as the Watts threshold model and generalized epidemic
models
\cite{chung2014generalized,miller2015complex,gleeson2007seed,Watts}, we
here focus only on the ``canonical'' processes of k-core and bootstrap
percolation explained above. For an extensive description of these
models see Refs.~\cite{lorenz2009systemic,pastor2015epidemic}.

Baxter {\it et al}.~\cite{Bax_2011} compared heterogeneous k-core and
bootstrap percolation and found that they have different structures of
active nodes, which suggests that these processes cannot map each
other. Miller \cite{miller2016equivalence} indicates that the two
processes are complementary because the behavior of active nodes in
heterogeneous k-core percolation is the same as that of inactive nodes
in heterogeneous bootstrap percolation.  Miller proposes that when
mapping the two processes the relationship of the node thresholds in
k-core and bootstrap percolation must be $k_b^\ast = k-k_c^\ast+1$,
where $k$ is the node degree or the number of node connections. In
addition, Janson proves the relation between these processes in random
regular graphs \cite{janson2009percolation}. However, this relation
has not been proven mathematically for a complex network of any degree
distribution $P(k)$, and for any distribution of the
activation/deactivation thresholds.

We here use a generating function formalism to examine the bootstrap
process theoretically and compare our results with those from
stochastic simulations. In Sec.~\ref{sec.equiv} we describe the
equivalence between k-core and bootstrap percolation for any degree
distribution. In Sec.~\ref{sec.GCMat} we present equations for
computing the GC for bootstrap percolation that include activation
events not taken into account in Ref.~\cite{Bax_2011}). Our
analytical results fully agree with our stochastic
simulations. Finally, in Sec.~\ref{sec.Concl} we present our
conclusions.

\section{Equivalence between Bootstrap and K-core percolation}\label{sec.equiv}

\noindent
In a k-core percolation process, $k_{c}^\ast$ is the threshold number
of active or functional neighbors below which an active node becomes
inactive. We assume that this threshold follows a cumulative
probability distribution $r_c(j,k)=P(k_c^\ast \leq j \mid k)$
\cite{di2017cascading}, where $k$ is the degree of the node and
$k_c^\ast$ is its functionality threshold in k-core percolation. The
function $r_c(j,k)$ is the probability that a node with degree $k$ has
a threshold $k_c^\ast$ lower than or equal to $j$. We assume that at
the beginning of the k-core process, the threshold of any node is not
larger than its degree. Thus, initially, the system is stable, which
is different from the original definition of k-core
\cite{dorogovtsev2006k}. We assume that as a result of the initial
attack, a fraction $f=1-p$ of nodes are destroyed and this initiates
the process of cascading failures at the end of which only the
fraction of active nodes $S_c(p)$ is left.

To connect k-core and bootstrap percolation, we first describe how to
use the generating function formalism to calculate the fraction of
active nodes in the k-core process.

When the process is in a steady state, if we follow a randomly chosen
link in one direction we will end up at a node which we will call
``target'', while in the opposite direction we will reach a node which
we will define as ``root''. In k-core percolation we then define $Z_c$
to be the probability of reaching a target node with at least
$k_c^*-1$ outgoing active neighbors when following a link chosen at
random. Here an outgoing neighbor node of the target node is any
neighbor node other than the root node. Note that root is assumed to
be in the active state, otherwise the node with $k_c^\ast-1$ outgoing
active neighbors must fail according to the rules of the k-core
percolation.  Following Ref.~\cite{di2017cascading}, the fraction of
active nodes $S_{c}$ in the steady state for an initial failure of a
fraction of $1-p$ nodes is
\begin{equation}\label{WWc}
S_{c} =p\Psi_c(Z_c,1-Z_c).
\end{equation}
Here $\Psi_c(Z_c,1-Z_c)$ is the probability that a random node has a
number of active neighbors greater than or equal to its threshold. As
a function of two arguments, $x$, and $y$, $\Psi_c(x,y)$ is defined as
\begin{equation}
  \Psi_c(x,y)=\sum_{k=0}^\infty P(k)\sum_{j=0}^k\binom{k}{j}r_c(j,k)x^jy^{k-j}.
  \label{e:Psi_c}
\end{equation}
The parameter $Z_c$ satisfies a recursion equation,
\begin{eqnarray}\label{ZZc}
Z_c =p\Phi_c(Z_c,1-Z_c),
\end{eqnarray}
and
\begin{equation}
\Phi_c(x,y)=\sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{j=0}^{k-1}\binom{k-\
  1}{j}r_c(j+1,k)x^{j}y^{k-j-1},
\label{e:Phi_c}
\end{equation}
where $\langle k\rangle=\sum_{k=1}^\infty kP(k)$ is the average degree of the network.

On the other hand, in the bootstrap percolation process a fraction $f$
of nodes becomes active at the beginning of the process. We call these
nodes that activate spontaneously the ``seed'' nodes, because they trigger
the activation cascade of the inactive nodes, forming extensive
branches of active nodes. Naturally, we define nodes that were not
activated initially as ``non-seed''.

After the initial activation, a non-seed
node with a degree $k$ becomes active if the number of its active
neighbors $j$ satisfies $j \geq k_b^\ast$, where $k_b^\ast$ is the
bootstrap functionality threshold.
Similar to k-core percolation, the cumulative distribution of the
bootstrap activation threshold is $r_b(j,k)=P(k_b^\ast \leq j |k)$.

It can be shown that the process of activation of nodes in the
bootstrap percolation with the fraction of seeds $f$ is equivalent to
deactivation of nodes in the complementary k-core percolation process,
in which the initial failure destroyed a fraction $1-p=f$ of nodes, if
their thresholds are complementary. Thus, the seed nodes in bootstrap
play the role of initially failed nodes in k-core. Furthermore, this
implies that the nodes that are active in bootstrap percolation are
inactive in k-core and vice versa.  We will call such nodes b-active
and c-inactive and b-inactive or c-active,
respectively. Fig.~\ref{gephi} illustrates that bootstrap and k-core
are complementary, when both process develop on the same graph with
complementary thresholds.

\begin{figure}[ht]
\vspace{0.2cm}
\begin{center}

  \includegraphics[width=0.9\textwidth]{Fig1.eps}
\end{center}
\vspace{-0.5cm}
\caption{Bootstrap and k-core percolation processes developed on
  a randomly generated network. The bootstrap threshold for a node
  with degree $k$ is $k_b^*=\lfloor{k/2}\rfloor+1$, where
  $\lfloor{x}\rfloor$ denotes the integer part of $x$. If we set the
  seed nodes in bootstrap as initially failed nodes in k-core, then if
  $k_c^*=k-\lfloor{k/2}\rfloor$, according to Eq.~(\ref{thresh}), then
  both process are complementary. All non-seed nodes activated in
  bootstrap coincide with deactivated nodes in k-core, and all
  non-seed nodes that were not activated in bootstrap are the same as
  those that remained active in the k-core process. The numbers
  indicate the thresholds corresponding to each process. Figure
  adapted from Ref.~\cite{miller2016equivalence}}\label{gephi}
\end{figure}

It can be shown that $Z_c=1-Z_b$, where $Z_b$ is the probability of
reaching, following a random link, a seed node or a non-seed with
$k^*_b$ outgoing links leading to activated nodes. Analogously, it can
be shown that $S_b=1-S_c$, where $S_b$ is the fraction of the active
nodes in the bootstrap percolation. We will provide a rigorous proof
of this equality by deriving the equations of bootstrap percolation
using the k-core equations. For this purpose we have to connect first
the thresholds distributions $r_c(j,k)$ and $r_b(j,k)$.

We have established that the activation of b-inactive nodes is
equivalent to the deactivation of c-active nodes. The condition of
activation is that the number of b-active neighbors, $j_b$ of a
b-inactive node with degree $k$ satisfies $j_b\geq k_b^\ast$. From the
point of view of the k-core percolation, this node has $j_c=k-j_b$
c-active neighbors, and the condition of its deactivation is that $j_c
=k-j_b< k_c^\ast$, or $j_b>k-k_c^\ast$ or $j_b\geq
k+1-k_c^\ast$. Since this last inequality must coincide with
$j_b\geq k_b^\ast$, then,
\begin{equation}\label{thresh}
k_b^\ast=k+1-k_c^\ast.
\end{equation}

This simple equality shows how the thresholds of both process are
related depending on the degree of the nodes. Note that this relation
indicates that in non-regular graphs, the complementary process of
homogeneous bootstrap percolation is heterogeneous k-core
percolation. Likewise, homogeneous k-core percolation is the
complement of heterogeneous bootstrap percolation.

Now we are in conditions to establish a connection between the
threshold distributions of both processes. Using Eq.~\ref{thresh},
\begin{eqnarray}
r_c(j,k)&=&P(k_c^\ast \leq  j  |k),\nonumber\\
r_c(j,k)&=&P(k+1-k_b^\ast \leq  j  |k),\nonumber\\
r_c(j,k)&=&P(k_b^\ast \geq k+1-j  |k),\nonumber\\
1-r_c(j,k)&=&P(k_b^\ast < k+1-j  |k),\nonumber\\
1-r_c(j,k)&=&P(k_b^\ast \leq k-j  |k) \equiv r_b(k-j,k).\nonumber
\end{eqnarray}

Thus, we obtain the relation between the threshold distributions,

\begin{equation}\label{rr}
r_c(j,k)=1-r_b(k-j,k).
\end{equation}

We will show that when the threshold distributions for k-core and
bootstrap percolation satisfy Eq.~(\ref{rr}) then both processes are
complementary.

Finally, we will derive the equations for the bootstrap percolation
using Eqs.~(\ref{e:Phi_c}), (\ref{e:Psi_c}) and (\ref{rr}) using the
k-core percolation as a starting point. Note that Eq.~(\ref{ZZc}) can be
rewritten using Eq.~(\ref{rr}) as
\begin{equation}
Z_c=(1-f)\Big(1- \sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{j=0}^{k-1}\binom{k-\ 1}{j}r_b(k-j-1,k)Z_c^{j}(1-Z_c)^{k-j-1}\Big)
\end{equation}

Introducing new summation index $i=k-(j+1)$ and using the
symmetry of binomial coefficients,
we see, that this equation is equivalent to
\begin{equation}
1-Z_c=f+(1-f)\sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{i=0}^{k-1}\binom{k-\ 1}{i}r_b(i,k)Z_c^{k-i-1}(1-Z_c)^{i}
\end{equation}

Introducing
\begin{equation}
\Phi_b(x,y)=\sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{i=0}^{k-1}\binom{k-1}{i}r_b(i,k)x^{i}y^{k-i-1},
\label{e:Phi_b}
\end{equation}
we arrive at the following recursive equation
\begin{equation}\label{ZZc2}
  1-Z_c=f+(1-f)\Phi_b(1-Z_c,Z_c).
\end{equation}

If we denote $Z_b=1-Z_c$, then we can write
Eq.~(\ref{ZZc2}) as,

\begin{equation}\label{ZZb3}
  Z_b=f+(1-f)\sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{j=0}^{k-1}\binom{k-1}{j}r_b(j,k)Z_b^{j}(1-Z_b)^{k-j-1},
\end{equation}
or
\begin{equation}\label{ZZb}
  Z_b=f+(1-f)\Phi_b(Z_b,1-Z_b),
\end{equation}
which is the generalization for the analogous equation for the
homogeneous bootstrap percolation~\cite{Bax_2011}.

Note that the meaning of $Z_b=1-Z_c$ is the probability of a link to
connect {\it any} (active or inactive) root to an already b-activated
node, while $Z_c$ is the probability of a link to connect a c-active
node to a c-active nodes. Indeed, there are three types of links:
those connecting b-active with b-active nodes, those connecting
c-active and b-active nodes and those connecting c-active and c-active
nodes. Since the last category constitute the probability $Z_c$, the
first two together constitute the probability $Z_b=1-Z_c$. Thus, we
conclude that $Z_b$ and $Z_c$ are complementary. The difference in the
meaning of $Z_c$ and $Z_b$ is also reflected in the structure of the
functions $\Phi_b$ and $\Phi_c$ in which the former has a term
$r_b(j,k)$ while the latter has a term $r_c(j+1,k)$.

Using the same techniques as we use for the derivation of $Z_b=1-Z_c$,
it is straightforward to show that $S_b=1-S_c$ and then obtain the
final equation for the active nodes in the bootstrap percolation:
\begin{equation}\label{WWb}
S_{b} =f+(1-f)\Psi_b(Z_b,1-Z_b),
\end{equation}
where
\begin{equation}
\Psi_b(x,y)=\sum_{k=0}^\infty
P(k)\sum_{j=0}^k\binom{k}{j}r_b(j,k)x^jy^{k-j}.\\
\end{equation}
This concludes the proof of the complementary of the k-core
percolation and bootstrap percolation with complementary threshold
distributions.

\section{Giant Component equation for bootstrap percolation}\label{sec.GCMat}

\noindent
In this section, we will generalize the equations for the size of the
giant component (GC) in heterogeneous k-core and bootstrap percolation
presented in Ref.~\cite{Bax_2010,Bax_2011} using a different
notation, and then we show that for the bootstrap percolation, their
equations underestimate the size of the GC. The source of this
discrepancy is the difference in the meaning of $Z_b$ and $Z_c$ as we
have shown in the previous section. In the k-core percolation, we
denote as $\alpha_c$ the probability that a randomly selected link,
originating at an active node, leads to the GC of active nodes, and
obviously this probability is less than or equal to $Z_c$. The
probability that a link coming from an active root node lead to an active target node
but not to the GC is $Z_c-\alpha_c$. Thus, the probability that a target node
with a degree $k$ and $j$ outgoing links leading to active neighbors,
is not connected to the GC is
\begin{equation}
\binom{k-1}{j}(Z_c-\alpha_c)^j(1-Z_c)^{k-j-1}.
\end{equation}
Summing up all these terms for different $k$ and $k_c^\ast$ and after
taking into account the probability of reaching a node with degree $k$
through a random link and the distribution of the thresholds $r_c$, we
conclude that the total probability that any node to which we arrive
by a random link is active but not connected to the GC is
\begin{equation}
  Z_c-\alpha_c=p\Phi_c(Z_c-\alpha_c,1-Z_c).
  \label{e:alpha_c}
\end{equation}
This equation can be solved together with Eq.~(\ref{ZZc}) for any initial survival probability $p$.
Note that if $r_c(1,k)=0$ for any $k>0$, this system of equations always have
a solution $\alpha=Z_c$ because if $r_c(1,k)=0$, each term of Eq.~(\ref{e:alpha_c}) has a factor $(Z_c-\alpha_c)$, and, thus, the first argument of the function $\Phi_c(Z_c-\alpha_c,1-Z_c)$
can be factored out.
The final equation for the size of the GC, $P_{\infty,c}$, can be written as the probability of randomly choosing an active node, $S_c$, minus the probability of choosing at random an active node with no links connected to the GC, which is $p\Psi_c(Z_c-\alpha,1-Z_c)$. Thus
\begin{equation}
  P_{\infty,c}=S_c-p\Psi_c(Z_c-\alpha,1-Z_c).
  \label{e:P_c}
\end{equation}
Therefore, if there are no nodes with $k_c^\ast=1$ and no autonomous
nodes ($k_c^\ast=0$), we have $P_{\infty,c}=S_c$, which means that all
active nodes are part of the GC.

Now we will turn to the derivation of the equation for the giant
component in the bootstrap percolation. For brevity we will drop
subscript $b$ in all the equations. Naively, one could expect that the
same equations (\ref{e:alpha_c}) and (\ref{e:P_c}) with small
modifications would work for the bootstrap:
\begin{equation}
  Z-\alpha =f G_1(1-\alpha) +(1-f)\Phi(Z-\alpha,1-Z)
  \label{e:alpha-wrong}
\end{equation}
and
\begin{equation}
  P_\infty =S- [f G_0(1-\alpha) +(1-f)\Psi(Z-\alpha,1-Z)],
 \label{e:P-wrong}
\end{equation}
where $G_0(x)$ and $G_1(x)$ are the standard generating functions of the network
degree distribution \cite{New_02}:
\begin{eqnarray}
  G_0(x)&=&\sum_{k=0}^\infty P(k)x^k\\
  G_1(x)&=&\sum_{k=1}^\infty \frac{kP(k)}{\langle k\rangle}x^{k-1}
\end{eqnarray}
The meaning of the terms involving $G_1$ and $G_0$ is the special
treatment of the seed nodes, which are active by default. Thus for
them the classical percolation equations are applied.  Our computer
simulations for a random regular network with degree  $k=3$ and
activation thresholds 2 and 3 ($k=3$ and $k^\ast=2$, $k^\ast=3$) do not agree with these
equations (see Fig.~\ref{RRok}).

To understand the origin of this discrepancy, we need to recall the
definition of $Z$ in bootstrap percolation, which is the probability
of connecting a root node with a seed node, or with an already active
non-seed node. By ``already active node'' we mean a node, whose
activation was triggered by its outgoing neighbors, or what is the
same, that at least $k^*$ of its outgoing links lead to active
nodes. Thus, the activation of the target node does not depend on the
root node, unlike in the k-core percolation, where the root must be
always active. Nevertheless, if the target non-seed node has $j=k^\ast
-1$ outgoing links leading to active neighbors and also the root is
active, the target should be also active, and this possibility has not
been considered in \cite{Bax_2010}.

Thus the outgoing links leading to the giant component can be of two
types, A or B. The A type include links leading to seed nodes or to
non-seed nodes with $j\geq k^*$ active outgoing neighbors. The B type
include links leading to nodes with $j=k^\ast-1$ outgoing active
neighbors, which can be activated only if the root is active.  Note
that A is the subset of a broader type of links that we will call
links of type I, connecting any root to b-active nodes which have
probability $Z$. In contrast, links of type B are the subset of nodes
of type II which is the complement of type I and, hence has the
probability $1-Z$ (see Fig.~\ref{schm}). We denote the probabilities
that a link of the A and B type lead to the GC by $\alpha$ and $\beta$
respectively.  Thus $\alpha \leq Z$ while $\beta \leq 1-Z$. The total
probability that a randomly selected link leads to the GC is
$X=\alpha+\beta$. Fig.~\ref{schm} illustrates different cases in which
the chosen edge is linked to the GC, with probability $\alpha$ or
$\beta$ for a random regular network with degree $k=6$ and threshold
$k^*=3$.
\begin{figure}[H]
\begin{center}

  \includegraphics[width=0.9\textwidth]{Fig2.eps}
\end{center}
\vspace{-0.5cm}
\caption{Schematic representation of some configurations when reaching
  a target node following a random edge, in a random 6-regular network
  and for a threshold $k^*=3$. Solid edges lead to an ``already active
  node'', which has $n_{act}=k^*$ active outgoing neighbors (enclosed by a
  solid line). We say these links are of type I. Dashed edges
  connect to a node with less than $n_{act}=k^*$ active outgoing
  neighbors (enclosed by a dashed line), and we call them links of type II. On the other hand,
  dotted lines are edges of type I that lead to the GC, which we call
  type A links, while dash-dotted lines are type II edges that lead to
  the GC, called type B links. Note that a type B link is connected to
  an active node if two conditions are fulfilled: it must lead to a
  target node with exactly $n_{act}=k^*-1$ active outgoing neighbors
  (if $n_{act}>k^*-1$ it would be a type A link), and also the root node must be
  active. In panel (a) we differentiate two types of links: I (top)
  and II (bottom). In panel (b) we show different configurations that
  lead to the GC for each type of link. On top we show a link of type
  A that leads with probability $\alpha$ to a target node connected to
  the GC, because one of its outgoing links is of type A (top-left) or
  of type B (top-right). These configurations are considered in
  Eq.~(\ref{e:alpha}).  On the bottom, we show a link of type B that
  leads with probability $\beta$ to a target node connected to the GC,
  since one of its outgoing links is of type A (bottom-left) or of
  type B (bottom-right). These configurations are considered in
  Eq.~(\ref{e:beta}).} \label{schm}
\end{figure}
Since it is sufficient that at least one of the outgoing links of the
target node leads to the giant component, it will be more convenient
to handle the probability that none of the outgoings links lead to the
GC. Thus, we will use the probability that the link of type I does not
lead to the GC, which clearly is $Z-\alpha$, and also the probability
that the link of type II does not lead to the
giant component, which is $1-Z-\beta$. Note that since we have two
types of links, we will need to solve a system of two recursive
equations to compute the GC.

The recursive equation for $\alpha$ can be obtained
by looking at the status of the target. Indeed, if a target is a seed
with probability $f$, the probability that it is not connected to the
GC by the outgoing links is the same as in classical percolation
theory $fG_1(1-X)$. If the target is not a seed node with probability
$1-f$, the probability, that it is not connected to $GC$ is
$(1-f)\Phi(Z-\alpha,1-Z-\beta)$, which differs from the analogous term
for the k-core percolation in Eq.~(\ref{e:alpha_c}) by the replacement
of $1-Z$ by $1-Z-\beta$. This is because the links leading to nodes with
threshold less than the activation threshold, whose probability is
$1-Z$, can still lead to the GC with probability $\beta$. Thus, $\alpha$
satisfies the recursive relation,
\begin{equation}
  Z-\alpha=fG_1(1-X)+(1-f)\Phi(Z-\alpha,1-Z-\beta).
\label{e:alpha}
\end{equation}
Note that this equation coincides with the old Eq. (\ref{e:alpha-wrong}) with a correction term $\beta$, replacing
$1-\alpha$ by $1-X$ and $1-Z$ by $1-Z-\beta$.

The recursive relation for $\beta$ can be obtained by the
following arguments.  Suppose that the random link leads to a target
node with threshold $j=k^\ast-1$, which could be activated by the
root. The probability of this event for given degree $k$ and threshold
$k^\ast$ is the $j$th term of Eq.~(\ref{ZZb3}), with $x=Z$, $y=1-Z$
and $j=k^\ast-1$. The probability that this node is not connected to
the GC is given by the same term with $x=Z-\alpha$ and
$y=1-Z-\beta$. Thus, we can compute the probability that such a node
is connected to the GC as the difference between these two
probabilities. After summing up all the contributions from different $k$
and $k^\ast$ and taking into account the degree and threshold
distributions we have
\begin{equation}
\beta=(1-f)[\Delta\Phi(Z,1-Z)-\Delta\Phi(Z-\alpha,1-Z-\beta)],
\label{e:beta}
\end{equation}
where
\begin{equation}
\Delta\Phi(x,y)=\sum_{k=1}^\infty \frac{k P(k)}{\langle
  k\rangle}\sum_{j=0}^{k-1}\binom{k-1}{j}[r_b(j+1,k)-r_b(j,k)]x^{j}y^{k-j-1}.
\label{e:beta2}
\end{equation}
Here $r_b(j+1,k)-r_b(j,k)$ is the probability that $k^\ast=j+1$, which
is equivalent to $j=k^\ast -1$. Thus, each term corresponds to a node
that is just one active outgoing neighbor short of being activated,
which will be active if the root is active.
To derive the final equation for the fraction of nodes in the GC,
we use a slightly modified Eq. (\ref{e:P-wrong}) with the correction term
$\beta$:
\begin{equation}
  P_\infty=S-[fG_0(1-X)+(1-f)\Psi(Z-\alpha,1-Z-\beta)].
  \label{e:P}
\end{equation}
 Recall that $X=\alpha+\beta$ is the probability of choosing a random
  link that leads to the GC.

As a simple example we
will illustrate these equations for a random regular network with $k=3$ and
$k^\ast=2$. For this network $P(3)=1$, $r_b(0,3)=r_b(1,3)=0$ and
$r_b(2,3)=r_b(3,3)=1$. Accordingly, we have a system of two algebraic
equations:
\begin{eqnarray}\label{e:ab}
  \alpha&=&Z-f(1-X)^2 -(1-f)(Z-\alpha)^2 \\
  \beta&=&(1-f)2[Z(1-Z)-(Z-\alpha)(1-Z-\beta)],\nonumber
 \end{eqnarray}
which can be solved for any fraction of seed nodes $f$ using Eq.~(\ref{ZZb})
\begin{equation}
 Z=f+(1-f)Z^2,
\end{equation}
from where we easily obtain $Z=f/(1-f)$.

For a random regular network with $k=3$, Eq.~(\ref{e:P}) is reduced
to
\begin{eqnarray}
 P_\infty=&f&+(1-f)[Z^3+3Z^2(1-Z)+3Z(1-Z)^2]\\
 &-&f(1-X)^3 -(1-f)[(Z-\alpha)^3+3(1-Z-\beta)(Z-\alpha)^2].\nonumber
  \end{eqnarray}
  We verified Eq.~(\ref{e:P}) by simulations for the case of a complex $r_b(j,k)$
  and for a random regular network.

  Note that for the percolation critical point, $\alpha=\beta=0$,
  the Eqs. (\ref{e:ab}) turn into identities with the equation for $\alpha$
  turning into Eq.~(\ref{ZZb}). To find the critical point we can
  present the system (\ref{e:ab}) in a symbolic recursive form
  \begin{equation}
    {\bf x}={\bf A}({\bf x}),
  \end{equation}
  where ${\bf x}\in R^2$ $(x_1=\alpha,x_2=\beta)$ and ${\bf A}({\bf
    x})$ is a nonlinear operator representing the right-hand side of
  the system of Eqs. (\ref{e:ab}). A sufficient condition of the attractive
  point ${\bf x}=0$ is $|{\bf A}({\bf x})|<|{\bf x}|(1-\epsilon)$,
  where $\epsilon$ is a small positive constant, which in the vicinity
  of zero is equivalent to the condition that the matrix of partial
  derivatives $\partial A_i/\partial x_j|_{{\bf x}=0}$ has absolute values of all its eigenvalues smaller than 1. The critical
  point should be right at the border of the converging and diverging
  behavior, so it should satisfy the condition $\lambda_{max}(f,Z)=\pm
  1$. Together with Eq.~(\ref{ZZb}), it gives the value of the
  critical parameter $f_{c2}$. For example, for a random regular network
  with $k=3$ and $k^*=2$, this condition together with $Z=f/(1-f)$ is
  equivalent to
  \begin{equation}
  \det\left[ \begin{matrix} 4f-1 &2f \\ 2(1-2f) & 2f-1 \end{matrix}\right] =0,
\end{equation}
which gives $f=1/2$ and $f=1/8$. For $f=1/2$, the second eigenvalue is
2, so the iterations do not converge, while for $f=1/8$ the second
eigenvalue is $-1/4$, so the iterations do converge. Thus, the
critical value for the continuous transition denoted as $f_{c2}$ is
$f_{c2}=1/8$. On the other hand, the old equation
(\ref{e:alpha-wrong}), which neglects $\beta$, gives $f_{c2}=1/4$
(Fig.~\ref{RRok}), predicting a GC much more fragile. A similar
treatment can be applied for $k^*=3$, which gives $f_{c2}\approx 0.344$.

\section{Stochastic Simulations}
We perform stochastic simulations using networks with $N=10^6$ nodes,
to assure a small statistical noise and a negligible probability of loops, so that finite networks can be well approximated by the theoretical results obtained in the limit of infinitely large networks. The networks were generated as randomly connected graphs with a given degree distribution by the Molloy-Reed algorithm \cite{Mol_02}.

Figure~\ref{RRok} compares the simulation results with
Eqs.~(\ref{e:P}) and with Eq.~(\ref{e:P-wrong})
corresponding to Ref.~\cite{Bax_2010}. Note that Eq.~(\ref{e:P}) exhibits a good agreement with our stochastic simulations,
while Eq.~(\ref{e:P-wrong}) strongly underestimates the size of GC because it neglects the probability $\beta$.

\begin{figure}[ht]
\begin{center}
  \includegraphics[width=0.6\textwidth]{Fig3.eps}
\end{center}
\vspace{-0.5cm}
\caption{$P_{\infty,b}$ as a function of the fraction of seeds $f$ for
  a random regular network with $k=3$, and thresholds $k^*=2$ (circles, dashed line) and
  $k^*=3$ (squares, dash-dotted line). The symbols represent the
  stochastic simulations with $N=10^{6}$ and the solid lines are the
  prediction of our theory [see Eq.~(\ref{e:P})]. The discontinuous lines represent the results from
  Eq.~(\ref{e:P-wrong}), which underestimate the size of the GC. We can see
  that there is an excellent agreement between the simulations and our equations.}\label{RRok}
\end{figure}

To test the theoretical equations for the most general case of
heterogeneous k-core and bootstrap percolation, we generate networks
with the Poisson degree distribution with $\langle k \rangle =8$ and a
distribution of the thresholds that satisfy the complementary
condition of Eq.~(\ref{rr}). The form of the cumulative distribution
of bootstrap and k-core percolation are given by:
$r_b(j,k)=F_\gamma(j/k)$, $r_c(j,k)=1-F_{1-\gamma}(1-j/k)$, where
$F_\gamma(x)$ is a fourth-order polynomial of $x$ monotonically
increasing from $F_\gamma(0)=0$, to
\begin{figure}[H]
\vspace{0.2cm}
\begin{center}
   \includegraphics[width=0.48\textwidth]{Fig4a.eps}
  \hspace{0.3cm}
  \includegraphics[width=0.48\textwidth]{Fig4b.eps}
\end{center}
\begin{center}
  \includegraphics[width=0.48\textwidth]{Fig4c.eps}
  \hspace{0.3cm}
  \includegraphics[width=0.48\textwidth]{Fig4d.eps}
\end{center}
\vspace{-0.5cm}
\caption{(a), (c) the fraction of active nodes, $S_c$ (circles,
  squares, solid lines) , and the fraction of nodes in the GC,
  $P_{\infty,c}$ (triangles, diamonds, dashed lines), for the
  heterogeneous k-core percolation as a function of the fraction of
  nodes that survived the initial failure $p$. (b), (d) the fraction
  of active nodes, $S_b$( circles, squares, solid lines), and the
  fraction of nodes in the GC, $P_{\infty,b}$ (triangles, diamonds,
  dashed lines), for the heterogeneous bootstrap percolation as
  function of the fraction of the seed nodes $f$. In the insets we
  plot the same in log-linear scale. The symbols represent stochastic
  simulations while the lines are the results from Eqs.~(\ref{WWb})
  and (\ref{e:P}). All simulations were performed for Erd\H{o}s
  R\'{e}nyi graphs with $\langle k\rangle=8$ and threshold
  distribution functions $r_c(j,k)=F_\gamma(j/k)$,
  $r_b(j,k)=1-F_{1-\gamma}(1-j/k)$, which are polynomials of the fourth power
  with an inflection point at $x=\gamma$: (a) $\gamma=0.5$, (b)
  $\gamma=0.6$, (c) $\gamma=0.4$, (d) $\gamma=0.5$. Note that
  $F_\gamma(x)=1-F_{1-\gamma}(1-x)$, satisfying Eq.~(\ref{rr}) for
  complementary of the k-core and bootstrap thresholds. Accordingly,
  the graphs on the diagonal pairs of panels (a)-(d) and (b)-(c) are
  complementary, that is, $S_c(p)=1-S_b(1-p)=1-S_b(f)$.
}\label{Fig3}
\end{figure}
\noindent $F_\gamma(1)=1$, has a minimum at $x=0$, a maximum at $x=1$
and an inflection point at $x=\gamma$ if $1/3\leq \gamma \leq 2/3$:
\begin{equation}
  F_\gamma(x)=\frac{x^2(18\gamma^2-12\gamma)+x^3(4-12\gamma^2)+x^4(6\gamma-3)}
  {6\gamma^2-6\gamma+1}.
\end{equation}
Note that $F_\gamma(x)$ is invariant under the transformation
$1-F_{1-\gamma}(1-x)$. For nodes with $k=0$, we assume $F_\gamma(0)=1$,
which means that isolated (autonomous) nodes are always
active. Figure~\ref{Fig3} shows the results of computer simulations for
the k-core and bootstrap percolation for different values of $\gamma$.
Depending on the position of the inflection point, we can observe the
emergence of the first order phase transition in both k-core and
bootstrap percolation. We also observe a predicted complementary of
the k-core and the bootstrap percolation
$S_c(p)=1-S_b(1-p)=1-S_b(f)$. In all cases we see excellent agreement
with simulations. Despite the fraction of active nodes of both
processes satisfy a complementary relation, it is clear that the
continuous thresholds of the giant components of these processes do
not complement each other. However, the giant component of inactive
nodes in bootstrap percolation corresponds to the giant component of
active nodes in the complementary k-core percolation process and vice versa.

\section{Conclusion}\label{sec.Concl}

We have provided theoretical insights into the bootstrap
percolation process. We prove mathematically that the heterogeneous
bootstrap percolation is the complement of the heterogeneous k-core
percolation for complex networks with any degree distribution in the
thermodynamic limit, as long as the thresholds of the nodes in both
processes complement each other. In particular, in nonregular graphs
we can map a homogeneous bootstrap percolation onto a heterogeneous
k-core percolation, and likewise, k-core homogeneous percolation onto
a heterogeneous bootstrap percolation, because the inactive nodes in
k-core/bootstrap behave the same as the active nodes in
bootstrap/k-core.

We also develop the equations for the size of the giant component (GC)
in the most general cases of heterogeneous k-core and bootstrap
percolation and confirm them by stochastic simulations. Our equations
for heterogeneous k-core percolation coincide with the equations for a
special case of heterogeneous k-core derived in
Ref.~\cite{Bax_2011}. However, our equations representing the size of
the GC in the bootstrap percolation disagree with the equations
presented in Refs.~\cite{Bax_2010,Bax_2011}. The disagreement comes
from the fact that Refs.~\cite{Bax_2010,Bax_2011} disregard some
branches of active nodes when analyzing the GC in bootstrap
percolation with the generating function formalism. More precisely,
when following a random link that connects a root node and a target
node with degree $k$ and activation threshold $k^*$, it is not
strictly necessary that at least $k^*$ of the $k-1$ outgoing neighbors
of the target be active to ensure its activation. Another possibility
is that only $k^*-1$ outgoing neighbors of the target node be active, and
the root node is also active, it will trigger the activation of the
target node.  We show that the probability of activation of the target
by the root must be explicitly taken into account in order to obtain
the correct equation for the GC in bootstrap
percolation. Nevertheless, to calculate the fraction of active nodes
$S_b$, this activation should not be taken into account since the root
and the target could not mutually depend on each other to be
active. Thus, the equations that represent $S_b$ in
Refs.~\cite{Bax_2010,Bax_2011} are correct.

In the k-core theoretical approach, both the root
and the target nodes are assumed to be active, thus, the root always
acts as a stabilizing neighbor and therefore, the equations from
Ref.~\cite{Bax_2011} predict correctly the size of the GC.

We also found that unlike the fraction of active nodes, the fraction
of nodes belonging to the giant component in both processes do not
satisfy a complementary relation, since these processes generate
different topological structures of active nodes. Indeed, active nodes
in the k-core percolation are inactive in the complementary bootstrap
percolation. However, the giant component of inactive nodes in the
bootstrap coincides with the giant component of active nodes in the
complementary k-core and vice versa.

Our results and theoretical equations here presented can be extended
into networks with multiple layers and can be used to describe the
evolution of the GC of active nodes during this dynamical process.

\section*{Acknowledgments}

\noindent
M.A.D. and L.A.B. thank to UNMdP (Grant No. EXA 853/18), and CONICET (Grant No. PIP 00443/2014) for
financial support. The Boston University Center for Polymer Studies is
supported by NSF Grants No. PHY-1505000, No. CMMI-1125290, and No. CHE-1213217, and
by DTRA Grant HDTRA1-14-1-0017. L.A.B.  acknowledges partial support of this research through
 DTRA Grant No. HDTRA1-14-1-0017. S.V.B. acknowledges financial support of DTRA, Grant No. HDTRA1-14-1-0017 and the partial support of this
research through the Dr. Bernard W. Gamson Computational Science Center at Yeshiva College.

redpajama_set_name: RedPajamaArXiv


text:
Coronavirus recovery – lessons from the eurozone crisis
Dr Stella Ladi, Senior Lecturer in Public Management in Queen Mary's School of Business and Management has written an opinion piece for The Conversation in which she discusses coronavirus recovery and the lessons that can be learnt from the eurozone crisis.
As governments around the world grapple with the public health and economic effects of the COVID-19 pandemic, there are striking similarities with the eurozone crisis that followed the 2008 financial crisis. Having researched this crisis, it is clear to us that there are some important lessons to apply to today's recovery. The early signs indicate that the EU is responding much more effectively to this crisis than it did in 2008.
Many European governments are increasing their spending to compensate for the economic losses of lockdowns, as they initially did in the wake of the 2008 financial crisis. This is necessary when an economy contracts but relies on a rise in public debt – and the figures are much higher this time around. According to IMF forecasts, by the end of the year public debt will reach almost 100% of GDP in the eurozone on average. Italy, Greece, France, Spain and Portugal will exceed this.
We know from 2008 that a problem associated with rising debt is that investors can sell the bonds of a given country to buy those of a more credible country denominated in the same currency. Prolonged uncertainty over whether or not the European Central Bank would bail out struggling members (Greece, Ireland) led to the skyrocketing of borrowing costs in these member states and their rapid decline in others (Germany, France). This resulted in a liquidity crisis in the EU's peripheral states. It wasn't until the ECB president, Mario Draghi, made it clear in 2012 that the bank would do whatever it took to preserve the euro that crisis was averted.
This time round the European Central Bank has acted a lot more quickly, which has kept borrowing costs low for all eurozone countries. In March, the ECB created a Pandemic Emergency Purchase Programme, a temporary €750 billion scheme (£670 billion) involving both government and private debt. And another €750 billion fund has been proposed to bankroll recovery efforts going forward.
The big difference this time compared to 2008 is that the Franco-German engine of the EU has led calls for financial assistance. But there remain the "frugal four" (Austria, Denmark, the Netherlands and Sweden) that oppose the idea of transfers and prefer an emergency fund financed mainly by loans. A decision will be attempted at the upcoming EU summit on July 17-18.
Conditions of support
One of the thorny issues, as with a decade ago, will be the conditions attached to EU support. The eurozone crisis was portrayed as a morality tale that pitted supposedly northern European values of hard work, prudent savings, moderate consumption and fiscal stability against perceived southern vices of low competitiveness, undeserved spending, inflated wages and profligacy. Financial support came with strict conditions, which took the form of austerity policies. This meant a reduction in public spending, wage cuts for government workers and tax rises.
Today this narrative has lost some of its strength. The north-south divide observed in 2009 is less clear since Germany seems to have changed camps. The last crisis also showed that austerity was not helpful in stopping the increase in public debt. GDP growth stalled and unemployment ballooned.
Above all, it is much harder (and obviously even more unfair) to blame individual countries for a pandemic. Although the crisis will be felt worse in the weakest countries that are still recovering from the previous crisis, the cause of coronavirus is the same for all member states.
Nonetheless, the details of how the EU's recovery fund will be given to member states is up for debate. This includes whether or not the money will be given as loans or grants, what the terms of repayment will be and how it should be spent.
Bailout negotiating tactics
The new funds may not be enough to meet member state needs – and for governments to borrow extra it will be crucial to reassure investors that they will be reimbursed. Interest rates are still low, but – if investors panic or if the ECB cannot prevent this panic – then things could change. Then governments may be obliged to accept certain conditions, austerity for example, to remain credible in international markets.
But there is room for manoeuvre. In our forthcoming book we show that, when there was trust between the lenders and the bailed-out governments, conditions were not dictated. The EU and IMF lenders, collectively known as the troika, were open to solutions proposed by member states, as long as they reached certain objectives.
Thus, when for example, Portugal negotiated its bailout, it could insert specific policies or revisions and fought for others to be dropped. After the bailout negotiations, some governments such as Greece, Ireland and Cyprus successfully resisted the implementation of some policies they disliked; and lenders were sometimes willing to turn a blind eye and let this go unsanctioned.
So an important lesson for today is that conditions of lending will only be met if both sides agree to them. The preferences of different member states must also be taken into account.
Ultimately, the eurozone crisis showed that it was delayed collective action by the EU that empowered financial markets to exploit differences between the bond prices in different member states. The response to coronavirus so far suggests that the EU's decision makers are aware of this. But the challenge for the 27-member bloc remains to act collectively, in agreement and for the good of all states.
News story: BBC social mobility film explores Queen Mary accent bias research

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text:
Expo to Showcase Medical Device Innovation
By staff-author
San Diego has a long tradition of being a nerve center for medical device innovation, and some of the more promising new devices and diagnostic tools on the market — or nearing commercialization — could be front and center this week in La Jolla.
"We are pretty excited about the lineup," said Joe Panetta, president and chief executive officer of Biocom, a trade association for the region's life sciences industry, which is sponsoring the Med Device and Diagnostics Expo.
The event is a showcase for some of the newest and most innovative devices from local companies, says Panetta, adding that there will be about 15 exhibitors at the Nov. 18 event.
"It's a pretty popular networking event," he added, as members and nonmembers show up to get a gander at some innovative technologies. "We also have investors here," he said, referring to an underlying goal of many exhibitors looking for funding.
"There's much more investment activity in the (med devices) space over therapeutics because the time to market is much shorter," said Panetta.
Investors sinking money in significant new drug development efforts are looking at a time frame of 12 to 15 years — and billions of dollars — from discovery to sales, says Panetta.
"Most devices can get to market at a tenth of that cost, which means a little more of a return on the investment in a more predictable time frame," he said.
Driving the Local Economy
Panetta says the companies' products at the expo, which usually attracts several hundred participants, are addressing diverse diseases and medical problems. They also represent a significant — and increasingly important — economic force in the region.
Volcano Corp., a Carmel Valley-based business that specializes in making catheters and other devices for working in veins, is the most well-known local company at the expo, according to Panetta. Volcano, which has about 1,200 employees, on Nov. 3 reported revenues of nearly $213 million for the first nine months of the year, a 36 percent increase from the same period a year ago.
Panetta says the expo — which is free to the public — is different from another Biocom event called DeviceFest. That full-day conference explores the implications of such forces as health care reform and its impact on the medical device industry. Others have addressed the roles of telehealth, reimbursement, regulatory agencies, intellectual property and financing strategies.
While his business isn't one of the 550 companies that are Biocom members, Ed Arkans, founder and president of ACI Medical Inc., says he's looking forward to exhibiting his company's latest devices: products that are focused on the peripheral disease market. In 1988, the company began design of a noninvasive diagnostic device for chronic venous disease. It was used on the Mir Space Station and iterations are being developed for other international space travelers.
"It's all about increasing blood flow to the legs and feet," Arkans said about the product line. One product applies a unique form of pneumatic compression to increase arterial blood flow to legs with poor circulation.
The San Marcos manufacturer has 30 employees and targets niche-market customers at hospitals and clinics.
Another company exhibiting at the event is La Jolla-based CorTechs Labs Inc. CorTechs' mission is to create advanced brain image analysis that would help physicians diagnose and treat serious neurological disorders, such as Alzheimer's disease, more effectively, says Kora Marinkovic, the company's director of marketing and sales.
Heady Stuff
Its premier product is called NeuroQuant, which is the first software cleared by the U.S. Food and Drug Administration on the market that provides information on brain structures, returning results in minutes. Several pharmaceutical companies have also recognized the value of NeuroQuant, and the software is being used in several clinical trials, says Marinkovic.
But the Biocom event isn't the first venue to feature the product. A couple of years ago, NeuroQuant was named among the top three new products at the world's largest medical imaging show sponsored by the Radiological Society of North America.
The company, which has about a dozen employees, has benefited from National Institutes for Health grants totaling $7 million to fund the development of NeuroQuant. But more money will be needed to help the company, incorporated in 2001, to grow its market.
"Greater visibility in the area (San Diego) will be helpful in advancing this technology," said Marinkovic.
Other San Diego area companies scheduled to exhibit are Cytori Therapeutics Inc., Epinex Diagnostics Inc., Naviscan Pet Systems Inc. and RF Surgical Systems Inc.
One of these companies just might be in the running for an award as well.
The evening will conclude with a panel of venture capitalists and industry experts selecting companies for technical excellence and medical significance, says Panetta.
And for the first time, the fifth annual event will include a "contract alley," he added. This will feature local firms that provide design and contract manufacturing services for device and diagnostic companies.
"This will be a great opportunity for businesses to preview what services are available and meet those individuals who could be an integral part of bringing a product to market," said Panetta.
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staff-author
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SDF, Dr. Seuss Foundation Offering $1M in Grants


text:
Kogod School of Business
About 2U – Our Program Partner
On-Campus Programs
About American University
Chartered by Congress in 1893, American University has upheld its commitment to educating service-minded students for more than a century. Today, the core values of social responsibility and a commitment to cultural and intellectual diversity continue to drive every university initiative. AU's student body is consistently ranked among the nation's most politically and socially active and represents all 50 states as well as more than 130 countries. More than 90 percent of faculty members hold the highest degree in their field and help American University develop leaders who are prepared to make a positive impact on their communities locally, nationally, and globally.
American University proudly supports military members and their families as well as students living internationally. Its commitment to diversity, service, and academic excellence has earned AU praise from a number of top organizations, including:
U.S. News & World Report, America's Best Colleges (2015), #71 Best National University
Princeton Review, Best Colleges (2014), #4 Most Politically Active Students
Princeton Review, Green Rating Honor Roll (2015)
U.S. Environmental Protection Agency (EPA), Green Power Leadership Award (2013)
Peace Corps (2015), #2 for medium-sized colleges with the most volunteers


Experience driving perfection in the 2012 Dodge Charger. This 4 door, 5 passenger sedan still has less than 80,000 miles! It features an automatic transmission, rear-wheel drive, and a refined 6 cylinder engine. All of the premium features expected of a Dodge are offered, including: front bucket seats, air conditioning, tilt steering wheel, power door mirrors, power windows, cruise control, and 1-touch window functionality. Premium sound drives 6 speakers, providing you and your passengers a sensational audio experience. Dodge ensures the safety and security of its passengers with equipment such as: dual front impact airbags, head curtain airbags, traction control, brake assist, anti-whiplash front head restraints, a panic alarm, and 4 wheel disc brakes with ABS. This car was designed with safety in mind, allowing you to drive with even greater assurance. Our experienced sales staff is eager to share its knowledge and enthusiasm with you. We'd be happy to answer any questions that you may have. Stop in and take a test drive!


Red-naped sapsuckers (Sphyrapicus nuchalis) are functionally important because they create sapwells and cavities that other species use for food and nesting. Red-naped sapsucker ecology within aspen (Populus tremuloides) has been well studied, but relatively little is known about red-naped sapsuckers in conifer forests.
Epiphytic lichen communities are included in the national Forest Health Monitoring (FHM) program because they help us assess resource contamination, biodiversity, and sustainability in the context of forest health. In 1996, field crews collected lichen samples on 141 field plots systematically located across all forest ownership groups in Idaho. Results presented here are the baseline assessment of the statewide field survey.


Today's enterprises have become a compilation of multiple data processing sites due to business expansion and/or corporate acquisitions. They are looking for simple and cost-effective ways to interconnect these sites to enable them to share resources, enable workload mobility and support disaster recovery plans.
In stark contrast to legacy approaches for DCI which required significant investments in complex rigid hardware, Pluribus Networks has created a fully software-defined technology, based on industry-standard VxLAN technology. Our approach simply stretches existing local area network layer-2 domains across these geographically dispersed locations at high speed. And because it is completely software-defined, the Pluribus DCI solution can address new requirements as they present themselves.
Pluribus Data Center Interconnect is based on industry standard VXLAN technology over Layer 3 via an Open Networking Switch running Pluribus Netvisor® ONE OS. You can connect multiple data center locations (or even pods) making location transparent using standardized VXLAN technology – not expensive and proprietary DCI hardware. Plus, the visibility inside Pluribus DCI tunnels is inherent, making capacity planning and resource utilization studies available at the touch of a button.
Pluribus Open DCI enables physically remote data centers to participate in any form of disaster recovery strategy. DCI enables all resources to logically exist within the same 'local' infrastructure. When the physical delineation between data centers is removed, critical business information can be replicated or accessed in real-time and configurations can be aligned to allow active-active or active-standby strategies to be implemented as desired.
When Pluribus Open DCI is implemented, the location of resources is insignificant. As capacity needs change over time, workloads can be migrated across all available resources, regardless of location. In the event of failures or IT maintenance schedules, the ability to continue processing across this much larger pool maintains the IT function for the business. DCI enables all resources to share in the process function for the business.
Pluribus Open DCI enables dynamic and virtualized processing to span across all available resources, regardless of location. This increases the utilization of each resource, and provides a mechanism to monitor the utilization of local versus remote resources, providing an opportunity to add additional capacity in the most needed locations.
Pluribus Open DCI completely eliminates the boundaries between data centers and the resources that they house. As workloads move for capacity or availability reasons, DCI enables the 3rd party mechanisms that move workloads to include all resources as migration destinations, regardless of location. Critical resources can now be accessed by these mechanisms if available anywhere within the entire infrastructure since everything appears as 'local' to the 3rd party mechanism.


text:
Q: Is it possible to update an iPhone 4 to iOS 6.1.6? I need the latest SSL security fix, as I'm running iOS 6.1.3. But, I don't have enough space to go to iOS 7 which is the only option iTunes and my phone are giving me to upgrade.
I have an 8 GB iPhone 4 with usually less than 100-200 MB free, and have deleted all apps and non-essential music/photos so I really don't have the space to go all the way to iOS 7 (I understand iOS 7 only takes a few hundred MB beyond that which iOS 6 occupies, but every little bit counts and I'm already driven crazy downloading photos of my daughter every few days because I've run out of room.)
Am I completely out of luck?

redpajama_set_name: RedPajamaStackExchange


text:
Sex Gang Children: After We Spent An Afternoon Stalking Him, Andi Politely Invited Us Round For A Cup Of Tea!
Originally published in Rave-Up #10 (1985)
Interview by Devorah Ostrov & Sara Brinker
Photos by Devorah Ostrov
Sex Gang Children at the time of this interview
L-R: Kevin, Andi, Cam & Terry
Andi Sex Gang is soooo nice! How nice is he? He's so nice that not only did he sneak these two fanzine journalists into Sex Gang Children's London Lyceum show last summer (along with several other kids waiting expectantly outside the backstage entrance), he also found relatively comfortable hiding places for everyone and mapped an escape route for us into the main hall. Our hero!
A few days later, Sara and I "bumped into" Andi again (some might say we'd been surreptitiously following him for hours!) on Carnaby Street and he invited us round to his place for a cup of tea. He's polite as well as nice! We swooned while he spoke of Édith Piaf and old movies, and while we waited for the rest of the band to turn up for rehearsal, we asked Andi a few questions...
This photo I took of Andi in 1984 was
used in CD booklet for Blind!
Rave-Up: We really admire Sex Gang Children's attitude towards the kids that come to see you. Is it important to you to take care of your fans?
Andi: That's human nature. You're either a cunt or you're not. It's not a selling point of the band. Our selling point is our music, the live shows, and our records.
Rave-Up: Sex Gang Children tends to be categorized as a "doom and gloom/ gothic/death rock" band. Do you ever feel a bit trapped by the cult following for that genre of music?
Andi: It's not a matter of being trapped so much by a cult following... I think most of our followers are basically big fans and have a great faith in the band. You just want to be able to prove to everyone that you're not as limited a band as everyone thinks you are.
Rave-Up: There seems to be a great desire in the music press to limit you and label you.
Andi: There is. It gives you a feeling of being picked apart and exposed. It can make you feel incredibly naked.
Rave-Up: From previous conversations we've had with the band, you guys seem to be great fans of a variety of music and still able to get excited over other's work.
Kevin Matthews & Cam Campbell
Photo: Devorah Ostrov
Andi: Yeah, it's true! We are fans of music and excited about what we do, excited about the people and the things in life. I'm excited by the fact that Steven Spielberg is in the position to do what he wants to do, and at the same time he's offering entertainment for millions of people. That's brilliant! It gives us faith.
Rave-Up: Who are your heroes?
Andi: I like a lot of film stars — Buster Keaton, Charlie Chaplin, Robert De Niro. I like Divine as well. He's a person of incredible style. I like the real stars, old film greats. They have no grand illusions about themselves.
You know who I really like and admire? Billy Joel! He doesn't go around saying, "I've got an image." Or, "I'm a Batcave artist." He doesn't need to sell himself with cheap slogans. He says it all with his music.
Rave-Up: Are you guys working on any videos?
Andi: We did a video for the Édith Piaf song ["Les Amants D'un Jour"]. Graham Bentley, who does our lights and works with us behind the scenes, set up an appointment with Radio Luxembourg because they were greatly interested in us and they had a European cable network. We went up to Northampton, chose a location, and made a video on the spur of the moment. Then we stayed up for four nights editing and sussing things out. We went back to London, went to Radio Luxembourg, and the video was flown out to their cable network in Europe to show that very night.
Andi proves he loves Billy Joel by posing with one of his albums.
Rave-Up: Is it true that you finance everything yourselves?
Andi: Everything we do is self-financed. We keep everything to a minimum. We have to!
Rave-Up: So, you don't need the limos or the big hotel rooms?
Andi Sex Gang & Terry MacLeay
Andi: No, we aren't spoiled by the money. I remember the first time we got involved in a huge festival [Futurama 4, 1982]… We drove up there in a shitty old van that leaked, and we were hungry, and we just jumped onstage. We showed them the best of ourselves, while everyone else had this complacent attitude. It was supposed to be the festival of the year. When we got there, we had never seen such a lethargic atmosphere. Everyone was just waiting for something to happen.
Rave-Up: Nothing was happening, so you made it happen!
Andi: Yeah... That sounds like such a cheap thing to say, but it's true! We blew a lot of bands off the stage. In fact, the only two bands that stood out that night were us and Southern Death Cult. Everyone else just went through the motions. We were the only two bands that gave it something!✨
Posted by Devorah Ostrov at 19:07
Labels: 1980s, Andi Sex Gang, Death Rock, Goth, London, Post Punk, Rave Up Fanzine, Sex Gang Children
Christy Betts Buckley 12 April 2019 at 17:20
I always admired what you and Sara created and wish we could've spent more time together when I would come up from L.A. to visit Verna! I can't wait to see what else you dig out of that absolute treasure trove of true 80's life!
Devorah Ostrov 12 April 2019 at 21:10
Many thanks! Glad you enjoyed this interview with Andi and the 'zine back in the day. Keep in touch!
Devorah Ostrov
Kenickie: Because Rizzo Didn't Have The Right Ring...
Sex Gang Children: After We Spent An Afternoon Sta...
David Kaffinetti Has A Good Time All The Time! Spi...


text:
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Anderson MEP hosts youth unemployment conference
6 June, 2013 - by Martina Anderson MEP
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Sinn Fein MEP Martina Anderson is hosting a conference tomorrow, Friday June 7th in Cavan town on the issues of youth unemployment in Ireland and the EU's 'Youth Guarantee' proposals.
Martina Anderson said:
"One of the most worrying consequences of the economic downturn across the EU is the sharp rise in youth unemployment levels, with those in both parts of Ireland hitting all-time highs, and so in this the Irish Presidency of the EU, I am holding an event on these issues in County Cavan.
"The event is entitled 'Guarantee Our Future' and the idea is to bring together young people and their representative organizations to speak of their experiences, and along with the relevant agencies, to look at what has been proposed to date, and how effective it has been. I'm delighted to be holding this event in Co Cavan, in association with my colleague Senator Kathryn Reilly, and am very pleased that the major youth organisations will be taking part. These include the National Youth Council of Ireland, the NI Youth Forum and the National Union of Students/Union of Students of Ireland as well as the European Youth Forum. We will also have speakers from the European Commission, European Parliament and from the Young Left campaign group from Sweden, as well as Sinn Fein members of both the Assembly and Oireachtas.
"We need leaders at EU and state level to put a focus on combating this growing problem, by fleshing out the detail of initiatives like the proposed 'Youth Guarantee' and making sure that such schemes are adequately resourced. Youth unemployment is leading to the return of the bad old days of mass youth emigration from this island - we must all work to ensure that the future options for our young people are not in Clapham or Canberra but here at home".
"Guarantee Our Future" conference will take place on Friday June 7th, in the Cavan Crystal Hotel, Cavan town.
Registration - 9.30am, opening 10am, lunch (complimentary) served at 1pm.
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The ultimate pecan pancake with sweet cream buttermilk and churned butter powder included in the mix. All you add is water and you can eat them without syrup they are so good! Our price is a little higher because we include a 2oz bag of homestyle pecans that are chopped and ready to mix into the batter and/or sprinkled on top.
DIRECTIONS: Preheat lightly greased griddle to 375 Degrees. Combine 1 cup water to mix with our pecan pancake mix and stir until batter is slightly lumpy. You can stir in most of the pecan pieces at this time so they will be in the batter. Flip pancakes when bubbles appear and stay on surface. Top with a few of the pecans and warm syrup.