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{"url":"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/mfc.2018010","text":"# American Institute of Mathematical Sciences\n\nAugust\u00a0 2018,\u00a01(3):\u00a0201-253. doi:\u00a010.3934\/mfc.2018010\n\n## Influence analysis: A survey of the state-of-the-art\n\n 1 Kennesaw State University, 1100 South Marietta Pkwy, Marietta, GA, 30060, USA 2 Georgia State University, 25 Park place, Atlanta, GA, 30303, USA\n\n* Corresponding author: Meng Han\n\nReceived\u00a0 December 2017 Revised\u00a0 February 2018 Published\u00a0 July 2018\n\nOnline social networks have seen an exponential growth in number of users and activities recently. The rapid proliferation of online social networks provides rich data and infinite possibilities for us to analyze and understand the complex inherent mechanism which governs the evolution of the new online world. This paper summarizes the state-of-art research results on social influence analysis in a broad sense. First, we review the development process of influence analysis in social networks based on several basic conceptions and features in a social aspect. Then the online social networks are discussed. After describing the classical models which simulate the influence spreading progress, we give a bird's eye view of the up-to-date literatures on influence diffusion models and influence maximization approaches. Third, we present the applications including web services, marketing, and advertisement services which based on the influence analysis. At last, we point out the research challenges and opportunities in this area for both industry and academia reference.\n\nCitation: Meng Han, Yingshu Li. Influence analysis: A survey of the state-of-the-art. Mathematical Foundations of Computing, 2018, 1 (3) : 201-253. doi: 10.3934\/mfc.2018010\n##### References:\n\nshow all references\n\n##### References:\nPublications Related Influence Analysis in the Recent Years\nA Social Network\nCommon Neighbors in a Community\nModels of Social Influence by Different Networks\nDiffusion Models of Social Influence\nProbing Community for Dynamic Network\nInfluence Maximization Models in Social Network\nInfluence Diffusion Processing 1.\nInfluence Diffusion Processing 2.\nHeterogeneous Models of Social Influence\nModels of Social Influence based on Biological Transmission\nComprehensive Models of Social Influence\nInfluence Analysis based Applications\nExtensions or improvements of $IC\/LT$ models\n References Extender $IC$ $LT$ Remarks Goyal [71] Learnt probability from the action log, simulation on both $IC$ and $LT$ models $\\surd$ $\\surd$ Chen et al.[42] Address the scalability issue, they proposed efficiency heuristic algorithm by restricting computations on the local influence regions of nodes $\\surd$ $\\times$ Showed that computing influence spread in the independent cascade model is #P-hard problem Chen et al.[41] Extended the classical $IC$ model to study time-delayed influence diffusion $\\surd$ $\\times$ Their technical report version paper provides the NP-complete hardness of LT with their time-delay feature Masahiro et al. [127] Improved the basic $IC$ and $LT$ by estimating marginal influence degrees $\\surd$ $\\surd$ Chen et al. [43] Degree discount heuristics achieve almost matching influence thread with the greedy algorithm, and run only in milliseconds which the traditional method run in hours $\\surd$ $\\surd$ Wang et al. [236] Heuristic algorithm for $IC$ model $\\surd$ $\\times$ Chen et al. [37] Extended the classical $IC$ model to incorporating negative opinions $\\surd$ $\\times$ Nam et al. [188] Focused on how to limit viral propagation of misinformation in OSNs $\\surd$ $\\surd$ Wang et al. [239] Extended $IC$ to mobile social networks, and use a dynamic programming algorithm to select communities then find influential nodes $\\surd$ $\\surd$ Kyomin et al. [121] Algorithm IRIE where IR for influence ranking, and IE for influence maximization are proposed to improve the classical algorithm developed previously $\\surd$ $\\times$ The algorithm was used in both classical $IC$ model and the extension $IC$-$N$ [37] Thang [58] Extended the $LT$ model by constrain the influence distance as constant $d$ $\\times$ $\\surd$\n References Extender $IC$ $LT$ Remarks Goyal [71] Learnt probability from the action log, simulation on both $IC$ and $LT$ models $\\surd$ $\\surd$ Chen et al.[42] Address the scalability issue, they proposed efficiency heuristic algorithm by restricting computations on the local influence regions of nodes $\\surd$ $\\times$ Showed that computing influence spread in the independent cascade model is #P-hard problem Chen et al.[41] Extended the classical $IC$ model to study time-delayed influence diffusion $\\surd$ $\\times$ Their technical report version paper provides the NP-complete hardness of LT with their time-delay feature Masahiro et al. [127] Improved the basic $IC$ and $LT$ by estimating marginal influence degrees $\\surd$ $\\surd$ Chen et al. [43] Degree discount heuristics achieve almost matching influence thread with the greedy algorithm, and run only in milliseconds which the traditional method run in hours $\\surd$ $\\surd$ Wang et al. [236] Heuristic algorithm for $IC$ model $\\surd$ $\\times$ Chen et al. [37] Extended the classical $IC$ model to incorporating negative opinions $\\surd$ $\\times$ Nam et al. [188] Focused on how to limit viral propagation of misinformation in OSNs $\\surd$ $\\surd$ Wang et al. [239] Extended $IC$ to mobile social networks, and use a dynamic programming algorithm to select communities then find influential nodes $\\surd$ $\\surd$ Kyomin et al. [121] Algorithm IRIE where IR for influence ranking, and IE for influence maximization are proposed to improve the classical algorithm developed previously $\\surd$ $\\times$ The algorithm was used in both classical $IC$ model and the extension $IC$-$N$ [37] Thang [58] Extended the $LT$ model by constrain the influence distance as constant $d$ $\\times$ $\\surd$\nExtensions or improvements of $IC\/LT$ models\n References Extender $IC$ $LT$ Remarks Chen et al. [44] A scalable heuristic algorithm for $LT$ were developed by constructing a local directed acyclic graphs (DAGs) $\\times$ $\\surd$ Showed that computing influence spread in the linear threshold model is #P-hard problem Borodin et al. [22] Introduced $K$-$LT$ as the extension of $LT$ involved the competition of influence $\\times$ $\\surd$ He et al. [104] Under the $LT$ model, they extended it to influence blocking maximization problem $\\times$ $\\surd$ Goyal et al. [77] Improved the $LT$ by cutting down on the number of calls made in the first iteration which is the key to estimation procedure. $\\times$ $\\surd$ Goyal et al. [74] Under both $IC$ and $LT$ model, pursing the alternative goals which motivated by resource and time constraints $\\surd$ $\\surd$ Barbieri et al. [16] Extended both $IC$ and $LT$ to topic-aware models $\\surd$ $\\surd$ Wang et al. [238] Extended $IC$ to incorporate similarity in social network $\\surd$ $\\times$ Rodriguez et al. [198] General case of $IC$ model with time constraint $\\surd$ $\\times$\n References Extender $IC$ $LT$ Remarks Chen et al. [44] A scalable heuristic algorithm for $LT$ were developed by constructing a local directed acyclic graphs (DAGs) $\\times$ $\\surd$ Showed that computing influence spread in the linear threshold model is #P-hard problem Borodin et al. [22] Introduced $K$-$LT$ as the extension of $LT$ involved the competition of influence $\\times$ $\\surd$ He et al. [104] Under the $LT$ model, they extended it to influence blocking maximization problem $\\times$ $\\surd$ Goyal et al. [77] Improved the $LT$ by cutting down on the number of calls made in the first iteration which is the key to estimation procedure. $\\times$ $\\surd$ Goyal et al. [74] Under both $IC$ and $LT$ model, pursing the alternative goals which motivated by resource and time constraints $\\surd$ $\\surd$ Barbieri et al. [16] Extended both $IC$ and $LT$ to topic-aware models $\\surd$ $\\surd$ Wang et al. [238] Extended $IC$ to incorporate similarity in social network $\\surd$ $\\times$ Rodriguez et al. [198] General case of $IC$ model with time constraint $\\surd$ $\\times$\n [1] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. 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\section{Introduction}
Consider the stochastic differential equation
\begin{eqnarray}
dX_{t} &=&b(X_{t})dt+\sigma (X_{t})dW_{t},\quad t>0, \label{eq:facil} \\
X_{0} &=&x_{0}. \notag
\end{eqnarray
Here $b,\sigma :{\mathbb{R}}\rightarrow {\mathbb{R}}$ are two locally
Lipschitz functions, $x_{0}\in {\mathbb{R}}$ and $\{W_{t}:t\geq 0\}$ is a
Brownian motion defined on a complete probability space $(\Omega ,\mathcal{F
,P)$.
It is well-known that the solution $X$ of equation (\ref{eq:facil}) may
explode in finite time. That is, $|X_{t}|$ goes to infinite as $t$
approaches to a stopping time that could be finite with positive
probability, which is called the explosion time of equation (\ref{eq:facil})
(see McKean \cite{MK}). The Feller test is an important tool of the
stochastic calculus to know if there is blow-up in finite time for (\re
{eq:facil}) (see, for example, Karatzas and Shreve \cite{KaS}). The reader
can consult de Pablo et al. \cite{dP} (and references therein) for
applications of blow-up.
In the case that $b$ is non-decreasing and positive, and $\sigma \equiv 1$,
Feller test is equivalent to Osgood criterion \cite{Os}, as it is proven in
Le\'{o}n and Villa \cite{L-V}. It means, the solution of (\ref{eq:facil})
explodes in finite time if and only if $\int_{x_{0}}^{\infty
}(1/b(s))ds<\infty $. Also, when $\sigma \equiv 0$ and $b>0$, Osgood \cit
{Os} has stated that explosion time is finite if and only if
\int_{x_{0}}^{\infty }(1/b(s))ds<\infty $. In this case, the explosion time
is equals to this integral.
Unfortunately, the distribution of the explosion time of equation (\re
{eq:facil}) is not easy to calculate. One way to do it is using linear
second-order ordinary differential equations. Indeed, Feller \cite{Wfe} has
pointed out the Laplace transformation of this distribution is a bounded
solution to some related ordinary differential equations (see Section \re
{sec:5.2} below for a generalization of this result). Also some numerical
schemes have been analyzed in order to approximate the time of explosion
(consult D\'avila et al. \cite{Da}). In this paper, in Section \re
{subsec:5.1}, we also obtain the partial differential equation that has the
distribution of the explosion time as a bounded solution.
Now consider the nonautonomous stochastic differential equation
\begin{eqnarray}
dX_{t} &=&b(t,X_{t})dt+\sigma (t,X_{t})dW_{t},\quad t>0, \label{eq:dificil}
\\
X_{0} &=&x_{0}. \notag
\end{eqnarray
For this equation, Feller test and Osgood criterion are not useful anymore,
but, in the case that $\sigma $ is independent of $x$, we are still able to
associate the Laplace transformation of the distribution of the explosion
time of (\ref{eq:dificil}) with a partial differential equation as Theorem
\ref{thm:22} below establishes.
The main purpose of this paper is to deal with some extensions of Osgood
criterion for some equations of the form (\ref{eq:dificil}). For instance,
Lemma \ref{lem:n7} provides a better understanding of Theorem 2.1 in \cit
{Co}, or if, in (\ref{eq:dificil}), $\sigma $ is independent of $x$, we
obtain an extension of Osgood criterion by means of the law of iterated
logarithm and comparison theorems. It is worth mentioning that versions of
these important tools have been used to analyze global solutions of integral
equations as it is done by Constantin \cite{Co}, or to obtain an extension
of Osgood criterion to integral equations with additive noise and with
0<b(t,x)=b(x)$ non-decreasing (see Le\'{o}n and Villa \cite{L-V}).
The paper is organized as follows. Our comparison theorem for integral
equations is introduced in Section \ref{sec:3}. Some extensions of Osgood
criterion are given is Sections \ref{sec:2}, \ref{sec:3} and \ref{sec:4}.
Finally, the relation between partial differential equations and finite
blow-up is considered in Section \ref{sec:5}.
\section{Osgood criterion for some stochastic differential equation with
diffusion coefficient}
\label{sec:2}
Let $\sigma:{\mathbb{R}}\rightarrow{\mathbb{R}}$ and $h:{\mathbb{R}
\rightarrow{\mathbb{R}}$ be a differentiable function and a continuous
function, respectively. We consider the stochastic differential equation
\begin{equation}
X_{t}^{\xi }=\xi +\frac{1}{2}\int_{0}^{t}\sigma (X_{s}^{\xi })\sigma
^{\prime }(X_{s}^{\xi })h^2(s)ds+\int_{0}^{t}\sigma (X_{s}^{\xi })
h(s)dW_{s}, \quad t\ge 0, \label{EDEa}
\end{equation
where $\xi\in{\mathbb{R}}$. Here and in what follows, $W=\{W_t: t\ge0\}$ is
a Brownian motion.
Now we assume that there are $-\infty \leq x_{1}<x_{2}\leq \infty $ such
that $\sigma \neq 0$ on $(x_{1},x_{2})$. Let $\xi \in (x_{1},x_{2})$ be
fixed and define $\Psi _{\xi }:(x_{1},x_{2})\rightarrow \mathbb{R}$ a
\begin{equation*}
\Psi _{\xi }(x)=\int_{\xi }^{x}\frac{dz}{\sigma (z)}.
\end{equation*
Set $l_{\xi }=\Psi _{\xi }(x_{1})\wedge \Psi _{\xi }(x_{2})$, $r_{\xi }=\Psi
_{\xi }(x_{1})\vee \Psi _{\xi }(x_{2})$ and $Y_{t}=\int_{0}^{t}h(s)dW_{s}$,
t\geq 0.$
The following result is our first extension of Osgood criterion.
\begin{theorem}
\label{the:v1} Let $\tau _{\xi }=\inf \{t\geq 0:Y_{t}\notin (l_{\xi },r_{\xi
})\}$. Then, the process $X_{t}^{\xi }=\{\Psi _{\xi }^{-1}(Y_{t}):0\leq
t<\tau _{\xi }\}$ is a solution of equation (\ref{EDEa}).
\end{theorem}
\begin{remark}
In this case, $\tau _{\xi}$ is called the explosion time of the solution to
equation (\ref{EDEa}).
\end{remark}
\begin{proof}
Applying It\^{o}'s formula with $f(x)=\Psi _{\xi }^{-1}(x)$, $x\in (l_{\xi
},r_{\xi })$ we hav
\begin{equation*}
f(Y_{t\wedge \tau _{\xi }^{k}})-f(0)=\frac{1}{2}\int_{0}^{t\wedge \tau _{\xi
}^{k}}f^{\prime \prime }(Y_{s})h^{2}(s)ds+\int_{0}^{t\wedge \tau _{\xi
}^{k}}f^{\prime }(Y_{s})h(s)dW_{s}, \label{famitoaos}
\end{equation*
wher
\begin{equation*}
\tau _{\xi }^{k}=\inf \{t>0:Y_{t}\notin (l_{\xi }+k^{-1},r_{\xi }-k^{-1})\}.
\end{equation*
Letting $k\rightarrow \infty $ in (\ref{famitoaos}) we get the result holds.
$\hfill $
\end{proof}
An immediate consequence of Theorem \ref{the:v1} is the following:
\begin{corollary}
\label{cor:dis} Let $\int_{0}^{\infty }h^{2}(s)ds=\infty $. Then the
solution of equation (\ref{EDEa}) explodes in finite time if and only if
either $l_{\xi }>-\infty $, or $r_{\xi }<\infty $. Moreover, if $l_{\xi }$
and $r_{\xi }$ are two real numbers, then
\begin{equation*}
P(\tau _{\xi }\in dt)=\sum\limits_{k=-\infty }^{\infty }(-1)^{k}\frac{r_{\xi
}+k(r_{\xi }-l_{\xi })}{\sqrt{2\pi }(H(t))^{3/2}}\exp \left( -\frac{(r_{\xi
}+k(r_{\xi }-l_{\xi }))^{2}}{2H(t)}\right) dt,
\end{equation*
with $H(t)=\int_{0}^{t}(h(s))^{2}ds$.
\end{corollary}
\begin{proof}
It is well-known that there is a Brownian motion $B=\{B_t:t\ge 0\}$ such
that $Y_{t}=B_{H(t)}$, $t\ge0$, (see, for instance, Durrett \cit
{Du}). Let ${\tilde\tau}_{\xi}=\inf \{t>0: B_t\notin(l_{\xi},r_{\xi})\}$.
Then, it is easy to show that $P(\tau_{\xi}\le t)= P({\tilde\tau}_{\xi}\le
H(t))$. Consequently, the proof follows from Borodin and Salminen \cite{B-S}
(page 212).$\hfill$
\end{proof}
\begin{remark}
Suppose that, for example, $\sigma >0$, $\Psi _{\xi }(x_{1})=-\infty $ and
\Psi _{\xi }(x_{2})<\infty $. Then, as an immediate consequence of the proof
of Corollary \ref{cor:dis}, we get that $\tau _{\xi }=\inf
\{t:\int_{0}^{t}h(s)dW_{s}=\Psi _{\xi }(x_{2})\}$ and
\begin{equation}
P(\tau _{\xi }\leq t)=\Phi \left( \frac{\Psi _{\xi }(x_{2})}{\sqrt{H(t)}
\right) , \label{disttiemplleBro}
\end{equation
where
\begin{equation*}
\Phi (x)=\frac{2}{\sqrt{2\pi }}\int_{x}^{\infty }e^{-z^{2}/2}dz.
\end{equation*
Observe that we get a similar result when $\sigma $ is negative, or the
involved interval has the form $(l_{\xi },\infty ).$
\end{remark}
Now we illustrate this remark with two examples.
\begin{example}
\label{ExamOSG1}Let $\sigma (x)=|x|^{\alpha }$, $x\in \mathbb{R}$, $\alpha
>1 $ and $\xi \in \mathbb{R}$. Then
\begin{equation*}
\Psi _{\xi }(x)=\left\{
\begin{array}{cc}
\frac{1}{1-\alpha }(|x|^{1-\alpha }-|\xi|^{1-\alpha }), & \xi>0,\ x\ge0, \\
\frac{1}{1-\alpha }(|\xi|^{1-\alpha }-|x|^{1-\alpha }), & \xi<0,\ x\le 0
\end{array
\right.
\end{equation*
Hence,
\begin{equation*}
\Psi_{\xi}(-\infty)=\frac{|\xi|^{1-\alpha}}{1-\alpha}\quad \hbox{\rm and
\quad \Psi_{\xi}(0)=\infty,\quad\hbox{\rm for}\ \xi<0,
\end{equation*}
and
\begin{equation*}
\Psi_{\xi}(\infty)=\frac{|\xi|^{1-\alpha}}{\alpha-1}\quad \hbox{\rm and
\quad \Psi_{\xi}(0)=-\infty,\quad\hbox{\rm for}\ \xi>0.
\end{equation*}
Therefore, there is explosion in finite time and
\begin{equation*}
P(\tau _{\xi }\leq t)=\Phi \left( \frac{|\xi |^{1-\alpha }}{(\alpha -1)\sqrt
H(t)}}\right) .
\end{equation*}
\end{example}
\begin{example}
\label{ExamOSG2}Let $\sigma (x)=e^{\alpha x}$, $x\in \mathbb{R}$, $\alpha
\neq 0$ and $\xi \in \mathbb{R}$. The
\begin{equation*}
\Psi _{\xi }(x)=\frac{1}{\alpha }(e^{-\alpha \xi }-e^{-\alpha x}),
\end{equation*
\begin{equation*}
\Psi _{\xi }(-\infty )=\left\{
\begin{array}{ll}
-\infty , & \alpha >0, \\
\frac{1}{\alpha }e^{-\alpha \xi }, & \alpha <0
\end{array
\right. \text{ \ \ and \ \ }\Psi _{\xi }(\infty )=\left\{
\begin{array}{ll}
\frac{1}{\alpha }e^{-\alpha \xi }, & \alpha >0, \\
\infty , & \alpha <0
\end{array
\right.
\end{equation*
Thus we deduce that there is explosion on the left for $\alpha <0$, there is
explosion on the right for $\alpha >0$ and
\begin{equation*}
P(\tau _{\xi }\leq t)=\Phi \left( \frac{e^{-\alpha \xi }}{|\alpha |\sqrt{H(t
}}\right) .
\end{equation*}
\end{example}
\section{An extension of Osgood criterion for integral equations}
\label{sec:3}
In this section we generalize recent results obtained in \cite{M-J-J} and
\cite{L-V}. Now we study the following nonautonomous integral equation
\begin{equation}
X_{t}^{\xi }=\xi +\int_{0}^{t}a(s)b(X_{s}^{\xi })ds+g(t), \quad t\ge0.
\label{eqdnhomo}
\end{equation}
The explosion time $T_{\xi}^X$ of this equation is defined as
T_{\xi}^X=\inf \{t\ge 0: X_t^{\xi}\notin {\mathbb{R}}\}$. In the remaining
of this paper we will need the following conditions:
\begin{description}
\item[H1:] $a:(0,\infty )\rightarrow (0,\infty )$ is a continuous function
such that
\begin{equation*}
\lim_{t\rightarrow \infty }\int_{t}^{t+\eta }a(s)ds>0, \qua
\hbox{\rm for
some}\ \eta>0.
\end{equation*}
\item[H2:] $b:\mathbb{R}\rightarrow \lbrack 0,\infty )$ is a continuous
function such that there exist $-\infty \leq l<\infty $ and $-\infty
<r<\infty $ satisfying that $b>0$ and locally Lipschitz on $(l,\infty )$,
and $b:[r,\infty )\rightarrow (0,\infty )$ is non-decreasing.
\item[H3:] $g:[0,\infty )\rightarrow \mathbb{R}$ is a continuous function
such that
\begin{equation*}
\limsup_{t\rightarrow \infty }\left( \inf_{0\leq h\leq {\tilde{\eta}
}g(t+h)\right) =\infty ,\quad \hbox{\rm for some}\ {\tilde{\eta}}>0.
\end{equation*}
\end{description}
Henceforth we utilize the convention
\begin{equation*}
A_t(x)=\int_{t}^{x}a(z)dz,\quad t\ge0\ \hbox{\rm and }x\in(t,\infty ),
\end{equation*}
and
\begin{equation*}
B_{\xi }(x)=\int_{\xi }^{x}\frac{dz}{b(z)},\quad x\in (l,\infty).
\end{equation*}
We begin with the following generalization of Osgood criterion.
\begin{lemma}
\label{lem:n7} Let \textbf{H1} and \textbf{H2} be satisfied and $x_{0}>l$.
Consider the ordinary differential equation
\begin{eqnarray}
\frac{dy(t)}{dt} &=&a(t)b(y(t))dt,\ \ t>t_0, \label{inrtosg} \\
y(t_0) &=&x_{0}. \notag
\end{eqnarray}
\begin{itemize}
\item[a)] Assume that $B_{x_{0}}(\infty )\geq A_{t_0}(\infty )$, then
\begin{equation*}
y(t)=B_{x_{0}}^{-1}(A_{t_0}(t)),\ \ t\ge t_0.
\end{equation*}
\item[b)] If $B_{x_{0}}(\infty )<A_{t_0}(\infty )$, then there is blow up in
finite time and the time of explosion $T_{x_{0}}^{y}$ is equal to
A_{t_0}^{-1}(B_{x_{0}}(\infty ))$.
\end{itemize}
\end{lemma}
\begin{remark}
Observe that equation (\ref{inrtosg}) (resp. equation (\ref{eqdnhomo})) has
a unique solution for $x_0>l$ (resp. for $\xi>l$) that may explode in finite
time because of Hypotheses \textbf{H1} and \textbf{H2} (resp. \textbf{H1}
\textbf{H3}). This fact will be used in the proof of Theorem \re
{TheOsnoiGral} below without mentioning
\end{remark}
\begin{proof}
From (\ref{inrtosg}) we see that
\begin{equation*}
\int_{t_0}^{t}\frac{y^{\prime }(s)}{b(y(s))}ds=\int_{t_0}^{t}a(s)ds.
\end{equation*
The change of variable $z=y(s)$ yields $B_{x_{0}}(y(t))= A_{t_0}(t)$.
Now we deal with Statement a). If $B_{x_{0}}(\infty )\geq A_{t_0}(\infty )$,
then $B_{x_{0}}(\infty )>A_{t_0}(t)$, for all $t>t_0$. Therefore
y(t)=B_{x_{0}}^{-1}(A_{t_0}(t)),$ $t>t_0$ is well-defined.
Finally we consider Statement b). In this case we have
B_{x_{0}}^{-1}(A_{t_0}(t))$ is only defined for $t<A_{t_0}^{-1}(B_{x_{0}}
\infty ))<\infty .\hfill $
\end{proof}
\bigskip
Also we are going to need the following elementary comparison result.
\begin{lemma}
\label{DesLemma}Let $x_{0}>r$ and $T>t_0$. Assume that \textbf{H1} and
\textbf{H2} are satisfied, and that $u,v:[t_0,T] \rightarrow{\mathbb{R}}$
are two continuous functions.
\begin{itemize}
\item[a)] Suppose that $u$ and $v$ are such that
\begin{eqnarray*}
v(t) &>&x_{0}+\int_{t_{0}}^{t}a(s)b(v(s))ds,\quad t\in \lbrack t_{0},T], \\
u(t) &=&x_{0}+\int_{t_{0}}^{t}a(s)b(u(s))ds,\quad t\in \lbrack t_{0},T].
\end{eqnarray*
Then $v(t)\geq u(t)$, for all $t\in \lbrack t_{0},T]$.
\item[b)] If
\begin{eqnarray*}
r\ <\ v(t) &<&x_{0}+\int_{t_{0}}^{t}a(s)b(v(s))ds,\quad t\in \lbrack
t_{0},T], \\
u(t) &=&x_{0}+\int_{t_{0}}^{t}a(s)b(u(s))ds,\quad t\in \lbrack t_{0},T].
\end{eqnarray*
Then $v(t)\leq u(t)$, for all $t\in \lbrack t_{0},T]$.
\end{itemize}
\end{lemma}
\begin{proof}
We first deal with Statement a). Let $N=\{t\geq t_0:b(u(s))\leq b(v(s)),\
s\in \lbrack t_0,t]\}.$ Since $t_0\in N$, then the continuity of of $v$ and
u$, together with the fact that $b$ is non-decreasing on $(r,\infty)$, leads
us to show that $\tilde{T}=\sup N>t_0.$ If $\tilde{T}<T $ then
\begin{equation*}
v(\tilde{T})-u(\tilde{T})>\int_{t_0}^{\tilde{T}}a(s)[b(v(s))-b(u(s))]ds \ge0,
\end{equation*
which is impossible due to the definition of ${\tilde T}$.
Finally, we proceed similarly to prove that b) is also true and to finish
the proof.$\hfill $
\end{proof}
\begin{theorem}
\label{TheOsnoiGral}Let $\xi \in{\mathbb{R}}$. Assume \textbf{H1}-\textbf{H3
. Then the explosion time $T_{\xi }^{X}$ of the solution $X^{\xi }$ of (\re
{eqdnhomo}) is finite if and only if
\begin{equation}
\int_{r}^{\infty }\frac{ds}{b(s)}<\infty . \label{conexisosgoog}
\end{equation}
\end{theorem}
\begin{proof}
Suppose that $T_{\xi }^{X}<\infty $. Since $g$ is continuous, then
\begin{equation*}
\int_{0}^{t}a(s)b(X_{s}^{\xi })ds\left\{
\begin{array}{cc}
<\infty , & t<T_{\xi }^{X}, \\
=\infty , & t=T_{\xi }^{X}
\end{array
\right.
\end{equation*
Hence, there is $t_{0}\in (0,T_{\xi }^{X})$ such that
\begin{equation*}
\xi +\int_{0}^{t_{0}}a(s)b(X_{s}^{\xi })ds+\inf_{s\in \lbrack 0,T_{\xi
}^{X}]}g(s)>r,
\end{equation*
and consequently $X_{t}>r$ for $t\in \lbrack t_{0},T_{\xi }^{X}]$.
Now set
\begin{equation*}
M=\sup \{|g(t)|:0\leq t\leq T_{\xi
}^{X}\}+\xi+\int_0^{t_0}a(s)b(X_s^{\xi})ds .
\end{equation*
This yield
\begin{equation*}
X_{t}^{\xi }< M+1+\int_{t_0}^{t}a(s)b(X_{s}^{\xi })ds,\ \ t\in \lbrack
t_0,T_{\xi }^{X}].
\end{equation*
On the other hand, we consider the integral equatio
\begin{equation*}
u(t)=(M+1)+\int_{t_0}^{t}a(s)b(u(s))ds,\ \ t\geq t_0.
\end{equation*
Because $M>r$, Lemmas \ref{lem:n7} and \ref{DesLemma} give $T_{M+1}^{u}=
A_{t_0}^{-1}(B_{M+1}(\infty ))\leq T_{\xi }^{X}<\infty $. Whenc
\begin{equation*}
\int_{M+1}^{\infty }\frac{ds}{b(s)}<\infty .
\end{equation*
The continuity and positivity of $b$ in $[r,\infty )$ implies (\re
{conexisosgoog}).
Reciprocally, suppose that $X^{\xi }$ does not explodes in finite time. From
Hypotheses \textbf{H1} and \textbf{H3}, we can find a sequence $\{t_{n}: n\i
{\mathbb{N}}\}$ such that $t_{n}\uparrow \infty $ and
\begin{equation*}
r+1<\xi +\inf_{0\leq h\leq {\tilde \eta} }g(t_{n}+h)\uparrow \infty \text{,\
\ as }n\rightarrow \infty.
\end{equation*}
Observe that
\begin{equation*}
X_{t+t_{n}}^{\xi }>\xi +\inf_{0\leq h\leq {\tilde\eta} }g(t_{n}+h)-1
\int_{0}^{t}a(s+t_{n})b(X_{s+t_{n}}^{\xi })ds,\ \ t\in \lbrack 0,{\tilde\eta}
].
\end{equation*
Now consider the integral equatio
\begin{equation*}
u(t)=\xi +\inf_{0\leq h\leq {\tilde\eta} }g(t_{n}+h)-1
\int_{0}^{t}a(s+t_{n})b(u(s))ds,\ \ t\in[0,{\tilde\eta}].
\end{equation*
Therefore Lemmas \ref{lem:n7} and \ref{DesLemma} yiel
\begin{equation*}
\int_{\xi +\inf_{0\leq h\leq {\tilde\eta} }g(t_{n}+h)-1}^{\infty }\frac{ds}
b(s)}>\int_{t_{n}}^{t_n+{\tilde \eta} }a(s)ds.
\end{equation*
Whence \textbf{H1} implies $\int_{r}^{\infty }\frac{ds}{b(s)}=\infty .\hfill
$
\end{proof}
We finish this section with the following result for bounded noise.
\begin{proposition}
\label{BNoise} Assume that Hypotheses \textbf{H1} and \textbf{H2} are true.
Also assume that $g$ in equation (\ref{eqdnhomo}) is a bounded function and
that $\xi +\inf_{s\geq 0}g(s)>r$. Then, we have the following statements:
\begin{itemize}
\item[a)] $\int_r^{\infty} (1/b(s))ds=\infty$ implies that the solution of
equation (\ref{eqdnhomo}) does not explode in finite time.
\item[b)] $\int_r^{\infty} (1/b(s))ds<\infty$ yields that the solution of
equation (\ref{eqdnhomo}) blows up in finite time and
\begin{equation*}
T_{\xi }^{X}\in (A_0^{-1}(B_{\xi +\sup_{s\geq 0}g(s)}(\infty
)),A^{-1}_0(B_{\xi +\inf_{s\geq 0}g(s)}(\infty ))).
\end{equation*}
\end{itemize}
\end{proposition}
\begin{proof}
Let $\varepsilon >0$ be such that $\xi +\inf_{s\geq 0}R(s)>r+\varepsilon $.
Set
\begin{equation*}
Z_{t}^{\xi }=\xi +\sup_{s\geq 0}g(s)+\varepsilon
+\int_{0}^{t}a(s)b(Z_{s}^{\xi })ds
\end{equation*
and
\begin{equation*}
Y_{t}^{\xi }=\xi +\inf_{s\geq 0}g(s)-\varepsilon
+\int_{0}^{t}a(s)b(Y_{s}^{\xi })ds.
\end{equation*
By Lemma \ref{DesLemma} we have,
\begin{equation*}
Y_{t}^{\xi }<X_{t}^{\xi }<Z_{t}^{\xi },\quad t<T_{\xi +\sup_{s\geq
0}g(s)+\varepsilon }^{Z}.
\end{equation*
Letting $\varepsilon \downarrow 0$ the proof is an immediate consequence of Lemma \ref{lem:n7}, and
Hypotheses \textbf{H1} and \textbf{H2}. \hfill
\end{proof}
\section{Stochastic differential equation with additive Wiener integral noise}
\label{sec:4}
In this section we study equation (\ref{eqdnhomo}) when the noise $g$ is a
Wiener integral. More precisely, here we study the stochastic differential
equation
\begin{equation}
X_{t}^{\xi }=\xi +\int_{0}^{t}a(s)b(X_{s}^{\xi })ds+I_{t},
\label{sdeintnoise}
\end{equation
where $I_{t}=\int_{0}^{t}f(s)dW_{s}$ and $f:[0,\infty )\rightarrow \mathbb{R}
$ is a square-integrable function on $[0,M]$, for any $M>0$.
In the remaining of this section we utilize the following assumption:
\begin{description}
\item[\textbf{H4}:] $\int_{0}^{\infty }f^{2}(s)ds=\infty $ and
\begin{equation}
\sum_{n=M}^{\infty}\frac{1}{\Upsilon^p (n)}\left( \int_{n}^{n+2
}f^{2}(s)ds\right) ^{p/2}<\infty, \label{condconvseri}
\end{equation
for some $M,p>0$, where
\begin{equation*}
\Upsilon (t)=\sqrt{2\left( \int_{0}^{t}f^{2}(s)ds\right) \log \log \left(
e^e\vee \int_{0}^{t}f^{2}(s)ds\right) }.
\end{equation*}
\end{description}
\begin{remark}
\label{rem:nic} Observe that (\ref{condconvseri}) holds if, for example,
\begin{equation*}
t\mapsto \left( \int_{0}^{t+2}f^{2}(s)ds\right) \left(
\int_{0}^{t}f^{2}(s)ds\right) ^{-1}-1.
\end{equation*
is a decreasing function in $L^{p}([M,\infty ))$ for some $M,p>0$.
\end{remark}
On the other hand, as a consequence of iterated logarithm theorem for
locally square integrable martingales, we can now state the following:
\begin{lemma}
Under the fact that $\int_0^{\infty}f^2(s)ds=\infty$, we have
\begin{equation}
\limsup_{t\rightarrow \infty }\frac{I_{t}}{\Upsilon (t)}=1 \quad
\hbox{\rm
with probability one}. \label{lit}
\end{equation}
\end{lemma}
\begin{proof}
The result is Theorem 1.1 in Qing Gao \cite{G}.$\hfill $
\end{proof}
The following theorem is the main result of this section.
\begin{theorem}
\label{TRI}Assume that \textbf{H1}, \textbf{H2} and \textbf{H4} are true.
Then the stochastic differential equation (\ref{sdeintnoise}) blows up in
finite time with probability 1 if and only if $\int_{r}^{\infty }\frac{ds}
b(s)}<\infty .$
\end{theorem}
\begin{proof}
We first observe that, by Theorem \ref{TheOsnoiGral}, we only need to show
that the paths of $I$ satisfy Hypothesis \textbf{H3} almost surely.
Burkholder-Davis-Gundy inequality (see, for instance, Theorem 3.5.1 in \cit
{Du}) yield
\begin{equation*}
E\left[ \left( \sup_{s,t\in \lbrack {n},{n}+2 ]}|I_{t}-I_{s}|\right) ^{p
\right] \leq c_{p}\left( \int_{{n}}^{{n}+2}f^{2}(s)ds\right) ^{p/2},
\end{equation*
where $c_{p}$ is a constant depending only on $p$. Then, by (\re
{condconvseri}),
\begin{equation*}
E\left[ \sum_{n=M}^{\infty }\left( \sup_{s,t\in \lbrack {n},n+2]}\frac
|I_{t}-I_{s}|}{\Upsilon ({n})}\right) ^{p}\right] \leq
c_{p}\sum_{n=M}^{\infty }\frac{1}{\Upsilon ^{p}({n})}\left( \int_{{n}}^{{n
+2}f^{2}(s)ds\right) ^{p/2}<\infty .
\end{equation*
Therefore, it is enough to prove that $I(\omega )$ satisfies \textbf{H3} for
$\omega \in \Omega $ for which there exists $n_{0}\in \mathbb{N}$ such tha
\begin{equation*}
\sup_{s,t\in \lbrack {n},{n}+2]}\frac{|I_{t}(\omega )-I_{s}(\omega )|}
\Upsilon ({n})}\leq \frac{1}{4},\quad \hbox{\rm for}\ n\geq n_{0}
\end{equation*
and (\ref{lit}) is satisfied. Hence, we can find a sequence $\{t_{n}:n\in
\mathbb{N}}\}$ such that $t_{n}>n$ an
\begin{equation*}
\frac{I_{t_{n}}(\omega )}{\Upsilon (t_{n})}\geq \frac{1}{2}\quad
\hbox{\rm
for all}\ n\in {\mathbb{N}}.
\end{equation*
Finally, using the properties established in this proof, we are able to
write, for $n\geq n_{0}$,
\begin{eqnarray*}
\inf_{s\in \lbrack t_{n},t_{n}+1]}I_{s}(\omega ) &=&I_{t_{n}}(\omega
)+\inf_{s\in \lbrack t_{n},t_{n}+1]}\left( I_{s}(\omega )-I_{t_{n}}(\omega
)\right) \\
&\geq &I_{t_{n}}(\omega )+\inf_{s\in \lbrack t_{n},t_{n}+1]}(-|I_{s}(\omega
)-I_{t_{n}}(\omega )|) \\
&\geq &I_{t_{n}}(\omega )-\left( \sup_{s,t\in \lbrack \lbrack
t_{n}],[t_{n}]+2]}\frac{|I_{s}(\omega )-I_{t}(\omega )|}{\Upsilon ([t_{n}])
\right) \Upsilon ([t_{n}]) \\
&\geq &\frac{1}{2}\Upsilon (t_{n})-\frac{1}{4}\Upsilon ([t_{n}])\geq \frac{
}{4}\Upsilon (t_{n})\rightarrow \infty ,
\end{eqnarray*
as $n\rightarrow \infty $, where $[t]$ is the integer part of $t$ and, in
the last inequality, we have used that $\Upsilon $ is a non-decreasing
function.$\hfill $
\end{proof}
\bigskip
Now, in order to state a consequence of Theorem \ref{TRI}, we consider the
equation
\begin{equation} \label{eq:nagre}
Y_t=\xi+\int_0^t{\tilde b}(s,Y_s)ds+I_t,\quad t\ge 0.
\end{equation}
Here, for each $T>0$, the function ${\tilde b}:[0,\infty))\times{\mathbb{R}
\rightarrow [0,\infty)$ is locally Lipschitz (uniformly on $s\in[0,T]$),
b(\cdot,x)$ is continuous, for $x\in{\mathbb{R}}$, and $I$ satisfy
Hypothesis \textbf{H4} with $f$ continuous. Remember that, in this case,
equation (\ref{eq:nagre}) has a unique solution that may explode in finite
time.
\begin{corollary}
Let $a$ and $b$ satisfy Conditions \textbf{H1} and \textbf{H2},
respectively. Assume that $\xi\in{\mathbb{R}}$, $b$ is locally Lipschitz,
\int_r^\infty (1/b(x))dx<\infty$ (resp. $\int_r^\infty (1/b(x))dx=\infty$)
and $a(s)b(x)\le {\tilde b}(s,x)$ (resp. ${\tilde b}(s,x)\le a(s)b(x)$),
(s,x)\in[0,\infty)\times{\mathbb{R}}$. Then, the solution to equation (\re
{eq:nagre}) explodes (resp. does not explode) in finite time.
\end{corollary}
\begin{proof}
We only consider the case that $\int_r^\infty (1/b(x))dx=\infty$ and $
\tilde b}(s,x)\le a(s)b(x)$, since the proof is similar for the other one.
Let $X^{\xi }$ and $Y$ be the solutions of equations (\ref{sdeintnoise}) and
(\ref{eq:nagre}), respectively. Then, from Milian \cite{Mi} (Theorem 2), we
get
\begin{equation*}
Y_{t}\leq X_{t}^{\xi },\quad t\geq 0.
\end{equation*
Thus, by Theorem \ref{TRI}, the solution $Y$ of equation (\ref{eq:nagre})
cannot explode in finite time because it cannot go to $-\infty $ in finite
time since ${\tilde{b}}$ is ${\mathbb{R}}_{+}$-valued and $I$ has continuous
paths and, consequently, bounded paths on compact intervals of $[0,\infty )
. Therefore the proof is complete.$\hfill $
\end{proof}
\begin{example}
Take
\begin{eqnarray*}
a(x) &=&x^{\alpha },\ \ x\in (0,\infty ), \\
b(x) &=&8x^{2}-36x+48,\ \ x\in \mathbb{R}, \\
f(x) &=&x^{\beta },\ \ x\in (0,\infty ),\ \ \beta >-\frac{1}{2}.
\end{eqnarray*
Henc
\begin{equation*}
\lim_{t\rightarrow \infty }\int_{t}^{t+1}x^{\alpha }dx=\left\{
\begin{array}{cc}
+\infty , & \alpha >0, \\
1, & \alpha =0, \\
0, & \alpha <0
\end{array
\right.
\end{equation*
and
\begin{equation*}
\frac{(t+2)^{2\beta +1}}{t^{2\beta +1}}-1=\left( 1+\frac{2}{t}\right)
^{2\beta +1}-1\leq C\frac{1}{t}.
\end{equation*
The last function belongs to $L^{p}([1,\infty ])$, for any $p>1$. Thus $f$
satisfied (\ref{condconvseri}) due to Remark \ref{rem:nic}.
On the other hand, it is clear that $\int_{\xi }^{\infty }\frac{dx}
8x^{2}-36x+48}<\infty $, $\xi >0$. The
\begin{equation*}
X_{t}^{\xi }=\xi +\int_{0}^{t}s^{\alpha }(8(X_{s}^{\xi })^{2}-36(X_{s}^{\xi
})+48)ds+\int_{0}^{t}s^{\beta }dW_{s},
\end{equation*
explodes in finite time when $\alpha \geq 0$. Notice that $b$ is not
necessarily increasing as in \cite{L-V} or \cite{M-J-J}. Moreover, we can
improve Theorem \ref{TRI} in some particular cases, see \cite{V}.
\end{example}
\begin{example}
\label{ExEXSC} The function $Y_{t}\equiv 1$ is solution t
\begin{equation*}
Y_{t}=1+\int_{0}^{t}(Y_{s})^{2}ds-t,\ \ t\geq 0.
\end{equation*
Although $\int_{1}^{\infty }(1/s^{2})ds<\infty $, $Y$ does not blow-up in
finite time because $g(t)=-t,\ t\geq 0,$ does not satisfies Hypothesis
\textbf{H3}.
\end{example}
Also notice that $f(t)=\exp (\exp (t))$, $t\geq 0,$ does not satisfies (\re
{condconvseri}). We intuitively understand that in this case the noise is to
strong and we have also blow up in finite time, for any initial condition.
We have a contrary effect as in Example \ref{ExEXSC}.
\begin{proposition}
Let $f$ and $I$ be defined in equation (\ref{sdeintnoise}). Suppose \textbf
H1}, \textbf{H2} and $\int_{0}^{\infty }f^{2}(s)ds<\infty $ are satisfied.
Then $I$ is bounded with probability one and, under the assumption $\xi
+\inf_{s\geq 0}I_{s}> r$, the stochastic differential equation (\re
{sdeintnoise}) blows up in finite time if and only if $B_{r}(\infty )
<\infty $.
\end{proposition}
\noindent\textbf{Remark} Observe that $\xi +\inf_{s\geq 0}I_{s}$ depends on
\omega$.
\begin{proof}
The result follows from \cite{Du} (Lemma 3.4.7 and Theorem 3.4.9), and
Proposition \ref{BNoise}.$\hfill $
\end{proof}
\section{An approach to obtain the distribution of the explosion time of a
stochastic differential equation}
\label{sec:5}
Now we study some stochastic differential equations of the form
\begin{equation}
X_{t}^{\xi }=\xi +\int_{0}^{t}b(s,X_{s}^{\xi })ds+\int_{0}^{t}\sigma
(s,X_{s}^{\xi })dW_{s},\quad t\ge 0. \label{edegral}
\end{equation
Namely, we propose a method to figure out the distribution of the explosion
time $\tau _{\xi }$ of $X^{\xi}$. Intuitively, $\tau_{\xi}$ is a stopping
time such that (\ref{edegral}) has a solution up to this stopping time and
\limsup_{t\uparrow \tau_{\xi}}|X_t|=\infty.$
\subsection{Autonomous case}
\label{subsec:5.1} This section is devoted to deal with the stochastic
differential equation
\begin{equation*}
X_{t}^{\xi }=\xi +\int_{0}^{t}b(X_{s}^{\xi })ds+\int_{0}^{t}\sigma
(X_{s}^{\xi })dW_{s},\quad t\geq 0,
\end{equation*
with $b,\sigma \in C^{1}({\mathbb{R}})$. In this case, McKean \cite{MK} has
shown that $X_{(\tau _{\xi })-}^{\xi }\in \{-\infty ,\infty \}$ on $[\tau
_{\xi }<\infty ]$. So, henceforth, we can utilize the convention
\begin{equation*}
\tau _{\xi }^{+}=\inf \{t>0:X_{t}^{\xi }=\infty \}\quad \hbox{\rm and}\quad
\tau _{\xi }^{-}=\inf \{t>0:X_{t}^{\xi }=-\infty \}.
\end{equation*}
\begin{theorem}
\label{thm:distet} Consider a bounded function $u:[0,\infty )\times \mathbb{
}\rightarrow \mathbb{R}$ that satisfies the following boundary value problem
\begin{eqnarray}
\frac{\partial u}{\partial t}(t,x) &=&\frac{1}{2}\sigma ^{2}(x)\frac
\partial ^{2}u}{\partial x^{2}}(t,x)+b(x)\frac{\partial u}{\partial x}(t,x),
\quad t> 0\ \hbox{\rm and}\ x\in{\mathbb{R}}, \label{eccalor} \\
u(0,x) &=&0,\quad \hbox{\rm for all}\ x\in \mathbb{R}. \label{conespac}
\end{eqnarray}
\begin{itemize}
\item[a)] Assume that $u(t,\infty)=u(t,-\infty)=1$. Then $P(\tau_{\xi}\le
t)=u(t,\xi).$
\item[b)] $u(t,\infty)=1$ and $u(t,-\infty)=0$ implies that
P(\tau_{\xi}^+\le t)=u(t,\xi).$
\item[c)] If $u(t,\infty)=0$ and $u(t,-\infty)=1$, we have
P(\tau_{\xi}^-\le t)=u(t,\xi).$
\end{itemize}
\end{theorem}
\noindent\textbf{Remarks}\textit{
\begin{itemize}
\item[1)] Maximum principle provides
with conditions on $b$ and $\sigma$ that guarantee the
solution of equation (\ref{eccalor}) is bounded (see Friedman \cite{F}).
\item[2)]
It is quite interesting to observe that (\ref{eccalor}) is related to
transition density of process $X^{\xi}$, or related to the fundamental
solution of the associated Cauchy problem (see \cite{F}). On the other hand,
(\ref{conespac}) and the conditions in Statement a)-c)
are intuitively clear. In fact, (\re
{conespac}) establishes that if we begin at a real point ($\xi\in \mathbb{R}$),
then we need some time to get blow-up. And other conditions mean
that if we
begin at cementery state ($\pm \infty $), then the time to blow-up is less
than any time.
\item[3)] Observe that $P(\tau^{\xi}\le t)=P(\tau^{\xi}_+\le
t)+P(\tau^{\xi}_-\le t)$ and that, for example in Statement a), we
have $P(\tau^{\xi}<\infty)=u(\infty,\xi).$
\item[4)] If $X^{\xi}$ does not explodes in finite time, then equation
(\ref{eccalor})-(\ref{conespac}) has not a bounded solution
satisfying conditions established in either Statement a), b), or c).
\end{itemize}}
\begin{proof}
Using It\^{o}'s formula on $0\leq s<t$ and that $u$ is solution to (\re
{eccalor})\ we obtai
\begin{equation*}
u(t-(s\wedge \tau _{\xi }^{m}),X_{s\wedge \tau _{\xi }^{m}}^{\xi })=u(t,\xi
)+\int_{0}^{s\wedge \tau _{\xi }^{m}}\frac{\partial u}{\partial x
(t-r,X_{r}^{\xi })dW_{r},
\end{equation*
where $\tau _{\xi }^{m}=\inf \{t>0:|X_{t}^{\xi }|>m\}$. Since $u$ is
bounded, then the above stochastic integral is a martingale. Therefore
\begin{equation*}
u(t,\xi )=E\left[ u(t-(s\wedge \tau _{\xi }^{m}),X_{s\wedge \tau _{\xi
}^{m}}^{\xi })\right] .
\end{equation*
Letting $s\uparrow t$, then continuity of $X^{\xi }$ and the boundedness of
u$, together with the dominated convergence theorem, allow us to write
\begin{eqnarray*}
u(t,\xi ) &=&E\left[ u(t-(t\wedge \tau _{\xi }^{m}),X_{t\wedge \tau _{\xi
}^{m}}^{\xi })\right] \\
&=&E\left[ u(t-(t\wedge \tau _{\xi }^{m}),X_{t\wedge \tau _{\xi }^{m}}^{\xi
}),\tau _{\xi }\leq t\right] \\
&&+E\left[ u(t-(t\wedge \tau _{m}^{\xi }),X_{t\wedge \tau _{m}^{\xi }}^{\xi
}),\tau _{\xi }>t\right] .
\end{eqnarray*
Taking $m\rightarrow \infty ,
\begin{equation}
u(t,\xi )=E\left[ u(t-\tau _{\xi },X_{\tau _{\xi }}^{\xi }),\tau _{\xi }\leq
t\right] +E\left[ u(0,X_{t}^{\xi }),\tau _{\xi }>t\right] \label{distrexp}
\end{equation
Now we consider Statement a),
\begin{equation*}
u(t,\xi )=E\left[ u(t-\tau _{\xi },X_{\tau _{\xi }}^{\xi }),\tau _{\xi }\leq
t\right] =P(\tau _{\xi }\leq t).
\end{equation*
Statement b) is proven as follows. From equality (\ref{distrexp}) we get
\begin{eqnarray*}
u(t,\xi ) &=&E\left[ u(t-\tau _{\xi },X_{\tau _{\xi }}^{\xi }),\tau _{\xi
}\leq t,\tau _{\xi }^{+}<\tau _{\xi }^{-}\right] \\
&&+E\left[ u(t-\tau _{\xi },X_{\tau _{\xi }}^{\xi }),\tau _{\xi }\leq t,\tau
_{\xi }^{-}<\tau _{\xi }^{+}\right] \\
&=&P(\tau _{\xi }^{+}\leq t).
\end{eqnarray*}
Finally, Statement c) is proven similarly. So the proof is complete. $\hfill
$
\end{proof}
\begin{examples}
\begin{itemize}
\item[a)] In Example \ref{ExamOSG1}, with $f\equiv 1$, we hav
\begin{equation*}
\bar{u}(t,\xi )=\left\{
\begin{array}{ll}
\Phi \left( \frac{|\xi |^{1-\alpha }}{(\alpha -1)\sqrt{t}}\right) , & \xi >0,
\\
0, & \xi \leq 0
\end{array
\right.
\end{equation*
and
\begin{equation*}
\text{\b{u}}(t,\xi )=\left\{
\begin{array}{ll}
0, & \xi >0, \\
\Phi \left( \frac{|\xi |^{1-\alpha }}{(\alpha -1)\sqrt{t}}\right) , & \xi
\leq 0
\end{array
\right.
\end{equation*
satisfy Statements b) and c) of Theorem \ref{thm:distet}, respectively. In
particular, if $\xi >0$, then $\bar{u}(\infty ,\xi )=1$, therefore we have a
positive blow-up. This phenomenon is explained by Milan \cite{Mi} (Theorem
1) due to the involved solution being a nonnegative process when $\xi >0$.
\item[b)] For $\beta >0$, the partial differential equatio
\begin{eqnarray*}
\frac{\partial u}{\partial t}(t,x) &=&\frac{a^{2}}{2}e^{2\beta x}\frac
\partial ^{2}u}{\partial x^{2}}(t,x)+\beta a^{2}e^{2\beta x}\frac{\partial
}{\partial x}(t,x), \\
u(0,x) &=&0,\ \ \forall x\in \mathbb{R},
\end{eqnarray*
has solution
\begin{equation*}
u(t,x)=\exp \left( -\frac{e^{-2\beta x}}{2(a\beta )^{2}t}\right) .
\end{equation*
Since $u(t,\infty )=1$ and $u(t,-\infty )=0$, then the distribution of
explosion time to the stochastic differential equatio
\begin{equation*}
X_{t}^{x}=x+\int_{0}^{t}\beta a^{2}e^{2\beta
X_{s}^{x}}ds+\int_{0}^{t}ae^{\beta X_{s}^{x}}dW_{s},
\end{equation*
is given by
\begin{equation*}
P(\tau _{\xi }\leq t)=\exp \left( -\frac{e^{-2\beta x}}{2(a\beta )^{2}t
\right)
\end{equation*
because of $P(\tau _{\xi }^{+}<\infty )=1$.
\end{itemize}
\end{examples}
\bigskip
\noindent\textbf{Remark}\textit{\ It is not difficult to see that Examples
\ref{ExamOSG1} and \ref{ExamOSG2} are solution of the corresponding partial
differential equations (PDEs), then we conjecture that the distribution of
the explosion time is the solution of such a PDE. If this is true, then we
have the following criterion of explosion: There is explosion in finite time
if and only if the corresponding PDE has a bounded solution. Moreover, this
criterion could be applied in more dimensions and for non autonomous
processes (see \cite{F}).}
\subsection{Laplace transform of the distribution of the explosion time}
\label{sec:5.2} Finally, in this subsection we indicate how we could calculate
the Laplace transformation of the distribution of the explosion time
\tau_{\xi}$ of the solution to equation (\ref{eq:nagre}). It means, we
assume that the equation
\begin{equation} \label{eq:lamisma}
X^{\xi}_t=\xi+\int_0^t{\ b}(s,X^{\xi}_s)ds+I_t,\quad t\ge 0,
\end{equation}
has a unique solution that may blow-up in finite time, where $b$ takes
values in ${\mathbb{R}}_+$ and $I_t=\int_0^tf(s)dW_s$. Note that if
\omega\in\Omega$ is such that $\tau_{\xi}(\omega)<\infty$, then
X^{\xi}_t>\xi+\inf_{0\le s\le \tau_{\xi}(\omega)}I_t(\omega),\ t\le
\tau_{\xi}(\omega)$, and consequently $\int_0^{\tau_{\xi}(\omega)}{\ b
(s,X^{\xi}_s)ds=\infty$. Thus, $X^{\xi}_{\tau_{\xi}-}=\infty$, on
[\tau_{\xi}<\infty]$, and $\tau_{\xi}=\tau_{\xi}^+$.
We begin with an auxiliary result.
\begin{lemma}
\label{lem:tl} let $\lambda >0$ and $\tau _{\xi }$ the explosion time of the
solution of equation (\ref{eq:lamisma}). Then
\begin{equation*}
E\left( e^{-\lambda \tau _{\xi }}\right) =\lambda \int_{0}^{\infty }P(\tau
_{\xi }\leq u)e^{-\lambda u}du.
\end{equation*}
\end{lemma}
\begin{proof}
Let us denote the distribution of $\tau _{\xi }$ by $F_{\tau _{\xi }}$.
Fubini theorem leads to justify
\begin{eqnarray*}
E\left( e^{-\lambda \tau _{\xi }}\right) &=&\int_{(0,\infty )}e^{-\lambda
s}F_{\tau _{\xi }}(ds)=\lambda \int_{(0,\infty )}\left( \int_{s}^{\infty
}e^{-\lambda u}du\right) F_{\tau _{\xi }}(ds) \\
&=&\lambda \int_{0}^{\infty }\left( \int_{(0,u]}F_{\tau _{\xi }}(ds)\right)
e^{-\lambda u}du=\lambda \int_{0}^{\infty }F_{\tau _{\xi }}(u)e^{-\lambda
u}du.
\end{eqnarray*
Consequently, the proof is complete.$\hfill $
\end{proof}
Now we can state the main result of this subsection.
\begin{theorem}
\label{thm:22} Consider $\lambda>0$, the explosion time $\tau_{\xi}$ of the
solution of (\ref{eq:lamisma}) and a bounded function $u:[0,\infty )\times
\mathbb{R}\rightarrow \mathbb{R}$ that is a solution of the partial
differential equation
\begin{eqnarray*} \label{eq:tlas}
-\frac{\partial u}{\partial t}(t,x) &=&\frac{1}{2}f^{2}(t)\frac{\partial
^{2}u}{\partial x^{2}}(t,x)+b(t,x)\frac{\partial u}{\partial x}(t,x)-\lambda
u(t,x), \ t>0\ \hbox{\rm and}\ x\in{\mathbb{R}}, \\
u(t,\infty)&=&1.
\end{eqnarray*
Then, $\lambda\int_0^{\infty} P(\tau_{\xi}\le u)e^{-\lambda u}du =u(0,\xi).$
\end{theorem}
\begin{proof}
As in the proof of Theorem \ref{thm:distet} It\^{o}'s formula gives
\begin{equation*}
u(0,\xi )=E\left( u(t\wedge \tau _{\xi }^{m},X_{t\wedge \tau _{\xi
}^{m}}^{\xi })\exp (-\lambda (t\wedge \tau _{\xi }^{m}))\right) .
\end{equation*
We can now easily complete the proof of this result by combining Lemma \re
{lem:tl}, the arguments used in the last part of the proof of Theorem \re
{thm:distet} and the fact that $X_{\tau _{\xi }^{m}}^{\xi }\rightarrow
\infty $ as $m\rightarrow \infty $ on $[\tau _{\xi }<\infty ]$. Indeed we
first take $m\uparrow \infty $, and then $t\uparrow \infty $. $\hfill $
\end{proof}
\bigskip
\noindent \textbf{Remark}\textit{\ In some cases we have the converse of
Theorem \ref{thm:22}. For example, consider the stochastic differential
equation
\begin{equation*}
X_{t}^{\xi }=\xi +\int_{0}^{t}(g(X_{s}^{\xi })+a-b)ds+cW_{t},\ \ t\geq 0,
\end{equation*
where $a,b,c\in \mathbb{R}$, $a>b$ and $g:{\mathbb{R}} \rightarrow \lbrack 0,\infty )$. Then the associated ordinary
differential equation is
\begin{eqnarray}
\frac{c^{2}}{2}w^{\prime \prime }(x)+(g(x)+a-b)w^{\prime }(x)-\lambda w(x)
&=&0,\ \ t>0, \label{exexpfeller} \\
w(\infty ) &=&1. \notag
\end{eqnarray}
Therefore, if $X^{\xi }$ explodes in finite then (\ref{exexpfeller}) has a bounded solution, in fact it is the Laplace transform
of the explosion time (see \cite{Wfe}). Then the solution of
\begin{eqnarray*}
-\frac{\partial u}{\partial t}(t,x) &=&\frac{c^{2}}{2}\frac{\partial ^{2}u}
\partial x^{2}}(t,x)+(g(x-bt)+a)\frac{\partial u}{\partial x}(t,x)-\lambda
u(t,x),\ \ t>0, \ x\in {\mathbb{R}}, \\
u(t,\infty ) &=&1.
\end{eqnarray*
is given by $u(t,x)=w(x-bt)$.}
\bigskip
\noindent \textbf{Acknowledgements:} Professor Villa-Morales was partially
supported by grant 118294 of CONACyT and grant PIM13-3N of UAA. The authors
Thanks Universidad Aut\'{o}noma de Aguascalientes y Cinvestav-IPN for their
hospitality and economical support. Other authors were also partially
supported by a CONACyT grant.
| {
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} | 2,344 |
Достопочтенный Дермот Ричард Клод Чичестер, 7-й маркиз Донегол (; 18 апреля 1916 — 19 апреля 2007) — британский аристократ, военный, землевладелец и член Палаты лордов. Он был известен как Достопочтенный Дермот Чичестер с 1924 по 1953 год и как барон Темплмор с 1953 по 1975 год. Лорд Донегол обычно был известен своей семье и друзьям как Дерми Донегол.
Биография
Родился 18 апреля 1916 года. Второй сын Артура Клода Спенсера Чичестера, 4-го барона Темплмора (1880—1953), и Достопочтенной Клэр Мэриел Уингфилд (1886—1969), дочери Мервина Уингфилда, 7-го виконта Пауэрскорта, и леди Джулии Кокс. Братья — майор достопочтенный Артур Патрик Спенсер Чичестер (1914—1942) и майор лорд Десмонд Клайв Чичестер (1920—2000).
2 октября 1953 года после смерти своего отца Дермот Чичестер унаследовал титул 5-го барона Темплмора. Он получил образование в школе Хэрроу и Королевском военном колледже в Сандхерсте.
Во время Второй мировой войны он служил капитаном в 7-м королевском гусарском полку в Египте. Он числился пропавшим без вести в бою и считался убитым, но был захвачен в плен в Ливии в ноябре 1942 года во время Североафриканской кампании. Он оставался военнопленным в Италии до побега в июне 1944 года. В том же году он получил звание майора и уволился из британской армии в 1949 году, но несколько лет служил в Лестерширском йоменском полку.
Его старший брат Артур Чичестер, убитый в 1942 году на службе в гвардии Колдстрима, Чичестер сменил своего отца на посту 5-го барона Темплмора в 1953 году. 24 мая 1975 года он также сменил своего дальнего кузена, Эдварда Чичестера, 6-го маркиза Донегола (1903—1975), став 7-м маркизом Донеголом, будучи потомком 1-го барона Темплмора, внука Артура Чичестера, 1-го маркиза Донегола. Он также унаследовал другие титулы и был лордом верховным адмиралом Лох-Ней.
Лорд Донегол стал членом Почетного Корпуса вооруженных джентльменов в 1966 году и был его знаменосцем с 1984 по 1986 год. Ему был пожалован Королевский Викторианский орден в 1986 году, он в течение многих лет был активным членом Консервативного клуба понедельника. В 1981 году он стал великим мастером Великой ложи Ирландии, этот пост он занимал до 1992 года. Лорд Донегол также служил мастером собак Уэксфорда. Он разводил лошадей, в том числе Прокламацию, победителя чемпионата Панчестауна по бегу с препятствиями в 1989 году, и Данброди Миллара, обладателя трофея Топхэма в Эйнтри в 2007 году.
Семья
16 сентября 1946 года Дермот Чичестер женился на леди Джоселин Габриэль Легг (22 мая 1918 — 19 июня 1995), дочери подполковника Уильяма Легга, 7-го графа Дармута (1881—1958), и леди Руперты Уинн-Карингтон (1883—1963). У супругов были один сын и две дочери:
Леди Дженнифер Эвелин Чичестер (3 апреля 1949 — 12 марта 2013), муж с 1971 года Джон Роберт Генри Фаулер (1946—2008), сын бригадного генерала Брайана Джона Фаулера. Двое сыновей
Артур Патрик Чичестер, 8-й маркиз Донегол (род. 9 мая 1952), преемник отца. С 1975 по 2007 год он носил титул учтивости — граф Белфаст.
Леди Джульетта Клэр Чичестер (род. 2 ноября 1954), муж с 1983 года Эндрю Дэвид Фрейзер, от брака с которым у неё двое детей.
Маркиз жил в семейном доме Данброди-Парк в Артурстауне на юго-западе графства Уэксфорд.
Примечания
Источники
Copping, Robert, The Monday Club — Crisis and After May 1975, page 25, published by the Current Affairs Information Service, Ilford, Essex, (P/B).
Obituary, The Daily Telegraph, 20 July 2007
Ссылки
Hansard 1803—2005: contributions in Parliament by the Marquess of Donegall
7
Члены палаты лордов Великобритании
Бароны Темплмор
Лейтенанты Королевского Викторианского ордена
Участники Второй мировой войны | {
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Being Human Season 3 Begins TONIGHT!
by Andrew Young | Jan 14, 2013 | Television
2 years ago, I got the opportunity to talk with the cast of the North American version of Being Human in a little night club/lounge in Toronto's club district. It was the day of their debut episode. At the time, I was taking the interview because it seemed like the right thing to do. I didn't know much about Being Human. I had seen the first season of the British series. That's it. I also didn't know much about the cast either. I knew Sam Huntington was Jimmy Olsen in Superman Returns and I had seen him in Fanboys. As for Meaghan Rath and Sam Witwer, they were pretty much foreign to me. I hadn't seen either of their work. It's funny because that interview ended up being one of the best experiences I've had since the beginning of Geek Hard. Since then, I've gotten to interview these cats many times over and hope to again in the near future. I'm also a huge fan of the show.
Last year's season of Being Human had an Empire Strikes Back like ending. The good guys didn't win the day….and in some cases, the good guys kind of became the bad guys for a bit. Aiden, who just lost the love of his life, was placed in a coffin and buried six feet under. Sally, after sending a large number of souls wrongly to the horrors of limbo, shreaded herself so that she could enter the realm herself and makes things right. And Josh and Nora were in a werewolf mexican standoff with Ray, the wolf that sired Josh. Like I said, not the greatest place to be for any of these characters. It might be a bit premature to say this but after all that these characters have been through, there's really no place for any of them to go but up. This season might see these folks finally getting a bit back to normal (for them at least) and enjoying eachother's company in their cozy little home.
There's lots to be excited about as we begin the 3rd Season. First of all, this is the first year where Kristen Hager is now an official member of the main cast as Nora. While I wasn't the hugest fan of what they did with her character in Season 2, I think it's great that she's risen above series regular and I look forward to her assimilating more in with the group. Another thing that I'm personally happy about is that there has been a promise from the cast that the undercutting humour that was a big part of Season 1 will be returning to the show. Everybody agrees that while the 2nd season was amazing, the chances for these great characters to just have fun with eachother was the special ingredient that was missing from many of the episodes. This was because Aiden, Josh and Sally had such complex individual plotlines going on, there was practically no room for any of them to really overlap into eachother's with the exception of a few key episodes (which also happened to be the best episodes of last year). It will be nice to see them teaming up again on their adventures. Finally, I think it's pretty safe to say that this show has now completely broken away from the British source material as they are exploring completely different storylines and themes. Where Season 1 played pretty close to the guideline set up by the UK series, Season 2 found a very unique voice which I believe will be fully explored in this season.
It all comes down to tonight. As with most artistic things, the audience usually remembers most how things end and how they begin. We usually gage our enjoyment of a product based on our like or dislike of these points. So although I have high hopes for It's A Shame About Ray, I also have a bit of trepidation. Last year's season finale was epic and is going to be pretty hard to top. I hope they can deliver the same level of gut-busting entertainment they have previously. Tune in and judge for yourself. You can catch it at 9pm tonight on Syfy in the States and SPACE here in Canada.
Wait a second. I thought Josh was suppose to be the wolf? Being Human Season 3 Begins tonight at 9pm on SPACE and Syfy.
Geek Hard Presents: One on One with Kristen Hager
Geek Hard @ Wizard World 2012: An Interview with the Cast of Being Human
Feeling Shred-Up, Under the Gun and Buried in the Details!: Looking Back on Season 2 of Being Human | {
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{"url":"https:\/\/www.studypug.com\/math-5\/representing-numbers-cardinals","text":"# Representing numbers: Cardinals\n\n#### Everything You Need in One Place\n\nHomework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.\n\n#### Learn and Practice With Ease\n\nOur proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.\n\n#### Instant and Unlimited Help\n\nOur personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!\n\n0\/2\n##### Intros\n###### Lessons\n1. Introduction to Cardinal Numbers:\n2. What are cardinal numbers and how do we count?\n3. What is the difference between cardinal, ordinal, and nominal numbers?\n0\/19\n##### Examples\n###### Lessons\n1. Distinguishing Cardinal Numbers\nCircle the cardinal numbers in the list.\n1. 14, two hundred fifty-nine, 38.6, 7$\\frac{2}{10}$\n2. Simplify the fractions first: $\\frac{2}{5} , \\frac{10}{2}, \\frac{3}{3}, \\frac{4}{6}, \\frac{56}{8}$\n3. Sixtieth, 794, eighty-three, 22nd, 15.$\\overline{8}$\n2. Counting the Number of Letters within a Word\nCount the letters in the word as specified.\n\nOne of the longest words found in an English dictionary is:\n\npneumonoultramicroscopicsilicovolcanoconiosis\n\n1. How many letters are there in this word?\n2. How many times does the letter \"o\" appear?\n3. How many times does the letter \"c\" appear?\n3. Listing Out Generally Known Facts and Counting\nList out what you know and then count:\n1. How many letters are there in the alphabet?\n2. How many days are there in a week?\n3. How many months are there in a year?\n4. How many vowels are there? (Not including Y)\n4. Counting Picture Objects\nPenny's class went on a field trip to the zoo. She drew all the animals that she saw. Use the picture to count:\n\n1. How many pandas did Penny see?\n2. How many frogs did Penny see?\n3. How many tigers did Penny see?\n4. How many animals did she see in total?\n\n5. Counting Using a Written List - 1\nVictoria is throwing a birthday party. She invites her friends: Olivia, Megan, Kyle, Tracy, Sophie, Michael, and Ethan.\n\nIncluding herself, how many people will be at Victoria's birthday party?\n1. Counting Using a Written List - 2\nIn a puzzle kit, there are 8 triangles, 5 squares, 10 circles.\n\n1. How many shapes are there in total?\n2. How many triangles AND squares are there?\n3. How many triangles and circles are there?\n4. If you can combine two triangles to become a square, how many squares can there be in total?\n0%\n##### Practice\n###### Free to Join!\nStudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.\n\u2022 #### Easily See Your Progress\n\nWe track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.\n\u2022 #### Make Use of Our Learning Aids\n\n###### Practice Accuracy\n\nSee how well your practice sessions are going over time.\n\nStay on track with our daily recommendations.\n\n\u2022 #### Earn Achievements as You Learn\n\nMake the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.\n\u2022 #### Create and Customize Your Avatar\n\nPlay with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.\n###### Topic Notes\n\nIn this lesson, we will learn:\n\n\u2022 Cardinal numbers are counting numbers (whole numbers)\n\u2022 How to count objects in a picture, letters in a word, and words in a list\n\nNotes:\n\n\u2022 Cardinal means Counting\n\u2022 Cardinal numbers answer the question \u201chow many\u201d?\n\u2022 Cardinal numbers are whole numbers only (no fractions nor decimals)\n\u2022 Ex. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, \u2026\n\n\u2022 There are 3 types of numbers: Cardinal, Ordinal, and Nominal\n\u2022 Cardinal means Counting (ex. there are 6 pool balls)\n\u2022 Ordinal means Order (ex. the purple pool ball is in 4th place)\n\u2022 Nominal means Name (ex. the green pool ball is labelled \u201c14\u201d)","date":"2022-10-07 13:22:57","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 3, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2071012705564499, \"perplexity\": 4505.843101018874}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-40\/segments\/1664030338073.68\/warc\/CC-MAIN-20221007112411-20221007142411-00768.warc.gz\"}"} | null | null |
{"url":"https:\/\/electronics.stackexchange.com\/tags\/math\/hot","text":"# Tag Info\n\n## Hot answers tagged math\n\n69\n\nOther answers haven't yet hit upon what makes e special: defining the time constant as the time required for something to drop by a factor of e means that at any moment of time, the rate of change will be such that--if that rate were continued--the time required to decay to nothing would be one time constant. For example, if one has a 1uF cap and a 1M ...\n\n49\n\nIt's built into the mathematics of exponential decay associated with first-order systems. If the response starts at unity at t=0, then after one \"unit of time\", the response is $e^{-1} = 0.36788$. When you're looking at a risetime, you subtract this from unity, giving 0.63212 or 63.2%. The \"unit of time\" is referred to as the \"time constant\" of the system,...\n\n36\n\nA divider maps much less elegantly to typical hardware. Take Lattice ICE40 FPGAs as examples. Let us compare two cases: this 8x8 bit to 16 bit multiplier: module multiply (clk, a, b, result); input clk; input [7:0]a; input [7:0]b; output [15:0]result; always @(posedge clk) result = a * b; endmodule \/\/ multiply and this divider that ...\n\n32\n\nComplex numbers are similar to vectors, but have some extra mathematical properties that make them useful. Most notably, using the complex exponential $e^{j\\omega t}$ instead of sines and cosines makes differential equations much easier to deal with. That's how you get to complex impedance in the first place: $$v(t) = A\\mathrm e^{\\mathrm{j} \\omega t + \\... 30 Typically high resolution sin(x) functions would be implemented with a CORDIC (COrdiate Rotation DIgital Computer) algorithm, which can be accomplished with a small number of iterations using only shifts and add\/subtract and a small lookup table. The original paper The CORDIC Computing Technique by Jack Volder is from 1959. It also works nicely when ... 19 These calculations are absolutely used by professional EEs, for some on a daily basis. However, for many this job has been given to simulation software, such as LTSpice, which is also used on a daily basis. Generally the simulation is much faster to complete, so it is much more productive than doing the calculations by hand. I generally use the formulas ... 18 Only a sketch of a solution. Take all 3 axes into consideration. Acceleration due to gravity, regardless of tilt, will always be 1G, as a vector sum of X,Y,Z, no matter what the tilt. You can picture the acceleration at rest or steady motion as a point on a sphere with radius 1G. (If you are perfectly horizontal, that point will be (0, 0, -1) i.e. directly ... 16 Ohm's law$$ 1: V(t) = I(t)R $$Instantaneous power dissipation is product of voltage and current$$ 2: P(t) = V(t)I(t)\\\\ $$Substitute 1 into 2 to get instantaneous power through a resistor in terms of voltage or current:$$ 3: P(t) = I^2(t)R = \\frac{V^2(t)}{R}\\\\ $$Average power is definitionally the integral of instantaneous power over a period, ... 16 The error is in the assumption the I2 = I1. The OpAmp can (in general) sink and source current. When it would be sourcing current, this current would have to go to ground, either through R2 or through R1 (less likely). The current through R2 returns to Vx as well as to the negative power terminal of the source that sources the OpAmp. Note you cannot omit ... 14 Most computer trig libraries are based on polynomial approximations, which gives the best balance between speed an accuracy. For example, a dozen or so multiplication and add\/subtract operations is enough to give full single-precision accuracy for sine and cosine. 13 In order to how much cap to use where, you need to know a fair bit about capacitors in general: The different types (electrolytic, film, ceramic, tantalum, OS-CON, metalized film, etc.) Their characteristics (impedance, ESR, ESL, polarity, temperature rise, dielectric, etc.) Their failure modes (aging, over voltage, reverse voltage, thermal runaway, etc.) ... 13 Assume the system is already precharged and operating in a steady state. The bridge has two discrete states: either the capacitor is charging (a diode pair is forward biased), or the capacitor is discharging. Call the period P, the charge time DP, and the discharge time (1-D)P. During the charge cycle, we can approximate the current entering the capacitor ... 13 I assume for \"high speed\" you mean a small delay from data collection to the resultant FFT. With a low sample rate, your computational ability isn't the limiting factor, given modern computers. The delay problem lies in having enough data for analysis. If you want your 1Hz bin to be different from DC\/0Hz, you have to accumulate enough signal data to capture ... 13 You refer to these basic formulae at first and then find the real world has a lot of non-linear characteristics like XOR phase detectors in a second PLL loop response when you exceed the phase limit or that all Low Pass filters cause Inter-Symbol-Interference (ISI) unless the filter resonates within the binary symbol then you apply \"Raised Cosine\" Filters ... 13 Why are complex numbers used and not Vectors? simply because there is no vector division defined in vector algebra, so simply you cannot use Ohm's law in division form, thereby making calculations more complicated. On the other hand the domain of complex number athematic has more progressed over time than vector counterpart, so you have many theorems at ... 12 I haven't done this for double precision FP, but the same principles apply as for single precision, for which I have implemented division (as multiply by reciprocal). What these FPGAs do have, instead of FPUs, is hardwired DSP\/multiplier blocks, capable of implementing a 18*18 or (Virtex-5) 18*25 multiplication in a single cycle. And the larger devices ... 12 This is not a compiler issue: doing the division first here is legal behaviour. (Also, when in doubt: use parentheses. There's no penalty.) You are working with integers, so reading \/ 0xFFFF will always return 0 if reading is a uint16_t unless reading == 0xFFFF. If you want to use integers, force the multiplications to be done first by using something like (... 11 The Laplace variable $s$ relates to Fourier's $j\\omega$ as follows:$$ s = \\sigma + j\\omega $$Fourier transform can be seen as a Laplace transform when $\\sigma=0$. The $\\sigma$ allows the Laplace integral transformation to converge for signals that Fourier transform does not, e.g. a unitary step (Heaviside function). If you are working with real ... 11 If you can only take measurement at discrete times, then summing up and dividing by the time between measurements is the only way possible \u2013 the integral$$E_\\text{total}=\\int\\limits_{T_\\text{start}}^{T_\\text{end}} P(t) dt$$really collapses to a sum, it $P(t)$ is only known for set of points. For example, assume the power value is constant for amount ... 11 One usually needs to acquire multiple samples per waveform period to get good results from an FFT. The Nyquist limit of 2 samples per period is a lower bound but usually 10 samples per period or more is what is practically used. So to analyze a 64Hz signal you probably want to acquire samples at a rate of 640Hz or more. Also (up to a point) you will get ... 11 The decay of an RC parallel circuit with capacitor charged to Vo v(t) = $Vo(1-e^{-t\/\\tau})$ , where $\\tau$ is the time constant R$\\cdot$C. So v($\\tau$)\/Vo is approximately 0.63212055882855767840447622983854 In other words, the time constant is defined by the RC product (or L\/R ratio), and the seemingly arbitrary voltage is a result of that ... 11 The standard C library is providing the optimized solutions for many problems with considerations based on the architecture, compiler in use and others. The abs() function defined in stdlib.h is one of these, and it is used for your purpose exactly. To emphasize the point, here is ARM compiler result when using abs vs a version of a homebrew abs: https:\/\/arm.... 11 Just to remark on that you can represent impedance as a matrix:$$ R + \\mathrm j X \\leftrightarrow \\begin{bmatrix} R & X \\\\ -X & R \\end{bmatrix} $$This is in fact the matrix representation of complex numbers. On the other hand you can represent sinusoidal signals (but not impedance) using vectors:$$ x_{\\cos} + \\mathrm j x_{\\sin} \\...\n\n10\n\nWe can have multiple layers of logic per clock cycle but there is a limit, exactly how many layers of logic we can have an how complex those layers can be will depend on our clock speed and our semiconductor process. However, there are many different multiplication algorithms, and I don't have a clue which one may be used by microcontrollers Afaict most ...\n\n10\n\nThis is a fundamental C issue: you need to be extremely clear whether you're doing integer or floating-point arithmetic. uint16_t temperature = reading*0.076295; That promotes \"reading\" to \"float\", because 0.076295 is a float literal, then does the multiplication. uint16_t temperature = reading\/0xFFFF*2.5*1000*2; The first two elements ...\n\n9\n\nECL is both the fastest logic family and has the simplest internal structure of modern logic families, but like other bipolar-only families it has a not insignificant power draw. It is also incompatible with other logic families due to its signal voltages. If you're looking for a logic family for general use, my recommendation would be the 74LVC CMOS family....\n\n9\n\nBoth sin and cos are considered sinusoidal waveforms. As a practical matter, sin and cos are essentially the same thing, just offset by 90 degrees.Since \"time 0\" is arbitrary, the distinction between sin and cos only matters if you are comparing phase against another signal. Since Euler's equation works out to cos for the real component and sin for the ...\n\n9\n\nSlow division is inherently iterative so it tends to take longer. There are somewhat faster slow division algorithms than the simple ones, using lookup tables. The SRT algorithm produces two bits per cycle. An error in such a table was the cause of the infamous Pentium FDIV bug (ca. 1994). Then there are so-called fast division algorithms. Of course, in ...\n\n9\n\nYour main mistake is in not treating acceleration as a single vector. When the car is at rest, that vector will always be 1 g upwards. Don't look at just the X component of the raw accelerometer data. Do the real vector math. But my problem is that when the device is on tilt (0g when no tilt) the acceleration is between (downward) 0g->-1g or between (...\n\n9\n\nAren't you both wrong? To me this sounds like arguing that if someone thinks in English then their neurons are wired in English, which is nonsensical. If you actually want to force application of the terms then I think it is just a matter of perspective. For example, an assembly instruction (or machine code) might tell a CPU to add. 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\section{Introduction}
Person retrieval, also known as person re-identification (Re-ID), is to match images of the same individual captured by non-overlapping camera views. There are many challenges in person Re-ID, including cluttered background, appearance variations (e.g., illumination, pose, occlusion, resolution) among different camera views and interference of similar images with different identities. Fig.~\ref{fig5} shows images from different camera views on DukeMTMC-reID~\cite{ristani2016performance}. As seen, the images in the same camera view have similar background, while the background differs in different camera views. In addition, appearance variations, such as illumination and resolution, also lead to noise in the extracted person feature representation. Moreover, since person Re-ID can be seen as an image retrieval task, there is an interference problem of similar negative samples in the retrieval precess.
\begin{figure
\centering
\includegraphics[width=9cm,height=4cm]{fig/fig5} %
\caption{Images from different cameras on DukeMTMC-reID.}
\label{fig5}
\vspace*{-20pt
\end{figure}
\begin{figure*
\centering
\includegraphics[width=15cm,height=3.5cm]{fig/fig3} %
\caption{The pipeline of the proposed method for person retrieval. The image segmentation network is firstly employed to obtain the segmentation results of a person image. Then a mask based deep ranking neural network with a skipped feature fusion layer is proposed to extract robust person features. Finally, a novel ranking loss is designed to train the overall deep neural network.}
\label{fig3}
\vspace*{-15pt
\end{figure*}
Many efforts have been made to address the challenges in person retrieval~\cite{DBLP:conf/eccv/VariorSLXW16}\cite{DBLP:conf/cvpr/XiaoLOW16}\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17}\cite{DBLP:conf/cvpr/ChengGZWZ16}\cite{DBLP:conf/cvpr/ZhouWWGZ17}\cite{DBLP:conf/cvpr/ChenCZH17}. However, most existing methods neglect the problem of background clutter which leads to degraded performance. Besides, these methods adopt the general neural network structure for Re-ID~\cite{DBLP:conf/eccv/VariorSLXW16}\cite{DBLP:conf/cvpr/XiaoLOW16}\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17}. However, there are usually large intra-personal appearance variations in person images. It is thus important to design more specific network structures to capture the fine-grained information from person images. Moreover, as person Re-ID is also an image retrieval problem, most existing Re-ID frameworks are optimized by contrastive loss or triplet loss~\cite{DBLP:conf/cvpr/ChengGZWZ16}\cite{DBLP:conf/eccv/VariorHW16}, which employ only one negative sample and one positive sample for an anchor at each iteration. As the ranking process in fact involves a set of samples, using the above loss functions may lead to poor results, which may be interfered by similar negative images.
To address the above mentioned problems, we develop a mask based deep ranking neural network with skipped fusing layer (MaskReID), as shown in Fig.~\ref{fig3}. First, to reduce the impact of cluttered background, an image segmentation network is employed to obtain the segmentation results of a person image. The masked image with removed background is adopted as an additional input for feature extraction. Second, considering that person Re-ID is a special fine-grained image recognition task and the different layers of deep neural networks can extract low-, middle- and high-level features, we employ a skipped feature fusion layer scheme to fuse the multi-layer features in the deep neural network. This strategy can extract invariant person representation from different camera views, as it combines all low-level edge and shape information, middle-level structure information and high-level semantic information together. Besides, it can also better propagate the loss to lower layers of neural network for training, making the learning of low-level and middle-level features more accurate. Last, as person Re-ID is a ranking task, i.e., one person has multiple images from different camera views, a ranking loss function is developed to reduce the impact of similar negative samples when producing ranking results. Particularly, an anchor sample interacts with multiple positive and negative samples via exploiting the proposed ranking loss in each iteration. Together, the above three improvements give rise to a novel deep learning framework for person retrieval.
In summary, the major contributions in this work include:
i) A novel deep learning framework is proposed, which accepts both the original and masked images as input. Besides, we develop a skipped feature fusion layer to extract robust features;
ii) For the person retrieval task, a novel ranking loss function is proposed to further mitigate the interference issue of similar negative samples;
iii) Extensive experiments on multiple benchmark datasets demonstrate the superiority of the proposed method when compared with the state-of-the-art methods. Moreover, through ablation studies, the efficacy of the proposed masked input, the skipped feature fusion scheme and the ranking loss is also verified.
\section{MASK BASED DEEP RANKING NEURAL NETWORK}
The framework of the proposed mask based deep ranking neural network is shown in Fig.~\ref{fig3}. An image segmentation deep network is employed to capture person (foreground) region and remove the background. Besides, there is a feature fusion layer which merges the multi-level information of the proposed network to extract robust person representation. Lastly, a ranking loss is developed to optimize the proposed network, which aims to rank person images with the same identity at top positions in a training batch.
\subsection{A New Mask Based Deep Neural Network Structure}~\label{sec:framework}
\textbf{Masked Input.}
Person images, captured under complex scenes (e.g., airport or station), have very messy background. Besides, the images of different identities in the same camera view have similar background, while the background of the same identity differs in different camera views. These factors result in a challenge that the neural network cannot fully focus on foreground regions. The ideal feature extraction module should try to distinguish the silhouette of the person so as to focus more on the person region instead of the background. Thus it can improve the performance of person retrieval. Currently, image segmentation can effectively separate the foreground from the background. In this paper, Fully Convolutional Networks (FCN)~\cite{DBLP:conf/cvpr/LongSD15} is employed to obtain the masked images. Particularly, for low quality images such as low resolution, poor segmentation results could be generated by the segmentation network. To address this issue, we employ both the original and masked images as the input of the proposed network.
\textbf{Skipped Feature Fusion Layer Structure.} As for the network structure, the network of Xiao \emph{et al.}~\cite{DBLP:conf/cvpr/XiaoLOW16}, which has an inception structure, is adopted as the basic network. Especially, domain guided dropout, which is designed to activate the neurons from a special domain, is not utilized in the proposed framework. The proposed network structure is shown in Fig.~\ref{fig1}. The two images are processed with several separated layers. Then the two separated features are concatenated and fed into a shared network with three levels, which extract the low-, middle-, and high-level features, respectively. The features of these three levels are fused by a skipped fusing layer to produce the merged feature. The benefits of using different levels of features have been proved in style transfer tasks~\cite{DBLP:conf/cvpr/GatysEB16}. In our experiments, we also validate the effectiveness of the scheme. This is because person retrieval is a special fine-grained image recognition task, and the network should focus on fine-grained person information. Fusing the features of three levels can bring more detailed features into consideration and thus improve the Re-ID performance. Another appealing property of this network structure is that it can propagate the loss to lower layers in a more efficient way, as lower layers may experience vanishing gradient issues.
\subsection{Ranking Loss}\label{sec:rank_loss}
\begin{figure
\centering
\includegraphics[width=8cm]{fig/fig1}
\caption{Illustration of the proposed framework. First, original and masked images are utilized as input. Second, a multi-layer feature fusion scheme is developed in the proposed network. Last, the network outputs a 256-d (dimensional) feature.}
\label{fig1}
\vspace*{-15pt
\end{figure}
Currently, for person retrieval, most existing deep-learning-based methods use classification loss or verification loss (e.g., triplet loss and contrastive loss) to train networks. However, person retrieval is in fact a ranking task. Hence, an anchor sample (a query image) needs to interact with multiple positive and negative samples in the retrieval process. We expect that samples having the same identity with the anchor sample should be ranked at top positions. Inspired by the N-pair loss in \cite{DBLP:conf/nips/Sohn16}, a novel ranking loss is developed for person retrieval. Define a batch for training a deep network, as $\mathcal{B}=\{I_{1}, ..., I_{|\mathcal{B}|}\}$. For any $I_{k}, k=1, 2, ...,|\mathcal{B}|$, let $\mathcal{B}^{+}$ and $\mathcal{B}^{-}$ denote positive and negative image sets in $\mathcal{B}$, respectively. $\{x_{1}, ..., x_{|\mathcal{B}|}\}=\{f(I_{1}), ..., f(I_{|\mathcal{B}|})\}$, $f(x_{k})$ is the feature vector normalized by $L2$-norm. The N-pair loss for an anchor $x_{k}$ is defined as
\begin{equation}\label{eq03}
\begin{aligned}
&\mathcal{L}_{\textrm{N-pair}}(x_{k})=\\
&\textrm{log}\Big(1+\sum_{j:x_{j}^{-}\in \mathcal{B}^{-}}\textrm{exp}\big(\mathcal{S}(x_{k},x_{j}^{-})-\mathcal{S}(x_{k},x_{k}^{+})\big)\Big),
\end{aligned}
\end{equation}
where $\mathcal{S}(x_{i},x_{j})=x_{i}^{T}x_{j}$ denotes the similarity between two images.
$x_{k}^{+}$ and $x_{j}^{-}$ are positive and negative samples with $x_{k}$, respectively. Different from existing contrastive loss and triplet loss, the N-pair loss interacts with multiple negative samples simultaneously, while it is only influenced by one positive sample at each iteration.
Considering the ranking process of person retrieval needs to consider not only multiple negative samples, but also multiple positive samples, we formulate a new ranking loss as
\begin{equation}\label{eq04}
\begin{aligned}
&\mathcal{L}_{\textrm{Rank}}(x_{k})=\\
&\textrm{log}\Big(1+\sum_{i:x_{i}\in \mathcal{B}^{+} }\sum_{j:x_{j}\in \mathcal{B}^{-}}\textrm{exp}\big(\mathcal{S}(x_{k},x_{j})-\mathcal{S}(x_{k},x_{i})\big)\Big).
\end{aligned}
\end{equation}
However, Eq.~(\ref{eq04}) needs to calculate $|\mathcal{B}^{+}|\times|\mathcal{B}^{-}|$ pairs of samples in a training batch. To reduce the computational cost, the most dissimilar positive sample of the query sample is chosen as a reference sample. Meanwhile, to prevent overfitting (\emph{i.e.}, too much attention is paid on predicted correct samples in the ranking), we only select some negative samples which have large similarity with the anchor. Moreover, considering that the similarity of the same identity should be large, we force the similarity between all positive samples and the anchor to be close to one (the largest possible similarity value, as features have been normalized by $L2$-norm). Thus, by rewriting Eq.~(\ref{eq04}), we get the final ranking loss for the proposed neural network as
\begin{equation}\label{eq06}
\begin{aligned}
&\mathcal{L}_{\textrm{Rank}}(x_{k})=\\
&\textrm{log}\Big(1+\sum_{j:x_{j}\in \mathcal{B}^{-}}[\textrm{exp}\big(\mathcal{S}(x_{k},x_{j})-\min_{i:x_{i}\in \mathcal{B}^{+}}\mathcal{S}(x_{k},x_{i})+\alpha\big)]_{1+}\Big) \\
&+\frac{\lambda}{2|\mathcal{B^{+}}|}\sum_{i:x_{i}\in \mathcal{B}^{+} }\big( \mathcal{S}(x_{k},x_{i})-1\big)^{2},
\end{aligned}
\end{equation}
where $[t]_{1+}$ denotes that if $t>1$, it is equal to $t$, otherwise, 0. $\alpha$ is the margin. In Eq.~(\ref{eq06}), the first term guarantees the negative samples and the most dissimilar positive samples have a margin. The objective of the second term is to make all positive samples similar with the query image. $\lambda$ is a parameter to balance the two terms.
Compared with the conventional verification loss, as shown in Fig.~\ref{fig4}, the advantage of the proposed ranking loss is that it simultaneously considers multiple positive and negative samples for an anchor at each iteration. Thus, it can make the same ID images from different views closer to query images, and different ID images become farther.
\begin{figure*
\centering
\subfigure[Triplet loss]{
\centering
\raisebox{15pt}{
\includegraphics[width=3cm]{fig/fig4-1}}
}
\subfigure[N-pair loss]{
\centering
\includegraphics[width=4.5cm]{fig/fig4-2}
}
\subfigure[The proposed ranking loss]{
\centering
\includegraphics[width=4.5cm]{fig/fig4-3}
}
\caption{Illustration of triplet loss, N-pair loss and the proposed ranking loss. For triplet loss, the anchor only interacts with one positive sample and one negative sample. Different from triplet loss, N-pair loss considers that an anchor interacts with one positive sample and multiple negative samples. Moreover, an anchor interacts with multiple positive and negative samples via the proposed ranking loss at each iteration.}
\label{fig4}
\vspace*{-15pt}
\end{figure*}
\section{Experiments}
\subsection{Datasets and Evaluation Protocol}\label{exp1}
In this paper, we utilize multiple datasets including small-scale and large-scale datasets to validate the effectiveness of the proposed method.
These small-scale datasets with few persons are collected by few cameras, such as VIPeR, 3DPeS, iLIDS, PRID, Shinpuhkan and CUHK01, as described in~\cite{DBLP:conf/cvpr/XiaoLOW16}.
In recent years, with the extensive application of deep learning in Re-ID, several large-scale datasets have been published. CUHK03 \cite{DBLP:conf/cvpr/LiZXW14} consists of five different camera views and more than $14,000$ images of $1,467$ person. Market1501~\cite{DBLP:conf/iccv/ZhengSTWWT15} contains $32,668$ images of $1,501$ persons. As defined by~\cite{DBLP:conf/iccv/ZhengSTWWT15}, the dataset is split into training$/$testing sets of $12,936/19,732$ images. DukeMTMC-reID~\cite{ristani2016performance} has $16,522$ training images with $1,404$ identities. $2,228$ queries and $17,661$ gallery images are used for evaluation.
Rank-1 accuracy of CMC and mAP are adopted for performance evaluation on Market1501 and DukeMTMC-reID~\cite{DBLP:conf/iccv/ZhengSTWWT15}. We only report Rank-1 accuracy on CUHK03 and all small-scale datasets. Following most of the related work~\cite{DBLP:conf/cvpr/LiC0H17}\cite{DBLP:conf/cvpr/BaiBT17}, all experiments on Market1501 are performed under single query and multiple query settings.
\subsection{Implementation Details}\label{exp2}
Our experiments are done by Caffe with 1080ti (11GB). All small-scale datasets and CUHK03 are combined together to train a model. The scheme to divide the datasets into the training and testing sets is the same with \cite{DBLP:conf/cvpr/XiaoLOW16}. Since many identities have only two images on these datasets, such as VIPeR, softmax loss is employed for training the proposed deep model. For Market1501 and DukeMTMC-reID, based on the pre-trained model on small-scale datasets, two networks are trained separately with the proposed ranking loss.
For the small-scale datasets, we set the learning rate and iteration to $0.1$ and $55,000$, respectively. In addition, we train the MaskReID with the proposed ranking loss by $20,000$ iterations on Market1501 and DukeMTMC-reID.
In the training stage, to construct the ranking task, we randomly select one person, then $P$ images with the same identity are chosen randomly. Afterwards, $N$ negative samples are sampled from $N$ person randomly (i.e., one person has only one image). Therefore, in each batch, we can have more negative samples than conventional sampling schemes, which is more reasonable for the retrieval task. In the experiments, we set $P/N$ to $10/54$. Especially, if the chosen person has only $k < 10$ images, $P/N$ is set to $k/(64-k)$.
\subsection{Comparison with Related Methods}\label{exp3}
\renewcommand{\cmidrulesep}{0mm}
\setlength{\aboverulesep}{0mm}
\setlength{\belowrulesep}{0mm}
\setlength{\abovetopsep}{0cm}
\setlength{\belowbottomsep}{0cm
\begin{table
\centering
\caption{Comparison with the state-of-the-art methods on some benchmark datasets. Note that $1^{st}/2^{nd}$ best in red/blue.}
\begin{adjustbox}{width=8.5cm}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\toprule
\textbf{Method} & \textbf{VIPeR} & \textbf{PRID} & \textbf{3DPeS} & \textbf{ iLIDS} & \textbf{CUHK01} & \textbf{CUHK03} \\
\midrule
MGCNN~\cite{DBLP:conf/eccv/VariorHW16} & 37.80 & -- & -- & -- & -- & 68.10 \\
SLSTM~\cite{DBLP:conf/eccv/VariorSLXW16} & 42.40 & -- & -- & -- & -- & 57.30 \\
DGD~\cite{DBLP:conf/cvpr/XiaoLOW16} & 38.60 & 64.00 & 56.00 & 64.60 & 66.60 & 75.30 \\
Spindle~\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17} & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{53.80} } & \textcolor[rgb]{0.000, 0.000, 1.000}{ \textbf{67.00} } & 62.10 & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{66.30}} & 79.90 & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{88.50}} \\
\midrule
TCP~\cite{DBLP:conf/cvpr/ChengGZWZ16} & 47.80 & -- & -- & -- & 53.70 & -- \\
P2S~\cite{DBLP:conf/cvpr/ZhouWWGZ17} & -- & -- & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{71.16} } & -- & 77.34 & -- \\
Quadruplet~\cite{DBLP:conf/cvpr/ChenCZH17} & 49.05 & -- & -- & -- & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{81.00}} & 75.53 \\
\midrule
MaskReID (Ours) & 45.57 & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{70.00} } & \textcolor[rgb]{0.000, 0.000, 1.000}{ \textbf{68.60} } & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{70.43} } & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{84.05} } & \textcolor[rgb]{1.000, 0.000, 0.000}{ \textbf{92.25} } \\
\bottomrule
\end{tabular}%
\end{adjustbox}
\label{tab1}%
\vspace*{-15pt}
\end{table}%
\textbf{Small-Scale Datasets.}
For the small-scale datasets, all datasets are combined to train a model. The settings are the same with \cite{DBLP:conf/cvpr/XiaoLOW16}. Since several persons only have two images, softmax loss is used for training our network (MaskReID). The proposed method is compared with different deep learning methods~\cite{DBLP:conf/eccv/VariorHW16}\cite{DBLP:conf/eccv/VariorSLXW16}\cite{DBLP:conf/cvpr/XiaoLOW16}\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17}, and different loss function based methods~\cite{DBLP:conf/cvpr/ChengGZWZ16}\cite{DBLP:conf/cvpr/ZhouWWGZ17}\cite{DBLP:conf/cvpr/ChenCZH17}.
Experimental results are reported in Table~\ref{tab1}.
As seen, some observations can be made as follows: i) Performance varies on different datasets. In particular, the Rank-1 is up to $92.25\%$ on the CUHK03. This may be because CUHK03 has more training images than other datasets. However, the relatively poor performance on VIPeR is partly because the images of VIPeR are of low resolution which makes the segmentation results poor; ii) The proposed method can achieve competitive results when compared with the state-of-the-art methods on several benchmark datasets. This confirms the effectiveness of our proposed MaskReID.
\begin{table
\centering
\caption{Comparison with the state-of-the-art methods on Market1501. Note that $1^{st}/2^{nd}$ best in red/blue.}
\begin{adjustbox}{width=8cm}
\begin{tabular}{|c|cc|cc|c|}
\toprule
& \multicolumn{2}{c|}{~~Single query~~} & \multicolumn{2}{c|}{~~Multiple query~~} \\
\midrule
Method & Rank-1 & mAP & Rank-1 & mAP \\
\midrule
DLPAR~\cite{DBLP:conf/iccv/ZhaoLZW17} & 81.00 & 63.40 & -- & -- \\
Spindle~\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17} & 76.90 & -- & -- & -- \\
MSCAN~\cite{DBLP:conf/cvpr/LiC0H17}& 80.31 & 57.53 & 86.79 & 66.70 \\
S2S~\cite{zhou2018large} & 65.32 & 39.83 & 80.49 & 52.69 \\
P2S~\cite{DBLP:conf/cvpr/ZhouWWGZ17} & 70.72 & 44.27 & 85.78 & 55.73 \\
SSM~\cite{DBLP:conf/cvpr/BaiBT17} & 82.21 & 68.80 & 88.18 & 76.18 \\
JLML~\cite{DBLP:conf/ijcai/LiZG17} & 83.90 & 64.40 & 89.70 & 74.50 \\
\midrule
MaskReID (Ours) & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{90.44}} & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{75.36}} & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{93.35}} & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{82.37}} \\
MaskReID{\tiny re-ranking} (Ours)& \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{92.46}} & \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{88.13}} & \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{94.77}} & \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{92.11}} \\
\bottomrule
\end{tabular}%
\end{adjustbox}
\label{tab2}%
\vspace*{-10pt}
\end{table}%
\begin{table
\centering
\caption{Comparison with the state-of-the-art methods on DukeMTMC-reID. Note that $1^{st}/2^{nd}$ best in red/blue.}
\begin{tabular}{|c|cc|c|}
\toprule
Method & ~~Rank-1~~ & ~~mAP~~ \\
\midrule
LSRO~\cite{DBLP:conf/iccv/ZhengZY17} & 67.68 & 47.13 \\
SVDNet~\cite{DBLP:conf/iccv/SunZDW17} & 76.70 & 56.80 \\
OIM~\cite{DBLP:conf/cvpr/XiaoLWLW17} & 68.10 & -- \\
ACRN~\cite{DBLP:conf/cvpr/SchumannS17} & 72.58 & 51.96 \\
\midrule
MaskReID (Ours) & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{78.86}} & \textcolor[rgb]{0.000, 0.000, 1.000}{\textbf{61.89}} \\
MaskReID{\tiny re-ranking} (Ours)& \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{84.07}} & \textcolor[rgb]{1.000, 0.000, 0.000}{\textbf{79.73}} \\
\bottomrule
\end{tabular}%
\label{tab3}%
\vspace*{-10pt}
\end{table}%
\textbf{Large-Scale Datasets.}
The proposed method is also validated on Market1501~\cite{DBLP:conf/iccv/ZhengSTWWT15} and DukeMTMC-reID~\cite{ristani2016performance}. In this experiment, the proposed method is compared with a set of the state-of-the-art methods, i.e., DLPAR~\cite{DBLP:conf/iccv/ZhaoLZW17}, Spindle~\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17}, MSCAN~\cite{DBLP:conf/cvpr/LiC0H17}, S2S~\cite{zhou2018large}, P2S~\cite{DBLP:conf/cvpr/ZhouWWGZ17}, SSM~\cite{DBLP:conf/cvpr/BaiBT17} and JLML~\cite{DBLP:conf/ijcai/LiZG17}.
Experimental results are given in Table~\ref{tab2} and~\ref{tab3}.
From the two tables, we can observe that: i) Comparison with several part-based methods, such as MSCAN~\cite{DBLP:conf/cvpr/LiC0H17} and JLML~\cite{DBLP:conf/ijcai/LiZG17}, the proposed method has a competitive performance. Although MaskReID is a global method which extracts features from the global image, it attends more on the foreground region and fuses features of different layers to obtain the low-level detailed information and high-level semantic information from person images. Moreover, the proposed method outperforms DLPAR~\cite{DBLP:conf/iccv/ZhaoLZW17} that used attention mechanism and Spindle~\cite{DBLP:conf/cvpr/ZhaoTSSYYWT17} that employed human pose information; ii) The proposed method consistently outperforms the state-of-the-art methods on large-scale datasets. Especially, on Market1501, Rank-1$/$mAP of the multiple query is up to $93.35/82.37\%$. As demonstrated, it can effectively learn a more discriminative feature representation for person retrieval;
iii) Employing the re-ranking algorithm~\cite{DBLP:conf/cvpr/ZhongZCL17} can further improve the performance of our proposed method. Re-ranking algorithm~\cite{DBLP:conf/cvpr/ZhongZCL17} is commonly used for Re-ID, which can further enhance the performance of person retrieval via exploring the relationship of each sample in the ranking list. As can be seen in both Table~\ref{tab2} and~\ref{tab3}, performance can be further improved. On Market1501, Rank-1$/$mAP of the single query is now up to $92.46/88.13\%$.
\begin{table
\centering
\caption{Performance of the proposed method when employing different network components on many benchmark datasets. Note that $1^{st}/2^{nd}$ best in red/blue.}
\begin{adjustbox}{width=8.5cm}
\begin{tabular}{|c|c|c|c|c|c|c|}
\toprule
\textbf{Method} & \textbf{VIPeR} & \textbf{PRID} & \textbf{3DPeS} & \textbf{ iLIDS} & \textbf{CUHK01} & \textbf{CUHK03} \\
\midrule
DGD & 38.60 & 64.00 & 56.00 & 64.60 & 66.60 & 75.30 \\
MaskReID-F & 39.24 & 64.00 & 64.88 & 66.09 & 77.16 & 87.47 \\
MaskReID-M & \textcolor[rgb]{ 0, 0, 1}{\textbf{44.62 }} & \textcolor[rgb]{ 0, 0, 1}{\textbf{65.00 }} & \textcolor[rgb]{ 0, 0, 1}{\textbf{66.12 }} & \textcolor[rgb]{ 0, 0, 1}{\textbf{69.57 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{84.26 }} & \textcolor[rgb]{ 0, 0, 1}{\textbf{88.75 }} \\
\midrule
MaskReID (Ours) & \textcolor[rgb]{ 1, 0, 0}{\textbf{45.57 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{70.00 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{68.60 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{70.43 }} & \textcolor[rgb]{ 0, 0, 1}{\textbf{84.05 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{92.25 }} \\
\bottomrule
\end{tabular}%
\end{adjustbox}
\label{tab5}%
\vspace*{-10pt}
\end{table}%
\subsection{Ablation Studies}
\textbf{Effectiveness of Different Network Components.}
In this section, we validate the effectiveness of different network components. Table~\ref{tab5} shows the experimental results on multiple datasets. DGD is the original network framework. MaskReID is built on DGD with both masked image as input and the multi-level feature fusion. Compared with MaskReID, MaskReID-F and MaskReID-M denote the removal of the input masked images and multi-level feature fusion structure, respectively. By comparing with the reports on multiple datasets in Table~\ref{tab5}, some observations can be made as follows: i) The fusion of multi-layer features is effective for the person Re-ID, i.e., MaskReID-F outperforms the original DGD. This demonstrates the effectiveness of the multi-layer feature fusion in the proposed framework; ii) Using masked images can improve the performance of person Re-ID, i.e., MaskReID-M outperforms the original DGD. Employing masked images can reduce the impact of background clutter, and only focus on the person region; iii) MaskReID, including masked input and stacking the multi-layer features, further improves the performance of the person Re-ID. In summary, the experimental results are consistent with the analysis in Section~\ref{sec:framework}.
\begin{table}[htbp]
\centering
\caption{Evaluation of different loss functions on Market1501.}
\begin{tabular}{|c|cc|cc|}
\toprule
& \multicolumn{2}{c|}{~~Single query~~} & \multicolumn{2}{c|}{~~Multiple query~~} \\
\midrule
~~Loss function~~ & Rank-1 & mAP & Rank-1 & mAP \\
\midrule
Softmax loss & 88.18 & 70.57 & 91.48 & 78.06 \\
Triplet loss & 88.54 & 71.17 & 92.13 & 78.66 \\
N-pair loss & 89.52 & 73.09 & 91.66 & 79.17 \\
\midrule
Ranking loss (Ours) & \textcolor[rgb]{1, 0, 0}{\textbf{90.44}} & \textcolor[rgb]{ 1, 0, 0}{\textbf{75.36}} & \textcolor[rgb]{ 1, 0, 0}{\textbf{93.35}} & \textcolor[rgb]{ 1, 0, 0}{\textbf{82.37}} \\
\bottomrule
\end{tabular}%
\label{tab6}%
\vspace*{-10pt}
\end{table}%
\begin{table*}[htbp]
\centering
\caption{Performance of the proposed method when setting different $\alpha$ and $\lambda$ on Market1501. Note that red/green denotes the best/worst result.}
\begin{tabular}{|c|cc|cc|cc|cc|cc|}
\toprule
& \multicolumn{2}{c|}{$\alpha$=0.1} & \multicolumn{2}{c|}{$\alpha$=0.15} & \multicolumn{2}{c|}{$\alpha$=0.2} & \multicolumn{2}{c|}{$\alpha$=0.5} & \multicolumn{2}{c|}{$\alpha$=1.0} \\
\midrule
$\lambda$ & Rank-1 & mAP & Rank-1 & mAP & Rank-1 & mAP & Rank-1 & mAP & Rank-1 & mAP \\
\midrule
0 & \textcolor[rgb]{ 0, .69, .314}{\textbf{89.79 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{72.78 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{89.76 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{72.71 }} & 90.11 & \textcolor[rgb]{ 0, .69, .314}{\textbf{72.99 }} & 89.46 & 74.19 & \textcolor[rgb]{ 1, 0, 0}{\textbf{79.87 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{58.87 }} \\
1 & 89.85 & 74.97 & 89.93 & 75.22 & \textcolor[rgb]{ 1, 0, 0}{\textbf{90.44 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{75.36 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{89.55 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{74.60 }} & 79.72 & 57.81 \\
2 & \textcolor[rgb]{ 1, 0, 0}{\textbf{90.05 }} & 75.12 & \textcolor[rgb]{ 1, 0, 0}{\textbf{90.02 }} & \textcolor[rgb]{ 1, 0, 0}{\textbf{75.30 }} & 90.17 & 75.27 & 89.04 & 73.74 & 79.66 & 57.33 \\
5 & 89.90 & \textcolor[rgb]{ 1, 0, 0}{\textbf{75.23 }} & 89.88 & 75.04 & 89.31 & 74.54 & 87.44 & 71.75 & 78.95 & 58.03 \\
10 & 89.88 & 74.90 & 89.22 & 74.42 & \textcolor[rgb]{ 0, .69, .314}{\textbf{88.36 }} & 73.36 & \textcolor[rgb]{ 0, .69, .314}{\textbf{86.02 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{69.50 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{77.73 }} & \textcolor[rgb]{ 0, .69, .314}{\textbf{57.30 }} \\
\bottomrule
\end{tabular}%
\label{tab4}%
\vspace*{-10pt}
\end{table*}%
\textbf{Effectiveness of the Ranking Loss.}
In this part, we utilize different loss functions, including softmax loss, triplet loss, N-pair loss and the proposed ranking loss, to train the proposed network on Market1501. Specifically, we train our model with triplet loss by online hard sample mining and utilize the same parameters (e.g., the number of iterations, learning rate, batch size, etc.) for all loss functions.
Table \ref{tab6} reports the experimental results. We can observer that: i) N-pair loss outperforms the triplet loss. Compared with the conventional triplet loss, N-pair loss interacts with one positive sample and multiple negative samples; ii) The proposed method has better performance than N-pair loss and triplet loss. This validates the analysis in Section~\ref{sec:rank_loss}.
\subsection{Evaluation of Parameters in Ranking Loss}
In this section, parameters of the proposed ranking loss function are analyzed, i.e., parameters in Eq.~(\ref{eq06}).
From Table~\ref{tab4}, we can observe that: i) when $\lambda$ is set to 0, i.e., removing the second item in Eq.~(\ref{eq06}), the performance is poor on mAP. This demonstrates that enhancing the similarity between all the positive images and the query image in the optimization process is useful; ii) In addition, when $\lambda$ increases to values larger than 2, the performance decreases slightly. This implies that focusing too much on the second term of Eq.~(\ref{eq06}) could hurt the performance. We need a reasonable $\lambda$ to balance the two terms in Eq.~(\ref{eq06}); iii) The results of setting $\alpha$ to 0.1, 0.15 and 0.2 are similar, with the results of 0.2 slightly better. As a margin parameter, $\alpha$ should not be too large as an over-large $\alpha$ may easily lead to overfitting problems. When $\alpha$ is over-large (say $\geq 0.5$), there will be excessive penalty from the loss function while optimizing the weights of the proposed network. In conclusion, we set $\lambda$/$\alpha$ to $1/0.2$ in all experiments.
\section{Conclusion}
In this paper, a mask based deep ranking neural network is developed to deal with person retrieval. First, to reduce the impact of messy background in different camera views, the masked images together with the original images are used as input. Second, to obtain more discriminative information, we can combine low-, middle- and high-level features to form a merged feature. Third, we put forward a novel ranking loss function to optimize the weights of the network to further alleviate the interference of similar appearance in person retrieval. Results on various datasets, including both small-scale and large-scale datasets, show the effectiveness of the proposed method compared with a set of state-of-the-art methods
\bibliographystyle{IEEEbib}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,219 |
Габриэль Очоа Урибе (; 20 ноября 1929, Сопетран — 8 августа 2020, Кали) — колумбийский футболист, вратарь. После завершения футбольной карьеры работал тренером. Является самым титулованным тренером в истории чемпионатов Колумбии — 13 побед. Занимает первое место по числу матчей в Кубке Либертадорес в качестве главного тренера — 116 игр. Является рекордсменом по числу матчей, проведенных в качестве главного тренера, в истории колумбийского футбола — 1563 игры.
Карьера
Габриэль Очоа рано лишился отца: тот погиб на угольной шахте, когда Габриэлю было только два года. После этого семья переехала в Медельин. Его мать видела сына либо священником, либо врачом. Гильермо предпочёл получить медицинское образование, став ортопедом-травматологом. Одновременно он играл в футбол и участвовал в скачках на ипподроме Сан-Фернандо Итагуи. Он даже стал чемпионом национального Гран-при, но отказался от карьеры жокея из-за того, что в подростковом возрасте слишком вырос.
Очоа начал карьеру в клубе «Атлетико Мунисипаль». 15 августа 1948 года он провёл первый матч за основной состав против команды «Универсидад», а спустя 8 дней перешёл в «Америку» из Кали. В 1949 году он перешёл в клуб «Мильонариос», с которым выиграл четыре титула чемпиона Колумбии, выступая вместе с Адольфо Педернерой, Альфредо Ди Стефано и Нестором Росси. С приходом в клуб ещё одного аргентинца, вратаря , Гильермо стал только запасным, будучи им до ухода из команды. А одну встречу Очоа провёл в качестве полевого игрока: из-за болезни партнёра по команде он вышел на поле в атаке в матче с «Атлетико Букараманга», в котором даже забил гол, а его команда победила со счётом 7:1. Затем Очоа играл за бразильский клуб «Америка» из Рио-де-Жанейро, где одновременно получал медицинское образование. Любопытно, что за трансфер футболиста клуб заплатил символическую сумму в 100 долларов. Таким образом он стал вторым вратарём из Колумбии после Эфраина Санчеса, игравшим за границей. Как и в предыдущей команде, Гильермо был в клубе лишь запасным. А завершил карьеру, возвратившись в «Мильонариос», в 28 лет из-за травмы.
В 1958, сразу после завершения игровой карьеры, Очоа стал тренером «Мильонариоса». В 1959 году он выиграл свой первый «тренерский» титул чемпиона страны. А с 1961 года три сезона подряд приводил клуб к выигрышу национального первенства. Перед чемпионатом 1964 года Очоа поссорился с руководством клуба из-за того, что в товарищеской игре с «Ривер Плейтом» выставил в составе игрока, не принадлежащего клубу, несмотря на указание того, что этого делать нельзя, и покинул «Мильонариос». В 1965 году Гильерме стал тренером клуба «Индепендьенте Санта-Фе», с которым занял пятое место, а на следующий год привёл и этот клуб к выигрышу чемпионата. Затем он снова тренировал «Мильонариос», с которым выиграл ещё один титул чемпиона. Уйдя из клуба, Очоа вновь стал работать в системе здравоохранения, а потом опять тренировал «Мильонариоса». И, покинув команду, он опять вернулся в медицину, устроившись работать в клинику в Боготе. В 1979 году Гильерме возглавил «Америку» из Кали, клуб который никогда не становился чемпионом Колумбии. И который, по расхожему мнению, был проклят Бенхамином Урреа, сказавший, во времена перехода клуба в профессиональный статус: «Пусть делают с "Америкой", что хотят… Но я клянусь Богом, что они никогда не станут чемпионами». С этой командой Очоа выиграл семь чемпионатов Колумбии, из которых пять подряд с 1982 по 1986 год. Также три года подряд, в 1985, 1986 и 1987 годах Гильерме приводил «Америку» к выходу в финал Кубка Либертадорес, но все три финала клуб проиграл. 22 сентября 1991 года Очоа провёл свой последний матч в качестве главного тренера.
В 1959 году Очоа работал главным тренером Олимпийской сборной Колумбии на . В 1963 году он тренировал первую сборную на чемпионате Южной Америки, в котором колумбийцы заняли последнее место, проиграв пять матчей из шести. В 1985 году он во второй раз тренировал сборную Колумбии в отборочном турнире чемпионата мира. Команда заняла в группе 3 место, выйдя в стыковые матчи, где проиграла Парагваю.
Завершив тренерскую карьеру, он остался в футболе, выступая с лекциями и семинарами. Одновременно он часто появлялся на телевидении в качестве эксперта. 8 августа, в возрасте 90 лет, он умер в своем доме в Кали после продолжительной болезни, связанной с проблемами с дыхательным аппаратом, из-за чего даже был госпитализирован. 9 августа Очоа был похоронен на кладбище на юге Кали. Одним из людей, принёсших соболезнования родным и близким тренера, стал президент Колумбии Иван Дуке.
Достижения
Как игрок
Чемпион Колумбии (4): 1949, 1951, 1952, 1953
Обладатель Кубка Колумбии: 1952/1953
Как тренер
Чемпион Колумбии (13): 1959, 1961, 1962, 1963, 1966, 1972, 1979, 1982, 1983, 1984, 1985, 1986, 1990
Обладатель Кубка Колумбии: 1962/1963
Личная жизнь
Очоа был женат. Он познакомился со своей будущей супругой Сесилией Перейра во время прохождения интернатуры в полицейской клинике в Боготе: девушка попала в ДТП, получив 14 переломов. У них родилось двое сыновей Габриэль и Херман, также ставших врачами.
Примечания
Ссылки
Профиль на footballdatabase.eu
Футболисты Колумбии
Футбольные тренеры Колумбии
Тренеры сборной Колумбии по футболу
Игроки ФК «Атлетико Насьональ»
Игроки ФК «Америка» Кали
Игроки ФК «Мильонариос»
Игроки ФК «Америка» Рио-де-Жанейро
Тренеры ФК «Мильонариос»
Тренеры ФК «Индепендьенте Санта-Фе»
Тренеры ФК «Америка» Кали | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,847 |
Q: Python progroam, Exclude Groups kicked = 0
def calculate():
room = 0
global kicked
N = input("Write the number of groups\n")
M = input("Write the size of the groups, separated with space:\n").split()
for elem in M:
if room+int(elem)<int(N)+1:
room += int(elem)
else:
kicked += 1
while True:
try:
calculate()
print(kicked, "groups did not fit")
break
except:
print("An exception occurred, try again:\n")
Mainly I need help to explain my for loop.
secondly I can't use a splitter input on my first input, why?
A: Transforming the previous comment into an answer, and adding some optimization hints that would not fit in a comment:
Asking for help "to explain my for loop" is a bit unusual - it's your loop, you should know what it does :D Anyhow it basically checks if the sum of all elements in M insofar is still less than or equal to N; if not it "kicks" every remaining elements. Not the most efficient way to do that, but it works. For the second question: you surely can use split() on your first input, but you will get a list, not a single value - so you will need to do something like int(N[0]) to get the number.
Optimizations:
*
*casting a string to an int is not particularly slow, but there is no need to repeat the same operation many times. So let's convert N to int once and for all:
N = int(input("Write the number of groups\n"))
*
*for the same reason, let's convert each elem to int once, not twice, and while we're here let's test for less or equal instead of adding 1 and testing for less than (this last point will only give a very slight improvement but improves readability):
for elem in M:
e = int(elem)
if room + e <= int(N):
room += e
*
*finally once we kick a group there's no need to continue looping - we are kicking everything else. So let's compute how many groups we are kicking and exit the loop:
for i,elem in enumerate(M):
e = int(elem)
if room + e <= int(N):
room += e
else:
kicked = len(M) - i
break
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,638 |
POLSON — As the walls go up on the O'Reilly Auto Parts store in the Ridgewater Subdivision, locals wonder if Polson can support another auto parts store.
With stores in 17 Montana towns and cities, O'Reilly's has also expanded to Columbia Falls, Hamilton and currently is constructing a store in Polson with rumors of an opening date in October.
The two other auto parts businesses in Polson are Auto Zone, which opened in August of 2013, and NAPA Auto Parts, which has been in business in Polson since 1959.
Originally owned and operated by Roy Curry. Boyd Vandeberg bought Polson's NAPA from Curry, and now his son Todd Vandeberg runs the business.
After 30 years in business, Todd said Polson gets a lot of traffic in the summer, but it's been his experience there's "a big slow down" after Labor Day. He hasn't noticed many more people moving to the area, either.
"Auto Zone affected us a little, but not a whole lot," Todd said.
His main beef with the other stores was that he believes they brought out-of-town people to do all the construction work, not locals.
He added that he doesn't know too much about O'Reilly's but has noticed their new stores springing up in Missoula, Columbia Falls and Hamilton.
NAPA is focused more on engines, chassis and hard parts, he said.
Auto Zone managers and employees aren't allowed to speak to the press, and their corporate office public relations staff did not return a call by press time. The Auto Zone website notes that the business targets do-it-yourselfers and commercial customers.
A customer at the store said three auto parts stores in town will be a plus for customers. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,922 |
\section{introduction}
Strong gravitational lensing uniquely demonstrates the interplay between energy and space-time.
The light rays from background sources, like galaxies and quasars, are deflected by massive dark matter halos that are in alignment along an observer's line of sight, producing highly distorted images of these sources.
In this role, strong lensing provides opportunities to study multiple astrophysical and cosmological phenomena --- from the evolution of highly magnified distant galaxies in the early universe to the matter distribution on the scales of galaxies, as well as cosmic acceleration \citep[e.g.,][]{treu10}.
About a thousand lensing systems have been discovered over the last few decades, which we detailed in \cite{nord16}. Modern large-scale surveys have the potential to increase this sample by orders of magnitude by virtue of their relatively large depth and sky area.
For example, based on selection function estimates of spectroscopic confirmations \citep{nord16} and simulation-based forecasts of future surveys \citep{collett12}, \nord{the Dark Energy Survey \citep[DES\footnote{\url{darkenergysurvey.org}};][]{diehl14,flaugher15,2016MNRAS.460.1270D}} is likely to observe more than 2000 galaxy- and cluster-scale lensing systems with arcs, and over a hundred lensed quasars \citep{oguri10}.
The Large Synoptic Survey Telescope \citep[LSST\footnote{\url{lsst.org}};][]{iveziclsst08} data will contain an order of magnitude more \citep{oguri10, collett15}.
Each species of strong lens --- characterized by the scale of the lens, the objects being lensed, and image morphology --- has particular strengths for studying dark matter, dark energy, the cosmic expansion rate, galaxy evolution, and other phenomena.
For example, modeling individual lens systems can constrain mass profiles and mass-to-light ratios of early-type galaxies \citep[e.g.,][]{sonnenfeld2013}.
Modeling the population of galaxy- and group-scale lenses can provide constraints on profiles of dark matter haloes in lenses \citep[e.g.,][]{more12,more16}.
Double-source-plane lenses --- when there are two sources along the line of sight behind a lens --- can constrain cosmic dark matter and dark energy densities, largely independent of the Hubble constant \citep{collett15, linder16}; to date only a few have been discovered \citep[e.g.,][]{gavazzi08, tanaka16}.
Time-delay cosmology uses variable objects, like lensed quasars and supernovae to measure the Hubble rate, in a manner largely independent of dark matter and dark energy densities \citep{refsdal64, blandford92} or the dark energy equation of state \citep{linder11}.
Recent work by the H0liCoW ($H_0$ Lenses in COSMOGRAIL's Wellspring) collaboration provide constraints on the Hubble constant with precision that is competitive with other standard cosmological probes \citep{suyu17, bonvin16}.
Lenses of different kinds have been the object of targeted searches in DES, including quasar lenses \citep{agnello15, agnello17, lin17, ostrovski17}, as well as galaxy-galaxy lenses \citep{nord16}.
The lensed quasar search is the focus of the STRong-lensing Insights into Dark Energy Survey (STRIDES) program\footnote{\url{http://strides.astro.ucla.edu/}}.
The current work extends this line of DES-wide investigation, with galaxy-galaxy lenses spanning different environments: isolated galaxies, groups, and clusters.
\nord{Spectroscopic confirmation is a time-consuming, yet critical process for astrophysical and cosmological analyses.
While thousands of candidates may be observable with DES, the sample size that is optimized for the aforementioned science goals is constrained by observational resources and the number of systems with science potential.}
In this work, we describe the spectroscopic confirmation of nine\ new strong lensing systems discovered in DES Year 1 (Y1) data.
We selected these systems based on the brightness of source galaxies, as well as on the potential for modeling the system --- i.e., morphological simplicity and potential to examine the mass profile of the underlying dark matter halo.
We first created lists of candidates based on a) samples of galaxy groups and clusters and b) photometrically selected galaxies --- totaling $\sim9500$ candidates.
We then visually inspected an image of each candidate system.
This led to the selection of 46\ candidates, \nord{and we performed spectroscopic follow-up on 21\ of those. We then analyzed the spectroscopic data to determine the redshifts of the sources in those lenses to discern if the systems are indeed strong lenses. We describe in more detail the lens candidate search process in \S\ref{sec:search}.}
In this work, we focus on nine\ systems (shown in Fig.~\ref{fig:multipanel}) that show evidence --- morphology, photometry, and spectroscopy --- of strong gravitational lensing: three of the systems are galaxy-scale lenses, five are group-scale and one is a cluster-scale lens.
All of them are newly discovered and confirmed objects.
Detailed mass models of a subset of the confirmed systems will be presented in a separate paper \citep{poh17}.
The paper has the following structure.
We describe the DES Y1 data in \S\ref{sec:data}.
We discuss the search for lens candidates in \S\ref{sec:search} and then the follow-up spectroscopic observations and analysis in \S\ref{sec:follow-up}.
We present the nine\ confirmed systems and their properties in \S\ref{sec:sample}.
We then conclude in \S\ref{sec:summary}.
The AB system is used for all magnitudes.
A Planck $\Lambda$CDM cosmology with spatially-flat priors is assumed: $\Omega_{\rm M}=0.308$, $\Omega_{\Lambda}=0.692$, and $H_0=67.8\, {\rm km\, s^{-1}}\,{\rm Mpc}^{-1}$ \citep{planckcosmo15}.
\section{DES Year 1 Data}\label{sec:data}
DES covers $\sim5000$ sq. deg.} %{${\rm deg}^2$\ in a deep, wide-field survey of the southern Galactic Cap in five optical filters ($grizY$).
It extends to a depth of $i\sim24$ mag at $10\sigma$ detection threshold and a 27-sq.-deg.\ \ supernova survey across 10 fields --- two deep and eight shallow.
The depth in the repeated supernova area is typically two magnitudes deeper than the wide-field survey.
The survey is undertaken with the Dark Energy Camera \citep[DECam][]{flaugher15}, which is a 3-sq.-deg. CCD mosaic camera mounted on the Blanco 4m telescope at the Cerro Tololo Inter-American Observatory (CTIO) in the Chilean Andes.
The DES footprint is observable between August and mid-February.
Each year, DES is allocated $\sim105$ nights, and it has now completed all five and a half years of planned observations.
Because of its large field of view and red-sensitive CCDs, DECam is particularly suited to high-redshift survey work
For this work, we use the Year One First Annual (Y1A1) internal collaboration release of the DES data.
The survey and operations are described in \citet{diehl14}.
The data in the Y1A1 release were acquired between 2013 August 15th and 2014 February 9th.
\nord{These data cover $\sim1840$ sq. deg.} %{${\rm deg}^2$\ to a median $10\sigma$ point source depth calculated with Source Extractor's fixed-aperture magnitudes (MAG APER), with 1.95`` apertures, of 24.19, 23.85, 23.25, 22.55, and 21.20 in the $g$, $r$, $i$, $z$, and $Y$ bands, respectively \citep{2018ApJS..235...33D}.}
\nord{The reduction of the images from DES Y1 data was performed by the DES data management (DESDM) team \citep{2018PASP..130g4501M}.}
After detrending, the single-epoch images were combined into `coadd tiles' after first being calibrated and background-subtracted.
The tiles are coadd images comprising one to five exposures in each of the five wavelength bandpasses.
On average, in each tile, the coverage comprised 3.5 exposures.
Each coadd tile has dimensions $0.73\ {\rm deg.}\times 0.73\ {\rm deg.}$, which are defined to cover the full footprint of DES homogeneously.
The final survey depth is deeper than the Y1A1 release, which consists of 3707 coadded tiles.
This footprint covers two non-contiguous regions: one overlaps the deeply imaged Stripe 82 \citep{jiang14} from SDSS \citep{york00, abazajian09}; the other overlaps the area that is covered by the South Pole Telescope \citep[SPT;][]{carlstrom11}.
More details of the reductions are available in \citet{drlicawagner17arxiv}.
Source Extractor \citep[][]{bertin96, bertin11} image detection software is used for catalog source detection.
It is deployed in double-image mode, and for the detection image, uses the $\chi^2$ detection image, which is constructed from the combination of the $r$, $i$, and $z$ band images.
Positional and photometric data of all the objects in this study (see Table~\ref{table:lensingobjects}) come from this object catalog.
While MAG APER is used for the measures of depth in the Y1A1 catalog release, in this work, we use the magnitude measure, MAG AUTO to perform catalog searches for lens candidates.
\section{Lens Search}
\label{sec:search}
\nord{To identify candidates in DES Y1 data, we used a) samples of galaxy clusters selected via DES data or via SPT data, and b) galaxies selected based on photometry.}
A number of expert scanners visually inspected candidates in search of visually compelling evidence (e.g., morphology, color, brightness) that the systems would be useful for mass modeling.
\nord{The search method used to create candidate lists for visual inspection selects primarily for blue or red source galaxies near single galaxies or within groups or clusters of galaxies.}
Searches of 7328 optically selected galaxy clusters --- found with the redMaPPer\ algorithm \citep{rykoff14} --- as well as a selection of galaxies from the redMaGiC\ catalog \citep{rozo2016,cawthon2017} yielded 374 candidates in the DES Y1 footprint. This is described in \S~3.3 of \citet{diehl17pub}, which will from here on be referred to as {\it Diehl17}.
A third search of SPT galaxy clusters yielded 66 more candidates (described in \S3.1 {\it Diehl17}).
Candidates from searches described elsewhere in {\it Diehl17}\ added 88 more.
Some candidates were the result of serendipitous discovery, and those were not described in {\it Diehl17}.
The combined searches resulted in a list of 112 candidate systems.
A sample of 46 candidates were selected on the bases of 1) science cases (e.g., the potential for modeling the dark matter halo of the lens itself) and 2) objects that are already targeted by other follow-up efforts (e.g., some SPT clusters).
Note that the ranking discussed in {\it Diehl17}\ is based purely on how likely an object is to be a lens (not on how easy it would be to follow up).
We cross-checked both our follow-up candidate sample and the full Y1A1 footprint against the Master Lens Database (MLDB; last updated 2 February 2018), which contains 674 candidates and confirmed systems. None of the candidates we observed during our follow-up for this paper are found in the MLDB.
There are two areas in the DES Y1A1 footprint: one overlaps with SPT, and the other overlaps with SDSS Stripe 82. From MLDB, 202 lenses are within the Y1A1 footprint --- 28 in the SPT area and 174 in Stripe82 area. Those in the SPT area are sufficiently high redshift to not be visible within wavelengths observed by DES. Those in the Stripe82 area were already discovered and are not within our follow-up sample.
\section{Spectroscopic Follow-up at Gemini/GMOS}
\label{sec:follow-up}
In this paper, we aim to report the spectroscopic evidence for strong gravitational lensing in a sample of candidates that were selected through visual scans of images.
We identified 46\ candidates during the lens search, from which we chose the 21\ candidates that are most suitable for follow-up with spectroscopic observations and analysis.
The bases for this down-selection are 1) brightness of source galaxies and 2) suitability of system for observation (e.g., mask alignment).
\nord{We measure the spectroscopic redshifts of source galaxies to determine if they are larger than the putative lens redshifts.}
We require a wide spectral range to search for patterns of narrow emission lines.
We expect some sources to be late-type emission-line galaxies.
With these, we look for several features, such as [OIII]\ and H$\beta$\ to $z\sim 1.0$; H$\delta$, H$\gamma$, and [OII]\footnote{Here, we refer to the doublet, because our resolution is not sufficient to resolve both lines in the doublet.} to $z\sim 1.7$; and Ly$\alpha$\ in the range $z\sim 2.7 - 7.2$.
As part of the Gemini Large and Long Program (GS-2015B-LP-5 and GS-2016B-LP-5)\footnote{\url{http://www.gemini.edu/?q=node/12238\#Buckley}}, we used the multi-object mode of the Gemini Multi-Object Spectrograph \citep[GMOS;][]{2004PASP..116..425H} the Gemini South Telescope to spectroscopic observations of our candidates.
\nord{This proposal includes the goal of creating a spectroscopic sample of red galaxies for photometric redshift calibration.}
Below, we describe the observing strategy and the reductions of the spectroscopic data.
\subsection{Observing Strategy}
\label{sec:followup:observingstrategy}
We used the following procedure for planning the follow-up.
For the purposes of planning the follow-up, the were
We first ranked 21\ candidates by their $i$-band surface brightness, which is calculated using an aperture that is $2''$ in diameter.
We defined three sets of gratings and exposure times.
The combinations depend on these surface brightness classes:
for objects with surface brightness $i_{\rm SB} < 23 $, we integrate for 1 hour in the R400 grating;
for objects with surface brightness $23 < i_{\rm SB} < 24$, we integrate for 3.7 hours in the R400 grating and then for 1 hour in the B600 grating;
for objects with surface brightness, $i_{\rm SB} >24$, we integrate for 1 hour in the B600 grating.
See Table~\ref{table:observationlog} for details of the observations that were performed.
We mostly performed 1-hour observations, which allowed us to obtain sufficient signal in the cases for which a lens could be confirmed in that amount of time.
More than one hour of integration would be unlikely to yield enough additional signal-to-noise to warrant spending the time.
In the event that a clear signal did not appear during the prescribed observations, we chose to not perform additional observations or longer integration times for any system.
We made this decision to conserve telescope time and to maximize the number of strong lens system confirmations.
Moreover, consistent integration time across the observation fields incur consistent depth---a requirement for the photo-z calibration targets.
We centered each field's mask on the lens of the candidate system, and we placed slists on the images of the sources.
In some cases, we shifted the center of the field to accommodate a suitable guide star.
We also rotated the slit mask (i.e., rotated teh position angle of the system) to include as many source targets as possible.
Slits were first placed on as many of the source images as possible.
Then, for the calibration of DES photometric redshifts, the unused slits (about 40) were placed on galaxy targets.
While the slit lengths varied, all the slits were $1''$ in width.
This setting accommodated both the object and the amount of sky sufficient for reliable background subtraction.
In some cases, the slits were tilted to maximize the flux captured from an extended source.
To obtain spectra of objects with redshift $z<1.7$ and wavelength coverage $\sim5000-10000$\AA, we use the R400 grating in conjunction with the GG455 filter.
For spectra of objects with redshift $z>2$ and within the wavelength range $3250-6250$\AA, we use the B600 grating without a filter.
For an observing sequence with a 1-hour science integration, we first took a pair of half-hour 900-second science exposures.
Then, we used a Quartz-Halogen lamp to take a flat field and a Quartz-Halogen lamp to take a calibration spectrum.
To cover the gap between the CCDs, we then shifted to a different central wavelength.
Finally, we repeated this sequence in reverse order.
For the The 3.7-hour science integration, we instead used 840-second science exposures and repeated the above sequence 16 times.
We facilitate the removal of cosmic rays by dividing the integration time into multiple exposures.
We binned the data $2\times2$, which gave effective dispersions of $1.0$ and $1.5$ \AA/pixel for the B600 and R400 gratings, respectively.
\subsection{Spectroscopic Reductions}
\label{sec:followup:reductions}
We used the Gemini IRAF package v1.13.1\footnote{\url{http://www.gemini.edu/sciops/data-and-results/processing-software}} for IRAF v2.16 to reduce the exposures.
Some of the Gemini IRAF tasks were modified to provide additional flexibility in the data reduction.
First, for each wavelength dither in a given system, we use the {\tt gsflat} task to process (including bias subtraction) the flat field.
We then use these processed flat images and {\tt gsreduce} to reduce each science exposure.
Then, the two exposures are combined with {\tt gemcombine}.
We then use the {\tt gswavelength} and {\tt gstransform} tasks to perform wavelength calibration and transformation on each dither.
Then we coadd a pair of dithers on the new common wavelength scale, which eliminates CCD chip gaps.
We use {\tt gsextract} (which calls the {\tt apall} task) to perform sky subtraction and 1D spectral extraction.
We use night sky lines from the science spectra to add calibration lines to the 5500\AA-6400\AA\ wavelength range.
We modified the canonical reduction process by taking the log of the fluxes in the calibration spectra to enable simultaneous automated identification of both the strong lines above 7000\AA\ and the weaker lines below.
For improved interactive flexibility in this part of the reduction, {\tt gswavelength} and {\tt gsextract} were modified to allow wavelength calibration and 1D spectral extraction, respectively, for selected individual slits, as needed.
Finally, we use the {\tt emsao} task within the {\tt rvsao} IRAF package \citep{kurtz98} for feature identification and redshift estimation.
\section{Sample of Confirmed Lenses}
\label{sec:sample}
We confirmed that nine\ of the 21\ observed candidate systems are indeed strong lensing systems, and we rejected two\ candidates. The remaining ten\ were not confirmed, and spectroscopic analysis was inconclusive for those candidates.
One of the two rejected systems contains a foreground star-forming galaxy, and the other contains a background group (rather than the apparent multiply lensed red galaxy).
The systems that we failed to confirm exhibit promising lensing features, but the sources have no discernible continuum emission, no spectral features, or both.
The measurements of spectroscopic features are too low signal-to-noise with the integration times in our observing program, or they have redshifts that are outside the range of the optical observations in our observing program (i.e., in the redshift desert).
We list the rejected and inconclusive systems in Table~\ref{table:notlensingobjects}.
In Fig.~\ref{fig:multipanel}, we show a multi-panel figure of the confirmed systems.
In Table~\ref{table:lensingobjects}, for each observed lensing system, we list the positions and photometry of the candidate lens and source(s).
The sample is comprised of three galaxy-scale lenses (b, f, g), five group-scale lenses (a, c, d, h, i) and one cluster-scale lens (e).
In this section, we provide details for each system --- the important spectral features, the measured redshifts, and simple mass estimates.
Fig.'s~\ref{fig:SystemA}-\ref{fig:SystemG} show the reduced 1D spectra and a cut-out of the field centered on the central lensing object, including labeled source positions for each system.
We estimate the enclosed mass $M_{\rm enc}$ of the lensing system under the assumption of a singular isothermal sphere (SIS) mass profile \citep{narayan96}:
\begin{equation}
M_{\rm enc} = \frac{c^2}{4G} \theta_{\rm e}^2 \left(\frac{D_{\rm L} D_{\rm S}}{D_{\rm L S}}\right), \label{eqn:menclosed}
\end{equation}
where $c$ is the speed of light, $G$ is Newton's gravitational constant, $\theta_{\rm e}$ is the Einstein radius, and $D$ is the angular diameter distance.
In particular, $D_{\rm L}$, $D_{\rm S}$, and $D_{\rm LS}$ are the angular diameter distances to the lens, to the source, and between the lens and the source, respectively.
\nord{We use the source image-lens separation\ (calculated in {\it Diehl17}) as an approximation for the Einstein radius $\theta_{\rm sep}$.
It is measured by taking the average of the distances between a targeted source image and the selected central lensing galaxy.
This estimate of the Einstein radius is only accurate to a factor of 2, and it's an overestimate for cases in which only the brightest source image is used to approximate the radius.}
We use the standard deviation of the distances summed in quadrature with the pixel scale of DECam (0.263''/pix) to estimate the uncertainty in this distance.
The angular diameter distances only depend on redshifts of the objects and on cosmological parameters.
Table~\ref{table:lensingfeatures} summarizes key information for all the confirmed systems --- spectral features, photometric redshifts of lenses, spectroscopic redshifts of sources, source image-lens separation, and enclosed masses.
This strategy is similar to that used in the Sloan Bright Arc Survey \citep[SBAS; e.g.,][]{diehl09}.
We combine uncertainties from the measurements of the distances and source image-lens separation\ to estimate frequentist uncertainties for the enclosed mass.
According to the prescription of \citet{sanchez14} for photometric redshifts in DES, the photometric redshift uncertainties have been multiplied by a factor of $1.5$.
The spectroscopic redshift uncertainties are the result of a sum in quadrature of a) the uncertainty in wavelength calibration and b) the uncertainty in the redshift determination from the IRAF function {\tt emsao}.
These spectroscopic redshift uncertainties are then propagated to the angular diameter distances.
The mass uncertainty results from the sum in quadrature of uncertainties from the source image-lens separation, and the angular diameter distances.
The uncertainty on each angular diameter distance scales with the redshift error, which ranges $\sim0.008 - 0.19\%$ for spectroscopic redshifts and $\sim 3.2 - 17.5\%$ for lens redshifts.
The uncertainty in the source image-lens separation, which ranges $\sim 6-22\%$ is purely statistical.
This results in mass uncertainties in the range $\sim25-80\%$.
Table~\ref{table:lensingfeatures} summarizes the lensing features for the confirmed systems.
A subset of the systems have sources with multiple, detailed images, making them amenable to detailed modeling, which will be performed in a separate paper \citep{poh17}.
\subsection{\mbox{DES J0041-4155}}
\label{sec:sample:systemA}
\mbox{DES J0041-4155}\ is a group-scale system.
The largest central red galaxy has a DESDM photometric redshift of $z_{\rm lens}=0.716\pm0.031$.
As shown in Fig.~\ref{fig:multipanel}a, there are three prominent blue-pink arcs, A1, A2, and A3\ to the north, northwest, and west, respectively, of the lensing galaxy.
The right panel of Fig.~\ref{fig:SystemA} also displays these arcs.
We identify emission lines in the follow-up B600 spectroscopy of the three images near the observed wavelength of $\sim4329$\AA\ in all three spectra (Fig.~\ref{fig:SystemA}, left panel).
When we account for the absence of spectral features in the R400 spectra, as well as the photometric redshift of the lens galaxy, we can assign spectral features to be Ly$\alpha$.
This then gives redshifts $z_{\rm source}=2.5619\pm0.0001$, $2.5618\pm0.0001$, and $2.5616\pm0.0002$ for A1, A2, and A3, respectively.
We identified no counter-images.
In the R400 spectrum for A1, there is an [OII]\ line at $\sim6620$\AA (not shown in Fig.~\ref{fig:SystemA}), which corresponds to a redshift of $z=0.7761\pm0.00007$ of a foreground object. This is clearly visible as a bluer galaxy superimposed on A1.
We use the redMaPPer\ redshift $z_{\rm lens}=0.755566 \pm 0.0178898$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=7.23 \pm 0.50''$ to calculate an enclosed mass of $M_{\rm enc}=1.74 \pm 0.47 \times 10^{13}\, \msol$ for this system.
\subsection{\mbox{DES J0104-5341}}
\label{sec:sample:systemB}
\mbox{DES J0104-5341}\ is a galaxy-scale lensing system.
The red lensing galaxy has a photometric redshift $z_{\rm lens}=0.679\pm0.022$, and there are two relatively red arcs to the west and south, labeled A1\ and A2, respectively, as shown in Fig.~\ref{fig:multipanel}b and in Fig.~\ref{fig:SystemB}.
We identify strong emission lines for A1\ and A2\ (Fig.~\ref{fig:SystemB}, left panel) in both R400 spectra near an observed wavelength of $\sim8319$\AA.
In the absence of features in the B600 spectra, we associate this feature with [OII], yielding redshifts $z_{\rm source}=1.2318\pm0.0001$ and $1.2318\pm0.0001$ for A1\ and A2, respectively. We see no counter-images for this source.
We use the redMaPPer\ redshift $z_{\rm lens}=0.615464 \pm 0.0113758$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=2.18 \pm 0.43''$ to calculate an enclosed mass of $M_{\rm enc}=2.42 \pm 1.10 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J0120-5143}}
\label{sec:sample:systemC}
The central red galaxy of this group-scale system \mbox{DES J0120-5143}\ has a photometric redshift $z_{\rm lens}=0.603\pm0.063$.
There exist three source images, A1, A2, and A3\ to the east, northeast, and north-northwest, respectively, of the central red galaxy in the image, as shown in Fig.~\ref{fig:multipanel}c and in the right panel of Fig.~\ref{fig:SystemC}.
In all R400 data (Fig.~\ref{fig:SystemC}, left panel), there are emission-line features near $\sim8557$\AA, which we attribute to [OII].
The resulting redshifts for the source images are $z_{\rm source}=1.2955\pm0.0001$, $1.2957\pm0.0000$, and $1.2957\pm0.0005$ for arcs A1, A2, and A3, respectively.
This lensing system resides in a group environment.
There is a counter-image at the southwest that lies nearly on top of the central red lensing galaxy.
We were not able to target it for follow-up spectroscopic observation.
We use the redMaPPer\ redshift $z_{\rm lens}=0.550283 \pm 0.00960631$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=3.35 \pm 0.51''$ to calculate an enclosed mass of $M_{\rm enc}=4.46 \pm 2.78 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J0227-4516}}
\label{sec:sample:systemI}
\mbox{DES J0227-4516}\ is a group-scale lens with DES photometric redshift, $z_{\rm lens}=0.4300 \pm 0.0400$, and one blue knot (A1) to the south.
The system is shown in Fig.~\ref{fig:multipanel}i and in the right panel of Fig.~\ref{fig:SystemI}.
Near wavelength $\sim8396$\AA, we identify an [OII]\ emission line in the R400 spectra of the blue knot.
This yields source redshifts of $z_{\rm source}=1.25264 \pm 0.00009$ A1\ (Fig.~\ref{fig:SystemI}, left panel).
We used the data from Dec 2016 to do the redshift determination, because the seeing was much better.
We also targeted the faint arc to the east, but the signal-to-noise of the data was too low, and we could not obtain a redshift.
We use the redMaPPer\ redshift $z_{\rm lens}=0.4154 \pm 0.0134$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=4.11 \pm 0.28''$ to calculate an enclosed mass of $M_{\rm enc}=4.32 \pm 1.32 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J0357-4756}}
\label{sec:sample:systemD}
\mbox{DES J0357-4756}\ is a cluster-scale lens, where the central lensing galaxy has photometric redshift $z_{\rm lens}=0.257\pm0.024$.
There is a red arc (A1) to the west, a large red arc (A2) to the southwest, and a red arc (A3) to the south, respectively, as shown in Fig.~\ref{fig:multipanel}d and in the right panel of Fig.~\ref{fig:SystemD}.
In the follow-up R400 spectroscopy of all three arcs (Fig.~\ref{fig:SystemD}, left panels), we identify an emission line at $\sim7141$\AA, which we identify as [OII].
From this emission line, we obtain redshifts of $z_{\rm source}=0.9156\pm0.0001$, $0.9155\pm0.0001$, and $0.9156\pm0.0001$ (Fig.~\ref{fig:SystemD}).
The red 'x' near the center of the color image in the upper right panel marks the location of the lens designated for measurement of the Einstein radius.
The position of the red 'x' is chosen to simplify the drawing of a circle through the arcs of the source galaxy images.
Because the goal is to obtain a simple estimate of the lens mass, our goals is to first obtain a reasonable estimate of the Einstein radius.
We use the redMaPPer\ redshift $z_{\rm lens}=0.285713 \pm 0.0082556$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=9.39 \pm 0.91''$ to calculate an enclosed mass of $M_{\rm enc}=1.38 \pm 0.36 \times 10^{13}\, \msol$ for this system.
\subsection{\mbox{DES J0418-5457}}
\label{sec:sample:systemH}
\mbox{DES J0418-5457}\ is a galaxy-scale lens with the DES photometric redshift, $z_{\rm lens}=0.345\pm0.032$, and one blue arc (A1) to the north.
The system is shown in Fig.~\ref{fig:multipanel}h and in the right panel of Fig.~\ref{fig:SystemH}.
Near a wavelength of $\sim9030$\AA, we identify an [OII]\ emission line in the R400 spectra of both arcs.
This yields a source redshift of $z_{\rm source}=1.3938\pm0.0001$ A1\ (Fig.~\ref{fig:SystemH}, left panel).
We use the redMaGiC\ redshift $z_{\rm lens} = 0.6830 \pm 0.0421$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=1.97 \pm 0.27''$ to calculate an enclosed mass of $M_{\rm enc}=1.47 \pm 0.65 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J2113-0114}}
\label{sec:sample:systemE}
\mbox{DES J2113-0114}\ is a galaxy-scale system with two small source images, A1\ and A2, which lie to the southwest of the central red galaxy, as shown in Fig.~\ref{fig:multipanel}e and in the right panel of Fig.~\ref{fig:SystemE}.
The lensing galaxy has photometric redshift $z_{\rm lens}=0.406\pm0.071$.
In the R400 spectra for A1, we identify emission line features near $\sim6689$\AA, $\sim6942$\AA, $\sim7361$\AA, $\sim7790$\AA, $\sim8723$\AA, $\sim8898$\AA, and $\sim8984$\AA.
In both images, we take these emission lines to be [OII], [NeIII]3869, H$\delta$, H$\gamma$, H$\beta$, [OIII]4959, [OIII]5006, respectively, from which we obtain redshifts of $z_{\rm source}=0.7943\pm0.0002$ and $0.7947\pm0.0002$ (Fig.~\ref{fig:SystemE}) for these source images.
We use the redMaGiC\ redshift $z_{\rm lens}=0.461598 \pm 0.0120324$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=1.98 \pm 0.51''$ to calculate an enclosed mass of $M_{\rm enc}=1.28 \pm 1.06 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J2321-4630}}
\label{sec:sample:systemF}
\mbox{DES J2321-4630}\ is a group-scale lens with two central galaxies with DESDM photometric redshifts, $z_{\rm lens}=0.644\pm0.025$ and $z_{\rm lens}=0.70\pm0.02$.
There are two small red arcs, A1\ and A2, to the east and northeast, respectively, of the central red galaxy.
These are shown in Fig.~\ref{fig:multipanel}f and in the right panel of Fig.~\ref{fig:SystemF}.
The R400 spectrum of A1\ shows prominent emission lines near five different observed wavelengths---$\sim6385$\AA, $\sim6658$\AA, $\sim9413$\AA, and $\sim10242$\AA, which we identify as CII]2326, [NeIV]2424, [NeV]3346, and [OII], respectively.
This gives a redshift of $z_{\rm source}=1.7479\pm0.0031$.
The R400 spectrum of A2\ presents a similar pattern for these emission lines---$\sim6391$\AA, $\sim6661$\AA, $\sim9413$\AA, and $\sim10242$\AA --- which yields a source redshift of $z_{\rm source}=1.7469\pm0.0014$ (Fig.~\ref{fig:SystemF}, left panel).
There is a possible counter-image to the west south-southwest of the lensing galaxy, but it could not be targeted due to its proximity to the central red galaxy and available telescope time.
The presence of the Ne emission lines in combination with OII lines suggests the possibility that the source is a radio galaxy.
\citep{humphrey07} identifies NeV and NeIV emission in z$\sim$2.5 radio galaxies as a potential signature of AGN photo-ionization.
The two central galaxies are found in the redMaGiC\ catalog with redshifts $z_{\rm lens}=\redshiftRMFa$ and $z_{\rm lens}=\redshiftRMFa$.
We use the redMaGiC\ redshifts and the estimated source image-lens separation\ of $\theta_{\rm sep}=3.30 \pm 0.74''$ to calculate an enclosed mass of $M_{\rm enc}=3.84 \pm 1.87 \times 10^{12}\, \msol$ for this system.
\subsection{\mbox{DES J2349-5113}}
\label{sec:sample:systemG}
\mbox{DES J2349-5113}\ is a group-scale lens.
The central galaxy has photometric redshift $z_{\rm lens}=0.345\pm0.032$, and there are two blue arcs (A1\ and A2) to the east and the west.
These are shown in Fig.~\ref{fig:multipanel}g and in the right panel of Fig.~\ref{fig:SystemG}.
Near wavelengths of $\sim8920$\AA, we identify [OII]\ emission lines in the R400 spectra of both arcs.
These yield source redshifts of $z_{\rm source}=1.3938\pm0.0001$ and $1.3932\pm0.0001$ for A1\ and A2, respectively (Fig.~\ref{fig:SystemG}, left panel).
Only after sky subtraction was the line in A2\ revealed.
Note that A2\ appears more extended and much fainter than A1, and thus has much lower signal-to-noise.
The faintness of the source, along with a sky line on top of the data (which affected the subtraction), likely reduced the signal in this emission line.
The low signal-to-noise for A2\ likely contributes to an error in redshift that causes the spectroscopic redshifts to differ beyond their estimated errors.
We use the redMaPPer\ redshift $z_{\rm lens}=0.415383 \pm 0.0134149$ and the estimated source image-lens separation\ of $\theta_{\rm sep}=4.46 \pm 0.71''$ to calculate an enclosed mass of $M_{\rm enc}=3.77 \pm 1.42 \times 10^{12}\, \msol$ for this system.
\section{Discussion and Summary}\label{sec:summary}
In this paper, we have presented new confirmations of galaxy- to cluster-scale strong lenses in Y1 DES data.
We first identified candidates in DES data through investigation of cluster sub-samples, and through catalog searches of galaxies based on photometry and proximity of lenses and source images.
We then visually inspected these subsamples to identify 46\ candidates for spectroscopic follow-up.
The search was conducted over 1800 sq. deg.} %{${\rm deg}^2$.
We confirmed these systems with spectroscopy from GMOS on the Gemini South telescope.
The confirmed sample comprises three galaxy-scale lenses, five group-scale and one cluster-scale lens.
They have been identified through known emission lines, such as Ly$\alpha$\ and $[{\rm OII}]$3727.
Of particular note is one system, \mbox{DES J2321-4630}, in which the presence of Ne emission lines suggest it may be a radio galaxy.
For all the confirmed lenses, we provide a rough estimate of the lens mass based on an \nord{average of the source image-lens separation} from {\it Diehl17}.
Detailed modeling of these systems can contribute to studies of mass profiles and mass-to-light ratios of early-type galaxies.
\citet{poh17} will report the modeling of a subset of these confirmed systems.
The redshift desert is a key problem in the spectroscopic follow-up of strong lenses.
A number of our candidates could not be confirmed or rejected, because they may exist in a redshift range not covered by GMOS spectrographs.
One possible solution to this challenge is to seek improved photometric redshift estimations of high-redshift source galaxies.
The measurement or prediction of photometric redshifts of distance objects, is itself a long-time challenge, largely due to the small number of training sets at high redshift.
Another solution is to perform observations in a higher wavelength range --- e.g., in the (near) infrared with \nord{Gemini South's FLAMINGOS-2 instrument\footnote{\url{https://www.gemini.edu/sciops/instruments/flamingos2/}}} and Paranal Observatory's Very Large Telescope, which has MUSE and X-Shooter\footnote{\url{https://www.eso.org/public/usa/teles-instr/paranal-observatory/vlt/vlt-instr/} for example}.
The search in DES Y1 data and in that of \cite{nord16} produced many more candidates than feasibly can be followed up with modern spectroscopic observation resources.
We confirmed fewer than of those we observed, with an observational strategy that efficiently used the available observing time.
The best way to improve chances of positive spectroscopic confirmation in future work is to more accurately and precisely predict strong lens candidates from their imaging.
Future searches of DES data are set to take place with more advanced algorithms, stemming from machine learning and citizen science programs, among others.
We expect that these algorithms will provide more flexibility, power, and efficiency in identifying high-quality strong lens candidates.
\section*{Acknowledgments}
We are grateful for the extraordinary contributions of our CTIO colleagues and the DES Camera, Commissioning and Science Verification teams for achieving excellent instrument and telescope conditions that have made this work possible.
The success of this project also relies critically on the expertise and dedication of the DES Data Management organization.
Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A\&M University, Financiadora de Estudos e Projetos, Funda\c{c}\~{a}o Carlos Chagas Filho de Amparo \`{a} Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnol\'{o}gico and the Minist\'{e}rio da Ci\^{e}ncia e Tecnologia, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766.
The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ESP2013-48274, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234, some of which include ERDF funds from the European Union.
The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energ\'{e}ticas, Medioambientales y Tecnol\'{o}gicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the Eidgenoessische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Edinburgh, the University of Illinois at Urbana-Champaign, the Institut de Ci\`{e}ncies de l'Espai (IEEC/CSIC), the Institut de F\'{i}sica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universit\"{a}t and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A\&M University.
This work is based in part on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Minist\'{e}rio da Ci\^{e}ncia, Tecnologia e Inova\c{c}\~{a}o (Brazil) and Ministerio de Ciencia, Tecnolog\'{i}a e Innovaci\'{o}n Productiva (Argentina). The data was processed using the Gemini IRAF package v2.16.
This research has made use of NASA's Astrophysics Data System.
This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,129 |
Джа́ггер () — англійське прізвище. Відомі носії:
Б'янка Джаггер (; 1945) — нікарагуанська та британська правозахисниця, адвокат, колишня дружина Міка Джаггера.
Дін Джаггер (; 1903—1991) — американський актор, лауреат премії «Оскар» (1950).
Елізабет Джаггер (; 1984) — американська модель і акторка англійського походження.
Мік Джаггер (; 1943) — британський рок-музикант, актор, продюсер, вокаліст гурту «The Rolling Stones».
Інше
«Йоссі і Джаггер» () — ізраїльський фільм (2002) режисера Ейтана Фокса.
Англійські прізвища | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,973 |
Home / 30 / Adele / Columbia Records / English Lyrics / Can't Be Together Lyrics - Adele
Can't Be Together Lyrics - Adele
30, Adele, Columbia Records, English Lyrics
Can't Be Together Lyrics - Adele is a new upcoming English song. Can't Be Together lyrics sung by popular singer Adele. This song written by Adele. Song of Can't Be Together lyrics started by the line in the pronunciation language in English is You've got your eye on me after all these years. This song will be create an average hype in YouTube after released. Can't Be Together song video director by update soon. This beautiful song sung in the language of English. Can't Be Together song distributor by Sony Music Entertainment. This beautiful song released in the YouTube November 19, 2021.
Can't Be Together song got a music label which name is Melted Stone and Columbia Records. This beautiful song created in the album of 30. So, let's know the song of Can't Be Together lyrics and also play the music in below.
Can't Be Together Song Information
Can't Be Together
Columbia Records and Melted Stone
You can also know Wild Wild West and Wah Kya Nazare song lyrics.
You've got your eye on me after all these years
You think that I can't see you from over here
I may be out of your view but I can hear you
I may be out of the room but I can see you
I know you still want me you always will
And I can guarantee I know just how it feels
To never be free completely
Sometimes you just feel so empty
Like lately when I have been missing you
And I would still do anything for you
But we need to learn how to love who we're loving
It's hard but we must we've got to let it go
And turn off the urge to know what could have been
But I will love you forever
I was far too reckless I know that now
Trying to make you jealous made me feel proud
But now I'm in too deep to climb out
But know that I live with my doubt
And I want to do everything with you
Since we were together everybody's changed
Our reflections in the mirror no longer look the same
And we're only just beginning to live the lives we'll make
But I will always miss you at the end of each day
My love let's learn how to love who we're loving
It's so hard but we must
We've got to let it go
But we can't be together
No we won't be together | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,489 |
Even though project management certification is not compulsory but it would be good especially if you are involved in government related projects.
Project Management Institute (PMI) first published PMBoK® Guide as a white paper in 1987 in an attempt to document and standardize generally accepted project management information and practices. The current edition, A Guide to the Project Management Body of Knowledge (PMBoK® Guide) – Sixth Edition, was released on September 6, 2017 and provides a basic reference for Project Management.
It is originated from the earlier PRINCE technique, which was initially developed in 1989 by the Central Computer and Telecommunications Agency (CCTA) as a UK Government standard for information systems project management; however, it soon became regularly applied outside the purely IT environment. PRINCE2® was released in 1996 as a generic project management method. PRINCE2® has become increasingly popular and is now the de facto standard for project management in the UK. Its use has gone beyond the UK to other countries.
The most current revision was released in 2005 by the Office of Government Commerce (OGC) and it is currently undergoing a refresh for 2008/9.
The "PRINCE2" name is a Registered Trade Mark of the OGC. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,234 |
We were asked to be a guest on the Resilient Advisor Podcast. Our host, Jay Coulter, wanted us to help his audience of financial advisors work with wholesalers more effectively.
In this 20 minute show, Rob Shore outlines the attributes that advisors should look for in great wholesaling partners - and along the way you'll pick up a few wholesaling tips too! | {
"redpajama_set_name": "RedPajamaC4"
} | 2,167 |
package com.linkedin.android.litr.transcoder;
import android.media.MediaCodec;
import android.media.MediaFormat;
import android.view.Surface;
import com.linkedin.android.litr.codec.Decoder;
import com.linkedin.android.litr.codec.Encoder;
import com.linkedin.android.litr.codec.Frame;
import com.linkedin.android.litr.exception.TrackTranscoderException;
import com.linkedin.android.litr.io.MediaRange;
import com.linkedin.android.litr.io.MediaSource;
import com.linkedin.android.litr.io.MediaTarget;
import com.linkedin.android.litr.render.GlVideoRenderer;
import org.junit.Before;
import org.junit.Test;
import org.mockito.ArgumentCaptor;
import org.mockito.Mock;
import org.mockito.MockitoAnnotations;
import java.nio.ByteBuffer;
import static org.hamcrest.MatcherAssert.assertThat;
import static org.hamcrest.core.Is.is;
import static org.mockito.ArgumentMatchers.any;
import static org.mockito.ArgumentMatchers.anyBoolean;
import static org.mockito.ArgumentMatchers.anyInt;
import static org.mockito.ArgumentMatchers.anyLong;
import static org.mockito.ArgumentMatchers.eq;
import static org.mockito.ArgumentMatchers.isNull;
import static org.mockito.Mockito.atLeast;
import static org.mockito.Mockito.doReturn;
import static org.mockito.Mockito.doThrow;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.never;
import static org.mockito.Mockito.spy;
import static org.mockito.Mockito.verify;
import static org.mockito.Mockito.when;
public class VideoTrackTranscoderShould {
private static final int VIDEO_TRACK = 0;
private static final int AUDIO_TRACK = 1;
private static final int BUFFER_INDEX = 0;
private static final int BUFFER_SIZE = 42;
private static final long DURATION = 84;
private static final long CURRENT_PRESENTATION_TIME = 42L;
private static final float CURRENT_PROGRESS = 0.5f;
private static final String TARGET_MIME_TYPE = "video/avc";
private static final int TARGET_WIDTH = 1280;
private static final int TARGET_HEIGHT = 720;
private static final int TARGET_BITRATE = 4000000;
private static final int TARGET_KEY_FRAME_INTERVAL = 3;
private static final long SELECTION_START = 16;
private static final long SELECTION_END = 64;
@Mock private MediaSource mediaSource;
@Mock private MediaTarget mediaTarget;
@Mock private MediaFormat sourceMediaFormat;
@Mock private Surface surface;
@Mock private MediaCodec.BufferInfo bufferInfo;
@Mock private Encoder encoder;
@Mock private Decoder decoder;
@Mock private GlVideoRenderer renderer;
@Mock private MediaFormat targetVideoFormat;
private VideoTrackTranscoder videoTrackTranscoder;
private ByteBuffer[] sampleByteBuffers;
private Frame sampleFrame;
private MediaRange fullMediaRange;
private MediaRange trimmedMediaRange;
@Before
public void setup() throws Exception {
MockitoAnnotations.initMocks(this);
ByteBuffer buffer = ByteBuffer.allocate(BUFFER_SIZE);
sampleByteBuffers = new ByteBuffer[] {buffer};
sampleFrame = new Frame(BUFFER_INDEX, buffer, bufferInfo);
fullMediaRange = new MediaRange(0, Long.MAX_VALUE);
trimmedMediaRange = new MediaRange(SELECTION_START, SELECTION_END);
doReturn(sourceMediaFormat).when(mediaSource).getTrackFormat(anyInt());
doReturn(surface).when(encoder).createInputSurface();
doReturn(surface).when(renderer).getInputSurface();
doReturn(true).when(decoder).isRunning();
doReturn(true).when(encoder).isRunning();
when(mediaSource.getSelection()).thenReturn(fullMediaRange);
when(targetVideoFormat.containsKey(MediaFormat.KEY_MIME)).thenReturn(true);
when(targetVideoFormat.getString(MediaFormat.KEY_MIME)).thenReturn(TARGET_MIME_TYPE);
when(targetVideoFormat.containsKey(MediaFormat.KEY_WIDTH)).thenReturn(true);
when(targetVideoFormat.getInteger(MediaFormat.KEY_WIDTH)).thenReturn(TARGET_WIDTH);
when(targetVideoFormat.containsKey(MediaFormat.KEY_HEIGHT)).thenReturn(true);
when(targetVideoFormat.getInteger(MediaFormat.KEY_HEIGHT)).thenReturn(TARGET_HEIGHT);
when(targetVideoFormat.containsKey(MediaFormat.KEY_BIT_RATE)).thenReturn(true);
when(targetVideoFormat.getInteger(MediaFormat.KEY_BIT_RATE)).thenReturn(TARGET_BITRATE);
when(targetVideoFormat.containsKey(MediaFormat.KEY_I_FRAME_INTERVAL)).thenReturn(true);
when(targetVideoFormat.getInteger(MediaFormat.KEY_I_FRAME_INTERVAL)).thenReturn(TARGET_KEY_FRAME_INTERVAL);
// setting up and starting test target, which will be used for frame processing testing below
videoTrackTranscoder = spy(new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder));
videoTrackTranscoder.start();
}
// region: starting/stopping tests
// they use their own non-shared mocks of CodecFinder and VideoTrackTranscoder, because we don't want to
// interfere with the "running" state of the class level mocks
@Test(expected = TrackTranscoderException.class)
public void notStartWhenCannotFindEncoder() throws Exception {
doThrow(new TrackTranscoderException(TrackTranscoderException.Error.ENCODER_FORMAT_NOT_FOUND))
.when(encoder)
.init(any(MediaFormat.class));
VideoTrackTranscoder videoTrackTranscoder = spy(new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder));
videoTrackTranscoder.start();
}
@Test(expected = TrackTranscoderException.class)
public void notStartWhenCannotFindDecoder() throws Exception {
Decoder decoder = mock(Decoder.class);
doThrow(new TrackTranscoderException(TrackTranscoderException.Error.DECODER_FORMAT_NOT_FOUND))
.when(decoder)
.init(any(MediaFormat.class), any(Surface.class));
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
//videoTrackTranscoder.start();
}
@Test
public void startWhenEncoderAndDecoderAreStarted() throws Exception {
GlVideoRenderer renderer = mock(GlVideoRenderer.class);
Decoder decoder = mock(Decoder.class);
Encoder encoder = mock(Encoder.class);
doReturn(surface).when(encoder).createInputSurface();
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
videoTrackTranscoder.start();
verify(encoder, never()).stop();
verify(decoder, never()).stop();
verify(encoder).start();
verify(decoder).start();
verify(renderer).init(surface, sourceMediaFormat, targetVideoFormat);
}
@Test
public void stopAndReleaseEncoderAndDecoderWhenStopped() throws Exception {
VideoTrackTranscoder videoTrackTranscoder = spy(new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder));
videoTrackTranscoder.stop();
verify(decoder).stop();
verify(decoder).release();
verify(encoder).stop();
verify(encoder).release();
verify(renderer).release();
}
// endregion: starting/stopping tests
// region: extracting & decoding frames
@Test
public void notProcessFrameWhenNotStarted() throws Exception {
GlVideoRenderer renderer = mock(GlVideoRenderer.class);
Decoder decoder = mock(Decoder.class);
Encoder encoder = mock(Encoder.class);
doReturn(surface).when(encoder).createInputSurface();
// use a method level test target, because we want it to be in the stopped state
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
int result = videoTrackTranscoder.processNextFrame();
assertThat(result, is(TrackTranscoder.ERROR_TRANSCODER_NOT_RUNNING));
}
@Test
public void notTryToDecodeFrameWhenOtherTrackIsSelected() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(VIDEO_TRACK + 1).when(mediaSource).getSampleTrackIndex();
int result = videoTrackTranscoder.processNextFrame();
verify(decoder, never()).dequeueInputFrame(anyLong());
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void tryToDecodeFrameWhenNoTrackIsSelected() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(TrackTranscoder.NO_SELECTED_TRACK).when(mediaSource).getSampleTrackIndex();
doReturn(MediaCodec.INFO_TRY_AGAIN_LATER).when(decoder).dequeueInputFrame(anyLong());
int result = videoTrackTranscoder.processNextFrame();
verify(decoder).dequeueInputFrame(anyLong());
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void tryToDecodeFrameWhenVideoTrackIsSelected() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(VIDEO_TRACK).when(mediaSource).getSampleTrackIndex();
doReturn(MediaCodec.INFO_TRY_AGAIN_LATER).when(decoder).dequeueInputFrame(anyLong());
int result = videoTrackTranscoder.processNextFrame();
verify(decoder).dequeueInputFrame(anyLong());
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void extractAndDecodeFrameWhenNotEos() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(VIDEO_TRACK).when(mediaSource).getSampleTrackIndex();
doReturn(BUFFER_INDEX).when(decoder).dequeueInputFrame(anyLong());
doReturn(sampleFrame).when(decoder).getInputFrame(BUFFER_INDEX);
doReturn(BUFFER_SIZE).when(mediaSource).readSampleData(any(ByteBuffer.class), anyInt());
doReturn(CURRENT_PRESENTATION_TIME).when(mediaSource).getSampleTime();
doReturn(0).when(mediaSource).getSampleFlags();
int result = videoTrackTranscoder.processNextFrame();
verify(mediaSource).readSampleData(eq(sampleFrame.buffer), eq(0));
verify(decoder).queueInputFrame(sampleFrame);
verify(bufferInfo).set(0, BUFFER_SIZE, CURRENT_PRESENTATION_TIME, 0);
verify(mediaSource, atLeast(1)).advance();
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void extractAndDecodeFrameWhenNoBytesRead() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(VIDEO_TRACK).when(mediaSource).getSampleTrackIndex();
doReturn(BUFFER_INDEX).when(decoder).dequeueInputFrame(anyLong());
doReturn(sampleFrame).when(decoder).getInputFrame(BUFFER_INDEX);
doReturn(0).when(mediaSource).readSampleData(any(ByteBuffer.class), anyInt());
doReturn(CURRENT_PRESENTATION_TIME).when(mediaSource).getSampleTime();
doReturn(0).when(mediaSource).getSampleFlags();
int result = videoTrackTranscoder.processNextFrame();
verify(mediaSource).readSampleData(eq(sampleFrame.buffer), eq(0));
verify(decoder).queueInputFrame(sampleFrame);
verify(bufferInfo).set(0, 0, CURRENT_PRESENTATION_TIME, 0);
verify(mediaSource, atLeast(1)).advance();
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void signalDecoderWhenEos() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(VIDEO_TRACK).when(mediaSource).getSampleTrackIndex();
doReturn(BUFFER_INDEX).when(decoder).dequeueInputFrame(anyLong());
doReturn(sampleFrame).when(decoder).getInputFrame(BUFFER_INDEX);
doReturn(-1).when(mediaSource).readSampleData(any(ByteBuffer.class), anyInt());
int result = videoTrackTranscoder.processNextFrame();
verify(mediaSource).readSampleData(eq(sampleFrame.buffer), eq(0));
verify(decoder).queueInputFrame(sampleFrame);
verify(bufferInfo).set(0, 0, -1L, MediaCodec.BUFFER_FLAG_END_OF_STREAM);
assertThat(result, is(TrackTranscoder.RESULT_EOS_REACHED));
}
// endregion: extracting & decoding frames
// region: resizing frames
@Test
public void notResizeWhenNoDecodedFrameReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
doReturn(MediaCodec.INFO_TRY_AGAIN_LATER).when(decoder).dequeueOutputFrame(anyLong());
int result = videoTrackTranscoder.processNextFrame();
verify(decoder, never()).releaseOutputFrame(anyInt(), anyBoolean());
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void resizeWhenDecodedFrameReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = 0;
bufferInfo.presentationTimeUs = CURRENT_PRESENTATION_TIME;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
doReturn(BUFFER_INDEX).when(decoder).dequeueOutputFrame(anyLong());
doReturn(frame).when(decoder).getOutputFrame(BUFFER_INDEX);
int result = videoTrackTranscoder.processNextFrame();
verify(decoder).releaseOutputFrame(BUFFER_INDEX, true);
ArgumentCaptor<Long> presentationTimeCaptor = ArgumentCaptor.forClass(Long.class);
verify(renderer).renderFrame((Frame) isNull(), presentationTimeCaptor.capture());
assertThat(presentationTimeCaptor.getValue(), is(CURRENT_PRESENTATION_TIME * 1000L));
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void signalEncoderWhenEosReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = MediaCodec.BUFFER_FLAG_END_OF_STREAM;
bufferInfo.presentationTimeUs = -1;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
doReturn(BUFFER_INDEX).when(decoder).dequeueOutputFrame(anyLong());
doReturn(frame).when(decoder).getOutputFrame(BUFFER_INDEX);
int result = videoTrackTranscoder.processNextFrame();
verify(decoder).releaseOutputFrame(BUFFER_INDEX, false);
verify(encoder).signalEndOfInputStream();
assertThat(videoTrackTranscoder.lastDecodeFrameResult, is(TrackTranscoder.RESULT_EOS_REACHED));
assertThat(result, is(TrackTranscoder.RESULT_EOS_REACHED));
}
// endregion: resizing decoded frames
// region: receiving & writing encoded frames
@Test
public void notWriteWhenNoEncodedFrameReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
doReturn(MediaCodec.INFO_TRY_AGAIN_LATER).when(encoder).dequeueOutputFrame(anyLong());
int result = videoTrackTranscoder.processNextFrame();
verify(encoder, never()).releaseOutputFrame(anyInt());
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void addTrackWhenEncoderMediaFormatReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
MediaFormat encoderMediaFormat = new MediaFormat();
doReturn(MediaCodec.INFO_OUTPUT_FORMAT_CHANGED).when(encoder).dequeueOutputFrame(anyLong());
doReturn(encoderMediaFormat).when(encoder).getOutputFormat();
doReturn(VIDEO_TRACK).when(mediaTarget).addTrack(any(MediaFormat.class), anyInt());
int result = videoTrackTranscoder.processNextFrame();
ArgumentCaptor<MediaFormat> mediaFormatArgumentCaptor = ArgumentCaptor.forClass(MediaFormat.class);
verify(mediaTarget).addTrack(mediaFormatArgumentCaptor.capture(), eq(VIDEO_TRACK));
assertThat(mediaFormatArgumentCaptor.getValue(), is(encoderMediaFormat));
assertThat(videoTrackTranscoder.targetTrack, is(VIDEO_TRACK));
assertThat(result, is(TrackTranscoder.RESULT_OUTPUT_MEDIA_FORMAT_CHANGED));
}
@Test
public void writeWhenEncodedFrameReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
videoTrackTranscoder.targetTrack = VIDEO_TRACK;
videoTrackTranscoder.duration = DURATION;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = 0;
bufferInfo.size = BUFFER_SIZE;
bufferInfo.presentationTimeUs = CURRENT_PRESENTATION_TIME;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
doReturn(BUFFER_INDEX).when(encoder).dequeueOutputFrame(anyLong());
doReturn(frame).when(encoder).getOutputFrame(BUFFER_INDEX);
int result = videoTrackTranscoder.processNextFrame();
ArgumentCaptor<Integer> targetTrackArgumentCaptor = ArgumentCaptor.forClass(Integer.class);
ArgumentCaptor<ByteBuffer> bufferArgumentCaptor = ArgumentCaptor.forClass(ByteBuffer.class);
ArgumentCaptor<MediaCodec.BufferInfo> bufferInfoArgumentCaptor = ArgumentCaptor.forClass(MediaCodec.BufferInfo.class);
verify(mediaTarget).writeSampleData(targetTrackArgumentCaptor.capture(), bufferArgumentCaptor.capture(), bufferInfoArgumentCaptor.capture());
assertThat(targetTrackArgumentCaptor.getValue(), is(VIDEO_TRACK));
assertThat(bufferArgumentCaptor.getValue(), is(sampleByteBuffers[BUFFER_INDEX]));
assertThat(bufferInfoArgumentCaptor.getValue().presentationTimeUs, is(CURRENT_PRESENTATION_TIME));
assertThat(videoTrackTranscoder.progress, is(CURRENT_PROGRESS));
verify(encoder).releaseOutputFrame(eq(BUFFER_INDEX));
assertThat(result, is(TrackTranscoder.RESULT_FRAME_PROCESSED));
}
@Test
public void finishWhenEosReceived() throws Exception {
videoTrackTranscoder.lastExtractFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastDecodeFrameResult = TrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = TrackTranscoder.RESULT_FRAME_PROCESSED;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = MediaCodec.BUFFER_FLAG_END_OF_STREAM;
bufferInfo.size = 0;
bufferInfo.presentationTimeUs = -1L;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
doReturn(BUFFER_INDEX).when(encoder).dequeueOutputFrame(anyLong());
doReturn(frame).when(encoder).getOutputFrame(BUFFER_INDEX);
int result = videoTrackTranscoder.processNextFrame();
assertThat(videoTrackTranscoder.progress, is(1.0f));
verify(encoder).releaseOutputFrame(eq(BUFFER_INDEX));
assertThat(result, is(TrackTranscoder.RESULT_EOS_REACHED));
}
// endregion: receiving & writing encoded frames
// region: trimming media
@Test(expected = IllegalArgumentException.class)
public void failWhenSelectionEndIsBeforeStart() throws Exception {
MediaRange selection = new MediaRange(42L, 6L);
when(mediaSource.getSelection()).thenReturn(selection);
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(
mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
}
@Test
public void adjustDurationToMediaSelection() throws Exception {
when(sourceMediaFormat.containsKey(MediaFormat.KEY_DURATION)).thenReturn(true);
when(sourceMediaFormat.getLong(MediaFormat.KEY_DURATION)).thenReturn(DURATION);
when(mediaSource.getSelection()).thenReturn(trimmedMediaRange);
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(
mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
assertThat(videoTrackTranscoder.duration, is(SELECTION_END - SELECTION_START));
}
@Test
public void notRenderFrameBeforeSelectionStart() throws Exception {
int tag = 1;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = 0;
bufferInfo.presentationTimeUs = SELECTION_START - 1;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
when(decoder.isRunning()).thenReturn(true);
when(encoder.isRunning()).thenReturn(true);
when(mediaSource.getSelection()).thenReturn(trimmedMediaRange);
when(decoder.dequeueOutputFrame(anyLong())).thenReturn(tag);
when(decoder.getOutputFrame(tag)).thenReturn(frame);
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(
mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
videoTrackTranscoder.lastExtractFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.processNextFrame();
verify(renderer, never()).renderFrame(any(Frame.class), anyLong());
verify(decoder).releaseOutputFrame(tag, false);
}
@Test
public void renderFrameWithinSelection() throws Exception {
int tag = 1;
MediaCodec.BufferInfo bufferInfo = new MediaCodec.BufferInfo();
bufferInfo.flags = 0;
bufferInfo.presentationTimeUs = CURRENT_PRESENTATION_TIME;
Frame frame = new Frame(BUFFER_INDEX, ByteBuffer.allocate(BUFFER_SIZE), bufferInfo);
when(decoder.isRunning()).thenReturn(true);
when(encoder.isRunning()).thenReturn(true);
when(mediaSource.getSelection()).thenReturn(trimmedMediaRange);
when(decoder.dequeueOutputFrame(anyLong())).thenReturn(tag);
when(decoder.getOutputFrame(tag)).thenReturn(frame);
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(
mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
videoTrackTranscoder.lastExtractFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.processNextFrame();
verify(renderer).renderFrame(null, (CURRENT_PRESENTATION_TIME - SELECTION_START) * 1000);
verify(decoder).releaseOutputFrame(tag, true);
}
@Test
public void notDecodeFrameAndAdvanceToOtherTrackAndSendEosWhenFrameAfterSelectionEnd() throws Exception {
int tag = 1;
when(decoder.dequeueInputFrame(anyLong())).thenReturn(tag);
when(decoder.getInputFrame(tag)).thenReturn(sampleFrame);
when(mediaSource.getSelection()).thenReturn(trimmedMediaRange);
when(mediaSource.getSampleTime()).thenReturn(SELECTION_END + 1);
when(mediaSource.getSampleFlags()).thenReturn(0);
when(mediaSource.readSampleData(sampleFrame.buffer, 0)).thenReturn(BUFFER_SIZE);
when(mediaSource.getSampleTrackIndex())
.thenReturn(VIDEO_TRACK)
.thenReturn(VIDEO_TRACK)
.thenReturn(AUDIO_TRACK);
VideoTrackTranscoder videoTrackTranscoder = new VideoTrackTranscoder(
mediaSource,
VIDEO_TRACK,
mediaTarget,
VIDEO_TRACK,
targetVideoFormat,
renderer,
decoder,
encoder);
videoTrackTranscoder.lastDecodeFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.lastEncodeFrameResult = VideoTrackTranscoder.RESULT_EOS_REACHED;
videoTrackTranscoder.processNextFrame();
verify(decoder).queueInputFrame(sampleFrame);
verify(sampleFrame.bufferInfo).set(0, 0, -1, MediaCodec.BUFFER_FLAG_END_OF_STREAM);
assertThat(videoTrackTranscoder.lastExtractFrameResult, is(VideoTrackTranscoder.RESULT_EOS_REACHED));
}
// endregion: trimming media
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,129 |
\part{Cosmological Thermodynamics}
\section{Introduction}
Part I of this article suggests that the concepts of Quantum Cosmology should
be addressed in terms of topological concepts rather than metrical geometric
concepts. \ Gravitational metric concepts enter through congruent subsets of a
thermodynamic topology \cite{rmkpv}. \ A primary objective of this article is
to examine the continuous topological\ evolution of various thermodynamic
systems on a cosmological scale without invoking geometric constraints of
metric. \ As a starting point, it is assumed that thermodynamic systems can be
encoded by exterior differential 1-forms on a 4D variety. \ The environment of
the universe will be considered to be a physical vacuum encoded by a
differential 1-form with a Pfaff topological dimension (or class)
\cite{Schouten} equal to 4. \ A thermodynamic system of Pfaff topological
dimension 4 is considered to be an Open thermodynamic system that can exchange
matter and energy with its neighbors. \ It is a nonequilibrium dissipative
system that supports irreversible evolutionary processes.
Emphasis\ in Part I will be placed upon those processes of continuous
topological evolution which cause observable stars and galaxies to emerge as
metastable topological defects of Pfaff topological (not geometric) dimension
3, embedded in the very dilute cosmological, turbulent, nonequilibrium,
environment of Pfaff topological dimension 4. \ The defect structures are
topologically coherent states with properties similar to those found in
"macroscopic" quantum states. \ Various older versions of the basic ideas may
be found at \cite{RMKBilbao}, \cite{RMKVig2003}, \cite{RMKcos004}. \ Extensive
detail can be found in \cite{vol2}. \ \
A secondary objective presented in Part II is to update the concept of
topological quantization \cite{rmkperiods}, which can yield macroscopic,
topologically coherent, structures on both cosmological as well as microscopic
scales. \ The details depend upon the existence of closed but not exact
singular p-forms that can be used as integrands in deRham period integrals.
The cosmology constructed herein is based upon continuous topological
evolution of thermodynamic systems. \ When compared to the "bottom up" methods
used to understand the universe in terms of properties deduced from the
microscopic quantum world of Bose-Einstein condensates, super conductors, and
superfluids \cite{volovik}, the cosmology herein, based upon continuous
topological evolution, is a "top down" method. \ Both approaches are similar
in that they utilize the idea that topological defects can support both
microscopic and macroscopic topologically coherent (quantum) states.
\ Thermodynamically,\ the "bottom up" method involves low temperature
equilibrium systems, while the "top down" method is based upon nonequilibrium
thermodynamic systems. \
Stars and Galaxies are not equilibrium systems; they are radiating into the
environment. \ They are domains of Pfaff topological dimension 3, while
isolated or equilibrium systems are Pfaff topological dimension 2 or less.
\ Topological defects of Pfaff topological dimension 3 can be far from
equilibrium, and yet can have long metastable, and observable, lifetimes.
\ The thermodynamic method suggests that "dark matter/energy" could have a
mundane explanation in terms of thermodynamic states of Pfaff dimension 2 or
less, representing isolated thermodynamic systems. \ Isolated or equilibrium
thermodynamic domains do not exchange matter or energy with their neighbors,
but could influence gravitational dynamics. \ This topic will be discussed later.
\subsection{Motivation in terms of a Universal van der Waals gas}
As will be demonstrated, an interesting cosmological model for the universe
can be described in terms of a turbulent, dissipative, nonequilibrium, very
dilute, (topologically universal)\footnote{Homeomorphically equivalent}\ van
der Waals gas near its critical point. \ The motivation for treating cosmology
herein from point of view of topological thermodynamics is based upon remarks
made in the Landau-Lifshitz volume on statistical mechanics \cite{LLthermo}.
\ However, the methods used in this article are not statistical, not quantum
mechanical, not metrical, and instead are based on Cartan's methods of
exterior differential forms and their application to the topology of
thermodynamic systems and their continuous topological evolution
\cite{rmkcontopevol}. \
Landau and Lifshitz emphasized that real thermodynamic substances, near the
thermodynamic critical point, exhibit (experimentally) extraordinary large
fluctuations of density and entropy. \ In fact, these authors demonstrate that
for an almost perfect gas near the critical point, the correlations of the
fluctuations can be interpreted as a 1/r potential giving a 1/r$^{2}$ force
law of attraction. \ Hence, as a primitive cosmological model, the almost
perfect gas - such as a very dilute van der Waals gas near the critical point
- yields a reason for both the granularity of the night sky and for the
1/r$^{2}$ force law ascribed to gravitational forces between for massive
aggregates. \ The topological thermodynamic methods used in this current
article lead to a similar possibility: the topological defect structures of a
nonequilibrium environment of Pfaff topological dimension 4 can be related to
a topologically universal structure,\ homeomorphic (deformably equivalent) to
a van der Waals gas. \
It is assumed that physical thermodynamic systems can be encoded in terms of
an exterior differential 1-form of Action (potentials) on a 4D\ variety of
independent variables. \ A Jacobian matrix can be generated in terms of the
partial derivatives of the coefficient functions that define the 1-form of
Action. \ When expressed in terms of intrinsic variables, known as the
similarity invariants, the Cayley-Hamilton 4 dimensional characteristic
polynomial of the Jacobian matrix generates a universal thermodynamic phase
function. \ Interesting topological defect structures can be put into
correspondence with constraints placed upon the similarity (curvature
symmetry) invariants generated by the Cayley-Hamilton 4 dimensional
characteristic polynomial. \ These constraints define equivalence classes of
topological properties.
The characteristic polynomial of the Jacobian matrix, or Phase function, can
be viewed as representing a family of implicit hypersurfaces in 4D. \ The
hypersurface has an envelope which, when further constrained to be a minimal
hypersurface, is homeomorphic to the Gibbs surface of a van der Waals gas.
\ Another, but different, topological constraint is associated with those
domains for which the determinant of the Jacobian matrix is zero. This
topological constraint on the characteristic polynomial leads to a cubic
factor that mimics the equation of state for a van der Waals gas. \ Hence this
universal topological method for describing a low density turbulent
nonequilibrium media leads to the setting (mentioned above) examined
statistically by Landau and Lifschitz in terms of classical fluctuations about
the critical point. \
To repeat, the model presented herein claims that nonequilibrium topological
defects\ in a nonequilibrium 4 dimensional medium represent the stars and
galaxies, which are gravitationally attracted singularities (correlations of
fluctuations of density fluctuations) of a real gas near its critical point.
Note that the Cartan methods do not impose (\textit{a priori)} a constraint of
a metric, connection, or gauge, but do utilize the topological properties
associated with constraints placed on the similarity invariants of the
universal phase function. \
Part I of this 2 part article will focus on the topological features of
thermodynamic systems that can be encoded in terms of a 1-form of Action on a
4D variety, and those processes that cause defects to emerge in terms of
continuous topological (not geometrical) evolution. Part II of this 2 part
article will focus on the methods of (macroscopic) topological quantization in
terms of emergent period integrals of closed but not exact p-forms.
What is missing in this approach (based upon the symmetric similarity
invariants)? \ It is the anti-symmetric features of a thermodynamic systems
which lead to torsion, and the source of charge and spin. \ In a recent
development \cite{rmkpv}, a Physical Vacuum was defined in terms of a vector
space of infinitesimal neighborhoods. \ The sole starting point of the theory
resides with the functional format of a matrix Basis Frame of sixteen
functions which can serve as a basis set for the vector space of
infinitesimals. \ A question remains: \newline"Is there any primitive rational
to choose the functional format of the Basis Frame?" \ It will become apparent
from the current presentation that a possible primitive starting point is to
substitute the Jacobian matrix (constructed from the 1-form of Action that
defines a thermodynamic system) as a starting element of an equivalence class
of Basis Frames. \
\begin{remark}
The bottom line is: \ The fundamental starting point for an understanding of
cosmology is thermodynamics, not geometry.
\end{remark}
\section{Topological Thermodynamics}
The topological thermodynamic methods \cite{vol1} used herein are based upon
Cartan's theory of exterior differential forms. \ The topological methods
offer an understanding of the cosmos which is considerably different from the
geometric approach assumed by the metrical theory of general relativity. \ The
thermodynamic view assumes that the physical systems to be studied can be
encoded in terms of a 1-form of Action Potentials, $A,$ on a 4 dimensional
variety of ordered independent variables, $\{\xi^{1},\xi^{2},\xi^{3},\xi
^{4}\}.$ \ The variety supports a differential volume element $\Omega_{4}%
=d\xi^{1}\symbol{94}d\xi^{2}\symbol{94}d\xi^{3}\symbol{94}d\xi^{4}. $ \ No
metric, no connection, no constraint of gauge symmetry is imposed upon the 4
dimensional variety. \ \ Topological constraints will be imposed in terms of
exterior differential systems $\cite{Bryant}$
In order to make the equations more suggestive to the reader, the symbolism
for the variety of independent variables will be of the format $\{x,y,z,t\},$
but be aware that no constraints of metric or connection are imposed upon this
variety. \ For instance, it is NOT assumed that the variety is euclidean. \ In
that which follows another useful formalism of independent variables will be
constructed in terms of the ordered set of similarity invariant functions,
which are given the symbols $\{X_{M},Y_{G},Z_{A},T_{K}\}.$ \ The similarity
invariant functions are those deduced from the Jacobian matrix of the
coefficients of that 1-form of Action, $A,$ which is presumed to encode the
thermodynamic properties of a physical system. \ \
The 1-form of Action, $A,$ will have components that form a covariant
direction field, $A_{k}(x,y,z,t),$ to within a nonzero factor. \ Evolutionary
processes will be determined in terms of 4 dimensional contravariant direction
fields, $\mathbf{V}_{4}(x,y,z,t)$, to within a nonzero factor. \ Continuous
topological evolution \cite{rmkcontopevol} will be defined in terms of
Cartan's magic formula for the Lie differential, which, when acting on an
exterior differential 1-form of Action, \thinspace$A=A_{k}dx^{k}$, is
equivalent \textit{abstractly} to the first law of thermodynamics. \
\begin{align}
\text{Cartan's Magic Formula \ \ \ }L_{(\mathbf{V}_{4})}A & =i(\mathbf{V}%
_{4})dA+d(i(\mathbf{V}_{4})A)\\
\text{First Law of Thermodynamics \ \ \ \ } & :W+dU=Q,\\
\text{Inexact 1-form of Heat \ \ \ }L_{(\mathbf{V}_{4})}A & =Q\\
\text{Inexact 1-form of Work\ \ \ \ \ \ \ \ \ \ \ \ }W & =i(\mathbf{V}%
_{4})dA,\\
\text{Internal Energy \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }U &
=i(\mathbf{V}_{4})A.
\end{align}
In effect, Cartan's methods establish a topological basis of thermodynamics in
terms of a theory of cohomology. \ The methods can be used to formulate
precise mathematical definitions for many thermodynamic concepts in terms of
topological properties - without the use of statistics or metric constraints.
\ Moreover, the method applies to nonequilibrium thermodynamical systems and
irreversible processes, again without the use of statistics or metric constraints.
\subsection{The Pfaff Topological Dimension}
One of the most useful topological properties that can be used with exterior
differential forms is that property defined as the Pfaff topological
dimension. \ The Pfaff topological dimension is related to the minimal number
M of functions required\ to define the topological properties of the given
form in a pregeometric variety of dimension N. \ Recall that it is possible to
define many (simultaneous) topologies on the same set of elements. \ For any
(or each) given exterior differential 1-form of functions, say $A=A_{k}%
(x,y,z,t)dx^{k},$ it is possible to construct the Pfaff sequence of terms,
$\{A,dA,A\symbol{94}dA,dA\symbol{94}dA\}.$ \ These elements may be used to
construct a Cartan Topology (relative to the specific 1-form chosen
\cite{baldwin}). \ In the Cartan topology, the exterior differential acts as
limit point generator. \ Hence the union of a form and its exterior
differential create the topological closure of the form \cite{vol1}.
For any given 1-form, the Pfaff sequence will contain $M$ successive nonzero
terms equal to or less than $N$, the number of geometric dimensions of the
base independent variables. \ \ The number $M$ is defined as the "Pfaff
topological dimension", or class, of the given 1-form. \ The three important
1-forms of thermodynamics, $A,\ W,$ and $Q,$ can have different Pfaff
dimensions. \ Suppose the 1-form of work is defined in terms of two functions
as $W=PdV.$ \ The Pfaff sequence consists of the terms $\{W,dW,0,0\};$ hence
in this example, the Pfaff dimension of $W$ is 2. \ From the first law, under
the assumption that $W=PdV,$
\begin{align}
Q & =W+dU=PdV+dU,\\
dQ & =dW=dP\symbol{94}dV,\\
Q\symbol{94}dQ & =W\symbol{94}dW+dU\symbol{94}dW=0+dU\symbol{94}%
dP\symbol{94}dV\\
dQ\symbol{94}dQ & =0.
\end{align}
Hence, a Pfaff dimension of 2 for the work 1-form can be associated with a
Pfaff dimension of 3 for the Heat 1-form, unless the Pressure is a function of
the internal energy and the volume. \ In this latter case, the Pfaff dimension
of $Q$ and $W$ are both 2.
In this article, attention will be focused on dissipative turbulent systems
with thermodynamic irreversible processes such that the Pfaff topological
dimensions of $A,\ W,\ $and $Q$ will be maximal and equal to 4. \ (The
techniques can be extended to higher dimensional spaces.) \ These turbulent
systems of Pfaff dimension 4 are not topologically equivalent to Equilibrium
or Isolated systems (for which the topological dimension is 2, at most).
\ Topological defects in the turbulent state will be associated with embedded
sets of space time where the Pfaff topological dimensions are not maximal.
\ It is remarkable that such topological defect sets can form attractors
causing self organization and long lived states of Pfaff dimension 3, which
are far from equilibrium. \ These defects are to be associated with the
emergence of the observable stars and galaxies.
\subsection{Physical Systems}
\subsubsection{Isolated, Closed and Open Systems}
Physical systems and processes are elements of topological categories
determined by the Pfaff topological dimension (or class) of the 1-forms of
Action, $A,$ Work, $W$, and Heat, $Q.$ \ For example, the Pfaff topological
dimension of the exterior differential 1-form of Action, $A,$ determines the
various species of thermodynamic systems in terms of distinct topological
categories: \ %
\begin{align}
Systems & :\text{defined by the Pfaff dimension of }A=\rho A^{(0)}%
\nonumber\\
A\symbol{94}dA & =0\ \ \ \ \ \ \text{Isolated - Pfaff dimension 2}\\
d(A\symbol{94}dA) & =0\ \ \ \ \ \ \text{Closed - Pfaff dimension 3}\\
dA\symbol{94}dA & \neq0.\ \ \ \ \text{Open - Pfaff dimension 4.}%
\end{align}
In classical thermodynamics it is often stated that isolated systems do not
permit transport of energy or matter to the environment. \ Closed systems
permit energy (radiation) transport, but not matter transport to the
environment. \ Open systems permit both energy and matter transport to the
environment. \ Note that these topological specifications as given above are
determined entirely from the functional properties of the physical system
encoded as a 1-form of Action, $A$. \ The system topological categories do not
involve a process, which is assumed to be encoded by some vector direction
field, $\mathbf{V}_{4}.$ $\ $The cosmological model presented herein is based
on an open, Pfaff dimension 4, nonequilibrium, turbulent physical system, with
internal defect structures of lesser Pfaff topological dimension acting as
stars and galactic mass aggregates\footnote{Could it be that "dark matter" is
simply related to those thermodynamic states which are isolated, and are of
Pfaff topological dimension 2 or less?}.
\subsubsection{Equilibrium vs. Non-Equilibrium Systems}
The intuitive idea for an equilibrium system comes from the experimental
recognition that the intensive variables of pressure and temperature become
domain constants in an equilibrium state: \ $dP\Rightarrow0,\ dT\Rightarrow0$.
\ A definition made herein is that the Pfaff dimension of a physical system in
the equilibrium state is at most 2 \cite{Bamberg}. \ The Cartan topology
generated by the elements of the Pfaff sequence for $A$\ is then a connected
topology of one component, $\{A\neq0,dA\neq0,A\symbol{94}dA=0\}.$ \ Although
the Pfaff dimension of $A$ is at most 2 in the equilibrium state, processes in
the equilibrium state are such that the Work 1-form and the Heat 1-form must
be of Pfaff dimension 1. \ For suppose $W=PdV,$ then $dW=dP\symbol{94}%
dV\Rightarrow0$ if the pressure is a domain constant. \ Similarly, suppose
$Q=TdS,$ the $dQ=dT\symbol{94}dS\Rightarrow0$ if the temperature is a domain
constant. \ Hence both $W$ and $Q$ are of Pfaff dimension 1 for this example.
A more stringent sufficient condition for equilibrium can be constructed in
terms of the structure of the system, valid for any choice of process. \ For
if the Pfaff dimension of the 1-form of Action is 1, then $dA\Rightarrow0.$
\ It follows that $W\Rightarrow0,$ hence the Pressure must vanish, and Heat
1-form is a perfect differential, $Q=d(U).$ \
The cosmological model proposed herein presumes that the physical vacuum is of
Pfaff dimension 4, containing defect structures of Pfaff dimension 3, or less.
\ Both non-equilibrium domains of Pfaff dimension 4 or 3 can admit processes
that are thermodynamically irreversible. \ Extremal processes of the
Hamiltonian type do not exist in domains of Pfaff topological dimension 4.
\ The theory of continuous topological evolution indicates that embedded non
equilibrium (they are radiating) topological defects of Pfaff dimension 3, can
emerge in domains of Pfaff topological dimension 4 via irreversible processes.
\ Once formed and self-organized as coherent topological attractors, the
defect structures of Pfaff topological dimension 3 can continue to evolve
along extremal trajectories that are not irreversibly dissipative. \ They can
have finite lifetimes modified by topological fluctuations. \ In this sense,
these topologically coherent defect structures are analogues of "stationary
excited states" far from equilibrium. \
The descriptive words of self-organized states far from equilibrium are
abstracted from the intuition and conjectures of I. Prigogine \cite{Prig}.
\ However, the topological theory presented herein presents for the first time
a solid formal justification (with examples) for the Prigogine conjectures.
\ Precise definitions of equilibrium and nonequilibrium systems, as well as
reversible and irreversible processes can be made in terms of the topological
features of Cartan's exterior calculus. Thermodynamic irreversibility and the
arrow of time are well defined in a topological sense \cite{rmkarw}, a
technique that goes beyond (and without)\ statistical analysis.
\subsubsection{Multiple Components}
One of the most remarkable properties of the Cartan topology generated by a
Pfaff sequence is associated with the fact that when $A\symbol{94}dA=0,$
(Pfaff dimension 2 or less) the physical system is reducible to a single
connected topological component. \ On the other hand when $A\symbol{94}%
dA\neq0,$ (Pfaff dimension 3 or more) the physical system admits more than one
topological component. \ The bottom line is that when the Pfaff dimension is 3
or greater (such that conditions of the Frobenius unique integrability theorem
are not satisfied), solution uniqueness to the Pfaffian differential equation,
$A=0,$ is lost. \ If there exist solutions, there is more than one. \ Such
concepts lead to propagating discontinuities (signals), envelope solutions
(Huygen wavelets), an edge of regression and lack of time reversal invariance,
and the existence of irreducible affine torsion in the theory of connections.
\ \ \ It is the opinion of this author that a dogmatic insistence on
uniqueness historically has hindered the understanding of irreversibility and
nonequilibrium systems.
\subsection{Processes}
\subsubsection{Reversible and Irreversible Processes}
The Pfaff topological dimension of the exterior differential 1-form of Heat,
$Q,$ determines important topological categories of processes. \ From
classical thermodynamics "The quantity of heat in a reversible process always
has an integrating factor" \cite{Goldenblat} \cite{Morse} . \ Hence, from the
Frobenius unique integrability theorem, all reversible processes are such that
the Pfaff dimension of $Q$ is less than or equal to 2. \ Irreversible
processes are such that the Pfaff dimension of $Q$ is greater than 2. \ A
dissipative irreversible topologically \textit{turbulent} process is defined
when the Pfaff dimension of $Q$ is 4. \ \
\begin{align}
Processes & :\text{defined by the Pfaff dimension }Q\nonumber\\
Q\symbol{94}dQ & =0\ \ \ \ \ \text{\ \ Reversible - Pfaff dimension 2 }\\
d(Q\symbol{94}dQ) & \neq0.\ \ \ \ \text{\ Turbulent - Pfaff dimension 4. }%
\end{align}
Note that the Pfaff dimension of $Q$ depends on both the choice of a process,
$\mathbf{V}_{4},$ and the system, $A$, upon which it acts. \ As reversible
thermodynamic processes are such that $Q\symbol{94}dQ=0,$ and irreversible
thermodynamic processes are such that $Q\symbol{94}dQ\neq0,$ Cartan's formula
of continuous topological evolution can be used to determine if a given
process, $\mathbf{V}_{4},$ acting on a physical system, $A$, is
thermodynamically reversible or not: \ \
\begin{equation}
\left[
\begin{array}
[c]{c}%
\text{Reversible Processes\ }\mathbf{V}_{4}:\text{\ }L_{(\mathbf{V}_{4}%
)}A\symbol{94}L_{(\mathbf{V}_{4})}dA=0,\\
\text{Irreversible Processes }\mathbf{V}_{4}:L_{(\mathbf{V}_{4})}%
A\symbol{94}L_{(\mathbf{V}_{4})}dA\neq0.
\end{array}
\right]
\end{equation}
In this article it is assumed that the cosmological background for space-time
belongs to the dissipative irreversible turbulent\ nonequilibrium category,
where the Pfaff topological dimension (or class) is maximal and equal to 4,
almost everywhere, for each of the 1-forms of Action, $A,$ Work, $W$, and
Heat, $Q.$ \ Of particular interest will be those subsets of space and time
where the turbulent nonequilibrium category admits, or evolves into,
topological defects such that the Pfaff topological dimension for all three
1-forms is no longer maximal and equal to 4. \ Remarkably, Cartan's magic
formula can be used to describe the continuous dynamic possibilities of both
reversible and irreversible processes, in equilibrium or nonequilibrium
systems, even when the evolution induces topological change, transitions
between excited states, and changes of phase, such as condensations.
It is important to note that the velocity field need not be topologically
constrained such that it is singularly parameterized. \ That is, the
evolutionary processes described by Cartan's magic formula are not necessarily
restricted to vector fields that satisfy the topological constraints of
kinematic perfection, $dx^{k}-V^{k}dt=0$. \ A discussion of topological
fluctuations and an example fluctuation process is described in section 6.
\subsubsection{Adiabatic Processes - Reversible and Irreversible}
The topological formulation permits a precise definition to be made for both
reversible and an irreversible adiabatic processes in terms of the topological
properties of $Q.$ \ On a geometrical space of N dimensions, a 1-form will
admit N-1 vector fields such that $i(V_{A})Q=0.$ \ Such processes $V_{A}$ are
defined as adiabatic processes \cite{Bamberg}. \ Note that adiabatic processes
are defined by vector direction fields, to within an arbitrary factor,
$\beta(x,y,z,t)$. \ That is, if $i(V_{A})Q=0,$ then it is also true that
$i(\beta V_{A})Q=0.$ The differences between the inexact 1-forms of Work and
Heat become obvious in terms of the topological format. \ Both 1-forms depend
on the process and on the physical system. \ However, Work is\ always
transversal to the process, as $i(\mathbf{V}_{4})W=i(\mathbf{V}_{4}%
)i(\mathbf{V}_{4})dA=0,$ but Heat is\ not, as $i(\mathbf{V}_{4})Q=i(\mathbf{V}%
_{4})dU\Rightarrow0,$ only for adiabatic processes.
It is not obvious that the adiabatic direction fields are such that the Pfaff
dimension of $Q$ is 2. \ That is, it is not obvious that $Q$ can be written in
the form, $Q=TdS,$ as is possible on the manifold of equilibrium states.\ From
the Cartan formulation it is apparent that if $Q$ is not zero, then%
\begin{align}
i(\mathbf{V}_{A})L_{(\mathbf{V}_{A})}A & =i(\mathbf{V}_{A})i(\mathbf{V}%
_{A})dA+i(\mathbf{V}_{A})d(i(\mathbf{V}_{A})A)\\
& =0+i(\mathbf{V}_{A})d(i(\mathbf{V}_{A})A)=i(\mathbf{V}_{A})Q
\end{align}
Hence, for an Adiabatic process:%
\begin{equation}
\text{Adiabatic process }0+i(\mathbf{V}_{A})d(i(\mathbf{V}_{A})A)=i(\mathbf{V}%
_{A})Q\Rightarrow0,\ \ Q\neq0.
\end{equation}
A reversible process is defined such that $Q$ is less than Pfaff dimension 3,
or $Q\symbol{94}dQ=0$ \ Hence $i(\mathbf{V}_{A})(Q\symbol{94}dQ)=0.$ \ \ But
\begin{equation}
i(\mathbf{V}_{A})(Q\symbol{94}dQ)=(i(\mathbf{V}_{A})Q)\symbol{94}%
dQ-Q\symbol{94}i(\mathbf{V}_{A})dQ
\end{equation}
which permits reversible and irreversible adiabatic processes to be well
defined\footnote{It is apparent that i(V)Q= 0 defines an adiabatic process,
but not necessarily a reversible adiabatic process. \ This topological point
clears up certain misconceptions that appear in the literature.} when $Q\neq0$:%
\begin{align}
\text{Reversible Adiabatic Process } & =-Q\symbol{94}i(\mathbf{V}%
_{A})dQ\Rightarrow0,~i(\mathbf{V}_{A})Q\Rightarrow0,\\
\text{Irreversible Adiabatic Process } & =-Q\symbol{94}i(\mathbf{V}%
_{A})dQ\neq0,~\ ~i(\mathbf{V}_{A})Q\Rightarrow0.
\end{align}
It is certainly true that if $L_{(\mathbf{V})}A=Q=0,$ \textit{identically},
then all such processes are adiabatic, and reversible. \ In such cases, the
Cartan formalism implies that $W+dU=0.$ \ \ Such systems are elements of the
Hamiltonian class of processes, where $W=d\Theta$. \ Recall that \textit{all}
Hamiltonian processes are thermodynamically reversible. \ Hamiltonian
processes are adiabatic when the internal energy $U=(i(V)A)$ is an
evolutionary invariant. \ %
\begin{align}
\text{Hamiltonian Adiabatic Process } & =L_{(\mathbf{V})}%
\{i(V)A\}=i(V)Q=0,\text{ }\\
W & =i(V)dA=d\Theta,\ \ \\
i(V)W & =0,\ \ \ \ \ i(V)A=U.
\end{align}
Note that for a given 1-form of heat, $Q$, it is possible to construct a
matrix of N-1 null vectors, and then to compute the adjoint matrix of
cofactors transposed to create the unique direction field (to within a
factor), $\mathbf{V}_{NullAdjoint}.$ \ Evolution in the direction of
$\mathbf{V}_{NullAdjoint}$ does not represent an adiabatic process path, as
$i(\mathbf{V}_{NullAdjoint})Q\neq0$. \ For a given $Q$, the N-1 null vectors
need not span a smooth hypersurface whose surface normal is proportional to a
gradient field. \ The components of the 1-form may be viewed as the normal
vector to an implicit hypersurface, but the implicit hypersurface is not
necessarily defined as the zero set of some function. \
\subsubsection{Topological Torsion}
For maximal, nonequilibrium, turbulent systems in space-time, the maximal
element in the Pfaff sequence generated by $A,W,$ or $Q,$ is a 4-form. \ On
the geometric space of 4 independent variables, every 4-form is globally
closed, in the sense that its exterior differential vanishes everywhere. \ It
follows that every 4-form is exact and can be generated by the exterior
differential of a 3-form. \ The exterior differential of the 3-form is related
to the concept of a divergence of a contravariant direction (vector) field.
\ Most of the development in this article will be devoted to the study of such
3-forms, and their kernels. \ It is a remarkable fact that all 3-forms admit
integrating denominators, such that their exterior differential of a rescaled
3-form is zero almost everywhere. \ Space time points upon which the
denominator has a zero value form defect topological structures.
When the Action for a physical system is of Pfaff dimension 4, there exists a
unique direction field, $\mathbf{T}_{4},$ defined as the topological torsion
4-vector, that can be evaluated \textit{entirely} in terms of those component
functions of the 1-form of Action which define the physical system. \ To
within a factor, this direction field\footnote{A direction field is defined by
the components of a vector field which establish the "line of action" of the
vector in a projective sense. \ An arbitrary factor times the direction field
defines the same projective line of action, just reparameterized. \ In metric
based situations, the arbitrary factor can be interpreted as a renormalization
or conformal factor.} has the four components of the 3-form $A\symbol{94}dA,$
with the properties such that%
\begin{align}
i(\mathbf{T}_{4})\Omega_{4} & =A\symbol{94}dA\\
W & =i(\mathbf{T}_{4})dA=\sigma\ A,\\
U & =i(\mathbf{T}_{4})A=0,\\
Q\symbol{94}dQ & =L_{(\mathbf{T}_{4})}A\symbol{94}L_{(\mathbf{T}_{4}%
)}dA=\sigma^{2}A\symbol{94}dA\\
dA\symbol{94}dA & =2\ \sigma\ \Omega_{4}.
\end{align}
Hence, evolution in the direction of $\mathbf{T}_{4}$ is thermodynamically
irreversible, when $\sigma\neq0$ and $A$ is of Pfaff dimension 4. \ The kernel
of this vector field is defined as the zero set under the mapping induced by
exterior differentiation. \ In engineering language, the kernel of this vector
field are those point sets upon which the divergence of the vector field
vanishes. \ The Pfaff dimension of the Action 1-form is 3 in the defect
regions defined by the kernel of $\mathbf{T}_{4}$.
For purposes of more rapid comprehension, consider a 1-form of Action, $A$,
with an exterior differential, $dA,$ and a notation that admits an
electromagnetic interpretation ($\mathbf{E=-\partial A/\partial}t-\nabla\phi,
$ and $\mathbf{B}=\nabla\times\mathbf{A)}\footnote{The bold letter
$\mathbf{A}$ represents the first 3 components of the 4 vector of potentials,
with the order in agreement with the ordering of the independent variables.
\ The letter A represents the 1-form of Action.}.$ \ The explicit format of
$\ \textbf{T}_4$ becomes:
\begin{align}
\mathbf{T}_{4} & =-[\mathbf{E}\times\mathbf{A}+\mathbf{B}\phi,\ \mathbf{A}%
\circ\mathbf{B]}\text{ \ Topological Torsion 4 vector}\mathbf{,}\\
A\symbol{94}dA & =i(\mathbf{T}_{4})\Omega_{4}\\
& ={\small T}_{4}^{x}{\small dy\symbol{94}dz\symbol{94}dt-T}_{4}%
^{y}{\small dx\symbol{94}dz\symbol{94}dt+T}_{4}^{z}{\small dx\symbol{94}%
dy\symbol{94}dt-T}_{4}^{t}{\small dx\symbol{94}dy\symbol{94}dz,}\\
dA\symbol{94}dA & =2(\mathbf{E}\circ\mathbf{B)}\ \Omega_{4}\\
& =\{{\small \partial T}_{4}^{x}{\small /\partial x+\partial T_{4}%
^{y}/\partial y+\partial T_{4}^{z}/\partial z+\partial T_{4}^{t}/\partial
t\}}\ \Omega_{4}\mathbf{.}%
\end{align}
When the divergence of the topological torsion vector is not zero, $%
\sigma=(\textbf{E}\circ\textbf{B)}\neq0,$ and $A$ is of Pfaff dimension 4,
\thinspace$W$ is of Pfaff dimension 4, and $Q$ is of Pfaff dimension 4. \ The
process generated by $\textbf{T}_4$ is thermodynamically irreversible. \ The
evolution of the volume element relative to the irreversible process
$\textbf{T}_4$\ is given by the expression,%
\begin{align}
L(\mathbf{T}_{4})\Omega_{4} & =i(\mathbf{T}_{4})d\Omega_{4}+d(i(\mathbf{T}%
_{4})\Omega_{4})\\
& =0+d(A\symbol{94}dA)=2(\mathbf{E}\circ\mathbf{B)}\ \Omega_{4}.
\end{align}
Hence, the differential volume element (and therefore the turbulent
cosmological universe)\ is expanding or contracting depending on the sign and
magnitude of $\mathbf{E}\circ\mathbf{B.}$ \ In a fluid model, the coefficient
$\mathbf{E}\circ\mathbf{B}$ plays the role of a bulk viscosity coefficient.
If $A$ is (or becomes) of Pfaff dimension 3, then $dA\symbol{94}%
dA\Rightarrow0$ which implies that $\sigma^{2}\Rightarrow0,$ but
$A\symbol{94}dA\neq0.$ \ The differential volume element $\ \Omega_{4}~$\ is
subsequently an evolutionary invariant, and evolution in the direction of the
topological torsion vector is thermodynamically reversible. \ The physical
system is not in equilibrium, but the divergence free $\mathbf{T}_{4}$
evolutionary process forces the Pfaff dimension of $W$ to be zero, and the
Pfaff dimension of $Q$ to be at most 1. \ Indeed, a divergence free
$\mathbf{T}_{4}$ evolutionary process has a Hamiltonian representation. \ \ In
the domain of Pfaff dimension 3 for the Action, $A$, the subsequent continuous
evolution of the system, $A$, relative to the process $\mathbf{T}_{4},$
proceeds in an energy conserving manner, representing a "stationary" or
"excited" state far from equilibrium. \ These excited states can be
interpreted as the evolutionary topological defects in the turbulent
dissipative system of Pfaff dimension 4.
On a geometric domain of 4 dimensions, assume that the evolutionary process
generated by $\mathbf{T}_{4}$ starts from an initial condition (or state)
where the Pfaff topological dimension of $A$ is also 4. \ Depending on the
sign of the divergence of $\mathbf{T}_{4},$ the process follows an
irreversible path for which the divergence represents an expansion or a
contraction. \ If the irreversible evolutionary path is attracted to a region
(or state) where the Pfaff topological dimension of the 1-form of Action is 3,
then $\mathbf{E\circ B}$ becomes (or has decayed to) zero. \ The zero set of
the function $\mathbf{E\circ B}$ defines a hypersurface in the 4 dimensional
space. \ If the process remains trapped on this hypersurface of Pfaff
dimension 3, $\mathbf{E\circ B}$ remains zero, and the $\mathbf{T}_{4}$
process becomes an extremal field. \ Such extremal fields are such that the
virtual work 1-form vanishes, $W=$ $i(\mathbf{T}_{4})dA=0,$ and the now
reversible $\mathbf{T}_{4}$ process has a Hamiltonian representation. \ The
system is conservative in a Hamiltonian sense, but it is in an "excited" state
on the hypersurface that is far from equilibrium, as the Pfaff dimension of
the 1-form of Action is 3, and not 2. \ (Further evolution could lead to limit cycles.)
The fundamental claim made in this article is that it is these topological
defects, that self organize (emerge) from the dissipative irreversible
evolution of the turbulent state into "stationary metastable" states far from
equilibrium, that form the stars and the galaxies of the cosmos. \ They are
the long lived remnants or "wakes" generated from irreversible processes in
the dissipative nonequilibrium turbulent medium.
\section{Thermodynamic Cosmology}
\subsection{The Jacobian Matrix of the Action 1-form.}
The idea is to express the Jacobian matrix of the coefficient functions that
define the 1-form of Action, $A$, in terms of "universal" coordinates.
\ \ These universal coordinates will be the similarity invariants of the
Jacobian matrix. \ For a 1-form of Action of Pfaff topological dimension 4,
the Cayley-Hamilton theorem produces a Universal Phase function as a
polynomial of 4th degree. \ What is remarkable about this Universal Phase
function is that it has properties that are homeomorphically deformable into
the format of a classic van der Waals gas. \ It is this universality that
gives credence to the idea that the universe could be a nonequilibrium van der
Waals gas near its critical point.
\subsubsection{The Universal Characteristic Phase Function}
The 1-form of Action, used to encode a physical system, contains other useful
topological information, as well as geometric information. \ Consider the
turbulent thermodynamic state generated by a 1-form of Action, $A,$ of Pfaff
topological dimension 4. \ \ The component functions of the Action 1-form can
be used to construct a 4x4 Jacobian matrix of partial derivatives, $\left[
\mathbb{J}_{jk}\right] =[\partial(A_{j})/\partial x^{k}] $. \ In general,
this Jacobian matrix will be a 4 x 4 matrix that satisfies a 4th order
Cayley-Hamilton characteristic polynomial equation, $\Theta(x,y,z,t;\ \Psi
)=0,$ where $\Psi$ is a possibly complex order parameter with 4 perhaps
complex roots $\rho_{k}$ representing the complex eigenvalues of the Jacobian
matrix. \ %
\begin{equation}
\Theta(x,y,z,t;\ \Psi)=\Psi^{4}-X_{M}\Psi^{3}+Y_{G}\Psi^{2}-Z_{A}\Psi
^{1}+T_{K}\Rightarrow0.
\end{equation}
The functions $X_{M}(x,y,z,t),Y_{G}(x,y,z,t),Z_{A}(x,y,z,t),T_{K}(x,y,z,t)$
are the similarity invariants of the Jacobian matrix. \ If the eigenvalues are
distinct, then the similarity invariants are given by the expressions:%
\begin{align}
X_{M} & =\rho_{1}+\rho_{2}+\rho_{3}+\rho_{4},\\
Y_{G} & =\rho_{1}\rho_{2}+\rho_{2}\rho_{3}+\rho_{3}\rho_{1}+\rho_{4}\rho
_{1}+\rho_{4}\rho_{2}+\rho_{4}\rho_{3},\\
Z_{A} & =\rho_{1}\rho_{2}\rho_{3}+\rho_{4}\rho_{1}\rho_{2}+\rho_{4}\rho
_{2}\rho_{3}+\rho_{4}\rho_{3}\rho_{1},\\
T_{K} & =\rho_{1}\rho_{2}\rho_{3}\rho_{4}.
\end{align}
The similarity invariants may be considered as a coordinate map from the
original variety of independent variables, $\{x,y,z,t\}\Rightarrow
\{X_{M},Y_{G},Z_{A},T_{K}\}.$ When the similarity invariants are treated as
generalized coordinates, then the characteristic polynomial becomes a
Universal Phase function, and will be used to encode universal thermodynamic properties.
\subsubsection{Minimal surfaces}
The Universal Phase function, $\Theta,$ may be considered as a family of
hypersurfaces in the 4 dimensional space, $\{X_{M},Y_{G},Z_{A},T_{K}\}$ with a
complex family (order) parameter, $\Psi.$ \ Moreover, it should be realized
that the Universal Phase Function is a holomorphic function, $\Theta
=\phi+i\chi$ in the complex variable $\Psi=u+iv.$ \ That is%
\begin{equation}
\Theta(X_{M},Y_{G},Z_{A},T_{K};\ \Psi)\Rightarrow\phi+i\chi,\
\end{equation}
where
\begin{align}
\phi & =u^{4}-6u^{2}v^{2}+v^{4}-X_{M}(u^{3}-3uv^{2})+Y_{G}(u^{2}-v^{2}%
)-Z_{A}u+T_{K}\\
\chi & =4u^{3}v-4uv^{3}-X_{M}(3u^{2}v-v^{3})+2Y_{G}uv-Z_{A}v.
\end{align}
As such, in the 4D space of two complex variables, \{$\phi+i\chi,u+iv\},$
according to the theorem of Sophus Lie, any such holomorphic function produces
a pair of conjugate \textit{minimal} surfaces in the 4 dimensional space
$\{\phi,\chi,u,v\}.$ \ It follows that there exist a sequence of maps,
\begin{equation}
\{x,y,z,t\}\Rightarrow\{X_{M},Y_{G},Z_{A},T_{K}\}\Rightarrow\{\phi,\chi,u,v\}
\end{equation}
such that the family of hypersurfaces can be decomposed into a pair of
conjugate minimal surface components. \ The criteria for a minimal surface is
equivalent to the idea that $X_{M}=0.$ \ By suitable renormalization, the
similarity invariant $X_{M}$ is equivalent to the Mean Curvature of the hypersurface.
\subsection{Envelopes}
The theory of implicit hypersurfaces focuses attention upon the possibility
that the Universal Phase function has an envelope. \ The existence of an
envelope depends upon the possibility of finding a simultaneous solution to
the two implicit surface equations of the family:
\begin{equation}
\Theta(x,y,z,t;\ \Psi)=\Psi^{4}-X_{M}\Psi^{3}+Y_{G}\Psi^{2}-Z_{A}\Psi
+T_{K}\Rightarrow0.
\end{equation}%
\begin{equation}
\text{ \ }\partial\Theta/\partial\Psi=\Theta_{\Psi}=4\Psi^{3}-3X_{M}\Psi
^{2}+2Y_{G}\Psi-Z_{A}\Rightarrow0.
\end{equation}
For the envelope to be smooth, it must be true that $\partial^{2}%
\Theta/\partial\Psi^{2}=\Theta_{\Psi\Psi}\neq0,$ and that the exterior 2-form,
$d\Theta\symbol{94}d\Theta_{\Psi}\neq0$ subject to the constraint that the
family parameter is a constant: $d\Psi=0.$ \ The envelope as a smooth
hypersurface does not exist unless both conditions are satisfied. \ \ Recall
that the envelope, if it exists, is a hypersurface in the space of similarity
coordinates, $\{X_{M},Y_{G},Z_{A},T_{K}\}.$
The envelope is determined by the discriminant of the Phase Function
polynomial, which as a zero set is equal to a universal hypersurface in the 4
dimensional space of similarity variables $\{X_{M},Y_{G},Z_{A},T_{K}\}.$
\ This function can be written in terms of the similarity "coordinates"
(suppressing the subscripts) :%
\begin{align}
& \text{Discriminant of the Universal Phase Function}\nonumber\\
& {\small =}{\small 18X}^{3}{\small ZYT-27Z}^{4}{\small +Y}^{2}{\small X}%
^{2}{\small Z}^{2}{\small -4Y}^{3}{\small X}^{2}{\small T+144YX}^{2}%
{\small T}^{2}\\
& {\small +18XZ}^{3}{\small Y-192XZT}^{2}{\small -6X}^{2}{\small Z}%
^{2}{\small T+144TZ}^{2}{\small Y-4X}^{3}{\small Z}^{3}\\
& {\small -27X}^{4}{\small T}^{2}{\small -4Y}^{3}{\small Z}^{2}%
{\small +16Y}^{4}{\small T-128Y}^{2}{\small T}^{2}{\small +256T}%
^{3}{\small -80XZY}^{2}{\small T.}%
\end{align}
The discriminant has eliminated the family order parameter. \ \ Remarkably, if
the linear similarity invariant related to the Mean Curvature is set to zero,
$X_{M}\Rightarrow0,$ then the constrained discriminant describes a universal
swallow tail surface homeomorphic (deformable) to the Gibbs surface (see the
figure below) of a van der Waals gas (subscripts suppressed):%
\begin{align}
& \text{Universal Gibbs Swallowtail Envelope }(X=0,Y,Z,T)\\
& ={\small -27Z}^{4}{\small +144TZ}^{2}{\small Y-4Y}^{3}{\small Z}%
^{2}{\small +16Y}^{4}{\small T-128Y}^{2}{\small T}^{2}{\small +256T}%
^{3}\Rightarrow0.
\end{align}
In other words, the Gibbs function for a van der Waals gas is a universal idea
associated with minimal hypersurfaces, $X_{K}$ $=0$, of thermodynamic systems
of Pfaff topological dimension 4. \
\begin{center}
The 26 kb color presentation of Figure 1 can be downloaded from
http://www22.pair.com/csdc/pdf/univgibb.jpg
\textbf{Fig 1. \ Universal Topological Gibbs function.}
\end{center}
The similarity coordinate $T_{K}$ plays the role of the Gibbs free energy, in
terms of the Pressure $(\symbol{126}Z_{A})$ and the Temperature $(\symbol{126}%
Y_{G})$. \ The Spinodal line as a limit of phase stability, and the critical
point are ideas that come from the study of a van der Waals gas, but herein it
is apparent that these concepts are universal topological concepts that remain
invariant with respect to deformations. \ The universal formulas for such
constraints are presented in the next section. \ The result is that all
thermodynamic systems of Pfaff topological dimension 4 are deformably
equivalent to a van der Waals gas.
It is important to recognize that the development of a universal
nonequilibrium van der Waals gas has not utilized the concepts of metric,
connection, statistics, relativity, gauge symmetries, or quantum mechanics.
\subsubsection{The Edge of Regression and Self Intersections}
The envelope is smooth as long as $\partial^{2}\Theta/\partial\Psi^{2}%
=\Theta_{\Psi\Psi}\neq0,$ and $d\Theta\symbol{94}d\Theta_{\Psi}\neq0,$ subject
to the further constraint that the family parameter is a constant: $d\Psi=0.$
\ If $d\Theta\symbol{94}d\Theta_{\Psi}\neq0$, but $\Theta_{\Psi\Psi}=0,$ then
the envelope has a self intersection singularity. \ If $d\Theta\symbol{94}%
d\Theta_{\Psi}=0$, but $\Theta_{\Psi\Psi}\neq0,$ there is no self
intersection, and no envelope. \
If the envelope exists, further singularities are determined by the higher
order partial derivatives of the Universal Phase function with respect to
$\Psi$. \
\begin{equation}
\partial^{2}\Theta/\partial\Psi^{2}=\Theta_{\Psi\Psi}=12\Psi^{2}-6X_{M}%
\Psi+2Y_{G}.
\end{equation}%
\begin{equation}
\partial^{3}\Theta/\partial\Psi^{3}=\Theta_{\Psi\Psi\Psi}=24\Psi-6X_{M}%
\end{equation}
When $\partial^{3}\Theta/\partial\Psi^{3}=\Theta_{\Psi\Psi\Psi}\neq0,$ and
$d\Theta\symbol{94}d\Theta_{\Psi}\symbol{94}d\Theta_{\Psi\Psi}\neq0$, the
envelope terminates in a edge of regression. \ The edge of regression is
determined by the simultaneous solution of \ $\Theta=0,\Theta_{\Psi}=0$ and
$\Theta_{\Psi\Psi}=0.$ \ For the minimal surface representation of the Gibbs
surface for a van der Waals gas, the edge of regression defines the Spinodal
line of ultimate phase stability. \ The edge of regression is evident in the
Swallowtail figure\ (above) describing the Gibbs function for a van der Waals
gas. \
If $\Theta_{\Psi\Psi\Psi}=0,$ then for $X_{M}=0,$ it follows that
$Y_{G}=0,\ Z_{A}=0,\ T_{K}=0,$ which defines the critical point of the \ Gibbs
function for the van der Waals gas. \ In other words, the critical point is
the zero of the 4-dimensional space of similarity coordinates.
If $\Theta_{\Psi\Psi}=0,$ then for $X_{M}=0$ the envelope has a self
intersection. \ It follows from $\Theta_{\Psi\Psi}=0,$ that $\Psi^{2}%
=-Y_{G}/6,$ which when substituted into%
\begin{equation}
\Theta_{\Psi}=4\Psi^{3}+2Y_{G}\Psi-Z_{A}\Rightarrow0,
\end{equation}
yields the%
\begin{equation}
\text{Universal Gibbs Edge of Regression:\ }Z_{A}^{2}+Y_{G}^{3}(8/27)=0,
\end{equation}
which defines the Spinodal line, of the minimal surface representation for a
universal nonequilibrium van der Waals gas, in terms of
"similarity"\ coordinates. \
\ Within the swallow tail region the "Gibbs" surface has 3 real roots and
outside the swallow tail region there is a unique real root. \ The edge of
regression furnished by the Cardano function defines the transition between
real and imaginary root structures. \ The details of the universal
nonequilibrium van der Waals gas in terms of envelopes and edges of regression
with complex molal densities or order parameters will be presented elsewhere.
\ These systems are not equilibrium systems for the Pfaff dimension is not 2.
\ \ Of obvious importance is the idea that the a zero value for both $Z_{G}$
and $T_{K}$ are required to reduce the Pfaff dimension to 2, which is the
necessary condition for an isolated or equilibrium system.
\subsection{Ginsburg Landau Currents}
The Universal Phase function can be solved for the determinant of the Jacobian
matrix, which is equal to the similarity invariant $T_{K},$%
\begin{equation}
T_{K}=-\{\Psi^{4}-X_{M}\Psi^{3}+Y_{G}\Psi^{2}-Z_{A}\Psi\}.
\end{equation}
All determinants are, in effect, N - forms on the domain of independent
variables. \ All N-forms can be related to the exterior differential of some
N-1 form or current, $J.$ \ Hence%
\begin{equation}
dJ=K\Omega_{4}=div\mathbf{J}+\partial\rho/\partial t=-(\Psi^{4}-X_{M}\Psi
^{3}+Y_{G}\Psi^{2}-Z_{A}\Psi)\Omega_{4}.
\end{equation}
For currents of the form%
\begin{align}
\mathbf{J} & =grad\ \Psi,\\
\rho & =\Psi,
\end{align}
the Universal Phase function generates the universal Ginsburg Landau equations%
\begin{equation}
\nabla^{2}\Psi+\partial\Psi/\partial t=-(\Psi^{4}-X_{M}\Psi^{3}+Y_{G}\Psi
^{2}-Z_{A}\Psi),.
\end{equation}
and establishes contact with the "bottom up" methods.
\subsection{Singularities as defects of Pfaff dimension 3}
The family of hypersurfaces can be topologically constrained such that the
topological dimension is reduced, and/or constraints can be imposed upon
functions of the similarity variables forcing them to vanish. \ Such regions
\ in the 4 dimensional topological domain indicate topological defects or
thermodynamic changes of phase. \ It is remarkable that for a given 1-form of
Action there are an infinite number rescaling functions, $\lambda,$ such that
the Jacobian matrix $\left[ \mathbb{J}_{jk}^{scaled}\right] =[\partial
(A/\lambda)_{j}/\partial x^{k}]$ is singular (has a zero determinant). \ \ For
if the coefficients of any 1-form of Action are rescaled by a divisor
generated by the Holder norm,
\begin{equation}
\text{Holder Norm: \ }\lambda=\{a(A_{1})^{p}+b(A_{2})^{p}+c(A_{3})^{p}%
+e(A_{4})^{p}\}^{m/p},\label{holder}%
\end{equation}
then the rescaled Jacobian matrix%
\begin{equation}
\left[ \mathbb{J}_{jk}^{scaled}\right] =[\partial(A/\lambda)_{j}/\partial
x^{k}]
\end{equation}
will have a zero determinant, for any index p, any set of isotropy or
signature constants, a, b, c, e, if the homogeneity index is equal to unity:
$m=1$. \ This homogeneous constraint implies that the similarity invariants
become projective invariants, not just equi-affine invariants. \ Such species
of topological defects can have the image of a 3-dimensional implicit
characteristic hypersurface in space-time:%
\begin{equation}
\text{Singular hypersurface in 4D: \ }\det[\partial(A/\lambda)_{j}/\partial
x^{k}]\Rightarrow0
\end{equation}
The singular fourth order Cayley-Hamilton polynomial of $\left[
\mathbb{J}_{jk}\right] $ then will have a cubic polynomial factor with one
zero eigenvalue. \
For example, consider the simple case where the determinant of the Jacobian
vanishes: $T_{K}\Rightarrow0.$ \ Then the Phase function becomes%
\begin{align}
\text{Universal Equation of State} & \text{: \ }\Theta(\{X_{M},Y_{G}%
,Z_{A},T_{K}=0\};\ \Psi)\label{pvt}\\
& =\Psi(\Psi^{3}-X_{M}\Psi^{2}+Y_{G}\Psi-Z_{A})\Rightarrow0.
\end{align}
The space has been topologically reduced to 3 dimensions (one eigen value is
zero), and the zero set of the resulting singular Universal Phase function
becomes a universal cubic equation that is homeomorphic to the cubic equation
of state for a van der Waals gas.
When the rescaling factor $\lambda$ is chosen such that $p=2,a=b=c=1,m=1$,
then the Jacobian matrix, $\left[ \mathbb{J}_{jk}\right] ,$ is equivalent to
the "Shape" matrix for an implicit hypersurface in the theory of differential
geometry. \ Recall that the homogeneous similarity invariants can be put into
correspondence with the linear Mean curvature, $X_{M}\Rightarrow C_{M}$, the
quadratic Gauss curvature, $Y_{G}\Rightarrow C_{G}$, and the cubic Adjoint
curvature, $Z_{A}\Rightarrow C_{A},$ of the hypersurface. \ The characteristic
cubic polynomial can be put into correspondence with a nonlinear extension of
an ideal gas \textit{not necessarily} in an equilibrium state. \
\subsection{The Universal van der Waals gas}
More that 100 years ago van der Waals introduced into the science of
thermodynamics the equation of state now called the van der Waals gas:%
\begin{equation}
P=\rho RT/(1-b\rho)+a\rho^{2}%
\end{equation}
The van der Waals equation may be considered as a cubic constraint on the
space of variables $\{n;P,V,T\}$ where $\rho=n/V$ is defined as the molar density.%
\begin{equation}
\rho^{3}-(1/b)\rho^{2}+\{-(RT+bP)/ab\}\rho+P/ab=0.
\end{equation}
This cubic equation is to be compared with the characteristic polynomial
written in terms of the similarity invariants, $M,\ G,\ $and $A.$ \ Note that
the roots of the characteristic polynomial are not necessarily real. \ This
observation leads to a well defined procedure for treating nonequilibrium
thermodynamics systems as complex deviations from the real, or equilibrium,
systems. \ The reality condition is determined by the Cardano function that
describes an edge of regression discontinuity. \
For a transformation such that
\begin{equation}
(8T+P)/3=Y_{G}/(M/3)^{2},
\end{equation}%
\begin{align}
P & =Z_{K}/(M/3)^{3},\\
\lambda & =-\rho/(M/3),
\end{align}
the characteristic polynomial becomes an equation in terms of dimensionless
parameters,%
\begin{equation}
U(\lambda,T,P)=(\lambda)^{3}-3(\lambda)^{2}+[(8T+P)/3](\lambda)-P=0.
\end{equation}
The last format given above is to be recognized as the Equation of State of a
van der Waals Gas (compare to \ref{pvt}), in terms of dimensionless Pressure,
Temperature relative to their values at the critical point. \ \
\section{The Falaco Cosmological Soliton}
Although of importance to the cosmological concept of a universe expressible
as a low density (nonequilibrium)\ van der Waals gas near its critical point,
the factorization of the Jacobian characteristic polynomial into a cubic is
not the only cosmological possibility. \ Of particular interest is the
factorization that leads to a Hopf bifurcation. \ In this case the
characteristic determinant vanishes, the Adjoint cubic curvature vanishes, the
mean curvature vanishes (indicating a minimal surface), but the Gauss
curvature is positive, and the two remaining eigenvalues of the characteristic
polynomial are pure imaginary conjugates. \ Such results indicate rotations or
oscillations (as in the chemical Brusselator reactions) and the possibility of
spiral concentration or density waves on such minimal surfaces. \ Such
structures at a cosmological level would appear to explain the origin of
spiral arm galaxies. \ The Hopf type minimal surfaces of positive Gauss
curvature do not represent thermodynamic equilibrium systems, for their
curvatures, although two in number, are pure imaginary. \ The molal density
distributions (or order parameters) are complex.
Evidence\ of such topological defects (at the macroscopic level) can be
demonstrated by the creation of Falaco Solitons in a swimming pool
\cite{rmkfalaco} \cite{vol2}. (See Figure 2). \
\begin{center}
The 54 kb color photo of Figure 2 can be downloaded from
http://www22.pair.com/csdc/pdf/falcolor.jpg
\textbf{Fig 2. \ Falaco Solitons}
\textbf{Cosmic strings in a swimming pool}
\end{center}
These experiments demonstrate that such topological defects are available at
all scales. \ The Falaco Solitons consist of spiral "vortex defect" structures
(analogous to CGL theory)\ on a two dimensional minimal surface, one at each
end of a 1-dimensional "vortex line" or thread (analogous to GPG theory).
\ Remarkably the topological defect surface structure is locally unstable, as
the surface is of negative Gauss curvature. \ Yet the pair of locally unstable
2-D surfaces is \textit{globally} stabilized by the 1-D line defect attached
to the "vertex" points of the minimal surfaces. \ It is remarkable to me that
the Falaco Solitons are obvious repeatable experimental examples of "strings
connected to branes", yet no string theorist that I have challenged to show
how his string "theory" describes the emergence of Falaco Solitons has
responded with a solution. \ My view is that I hold the fanciful claims\ of
string theory suspect, until those theorists can demonstrate a solution that
describes the experimental Falaco Solitons. \
\begin{center}
The 26 kb color presentation of Figure 3 can be downloaded from
http://www22.pair.com/csdc/pdf/tornqr3.jpg
\textbf{Fig 3. \ Falaco Solitons and Landau Ginsburg theory.}
\end{center}
For some specific physical systems it can be demonstrated that period
(circulation) integrals of the 1-form of Action potentials, $A,$ lead to the
concept of "vortex defect lines". \ The idea is extendable to "twisted vortex
defect lines" in three dimensions. \ The "twisted vortex defects" become the
spiral vortices of a Complex Ginsburg Landau (CGL) theory , while the
"untwisted vortex lines" become the defects of Ginzburg-Pitaevskii-Gross (GPG)
theory \cite{Tornkvist}. \ In my opinion, it is unfortunate that the word
"vortex" has been used so glibly in such descriptive phrases. \ To a fluid
dynamicist, the concept of a vortex implies the existence of vorticity (curl
of the velocity field). \ Circulation is a fluid property independent from the
existence of vorticity. \ I\ suggest that the descriptions "Vortex defect
lines" should be made more precise in terms of the phrase "Circulation defect lines".
\ In the macroscopic domain, the fluid experiments visually indicate the
emergence of "almost flat" spiral arm structures during the formative stages
of the Falaco solitons. \ In the cosmological domain, it is suggested that
these universal topological defects represent the ubiquitous "almost flat"
spiral arm galaxies. \ Based on the experimental creation of Falaco Solitons
in a swimming pool, it has been conjectured that M31 and the Milky Way
galaxies could be connected by a topological defect thread \cite{rmkfalaco}.
\ Only recently has photographic evidence appeared suggesting that galaxies
may be connected by "strings" (Figure 4).
\begin{center}
The 26 kb Hubble photo\ of Figure 4 can be downloaded from
http://www22.pair.com/csdc/pdf/spiralstring.jpg
\textbf{Fig 4. \ Interacting Spiral Galaxies}
\end{center}
At the other extreme, using drops of dye, the rotational minimal
surfaces\footnote{In euclean 3-space such minimal surfaces have a negative
Gauss curvature, but in Minkowski 3 space they have positive Gauss curvature.}
which form the two endcaps of the Falaco soliton, like quarks, apparently are
confined by a "string". If the "string" (whose "tension" induces global
stability of the unstable endcaps) is severed, the endcaps (like unconfined
quarks in the elementary particle domain)\ disappear (in a non-diffusive
manner). \ In the microscopic electromagnetic domain, the Falaco soliton
structure offers an alternate, topological, pairing mechanism on a Fermi
surface, that could serve as an alternate to the Cooper pairing in superconductors.
\section{The Adjoint Current and Topological Spin}
From the singular Jacobian matrix, $\left[ \mathbb{J}_{jk}^{scaled}\right]
=[\partial(A/\lambda)_{j}/\partial x^{k}],$ it is always possible to construct
the Adjoint matrix as the matrix of cofactors transposed: \
\begin{equation}
\text{Adjoint Matrix : }\left[ \widehat{\mathbb{J}}^{kj}\right]
=adjoint\left[ \mathbb{J}_{jk}^{scaled}\right]
\end{equation}
When this matrix is multiplied times the rescaled covector components, the
result is the production of an adjoint current,%
\begin{equation}
\text{Adjoint current : }\left\vert \widehat{\mathbf{J}}^{k}\right\rangle
=\left[ \widehat{\mathbb{J}}^{kj}\right] \circ\left\vert \mathbf{A}%
_{j}/\lambda\right\rangle
\end{equation}
It is remarkable that the construction is such that the Adjoint current
3-form, if not zero, has zero divergence globally \cite{rmkpoincare}:%
\begin{align}
\widehat{J} & =i(\widehat{\mathbf{J}}^{k})\Omega_{4}\\
d\widehat{J} & =0.
\end{align}
From the realization that the Adjoint matrix may admit a nonzero globally
conserved 3-form density, or current, $\widehat{J},$ it follows abstractly
that there exists a 2-form density of "excitations", $\widehat{G},$ such that%
\begin{equation}
\text{Adjoint current : }\widehat{J}\Leftarrow d\widehat{G}.
\end{equation}
$\widehat{G}$ is not uniquely defined in terms of the adjoint current, for
$\widehat{G}$ could have closed components (gauge additions $\widehat{G}_{cl},
$ such that $d\widehat{G}_{cl}=0$), which do not contribute to the current,
$\widehat{J}.$
From the topological theory of electromagnetism \cite{rmktop} \cite{rmk4eyes1}%
\ there exists a fundamental 3-form, $A\symbol{94}\widehat{G},$ defined as the
"topological Spin" 3-form,%
\begin{equation}
\text{Topological Spin 3-form \ : \ }A\symbol{94}\widehat{G}.
\end{equation}
The exterior differential of this 3-form produces a 4-form, with a coefficient
energy density function that is composed of two parts:%
\begin{equation}
d(A\symbol{94}\widehat{G})=F\symbol{94}\widehat{G}-A\symbol{94}\widehat{J}.
\end{equation}
The first term is twice the difference between the "magnetic" and the
"electric" energy density, and is a factor of 2 times the Lagrangian usually
chosen for the electromagnetic field in classic field theory:
\begin{equation}
\text{Lagrangian Field energy density : }F\symbol{94}\widehat{G}%
=\mathbf{B\circ\,H-D\circ E}%
\end{equation}
The second term is defined as the "interaction energy density"%
\begin{equation}
\text{Interaction energy density : }A\symbol{94}\widehat{J}=\mathbf{A\circ
}\widehat{\mathbf{J}}-\rho\phi.
\end{equation}
For the special (Gauss)\ choice of integrating denominator, $\lambda$ with
$(p=2,a=b=c=1,m=1)$ it can be demonstrated that the Jacobian similarity
invariants are equal to the classic curvatures:%
\begin{equation}
\{X_{M},Y_{G},Z_{A},T_{K}\}\Rightarrow\{C_{M(mean\_linear)}%
,C_{G(gauss\_quadratic)},C_{A(adjoint\_cubic)},0\}.
\end{equation}
\ It can be demonstrated further that the interaction density is exactly equal
to the Adjoint curvature energy density:
\begin{equation}
\text{Interaction energy }A\symbol{94}\widehat{J}=C_{A}\ \Omega_{4}\text{
\ \ (The Adjoint Cubic Curvature).}%
\end{equation}
The conclusion reached is that a nonzero interaction energy density implies
the thermodynamic system is not in an equilibrium state. \
\ However, it is always possible to construct the 3-form, $\widehat{S}:$%
\begin{equation}
\text{Topological Spin 3-form : }\widehat{S}=A\symbol{94}\widehat{G}%
\end{equation}
The exterior differential of this 3-form leads to a cohomological structural
equation similar the first law of thermodynamics, but useful for
nonequilibrium systems. \ This result, now recognized as a statement
applicable to nonequilibrium thermodynamic processes, was defined as the
"Intrinsic Transport Theorem" in 1969 \cite{rmkintrinsic} :%
\begin{align}
\text{Intrinsic Transport Theorem (Spin)} & :\ \ \ d\widehat{S}%
=F\symbol{94}\widehat{G}-A\symbol{94}\widehat{J},\\
\text{First Law of Thermodynamics (Energy)} & :dU=Q-W
\end{align}
If one considers a collapsing system, then the geometric curvatures increase
with smaller scales. \ If Gauss quadratic curvature, $C_{G},$ is to be related
to gravitational collapse of matter, then at some level of smaller scales a
term cubic in curvatures, $C_{H},$ would dominate. \ It is conjectured that
the cubic curvature produced by the interaction energy effect described above
could inhibit the collapse to a black hole. \ \ Cosmologists and relativists
apparently have ignored such cubic curvature effects.
\section{Topological Fluctuations}
\ Topological fluctuations are admitted when the evolutionary vector direction
fields are not singly parametrized:%
\begin{align}
\text{Fluctuations in position (pressure) }\text{: } & d\mathbf{x}%
-\mathbf{v}dt=\Delta\mathbf{x}\neq0\\
\text{Fluctuations in velocity (temperature) }\text{: } & d\mathbf{v}%
-\mathbf{a}dt=\Delta\mathbf{v}\neq0\\
\text{Fluctuations in momenta (viscosity) }\text{: } & d\mathbf{p}%
-\mathbf{f}dt=\Delta\mathbf{p}\neq0.
\end{align}
These failures of kinematic perfection undo the topological refinements
imposed by a "kinematic particle" point of view, and place emphasis on the
continuum methods inherent in fluids and plasmas. \ For example, consider the
Cartan-Hilbert 1-form of Action on a space of 3n+1 independent
variables\footnote{The domain of independent variables is not restricted to
dimension 4 in this section.} (the $p_{\mu}$ are presumed to be independent
Lagrange multipliers):%
\begin{equation}
A=L(\mathbf{x},\mathbf{v},t)dt+p_{\mu}(dx^{\mu}-v^{\mu}dt)=L(x,v,t)dt+p_{\mu
}\Delta x^{\mu})
\end{equation}
The Top Pfaffian in the Pfaff sequence is%
\begin{equation}
(dA)^{n+1}=(n+1)!\{\Sigma_{\mu=1}^{n}(\partial L/\partial v^{\mu}-p_{\mu
})\bullet d\mathbf{v}^{\mu}\}\symbol{94}dp_{1}\symbol{94}...dp_{n}%
\symbol{94}dq^{1}\symbol{94}..dq^{n}\symbol{94}dt,
\end{equation}
and yields a Pfaff dimension of 2n+2 for the 1-form of Action, defined on the
geometric space of 3n+1 variables $\{x^{\mu},p_{\mu},v^{\mu},t\}$. \ This even
dimensional space defines a symplectic manifold. \
For the maximal non-canonical symplectic physical system of Pfaff dimension
2n+2, consider evolutionary processes to be representable by vector fields of
the form $\gamma V_{3n+1}=\gamma\{\mathbf{v,a,f},1\},$ relative to the
independent variables $\{\mathbf{x,v,p},t\}.$ Define the \textquotedblright
virtual work\textquotedblright\ 1-form, $W$, as $W=i(\mathbf{W})dA$, a 1-form
which must vanish for the extremal case, and be nonzero, but closed, for the
symplectic case. For any n, it may be shown by direct computation that the
virtual work 1-form consists of two distinct terms, each involving a different
fluctuation:%
\begin{equation}
W=\{\mathbf{p}-\partial L/\partial\mathbf{v}\}\bullet\Delta\mathbf{v}%
+\{\mathbf{f}-\partial L/\partial\mathbf{x}\}\bullet\Delta\mathbf{x}%
\end{equation}
When the fluctuations in velocity are zero (temperature) and the fluctuations
in position are zero (pressure), then the work 1-form will vanish, and the
process and physical system admits a Hamiltonian representation. \ On the
other hand if the fluctuations in velocity are not zero and the fluctuations
in position are not zero, then the Work 1-form vanishes only if the momenta
(the Lagrange multipliers, $\mathbf{p,}$ are canonically defined
($\{\mathbf{p}-\partial L/\partial\mathbf{v}\}\Rightarrow0$) and the Newtonian
force is a gradient, \ $\{\mathbf{f}-\partial L/\partial\mathbf{x}%
\}\Rightarrow0.$ \ These topological constraints are ubiquitously assumed in
classical mechanics.
When $\Delta x^{k}\Rightarrow0,$ such that all topological fluctuations
vanish, then the Pfaff dimension of the physical system defined in terms of
the Cartan-Hilbert 1-form of Action, $A,$ is 2 (the equilibrium requirement).
\section{Examples of thermodynamic 1-forms}
In order to demonstrate content to the thermodynamic topological theory, two
algebraically simple examples are presented below. \ The first corresponds to
a Jacobian characteristic equation that has a cubic polynomial factor, and
hence can be identified with a van der Waals gas. \ The second example
exhibits the features associated with a Hopf bifurcation, where the
characteristic equation has a quadratic factor with two pure imaginary roots,
and two null roots. \ Another example, given in \cite{vol2}, \cite{rmkarw},
demonstrates how a bowling ball, given initial angular momentum and energy,
skids and/or slips changing its angular momentum and kinetic energy
irreversibly via friction effects, until the dynamics is such that the ball
rolls with out slipping. \ Once that "excited" state is reached, and
topological fluctuations are ignored, the motion continues without
dissipation. \ The system is in an excited state far from equilibrium. \
\subsection{Example 1: van der Waals properties from rotation and contraction}
\vspace{1pt}In this example,the Action 1-form is presumed to be of the form
\begin{equation}
A_{0}=a(ydx-xdy)+b(tdz+zdt).
\end{equation}
The 1-form of Potentials depends on the coefficients $a$ and $b.$ \ The
results of the topological theory are (for $r^{2}=x^{2}+y^{2}+z^{2}+t^{2})$:
\begin{align}
\text{ Mean curvature} & \text{:}C_{M}=-2btz/(r^{2})^{3/2}\\
\text{Gauss curvature} & \text{:}C_{G}=-\{b^{2}(x^{2}+y^{2})-a^{2}%
(z^{2}+t^{2})\}/(r^{2})^{2}\\
\text{ Adjoint curvature} & \text{:}C_{A}=A\symbol{94}J_{s}\;=-2a^{2}%
btz/(r^{2})^{5/2}\\
Top\_Torsion & =2ab\ \cdot\lbrack0,0,z,-t]/(r^{2})\\
\text{ Adjoint Current \ \ } & \text{:}J_{s}=(a^{2}b^{2}\cdot\lbrack
x,y,z,t])\ /(r^{2})^{2}\\
\text{Pfaff Dimension 4} & \text{:}dA\symbol{94}dA=2ba(t^{2}-z^{2}%
)/(r^{2})^{2}\ \Omega_{4}%
\end{align}
The Jacobian matrix has 1 zero eigen value and three nonzero eigenvalues.
\ Hence, the cubic polynomial will yield an interpretation as a van der Waals
gas. \ The Adjoint current represents a contraction in space-time, while the
flow associated with the 1-form has a rotational component about the z axis.
\subsection{\vspace{1pt}\vspace{1pt}Example 2: A Hopf 1-form \ }
\vspace{1pt}In this example,the Hopf 1-form is presumed to be of the form
\begin{equation}
A_{0}=a(ydx-xdy)+b(tdz-zdt).
\end{equation}
The 1-form of Potentials depends on the coefficients $a$ and $b.$ \ There are
two cases corresponding to left and right handed \textquotedblright
polarizations\textquotedblright: \ $a=b$ or $a=-b$. \ The results of the
topological theory are (for $r^{2}=x^{2}+y^{2}+z^{2}+t^{2})$:
\begin{align}
\text{ Mean curvature} & \text{:}C_{M}=0,\\
\text{Gauss curvature} & \text{:}C_{G}=\{b^{2}(x^{2}+y^{2})+a^{2}%
(z^{2}+t^{2})\}/(r^{2})^{2}\\
\text{ Adjoint Cubic curvature} & \text{:}C_{A}=A\symbol{94}J_{s}\;=0\\
Top\_Torsion & =2ab\ \cdot\lbrack x,y,z,t]/(r^{2})\\
\text{ Adjoint Current \ \ } & \text{:}J_{s}=(ab/2)\ \cdot Top\_Torsion\\
\text{Pfaff Dimension 4} & \text{:}dA\symbol{94}dA=4ab/(r^{2})\ \Omega_{4}%
\end{align}
What is remarkable for this Action 1-form is that both the mean curvature and
the Adjoint curvature of the implicit hypersurface in 4D vanish, for any
choice of a or b. \ The Gauss curvature is nonzero, positive real and is equal
to the inverse square of the radius of a 4D euclidean sphere, when
$a^{2}=b^{2}$. \ The Adjoint cubic interaction energy density is zero. \ The
two nonzero curvatures are pure imaginary conjugates equal to
\begin{equation}
\ \rho=\pm\sqrt{-b^{2}(x^{2}+y^{2})-a^{2}(z^{2}+t^{2})}/(r^{2}).\
\end{equation}
\ The Hopf surface is a 2D imaginary \textit{minimal} two dimensional hyper
surface in 4D and has two nonzero imaginary curvatures! \ Strangely enough the
charge-current density is not zero, but it is proportional to the Topological
Torsion vector that generates the 3 form $A\symbol{94}F.$ \ The topological
Parity 4 form is not zero, and depends on the sign of the coefficients a and
b. \ In other words the 'handedness' of the different 1-forms determines the
orientation of the normal field with respect to the implicit surface. \ It is
known that a process described by a vector proportional to the topological
torsion vector in a domain where the topological parity is nonzero
$4ba/(x^{2}+y^{2}+z^{2}+t^{2})$ $\neq0$ is thermodynamically irreversible. \
\subsection{Example 3 \ A repeatable experiment that demonstrates emergence}
As an example that can be experimentally replicated regard the photo below
(Figure 5). \ The fascinating thing to me\footnote{In 1957 as I stood in the
Yucca Flats valley of Nevada} was how, in the midst of all the turbulent
irreversible dissipation (Pfaff topological dimension 4) associated with a
nuclear explosion, there would emerge a topologically coherent, nonequilibrium
macroscopic state that was radiating (Pfaff topological dimension 3) in the
form of a toroidal topological defect. \ A surprising observation was that
this excited nonequilibrium state had relative long lifetime.
\begin{center}
The 36 kb Color Photo of Fig 5 can be downloaded from
http://www22.pair.com/csdc/pdf/priscila.jpg
\textbf{Figure 5} \textbf{Ionized toroidal topological defect}
\textbf{Pfaff topological dimension 3}
\end{center}
\section{Conclusions Part I}
Based upon the single assumption that the universe is a nonequilibrium
thermodynamic system of Pfaff topological dimension 4 leads to a cosmology
where the universe, at present, can be approximated in terms of the
nonequilibrium states of a very dilute van der Waals gas near its critical
point. \ The stars and the galaxies are the topological defects and coherent
(but not equilibrium) self-organizing structures of Pfaff topological
dimension 3 formed by irreversible topological evolution in this
nonequilibrium system of Pfaff topological dimension 4.
The turbulent nonequilibrium thermodynamic cosmology of a real gas near its
critical point yields an explanation for:
\begin{enumerate}
\item The granularity of the night sky as exhibited by stars and galaxies.
\item The Newtonian law of gravitational attraction proportional to 1/r$^{2}.
$
\item The expansion of the turbulent dissipative universe.
\item The emergence of nonequilibrium (radiating) Pfaff dimension 3,
topological defect structures such as stars and galaxies.
\item A possible understanding of non radiating systems (dark energy, dark
matter) in terms of ordinary thermodynamic defect systems of Pfaff topological
dimension less than 3. \ Such thermodynamic systems do not exchange matter or
radiative energy with the turbulent dissipative environment of the physical
cosmological vacuum.
\end{enumerate}
\begin{quote}
The color photos described above in Part I have been presented in a somewhat
awkward manner as there is an arXiv limit on file size. \ A pdf file (1.46 Mb)
that includes the color photos in place can be downloaded from
\end{quote}
\begin{center}
http://www22.pair.com/csdc/pdf/coscolor.pdf
\end{center}
\part{Macroscopic Topological Quantization}
Part II examines how continuous topological evolution can be used to describe
the thermodynamic emergence of topological defect singular structures without
regard to geometric scales. \ Moreover, these deformable, but topologically
coherent, signular structures can exhibit macroscopic, topologically
quantized, (rational) properties which can be used to describe the features of
quantum cosmology. \ The bottom line is the idea that Quantum Cosmology should
be treated as a topological, not a metrical, concept. \ The work is motivated
by the conjecture that the cosmology of the observable universe can be
described as a dilute, but turbulent, thermodynamic state of Pfaff topological
dimension 4. \ Irreversible thermodynamic processes cause the emergence of
various regional defect domains (such as condensates) of coherent, but
deformable, topological features, of Pfaff topological dimension 3, or less.
\ Tangential discontinuities such as wakes in fluids, and propagating
electromagnetic signals are examples of such emergent singular topological
defects. \
In addition, certain homogeneous defect structures, which can occur over
microscopic or cosmological domains, admit features of quantization in terms
of deRham period integrals, which are known to have rational values. \ The
homogeneous structures introduce singularities of many different forms into
the topological background. \ The simplest of these structures are related to
fixed points of rotation and expansion. \
\section{Emergence}
During the last 5 years, or so, the old concept of "emergent physics" has
developed into a buzzword that attracts attention in the scientific community.
\ From a topological perspective, the word \textit{emergence}, describing a
process that causes something "new" to be observed could have two
interpretations.\ \ Both involve topological change. \
\begin{enumerate}
\item The first suggestion is associated with the idea of creation; the
emergence of something as a "new" entity (or final state), with topological
properties\footnote{Note that herein the emphasis is on topological
properties, not geometric properties. \ Metric features, more or less, are
ignored.} that are different from preceding entity (or initial state).
\ Separation of a checkerboard into its many black parts and its many red
parts is an elementary example of a "cutting" process. \ Indeed, the
topological property of connectivity has changed during the process, but the
(cutting)\ process cannot be represented by a topologically continuous
mapping. \ The disconnected pieces are the "new" entity that emerges after the
cutting process takes place. \
\item The second suggestion is based on the observation that it is possible to
start with a strip of ribbon, which is simply connected and orientable, and
cause it to emerge (evolve) into a "new" entity which is not orientable and
not simply connected. \ This "twisting" and "pasting" process does indeed
describe topological change, but the (twisting and pasting)\ process can be
represented by a topologically continuous mapping. \
\end{enumerate}
Other examples include the emergence of a turbulent state, from an equilibrium
state of rest; \ but such a process can not be described in terms of a
topologically continuous process. \ \ On the other hand the decay of a
turbulent state, to state of rest, does involve topological change that can be
mapped by a continuous process. \ In general, it is known that a physical
system encoded by a connected topology can not continuously be mapped (evolve)
into a disconnected topology. \ On the other, a disconnected topology can
continuously be mapped (evolve) into connected topology. \
\ For systems encoded in terms of a Cartan 1-form, the induced Cartan topology
is such that the domains of Pfaff topological dimension 1 or 2 form connected
topologies (which are representative of thermodynamic equilibrium, or
thermodynamic isolated states), and the domains of Pfaff topological dimension
3 or 4 form disconnected topologies (which are representative of thermodynamic
states far-from-equilibrium or thermodynamic turbulent states). \ These ideas
do not depend upon metric scales. \
The focus herein is on continuous topological evolution, for which the use of
Cartan's exterior calculus will lead to progress in scientific understanding.
\ Discontinuous\footnote{Topological continuity requires that the limit points
of the topology of the initial state map into the closure of the
(different)\ topology of the final state. \ Topology can change continuously.}
topological evolution is ignored herein. \ \ The turbulent state on a
pregeometric variety (no metric) \ of 4 variables is defined to be of Pfaff
topological dimension 4. \ The initial turbulent state can decay (or evolve)
continuously into macroscopic topological coherent structures of lesser Pfaff
topological dimension. \ These emergent structures can be considered to be
topological defects in the domain of Pfaff topological dimension 4. \ Those
emergent states (domains) that are of Pfaff dimension 3, created from
dissipative irreversible processes in the turbulent environment (domain) of
Pfaff topological dimension 4, are topological defect structures that can have
remarkably long lifetimes. \ They are not thermodynamic equilibrium states,
for they have a Pfaff topological dimension 3.
Limit cycles, envelopes, excited atomic states, Solitons, wakes, galaxies,
envelopes, stars are all examples of such topologically coherent but
deformable structures of Pfaff topological dimension 3. \ Perhaps even more
remarkable is the idea that these coherent topological defect structures, if
homogeneous, can be used to generate topological quantization effects that are
not dependent upon scales. \ Such macroscopic "quantum" states can occur at
the size of galaxies as well as at the size of Bose condensates. \
An interesting experiment relating to the concept of irreducible Pfaff
dimension 3, non-equilibirum thermodynamics, topological quantum states, and
the fact that a twisting and pasting continuous process can store energy in
physical systems by means of curvature and torsion can be conducted by using a
length of thick wall elastic vacuum hose. \ Bend the hose into a circle and
join the ends together without twisting. \ The curvature deformation of
compression of the inside fibers,and extension of the outside fibers required
work to be done. \ The stored energy of deformation can be retrieved. \ If the
hose is placed on a table top it lies flat; the deformed fibers reside in a
plane. \ Now before joining the ends together give the hose a pi twist.
\ There is now obvious deformation energy associated with the curvature, but
there also is an additional energy associated with the twist or torsion
deformation. \ Place the hose with both curvature and torsion on the table
top. \ It does not lie flat. \ It is irreducibly 3 dimensional as it has torsion.
An open question is: Does the physical vacuum have this torsional energy;
\ can it be retrieved? \ If the physical vacuum is\ described by a matrix of
Basis vector functions, then it appears that the Affine torsion of the
associated Cartan connection leads to PDE's of the format equivalent to both
the Maxwell-Ampere equations and the Maxwell-Faraday equations. \ The
conclusion is reached that the source of charge is Affine Torsion of the
Cartan Connection Matrix constructed from the Basis Frame of Functions that
define the Physical Vacuum \cite{rmkpv}. \ Of particular interest is the
theoretical conjecture that Affine torsion of the Cartan Connection for the
physical vacuum is the source of charge.\bigskip
\subsection{Historical}
More than 25 years ago (1977), the present author published an article
entitled,\ "Periods on Manifolds, Quantization and Gauge"\ \cite{rmkperiods}.
\ At that time, it had become apparent that at least some of the quantum
mechanical features of measurables with rational ratios (the quantum numbers)
could be interpreted in terms of topological period integrals (which have
ratios of values that are rational). \ The method was championed then and now
by E. J. Post \cite{PostQuRe}, who, using the methods of topological
quantization, predicted in 1981 the fractional quantum Hall effect
\cite{PostQHall}. \ Further motivation for the original publication was based
on the recognition that the evolution of the Sommerfeld closed integrals might
be used to explain the details of that Copenhagen mystery, whereby the quantum
jump, or radiative transition from one quantum state to another quantum state,
had been described (paraphrasing Bohr) as a "miracle". \ It was recognized
that a quantum transition, which was described by integer changes of the
Sommerfeld Period integrals, implied a topological change had taken place.
A few years earlier it had been realized that what was, and still is, needed,
for understanding thermodynamic irreversibility, was a method capable of
describing continuous topological evolution. \ \ It was apparent from Cartan's
work \cite{Cartanlecon} that all Hamiltonian processes preserve the Sommerfeld
integrals (closed 1-forms of action), as evolutionary invariants, and could
not describe the dynamics of topological evolution, much less the dynamics of
a radiative transition. \ Clues from prior work had indicated that a
modification of the Hamiltonian method based on Cartan techniques might be
used to explain topological evolution \cite{rmkhamp}. \ Only years later was
this modification recognized to be equivalent to Cartan's magic formula
\cite{Marsden}, where the Lie differential with respect to a direction field,
V, acts on a 1-form of Action, to produce the topological equivalent of the
first law of thermodynamics \cite{vol1}. \ Then it was easy to show
that\ Hamiltonian processes implied that the Heat 1-form, Q, was closed: dQ =
0. \ Recall that the Caratheodory concept of irreversibility was that
Q\symbol{94}dQ $\neq0.$ \ Hence all Hamiltonian processes are
thermodynamically reversible. \ The Cartan topology constructed from the
1-form of Action, was invariant to all Hamiltonian extremal processes. \ The
early objective was determine how to modify the concept of a Hamiltonian
process, and link the idea that topological change was a requirement of
thermodynamic irreversibility \cite{rmkhamp}. \
\ Part of the presentation herein will be the demonstration of certain Cartan
techniques that can be used to describe continuous topological evolution and
thermodynamic irreversibility. \ The major objective, however, is to give
examples and methods of construction of closed p-forms, which may serve as the
integrand of period integrals with non-zero values along closed integration
chains which are not boundaries. \ The basic idea stems from the recognition
that the integrands of topological period integrals can be encoded in terms of
homogeneous p-forms of degree zero. \ Homogeneous p-forms of degree not zero
are always exact \cite{PL2}, hence such exact p-forms would yield zero values
for their period integrals along closed integration chains. \ Homogeneous
p-forms of degree zero are independent from "scale changes", not only at a
point, but globally over the homogeneous domain, even though the scale factor
is not a global constant. \ The most common of such objects is to be found in
projective geometry, where the fractional linear, or Moebius transformation,
is used to deduce the important projective invariants. \ All projective
invariants are universally homogeneous functions of cross ratios. \ It is
remarkable that the transition probability of quantum mechanics, according to
Fermi's golden rule, is such a cross ratio invariant.
The concept of "gauge invariance", as introduced by Weyl, was an attempt to
answer the question: Can parallel displacement change the length, or scale, of
a vector. \ Before Weyl, it was recognized that parallel displacement in
Riemannian geometry around closed circuits could change the orientation of a
vector. \ The orientation at the start of the process of parallel transport
around a closed path need not be the same as the orientation of the vector
when it returned to the starting point. \ Orientation changes in the tangent
plane of the starting point were known to be related to curvature, and
orientation changes orthogonal to the tangent plane had been related to the
concepts of torsion. \ Apparently, before Weyl, the idea of a length change
had been ignored in framing the conditions of what was meant by a parallel
displacement in a Riemannian geometry. \ Could the geometric concepts of
metric and connection be reformulated beyond the constraints of Riemannian
geometry to produce scale change and path dependence relative to parallel
transport? \ The details of such reformulations in terms of metrics and
connections appear most cogently in the book by Eddington \cite{EddingtonREL},
and in the concept of Finsler spaces \cite{Antonelli}.
In the language of differential forms, without recourse to geometric
assumptions of metric or connections, the concept of displacement inducing a
change of scale is encoded in terms of the Lie differential with respect to a
direction field, $X=[x^{k}],$ acting on p-forms, $\omega$, to create the same
p-form magnified by a scale factor, $D$. \ A homogeneous differential form
satisfies an equation of the type:%
\begin{equation}
L_{(X)}\omega=D\omega.\label{homopform}%
\end{equation}
Differential forms that satisfy such a formula are said to be homogeneous of
degree $D$. \ The formula is exactly equivalent to Euler's formula for
homogeneous scalar functions, $\Theta(X)$ of homogeneity degree $D.$ \ The
homogeneity index need not be an integer, and the components $x^{k}$ of the
process $X$\ need not be functions of the same (physical) dimension.%
\begin{align}
L_{(X)}\Theta(x^{k}) & =i(x^{k})d\Theta=\left\langle \partial\Theta/\partial
x^{k}\right\vert \circ\left\vert x^{k}\right\rangle =D\cdot\Theta(x^{k})\\
\Theta(X) & =\text{ a zero form.}%
\end{align}
\begin{remark}
Topological evolution can describe changes of scale, without recourse to
specific geometrical constraints.
\end{remark}
The homogeneous formula can be extended to processes, $X$, of arbitrary
direction fields, acting on both pair and impair p-forms. \ Herein, the
concept of relative gauge invariance of functional form is related to
homogeneous functions of degree $D$, and absolute (projective) invariance to
homogeneous functions of degree $D$ equal to zero. \
One of the principle results of the first cited article \cite{rmkperiods} was
the presentation and utilization of three period integrals, of dimension 1, 2,
and 3, which have dominant physical significance. \ A period integral is
defined as a closed p-form, $\omega,$ with $d\omega=0,$ integrated over a
(closed)\ cycle of dimension p, $z_{p}$, which is not a boundary. \ In this
article, another 3-dimensional period integral (originally presented in 1977
\cite{rmkames}, \cite{rmkmoffat}) is added to the list. \ The format chosen
will emphasize, for purposes of more rapid comprehension, an electromagnetic
notation and application, but the basic ideas apply to many other areas of
physical speciality, such as hydrodynamics and thermodynamics. \
The idea utilizes the topological decomposition of the arbitrary p-form into 3 components:%
\begin{align}
\omega & =\omega_{no}+\omega_{cl}+\omega_{ex}\\
\omega_{no} & =\text{Non-closed (Noether potential) component",}\\
\omega_{cl} & =\text{"Closed but not exact singular component",}\\
\omega_{ex} & =\text{"Exact component"}%
\end{align}
In another format, the p-form decomposition theorem can be written as%
\begin{align}
\omega^{p} & =\omega_{no}^{p}+\partial_{z}\omega^{p+1}+d\omega^{p-1},\\
d(d\omega^{p-1}) & =d(\omega_{ex})=0,\ \ \ \\
d(\partial_{z}\omega^{p+1}) & =d(\omega_{cl})=0.
\end{align}
This formulation is similar to the Hodge decomposition theorem, but the "cycle
operator", $\partial_{z},$ is not a boundary operator, and definitely is not
the Hodge boundary operator, $\ast d\ast$, which depends upon metric.%
\begin{align}
\partial_{z} & \neq\partial_{B}\\
\partial_{z} & \neq\ast d\ast
\end{align}
The cycle operator, $\partial_{z},$ will be defined with examples in the next section.
The decomposition concept goes back at least as far as Hodge-deRham, but the
designation "Noether" component is used herein to tie in with the gr-qc
notation used by Wald \cite{Wald} and others. \ The Wald development utilizes
the fact that "Noether potentials", $\omega_{no},$ of p-forms, upon exterior
differentiation, lead to exact p+1 forms, called Noether currents, whose
closed integrals are evolutionary invariants. \ The integrals of the exact p+1
forms over a domain M are related by Stokes theorem to integrations of
$\omega_{no}$ over the boundary of M. \ The components $\omega_{cl}$ and
$\omega_{ex}$ do not contribute to such integrals over a boundary. \ These
Wald integrals are NOT\ quantized.
Quantized period integrals involve the closed integrals of the closed but not
exact components, $\omega_{cl}.$ \ Such closed but not exact p-forms can be
constructed from a universal algorithm that produces a p-form which is
homogeneous of degree zero relative to its p independent variables and
differentials. \ \ They are quantities defined without use of a metric, and
create closed integrals that are absolute integral invariants relative to any
evolutionary process, $\beta$V, independent from the parametrization
parameter, $\beta.$ \ The notion of a "period" integral is related to the fact
that such structures are singular in the sense that they have fixed points
(singularities of affine transformations) which can be related to physical
concepts of rotation and expansion.
\subsection{Four fundamental topologically quantized period integrals.}
\ The four important topological period integrals (presented here in
electromagnetic format and notation but universal in application) are:
\begin{enumerate}
\item The Flux quantum = $\int_{z1}A_{cl}.$\ \ The integrand\ $A_{cl}$ is a
pair 1-form, and the cycle is a 1-dimensional closed integration chain,
$z_{1}$, in regions where $dA=0.$\ In electromagnetic format the physical unit
of the flux quantum period integral is $h/e$. \ It is important to realize
that the flux quantum is not related to the magnetic flux, nor to the closed
integral of the 2-form, $F=dA.$ \ In hydrodynamics, the flux quantum is
related to the concept of circulation, and is independent from the concept of
vorticity. \ It is important to recognize that the flux quantum occurs only in
domains where the 1-form $A$\ is of Pfaff dimension
$>$
1. \
\item The Charge quantum = $\int\int_{z2}G_{cl}.$ \ The integrand\ $G_{cl}$ is
an impair 2-form, and the closed cycle is 2-dimensional, $z_{2}$ in domains
where $dG=0$. \ In electromagnetic format the physical unit of the charge
quantum period integral is $e$. \ The fact that the charge quantum is impair
implies that charge is a pseudo-scalar, a fact not in agreement with the
current mainstream convention, but in agreement with the experiments in
crystal physics. \ Recall that integrals of impair forms are not sensitive to orientation.
\item The Topological Torsion or Polarization quantum = $\int\int\int
_{z3}(A\symbol{94}F)_{cl}.$ \ The integrand\ ($A\symbol{94}F)_{cl}$ is a pair
3-form, and the closed cycle is 3-dimensional, $z_{3}$, in a domain where
$d(A\symbol{94}F)=0.$ \ In electromagnetic format the physical unit of the
Topological Torsion quantum period integral is $(h/e)^{2}.$ \ Note that this
physical unit is equal to the spin quantum, $\hbar$, times the Hall
coefficient, $\hbar/e^{2}$. \ Also recall that the non-zero value of
$(A\symbol{94}F)_{cl}$, indicates that the Cartan topology (Chapter
\ref{CTSTRU}) is a disconnected topology, and in a thermodynamic sense implies
that the corresponding thermodynamic system is a nonequilibrium system.
\item The Topological Spin quantum = $\int\int\int_{z3}(A\symbol{94}G)_{cl}$.
\ The integrand\ $(A\symbol{94}G)_{cl}$ is an impair 3-form, and the cycle is
3-dimensional, $z_{3}$ \ in domains where $d(A\symbol{94}G)=0.$ \ In
electromagnetic format the physical unit of the Topological Spin quantum
period integral is $h$. \ The fact that the spin quantum is impair implies
that spin is a pseudo-scalar.
\end{enumerate}
The application of these ideas to EM theory appears in \cite{rmksc3},
\cite{rmktimerev}.
As the integration cycles, $z$, are in domains where the exterior
differentials of the integrands vanish, then the values of the integrals have
rational ratios \cite{deRham} which leads to the idea of topological
"quantization" \ The cycle $z$ wraps around the singular (or fixed) point of
the closed but not exact p-form, which leads to the term "period integral".
\ The integrands for the Flux quantum and Topological Torsion quantum behave
as scalars with respect to transformations of the independent variables in
their arguments. \ Such scalars are, in the language of invariant theory,
called "absolute"\ invariants. \ The closed integrals are sensitive to
orientation. \
The Charge quantum and the Topological Spin quantum, are W-densities, and
therefor depend upon the magnitude of determinant of the transformation, but
not upon the sign of the determinant. \ The values of the integrals do not
depend upon the orientation of the domain of integration, nor the fact that
the domain may be non orientable. \ \ Such objects related to the
determinants, in the language of invariant theory are called
"relative"\ invariants \cite{Turnbull}, or pseudo-scalars \cite{PostQuRe}.
The Flux quantum (\symbol{126}Sommerfeld integrals) and the Charge quantum
(\symbol{126}Gauss law) were\ more or less well known in 1977, but the concept
that these period integrals were independent from any metrical constraints was
not so well known. Even now (2006) the fact that these concepts are
independent from metric is not fully appreciated. \ In fact, gravitational
theory emphasizing metric based concepts, has utilized the differential form
argument using closed integrals of 2-form densities to \textit{force} a
relationship between "entropy" and "black hole horizon area" \cite{Jacobsen}.
\ The fact that the closed integrals over W-densities are impair (implying
that the result is a pseudoscalar) is almost completely ignored. \ The idea
that there could exist closed integrals that are period integrals yielding
macroscopic topological quantization at all scales is also almost completely ignored.
In 1977, the third period integral, the Topological Spin quantum, was somewhat
novel, having been discovered\ just a few years before (1969) in a somewhat
different context \cite{rmkintrinsic}. \ \ About the same time \cite{rmkames},
the second 3 dimensional period integral of Topological Torsion was created to
study the topological transition from
\index{Turbulence}
to the streamline state in a fluid. \ It took some 10 to 20 years before it
was appreciated that the nonzero closure of the pair 3-form, $A\symbol{94}F,$
defined domains that could be put into correspondence with thermodynamic
irreversibility. \ In addition, it is only very recently that it has been
appreciated that the 3-form of Topological Torsion has an eigen direction
field that is composed of Spinors, not classical diffeomorphic vectors.
\ Hence in a hydrodynamic context, as a turbulent flow must be irreducibly 4
dimensional, $d(A\symbol{94}F)\neq0$, then the cause of turbulence ultimately
must be traced back to the Spinor content generated by the eigen direction
fields of the 2-form, $dA.$ \ The 3-form $A\symbol{94}F$ is of utmost
importance to (and is nonzero in) the thermodynamic theory of nonequilibrium
systems. \ The use of spinors in macroscopic physics is almost completely
ignored, yet mathematicians have demonstrated that spinors are generators of
minimal surfaces, which are macroscopically observable as wakes and other
modes of propagating tangential discontinuities.
Although each of these period integrals described above\footnote{Yet Torsion
quanta and Spin quanta 3-forms appear sparcely in the literature.} appear to
have application to the microphysical world, an objective of this article is
to emphasize that such macroscopic quantized period integrals also should have
applicability to the cosmological universe. \ After all, period integrals are
topological objects independent from metric constraints of size and shape.
\ The integrands of period integrals are closed p-forms which are homogeneous
of degree zero. \ The p-form, like a cross-ratio in projective geometry, is
independent from metrical scales. \ Size and shape are not important to these
continuous deformation invariants. \ This fact initially posed an ontological
conflict, for experience (or prejudice)\ seems to indicate that "quantum"
features are artifacts of the microphysical world, alone. \ Now it is apparent
that the concept of Spinors is another topological idea based upon the eigen
direction fields of infinitesimal rotations, and does not depend upon scales.
\ Spinors and their importance on macroscopic physical systems has long been ignored.
\begin{remark}
As E. Cartan \cite{Cartanspinors} has demonstrated, Spinors are not vectors
(tensors) with respect to infinitesimal rotations.
\end{remark}
E. J. Post became interested in this predicament, and now champions the idea
that Quantum Mechanics of the microworld should be developed in terms of
metric free ideas \cite{PostTG}. \ On the other hand, the physics of gravity,
constitutive relations, and the synergetic aggregates of the macrophysical
world appear to have geometric, metric-dependent, features. \ Indeed, many of
these geometric features are topological properties, especially when they are
elements of a diffeomorphic equivalence class. \ In order to examine
metric-based topological features, Post recommends the use of general
diffeomorphic invariance principle be used to determine metrical based
topological features. \ That is, the diffeomorphic maps should not be
restricted to some particular geometrical group, such as is presumed in gauge
theories. \ The problem with the use of diffeomorphic maps is that they miss
the discrete symmetry breaking features of handedness of polarization and
to-fro evolution. Diffeomorphic maps imply covariance with respect to both
translations and rotations. \ Spinors are diffeomorphic covariants with
respect to translations, but they are not diffeomorphic covariants with
respect to rotations. \
Another method to discover metric independent features is to choose a metric
arbitrarily, and then show (as did Hodge) that certain topological invariants
arise which do not depend upon the choice of metric. \ Such invariants include
those invariants which are "gauge"\ invariant, in the sense that they are
independent from metric based scales. \ At what physical level a metric-based
topology evaporates into a non-metric based topology is still unknown.
\ Conversely, at what level a non-metric based topology condenses or "emerges"
into a metric based topology is intuitively at the level of forming coherent%
\index{Phase (topological)!Coherent Structures}
quantum macro states, such as those that appear in superconductivity, or as
non-dissipative solitons in macro structures. \ It is conjectured that such a
process occurs when the closed, but not exact, homogeneous differential forms
used to construct period integrals become harmonic. \
Another suggestive concept that requires investigation is related to how and
if a given metric can undergo topological evolution and change. \ In particular,
\begin{remark}
The signature of a metric may be a process dependent topological feature.
\end{remark}
As mentioned in \cite{vol1} and in more detail in Vol 2, \ \cite{vol2}, the
experimental observations of the features of the nonequilibrium Falaco
Solitons appear to be best represented by a 3D Minkowski metric of signature
\{+,+,-\}, yet the initial state of the fluid, and the ultimate (equilibrium)
state, appear to be Euclidean with a signature \{+,+,+\}. \ If the
observations are correct, the Falaco Solitons \cite{vol2} yield some of the
first experimental results that physics recognizes situations where 3 spatial
dimensions will support a signature which is negative, and non Euclidean. \ \
\section{\textbf{Emergent states as coherent topological structures}}
\subsection{1-forms}
Rather than starting with the usual Lagrangian field theory approach
constructed in terms of a Lagrange density N-form and its associated N-1-form
current\footnote{Which are the usual tools of a variational field theory.},
consider those thermodynamic systems that can be encoded in terms of an
exterior differential 1-form of Action, $A$, over a pregeometric (metric not
assigned) variety of dimension N. \ The method is related to the
Cartan-Hilbert invariant integral. \
Topological properties of such a 1-form of Action include the Pfaff
topological dimension, which is a statement of the irreducible minimum number
of functions (of the base variables)\ that are required to describe continuous
topological features of the system. \ This minimal number of functions, or
class of a 1-form, can be evaluated by one exterior differentiation, and
subsequent algebraic constructions defined as the Pfaff sequence: \
\begin{equation}
\text{ Pfaff Sequence \ \ }\{A,dA,A\symbol{94}dA,dA\symbol{94}dA...\}.
\end{equation}
\ The number of non-zero entries in the sequence determines the Pfaff
Topological dimension.
As mentioned in the previous section, any 1-form can have three topologically
distinct parts, depending upon the Pfaff topological dimension. \
\begin{align}
A & =A_{no}+\partial_{z}\omega^{p+1}+d\omega^{p-1},\\
d(d\omega^{p-1}) & =d(\omega_{ex})=0,\ \ \ \\
d(\partial_{z}\omega^{p+1}) & =d(\omega_{cl})=0.
\end{align}
If the Pfaff dimension is 1, then only 1-function, say $U(x,y,z,t)$, is
required and $A=dU,\,\ $which is the exact component. \ The "Noether current",
$dA,$ is zero. \ If the Pfaff dimension is 2, then only 2 functions are
required, say $U(x,y,z,t)$ and $V(x,y,z,t).$ A canonical representation is
given by the formulae%
\begin{align}
A & =UdV\\
dA & =dU\symbol{94}dV\\
A\symbol{94}dA & =0.
\end{align}
However there are other possibilities. \ For example, consider the
representation%
\begin{align}
A & =UdV+\Gamma(U,V)(VdU-UdV)=\\
dA & =(1-2\Gamma-V\partial\Gamma/\partial V-U\partial F/\partial
U)dU\symbol{94}dV\\
A\symbol{94}dA & =0.
\end{align}
Only two primitive functions, $U$ and $V$ are required in its construction,
but now the second term has interesting interpretations. \ Orbits of the
second term, can be graphed as rotations if $\Gamma(X,Y)$ is a constant. \
\ In general, the second term contributes to the Noether current $dA,$ unless%
\begin{equation}
(Y\partial\Gamma/\partial Y+X\partial F/\partial X)=-2\Gamma,
\end{equation}
which is Euler's equation for homogeneous functions of degree -2. \ In this
special homogenous case, the factor $\Gamma$ becomes an "integrating" factor
for the rotation, such that $dA=0.$ \ In such cases, the rotation is called a
"circulation", and is topologically without limit points, for the "Noether
current" or "vorticity", $dA=0.$ \ It is this construction that defines the
closed but not exact components of the 1-form in terms of a cycle operator
$\partial_{z}$.%
\begin{align}
A_{cl} & =\partial_{z}\omega^{p+1}=\partial_{z}(dU\symbol{94}dV)\\
& =i([U,V])dU\symbol{94}dV/\lambda\\
& =(UdV-VdU)/\lambda,\\
\lambda & =(aU^{m}+bV^{m})^{(2)/m},\\
\Gamma & =1/\lambda
\end{align}
The coefficients a,b... and the exponent m are constants. \ The function
$\lambda$ is a form of the Holder norm, with a zero set that establishes the
singularities of $A_{cl}.$
Stoke's Law states that%
\begin{align}
\text{ \ for }A & =A_{no}+A_{cl}+A_{ex}\\%
{\textstyle\iint\limits_{M}}
dA & =%
{\textstyle\iint\limits_{M}}
F=%
{\textstyle\int\limits_{\partial M}}
\{A_{no}+A_{cl}+A_{ex}\}=%
{\textstyle\int\limits_{\partial M}}
\{A_{no}\}\\
& \text{where }\partial M\text{ is a boundary of M.}%
\end{align}
Note that only the Noether term, $A_{no}$, contributes to the integration over
a boundary:%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{For the Noether Component}\\
\text{"The Flux Conservation law"}\\
\text{an absolute evolutionary integral invariant}%
\end{array}
&
{\textstyle\iint\limits_{M}}
F=%
{\textstyle\int\limits_{\partial M}}
A_{no}\neq0
\end{array}
\end{equation}%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{for the Closed component }\\
\text{Flux quanta balance}%
\end{array}
&
{\textstyle\iint\limits_{M}}
F=%
{\textstyle\int\limits_{\partial M}}
A_{cl}=0
\end{array}
\end{equation}%
\begin{equation}%
\begin{array}
[c]{cc}%
\text{for the Exact component } &
{\textstyle\iint\limits_{M}}
F=%
{\textstyle\int\limits_{\partial M}}
A_{ex}=0
\end{array}
\end{equation}
However, integration over a cycle, $z1,$ which is not a boundary and in a
domain where $F=dA=0$, yields%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{for the Closed component}\\
\text{The flux quantum}%
\end{array}
&
{\textstyle\int\limits_{z1}}
A_{cl}\neq0
\end{array}
\end{equation}%
\begin{equation}%
\begin{array}
[c]{cc}%
\text{for the Exact component} &
{\textstyle\int\limits_{z1}}
A_{ex}=0
\end{array}
\end{equation}
It is the closed component that yields topological quantization by deRham's
theorems. \ In EM notation the expression for the Bohm-Aharanov flux quantum becomes%
\begin{equation}
\text{Bohm-Aharanov Flux quantum}=%
{\textstyle\int\limits_{z1}}
A_{cl}\neq0.
\end{equation}
As the integration chain and the integrand are in domains where $F=dA=0,$ the
flux quantum has nothing to do (explicitly) with the classic electromagnetic
flux conservation law, constructed from $%
{\textstyle\iint}
dA(E,B)$, as $dA_{cl}=0.$ \ The flux quantum integral will have values which
are rational multiples of one another, depending upon the cycle, $z1$. \ In
fluid mechanics the closed integral of a closed but not exact velocity field,
such as that encoded by 1-form,
\begin{equation}
A_{cl}(x,y)=\Gamma(ydx-xdy)/(x^{2}+y^{2}),
\end{equation}
defines the circulation integral with value $2\pi\Gamma$, a value that does
not depend upon the 2-form of vorticity. \ Note that if x and y are defined in
terms of a polar coordinate system, $(r,\theta)$, the pullback of
$A_{cl}(x,y)$ becomes%
\begin{equation}
A_{cl}(r,\theta)=\Gamma_{0}d(\theta)\Leftarrow\Gamma_{0}(ydx-xdy)/(x^{2}%
+y^{2})=A_{cl}(x,y).
\end{equation}
It would appear the 1-form $A_{cl}(x,y)$ when pulled back to the space of
variables $\{r,theta\}$ is an exact differential, $d(\theta).$ \ The notation
is decieving, but it must be remembered that $\theta$ as used above is a
cyclic variable; \ the coordinate mapping fails at r = 0. \ The excluded
point, $r=0,$ represents a topological defect, a hole in the Cartesian fabric
of 2 dimensions.
Many other examples of constructing deRham period integrals in terms of
homogeneous p-forms can be found in chapter 8 of \cite{vol1}.
\subsection{2-form densities}
As the Wald description of blackhole entropy has a realization in terms of
"Noether" currents (3-forms), it is of some interest to formulate the concept
of impair 2-form densities (the Noether "potentials). \ This will be done
first in terms of EM notation .
\subsubsection{EM notation \ \ \ \ }
The story for 2-form densities is comparable to the story for\ 1-forms given
above. \ Consider the impair 2-form density $G$ in EM notation, (or $Q$ in GR
notation):%
\begin{align}
\text{"Noether potential" component, }G_{no} & :dG_{no}\neq0\\
\text{Closed but not Exact singular component, }G_{cl}. & :dG_{cl}=0\\
\text{Closed and Exact component, }G_{ex} & :dG_{ex}=0.
\end{align}
Stoke's Law states that%
\begin{align}
\text{ \ \ for }G & =G_{no}+G_{c\text{ }l}+G_{ex}\\%
{\textstyle\iiint\limits_{M}}
dG & =%
{\textstyle\iiint\limits_{M}}
J=%
{\textstyle\iint\limits_{\partial M}}
\{G_{no}+G_{cl}+G_{ex}\}=%
{\textstyle\iint\limits_{\partial M}}
\{G_{no}\}\\
& \text{where }\partial M\text{ is a boundary of M.}%
\end{align}
Note that only the Noether term, $G_{no}$, contributes to the integration over
a boundary:%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{for the Noether component}\\
\text{"The Charge Conservation law" }\\
\text{an absolute evolutionary integral invariant}%
\end{array}
&
{\textstyle\iiint\limits_{M}}
J\Rightarrow%
{\textstyle\iint\limits_{\partial M}}
G_{no}\neq0
\end{array}
\end{equation}%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{For the closed component:}\\
\text{Equal and opposite charge pairs cancel}\\
\text{charge neutrality as an impair effect}%
\end{array}
& \Rightarrow%
{\textstyle\iint\limits_{\partial M}}
G_{cl}=0
\end{array}
\end{equation}%
\begin{equation}%
\begin{array}
[c]{cc}%
\text{for the Exact component } & \Rightarrow%
{\textstyle\iint\limits_{\partial M}}
G_{ex}=0
\end{array}
\end{equation}
However, integration over a cycle, $z2,$ which is not a boundary and in a
domain where $J=dG=0$, yields%
\begin{equation}%
\begin{array}
[c]{cc}%
\begin{array}
[c]{c}%
\text{for the Closed component}\\
\text{The Charge quantum}%
\end{array}
&
{\textstyle\iint\limits_{z2}}
G_{cl}\neq0
\end{array}
\end{equation}
\begin{equation}%
\begin{array}
[c]{cc}%
\text{for the Exact component} &
{\textstyle\iint\limits_{z2}}
G_{ex}=0
\end{array}
.
\end{equation}
It is the singular closed but not exact component that yields topological
quantization by deRham's theorems. \ In EM notation the expression for the
Charge quantum becomes an integration over a cycle, not a boundary,%
\begin{equation}
\text{Charge quantum}=%
{\textstyle\iint\limits_{z2}}
G_{cl}\neq0.\label{Qq}%
\end{equation}
A construction for representing a closed but not exact component of a 2-form,
$G_{cl},$ follows the same procedure given for the closed but not exact
1-form. \ The 2-form is defined in terms of a cycle operator $\partial_{z}$
acting on a 3-form. \ The 3-form is constructed as the monomial differential
volume element of three arbitrary independent functions, $\{U,V,W\}$ (over the
N=4 base variables). \ The cycle operator is defined in terms of the 2-form
"current" multiplied by an integrating factor, $1/\lambda(U,V,W)$ such that
$dG_{cl}=0.$ \
\begin{align}
G_{cl} & =\partial_{z}\omega^{p+1}=\partial_{z}(dU\symbol{94}dV\symbol{94}%
dW)\\
& =i([U,V,W])dU\symbol{94}dV\symbol{94}dW/\lambda\\
& =(UdV\symbol{94}dW-VdU\symbol{94}dW+WdU\symbol{94}dV)/\lambda,\\
\lambda & =(aU^{m}+bV^{m}+eW^{m})^{(3/m)},\\
\Gamma & =1/\lambda,\ \ \ \ dG_{cl}=0.
\end{align}
The closed non-exact component of the 2-form, $G_{cl}$, is homogeneous of
degree zero in terms of its functions. \ The choice of integrating factor
given above is based on an extension of the Holder norm. \ The homogeneous
2-form, $G_{cl}$, has many representations in terms of the arbitrary constants
(signature) $\{a,b,c\}$ and the exponent $m$. \ Note that the choice of the
cubic format, $m=3,$ yields a simple algebra.
\subsection{3-form Currents}
The construction for the closed but not exact component of a 3-form follows
the procedure given for the 1-form. \
\begin{align}
J_{cl} & =\partial_{z}\omega^{p+1}=\partial_{z}(dU\symbol{94}dV\symbol{94}%
dW\symbol{94}dS)\\
& =i([U,V,W,S])dU\symbol{94}dV\symbol{94}dW\symbol{94}dS/\lambda\\
& =(UdV\symbol{94}dW\symbol{94}dS-VdU\symbol{94}dW\symbol{94}dS+WdU\symbol{94}%
dV\symbol{94}dS-SdU\symbol{94}dV\symbol{94}dW)/\lambda,\\
\lambda & =(aU^{m}+bV^{m}+eW^{m}+fS^{m})^{(4/m)},\\
\Gamma & =1/\lambda,\ \ \ \ \ dJ_{cl}=0.
\end{align}
The closed non-exact component of the 3-form is homogeneous of degree zero in
terms of its functions.
The results constructed above for 1, 2, and 3-forms can be generalized as a theorem.
\begin{theorem}
On a pregeometric variety of N independent base variables, a projective
differential volume element of M independent functions, $d(Vol)=dV^{1}%
\symbol{94}...dV^{M},$ can always be associated with an M-1 current,
$J=i([V^{1},..,V^{M})d(Vol)$ that admits an integrating factor of the form
$1/\lambda$ where $\lambda=((a1(V^{1})^{m}...+am(V^{M}))^{(M/m)}$ such that
$d(J/\lambda)=0,$ and the renormalized current is homogeneous of degree zero.
\ It is thereby possible to construct an infinite number of conservation laws
on an N volume.
\end{theorem}
\begin{remark}
I\ was led to this theorem from a study of singularities presented in Chapter
2 of Sewell \cite{Sewell}, especially the problem 2.3.3 on page 108. \ The
idea of a homogeneity "integrating factor" can also be accomplished in terms
of the Buckingham Pi product, a format which is utilized in the same problem.
\end{remark}
\subsubsection{GR QC notation}
In GR applications \cite{Jacobsen}, the notation changes but the game is the
same. \ \ Merely substitute the symbol $Q$ in the 2-form expressions above,
such that $Q=Q_{no}+Q_{cl}+Q_{ex}$. \ Then the "Noether Current" (as used by
Wald and Jacobsen) is defined \ as $J=dQ=dQ_{no},$ and does not depend upon
either the closed or exact components of $Q.$ \ Wald uses the idea that $Q$ is
the "Noether potential" for which "entropy" is defined as
\begin{equation}
"\text{Entropy" }S=2\pi%
{\textstyle\oint}
Q,
\end{equation}
which unfortunately gives the (incorrect) impression that this formula is
somehow related to a 1 dimensional integral of some 1-form. \ Indeed, it
appears that the expression for the equilibrium thermodynamic system described
by the formula,
\begin{equation}
PdV+dU-TdS=0,
\end{equation}
motivated the early conjectures about "Black Hole Entropy". \ This expression
of the first law in isolated equilibrium systems is indeed an exterior
differential system based upon a 1-form. \ However, the method employed by
Wald and Jacobsen is not related to such a 1-form, but instead is related to
the evaluation of a 2-form over a boundary which is an area. \ A somewhat more
precise notation for the Wald formula would be written as:%
\begin{align}
\text{"Entropy"\ }S & =2\pi%
{\textstyle\iint\limits_{\partial M}}
Q=2\pi%
{\textstyle\iint\limits_{\partial M}}
\{Q_{no}+Q_{cl}+Q_{ex}\}\\
& =2\pi%
{\textstyle\iint\limits_{\partial M}}
\{Q_{no}\}+0+0\\
& =%
{\textstyle\iiint\limits_{M}}
dQ_{no}=%
{\textstyle\iiint\limits_{M}}
J\neq0,\text{ \ }\\
J & =dQ_{no}\ \ \ \text{defined as the "Noether" current.}%
\end{align}
It is not at all clear that this formulation has anything to do with
Thermodynamic entropy. \ Note that by merely changing the letters, the
formalism is exactly that given above relating to the Charge-Current 4 vector
of electromagnetism and the conservation of charge-current in EM theory. \ %
\begin{equation}%
{\textstyle\iint\limits_{\partial M}}
G_{no}=%
{\textstyle\iiint\limits_{M}}
dG_{no}=%
{\textstyle\iiint\limits_{M}}
J\neq0
\end{equation}
From the topological perspective, changing the symbols does not change the
universality of the ideas. \ Should I then believe that the Entropy - Area
formula is nothing more than using different symbols, but is equivalent to
Gauss' law relating a surface area integration of the D field on a boundary to
the integral of the charge density in the bounded volume in EM theory? \ Is
the integral of G(D,H) over a bounding area somehow related to entropy? \ What
has charge to do with Entropy? \ Do not these questions leave the Bekenstein -
Hawking concept of black hole entropy, and especially Wald's formulation
somewhat suspect, and perhaps the result of speculative wishful thinking.
\ The Wald integrals have nothing to do with topological quantization.
In my opinion, the (somewhat suspect) Wald formulation\ does open Pandora's
box. \ What about the possible quantum features? \ Could it be that there
exist cosmological quanta associated with period integrals of a closed but
non-exact, $Q_{cl}$? \ These possibilities will be discussed below. \ First it
is necessary to discuss the difference between pair and impair differential
forms, and their relationships to Lagrangian N-form densities. \
\subsection{Lagrangian pair and impair N-forms}
Consider maps defining the range of vector arrays with coefficients, $V^{m},$
as functions of the domain of independent variables $x^{k}$ :%
\begin{align}
\phi & :x^{k}\Rightarrow V^{m}=V^{m}(x^{k})\\
d\phi & :dx^{k}\Rightarrow dV^{m}=\{\partial V^{m}(x^{k})/\partial
x^{n}\}dx^{n}.
\end{align}
These maps $\phi$\ need \textit{not} be diffeomorphisms. \ The function
$\Delta$ is defined as the determinant of the mapping Jacobian matrix, \
\begin{equation}
\Delta(x^{m})=\det[\partial V^{m}(x^{k})/\partial x^{n}],
\end{equation}
which is not zero, if the map is a diffeomorphism. \ Another construction
defines the sign of the determinant as%
\begin{equation}
\left\vert \Delta\right\vert /\Delta=sign[\partial V^{m}(x^{k})/\partial
x^{n}],
\end{equation}
\subsubsection{Pair and Impair}
Consider various field functions defined on the range variables, $V^{m}$, and
collectively named $\varphi(V^{m}).$ \ Next, consider a special function
L\ (the Lagrange function) of these variables, denoted by the symbol
L$(\varphi(V^{m}))=\rho(V^{m}).$ \
There now are two possibilities: \
\begin{enumerate}
\item Construct the Pair N-form on the range $dV^{m}:\{\rho\}dV^{1}%
\symbol{94}dV^{2}..\symbol{94}dV^{N}$\bigskip
\item or the Impair N-form on the range $dV^{m}:\{\rho\cdot(\left\vert
\Delta\right\vert /\Delta\}dV^{1}\symbol{94}dV^{2}..\symbol{94}dV^{N}$
\end{enumerate}
Use functional substitution defined by the map $\phi$ and its differentials to
evaluate the pullbacks of both the pair and impair p-forms:
\begin{equation}
\text{Using }dV^{1}\symbol{94}dV^{2}..\symbol{94}dV^{N}\Rightarrow\Delta
(x^{m})dx^{1}\symbol{94}dx^{2}..\symbol{94}dx^{N},
\end{equation}
\begin{align}
\text{Pair N-form }\{\rho(x^{k})\Delta(x)\}dx^{1}\symbol{94}dx^{2}%
..\symbol{94}dx^{N} & \Leftarrow\{\rho(V)\}dV^{1}\symbol{94}dV^{2}%
..\symbol{94}dV^{N},\\
\text{A "scalar\ }\Delta\text{-density"} & \text{:}\rho(x^{k})\Delta
(x)\Leftarrow\rho(V).
\end{align}%
\begin{align}
\text{Impair N-form \ }\{\rho(x^{k})\left\vert \Delta(x)\right\vert
\}dx^{1}\symbol{94}dx^{2}..\symbol{94}dx^{N} & \Leftarrow\{\rho
(V)\cdot(\left\vert \Delta\right\vert /\Delta)\}dV^{1}\symbol{94}%
dV^{2}..\symbol{94}dV^{N},\\
\text{A\ "pseudoscalar }\Delta\text{-density"} & \text{:}\{\rho
(x^{k})\left\vert \Delta(x)\right\vert \}\Leftarrow\rho(V)(\left\vert
\Delta\right\vert /\Delta).
\end{align}
The important thing to remember is that the integrals of Pair p-forms depends
upon the sign of the orientation of the integrand, and the integrals of Impair
p-forms do not depend upon sign of the orientation of the integrand. \ %
\begin{align}
\text{Scalar-densities } & \text{:}\rho(x^{k})\cdot\Delta(x)\\
\text{PseudoScalar-densities} & \text{: }\rho(x^{k})\cdot\left\vert
\Delta(x)\right\vert
\end{align}
The Lagrangian N-form can have two representations (or sometimes the complex
N-form that consists of both the Pair and the Impair structure). \ One
representation recognizes that orientation is important, so that the
Lagrangian is written as a pair N-form on the range space:%
\begin{equation}
\text{Pair Lagrangian N-form}=\{\text{L}(\varphi(V^{k}))\}dV^{1}%
\symbol{94}dV^{2}..\symbol{94}dV^{N}\}.
\end{equation}
Next construct the Lie differential of the N-form as%
\begin{equation}
L_{(V^{m})}\{\text{L}(\varphi)\}dV^{1}\symbol{94}dV^{2}..\symbol{94}%
dV^{N}\}=d\{\text{L}(\varphi)i(V^{m})dV^{1}\symbol{94}dV^{2}..\symbol{94}%
dV^{N}\}.\label{dfnform}%
\end{equation}
Hence there exists an N-1 form Current of the format:%
\begin{equation}
J(V)=\text{L}(\varphi)\{i(V^{m})dV^{1}\symbol{94}dV^{2}..\symbol{94}dV^{N}\}
\end{equation}
that pulls back to the domain space as%
\begin{align}
\text{Pair }J(x) & =\text{L}(\psi(x))\Delta(x)\{i(V^{m})dx^{1}%
\symbol{94}dx^{2}..\symbol{94}dx^{N}\},\\
\psi(x) & =\varphi(V(x)).
\end{align}
The formula for the Impair pullback is (the only difference is the use of the
absolute magnitude of the determinant):%
\begin{align}
\text{Impair }J(x) & =\text{L}(\psi(x))\left\vert \Delta(x)\right\vert
\{i(V^{m})dx^{1}\symbol{94}dx^{2}..\symbol{94}dx^{N}\},\\
\psi(x) & =\varphi(V(x)).
\end{align}
\begin{remark}
The integrals of pair forms depend upon the choice of orientation of the
integration chain. \
The integrals of impair forms do not depend upon an orientation of the
integration chain.
\end{remark}
\subsection{Thermodynamic Quantized Currents (3-forms)}
\subsubsection{The exterior differential form method}
The idea is to use topological thermodynamics (where physical systems are
encoded in terms of various 1-forms and 2-forms and p-forms), and exterior
calculus of Cartan to algebraically deduce 3-form currents with their Noether
components and their closed components. \ The method is to be compared with
the ubiquitous, but topologically awkward, Lagrangian approach that is based
upon a starting point of N-form densities, and their associated Noether
currents, but leaves undetermined the closed and the exact components of these
currents. \ Note that in physical thermodynamic systems both species of pair
and impair p-forms are useful. \ Pair forms are related to "intensities" such
as pressure and temperature, while impair p-forms are related to "additive
quantities, or source excitations" such as volumes and entropy. \
The most familiar examples of the thermodynamic method are exhibited by the
topological features \ of electromagnetism. \ In EM theory, the 2-form of
intensities, $F(E,B)=dA,$ is a pair 2-form (which is exact), and the 2-form of
excitations, $G(D,H),$ is impair. \ These facts have been experimentally
verified from studies of the behavior of electromagnetic signals in
crystalline media with and without a center of symmetry \cite{PostTG}. \ The
symbols of EM theory will be used in this section, as the notation is more
familiar to most (physicist)\ readers. \ It does not mean that the ideas are
restricted to an EM\ interpretation. \ Thermodynamics is universal to all
physical systems.
An example of a Pair 4-form algebraically can be constructed from the 1-form,
$A,$ and its 2-form, $F=dA,$ such that the exterior product of $A\symbol{94}F$
generates a Pair 3-form "current", $J_{pair}=H=A\symbol{94}F$. \ This 3-form
is a Pair 3-form as $F$\ is a Pair 2-form, and $A$ is a pair 1-form. \ This
form I\ have called the 3-form of Topological Torsion. \ It has the usual
3-part decomposition in terms of Noether, closed, and exact components. \
\begin{align}
\text{Pair } & :\text{\ Topological Torsion 3-form}\\
J_{pair} & \Rightarrow H=A\symbol{94}F\text{ \ }\\
& =H_{no}+H_{cl}+H_{ex}%
\end{align}
The 3-form is a current that can be explicitly determined from the formula for
the Topological Torsion Vector, $\mathbf{T}_{4}$, such that
\begin{equation}
i(\mathbf{T}_{4})d(Vol)=A\symbol{94}F.
\end{equation}
It is remarkable that the 4 components (relative to x,y,z,t) of this vector
can be evaluated in terms of the functions (and their partial differentials)
that define the 1-form of Action, $A$,
\begin{equation}
\mathbf{T}_{4}=[\mathbf{E\times A}+\mathbf{B}\phi,~\mathbf{A\cdot B]}%
\end{equation}
\subsubsection{The Second Poincare Invariant (a Pair 4-form)}
The exterior differential of the Topological Torsion\footnote{Sometimes
refered to as the Helicity 3-form} current 3-form leads to the Topological
Parity 4-form, $K=F\symbol{94}F$. \ The closed integrals of $F\symbol{94}F$
define the Second Poincare Invariant.
\begin{align}
\text{Pair } & :\text{Topological Parity 4-form}\\
dH & =dH_{no}=d(A\symbol{94}F)=F\symbol{94}F=K\\
K & =F\symbol{94}F=2(\mathbf{E\cdot B})dx\symbol{94}dy\symbol{94}%
dz\symbol{94}dt\\%
{\textstyle\iiiint\limits_{closed}}
F\symbol{94}F & =\text{ Second Poincare Invariant.}%
\end{align}
When evaluated in EM symbols, it is apparent that the ($\Delta)$ density
coefficient of $F\symbol{94}F$ is\ $2(\mathbf{E\cdot B}).$ \
The second Poincare invariant, indeed, is an evolutionary invariant, for the
continuous topological evolution generated by the Lie differential (with
respect to \textit{any} evolutionary direction field, $\beta V^{k}$) acting on
the closed integrals of $F\symbol{94}F$ is zero. \ That is, continuous
topological evolution produces no change in the closed integrals of
$F\symbol{94}F$:%
\begin{align}
L_{(\beta V^{k})}%
{\textstyle\iiiint\limits_{closed}}
F\symbol{94}F & =%
{\textstyle\iiiint\limits_{closed}}
\{i(\beta V^{k})d(F\symbol{94}F)+d(i(\beta V^{k})F\symbol{94}F)\}\\
& =%
{\textstyle\iiiint\limits_{closed}}
\{0+d(i(\beta V^{k})F\symbol{94}F)\}=0.
\end{align}
Note that the evolutionary invariance of the closed integral is valid
independent from the parameterization factor, $\beta(x,y,z,t),$ of the
direction field, $V^{k}.$
It is further remarkable that evolution of the Cartan topology (generated\ by
the 1-form of Action) in the direction\ of the topological Torsion vector,
$\mathbf{T}_{4},$ is thermodynamically irreversible when $F\symbol{94}F$ is
not zero, for%
\begin{align}
L_{(\mathbf{T}_{4}^{k})}A & =(\mathbf{E\cdot B})A=Q\\
L_{(\mathbf{T}_{4}^{k})}dA & =d(\mathbf{E\cdot B})\symbol{94}%
A+(\mathbf{E\cdot B})dA=dQ,\\
Q\symbol{94}dQ & =(\mathbf{E\cdot B})^{2}(A\symbol{94}dA)\neq0
\end{align}
The fact that $Q\symbol{94}dQ$ is NOT zero implies that $Q$ does not admit an
integrating factor, which is the classical idea \cite{Morse} that the process
that generated $Q$ is thermodynamically irreversible. \ The fact that
$\mathbf{E\cdot B}$ cannot be zero implies that the Pfaff topological
dimension of the 1-form of Action, $A$, must be 4.
The topological evolution of the volume element with respect to the
irreversible process represented by $\mathbf{T}_{4}$ is given by the
expression:%
\begin{equation}
L_{(\mathbf{T}_{4}^{k})}d(Vol)=2(\mathbf{E\cdot B})d(Vol).
\end{equation}
The dissipative irreversible evolution of the volume element can be positive
or negative, representing an expansion or contraction of space time, depending
upon the sign of the dissipation coefficient, $(\mathbf{E\cdot B}). $ \
\begin{remark}
The expanding universe is an artifact of thermodynamic irreversibility.
\end{remark}
\subsubsection{The First Poincare Invariant (an Impair 4-form)}
An example of a Impair 4-form can be given by the expression related to the
First Poincare invariant, a portion of which is often used to define the
electromagnetic impair Lagrange density for the electromagnetic field. \ The
impair 4-form also has a Current that can be written in the format of the
impair 3-form $A\symbol{94}G$, herein called "Topological Spin". \ \ This
3-form I\ have called the 3-form of Topological Spin. \ It has the usual
3-part decomposition in terms of Noether, closed, and exact components. \
\begin{align}
\text{Impair } & :\text{\ Topological Spin 3-form}\\
J_{impair} & \Rightarrow S_{impair}=A\symbol{94}G\text{ \ }\\
& =S_{no}+S_{cl}+S_{ex}%
\end{align}
The exterior differential of the Topological Spin current 3-form leads to the
Lagrange density 4-form, \textbf{L}. \ The closed integrals of \textbf{L}
define the Second Poincare Invariant.
\begin{align}
\text{Impair } & :\text{Lagrange density 4-form}\\
dS & =dS_{no}=d(A\symbol{94}G)=F\symbol{94}G-A\symbol{94}J=\text{\textbf{L}%
}\\
\text{\textbf{L}} & \mathbf{=}F\symbol{94}G-A\symbol{94}J\\
& =\{(\mathbf{B\cdot H-D\cdot E})-(\mathbf{A\cdot J}-\rho\phi)\}dx\symbol{94}%
dy\symbol{94}dz\symbol{94}dt,\\%
{\textstyle\iiiint\limits_{closed}}
F\symbol{94}G-A\symbol{94}J & =\text{ First Poincare Invariant.}%
\end{align}
The topological 4-form (deducible from the topological Spin 3-form,
$A\symbol{94}G)$\ was "discovered" in 1974 \cite{rmkintrinsic}.
The second Poincare invariant, indeed, is an evolutionary invariant, for the
continuous topological evolution generated by the Lie differential (with
respect to \textit{any} evolutionary direction field, $\beta V^{k}$) acting on
the closed integrals of $F\symbol{94}G-A\symbol{94}J=d(A\symbol{94}G)$ is
zero. \ That is, continuous topological evolution produces no change in the
closed integrals of $d(A\symbol{94}G)$:%
\begin{align}
L_{(\beta V^{k})}%
{\textstyle\iiiint\limits_{closed}}
d(A\symbol{94}G) & =%
{\textstyle\iiiint\limits_{closed}}
\{i(\beta V^{k})dd(A\symbol{94}G)+d(i(\beta V^{k})d(A\symbol{94}G)\}\\
& =%
{\textstyle\iiiint\limits_{closed}}
\{0+d(i(\beta V^{k})d(A\symbol{94}G)\}=0.
\end{align}
Note that the evolutionary invariance of the closed integral of the first
Poincare 4-form is valid independent from the parameterization factor,
$\beta(x,y,z,t),$ of the direction field, $V^{k}.$
\subsubsection{Period integrals of 3-forms}
Period integrals are integrals over closed integration chains that are not
boundaries of closed but not exact forms. \ Each 3-form is a current of the
format$:$%
\begin{equation}
J_{pair}=J_{no}+J_{cl}+J_{ex}.
\end{equation}
Period integrals have integrands which are closed but not exact. \ Hence the
domains of interest are where the Noether component is zero, and the exact
component is of no consequence to the value of the integral.%
\begin{equation}
\text{3-form Period Integral}=%
{\textstyle\iiint\limits_{z3}}
J_{cl}.
\end{equation}
By deRham's theorems, the value of the integral is an integer times a constant
depending upon the cycle z3. \
There are two types of period integrals, depending upon whether the integrand
is Pair or Impair. \ The Pair 3-form, $A\symbol{94}F$, of topological Torsion
has possible periods in domains where the second Poincare invariant vanishes,
$F\symbol{94}F=0.$ \ In such domains, the Pfaff topological dimension of $A$
must be $<4.$ \ As $A\symbol{94}F$ vanishes in domains of Pfaff topological
dimension $<3$, it follows that period integrals of Torsion must exist in
domains of Pfaff dimension 3. \ If continuous topological evolution causes a
domain of Pfaff dimension 3 to emerge (like a condensation)\ from the physical
vacuum of Pfaff dimension 4, then such domains could be topologically
quantized. \ The period integral 3-form\ $%
{\textstyle\iiint\limits_{z3}}
J_{cl}$ would have values n times a constant representing physical units. \ In
EM theory the physical units of $A\symbol{94}F$ are $(\hbar/e)^{2}%
=Z_{Hall}\cdot\hbar.$ \ Hence the periods for $J_{cl}=H_{cl}$ would be of the form,%
\begin{equation}
\text{Topological Torsion Quanta: }%
{\textstyle\iiint\limits_{z3}}
J_{cl}\Rightarrow%
{\textstyle\iiint\limits_{z3}}
H_{cl}=\pm\ n~(Z_{Hall}\cdot\hbar).
\end{equation}
The periods are sensitive to the orientation of the integration chain, hence
they have plus and minus values. \ For the 3-form of topological torsion to be
closed it is necessary that $F\symbol{94}F=0=2(\mathbf{E\circ B}%
)dx\symbol{94}dy\symbol{94}dz\symbol{94}dt$. \ The constraint means the second
Poincare invariant must be zero. \ The macroscopic domains that satisfy the
conditions of a period integral, are defined as topological Torsion quanta.
Similarly, when the first Poincare Invariant vanishes, that is in domains
where the exterior differential of the impair 3-form, $A\symbol{94}G$
vanishes, closed but not exact components of $A\symbol{94}G$ can have
"quantized" period integrals in the sense of deRham. \ That is, the integrals
of the closed but not exact integrands, relative to closed integration chains
which are cycles and not boundaries, can have values which are rational
numbers times a constant. \ In EM theory, the physical units of $A\symbol{94}%
G$ are $\hbar,$such that the periods of the 3-form $A\symbol{94}G$ become:%
\begin{equation}
\text{Topological Spin Quanta: }%
{\textstyle\iiint\limits_{z3}}
J_{cl}\Rightarrow%
{\textstyle\iiint\limits_{z3}}
S_{cl}=n~(\hbar).
\end{equation}
Such objects are defined as Topological Spin quanta. \ The macroscopic domains
of topological Spin quanta admit several possibilities, as the necessary
algebraic constraint of closure, $d(A\symbol{94}G)\Rightarrow0:$
\begin{equation}
\{(\mathbf{B\cdot H}-\mathbf{D\cdot E})-(\mathbf{A\cdot J}-\rho\phi
)\}\Rightarrow0,
\end{equation}
can be satisfied in several ways. \ The Spin quanta are not sensitive to the
orientation of the integration domain.
\section{Conclusions}
In Part I the idea was to describe a topological cosmology in terms of an open
thermodynamic system. \ Such systems can be encoded by means out a 1-form of
action, A, of Pfaff topological dimension 4. \ Such systems support continuous
topological evolution to states of the lower Pfaff dimension, and such states
may be viewed as topological defects in the Open system environment. \ These
states emerge from the open system forming topologically coherent structures
of Pfaff dimension 3, which are not in thermodynamic equilibrium in the sense
that they exchange radiation with their environment. \ They represent stars
and galaxies which have "condensed" out of the background cosmology.
These Pfaff dimension 3 states can continue to evolve to thermodynamic states
of lower Pfaff dimension that represent isolated or equilibrium systems.
\ Rotational spirals to a limit cycle are typical artifacts of such processes.
\ It is remarkable that one of the possible evolutionary processes supported
\ by thermodynamic systems of Pfaff dimension 3 is a Hamiltonian process,
where the topology remains constant for appreciable lifetimes (mod topological fluctuations).
In Part II it was noted that during processes of continuous topological
evolution it is possible that topologically coherent macroscopic (at all
scales) states will emerge which have closed integrals that are proportional
to the integers. These are the states of a quantum cosmology, and they are
seen at all scales. \ The key feature is that these states are represented by
p-forms which are homogeneous of degree zero (self-similarity). \ Mathematical
examples of such singularity defect structures appear at Pfaff topological
dimensions of 1, 2, and 3. \ These topologically quantized states - the flux
quantum, the charge quantum, the torsion quantum and the spin quantum - are
not dependent upon metric issues. \
An open question is the description of a black hole in terms of thermodynamic
states. \ It must be a non equilbrium state for it is accepting radiation and
matter from its enviroment. \ For excited states (with a black hole
temperature) it could be thermodynamically closed in the sense that it
exchanges radiation with its environment; \ but mass is not exchanged, only
absorbed. \ It is conjectured that the one way process for mass is to be
associated with fact that 3-form of topological Spin is not sensitive to
orientation. \ On the otherhand, radiation and the 3-form of topological
Torsion is orientation (polarization)\ sensitive. \ These issues are under investigation.
The bottom line is that quantum cosmology is a topological issue not a
geometrical issue.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,537 |
How to watch very major NRL event live in Australia
Whether you're in NSW, QLD, TAS, VIC, SA, WA and NT.
https://www.reviews.org/au/entertainment/watch-nrl-live-online/
Depending on where you live, restrictions on NRL broadcasts vary. We've covered where you can watch NRL online and live in every state.
Reviews AU team
Because finding out the what, where and when of every NRL game should never be trying.
This guide was produced by Reviews AU freelancer Adam Mathew.
When it comes to cracking a cold one and catching some footy on your telly, the game of watching has changed in the last couple of years. Yes, the NRL inked a $1.8 billion TV deal that was put into effect in 2016, but that's not the end of what is a slightly more complex story.
Everything has been divvied up. For starters, screen junkies willing to pay a little bit more to endure fewer ads can get coverage of each and every game. Those on a budget can also catch a few of those as the Thursday Night, second Friday night and Sunday afternoon games in each round are simulcast to Channel Nine.
You should also know that the NRL season runs over the course of four weeks of finals after 25 home-and-away rounds, (literally) kicking off in the first week of March and culminating on the last Sunday of September.
Be that as it may, the following table will give you an outline until we know.
Match Game Time (AEDT/AEST) Broadcasters
1 Thursday night 7:50pm Nine, Fox League
2 Friday evening 6:00pm Fox League
3 Friday night 7:55pm Nine, Fox League
4 Saturday afternoon 3:00pm Fox League
5 Saturday evening 5:30pm Fox League
6 Saturday night 7:35pm Fox League
7 Sunday afternoon 4:05pm Nine, Fox League
8 Sunday night 6:10pm Fox League
$25 p/month
No contract or commitments
Kayo is Australia's on-demand option for a massive roster of popular sports. Take it for a whirl at no cost at all.
How to watch NRL in QLD, NSW, SA, NT, WA, VIC and TAS
Warring States of Play
Where you watch from will determine what's available. If you're in Queensland or New South Wales
you can expect to be lavished with the full range of NRL coverage from Fox and Channel Nine. However, any fans in South Australia and the Northern Territory won't be catered to anywhere near as well.
South Australians once enjoyed a deal where the Sunday afternoon fixture and all three games were broadcast but delayed until midnight or the wee hours of the next day. Things have marginally improved here in recent years, however, as the Sunday match is now shown live.
That said, folks in what we like to call borderline NRL states – Victoria, Tasmania and Western Australia – can get full coverage, though these free-to-air offerings will be delivered via GEM, instead of Nine.
The good news is that every NRL Finals match is set to be shown live across the country. Whether you only have the Nine Network to rely upon, or if you're a paying Foxtel subscriber, you're covered and all set! There's one small caveat here, however, as the grand final game (and all of the State of Origin matches also) will only be screened on Channel Nine. You can thank an exclusive rights deal for that one.
Anybody who is going to be in a sans-TV environment will have little to worry about. Providing you have an Internet-enabled device you can get access to every game of the season via a digital subscription to either Kayo Sports or Foxtel Now. That said, the earlier mentioned limitation still applies – Channel Nine has exclusive dibs on the Grand Final match and all State of Origin content.
International fans from afar
The far-flung among you can still get their NRL fix by subscribing to Watch NRL. This imaginatively named service lets you stream all of the games live, from pretty much any continent you please. Visit WatchNRL.com for more specifics here.
Watch NRL pricing
Subscription AUD USD GBP EUR
Weekly $19 $17 £13 €17
Monthly $33 $28 £22 €28
12 Months $189 $149 £125 €149
Final Series Pass $79 $60 £48 €50
Streaming on-demand? See what we think of the providers
Read the reviews from our experts and community.
KAYO REVIEW
Got the speed to stream?
Have a gander at the most popular NBN 50 plans on the market according to WhistleOut's broadband comparison engine.
NRL broadcast schedule
Difference between states
How to watch NRL finals
How to live stream NRL
Watching NRL overseas
Every NRL Premiership game live (except Finals) | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,226 |
Q: Deadlock with ReadUncommitted? In ADO.NET, does setting the transactions isolation level to ReadUncommitted and then rolling back that transaction work effectively as a "dirty read"?
If so, why does it get deadlocked on ExecuteReader?
Code:
command.Transaction = connection.CreateTransaction(IsolationLevel.ReadUncommitted);
command.CommandTimeout = 0;
command.CommandText = query;
command.CommandType = CommandType.Text;
var reader = command.ExecuteReader(CommandBehavior.Default);
...
A: Read Uncommitted will allow the transaction to read inserts/updates made by other transactions that have not yet committed, essentially functioning as a dirty read.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,764 |
'use strict';
var rarity = require('rarity');
var uploadCard = require('./helpers/upload.js');
module.exports.addition = function additionQueueWorker(job, cb) {
uploadCard(job.task, job.anyfetchClient, job.serviceData.accessToken, cb);
};
module.exports.deletion = function deletionQueueWorker(job, cb) {
job.anyfetchClient.deleteDocumentByIdentifier(job.task, rarity.slice(1, function(err) {
// If the document has already been deleted
if(err && err.toString().match(/expected 204 "No Content", got 404 "Not Found"/i)) {
err = null;
}
cb(err);
}));
};
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,262 |
City Council offers support for NWCC name change; along with a bit of advice
A delegation from Northwest Community college provided
an update at Monday's Council session, providing some background
on the college's plans, while seeking support for their
proposed name change
City Council members explored a range of themes and offered up some local advice on post-secondary education on Monday evening, as Council received a delegation from Northwest Community college which provided an update on their vision and strategic planning as well as their work towards introducing a new name for the educational institution.
Sarah Zimmerman, the Director of Communications and Public Relations at NWCC took the lead for the group, which also included Herb Pond from the College Board of Directors and Pouan Mahboubi the Dean of instruction at the Prince Rupert campus.
Her fifteen minute overview, which consisted of a slide show presentation, provided some background to recent planning at the college and how they have addressed some of the economic challenges and to address their enrolment decline.
Among her notes was a review of how the college is looking to increase the number of international students in the region, with Prince Rupert's campus set to receive a number of students in the fall as part of those programs.
The main focus for her presentation was to offer up a review and a bit of a timeline towards the name change initiative and how the college believes it will assist their efforts in attracting new students to the Northwest campuses.
Ms. Zimmerman also observed that the college is seeking letters of support from around the Northwest to support the college's name change initiative, noting that they have received letters from the City of Terrace and a number of School District's in the region.
Council members voted Monday to approve
a letter of support for the quest by NWCC to change
its name to Coast Mountain College
Following her review Council members offered up a number of comments over an additional fifteen minutes and asked questions related to the name change theme, with many expressing their support for the project.
Councillor Mirau offered up his strong support for the name change initiative and how he would be urging council to write the letter of support and highlighted his support for the college's desire to develop their vision towards "experiential place based learning"
He further added that the name change would also serve as a tool to make the region a destination for international students to come and study and help to boost enrolment.
He had one question, noting that he had heard through the grapevine that the local School District (SD52) had not supported the name change, asking if they had received the same presentation as the one council had just hosted, and how he was at a loss as to why they are opposed to the name change.
Ms. Zimmerman observed that while she had offered to make a presentation to the School District they had chosen to not take her up on that offer and instead based their decision on the news release that had been forwarded to them.
She further outlined that she did not know the nature of their opposition to the name change initiative but would be willing to meet with them if they wish.
The NWCC communications officer might have asked for access to Mr. Mirau's "grapevine" perhaps found here(?) where some background on the SD52 decision not to support the name change proposal might be found.
Other Council members spoke to the theme of the name change and issues related to the college's programs in Prince Rupert.
Councillor Gurvinder Randhawa, expressed his support for the name change, but offered up a cautionary note when it comes to attracting international students and how there should be a preference for local students when it comes to enrolment.
Councillor Cunningham also offered up his full support for the name change initiative and was pleased to hear of the upcoming project to bring some of those international students to Prince Rupert, noting of his concern of the lack of courses that NWCC makes available in Prince Rupert.
Councillor Niesh recounted a dinner conversation with Herb Pond at a recent event and how Mr. Pond provided further background from the Board's point of view on how the proposed name change will assist the college in its plans for the region.
Councillor Thorkelson conceded to the consensus that it's probably a good thing that the college changes its name, but did offer up some concerns about the level of course content available in Prince Rupert and recounted for the delegation the mandate for the college when it was established.
From those early days, she highlighted the three pillars of labour, aboriginal and academic that made for that foundation to build the college, observing that those pillars had been dropped sometime in the 1980's.
She expressed a cautionary note that in their ambition to attract international students that the college not lose the flavour of the area and using the college's vision statement of experiential place based learning, observing how the college should continue to reflect the unique nature of the Northwest and not reduce the trades programs and other courses that reflect the interests of the region.
For his part Mayor Brain also offered his support to the name change and outlined how he has benefited from experiential learning himself and how he believes its the right strategy for the college to pursue.
He also called attention to some of the conversations that he had at the recent UBCM conference and the perception for many in the region (perhaps through the same grapevine that Mr. Mirau relies on) that NWCC is very much a Terrace college and that there is a consolidation taking place in Terrace, particularly after the closing of the Houston campus.
The Mayor also observed that the perception for many, whether right or wrong, is that there is a plan to make Terrace the benefactor of all the provincial funding and that the outlying areas are left with crumbs.
To further his themes, Mayor Brain offered up his message to the college that as part of any re-branding initiative that they should recommit to the communities in the area and strengthen the student associations in those communities.
Ms. Zimmerman noted that she would be bringing the Council's comments back to the college for further review.
A more expansive review of the NWCC presentation can be reviewed on our Council Timeline feature.
You can review the full presentation to Council from the City's Video Archive of the Monday night session, which starts in the opening minutes of the Council Meeting.
To bring the agenda item to a conclusion, the Mayor called for a friendly motion to offer support for the name change, with Councillor Randhawa noting that they should include an element to encourage that preference should be given for local students.
Council then voted to approve the request to provide a letter of support.
For more items related to Northwest Community College and other education opportunities in the community see our archive page here.
Further background on civic issues and notes can be examined on our Council Discussion archive.
Labels: Council to support NWCC name change quest | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,348 |
Себастьен Шарль Жиро (; 1819—1892) — французский художник.
Биография
Брат и ученик Пьера Франсуа Эжена Жиро. Писал в основном жанровую живопись.
В 1843—1847 совершил путешествие на Вест-Индские острова. В 1846 году участвовал в военной экспедиции вместе с королем Луи-Филиппом на Таити. В это время ему удалось сделать множество набросков острова: растительность, люди, их дома. Когда он вернулся во Францию, его прозвали «Giraud le Tahitien» (Жиро Таитянский). Сопровождал в 1856 году принца Ж. Наполеона в его экспедиции на Север, и с того времени писал, помимо бытовых сцен, внутренние виды зданий и частично ландшафтные пейзажи.
Как на лучшие его картины, отличающиеся вообще превосходной передачей перспективы и тонкой отделкой деталей, можно указать на «Столовую принцессы Матильды» (1855), «Ловлю тюленей» (1857), «Рабочий кабинет графа Ньевенкерке», «Наполеоновский зал в Лувре», «Галерею оружия, в музее Клюни», «Внутренность богатого фламандского дома», «Воскресенье в Бретани» (1878) и некоторые другие.
Примечания
Источники
Художники Франции XIX века
Рисовальщики Франции | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,871 |
Breakfast is one of Kansas' favorite meals, and breakfast foods are a special comfort that many of us would eat all day if we could. Whether your favorite is pancakes, eggs, hash browns, or biscuits and gravy, you're bound to find plenty of diners across the state that'll serve you. However, this small town diner in eastern Kansas serves biscuits and gravy so good, people travel from hours away. Let's take a look!
Welcome to Commercial Street Diner, a place in Emporia that charms everyone with their breakfast.
No, it's true. People have driven from hours away just to satisfy their craving for biscuits and gravy.
This diner itself has been in operation since 1994, but it was revived in 2010 by the Lairds.
Because of their decision to make this restaurant a second home, we now have dishes that people will travel for. If that doesn't say something, I don't know what does!
Here's the star of the show, biscuits smothered with gravy so much that you can't see them at all.
But that's how we love them! Whether you get a side or not, you won't usually see much biscuit under the gravy blanket.
For those of you who might want to try something else, check out the rest of the menu!
Their chicken fried steak is another one of their most popular items, and everything on the menu is homemade from the heart.
They do big breakfasts the best, and if you leave hungry, it's no fault of theirs, because the portions are more than plenty.
Another thing to note, is to come hungry! Even the pancakes are the size of your head.
They're open from 6 a.m. to 2 p.m. Tuesdays through Sundays, and closed on Mondays.
You'll find Commercial Street Diner at 614 Commercial St., Emporia, KS. It's a good thing that you'll never forget the street name, because the diner has the same! Here's a map, for anyone to use as they travel.
If lunch is your favorite time of day, you should also check out this all-you-can-eat lunch buffet in Kansas that's sure to satisfy.
How This Small Town In Kansas Quietly Became One Of The Most Unique Places In The U.S. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,923 |
XtrakR is an ultra-low power connected GPS beacon that is very easy to use. It has many options of outdoor connectivity (GPS) & indoor (Bluetooth, NFC, Wi-Fi). The beacon is waterproof and rechargeable by a micro-USB cable (supplied).
In addition to having all the features available on the TiFiz Xpress, the TiFiz XtrakR can be used in all environments. Whether you enjoy water sports or hiking it will work in any conditions thanks to its tightness.
Whether you want to trace your personal vehicle in case of a flight thanks to the geolocation or to have extra security for people isolated at sea thanks to the SOS button, the TiFiz XtrakR will be useful in all situations.
The TiFiz XtrakR beacon was created to geotag, track and secure isolated goods or people. In addition, this tag can serve as a backup button. A simple press of the central button instantly sends an SMS with a geolocation link to the person of my choice.
The beacon uses a new specialized network for connected objects (SIGFOX ™) that does not use a SIM card. It requires a subscription available from 4.20 € TTC / month. The tag also works with Bluetooth, NFC and Wi-Fi to always keep track. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,226 |
Polymer('flow-app-logs');
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,035 |
{"url":"https:\/\/voer.edu.vn\/c\/photon-momentum\/0e60bfc6\/da278131","text":"Gi\u00e1o tr\u00ecnh\n\nCollege Physics\n\nScience and Technology\n\nPhoton Momentum\n\nT\u00e1c gi\u1ea3: OpenStaxCollege\n\nMeasuring Photon Momentum\n\nThe quantum of EM radiation we call a photon has properties analogous to those of particles we can see, such as grains of sand. A photon interacts as a unit in collisions or when absorbed, rather than as an extensive wave. Massive quanta, like electrons, also act like macroscopic particles\u2014something we expect, because they are the smallest units of matter. Particles carry momentum as well as energy. Despite photons having no mass, there has long been evidence that EM radiation carries momentum. (Maxwell and others who studied EM waves predicted that they would carry momentum.) It is now a well-established fact that photons do have momentum. In fact, photon momentum is suggested by the photoelectric effect, where photons knock electrons out of a substance. [link] shows macroscopic evidence of photon momentum.\n\n[link] shows a comet with two prominent tails. What most people do not know about the tails is that they always point away from the Sun rather than trailing behind the comet (like the tail of Bo Peep\u2019s sheep). Comet tails are composed of gases and dust evaporated from the body of the comet and ionized gas. The dust particles recoil away from the Sun when photons scatter from them. Evidently, photons carry momentum in the direction of their motion (away from the Sun), and some of this momentum is transferred to dust particles in collisions. Gas atoms and molecules in the blue tail are most affected by other particles of radiation, such as protons and electrons emanating from the Sun, rather than by the momentum of photons.\n\nMomentum is conserved in quantum mechanics just as it is in relativity and classical physics. Some of the earliest direct experimental evidence of this came from scattering of x-ray photons by electrons in substances, named Compton scattering after the American physicist Arthur H. Compton (1892\u20131962). Around 1923, Compton observed that x rays scattered from materials had a decreased energy and correctly analyzed this as being due to the scattering of photons from electrons. This phenomenon could be handled as a collision between two particles\u2014a photon and an electron at rest in the material. Energy and momentum are conserved in the collision. (See [link]) He won a Nobel Prize in 1929 for the discovery of this scattering, now called the Compton effect, because it helped prove that photon momentum is given by\n\n$p=\\frac{h}{\\lambda },$\n\nwhere $h$ is Planck\u2019s constant and $\\lambda$ is the photon wavelength. (Note that relativistic momentum given as $p=\\gamma \\text{mu}$ is valid only for particles having mass.)\n\nWe can see that photon momentum is small, since $p=h\/\\lambda$ and $h$ is very small. It is for this reason that we do not ordinarily observe photon momentum. Our mirrors do not recoil when light reflects from them (except perhaps in cartoons). Compton saw the effects of photon momentum because he was observing x rays, which have a small wavelength and a relatively large momentum, interacting with the lightest of particles, the electron.\n\nElectron and Photon Momentum Compared\n\n(a) Calculate the momentum of a visible photon that has a wavelength of 500 nm. (b) Find the velocity of an electron having the same momentum. (c) What is the energy of the electron, and how does it compare with the energy of the photon?\n\nStrategy\n\nFinding the photon momentum is a straightforward application of its definition: $p=\\frac{h}{\\lambda }$. If we find the photon momentum is small, then we can assume that an electron with the same momentum will be nonrelativistic, making it easy to find its velocity and kinetic energy from the classical formulas.\n\nSolution for (a)\n\nPhoton momentum is given by the equation:\n\n$p=\\frac{h}{\\lambda }.$\n\nEntering the given photon wavelength yields\n\n$p=\\frac{6\\text{.}\\text{63}\u00d7{\\text{10}}^{\\text{\u201334}}\\phantom{\\rule{0.25em}{0ex}}\\text{J}\\cdot \\text{s}}{\\text{500}\u00d7{\\text{10}}^{\\text{\u20139}}\\phantom{\\rule{0.25em}{0ex}}\\text{m}}=\\text{1}\\text{.}\\text{33}\u00d7{\\text{10}}^{\\text{\u201327}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}.$\n\nSolution for (b)\n\nSince this momentum is indeed small, we will use the classical expression $p=\\text{mv}$ to find the velocity of an electron with this momentum. Solving for $v$ and using the known value for the mass of an electron gives\n\n$v=\\frac{p}{m}=\\frac{1\\text{.}\\text{33}\u00d7{\\text{10}}^{\\text{\u201327}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}}{9\\text{.}\\text{11}\u00d7{\\text{10}}^{\\text{\u201331}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}}=\\text{1460 m\/s}\\approx \\text{1460 m\/s}.$\n\nSolution for (c)\n\nThe electron has kinetic energy, which is classically given by\n\n${\\text{KE}}_{e}=\\frac{1}{2}{\\text{mv}}^{2}.$\n\nThus,\n\n${\\text{KE}}_{e}=\\frac{1}{2}\\left(9\\text{.}\\text{11}\u00d7{\\text{10}}^{\\text{\u20133}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\right)\\left(\\text{1455 m\/s}{\\right)}^{2}=\\text{9.64}\u00d7{\\text{10}}^{\\text{\u201325}}\\phantom{\\rule{0.25em}{0ex}}\\text{J}.$\n\nConverting this to eV by multiplying by $\\left(\\text{1 eV}\\right)\/\\left(1\\text{.}\\text{602}\u00d7{\\text{10}}^{\\text{\u201319}}\\phantom{\\rule{0.25em}{0ex}}J\\right)$ yields\n\n${\\text{KE}}_{e}=\\text{6.02}\u00d7{\\text{10}}^{\\text{\u20136}}\\phantom{\\rule{0.25em}{0ex}}\\text{eV}.$\n\nThe photon energy $E$ is\n\n$E=\\frac{\\text{hc}}{\\lambda }=\\frac{\\text{1240 eV}\\cdot \\text{nm}}{\\text{500 nm}}=2\\text{.}\\text{48 eV},$\n\nwhich is about five orders of magnitude greater.\n\nDiscussion\n\nPhoton momentum is indeed small. Even if we have huge numbers of them, the total momentum they carry is small. An electron with the same momentum has a 1460 m\/s velocity, which is clearly nonrelativistic. A more massive particle with the same momentum would have an even smaller velocity. This is borne out by the fact that it takes far less energy to give an electron the same momentum as a photon. But on a quantum-mechanical scale, especially for high-energy photons interacting with small masses, photon momentum is significant. Even on a large scale, photon momentum can have an effect if there are enough of them and if there is nothing to prevent the slow recoil of matter. Comet tails are one example, but there are also proposals to build space sails that use huge low-mass mirrors (made of aluminized Mylar) to reflect sunlight. In the vacuum of space, the mirrors would gradually recoil and could actually take spacecraft from place to place in the solar system. (See [link].)\n\nRelativistic Photon Momentum\n\nThere is a relationship between photon momentum $p$ and photon energy $E$ that is consistent with the relation given previously for the relativistic total energy of a particle as ${E}^{2}=\\left(\\text{pc}{\\right)}^{2}+\\left(\\text{mc}{\\right)}^{2}$. We know $m$ is zero for a photon, but $p$ is not, so that ${E}^{2}=\\left(\\text{pc}{\\right)}^{2}+\\left(\\text{mc}{\\right)}^{2}$ becomes\n\n$E=\\text{pc},$\n\nor\n\n$p=\\frac{E}{c}\\left(photons\\right).$\n\nTo check the validity of this relation, note that $E=\\text{hc}\/\\lambda$ for a photon. Substituting this into $p=E\/c$ yields\n\n$p=\\left(\\text{hc}\/\\lambda \\right)\/c=\\frac{h}{\\lambda },$\n\nas determined experimentally and discussed above. Thus, $p=E\/c$ is equivalent to Compton\u2019s result $p=h\/\\lambda$. For a further verification of the relationship between photon energy and momentum, see [link].\n\nPhoton Energy and Momentum\n\nShow that $p=E\/c$ for the photon considered in the [link].\n\nStrategy\n\nWe will take the energy $E$ found in [link], divide it by the speed of light, and see if the same momentum is obtained as before.\n\nSolution\n\nGiven that the energy of the photon is 2.48 eV and converting this to joules, we get\n\n$p=\\frac{E}{c}=\\frac{\\left(2.48 eV\\right)\\left(1\\text{.}\\text{60}\u00d7{\\text{10}}^{\\text{\u201319}}\\phantom{\\rule{0.25em}{0ex}}\\text{J\/eV}\\right)}{3\\text{.}\\text{00}\u00d7{\\text{10}}^{8}\\phantom{\\rule{0.25em}{0ex}}\\text{m\/s}}=\\text{1}\\text{.}\\text{33}\u00d7{\\text{10}}^{\\text{\u201327}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}.$\n\nDiscussion\n\nThis value for momentum is the same as found before (note that unrounded values are used in all calculations to avoid even small rounding errors), an expected verification of the relationship $p=E\/c$. This also means the relationship between energy, momentum, and mass given by ${E}^{2}=\\left(\\text{pc}{\\right)}^{2}+\\left(\\text{mc}{\\right)}^{2}$ applies to both matter and photons. Once again, note that $p$ is not zero, even when $m$ is.\n\nSection Summary\n\n\u2022 Photons have momentum, given by $p=\\frac{h}{\\lambda }$, where $\\lambda$ is the photon wavelength.\n\u2022 Photon energy and momentum are related by $p=\\frac{E}{c}$, where $E=\\text{hf}=\\text{hc}\/\\lambda$ for a photon.\n\nConceptual Questions\n\nWhich formula may be used for the momentum of all particles, with or without mass?\n\nIs there any measurable difference between the momentum of a photon and the momentum of matter?\n\nWhy don\u2019t we feel the momentum of sunlight when we are on the beach?\n\nProblems & Exercises\n\n(a) Find the momentum of a 4.00-cm-wavelength microwave photon. (b) Discuss why you expect the answer to (a) to be very small.\n\n(a) $\\text{1.66}\u00d7{\\text{10}}^{-\\text{32}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}$\n\n(b) The wavelength of microwave photons is large, so the momentum they carry is very small.\n\n(a) What is the momentum of a 0.0100-nm-wavelength photon that could detect details of an atom? (b) What is its energy in MeV?\n\n(a) What is the wavelength of a photon that has a momentum of $5\\text{.}\\text{00}\u00d7{\\text{10}}^{-\\text{29}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}$? (b) Find its energy in eV.\n\n(a) 13.3 \u03bcm\n\n(b) $9\\text{.}\\text{38}\u00d7{\\text{10}}^{-2}$ eV\n\n(a) A $\\gamma$-ray photon has a momentum of $8\\text{.}\\text{00}\u00d7{\\text{10}}^{-\\text{21}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}$. What is its wavelength? (b) Calculate its energy in MeV.\n\n(a) Calculate the momentum of a photon having a wavelength of $2\\text{.}\\text{50 \u03bcm}$. (b) Find the velocity of an electron having the same momentum. (c) What is the kinetic energy of the electron, and how does it compare with that of the photon?\n\n(a) $2\\text{.}\\text{65}\u00d7{\\text{10}}^{-\\text{28}}\\phantom{\\rule{0.25em}{0ex}}\\text{kg}\\cdot \\text{m\/s}$\n\n(b) 291 m\/s\n\n(c) electron $3\\text{.}\\text{86}\u00d7{\\text{10}}^{-\\text{26}}\\phantom{\\rule{0.25em}{0ex}}\\text{J}$, photon $7\\text{.}\\text{96}\u00d7{\\text{10}}^{-\\text{20}}\\phantom{\\rule{0.25em}{0ex}}\\text{J}$, ratio $2\\text{.}\\text{06}\u00d7{\\text{10}}^{6}$\n\nRepeat the previous problem for a 10.0-nm-wavelength photon.\n\n(a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 1.00% of the speed of light. (b) What is the energy of the photon in MeV? (c) What is the kinetic energy of the proton in MeV?\n\n(a) $1\\text{.}\\text{32}\u00d7{\\text{10}}^{-\\text{13}}\\phantom{\\rule{0.25em}{0ex}}\\text{m}$\n\n(b) 9.39 MeV\n\n(c) $4.70\u00d7{\\text{10}}^{-2}\\phantom{\\rule{0.25em}{0ex}}\\text{MeV}$\n\n(a) Find the momentum of a 100-keV x-ray photon. (b) Find the equivalent velocity of a neutron with the same momentum. (c) What is the neutron\u2019s kinetic energy in keV?\n\nTake the ratio of relativistic rest energy, $E={\\mathrm{\\gamma mc}}^{2}$, to relativistic momentum, $p=\\gamma \\text{mu}$, and show that in the limit that mass approaches zero, you find $E\/p=c$.\n\n$E={\\mathrm{\\gamma mc}}^{2}$ and $P=\\mathrm{\\gamma mu}$, so\n\n$\\frac{E}{P}=\\frac{{\\text{\u03b3mc}}^{2}}{\\text{\u03b3mu}}=\\frac{{\\text{c}}^{2}}{\\text{u}}.$\n\nAs the mass of particle approaches zero, its velocity $u$ will approach $c$, so that the ratio of energy to momentum in this limit is\n\n${lim}_{m\\to 0}\\frac{E}{P}=\\frac{{c}^{2}}{c}=c$\n\nwhich is consistent with the equation for photon energy.\n\nConsider a space sail such as mentioned in [link]. Construct a problem in which you calculate the light pressure on the sail in ${\\text{N\/m}}^{2}$ produced by reflecting sunlight. Also calculate the force that could be produced and how much effect that would have on a spacecraft. Among the things to be considered are the intensity of sunlight, its average wavelength, the number of photons per square meter this implies, the area of the space sail, and the mass of the system being accelerated.\nA car feels a small force due to the light it sends out from its headlights, equal to the momentum of the light divided by the time in which it is emitted. (a) Calculate the power of each headlight, if they exert a total force of $2\\text{.}\\text{00}\u00d7{\\text{10}}^{-2}\\phantom{\\rule{0.25em}{0ex}}\\text{N}$ backward on the car. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?\n(a) $3\\text{.}\\text{00}\u00d7{\\text{10}}^{6}\\phantom{\\rule{0.25em}{0ex}}\\text{W}$","date":"2019-11-22 13:50:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 68, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8449934124946594, \"perplexity\": 423.964986619235}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-47\/segments\/1573496671260.30\/warc\/CC-MAIN-20191122115908-20191122143908-00153.warc.gz\"}"} | null | null |
\section{Introduction}
Since the discovery of topological insulators, band structures of fermionic systems with non-trivial
momentum-space topology have received much attention in modern condensed matter physics.
Their low energy description involves Dirac-like band dispersions, which in some cases imply
gapless
band structures characterized by the presence of nodal points or lines.
Among these, are the
nodal line semimetals (NLSMs) \cite{mullen,hklattice}.
A NLSM has valence and conduction bands touching along one-dimensional (1D) lines in the three-dimensional (3D) momentum space, and feature two-dimensional (2D) ``drumhead" surface states surrounded by the nodal lines \cite{Burkov,Yang2014,Chen2015,Weng2015,Zhang2016}.
Contrary to the well-studied topological insulating phases and nodal point semimetals,
the 1D nodal lines of NLSMs provide rich topological structures such as links and knots \cite{Links_knots1,Links_knots2,Links_knots3,Links_knots4,Links_knots5}, which cannot be described unambiguously by a single sign (e.g. the $Z_2$ number) or a integer (e.g. the Chern number) \cite{multi_links_Li}.
On the other hand, a variety of gapped and gapless topological phases have been predicted in NLSMs
(while possibly breaking certain symmetries). For example, a spin-orbit interaction can induce 3D Dirac semimetals from a NLSM \cite{SOC1,SOC2}, and periodical driving such as linear or circular polarized light may induce different types of nodal points \cite{light_driven1,light_driven2,light_driven3,light_driven4,light_driven5,light_driven6}. By introducing various types of extra gapped terms, a NLSM can also be driven into several different types of topological insulators, including the recently discovered high-order topological insulators \cite{TI_NL1,TI_NL2}.
Spontaneous symmetry breaking from interactions
in three dimensional systems with Weyl/Dirac nodal points or lines have also been addressed.
For single nodal loop (NL) systems, superconducting and charge (or spin) density wave instabilities have been
investigated using renormalization of fermionic interactions\cite{Nandkishore2}, including also the mean-field
description of the ordered phases\cite{Nandkishore1,roy,ryu}.
Certain symmetries, such as spatial inversion or time-reversal,
imply that Weyl nodes must occur at an even number of Brillouin Zone (BZ) points.
Charge and spin density waves, as well as superconducting phases,
which arise from nested spherical Fermi surfaces (FSs) in doped (or uncompensated)
Weyl/Dirac points have been discussed\cite{wangye}.
Weyl or Dirac NLs, on the other hand, do not necessarily have to exist in pairs.
Although two-loop semimetals
have not yet been found in nature, pairs of linked NLs (or
Hopf-link structures) have been theoretically proposed\cite{Links_knots3,Links_knots4,Links_knots6}.
Furthermore,
a class of NLs protected by a combination of inversion
and time-reversal has recently been discussed\cite{Z2_loop}, which
carry $\mathbb{Z}_2$ monopole charges, and must therefore be created or annihilated in pairs.
This has motivated us to address the spontaneous symmetry breaking from short range
interactions in two-loop band structures, when the NLs are related
through a nesting vector ${\bf Q}$ in the BZ. We describe the density wave and superconducting phases, which
can be metallic, semimetallic (with double NLs) or fully gapped.
A systematic analysis for two-band NL models is given, where the NLs can either satisfy a local
reflection symmetry in the loop plane or not.
If a global PT symmetry exists, then a symmetry operation can relate the two NLs. These properties combined
determine the nature of the ordered phases. We also study specific four-band models that have
appeared in the recent literature, such as the $\mathbb{Z}_2$ NLs,
and NLs arising from perturbed Dirac points.
Superconducting phases arising from pairing of fermions in different loops
are also considered for all cases of singlet and triplet gap functions
in loop space as well as (pseuso)spin space. But we have restricted our search to order parameters
with time-reversal symmetry (TRS) and fully gapped phases, because the latter are expected to be more stable.
The possibility of gap functions with a winding number, which break TRS, is not addressed here.
The structure of the paper is as follows.
In Section \ref{modelsec} we introduce the local $k\cdot p$ Hamiltonians for two-band Weyl NLs, which can either satisfy
a local reflection symmetry in the NL plane, or not. The Hubbard interaction and the
density wave order parameters associated with the NL nesting vector are also introduced.
The density wave phases are described in Section \ref{densec}, and
Section \ref{examples}
is devoted to example models and to a four-band system that was not included in the general analysis of the
previous Sections: the nested $\mathbb{Z}_2$ NLs.
In Section \ref{Diracsec}, we study spin degenerate Dirac NLs and also NLs arising from perturbed Dirac points.
The superconducting pairing between nested NLs is studied in Section \ref{supersec}. The analysis is
focused on interloop pairing and time-reversal symmetric order parameters.
In Section \ref{concsec} we present our conclusions.
\section{Model}
\label{modelsec}
We consider spinless fermions and
let $\boldsymbol\tau$ denote the Pauli matrices acting on the pseudo-spin (orbital) degree of freedom.
We assume that the band structure has two degenerate loops.
If the Hamiltonian has PT symmetry, both loops involve the same Pauli matrices, $\tau_a\,,\tau_b$,
so that each one can be locally described by $k\cdot p$ Hamiltonians:
\begin{subequations}
\begin{eqnarray}
H_0({\bf k})&=& v_1\left( p_{\parallel} - p_o \right) \tau_a + v_2 p_\perp \tau_b \,, \\
H_0({\bf k}+\ {\bf Q})&=& g_1v_1\left( p_{\parallel} - p_o \right) \tau_a +g_2 v_2 p_\perp \tau_b\,,
\end{eqnarray}
\label{loop1}
\end{subequations}
Here, and throughout the paper, $\bf p=\hbar{\bf k}$ and the subscripts $\perp$($\parallel$) refer to the components perpendicular (parallel) to
the loop plane, and
$g_{1(2)}$ are + or - signs.
The loops are nested by the vector ${{\bf Q}}$.
We shall refer to the NLs in Eq. (\ref{loop1}) as ``model-1'' loops.
Such NLs
are protected by a local reflection\cite{bian} in the loop plane, ${\cal R}=(p_\perp\rightarrow -p_\perp)\otimes \tau_a$.
Such a NL can be topologically characterized by a $\pi$ Berry phase along a trajectory enclosing the NL \cite{Burkov,Zhang2016}.
At zero chemical potential, the system is a semimetal and the FS
consists of the two nested NLs.
We shall also take non-degeneracy into account by considering an energy offset $\delta$ between
the loops and make the replacement
$H_0({\bf k})\rightarrow H_0({\bf k}) -\delta$,
$H_0({\bf k}+\ {\bf Q})\rightarrow H_0({\bf k}+\ {\bf Q}) +\delta$.
For positive $\delta$ and zero chemical potential, the FSs are torus-shaped, the one from $H_0({\bf k}+\ {\bf Q}) $
is in the lower (hole) band, while the FS from $H_0({\bf k})$ is in the upper (electron) band.
However, NLs are not necessarily protected by reflection symmetry. Here we also
consider a more general model
of nested NLs without reflection symmetry. The Hamiltonian reads
\begin{subequations}
\begin{eqnarray}
H_0({\bf k})&=& \left[v_{1\parallel}\left( p_{\parallel} - p_o \right) + v_{1\perp} p_\perp \right] \tau_a + v_2 p_\perp \tau_b\,,
\\
H_0({\bf k}+\ {\bf Q})&=& \left[g_1'v_{1\parallel}\left( p_{\parallel} - p_o\right)+ g_2'v_{1\perp}p_\perp \right]\tau_a +
g_2 v_2 p_\perp \tau_b\,,
\nonumber\\
\end{eqnarray}
\label{loop2}
\end{subequations}
where $g_{1(2)}'$ are + or - signs.
We refer to these as ``model-2'' loops.
The extra $p_{\parallel}$ in the $\tau_a$ term changes the pseudospin texture near a NL,
but does not affect the topological properties associated with the Berry phase.
Examples of both types of NLs will be given in
Section \ref{modelsec}.
The above two types of loops respond differently to the interactions, as shown in the following sections.
Normaly, one should expect that a perturbation
arises that will lift the degeneracy between nested FSs.
The perturbation may result from interactions and, in a normal system, usually
takes the form of some charge or spin wave with the wave vector ${{\bf Q}}$.
Also, superconducting pairing between fermions in different NLs will be considered.
In the rest of the paper we shall set to unity
the velocity prefactors in the Hamiltonians (\ref{loop1}) and (\ref{loop2}),
as they are not really necessary for the analysis that follows.
\section{Density wave phases}
\label{densec}
\subsection{Interaction and mean-field theory}
We introduce a Hubbard interaction,
\begin{eqnarray}
\hat U &=& U\sum_{\bf r} \hat n_1({\bf r})\hat n_2({\bf r})\,,
\label{localU}
\end{eqnarray}
where the indices $1,2$ refer to the orbital degree of freedom.
Doing a mean field theory decoupling, the interaction takes the form
\begin{eqnarray}
\hat U_{MF} = U \sum_{\bf r} \left[
\langle n_1({\bf r}) \rangle \hat n_2({\bf r}) + \hat n_1({\bf r})\langle n_2({\bf r})\rangle
- \langle n_1({\bf r}) \rangle \langle n_2({\bf r})\rangle \right]\,.
\label{mfloop}
\end{eqnarray}
A pseudospin density wave (PSDW) phase with the same nesting wave vector ${{\bf Q}}$
is characterized by
\begin{eqnarray}
\langle n_j({\bf r})\rangle = \frac 1 2 n + \bar m (-1)^j\cos({{\bf Q}}\cdot{\bf r})\,,
\end{eqnarray}
where $\bar m$ is the amplitude and $j=1,2$.
Although this type of ordering describes an imbalance in orbital occupation, it
is not a charge density wave (CDW) because the charge at site ${\bf r}$ is spatially constant, $n$. \
Omitting the factor $(-1)^j$, then a true CDW is obtained.
We introduce the annihilation operator $\hat\psi_j({\bf r}) $,
at point ${\bf r}$, with pseudospin index $j$.
Then, Eq. (\ref{mfloop}) can be rewritten as:
\begin{eqnarray}
&&\hat U_{eff} = \frac{Un}{2} \sum_{\bf r} \left( \hat\psi_1^\dagger({\bf r}) \hat\psi_2^\dagger({\bf r}) \right) \tau_0
\left( \begin{array}{c} \hat\psi_1({\bf r}) \\ \hat\psi_2({\bf r}) \end{array} \right)\nonumber\\ &&+\
U \bar m \sum_{\bf r} \cos({\boldsymbol Q}\cdot{\bf r}) \left( \hat\psi_1^\dagger({\bf r}) \hat\psi_2^\dagger({\bf r}) \right) \tau_3
\left( \begin{array}{c} \hat\psi_1({\bf r}) \\ \hat\psi_2({\bf r}) \end{array} \right)\nonumber\\
&=&
\frac{Un}{2} \sum_{\bf k} \left( \hat c_{{\bf k} ,1}^\dagger \hat c_{{\bf k} ,2}^\dagger \right) \tau_0
\left( \begin{array}{c} \hat c_{{\bf k} ,1}\\ \hat c_{{\bf k} ,2} \end{array} \right)
\nonumber\\
&+&
\frac{U \bar m}{2} \sum_{\bf k} \left[
\left( \hat c_{{\bf k}+{\bf Q},1}^\dagger \hat c_{{\bf k}+{\bf Q},2}^\dagger \right) \tau_3
\left( \begin{array}{c} \hat c_{{\bf k} ,1}\\ \hat c_{{\bf k} ,2} \end{array} \right) +
\left( \hat c_{{\bf k},1}^\dagger \hat c_{{\bf k},2}^\dagger \right) \tau_3
\left( \begin{array}{c} \hat c_{{\bf k} +{\bf Q},1}\\ \hat c_{{\bf k}+{\bf Q} ,2} \end{array} \right)\right]\nonumber\\
\label{UEff}
\end{eqnarray}
Replacing $\tau_3\rightarrow\tau_0$ in Eq. (\ref{UEff}), we can describe a true CDW.
We write the effective Hamiltonian $H_{eff}({\bf k})$ matrix
in operator basis $( \hat c_{{\bf k} ,1}, \hat c_{{\bf k} ,2} \hat c_{{\bf k}+{\bf Q},1}, \hat c_{{\bf k}+{\bf Q},2})
\equiv( \boldsymbol c_{{\bf k}} \ \boldsymbol c_{{\bf k}+{\bf Q}} )$
and introduce a factor $\frac 1 2$ to avoid double counting of momenta in the BZ:
\begin{eqnarray}
\hat H_{eff}&=&
\frac 1 2
\sum_{\bf k} \left( \boldsymbol c^\dagger_{{\bf k}}\ \boldsymbol c^\dagger_{{\bf k}+{\bf Q}} \right)
H_{eff}({\bf k})
\left( \begin{array}{c} \boldsymbol c_{{\bf k}} \\ \boldsymbol c_{{\bf k}+{\bf Q}} \end{array}\right)\,,
\\
H_{eff}({\bf k}) &=& \left( \begin{array}{cc}
H_0({\bf k}) & U\bar m \tau_\alpha\\
U\bar m \tau_\alpha & H_0({\bf k}+{\bf Q})
\end{array}\right)
\,,
\label{martizHloops}
\end{eqnarray}
where $\alpha=0$ for CDW, or $\alpha=3$ for PSDW.
The mean field equations for this Hamiltonian are derived in Appendix \ref{APMF}.
The effective Hamiltonian
Eq. (\ref{martizHloops}) is by no means restricted to the case of a local interaction
as in Eq.
(\ref{localU}). A nearest-neighbor interaction, for instance, would produce an effective
Hamiltonian of the same form, but where the bare interaction parameter would be multiplied by
a ${\bf Q}$-dependent form factor which could still be denoted by ``$U$''.
The nesting property of the Fermi surface leads to a divergence
of the susceptibilities in momentum space at the nesting wavevector\cite{gruner}.
This always
leads to a density wave with momentum $\bf Q$, described by the mean field couplings
$<\hat c_{{\bf k}}^\dagger\hat c_{{\bf k}+{\bf Q}}>$,
and the relevant interaction "$U$" would be the Fourier component of the interaction
for the nesting wavevector.
\subsection{model-1 loops}
\label{model1_general}
We now introduce the Pauli matrices $t_\mu$ operating in loop space $({\bf k},{\bf k}+{\bf Q})$.
For type-1 models
the unperturbed double loop Hamiltonian has the form
\begin{eqnarray}
H_{eff}^0({\bf k}) = \left( p_{\parallel} - p_o \right) t_i\tau_a+ p_\perp t_j\tau_b -\delta\ t_3
\label{H0eff}
\end{eqnarray}
where $i,j$ can
only take values 0 or 3.
The effective Hamiltonian (\ref{martizHloops}) can be written as
\begin{equation}
H_{eff}({\bf k})= H_{eff}^0({\bf k}) + U\bar m\ t_1 \tau_\alpha
\label{umgap}
\end{equation}
Supose that $\delta=0$, that is, degenerate loops at perfect compensation.
It is clear that if the perturbing term $U\bar m t_1 \tau_\alpha$
anticommutes with only one term of $H_{eff}^0({\bf k}) $ then the resulting system still is a double NL semimetal.
On the other hand, if $U\bar mt_1\tau_\alpha$
anticommutes with $H_{eff}^0({\bf k})$ then the resulting system is a gapped insulator,
and if $\left[U\bar mt_1 \tau_\alpha, H_{eff}^0({\bf k})\right]=0$ then the original loops are shifted
and a metallic phase arises with torus-shaped FSs, one of them hole-like, and the other electron-like.
Next we establish a criterion based on how a unitary transformation maps one loop onto the other.
If the Hamiltonian has PT symmetry,
one can always find a rotation through a Pauli matrix $\tau_\beta$
that maps one model-1 loop at ${\bf k}$ into the other at ${\bf k}+{\bf Q}$:
\begin{eqnarray}
H_0({\bf k}) = \tau_{\beta} H_0({\bf k}+\ {\bf Q}) \tau_{\beta} \,.
\label{rotj}
\end{eqnarray}
It is then convenient to apply a unitary transformation to the effective Hamiltonian in Eq. (\ref{martizHloops})
according to
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=& \left( \begin{array}{cc}
H_0({\bf k}) -\delta & U\bar m \tau_\alpha\tau_{\beta}\\ U \bar m \tau_{\beta}\tau_\alpha & H_0({\bf k}) +\delta
\end{array} \right) \label{rotatedloops}\\
A&=&\left( \begin{array}{cc} 1 & 0 \\ 0 &\tau_{\beta} \end{array} \right)\,.\label{Amatrix}
\end{eqnarray}
The energy spectrum can be obtained by performing appropriate rotations on the matrix (\ref{rotatedloops}),
as shown in Appendix \ref{appa}.
We list all the four possibilities as follows.
\begin{enumerate}
\item
If $\tau_\alpha \tau_{\beta}=1$, the spectrum reads:
\begin{eqnarray}
E=\pm \sqrt{ \left( p_{\parallel} - p_o \right)^2+p_\perp^2}
\pm \sqrt{U^2\bar m^2 + \delta^2}
\,,\label{CDWk0}
\end{eqnarray}
(uncorrelated $\pm$ signs). In this case, $H_0({\bf k})=\tau_\alpha H_0({\bf k}+{\bf Q})\tau_\alpha$.
The density wave produces
a ``level repulsion'' effect by introducing (increasing)
an energy splitting between the degenerate (non-degenerate) NLs.
The density wave phase has two toroidal FSs, one hole-like and one electron-like.
\item
In the case where $\tau_\alpha \tau_{\beta}\propto\tau_a$, the energy spectrum is:
\begin{eqnarray}
E^2 &=& \left( p_{\parallel} - p_o \right)^2 + p_\perp^2+ U^2\bar m^2 +\delta^2 \nonumber\\
&\pm& 2\sqrt{\left( p_{\parallel} - p_o \right)^2(U^2\bar m^2 + \delta^2)+
p_\perp^2\delta^2}\,,\label{CDWka}
\end{eqnarray}
which yields two NLs at $p_\perp=0$,
$p_{\parallel}=p_o\pm\sqrt{U^2\bar m^2 + \delta^2}$. As $p_\parallel$ can only take a
positive
value, the loop with the
minus sign will shrink into a point and vanish when $\sqrt{U^2\bar m^2 + \delta^2}$ becomes larger then $p_o$.
\item
For $\tau_\alpha \tau_{\beta}\propto\tau_b$ we get:
\begin{eqnarray}
E^2 &=& \left( p_{\parallel} - p_o \right)^2 + p_\perp^2+ U^2\bar m^2 +\delta^2 \nonumber\\
&\pm& 2\sqrt{ p_\perp^2(U^2\bar m^2 + \delta^2)+
\left( p_{\parallel} - p_o \right)^2\delta^2}\,.\label{CDWkb}
\end{eqnarray}
This spectrum also gives two NLs, given by $p_\parallel = p_o$,
$p_\perp=\pm \sqrt{U^2\bar m^2 + \delta^2}$. Unlike the previous case, these two loops only move along
the $p_\perp$ direction when tuning $U$ or $\delta$, while their radii remain unchanged.
\item
For the case $\tau_\alpha \tau_{\beta}\propto\tau_{c(\neq a,b)}$ we have
\begin{eqnarray}
E^2 &=& U^2\bar m^2 +
\left[ \sqrt{ \left( p_{\parallel} - p_o \right)^2+p_\perp^2} \pm \delta \right]^2 \,,\label{CDWkc}
\end{eqnarray}
which is then fully gapped. This is the case where $H_0({\bf k})=-\tau_\alpha H_0({\bf k}+{\bf Q})\tau_\alpha$.
\end{enumerate}
At half filling (zero chemical potential), all the above energy dispersions lead to a lowering of the energy
for $U\bar m\neq 0$, so, the density wave phase is energetically favorable.
In a single NL, the density of states vanishes linearly at the chemical potential, so the broken symmetry
phase appears only for $U$ above a finite critical value, $U_{cr}$.
In any case if the phase transition is second order, then
$U\rightarrow U_{cr}^+ \Rightarrow\ \bar m\rightarrow 0$.
The PSDW cases occur for $U>U_{cr}>0$ but the CDW ordering requires negative $U<U_{cr}<0$, hence an attractive
interaction (see Appendices \ref{APMF} and \ref{MFloop}).
From Eq. (\ref{rotj}) we see that $\tau_\alpha H_0({\bf k}) \tau_\alpha =
\tau_\alpha\tau_{\beta} H_0({\bf k}+\ {\bf Q}) \tau_{\beta}\tau_\alpha$
and therefore, the density-wave phase is a nodal line semi-metal if
\begin{equation}
H_0({\bf k}) \neq \pm \tau_\alpha H_0({\bf k}+\ {\bf Q})\tau_\alpha \,,\label{critCDW}
\end{equation}
where $\alpha=0$ for CDW, or $\alpha=3$ for PSDW.
For model-1 loops we can make the following observations regarding symmetry.
The Hamiltonian (\ref{rotatedloops}) for $\delta=0$ is chiral as it anti-commutes with the operator $\tau_{c\neq a,b}$,
and contains the degenerate NLs.
This chiral symmetry can be broken by a term of the form:
{\it (i)} $t_\mu\tau_c$ which may fully gap the spectrum,
or yield a semimetal, depending on its exact form;
{\it (ii)} $t_\mu\tau_0$ which shifts the original loops and leads to a metallic spectrum.
On the other hand, a term of the form $t_j\tau_a$ or $t_j\tau_b$ ($j=1,2,3$), preserves the chiral symmetry
and yields the NL semimetal even if $\delta t_3 \neq 0$ is already present, as shown in Appendix \ref{appa}.
\subsection{model-2 loops}\label{model2_general}
As we shall see, the criteria (\ref{critCDW}) do not always apply to model-2 loops.
The type-2 loop Hamiltonian at $\mathbf{k}$ is (omitting velocity prefactors):
\begin{eqnarray}
H_0({\bf k})&=& \left( p_{\parallel} - p_o + p_\perp\right)\tau_a + p_\perp \tau_b\,,
\end{eqnarray}
and the loop at ${\bf k}+ {\bf Q}$ can always be related to that in ${\bf k}$ by either:
{\it (i)} a rotation through a Pauli matrix if $g'_1g'_2=1$ in Eq. (\ref{loop2}); or {\it (ii) } a reflection in the loop plane
if $g'_1g_2'=-1$.
If {\it (i)} holds, then one can again
rotate the effective Hamiltonian according to equations (\ref{rotatedloops})-(\ref{Amatrix}), and
the resulting spectra can be obtained from
Eqs (\ref{CDWk0})-(\ref{CDWkc}) for model-1 loops,
with the replacement
$p_{\parallel} - p_o\rightarrow p_{\parallel} - p_o+p_\perp$.
But in case {\it (ii)} the two NLs can be related through a reflection in the NL's plane,
\begin{subequations}
\begin{eqnarray}
H_0({\bf k}) &=& {\cal R} H_0({\bf k}+\ {\bf Q}) {\cal R}^\dagger\,,\\
{\cal R} &=& (p_\perp\rightarrow - p_\perp) \tau_{\beta}\,,
\end{eqnarray}\label{reflection}
\end{subequations}
which corresponds to the following cases, depending on $\tau_{\beta}$:
\begin{eqnarray}
\begin{aligned}
& H_0({\bf k}+\ {\bf Q})=\\
&= \left( p_{\parallel} - p_o - p_\perp\right)\tau_a - p_\perp \tau_b\equiv H_0(-k_\perp) &\beta&=0;\\
&= \left( p_{\parallel} - p_o - p_\perp\right)\tau_a + p_\perp \tau_b &\beta&=a;\\
&= \left[ -\left( p_{\parallel} - p_o\right) + p_\perp\right]\tau_a - p_\perp \tau_b & \beta&=b;\\
&= \left[ -\left( p_{\parallel} - p_o\right) + p_\perp\right]\tau_a + p_\perp \tau_b & \beta&=c\neq a,b\,.
\end{aligned}
\end{eqnarray}
We apply the same rotation to the effective Hamiltonian,
using Eqs. (\ref{rotatedloops})-(\ref{Amatrix}):
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=& \left( \begin{array}{cc}
H_0({\bf k}) & U\bar m \tau_\alpha\tau_{\beta} \\ U \bar m \tau_{\beta}\tau_\alpha & H_0(-k_\perp)
\end{array} \right)\label{difficult}\,.
\end{eqnarray}
For finite $\delta$ one cannot write the energy dispersion in closed form. We analytically deal
with the degenerate case at perfect compensation, $\delta=0$, below,
and show numerical results for nonzero $\delta$ in Fig.\ref{fig1}.
The figure shows the two inner bands
of Hamiltonians (\ref{mode2_case1}), (\ref{mode2_case2}), (\ref{mode2_case3}), and (\ref{mode2_case4}) in the two-dimensional space of $(p_{\parallel} ,p_\perp)$. A NL for $U\bar m = \delta=0$
then looks like a Dirac cone at point $(p_o ,0)$. The splitting of the original NLs can be seen as the appearance of
two Dirac cones in the plot. For finite $\delta$, the Dirac cone axis is tilted.
Similarly to the discussion for model-1 loops, we also list all the four possibilities.
\begin{enumerate}
\item
If $\tau_\alpha\tau_{\beta}=1$:
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=&
\left( p_{\parallel} - p_o \right)\tau_a + p_\perp t_3\tau_a + p_\perp t_3\tau_b\nonumber\\
&+& U\bar m \ t_1 - \delta t_3\,,\label{mode2_case1}
\end{eqnarray}
For $\delta=0$ (perfect compensation) the spectrum obeys
\begin{eqnarray}
E^2 = p_\perp^2 + \left[ \sqrt{p_\perp^2 + (U\bar m)^2} \pm \left( p_{\parallel} - p_o\right)
\right]^2
\end{eqnarray}
which has two nodal lines for $p_\perp=0$ and $p_{\parallel} - p_o=\pm U\bar m$.
By turning on $\delta$, the two NLs are tilted along the $p_{\perp}$ direction, and move
along the $p_{\parallel}$ direction, as shown in Fig. \ref{fig1}(a). It can also be seen from Eq. (\ref{mode2_case1})
that if $p_\perp=0$ the dispersion relation has two nodal lines: $|p_{\parallel} - p_o|=\sqrt{U^2\bar m^2+\delta^2}$.
Therefore, one of the loops will shrink into the origin as $p_{\parallel}\rightarrow 0$ when
$\delta^2+U^2\overline{m}^2\rightarrow p_0^2$,
and become gapped for larger $\delta$.
\item
If $\tau_\alpha\tau_{\beta}\propto\tau_a$:
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=&
\left( p_{\parallel} - p_o \right)\tau_a + p_\perp t_3\tau_a + p_\perp t_3\tau_b\nonumber\\
&+& \epsilon_{k\alpha a}U\bar m \ t_2\tau_a - \delta t_3\,,\label{mode2_case2}
\end{eqnarray}
For $\delta=0$ (perfect compensation) the spectrum obeys
\begin{eqnarray}
E^2 &=& \left( p_{\parallel} - p_o\right)^2 + 2 p_\perp^2 +(U\bar m)^2 \nonumber\\
& \pm &
2 \sqrt{
\left( p_{\parallel} - p_o\right)^2 \left( p_\perp^2 +U^2\bar m^2\right) + p_\perp^2 U^2\bar m^2
}
\end{eqnarray}
which, for $\delta=0$, has the same two nodal
lines as in the previous case, and behavior of these lines
with nonzero $\delta$ is also identical. However, these loops show a
quadratic dispersion along the $p_\perp$ direction, as shown in Fig. \ref{fig1}(b).
\item
If $\tau_\alpha\tau_{\beta}\propto\tau_b$:
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=&
\left( p_{\parallel} - p_o \right)\tau_a + p_\perp t_3\tau_a + p_\perp t_3\tau_b\nonumber\\
&+& \epsilon_{k\alpha b}U\bar m \ t_2\tau_b - \delta t_3\,, \label{mode2_case3}\\
E^2 &=& p_\perp^2 + \left(
\sqrt{ \left( p_{\parallel} - p_o\right)^2 + U^2\bar m^2} \pm p_\perp
\right)^2
\end{eqnarray}
which is a fully gapped insulator, and remains gapped with nonzero $\delta$ [Fig. \ref{fig1}(c)].
\item
If $\tau_\alpha\tau_{\beta}\propto\tau_c(\neq a,b)$:
\begin{eqnarray}
A H_{eff}({\bf k}) A^\dagger &=&
\left( p_{\parallel} - p_o \right)\tau_a + p_\perp t_3\tau_a + p_\perp t_3\tau_b\nonumber\\
&+& \epsilon_{k\alpha c}U\bar m \ t_2\tau_c - \delta t_3\,,\label{mode2_case4}
\end{eqnarray}
which for $\delta=0$ has the spectrum
\begin{eqnarray}
E^2 &=& \left( p_{\parallel} - p_o\right)^2 + 2 p_\perp^2 + U^2\bar m^2 \nonumber\\
&\pm&
2p_\perp\sqrt{
\left( p_{\parallel} - p_o\right)^2 + 2U^2\bar m^2
}
\end{eqnarray}
with two nodal lines at $p_{\parallel} - p_o=0$ and $\sqrt{2}p_\perp=\pm U\bar m$.
Unlike the nodal lines in the first two cases, these two are tilted along $p_{\parallel}$ and move away from each other along $p_{\perp}$ for $\delta\neq 0$.
\end{enumerate}
\begin{figure}
\includegraphics[width=1\linewidth]{fig1a.pdf}
\includegraphics[width=1\linewidth]{fig1b.pdf}
\includegraphics[width=1\linewidth]{fig1c.pdf}
\includegraphics[width=1\linewidth]{fig1d.pdf}
\caption{The energy dispersion of the two inner bands of the spectrum.
Panels (a)-(d) correspond to the four cases in Eqs. (\ref{mode2_case1}), (\ref{mode2_case2}), (\ref{mode2_case3}), and (\ref{mode2_case4}) respectively. The energy offset $\delta$ is: (a1)-(d1) $\delta=0$; (a2)-(d2) $\delta=0.5$; and (a3)-(d3) $\delta=1$. The other parameters are: $p_o=1$, and $U\bar m =0.5$. }\label{fig1}
\end{figure}
\section{Example models}
\label{examples}
In this section we investigate the density wave phases in several specific lattice models
which have been widely studied in the literature.
The examples in Secs. \ref{model1_example} and \ref{model2_example} fall into the two types of NLs discussed in previous sections.
The remainder of this section will be devoted to model beyond the simplest two-band cases.
\subsection{A model-1 loop example}\label{model1_example}
A lattice model with two ``model-1" loops can be described by the Hamiltonian,
\begin{eqnarray}
H_0({\bf k})&=& \left( \cos k_x + \cos k_y - m \right)\tau_a + \cos{k_z} \tau_b\label{model1}\,.
\end{eqnarray}
When $|m|<2$, the system has two NLs at $\cos{k_x}+\cos{k_y}-m=0$, in two parallel planes $k_z=\pm \pi/2$.
They are nested by the vector $\mathbf{Q}=(0,0,\pi)$, and can be mapped to each other as
\begin{eqnarray}
H_0({\bf k})=\tau_aH_0({\bf k}+{\bf Q})\tau_a\,.
\end{eqnarray}
Introducing a Hubbard interaction, the effective Hamiltonian can be written as
\begin{eqnarray}
H_{eff}({\bf k}) &=&
\left( \cos k_x + \cos k_y - m \right)t_0\tau_a + \cos{k_z} t_3\tau_b \nonumber\\
&+& U\bar m\ t_1\tau_{\alpha}\,.
\end{eqnarray}
We analyze first the CDW case ($\tau_\alpha=\tau_0$).
Following the discussion in the previous Section,
this condition corresponds to the second case in Sec. \ref{model1_general}, where each NL gets split into two.
Indeed, from the commuting relations between different terms, we can obtain the energy dispersion as
\begin{equation}
E_{CDW}= \pm \sqrt{\cos^2 {k_z} + \left[
\cos k_x + \cos k_y - m \pm U\bar m
\right]^2
}\,,
\end{equation}
and the split NLs are given by
\begin{eqnarray}
\cos{k_z} = 0\,,\mbox{and}\
\cos k_x + \cos k_y = m \pm U\bar m.
\end{eqnarray}
In the PSDW case ($\tau_\alpha=\tau_3$), different choices of $a$ and $b$ in Eq. (\ref{model1}) will lead to different phases of the system. In such case, the effective Hamiltonian reads
\begin{eqnarray}
H_{eff}({\bf k}) &=&
\left( \cos k_x + \cos k_y - m \right)t_0\tau_a + \cos{k_z} t_3\tau_b \nonumber\\
&+& U\bar m\ t_1\tau_3,
\end{eqnarray}
and the possibilities are summarized in Table \ref{tab1}, and listed explicitly as follows.
\begin{table
\begin{center}
\begin{tabular}{c|c|c|c}
a$\backslash$ b & 1 & 2 & 3 \\
\hline
1 & X & loops & gapped \\
\hline
2 & loops & X & gapped\\
\hline
3 & metal & metal & X
\end{tabular}
\end{center}
\caption{Possibilites for $\tau_a$, $\tau_b$ matrices in the loop model (\ref{model1}). And the resulting different outcomes
of the PSDW phase.}
\label{tab1}
\end{table}
In the case of $\tau_a=\tau_3$, the energy spectrum reads
\begin{eqnarray}E_{PSDW}&=&\pm\sqrt{
\left( \cos k_x + \cos k_y - m \right)^2 + \cos {k_z} ^2 }\pm U\bar m
\nonumber\\
\end{eqnarray}
with uncorrelated $\pm$ signs. This is the first case in Sec. \ref{model1_general}, and the ordered phase is metallic.
If $a,b\neq 3$, the spectrum reads
\begin{eqnarray}
E_{PSDW}^2&=&
\left( \cos k_x + \cos k_y - m \right)^2 + \left( \cos{k_z} \pm U\bar m \right)^2\,,
\end{eqnarray}
where each original NL splits into two with different $k_z$, as in the third
cases in Sec. \ref{model1_general}.
Finally, when $\tau_b=\tau_3$, the spectrum takes the form,
\begin{eqnarray}
E^2&=&
\left( \cos k_x + \cos k_y - m \right)^2 + \cos {k_z} ^2 + U^2\bar m^2\,.
\end{eqnarray}
Thus the system is fully gapped by a nonzero $U \bar m$ and becomes an insulator, as in the fourth case in Sec. \ref{model1_general}.
\subsection{A model-2 loop example}\label{model2_example}
By including $\cos{k_z}$ in the $\tau_a$ term in Eq. (\ref{model1}), we obtain a system with ``model-2" loops, described by
\begin{eqnarray}
H_0({\bf k})= \left( \cos k_x + \cos k_y + \cos k_z- m \right)\tau_a + \cos k_z \tau_b.\label{model2}
\end{eqnarray}
This system has two parallel NLs with $k_z=\pm\pi/2$ when $-2<m<2$.
The continuous approximation for these two loops, as in Eqs. (\ref{loop2}), satisfies $g'_1=1$, and $g_2=g'_2=-1$.
Thus, the effective Hamiltonian including the Hubbard interaction is given by
\begin{eqnarray}
H_{eff} &=& \left( \cos k_x + \cos k_y - m \right)t_0\tau_a + \cos k_z t_3\tau_a\nonumber\\ &+&
\cos k_z t_3\tau_b + U\bar m t_1\tau_{\alpha}\,.
\label{16}
\end{eqnarray}
For the CDW case ($\tau_{\alpha}=\tau_0$), the spectrum reads
\begin{eqnarray}
E^2_{CDW}&=& \left[
\cos k_x + \cos k_y - m \pm \sqrt{U^2\bar m^2+\cos^2{k_z}}
\right]^2\nonumber\\
&&+\cos {k_z}^2
\,,
\end{eqnarray}
thus each of the original NLs splits into two. The new NLs are given by
\begin{eqnarray}
\cos{k_z} = 0\,, \hspace{0.2cm}
\cos k_x + \cos k_y = m \pm U\bar m.
\end{eqnarray}
In the case of PSDW ordering ($\tau_{\alpha}=\tau_3$),
there are three possible outcomes as summarized in Table \ref{tab2}.
In the case of $\tau_a=\tau_3$, the energy spectrum reads
$$
E^2_{PSDW}=(\cos k_x+\cos k_y-m)^2+2\cos^2 k_z+U^2\bar m^2
$$
\begin{eqnarray}
\pm2\sqrt{(\cos k_x+\cos k_y-m)^2\left[ \cos^2 k_z + U^2\bar m^2 \right] + (U\bar m\cos k_z)^2 }\,,\nonumber\\
\end{eqnarray}
where each NL splits into two as in the second case in Sec. \ref{model2_general}.
The condition of the NLs is the same as for the CDW case;
however, as discussed in the
previous section [Fig. \ref{fig1}(b)], these NLs have a quadratic dispersion along $k_z$.
\begin{table
\begin{center}
\begin{tabular}{c|c|c|c}
a$\backslash$ b & 1 & 2 & 3 \\
\hline
1 & X & loops & gapped \\
\hline
2 & loops & X & gapped\\
\hline
3 & loops & loops & X
\end{tabular}
\end{center}
\caption{Possibilites for $\tau_a$, $\tau_b$ matrices in the loop model (\ref{model2}). And the resulting different outcomes
of the PSDW phase.}
\label{tab2}
\end{table}
If $\tau_b=\tau_3$ then the spectrum reads
\begin{eqnarray}
E_{PSDW}^2&=& \left[
\cos k_z\pm \sqrt{ U^2\bar m^2+ \left( \cos k_x + \cos k_y -m\right)^2}
\right]^2\nonumber\\
&+& \cos^2k_z \,,
\end{eqnarray}
which is an insulating phase as in the third case in Sec. \ref{model2_general}.
The remaining possibility, $a,b\neq 3$, where the spectrum reads
\begin{eqnarray}E^2_{PSDW}&=&(\cos k_x+\cos k_y-m)^2+2\cos^2 k_z+U^2\bar m^2\nonumber\\
&&\pm2\cos k_z\sqrt{
(\cos k_x+\cos k_y-m)^2
+2U^2\bar m^2
}\,,\nonumber\\
\end{eqnarray}
yields two NLs given by
\begin{eqnarray}
\cos{k_z} = \pm U\bar m /\sqrt{2}\,, \
\cos k_x + \cos k_y = m\,.
\end{eqnarray}
This is the splitting along $k_z$, as in the fourth case in Sec. \ref{model2_general}.
Finally, if we add an extra term $H_{\delta}=\delta\sin{k_z}\tau_0$ to the original Hamiltonian of Eq. (\ref{model2}), we can induce a energy offset $\delta$ of the two original NLs, and tilt the resulting NLs after the Hubbard interaction is introduced.
\subsection{Nested $\mathbb{Z}_2$ NLs }
\label{sec:Z2}
We have hitherto considered examples of two-band NLSMs, which verify our results for general two-band models. If an extra degree of freedom, say, a (pseudo)spin-1/2 subspace, is introduced, the Hilbert space is enlarged and the possibility of nodal lines
carrying a $\mathbb{Z}_2$ monopole charge arises, which must be created in pairs\cite{Z2_loop}.
It is beyond the scope of this paper to extend the general analysis of Sec III.
Instead, we explicitly consider a recent four-band model for $Z_2$ NLs \cite{Z2_loop}
and study density-wave order due to nesting.
The model reads
\begin{eqnarray}
H_0({\bf k}) &=& \sin k_x \tau_0\sigma_1+ \sin k_y \tau_2\sigma_2+
\sin k_z \tau_0\sigma_3 + m \tau_1\sigma_1\,,\nonumber\\
\label{Z2_H}
\end{eqnarray}
and has the spectrum
\begin{eqnarray}
E_0^2({\bf k})&=&
\left( \sqrt{\sin^2k_x + \sin^2k_y}\pm m \right)^2 + \sin^2k_z\,.\label{spectrum_Z2}
\end{eqnarray}
There are eight NLs, centered at momenta ${\bf k}$ with
Cartesian components
$k_i=0,\pi$ for $i=x,y,z$.
We introduce a Hubbard interaction in four-dimensional space assuming that the repulsion exists
between the two orbitals in subspace of $\boldsymbol\sigma$:
\begin{eqnarray}
\hat U&=& U \sum_{{\bf r} , \nu}n_{\nu 1}({\bf r}) n_{\nu 2}({\bf r}) = \frac{U}{2} \sum_{{\bf r}} n({\bf r})\tau_0\sigma_1 n({\bf r})\,,
\end{eqnarray}
so that the remaining index $\nu=1,2$ for the two components in the
subspace of $\boldsymbol\tau$
produces a two-fold degeneracy.
In the mean-field approximation, the interaction reads (apart from unimportant constants)
\begin{eqnarray}
\hat U_{eff}&=& U\bar m \sum_{{\bf k}} \hat c_{{\bf k}+{\bf Q}}^\dagger \tau_0\sigma_z \hat c_{{\bf k}} \,,
\end{eqnarray}
where we defined the PSDW as:
\begin{equation}
\langle n_{\nu j}({\bf r})\rangle = \frac{n}{2} + \bar m (-1)^j\cos({\bf Q}\cdot{\bf r}) \,,
\end{equation}
The effective 8x8 Hamiltonian has the same form as that in Eq. (\ref{martizHloops}), but the anti-diagonal blocks
are now written as $U\bar m \tau_0\sigma_3$.
Two of the original $\mathbb{Z}_2$ loops
are now coupled by the interaction.
Such coupling provides an extra pseudospin-1/2 subspace, and the interaction term breaks the SU(2) symmetry in this space.
As a result, the pair of NLs may either survive, shrink to point nodes, or be gapped out by the PSDW.
Depending on vector ${\bf Q}$, the effective Hamiltonian takes the form of
\begin{eqnarray}
H_{eff} &=& \sin k_x t_{\alpha_x} \tau_0\sigma_1 + \sin k_y t_{\alpha_y} \tau_2\sigma_2 + \sin k_z t_{\alpha_z} \tau_0\sigma_3 \nonumber\\
&+&m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,,
\end{eqnarray}
where the Pauli matrix $t_{\alpha_i}$ equals $t_0$ ($t_3$) for $Q_i=0$ ($Q_i=\pi$).
Thus, different choices of $Q_i$ determine whether each term commutes or anticommutes with the interaction term
$U\bar m t_1 \tau_0\sigma_3$.
The possibilities with different choices of ${\bf Q}$ are summarized as follows.
\begin{figure}
\includegraphics[width=1\linewidth]{fig2.pdf}
\caption{The effect of a PSDW on the $\mathbb{Z}_2$ loops for different nesting vectors ${\bf Q}$. (a) to (d) show four different cases of ${\bf Q}$ where the resulting system is still a semimetal. The red lines are the original NLs of Hamiltonian $H_0({\bf k})$ in Eq. (\ref{Z2_H}), whereas the blue lines and stars are the nodal lines or points in the PSDW phase.
The parameters are: $m=\sqrt{2}/2$ and $U\bar m=0.5$.
We only plot for $k_i\in [-\pi/2,\pi/2]$, as the graph repeats itself with a period of $\pi$.\label{fig2}}
\end{figure}
\begin{enumerate}
\item ${\bf Q}=(1,1,1)\pi$:
\begin{eqnarray}
H_{eff} &=& \sin k_x t_3 \tau_0\sigma_1 + \sin k_y t_3 \tau_2\sigma_2 + \sin k_z t_3 \tau_0\sigma_3 \nonumber\\ &+&
m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,,
\\
E^2 &=& \left( \sqrt{\sin^2 k_x + \sin^2k_y} \pm \sqrt{m^2 +U^2\bar m^2}\right)^2 + \sin^2k_z\,. \nonumber\\
\label{E111}
\end{eqnarray}
The spectrum is composed of four two-fold degenerate bands, and
has the same NLs as the original $H_0$, albeit with enlarged radius [Fig. \ref{fig2}(a)]:
\begin{eqnarray}
k_z=0,\pi; \ \sqrt{\sin^2 k_x + \sin^2k_y} = \sqrt{m^2 +U^2\bar m^2}\,.
\label{eq56}
\end{eqnarray}
Since the energy dispersions in Eq. (\ref{E111}) are two-fold degenerate, the NLs are four-fold degenerate.
\item ${\bf Q}=(1,1,0)\pi$:
\begin{eqnarray}
H_{eff} &=& \sin k_x t_3 \tau_0\sigma_1 + \sin k_y t_3 \tau_2\sigma_2 + \sin k_z t_0 \tau_0\sigma_3 \nonumber\\ &+&
m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,,
\end{eqnarray}
which has the same NLs as in Eq. (\ref{eq56}), and
as shown in FIg. \ref{fig2}(b), despite some minor variation of the spectrum near the NLs.
\item ${\bf Q}=(1,0,1)\pi$:
\begin{eqnarray}
H_{eff} &=& \sin k_x t_3 \tau_0\sigma_1 + \sin k_y t_0 \tau_2\sigma_2 + \sin k_z t_3 \tau_0\sigma_3 \nonumber\\ &+&
m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,.
\end{eqnarray}
The full spectrum also has the two-fold degeneracy. while the NLs are gapped in most regions, leaving only pairs of four-fold degenerate points at
\begin{eqnarray}
\sin k_y = \sin k_z=0; \ \sin k_x = \pm \sqrt{m^2 +U^2\bar m^2}\,,
\end{eqnarray}
as shown in Fig. \ref{fig2}(c).
We note that the case ${\bf Q}=(0,1,1)\pi$ has a similar spectrum, which can be obtained from
the above by performing the substitution $k_x\leftrightarrow k_y$.
\item
${\bf Q}=(1,0,0)\pi$:
\begin{eqnarray}
H_{eff} &=& \sin k_x t_3 \tau_0\sigma_1 + \sin k_y t_0 \tau_2\sigma_2 + \sin k_z t_0 \tau_0\sigma_3 \nonumber\\ &+&
m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,.
\end{eqnarray}
Energy zeros are obtained if two conditions are simultaneously satisfied:
\begin{subequations}
\begin{eqnarray}
\sum_{i=1}^3 \sin^2k_i = U^2\bar m^2 + m^2\\
m\sin k_z=\pm U\bar m \sin k_y\,.
\end{eqnarray}
\end{subequations}
Geometrically, one can think of the first condition as defining
a spherical surface, for small ${\bf k}$, and the second one as two planes.
The intersection between the surface and the planes yields two NLs,
obtained by rotating the original loops (in the XY plane) around the $x$ axis in opposite directions.
These two NLs are given by different pairs of energy bands, and thus form a nodal chain [Fig. \ref{fig2}(d)].
We note that spectrum for the case ${\bf Q}=(0,1,0)\pi$
is similar to the case ${\bf Q}=(\pi,0,0)$, and differs only in the interchange $k_x\leftrightarrow k_y$.
The nodal chain is obtained from the two original NLs by a rotation around the $y$ axis.
\item ${\bf Q}=(0,0,1)\pi$
\begin{eqnarray}
H_{eff} &=& \sin k_x t_0 \tau_0\sigma_1 + \sin k_y t_0 \tau_2\sigma_2 + \sin k_z t_3 \tau_0\sigma_3 \nonumber\\ &+&
m t_0 \tau_1\sigma_1 + U\bar m t_1 \tau_0\sigma_3\,.
\end{eqnarray}
In this case the system is a fully gapped insulator.
\end{enumerate}
\section{Nested NLs in Dirac systems}
\label{Diracsec}
In this Section we study density wave phases in four-band spinfull Hamiltonians
with NLs. The spin degree of freedom allows us to distinguish two types of ordered phases:
true and hidden spin density waves (SDWs). In subsection \ref{Diracperturb} we consider NLs
obtained from a perturbed\cite{Burkov,mitschell} Dirac Hamiltonian.
\subsection{Spin degenerate loops}
The simplest way to go from a Weyl to a Dirac loop is to introduce spin degeneracy,
\begin{equation}
H_0({\bf k})\ \rightarrow\ H_0({\bf k}) \sigma_0
\end{equation}
where $\sigma_\mu$ acts in spin space.
We assume Hubbard repulsion between two fermions having opposite spins in the same orbital
(labeled by the index $j$):
\begin{eqnarray}
\hat U = \sum_{{\bf r}, j=1,2} \hat n_{j\uparrow}({\bf r})\hat n_{j\downarrow}({\bf r})\,.
\label{Usigma}
\end{eqnarray}
In principle one could have ordered phases
with ferromagnetic (FM) or antiferromagnetic (or SDW) configurations of the spin:
\begin{eqnarray}
\langle n_{j\sigma}\rangle &=&
\frac 1 4 n + \bar m \sigma \qquad
\sigma=\pm 1\,,\qquad\mbox{Stoner FM}\\
\langle n_{j\sigma}\rangle &=&
\frac 1 4 n + \bar m \sigma (-1)^j \qquad\mbox{hidden Stoner FM}\\
\langle n_{j\sigma}\rangle &=&
\frac 1 4 n + \bar m \sigma \cos({\bf Q}\cdot{\bf r}) \qquad\mbox{true SDW}\\
\langle n_{j\sigma}\rangle &=&
\frac 1 4 n + \bar m \sigma (-1)^j \cos({\bf Q}\cdot{\bf r}) \qquad\mbox{hidden SDW} \label{hiddenSDW}
\end{eqnarray}
Because a NL's density of states vanishes linearly with energy,
the Stoner criterion precludes the FM orderings for weak interactions\cite{roy},
and they are not related to the nesting ${\bf Q}$.
In the following, we shall concentrate on SDW phases.
Considering the hidden SDW, Eq. (\ref{hiddenSDW}), the effective interaction reads:
\begin{eqnarray}
\hat U_{eff} &=&
-U\sum_{{\bf r},j} \left[ \left( \frac n 4 \right)^2 - \bar m^2 \cos^2({\bf Q}\cdot{\bf r})
- \frac n 4 \sum_{\sigma} \hat\psi^\dagger_{j\sigma}({\bf r}) \hat\psi_{j\sigma}({\bf r})
\right]\nonumber\\
&+&U\bar m\sum_{{\bf r},j,j',\sigma\sigma'} \hat\psi^\dagger_{j\sigma}({\bf r})\
\tau^{jj'}_3\sigma^{\sigma\sigma'}_3 \cos({\bf Q}\cdot{\bf r})\ \hat\psi_{j'\sigma'}({\bf r}) \,,\label{tSDW}
\end{eqnarray}
where the field operator $\hat\psi_{j\sigma}({\bf r})$ now includes the spin index $\sigma$.
Similarly, the
field operator in momentum space $\boldsymbol c_{\bf k}$ now denotes $ c_{{\bf k},j,\sigma}$ for all $j,\sigma$.
The Hamiltonian matrix in $\left( \boldsymbol c^\dagger_{{\bf k}}\ \boldsymbol c^\dagger_{{\bf k}+{\bf Q}} \right)$ space reads
(apart from unimportant constants),
\begin{eqnarray}
H_{eff}({\bf k}) &=& \left( \begin{array}{cc}
H_0({\bf k}) & U\bar m \tau_\alpha\sigma_3 \\
U\bar m \tau_\alpha\sigma_3 & H_0({\bf k}+{\bf Q})
\end{array}\right)\,,\label{SDWDirac}
\end{eqnarray}
where $\alpha=3$ describes a hidden SDW [as in Eq. (\ref{tSDW})],
and $\alpha=0$ describes a true SDW.
The off-diagonal block $U\bar m t_1\tau_3\sigma_3$ has exactly the same (anti)commutation
relations with the other
Hamiltonian terms,
as in the Weyl case of Sections \ref{model1_general} and \ref{model2_general} .
All the criteria and spectra established for the Weyl case still
hold, if one just replaces $\bar m\rightarrow\bar m \sigma_3$.
Since this term appears as $(U\bar m)^2$ in the dispersion relations, there is no spin splitting in the spectra.
We note that single antiferromagnetic NLs have been discussed in the literature\cite{jingwang}.
\subsection{Two perturbed Dirac points}
\label{Diracperturb}
A nodal line Dirac semimetal can be obtained starting from a pristine 3D Dirac semimetal\cite{mitschell}
of the form
$H_D({\bf k}) = -\tau_3{\bf p}\cdot\boldsymbol\sigma$ and perturbing it with terms of the form
$a_\mu\tau_\mu\otimes b_\nu\sigma_\nu$.
Suppose, for instance,
\begin{equation}
H_0({\bf k}) = -\tau_3{\bf p}\cdot\boldsymbol\sigma + \tau_1\boldsymbol b\cdot\boldsymbol\sigma
\end{equation}
Without loss of generality assume $\boldsymbol b \parallel \hat z$. The term
$p_z\tau_3\sigma_3$ anticommutes with the others, so:
\begin{equation}
E^2 =p_z^2 + \left( \sqrt{p_x^2+p_y^2}\pm b
\right)^2 \,.
\end{equation}
We note that this dispersion relation is very similar to that in Eq. (\ref{spectrum_Z2}) for the $\mathbb{Z}_2$ loops.
However, the effect of the Hubbard interaction is different, as these two systems couple the two sets
of (pseudo)spin-1/2 subspace in different ways. On the other hand,
Dirac points described by $H_D$ above
do not exist alone if an additional symmetry, such as time-reversal or inversion, is present.
For instance, a time-reversal symmetry (TRS) relates two Dirac points at $-\frac 1 2 {\bf Q}$ and $+\frac 1 2 {\bf Q}$
in such a way that:
\begin{eqnarray}
\sigma_2H_0^*\left(\frac {\bf Q} 2 -{\bf k}\right)\sigma_2 = H_0\left(-\frac {\bf Q} 2 +{\bf k}\right)\,,
\end{eqnarray}
it then follows that, for $\boldsymbol b=0$,
$H_0\left(- {\bf Q} /2 +{\bf k}\right) =H_0\left( {\bf Q} /2 +{\bf k}\right) =H_D({\bf k})$.
Therefore, the two unperturbed Dirac points have the same $k\cdot p$ Hamiltonian.
Including the $\tau_1\boldsymbol b\cdot\boldsymbol\sigma$ term, which breaks TRS,
we obtain the model,
\begin{subequations}
\begin{eqnarray}
H_0\left(-\frac {\bf Q} 2 +{\bf k}\right) &=& -\tau_3{\bf p}\cdot\boldsymbol\sigma +\tau_1\boldsymbol b\cdot\boldsymbol\sigma\,,\\
H_0\left(\frac {\bf Q} 2 +{\bf k}\right) &=& -\tau_3{\bf p}\cdot\boldsymbol\sigma +\tau_1\boldsymbol b\cdot\boldsymbol\sigma\,,
\end{eqnarray}\label{Tpartial}
\end{subequations}
and the effective Hamiltonian has equal diagonal blocks.
A different version of the above model that would preserve TRS symmetry reads:
\begin{subequations}
\begin{eqnarray}
H_0\left(-\frac {\bf Q} 2 +{\bf k}\right) &=& -\tau_3{\bf p}\cdot\boldsymbol\sigma +\tau_1\boldsymbol b\cdot\boldsymbol\sigma\,,\\
H_0\left(\frac {\bf Q} 2 +{\bf k}\right) &=& -\tau_3{\bf p}\cdot\boldsymbol\sigma -\tau_1\boldsymbol b\cdot\boldsymbol\sigma\,.
\end{eqnarray}\label{Tcase}
\end{subequations}
If we now consider the role of inversion symmetry ${\bf k}\rightarrow -{\bf k}$,
the two Dirac points are related by
\begin{subequations}
\begin{eqnarray}
H_0\left(\frac {\bf Q} 2 -{\bf k}\right) = H_0\left(-\frac {\bf Q} 2 +{\bf k}\right) &=& -\tau_3{\bf p}\cdot\boldsymbol\sigma + \tau_1\boldsymbol b\cdot\boldsymbol\sigma\,,\hspace{1cm} \\
\Rightarrow
H_0\left(\frac {\bf Q} 2 +{\bf k}\right) &=& \tau_3{\bf p}\cdot\boldsymbol\sigma +\tau_1\boldsymbol b\cdot\boldsymbol\sigma\,,
\label{Pcase}
\end{eqnarray}
\end{subequations}
therefore, the two Dirac points have different $k\cdot p$ Hamiltonians.
Next we study the effects of a hidden SDW and a true SDW for these different cases,
still assuming $\boldsymbol b \parallel \hat z$.
For a hidden SDW,
the effective Hamiltonian for the TRS breaking model in Eq. (\ref{Tpartial}) is then
\begin{eqnarray}
\hat H_{eff} = t_0 \left[-\tau_3{\bf p}\cdot\boldsymbol\sigma + b\tau_1 \sigma_3\right] + U\bar m t_1\tau_3\sigma_3\,,
\end{eqnarray}
which, by inspection produces the eight band spectrum:
\begin{equation}
E^2 = \left( - p_z\pm U\bar m \right)^2 + \left( \sqrt{p_x^2+p_y^2}\pm b \right)^2
\end{equation}
where the $\pm$ signs are uncorrelated. This corresponds to splitting each loop along the $k_z$ direction.
If one considers, instead, a true SDW phase,
\begin{eqnarray}
\hat H_{eff} = t_0 \left[-\tau_3{\bf p}\cdot\boldsymbol\sigma + b\tau_1\sigma_3\right]+ U\bar m t_1\tau_0\sigma_3\,,
\end{eqnarray}
then there are four doubly degenerate bands:
\begin{eqnarray}
E^2&=& b^2 + U^2\bar m^2+ {\bf p}^2\nonumber\\ &\pm& 2\sqrt{ b^2\left( U^2\bar m^2 + p_x^2 + p_y^2 \right) + U^2\bar m^2p_z^2
} \label{mathspec}
\end{eqnarray}
with nodal lines given by $ p_z=0\,, p_x^2 + p_y^2 = b^2 - U^2\bar m^2$.
So, the initial two loops still exist
but their radius shrinks.
In the TRS model, Eq. (\ref{Tcase}), the hidden SDW phase is described by the effective Hamiltonian:
\begin{eqnarray}
\hat H_{eff}&=& -t_0\tau_3{\bf p}\cdot\boldsymbol\sigma + bt_3\tau_1\sigma_3 + U\bar m t_1\tau_3\sigma_3\,.
\end{eqnarray}
The spectrum is the same as in Eq. (\ref{mathspec}).
So, the initial two loops still exist but their radius shrinks.
And a true SDW phase is described by the effective Hamiltonian:
\begin{eqnarray}
\hat H_{eff} &=& -t_0 \tau_3( p_x\sigma_1 + p_y\sigma_2) - p_z t_0\tau_3\sigma_3 + b\ t_3\tau_1\sigma_3 \nonumber\\ &+& U\bar m t_1\tau_0\sigma_3\,,
\end{eqnarray}
which produces the spectrum with eight bands:
\begin{equation}
E^2 =\left( \sqrt{p_x^2+p_y^2} \pm b \right)^2 + \left( p_z \pm U\bar m \right)^2\,,
\end{equation}
where the $\pm$ signs are uncorrelated. This corresponds to splitting each loop along $p_z=\pm U\bar m$.
For the case with inversion symmetry, in Eq. (\ref{Pcase}), a hidden SDW phase is described by the effective Hamiltonian:
\begin{eqnarray}
H_{eff} ({\bf k})= -t_3 \tau_3{\bf p}\cdot\boldsymbol\sigma + b \ t_0\tau_1\sigma_3 + U\bar m t_1\tau_3\sigma_3\,,
\label{PhiddenSDW}
\end{eqnarray}
which produces the eight band spectrum:
\begin{equation}
E^2 =p_z^2 + \left( \pm \sqrt{b^2 + U^2\bar m^2} \pm \sqrt{p_x^2+p_y^2}
\right)^2\,,
\end{equation}
(uncorrelated$\pm$ signs). This corresponds to splitting each nodal line by changing its radius.
A true SDW is obtained by changing $\tau_3\rightarrow\tau_0$ in the last term of Eq. (\ref{PhiddenSDW}).
The resulting spectrum, \
\begin{equation}
E^2 =p_z^2 + \left( \sqrt{p_x^2+p_y^2} \pm b \pm U\bar m \right)^2\,,
\end{equation}
(with uncorrelated $\pm$ signs) also has NLs given by $p_z=0$, $\sqrt{p_x^2+p_y^2} =|b\pm U\bar m|$.
In the remaining case, where $H_0(-{\bf Q}/2 + {\bf k})=-H_0({\bf Q}/2 + {\bf k})$,
a hidden SDW phase is described by the effective Hamiltonian:
\begin{eqnarray}
H_{eff} ({\bf k})= t_3 \left[ -\tau_3{\bf p}\cdot\boldsymbol\sigma + b \tau_1\sigma_3 \right]+ U\bar m t_1\tau_3\sigma_3\,,
\end{eqnarray}
which, by inspection produces the eight band spectrum:
\begin{equation}
E^2 =p_z^2 + \left( \sqrt{p_x^2+p_y^2} \pm b \pm U\bar m \right)^2\,,
\end{equation}
with uncorrelated$\pm$ signs. Therefore, each loop splits in the radial direction. The
true SDW is described by the effective Hamiltonian:
\begin{eqnarray}
\hat H_{eff} = t_3 \left[ -\tau_3{\bf p}\cdot\boldsymbol\sigma + b \tau_1\sigma_3 \right]+ U\bar m t_1\tau_0\sigma_3\,,
\end{eqnarray}
which, by inspection produces the eight band spectrum:
\begin{equation}
E^2 = p_z^2 + \left( \pm \sqrt{p_x^2+p_y^2} \pm \sqrt{ b^2 + U^2\bar m^2} \right)^2 \,,
\end{equation}
where the $\pm$ signs are uncorrelated. Again, this corresponds to splitting each nodal loop in the radial direction.
\section{Superconductivity}
\label{supersec}
When considering a single Weyl NL, the pairing block of the Bogolyubov-deGennes
(BdG) matrix
in the particle-hole basis\cite{sacramento1,sacramento2,beri}, takes the form
\begin{equation}
\hat \Delta({\bf k}) =
\left[
d_0({\bf k})\tau_0+ \boldsymbol d({\bf k})\cdot\boldsymbol\tau
\right] i\tau_2
\,,
\end{equation}
and fermionic statistics imposes that
$\hat \Delta({\bf k}) = \hat \Delta^T(-{\bf k})$.
Close to the nodal lines the 3D momentum, ${\bf p}=\hbar{\bf k}$,
can be parametrized as
\begin{subequations}
\begin{eqnarray}
p_x &=& (p_0 + \tilde p\cos\phi) \cos\theta\\
p_y &=& (p_0 + \tilde p\cos\phi) \sin\theta \,,\\
p_z&=&p_\perp=\tilde p\sin\phi\,,
\end{eqnarray}\label{pcoordinates}
\end{subequations}
which is to be inserted in the $k\cdot p$ loops models.
Here, $\theta$ is the azimuthal angle along the loop,
$\tilde p$ is the radius of a torus involving the NL, and the angle $\phi$ wraps around
the latter\cite{Nandkishore1}.
Note that, according to Eq. (\ref{pcoordinates}), momentum inversion ${\bf p}\rightarrow -{\bf p}$ is equivalent to
$\theta\rightarrow\theta+\pi$ and $\phi\rightarrow -\phi$, while reflection in the loop's
plane, $p_z\rightarrow -p_z$, is equivalent to $\phi\rightarrow -\phi$.
In the semimetal case (undoped, or compensated case) the FS reduces to the NL
and ${\bf p}$ reduces to the angle $\theta$ on the loop. In the doped case, any point on
the torus shaped FS can be labeled by two angles, $\theta,\phi$. The functions
$ d_0({\bf k})$ and $\boldsymbol d({\bf k})$ describe (pseudo-spin) singlet and
triplet pairing, respectively.
One can expand the singlet pairing function quite generally as
\begin{equation}
d_0({\bf k}) = \sum_{l_1,l_2} e^{il_1\theta}\left[ \Delta_{l_1l_2}\cos(l_2\phi) + \tilde \Delta_{l_1l_2}\sin(l_2\phi)
\right]\,.
\end{equation}
An analogous expansion can be written for $\boldsymbol d({\bf k})$.
If there are two nested Weyl loops, then an additional loop label
must be introduced and the Pauli matrix $t_\mu$ operates in the two-dimensional loop space. For a two-loop
system then, we write the pairing matrix as
\begin{equation}
\hat \Delta({\bf k}) =
\left[
d_0({\bf k})\tau_0+ \boldsymbol d({\bf k})\cdot\boldsymbol\tau
\right] i\tau_2
t_\mu\,.
\end{equation}
The BdG Hamiltonian matrix in the particle-hole basis has the form
\begin{equation}
H({\bf k})= \left( \begin{array}{cc}
\hat\Xi ({\bf k})& \hat \Delta ({\bf k})\\
\hat\Delta^\dagger ({\bf k}) & -\hat\Xi^T(-{\bf k})
\end{array}\right)
\label{BdGmatrix}
\end{equation}
with $\hat\Xi= diag(H_1, H_2)$ . The Hamiltonians $H_{1(2)}$ are the $k\cdot p$ Weyl NL models.
The total Hamiltonian is then
\begin{eqnarray}
\hat H=\frac 1 2 \sum_{{\bf k}}{\boldsymbol c}^\dagger H({\bf k})
{\boldsymbol c}\,,
\end{eqnarray}
where $ {\boldsymbol c}=(\hat {\boldsymbol c}_{{\bf k},1},\ \hat {\boldsymbol c}_{{\bf k},2},\
\hat {\boldsymbol c}_{-{\bf k},1}^\dagger,\ {\boldsymbol c}_{-{\bf k},2}^\dagger
)^T$.
If the two NLs are centered at BZ points $\pm{\bf Q}/2$ respectively, then the inter-NL pairing
is the ``usual'' pairing between opposite momenta, and we shall take this to be the case.
If not, then the Cooper pair would have
a finite quasi-momentum (a Fulde-Ferrel-Larkin-Ovchinnikov state\cite{LOFF1,LOFF2,LOFF3}).
The cases $\mu=0,1,3$, are different from the case $\mu=2$ regarding the parity of the functions
$ d_0({\bf k})$ and $\boldsymbol d({\bf k})$.
In the cases $\mu=1,2$, electrons
on different loops are being paired: an electron $({\bf k} ,1)$ is being paired with another $(-{\bf k} ,2)$.
The cases $\mu=0,3$ describe intra-NL pairing, where the scattering of two particles from one NL
into the other may be included, and $id_0\tau_2t_3$ would describe sign-reversed s-wave
pairing, analogous to that in pnictide superconductors\cite{BangChoi}.
Inter-NL pairing with $\mu=1$ (interloop triplet pairing), requires
$d_0$ to be even and ${\boldsymbol d}$ to be odd function of ${\bf k}$; if $\mu=2$ (interloop singlet), then
$d_0$ and ${\boldsymbol d}$ have the opposite parities.
The BdG matrix decouples into two blocks
each associated with
the vector spaces $(\hat c_{{\bf k},1}, \hat c_{-{\bf k},2}^\dagger)^T$
and $(\hat c_{{\bf k},2}, \hat c_{-{\bf k},1}^\dagger)^T$, respectively.
Since we expect a fully gapped excitation spectrum to have higher condensation energy than a nodal spectrum,
we shall examine the cases where $d_0$ and $\boldsymbol d$ are constant on the FS (in the
$\mu=1$ and $\mu=2$ cases, respectively). If TRS holds, then these order parameters must also be real.
\subsection{Model-1 loops}
Assuming a positive energy offset, $\delta$, the interband pairing occurs
between the electronic toroidal FS from the $H_1-\delta$ loop,
and the hole-like FS from the $H_2+\delta$ loop.
As in previous literature, this is best done by considering projective form factors\cite{wangye,Nandkishorepro}
onto the conduction or valence band.
Let $U_{1(2)}$ be the unitary matrices which diagonalize $H_{1(2)}$, so that
$U_sH_sU_s^\dagger=\sqrt{\left( |{\bf p}_\parallel| - p_0 \right)^2 + p_\perp^2}\ \tau_3\equiv \tilde p\tau_3$ for $s=1,2$.
The positive and the
negative branches are the conduction and valence bands, respectively.
Because for model-1 loops there is always a Pauli matrix $\tau_\beta$ such that
$H_1=\tau_\beta H_2\tau_\beta$,
it then follows that $U_2=U_1\tau_\beta$.
We can apply this same unitary transformation to the BdG matrix in Eq. (\ref{BdGmatrix}) as:
\begin{eqnarray}
\left( \begin{array}{cc}\Lambda & 0\\ 0 & \Lambda^*(-{\bf k})\end{array}\right)H({\bf k})
\left( \begin{array}{cc}\Lambda^\dagger & 0\\ 0 &\Lambda^T(-{\bf k}) \end{array}\right)
\nonumber\\ =
\left( \begin{array}{cc} \tilde p\tau_3t_0 -\delta\tau_0 t_3 & \Lambda \hat\Delta \Lambda^T(-{\bf k}) \\
\Lambda^*(-{\bf k}) \hat\Delta^\dagger \Lambda^\dagger& -\tilde p\tau_3t_0+\delta \tau_0 t_3 \end{array}\right)
\label{UBdGU}
\end{eqnarray}
where $\Lambda=diag(U_1, U_2)$.
The off-diagonal pairing block is then $\Lambda({\bf k}) \hat\Delta({\bf k}) \Lambda^T(-{\bf k})$.
For $\delta>0$, only the pairing between the conduction band of $H_1$ and the valence band of $H_2$ is considered.
From the BdG matrix in Eq. (\ref{UBdGU}) we obtain the submatrix operating in this two-fold subspace as:
\begin{eqnarray}
H^{FS}=\left( \begin{array}{cc} \tilde p -\delta &
\Delta_{FS}({\bf k}) \\
\Delta_{FS}^*({\bf k})
& \tilde p -\delta \end{array}\right)
\label{condval1}
\end{eqnarray}
where $\Delta_{FS}({\bf k})$ is
the pairing function on the FS which, from Eq. (\ref{UBdGU}) and for $\mu=1$ reads:
\begin{eqnarray}
\Delta_{FS}({\bf k}) =
\left[
U_1({\bf k}) \left(d_0+{\boldsymbol d}\cdot{\boldsymbol\tau}\right) i\tau_2U_2^T(-{\bf k})\right]_{12}
\label{pairingfunction}
\end{eqnarray}
It is then clear from Eq. (\ref{condval1}) that the spectrum is $E=\tilde p -\delta \pm |\Delta_{FS}({\bf k})|$, and is gapless.
At finite doping, no gapped state is to be expected from
FS interloop pairing between non-degenerate model-1 Weyl loops.
The situation is different for the degenerate ($\delta=0$) case, however, where the FS is composed of two nodal lines.
From Eq. (\ref{UBdGU}) and $t_\mu=t_1$ we obtain a BdG matrix restricted to the subspace $\left( U_1({\bf k}) \hat{\boldsymbol c}_{{\bf k},1} \,,
U_2^*(-{\bf k}) \hat{\boldsymbol c}_{-{\bf k}, 2}^\dagger \right)$, as
\begin{eqnarray}
H_{12}'=\left( \begin{array}{cc}
\tilde p\tau_3 & U_1(d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau})i\tau_2 U_2^T \\
-iU_2^*\tau_2 (d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau}) U_1^\dagger & -\tilde p\tau_3
\end{array}\right)
\label{UBU2}
\end{eqnarray}
For the sake of definiteness we consider the NL models with $\tau_a=\tau_1,\tau_b=\tau_2$, so that
\begin{eqnarray}
H_1(\phi) &=& \tilde p\left( \cos\phi\tau_1 + \sin\phi\tau_2\right)\,,\label{h1phi}\\
U_1({\bf k})&=& \frac{1}{\sqrt{2}}\left( \begin{array}{cc}
1 & e^{-i\phi}\\
-1 & e^{-i\phi}
\end{array}\right)\,.\label{u1phi}\
\end{eqnarray}
We note that all the other $(\tau_a,\tau_b)$ cases can be related to this through a suitable rotation in pseudo-spin space.
From Eq. (\ref{u1phi}), one can see that $U_1^\dagger({\bf k}) =U_1^T(-{\bf k}) $.
Interloop pairing is described by the off-diagonal block in Eq (\ref{UBU2}):
\begin{eqnarray}
&& U_1({\bf k}) \left(d_0+{\boldsymbol d}\cdot{\boldsymbol\tau}\right) i\tau_2\tau_\beta^TU_1^T(-{\bf k})=\nonumber\\
&=&
\left(\begin{array}{cc}
id_0\sin\phi + id_2+d_3\cos\phi & d_0\cos\phi + d_1 + id_3\sin\phi\\
-d_0\cos\phi + d_1 - id_3\sin\phi & - id_0\sin\phi + id_2-d_3\cos\phi
\end{array}\right) \,, \nonumber \\
&=& \left(\begin{array}{cc}
d_3 +id_2\cos\phi- id_1\sin\phi & -d_0 - d_1\cos\phi- d_2\sin\phi \\
-d_0 + d_1\cos\phi + d_2\sin\phi & d_3 -id_2\cos\phi+ id_1\sin\phi \end{array}\right) \,, \nonumber\\
&=& \left(\begin{array}{cc}
-id_0 -id_1\cos\phi-id_2\sin\phi & d_1\sin\phi - d_2\cos\phi +id_3\\
- d_1\sin\phi + d_2\cos\phi +id_3 & -id_0 +id_1\cos\phi+id_2\sin\phi \end{array}\right)\,, \nonumber\\
&=&
\left(\begin{array}{cc}
-d_0\cos\phi - d_1-id_3\sin\phi & -id_0\sin\phi - id_2 -d_3\cos\phi\\
id_0\sin\phi - id_2 +d_3\cos\phi & d_0\cos\phi - d_1+id_3\sin\phi \end{array}\right)\,,\nonumber\\
\label{udelu}
\end{eqnarray}
for the cases $\beta=0,1,2,3$, respectively. Note that for the case $t_\mu=t_2$,
we simply have to multiply
both sides of Eq. (\ref{udelu}) by $-i$.
For $\mu=1$ a fully gapped FS can only happen for constant $d_0$ because $\boldsymbol d$ is an
odd function and must have nodes on the NLs. In this case, only for $\beta=2$ a gapped
spectrum is obtained: $E^2 = \tilde p^2 + d_0^2$.
For $\mu=2$ (interloop singlet) and constant real $\boldsymbol d$ there are more possibilities.
If
$\beta=0$ a fully gapped spectrum $E^2 = \tilde p^2 + d_2^2$; if
$\beta=1$ a fully gapped spectrum $E^2 = \tilde p^2 + d_3^2$; for
$\beta=3$ the fully gapped spectrum $E^2 = \tilde p^2 + d_1^2$.
Gapped spectra result from intraband pairing.
Interband pairing leads to nodal spectra for the same reason as in
the $\delta>0$ case.
\subsection{Model-2 loops}
In a model-2 loop we replace Eqs. (\ref{h1phi})-(\ref{u1phi}) with
\begin{eqnarray}
H_1(\phi) &=& \tilde p\left[ (\cos\phi+ \sin\phi)\tau_1 + \sin\phi\tau_2\right]\,,\label{h21phi}\\
U_1({\bf k})&=& \frac{1}{\sqrt{2}}\left( \begin{array}{cc}
e^{i \omega} & 1\\
e^{-i \omega}& -1
\end{array}\right)\,,\label{u21phi}
\end{eqnarray}
where $\omega=arg(e^{i\phi}+\sin\phi)$. If $H_1 = \tau_\beta H_2\tau_\beta$, then
the conclusions are the same as for model-1 loops, with the replacement
$\tilde p\rightarrow \tilde p|e^{i\phi}+\sin\phi|$.
We now consider the case where the two loops are related through the reflection operation in Eq. (\ref{reflection}).
Because the reflection implies $\phi\rightarrow -\phi$, the energy dispersions are different for $H_1$ and $H_2$.
In the non-degenerate case ($\delta>0$), $H^{FS}$ now takes the form
\begin{eqnarray}
H^{FS}=\left( \begin{array}{cc} \tilde p |e^{i\phi}+\sin\phi|-\delta &
\Delta_{FS}({\bf k}) \\
\Delta_{FS}^*({\bf k})
& \tilde p|e^{i\phi}-\sin\phi| -\delta \end{array}\right)
\end{eqnarray}
and the resulting spectrum allows gapless excitations, as was the case for model-1 loops.
In the degenerate case, we find it more convenient not to perform the rotation in Eq. (\ref{UBdGU}), and diagonalize the
original BdG matrix restricted to the subspace
$\left( \hat{\boldsymbol c}_{{\bf k},1} \,, \hat{\boldsymbol c}_{-{\bf k}, 2}^\dagger \right)$, instead.
In this subspace, the two diagonal blocks of the BdG matrix, which follow from Eq. (\ref{BdGmatrix}), are
$ H_1(\phi)$ and
\begin{eqnarray}
-H_2^T(-\phi)&=&- \tau_\beta H_1^T(\phi)\tau_\beta\,,
\label{H1H2phi}
\end{eqnarray}
which follows from (\ref{h21phi}) and the reflection operation that relates both loops:
$H_2(\phi)=\tau_\beta H_1(-\phi)\tau_\beta$.
For $t_\mu=t_1$ (interloop triplet) the BdG reads:
\begin{eqnarray}
H_{12}'=\left( \begin{array}{cc}
H_1\phi) & (d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau})i\tau_2 \\
-i\tau_2 (d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau}) & - \tau_\beta H_1^T(\phi)\tau_\beta
\end{array}\right)
\label{UBU3}
\end{eqnarray}
We identify the TRS cases where the excitation spectrum is fully gapped.
For constant $d_0$ and ${\boldsymbol d}=0$, the gapped spectra are obtained for $\beta=1$ and $\beta=3$, respectively:
\begin{eqnarray}
\beta=1: E^2 &=&d_0^2 + {\tilde p}^2 \sin^2\phi + \left( d_0\pm \tilde p| \sin\phi+\cos\phi | \right)^2\,,\nonumber
\\ \\
\beta=3: E^2 &=&d_0^2 + {\tilde p}^2 \left[ \sin^2\phi + (\sin\phi+\cos\phi )^2\right]\,.
\end{eqnarray}
In the case of interloop singlet $t_\mu=t_2$, we consider $d_0=0$ and constant $\boldsymbol d$.
Gapped spectra exist for: $\beta=0$ and nonzero $d_3$; $\beta=1$ and nonzero $d_2$;
$\beta=2$ and nonzero $d_1$. All these cases have similar spectra:
\begin{subequations}
\begin{eqnarray}
\beta=0: E^2 &=&d_3^2 + {\tilde p}^2 \left[ \sin^2\phi + (\sin\phi+\cos\phi )^2\right] \,,\ \ \\
\beta=1: E^2 &=&d_2^2 + {\tilde p}^2 \left[ \sin^2\phi + (\sin\phi+\cos\phi )^2\right]\,,\ \ \\
\beta=2: E^2 &=&d_1^2 + {\tilde p}^2 \left[ \sin^2\phi + (\sin\phi+\cos\phi )^2\right]\,.\ \
\end{eqnarray}
\end{subequations}
\subsection{Pairing between Dirac loops}
Including the spin degree of freedom, we may discuss the pairing between spin degenerate loops
$H_1\otimes\sigma_0$ and $H_2\otimes\sigma_0$ described by the BdG matrix:
\begin{eqnarray}
H_{12,s}'=\left( \begin{array}{cc}
H_1\otimes\sigma_0 & (d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau})i\tau_2 (t_\mu)_{12}\sigma_s \\
-i\sigma_s\tau_2 (d_0 + {\boldsymbol d}\cdot{\boldsymbol \tau})(t_\mu)_{21} & -H_2^T \otimes\sigma_0
\end{array}\right)\nonumber\\
\end{eqnarray}
Whatever the choice for $s=1,2,3$, $H_{12,s}'$ decouples in subblocks for which the results obtained above
for Weyl systems can be applied.
The (anti)symmetric property of the matrices $t_\mu$, $\sigma_s$ will determine whether the functions
$d_0$,$\boldsymbol d$ should be odd of even: if for instance, $s=1,3$ then the parity of $d_0$,$\boldsymbol d$
is as in the Weyl case; if, however, $s=2$ (spin singlet), then the parities should be reversed.
\section{Summary and Conclusions}
\label{concsec}
We have described broken symmetry phases of nested Weyl and Dirac NLs that are induced by a short range interaction.
We made a systematic analysis for two-band Hamiltonians with PT symmetry, where the
two nested Weyl NLs can be mapped onto each other through a rotation or
reflection operator. Charge and (pseudo)spin density waves always lower the energy and the broken symmetry phase
can be metallic, semimetallic or insulating, depending on the operator that maps the
the initial NLs onto each other, and on whether they enjoy a local reflection symmetry in the loop plane.
This outcome does not depend
on whether the initial system is semimetallic or metallic (when the initial FS is composed of two toroidal FSs, one hole- and one electron-like).
If the initial system is semimetallic, spontaneous symmetry breaking requires a finite interaction which is
attractive for CDWs and repulsive for PSDWs.
We have also studied specific four-band models, including the $\mathbb{Z}_2$ NLs,
spin degenerate Dirac systems, and
NL's derived from perturbed spinful Dirac nodal points.
The PSDW phases from $\mathbb{Z}_2$ NLs include nodal point and nodal chain semimetals.
Fully gapped superconducting phases from electron pairing in different NLs (interloop pairing), with TRS, have been found.
They include all possibilities of triplet and singlet pairing in loop space and spin space.
There has recently been an
intensive search for topological semimetal materials.
Given that point nodes tend to appear in pairs for symmetry reasons, it is conceivable
that suitable engineering can produce double NLs.
Indeed, a recent proposal for realizing point nodes (Dirac or Weyl),
and pairs of NLs by strain engineering in
SnTe and GeTe is relevant here\cite{LauOrtix}.
Another recent proposal concerns layered ferromagnetic rare-earth-metal monohalides
{\it LnX} ({\it Ln}=La,
Gd; {\it X}=Cl, Br)
and a pair of mirror-symmetry protected nodal lines in La{\it X} and Gd{\it X}\cite{Nie}.
Also, splitting of Dirac rings into pairs of Weyl rings by spin-orbit interaction
in InNbS$_2$ has been proposed\cite{Du}.
Two groups of Dirac nodal rings have been experimentally
detected\cite{Lou} in ZrB$_2$.
However, the detection of pairs of NLs at the Fermi level is presently still lacking.
We have not addressed the competition between different orderings or interactions,
but such an extension of our work might be relevant to real materials.
We have also neglected the effect of the long-ranged tail of the Coulomb interaction
which could be present if the starting system is a NL semimetal with the screening radius
diverging near the Fermi level. In this respect, the study in Ref[\cite{roy}] for a single NL
suggests that the critical interaction strength
for orderings where a fully gapped spectrum
arises could be lowered.
Ordered phases\cite{gruner}, such as orbital and/or spin density waves, can be detected through
neutron scattering, or resonant soft x-ray scattering\cite{xray}.
The band structure itself may be studied with angle-resolved photoemission spectroscopy.
\section*{Acknowledgments}
M.A.N.A. acknowledges partial support from
Funda\c{c}\~ao para a Ci\^encia e Tecnologia (Portugal)
through Grant No. UID/CTM/04540/2013, and
the hospitality of Computational Science Research Center,
Beijing, China, where this work was initiated.
M.A.N.A. would like to thank V\'{\i}tor R. Vieira,
Bruno Mera, and Tilen Cadez for a discussion.
\vspace{0.5cm}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,226 |
Olympic sprinter Monica Brennan says positive self-talk is key to a healthy body.
Fact: Research has found 38% of 4-year-old girls are dissatisfied with their bodies, and 34% of 5-year-old girls intend to diet. Hard to imagine right? Well, not if you're an athlete.
Monica Brennan may be a world class sprinter, having taken out countless state titles, national championships and representing Australia at the 2016 Rio Olympics, but even as an elite athlete, she was never exempt from negative body image comments from those around her.
"Growing up as an athlete I was constantly told how important looking after your body was but then also was constantly judged by coaches and other athletes for how fit I looked," she tells whimn.
To add to this, there was pressure from social media and society to fit into a particular mould of what 'sporty' or 'athletic' should look like. It's only as time has passed that Brennan has stopped listening to other people's opinions of her body and instead focused on how great her body was, viewing it as a gift that enabled her to do what she loved: sprinting.
And while the 400m sprinter is looking towards the 2020 Olympics in Tokyo, she is tuning into what her body needs, instead of pushing it past its limits.
Like many athletes, Brennan has a full-time job, working as a brand sample coordinator for Lululemon Athletica, which is how she got involved with not-for-profit organisation, Pretty Foundation, to encourage young girls to instead focus on how their body feels, as opposed to how it looks. By celebrating girls from a young age, Pretty Foundation seeks to instil a gender equality mind-set within the next generation and to teach girls that they are not valuable for what they look like, but rather for who they are.
Her advice to do the same?
"Block out everything that everyone else is saying your body should look like and just focus on how it feels and what it can do," Brennan says. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,044 |
# Building a Corporate Culture of Security
## Strategies for Strengthening Organizational Resiliency
John Sullivant, CFC, CSC, CHS-IV, CPP, RAM-W
Diplomate, American Board of, Forensic Engineering & Technology, American College of Forensic, Examiners Institute
# Table of Contents
Cover image
Title page
Copyright
Dedication
About the Author
Foreword
Preface
Acknowledgments
1. Introduction
Overview
Building Security Resilience and Developing Relationships
Watch Out for Stumbling Blocks
Vulnerability Creep-in Just Showed Up—It Wasn't Here Before
Conclusion
2. Strategies That Create Your Life Line
Overview
A Need Exists to Create a Set of Uniform Security Strategies
Security Strategies and Guiding Principles
Conclusion
3. The Many Faces of Vulnerability Creep-in
Overview
Vulnerability Creep-in Eludes Many Security Professionals
Strategic Security Deficiencies Top the List
Programmatic Security Weaknesses Rank Second Place
Human and Technology Inadequacies Rate Third Place
Conclusions
4. The Evolving Threat Environment
Overview
The Threat Landscape Is Diversified and Sophisticated
Attack Modes Make Planning and Response a Challenge
Conclusions
5. The Cyber Threat Landscape
Overview
Who Is Responsible for Today's Cyber Attacks?
The Cyber Threat Continues to Devastate the U.S. Economy and National Security
Trusted Insiders Bear Watching
State-Sponsored Cyber Attacks Create Havoc With Our Economy and National Security
Cyber Practices and Incident Responses Need Improvement
Conclusions
6. Establishing a Security Risk Management Program Is Crucial
Overview
Risk Management Measures and Evaluates Risk Exposure and the Ability to Deal With Threats
Subscribing to a Security Risk Management Program
A Risk Management Program Establishes Creditability
When to Measure and Evaluate Performance
A Risk Management Program Is Key to Performance Success
Executives Need Compelling and Persuasive Information to Make Sound Business Decisions
Conclusions
Appendix A: Risk Management and Architecture Platform
Relationship Between Measurement and Evaluation
Architecture Platform
Evaluation Tools Mostly Used Within Security Organizations
Quality Assurance: Zero Defects
7. Useful Metrics Give the Security Organization Standing
Overview
Risk-based Metrics Are Often Underestimated
Setting the Metric Framework and Architecture Foundation
Well-Designed Risk-based Metrics Resonate with CEOs
Theory of Probability
Benefits of Using Risk-based Metrics
Conclusion
Appendix A: Metric Framework and Architecture Platform
Strategic Relevance
Operational Reasonableness
8. A User-Friendly Security Assessment Model
Overview
A Reliable Security Assessment Model That Resonates with C-Suite Executives
Measuring and Evaluating Performance Effectiveness
The Benefits Management Enjoys from Using a Risk-Based Model
Conclusions
9. Developing a Realistic and Useful Threat Estimate Profile
Overview
Providing Meaningful Strategic Threat Advice to Executive Management Is Essential
Threat Planning Relies on the Development of a Useful Threat Estimate Profile
Suggested Composition of a Threat Estimate Profile
The Local/Site-Specific Threat Assessment
Identifying the Range of Potential Threats and Hazards Is a Critical Planning Process
Consequence Analysis and Probability of Occurrence for Threats and Hazards
Benefits of Having a Threat Estimate Profile
Conclusions
Appendix A
Appendix B
10. Establishing and Maintaining Inseparable Security Competencies
Overview
Are Your Security Competencies a Top Priority?
Timely Interdependencies of Security Capabilities
Conclusions
11. A User-Friendly Security Technology Model
Overview
A Dire Need Exists to Embrace a Technical Security Strategy
The Technical Security Planning Process Is Often Misunderstood and Underestimated
Embracing The Challenges of New Technology Advancements
Technology Application Has High-Visibility Challenges
Importance of a Quality System Maintenance Program
Embracing Inspections and Tests Extends the System Life Cycle
System Failure Modes and Compensatory Measures
Conclusion
Appendix A: Selected Security Technology Deficiencies and Weaknesses
Overview of Selected Case Histories
Appendix B: Sample Test Logs
Safety Information
12. Preparing for Emergencies
Overview
Security Emergency Planning Is Critical to Organizational Survival
Planning for Prevention, Protection, Response, and Recovery
Alert Notification Systems Serve as Triggering Mechanisms to Carry Out Security Planning Considerations
Planning for Security Event-Driven Response and Recovery Operations
Strategies for Integrating and Prioritizing Security Response and Recovery Operations
Security Emergency Response Plan
Conclusions
Appendix A: Case Histories: Security Emergency Planning Fallacies
13. A User-Friendly Protocol Development Model
Overview
Adopting a Protocol Strategy Is Crucial to Quality Performance
Need for Protocols
Purpose of Protocol Reviews
Quality Review Process for Essential Security Protocols
Benefits Derived from Protocol Analysis
Conclusions
Appendix A
14. A Proven Organization and Management Assessment Model
Overview
Embracing the Mission of the Security Organization
A Reliable Organization and Management Assessment Model That Resonates with CEOs
Purpose of Measuring Organization and Management Competency
Measuring Security Management and Leadership Competencies
Benefits of an Operational and Management Audit
Conclusions
Appendix A: Case Histories – Management and Leadership
Overview of Selected Case Histories
15. Building Competencies That Count: A Training Model
Overview
Why Security Training Is Important
Goals and Value Are Drivers of Effective Training
A Reliable Training Model Resonates With Chief Executive Officers
Independent Research and Credence of the Model
Types of Security Awareness Training Programs
Specialized Security Staff Training Program
Course Design Brings Instruction to Life
Professional Development Is Key for Security Planners
Benefits Management Enjoys by Adopting the Model
Conclusions
16. How to Communicate with Executives and Governing Bodies
Overview
Why Would a CEO Ever Ask You for Help?
Why Should a Chief Executive Listen to You?
Speak the Language Executives and Board Members Understand, Care About, and Can Act On
Impressions Count
Tips That Will Help You Get Your Message Across
Think Strategically
Develop a Management Perspective
Be Trustworthy, Candid, and Professional
Be a Verbal Visionary
Be That Window for Tomorrow
Give Constructive Advice
Build a Solid Business Case
Know When to Pull Your Parachute Cord
Present Program Results Regularly
Conclusions
17. A Brighter Tomorrow: My Thoughts
Overview
A Perspective for the Future
The Evolving Business and Threat Landscape
Corporate Image, Brand, and Reputation Hang in the Balance
Measuring and Evaluating Performance and Productivity
Security Design Performance and Program Integration
Training Programs Need a Major Uplift
Security Emergency Plans and Response/Recovery Procedures
Communicating with Executives and Governing Bodies
Security Leadership Needs a Touch Up
Change Management in the Wind
What Does Work May Surprise You
Characteristics of Future Security Leaders
My Parting Thought
References
Index
# Copyright
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This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter ofproducts liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.
ISBN: 978-0-12-802019-7
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# Dedication
In loving memory to family who continues to energize me...
Peter (Serras) Sullivant
Stamatina (Serras) Sullivant
Jerry Sullivant
Nonda Sullivant
And to my beautiful grandchildren...
Maia and Jacobi who insist the better tomorrow is here
# About the Author
John Sullivant has a strong record—five decades of problem solving and leadership—in executive security management, governance, consulting, and strategic planning in industry, government, and academia, both domestically and abroad. He is one of America's leading, trusted advisor, with the unique ability to help executives look at problems from a variety of sensible, constructive, ethical, and principled perspectives.
For more than fifty years John Sullivant has advised, coached, and counseled executives who run very large corporations and organizations, such as the Los Angeles Department of Water and Power, World Financial Center, and Raytheon and MasterFoods; the states of Texas, Louisiana, and New Hampshire; the National Nuclear Security Administration, the Department of Defense, and the Federal Aviation Administration. Experiences include work with the national intelligence community; national and international RDT&E centers; university medical centers and medical research laboratories; telecommunication; food and agriculture; manufacturing; banking and financing; entertainment; and civil aviation. He has held numerous positions of responsibility as a former chief executive, Vice President of two corporations, and senior program manager of several highly visible projects. Formerly, he held key leadership positions on national councils, committees, and advisory boards. The situations he helps to resolve often involve performance and compliance audits, inspections, and special investigations; revitalizing dysfunctional unit performance; discovering security technology deficiencies; defending against activist opposition, criminal actions, and terrorist threats; improving security emergency planning capabilities; and investigating grassroot causes of image, brand, and reputational threats.
His publications include "Strategies for Protecting the Telecommunications Sector", in Wiley Handbook of Science and Technology for Homeland Security (John Wiley & Sons, 2009); and Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving (John Wiley & Sons, 2007). He also has authored numerous position papers for various U.S. government agencies and published articles for Security Magazine and Risk Mitigation Executive.
A disabled veteran, a cultivated and educated board-certified professional, a successful business owner, an ombudsman, and a renowned author, John Sullivant is widely recognized as an authority in developing strategies to reduce risk exposure and is a trusted advisor for changing the security landscape. He is a certified forensic consultant (CFC), certified security consultant (CSC), certified in Homeland Security (CHS-IV), a certified protection professional (CPP), certified in risk assessment methodology for water utilities (RAM-W), and a distinguished diplomate of the American Board of Forensic Engineering & Technology at the American College of Forensic Examiners Institute. He has addressed numerous industry and government forums, and lectured at the university level.
John Sullivant is a graduate of Southwest Texas University, received a bachelor of science in Occupational Education (Law Enforcement) with honors. He earned a master of science in Psychology (Counseling & Guidance) from Troy State University with high honors and academic fitness.
# Foreword
John Sullivant, CFC, CSC, CHS-IV, CPP, RAM-W and Diplomate of the American Board of Forensic Engineering & Technology at the American College of Forensic Examiners Institute, has provided strategic advice, counsel, and leadership to industry, government and academia for more than five decades. He has advised and counseled the executives who run very large corporations and organizations, helping them face tough, touchy, sensitive corporate security issues. He served his country while in the U.S. Air Force for 25 years rising through the ranks to Chief Master Sergeant, and then later as a researcher, analyst, planner, teacher, trusted advisor and author in his own right in the private sector for more than 33 years. Mr. Sullivant is a former senior program manager and chief executive of his own company, serving in high-visibility, high-tension business environments. He has held numerous key leadership positions on national councils, committees, and advisory boards. He is well respected, widely recognized as an authority in his field, and a trusted strategic advisor for changing the security landscape.
I take great delight in introducing John Sullivant. He has one of the best security minds in the business and has the unique ability to view security problems and solutions in three dimensions. I have personally known John as a colleague and friend for many years. I had the distinct privilege of working under his leadership daily for more than 4 years. His vision to create strategic initiatives to increase performance, improve competency and enhance processes from conceptual development to operational production is, in my opinion, without equal.
Through the pages of this book, John brings to bear courage and keenness to unveil security issues, so many corporate executives hesitate to address and too many security professionals fail to adequately communicate to top management in the language they understand, while significant vulnerabilities linger within the infrastructure of corporations, only to surface at the most embarrassing moments.
I know of no other author or security professional able to display the objectivity and convey the sense of urgency and body of knowledge, necessary to produce a work of this magnitude. It is full of fresh stimulating ideas and practical strategies and advice that will change the way we think, talk, teach, and practice the science of security as well as the art of security management.
Well researched and well written, this book is one of the most important contributions to the security field and risk management literature, ever envisioned. It offers an insightful overview of the dynamic problems facing the security industry that only John dares to expose, and he places the issues squarely on the agenda of security directors and chief executives to tackle head-on. Hundreds of actual case histories give creditability to his exhaustive research of verifiable evidence that supports his findings. His writing is articulate and persuasive, and I take off my hat to him for a job well done. You will not be able to put the book down once you read this page. I am honored to be his colleague and friend.
James F. Broder, CPP, CFE, FACFE
Author, Risk Analysis and the Security Survey, fourth edition
Butterworth-Heinemann, Newton, MA 2012
# Preface
## An Idea Is Born
The seeds for this book were planted in November 2013, during a lunch I had with a colleague of mine, Jim Broder,1 under the sunny skies of southern California. During lunch we discussed various topics, as we always do. Conversations with Jim are always meaningful and productive. Jim always finds the right moment in a conversation to ask, "When are you going to write your next book?" I always had an answer for him, but it never was acceptable.
A few days later, Brian Romer, a senior acquisitions editor at Butterworth-Heinemann, contacted me. I always suspected Jim put Brian up to making the call, but I never mentioned the matter to Jim—or Brian, for that matter. I submitted a proposal to Brian for review. Following a review by several anonymous reviewers to strengthen the material, I submitted a final proposal, which was entered into the publisher's system. Soon after the holidays, I had an offer from Butterworth-Heinemann. I called Jim for lunch and broke the news. Naturally, he looked surprised, congratulated me, treated me to lunch. When we departed he said, "Start writing today because you are doing another book after this one." The rest is history.
## What Could Possibly Make This Book Unequivocally Different?
Few books enable you to not only rethink the way you make decisions but also improve your performance and competency in the process. Building a Corporate Culture of Security: Strategies for Strengthening Organizational Resilience is one of those books—a milestone in both the theory and practice of, which will shock the security industry by cutting through the fog of political correctness to expose circumstances and conditions that too many chief executives and too many security managers hesitate to talk about or want others to know exist.
Within the pages of this book, I unveil the true roots of real problems in real-world situations: a consolidated reporting and analysis of strategic security deficiencies, programmatic weaknesses, and human and technology inadequacies never before available under a single cover. This work will make you look inward, to yourself and your organization, to help you navigate the often treacherous waters swirling around security management.
It offers leaders powerful ways to tackle the obstacles they face. From industry to government practices, I expose the many fallacies that surround the issues while providing a wealth of rich, practical, and relevant insights and practical strategies. Persuasively argued, I deliver a playbook for anyone in a leadership position who must act responsibly. My diverse background, depth of experience, and hands-on battle skills in the trenches deliver advice and counsel that make the difference.
Building a Corporate Culture of Security stands out among competitive works because of its immense value to the readership. I take a striking look into the business relationships and practices of many security organizations to expose the uniqueness of their vulnerabilities: their source or origin, and how they tend to fester within the bowels of organizations before being discovered and acknowledged as major problems. I call for executive management and security professionals to take responsible, reasonable actions to address these issues.
In this book I bridge two worlds: First, I take on the ambitious goal of identifying gaps between what executives perceive or believe the effectiveness of their security programs to be, versus the reality of actually measuring the performance of these security programs. Second, I present a far-reaching road map for both the student and professional to review topics that have intimidated too many security managers at all levels when approaching executive management with issues that most likely have festered within the corporation because of previous executive management decisions or management's resistance to implement. I question why corporate security resilience takes a backseat on the boardroom agendas of many chief executives, and what we need to do to today to raise the topic higher on their list of executive priorities.
As far as I know, no other author has made available such an array of industry homegrown deficiencies, weaknesses, and inadequacies in any real depth in any other single publication. And few readers will find a publication that addresses the (human) side of security I expose here. For these reasons alone, this book is a must-read. I encourage you to read it and be inspired by it.
My goal in writing Building a Corporate Culture of Security is to share the valuable insight gained from the cumulative experience of assessing, auditing, and inspecting thousands of security organizations spanning more than half a century. I do not want to waste my time and energy—or yours, for that matter—assigning blame and pointing fingers; rather, I want to put my energy to use learning from the patterns and trends of others to fix problems. This experience, knowledge, and judgment gives creditability to the theme embedded throughout this book.
This comprehensive body of work takes you on a vigorous voyage of laser-focused strategies that work and resonate with executives. The laser reaches beyond the outer boundaries of traditional protocol and lays bare an uncomfortable truth: that most security organizations have strategies, policies, protocols, and practices that are muddled and indistinguishable, along with inexperience and weak executive and security management, including a lack of leadership.
I offer the reader a treasure trove of insight, personal experience, and knowledge, and the opportunity to use your skill sets wisely to build a new trust relationship for chartering a new professional course.
Building a Corporate Culture of Security offers promise in delivering a much-needed look into corporate security practices. It poses the question, "What are you going to do about...?" Your answer to this question is key, because whatever step you take, it will directly and indirectly affect your image, brand, and reputation, as well as the success of your career path.
Through the pages of this book you will gain insight into the many challenges chief executives, security directors, and other security professionals confront everyday—many of which you may not even be aware exist. It is packed with practical and useful tips that will open the eyes of C-suite executives and security professionals to security issues that too many organizations are hesitant to tackle:
• It presents a no-nonsense look at topics that too many corporate executives hesitate to address and too many security managers fail to adequately communicate to top management in terms that fit their business frame of reference and lexicon.
• It highlights a state of affairs that has intimidated too many security managers from approaching executive management with problems that most likely have festered within the "bowels" of the corporation, sometimes for years.
• It identifies sensitive problem areas and their root causes, addresses their business consequences, and offers practical solutions in the language executive management can understand.
• It emphasizes the importance of early detection, identification, and understanding of security and security-related problems, and the expertise and knowledge base necessary to fix problems early, at the source, while they are still manageable.
• It emphasizes the importance of security planning development and implementation as a holistic discipline without losing site of its purpose to protect assets, resources, and information in the support of business goals and objectives.
• It addresses complex challenges facing today's security professionals. From current and emerging issues to industry best practices, you will find a wealth of information that will help you become a better security professional and security leader.
• It addresses the difficulty in establishing and maintaining communications between C-suite executives and the security professional.
• It points the direction to strategies that can help executives solve the many critical issues on the table—provided that corporate leadership wants to commit earnestly to advancing corporate security in a constructive manner, without hesitation or pause.
Last, Building a Corporate Culture of Security gives insight to hidden systemic failures and places those issues directly in the center of the radar screen of C-suite executives, keeping them there throughout the entire book.
These egregious revelations are not easy for me to report, but their disclosure is important work because these deficiencies, weaknesses, and inadequacies unduly influence our business philosophy, our decision-making capability, and our relationships with others—particularly executive management—and we must do everything possible to improve our lot. James E. Lukaszewski (2008, pp. 17), a prominent trusted strategic adviser, mints no words when he says "fit it now, challenge it now, change it now, stop it now. Leaders learn that most strategies fail because of timidity, hesitation and indecision." I will talk about these attributes again and again throughout the book.
It is also disappointing to report that too many executives and too many security professionals are ill prepared and ill equipped to face the many challenges they confront. Let me put this statement in perspective.
Security professionals are mostly groomed from a young age and early in their career path. They obtain degrees in security management and other disciplines, regularly attend professional seminars and other training courses, and often learn on their own.
Conversely, there are no schools for becoming a chief executive officer (CEO) or other executive leader. They obtain degrees in business administration, finance, and other disciplines. But everyday for a CEO is a new learning experience. There is no instruction manual to read, no checklist to follow and complete. While the staff tries to protect the boss and get them to change his or her mind, that is a difficult task at best. Executives need advice from people who see the world from their perspective. A staff does not always respond in this manner; they are usually busy organizing or inventing work for themselves and protecting their turf. Giving the CEO advice may be contrary to their personal agenda, priorities, or, perhaps, their succession plans (Lukaszewski, 2008, pp. 3–20). I talk more about this situation in Chapter, How to Communicate with Executives and Governing Bodies. Notwithstanding the good intentions of the staff, no one is really qualified to train a CEO in the politics of being a leader. And if this did happen, such coaching would in all probability be biased—except for that from an outside, trusted strategic advisor.
I must rebuke any colleagues who lack strategic vision, wisdom, or the skill sets to carry out their awesome responsibilities, or who fail to hold themselves accountable for their shortcomings. This is unfortunate and unacceptable in today's turbulent business world. Conversely, I would be remiss if I did not recognize those colleagues, past and present, who have performed and continue to perform in a sustained exemplary fashion in all endeavors. Do not falter in your responsibility.
## This Book Is as Important as You Want It to Be
Building a Corporate Culture of Security introduces proven security strategies that, when effectively embraced in a systematic manner, offer the potential to convert threats, hazards, risk exposure, vulnerabilities, and consequences of loss into actionable security strategies that will not only greatly improve security practices but also expressively enhance security awareness. I build security resilience in a common-sense fashion that is acceptable to executive management. The strategies I offer are practical, sensible, and proven to work in the real world, in all security organizations of all sizes.
This work is merely a stepping stone that uncovers flaws, ineffectiveness, inefficiencies, and poor management and leadership that must be overcome through strategic vision, determination, and exceptionalism. It moves past mere speculation and unfounded opinion to verifiable facts backed up by historical records, case histories and reliable human observations and judgments.
## Anyone in a Responsible Leadership Position Can Benefit from Reading This Book
Books that focus on a narrow topic often appeal to only a narrow readership. Here, I make the exception and cover the entire spectrum of security activity. I write to attract the broadest of audiences and hold their interest with straight talk and laser-focused strategies. It is a must-read for:
• Anyone responsible and accountable for security risk management, security leadership, and corporate governance and compliance.
• Executive-level security decision makers responsible for planning, approving, establishing, and maintaining security programs and security operations.
• The serious security professional who thirsts for knowledge and solutions to enhance security resilience. This quest for knowledge serves as an excellent platform for those security professionals who simply implement the common body of knowledge without understanding why some programs work and others fail. This book is extremely valuable to this group because it not only fills the knowledge void; it also takes the gained learning experience to the next level: application.
• Security professionals responsible for developing, administering, and conducting educational and training programs. This group will find this book to be extremely useful in developing new training programs or upgrades existing course instruction.
• Information technology security professionals with key security responsibilities will benefit greatly from the cyber security information presented, as well as other topics.
• Security professionals who have the skill sets and experience to manage security organizations but possess less expertise and confidence in solving complex problems but have the determination to gain insight into new ideas.
• Security professionals who are steadfast in their ways, yet flexible to adapting new approaches and techniques.
• Security professionals who may not even know they can gain any wisdom from this work, unless perhaps a gentle nudge to open its cover is given by a friend.
• Inspectors general, governing authorities, and their investigative staffs, auditors, investigators, and consultants will gain a wealth of insight into the deficiencies, weaknesses, and inadequacies that plague security organizations.
I offer a thorough and fundamental education on the art and science of performing security management and exercising security leadership. It represents years' worth of practical experience knowing how CEOs think, what matters to them, what they expect to here from you, and in the way it needs to be heard. It is a great reference tool to keep at your desk to refer to when needed.
## Features and Benefits
Building a Corporate Culture of Security
• is comprehensive and well organized. Fundamental concepts are dealt with first, followed by definition of problems and the identification of root causes; after which I delve into mitigation strategies
• is written in simple, direct language. A text reference designed with both students and professionals in mind, it presents specific information and methods for bringing security weakness and solutions forward to C-suite executives in a language they understand, enabling them to make sound, informed decisions
• is a useful textbook for university study and professional security management seminars
• provides a comprehensive understanding of the root causes of some of the most programmatic vulnerabilities that plague the security industry and how such root causes hinder moving security organizations forward
• contains a concentrated area of "hot topics" of significant importance to security practitioners, inspectors general, auditors, analysts, researchers, educators, attorneys, and C-suite executives
• emphasizes the importance of security planning, emergency preparedness planning, and problem development and implementation as a holistic discipline
• addresses the difficulty and importance in establishing and maintaining communications between the C-suite executive and the security professional, including the need and thirst for topics that security professionals often do not communicate in terms that fit the C-suite frame of reference.
## Organization and Presentation Is Important to Understand the Big Picture
Many books feature figures, illustrations, and tables that do not clearly support the text, but this is not the case here. This work is comprehensive, well organized, thoroughly thought through, and exhaustively researched, with more than 220 footnotes. More than 30 figures, and tables are strategically placed throughout the text and appendices to selected chapters to strengthen the main ideas presented. Many of these graphics make excellent PowerPoint slides for briefing C-suite executives and staff management. More than 150 actual case histories examining self-induced failures that create obstacles and stifle individual initiative are interwoven throughout the narrative or set into appendices to specific chapters to refute the cynics and give faith to those who believe in a brighter tomorrow. The narrative includes more than 20 useful and meaningful security strategies that resonate with C-suite executives. Short conclusions at the end of each chapter capture the main ideas expressed in the section. Chapter takeaways introduce each discussion.
Chapter 1, "Introduction" highlights the conditions, circumstances, and situations that repeatedly plague security organizations when performing their prime mission.
Chapter 2, "Strategies That Create Your Life Line" describes a family of integrated security strategies that, when properly designed, developed, and deployed, improve productivity and enhance security resilience. It provides systematic, pragmatic, and sensible processes for working at the highest levels and having maximum effect.
Chapter 3, "The Many Faces of Vulnerability Creep-in" describes the various forms of self-induced security deficiencies, programmatic weaknesses, and performance inadequacies that influence social behaviors and uniformed decision making.
Chapters 4, "The Evolving Threat Environment" and 5, "The Cyber Threat Landscape" survey the threat and hazard challenges facing corporations and agencies.
Chapter 6, "Establishing a Security Risk Management Program Is Crucial" describes strategies to forecast and manage challenges to reduce risk exposure. An appendix that resonates with CEOs contains a proven risk management framework and architecture platform that fits any size security organization.
Chapter 7, "Useful Metrics Give the Security Organization Standing" introduces useful and meaningful risk-based metrics that can be adapted for measuring any critical security activity. An appendix that resonates with CEOs offers a user-friendly metric framework and architecture platform strategy that resonates with chief executives.
Chapters 8, "A User-Friendly Security Assessment Model" and 11, "A User-Friendly Security Technology Model" address a family of proven strategies to help identify human, physical, and technology risk exposure; select mitigation strategies; increase competencies, performance, and productivity; and improve security resilience. Appendix A – Case Histories: Security Technology Deficiencies and Weaknesses.
Chapter 9, "Developing a Realistic and Useful Threat Estimate Profile" examines threats and hazards, vulnerabilities, and consequences; evaluates their effect on critical business operations and assets; and determines the impact of consequences and asset losses. It establishes a rank order of priorities to mitigate solutions, which helps to allocate resources and funds for those assets that need protection the most.
Chapter 10, "Establishing and Maintaining Inseparable Security Competencies" emphasizes how to measure and evaluate an organization's ability and capability to perform its prime security mission, identify and manage patterns of behavior, and recognize or forecast the results of various actions and decisions.
Chapter 12, "Preparing for Emergencies" highlights the systematic failures in effective security emergency planning that exist throughout the industry. Appendix A – Case Histories: Security Emergency Planning Fallacies.
Chapter 13, "A User-Friendly Protocol Development Model" presents the magnitude of ineffective protocol development that runs rampant throughout the industry, its affect on corporate risk exposure and liability, and how to measure and evaluate the effectiveness and efficiency of protocols. Appendix A – Case Histories: Protocols.
Chapter 14, "A Proven Organization and Management Assessment Model" describes a strategic integrated methodology to measure and evaluate the functional performance of an organization, including the effectiveness of the management and leadership elements. Appendix A - Case Histories: Management and Leadership
Chapter 15, "Building Competencies That Count: A Training Model" describes a proven, integrated strategy for a training needs analysis to help build competencies and proficiencies through the process of updating existing training programs or creating new ones.
Chapter 16, "How to Communicate with Executives and Governing Bodies" outlines the importance of speaking the language executives understand, and how to develop presentations and defend a business case that resonates with executives. It describes behaviors and attitudes of staff that may hold you back, making you less influential than you could be.
Chapter 17, "A Brighter Tomorrow: My Thoughts" ends the book with a discussion of predictable prospects for the future and anticipated challenges for the next-generation security leaders.
Running through every chapter in this book is the theme of management and leadership, performance effectiveness, competency, attitude, and knowledge of business operations other than the functional area of security activities. The shortcoming most quickly noticed by other operational managers is the failure of security professionals to gain any knowledge of corporate business or have serious interest in the actual work of the business. You need to learn what about the business matters and demonstrate by your actions and speech that you know what does matter.
Some of the topics presented here have been treated on an individual basis before by other authors, but never in the detail described in Building a Corporate Culture of Security and under a single cover. In this book, I tried not to duplicate these works (including my own previous writings) but to show a different and unique perspective to identified problems. I hope this work will help you profit from my experiences. A judgment on the extent to which I have succeeded remains the exclusive province of my readers. My critics will doubtlessly furnish me the necessary feedback to assist in revising and updating subsequence editions of this book.
John Sullivant, CFC, CSC, CHS-IV, CPP, RAM-W, Diplomate of the American Board of Forensic Engineering & Technology American College of Forensic Examiners Institute
* * *
1 James F. Broder, CFE, CPP, FACFE, is the author of Risk Analysis and the Security Survey, which is in its 4th edition (2012) and was translated and printed in Chinese for distribution in Asia in 2014. He has contributed to numerous other works: Investigation of Substance Abuse in the Workplace, Security Management, The Encyclopedia of Security Management, and the Handbook of Loss Prevention and Crime Prevention. Broder began his career as a special agent with the FBI and later joined the Foreign Service as a security advisor to the U.S. State Department. Initially employed as an instructor at the International Police Academy (Washington, D.C.), he subsequently served in Vietnam as an advisor to the South Vietnamese National Police Directorate, Counter Insurgency Division. Afterward, he worked as a special assistant to the chairman of the Special Investigations Subcommittee, U.S. House of Representatives, Washington, D.C. For many years Broder has been providing services as an independent security consultant. In 2005 I asked Jim to join me in a major security project, where we worked hand in hand for 4 years to improve the security resilience of a major U.S. utility. During this project we became staunch associates, creating a special bond of trust and confidence that continues to this day. I am honored to be dear friends.
# Acknowledgments
No book—or career, for that matter—can be successfully executed without the support of many colleagues, friends, and family: those serving as a sounding board and cheerleaders, sharing their insights and being inspirational, particularly in the toughest of times. I have been blessed to have these people by my side throughout my professional career, and family life. They are the silent heroes of this book. I thank them for their leadership, wise mentorship, and staunch support of my strategic vision of what should be rather than what is. I have served side by side with many others who inspired me through their individual careers and accomplishments. Both categories have influenced both my professional career and personal character, and throughout the years became the tapestry of all that I am and have accomplished. For those I know personally, I will always be grateful for their praise, criticism, and advice. The roll call goes far beyond the writing of this book; it spans five decades of friendship and association, working together with great professionals. For those I know only through the history of events, thanks for being a model for others, especially yours truly.
• M. F. Allington | • Richard H. Ellis | • Robert L. Mitchell
---|---|---
• James Baker | • Tommy Franks | • Oliver North
• Merton W. Baker | • Frederick P. Geier | • Robert A. Owen, Jr.
• Thomas D. Baldwin | • James W. Geist | • George S. Patton
• Benjamin N. Bellis | • Jack J. Gibson | • John W. Pauly
• James M. Bielinski | • Jack Gundrum | • Colin Powell
• Jack E. Bowerman | • Alexander Haig | • Elaine D. Rapanos
• Orval Brown | • John W. Hartman | • Gary W. Redecker
• Herbert R. Bull | • Gary R. Hichor | • Condoleezza Rice
• George W. Bush | • Raymond J. Huot | • Patrick M. Roddy
• George Campbell | • Jack Hurley | • Arthur B. Rupert
• Henry E. Carmine | • John F. Kennedy | • Norman Schwarzkopf
• Billy J. Carter | • Armin A. Krueger | • Bruce Seymour
Table Continued
• Gary Casali | • Albert J. Lilly | • Kalman D. Simon
---|---|---
• Larry Cassenti | • Jack E. Lockard | • William P. Smith
• Earnest A. Church | • Douglas MacArthur | • George B. Stackhouse III
• John J. Conley | • James Malloy | • John Sutton
• Philip J. Conley, Jr. | • Robert W. Maloy | • Ronald Thomas
• James A. Cook | • Melvin C. Manly | • Aubrey Tillman
• Steven C. Cote | • Robert C. Marcan | • Lowell H. Tillman
• Bobby R. Daniels | • John F. Marchi | • Lou Tyska
• Thomas Dexter | • Robert J. McClaurine | • John Wrona
• Joseph A. Duquette | • Wayne Messner
|
• Dwight D. Eisenhower | • Bonnie Micheiman
|
Clients and business associates have also been a valuable influence; they often shared their insights from the "trenches," I have always learned from their experiences, then translated the key ingredients into lessons that other leaders, associates, and peers need to hear. Their thoughts and viewpoints have been instrumental in guiding me in many different ways. I thank them for their efforts and enlightening debates.
Thanks to Butterworth-Heinemann for publishing this work and making me part of history. Thanks to Brian Romer and Tom Stover for believing in me, making this book happen, and introducing me to Hilary Carr, my editorial project manager. Her amazing chapter-by-chapter analysis, detailed review, and constructive comments give credit to the final book. Thanks to Hilary for her attentive coordination of the manuscript and to the Butterworth-Heinemann staff, whose editorial skills and constructive comments breathed life into the book. Thanks to Mohanapriyan Rajendran, my production manager, whose expert editorial skills and wisdom to offer penetrating commentary throughout the entire manuscript brought this book to life. Thank you for a job well done.
I thank the anonymous reviewers who provided useful suggestions not only to enhance the clarity of the original book outline but to go beyond in convincing me they had a better idea for some areas of the narrative than I first conceived. Their insight was invaluable, and I have embedded their individual footprints throughout the pages of this work. It is their product as much as it is mine.
I thank John Wiley & Sons for giving me permission to use some materials from my first book, Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving. And a very special thank to the University of Phoenix for permitting me to use of the results of their competency study.
I thank the students I have taught over the years—from Asia to Europe to Africa to the Middle East, and across America—for their intellectual insight and feedback. The seminar sessions were extremely valuable in forming my vision for this and other works. You have taught me well.
I also thank my family for their continued support and encouragement. I wish to recognize Nika and Tina, who were always asking, "How's it going, Dad?" What a great cheerleading section. I really missed Nika's expert research and editing talents on this book. A growing family and two working parents made it difficult for her to help with the research, typing, and editing of draft copies. For this book, these tasks fell on my shoulders, so any errors and omissions are mine and mine alone. Many thanks to Toula, for checking in on me from time to time: making sure I was taking my medication, following my diet, and keeping my doctor appointments.
To Pamela Aughey who provided help on two crucial levels. As, my youngest: she has been my pal, friend, and confidant and my anchor of sanity throughout this entire project. Thanks for looking in on Dad all times of the day and night to check up on my temperament, optimism, and soundness of mind. As a professional project manager implementing Cloud applications, she would unleash her encyclopedic knowledge of web intelligence to validate "unfounded" URLs, locate the original source of information and breathed new life into the reference footnotes. Without her skills I would have been forced to delete valuable statical data. While I would occasionally show my frustration in trying to imitate her technique, she always sought pleasure in continuously teaching me new skill sets. Thank you so much for your wisdom, talent, and patience in teaching this old dog new tricks.
I want to give special thanks my dear friend and colleague, James F. Broder, and to my brother, George P. Sullivant. They have been a constant source of wisdom and inspiration, as well as strengthening my performance curve. I am grateful for their council and advice.
Last, I want to recognize you, the reader. If you are chipping away at preventing or solving some of the problems mentioned herein, then the value of the information I am sharing with you is priceless, and for that I am grateful.
John Sullivant
1
# Introduction
## Abstract
This chapter encompasses a comprehensive, thought-provoking discussion focusing on the phenomena of strategic deficiencies, programmatic weaknesses, and performance inadequacies that consistently reoccur in security programs and security operations throughout the private, not-for-profit, nongovernmental, and public sector environments, despite the hard work hundreds of thousands of security professionals are doing to roll back this malignant growth. The chapter focuses on causative factors that dramatically influence security resiliency, such as the degrading capability and ability of a security organization to function, and the importance for decision makers to acknowledge and recognize the consequence of loss that these phenomena may bring to their enterprises. An earnest discussion to support the advancement of security resilience is presented.
### Keywords
Capitulation; Consequence; Deficiency; Inadequacy; Ineffectiveness; Inefficiency; Resilience; Risk exposure; Vulnerability creep-in; Weakness
When the goals of prevention, deterrence, protection, detection, assessment, response and recovery are not adequately addressed, or technology solutions sweep protocols, processes and people aside, the security organization will lack the capability to adequately perform its critical mission. When this occurs, the security organization has come face-to-face with the affects of vulnerability creep-in and must deal with the consequences: falling short of meeting performance expectations; a no confidence vote from business units that the security organization can support its business interests; and workforce physical and emotional stress.
John Sullivant
Top Takeaways
• Recognize some obstacles security professionals face when building security resilience and developing relationships
• Define the real meaning of "ability" and "capability" within the realm of security operations
• Identify some stumbling blocks that confront security professionals
• Describe the origin and theory of vulnerability creep-in
• Explain how vulnerability creep-in festers within an organization
• Identify factors causing vulnerability creep-in
## Overview
Throughout the pages of this book, I tell my story of research and experience over fifty years of insightful advice to influence decision makers and their choices. There are two dimensions to my story. The first dimension has to do with business and professional values: integrity, honesty, and trust as an individual and competency as a professional. The second dimension has to deal with management and leadership: positive attitude, team building, empowerment, coaching and training others, and influencing decision makers to embrace new standards of achievement and social behavior that lead to appropriate security and organizational resilience.
## Building Security Resilience and Developing Relationships
This book is packed with my personal experiences and research results that describe the frailty of security activity in both the private and public sectors, and the decision-making process that has shaped and continues to shape our security destiny. It focuses attention on our ability to achieve many security goals and objectives, our ability and capability to perform to expectations and standards, our craving to communicate effectively with chief executives and others, and our personal desire to improve our proficiency, competency, and productivity.
### But What Do Ability, Capability, and Preparedness Really Mean?
Two prominent sources answer this question: Presidential Policy Directive (PPD) 21, "Critical Infrastructure Security and Resilience," and Homeland Security Presidential Directive (HSPD) 8, National Preparedness Guidelines.
PPD 21 describes resilience as the ability of an organization to resist, engage in, recover from, or successfully adapt to adversity or to a change in conditions. This includes preparing for, adapting to, withstanding, and recovering rapidly from disruptions, deliberate attacks, industrial mishaps and hazards, and weather-related calamities, and the return to an acceptable level of performance in an acceptable time after being affected by an event or incident.1 Resilience is a concept that applies to individual assets, systems or networks of assets, and security activities and programs. Resiliency allows the asset, network, or system to fail gracefully rather than abruptly, or in such a way as to allow the consequences of failure to be minimized. Self-healing components, systems, and networks enhance resiliency.
HSPD-8 describes resilience as the capability of an organization to maintain its functions and structure in the face of internal and external change, and to degrade gracefully when it must. Under HSPD-8 guidance, "capability" means to accomplish the mission by performing one or more critical competencies under specified conditions and to a targeted level of performance standard or expectation. For security organizations, critical competencies include the ability and capability to deter, delay, prevent, protect, detect, assess, respond to, and recover from a security or security-related event. Chapter Establishing and Maintaining Inseparable Security Competencies relates to these capabilities. HSPD-8 further explains that capability may be delivered through any combination of properly planned, organized, equipped, and trained resources that can achieve the desired outcome. Capability also refers to features, operations, or policies that serve to benefit a protective environment and that may eliminate or reduce the need for particular protective measures without jeopardizing mission goals and objectives or performance outcome.2
I often come across chief executive officers (CEOs) and security professionals who have no clue what "ability" and "capability" really mean. Sometimes it seems that no matter how often we plead our case, or what actions we take, many strong-minded executives just do not get the message. I talk more about this topic in Chapter How to Communicate with Executives and Governing Bodies. For now, it is important to know that this lack of basic knowledge is strikingly reflected in corporate security and emergency preparedness planning, in the development of policies and protocols, in training programs, and in demonstrated performance outcomes that we have observed throughout our visits to all industry sectors. There is more on these topics in Chapters Preparing for Emergencies, A User-Friendly Protocol Development Model, and A Proven Organization and Management Assessment Model.
### How Do We Relate Security Goals to Business?
As a security professional, you must have a clear understanding of the organization's culture and management's knowledge base if you are to fully embrace the company's strategic vision for pursuing business goals and objectives. This understanding is essential if you expect to establish, implement, maintain, and effectively monitor the effects of building security resilience (Sullivant, 2007, pp. 111).
Let us briefly examine the three categories of this strategy: an understanding of the characterization of security requirements; the nurturing of business relationships both internally between upper management and organizational divisions, and externally among stockholders and governing bodies; and community entities that have an invested interest in the success of the company, its services, and security performance expectations.
Key to characterization is the ability to clearly define:
• business services and security operations,
• business continuity and emergency operations,
• the rank order of assets that are critically important to the enterprise's mission, and
• the degree of service interruption the enterprise and the security organization can sustain should an event occur before an entity can collapse.
It is essential for those individuals who have a responsibility to meet the challenges of achieving business and security goals and objectives to buy into this characterization, and to have the unconditional support of C-suite executives.3 I talk about these topics in Chapters Strategies That Create Your Life Line, The Evolving Threat Environment, The Cyber Threat Landscape, and Developing a Realistic and Useful Threat Estimate Profile.
### Can We Speak Intelligently About the Threat Environment?
Concurrent with characterizing business services and security operations, you need to begin developing strategies for building security resilience. The key to this characterization is defining the possible threats, hazards, risks, and vulnerabilities that a corporation will face, including perceived and postulated threats and hazards, adversary modes of attack, threat capabilities, the likelihood of threats occurring, the potential consequences of losing assets, and solutions to these problems in terms that are meaningful and useful to executive management (Sullivant, 2007, pp. 133). Key to a comprehensive threat analysis is to determine the security organization's ability and capability to perform its critical operational mission: deter, delay (or deny), prevent, protect, detect, assess, respond to, and recover from acknowledged threats. No other mission is more important for a security organization—it could determine the survivability of the corporation. I discuss these capabilities in Chapters Strategies That Create Your Life Line, The Evolving Threat Environment, The Cyber Threat Landscape, Establishing a Security Risk Management Program Is Crucial, Useful Metrics Give the Security Organization Standing, A User-Friendly Security Assessment Model, Developing a Realistic and Useful Threat Estimate Profile, and Establishing and Maintaining Inseparable Security Competencies.
## Watch Out for Stumbling Blocks
Let me briefly examine some significant conditions, circumstances, and situations that repeatedly plague the ability and capability of security organizations to perform as mandated or expected. First, if you are to gain acceptance and trust from executive management as a professional security expert, you must always—in all circumstances—demonstrate leadership value to the corporation. Second, you must not only understand the business and threat environments; you must also be able to achieve workable and practical solutions to security problems that mirror the corporate image, brand, and reputation that are acceptable to executive management. Last, to survive in today's business culture it takes resolve and strategic vision, which are really works in progress.
### Experience and Knowledge Base of Senior Decision-Makers Can Cause Us to Trip
Wherever I go, chief executives proudly proclaim their security organizations are doing a good job protecting the company. These CEOs and those around them are always optimistic when describing their progress and accomplishments, and they often overrate performance, whether it is people, processes, technology, or production. Some CEOs take on too many outside commitments and become detached from the staff and operational managers, losing sight of true operational conditions.
One explanation for this limited knowledge rests with those individuals who surround chief executives and routinely brief them on security matters, although they know little, if anything, about security principles, operational philosophies and techniques, or compliance or regulatory mandates. Every staff person who supports an executive has a view that is biased by his or her staff function or agenda of expectations. They are busy protecting their turf, do not freely share information, and spend an inordinate amount of time organizing for their own possible succession. Another disadvantage staff briefers face is the tendency to unjustifiably "distance" the boss from bad news, giving many executives a misguided perception about the wellness of the corporate security organization. We know that the information CEOs get from their staff is sanitized, organized, homogenized, and often made as inoffensive and generalized as possible. Information that could lead to decisions counter to the stakes of the staff is often withheld completely (Lukaszewski, 2008, pp. 23–32).
Because of some staffers' zealous behavior, too many executives believe their respective corporate security programs are effective, when in reality analyses of numerous security organizations across America tell a different story. Wherever I observe this or similar conditions, I find the fundamental principles of security are often ignored, and time-honored security management principles, as well as standards of acceptable practice, are dissuaded (Broder, 2007, pp. ix). Moreover, there is a consensus among many of my colleagues that some executives do not fully understand or appreciate what the security profession is all about, or the importance of the security mission to the overall corporate profit margin (Broder, 2007, pp. 45). A recent national survey reported that 60 percent of upper management believes that security is stronger than it actually is, whereas only 22 percent of top executives are aware of their company's true security readiness. Our experience is that these locations are some of the worst seen to date. It is astounding that almost two-thirds of the nation's CEOs say they are in the dark about the true security status of their corporation. Certainly, this finding qualifies as an agenda item both in the executive suite and in the halls of the security organization.
Yet many staffers continue to feed the boss incomplete, misguided, or erroneous information, and then believe they can work with the security director to resolve issues that may arise during or after the briefing. When dealing with the senior staff, you may not exactly be in friendly territory. The most zealous staffers may try to make you irrelevant whenever possible to place themselves in a favorable position with executives. If you are the senior security professional of your organization, you and only you should be the spokesperson for the security organization. You must do whatever it takes to work hand in hand with staff members to discuss security issues and to encourage them to step aside when it comes to briefing executive management. Nothing can be more devastating to the image, brand, and reputation of the security organization than allowing a staffer to commit your organization and its capabilities without your approval under any circumstances. You must make it clear to the staffer that you do not give him or her permission to speak on your behalf. If they insist, you must place them on notice that they own the decision, including the aftermath of any consequences that may materialize. Fortunately, experienced executives have the insight to see through this mirage. Most executives I know frown upon anyone (staffer or division head) usurping the legitimate territory of another—especially when critical security decision-making is involved. And that is how it should be.
This is a dangerous game played among some members of the senior staff and executives. Do not play it. The stakes are too high. There are no winners here, and you may just become a causality without knowing it. That means it may be time to look elsewhere for a position where your knowledge and expertise are better appreciated.
Most CEOs do not like staffers briefing them unless it pertains to nonoperational issues. Many exclude them from operations-related meetings because their vision is limited to their staff experience. Most prefer to have operational managers brief them because they are in the trenches in the real world and in real time. CEOs sometimes bypass the staff because staffers (Lukaszewski, 2008, pp. 95–97):
• have the inclination to teach their function
• constantly seem to seek approval for their behaviors and confirmation of their value
• fail to demonstrate that they understand the business or the key issues the business faces
• speak a language the boss neither needs nor cares to learn
• focus on the unimportant
• constantly take up too much time, telling executives things they already know
• have oral skills that are unfocused and fail to provide information management can act on
• whine a lot to everyone
I focus on fallacies such as these throughout the pages of this book with actual case histories, which I have strategically placed within the main narrative or appendices to make a specific point.
### What Do We Do with Misguided Executive Decision-Making?
A growing chorus of security consultants, including myself, have for years been advising chief executives and their security directors of the early telling signs that their security programs are on the brink of failure and in need of strengthening to keep pace with the changes in corporate business strategies, processes, and practices, as well as security technologies. For the most part, these warnings go unheeded, mainly because the staff believes they need to protect the boss from bad news.
As tough as I am on executives, I also have an obligation as a trusted strategic advisor to be objective and defend the worthy ones. The golden rule is that the boss is the boss for a reason. Unless what the boss is doing is immoral, illegal, unethical, completely stupid, or clearly financially irresponsible, the boss is the boss. He or she drives the bus and the bus belongs to him or her. They know where they have been and only they know where they are going. Where the boss takes the company and how the boss gets it there is clearly his or her decision to make. Enjoy the ride and contribute the best you can, or dust off your resume and hop on another bus line (Lukaszewski, 2008, pp. xxxix).
Executives react to pressures and the urgency of time. Often they just do not have the time to address the crux of the problem, as it should be studied. Against their better judgment, they find a quick "Band-Aid" to silence critics, governing bodies, and the media, hoping they can rebound with a long-term solution afterward. Unfortunately history tells us that competing demands always consume their valuable time and follow-up analysis to uncover the root causes of many problems to find a practicable and workable solution is seldom accomplished—yet another sign of vulnerability creep-in surfacing its head. Vulnerability creep-in is a topic I discuss in Chapter The Many Faces of Vulnerability Creep-in.
### Experience of Security Professionals
The problem is further compounded because too many security managers have no clue they have a problem, and most do not want to know a problem exists (Broder, 2007, p. 45). Some of these professionals regard any suggestion to improve or enhance security as a criticism of their ability to manage and lead. Guess what? They are right, and they know it! How they can hide this ineptitude and incompetency from others in high positions of responsibility is a discussion for another time. These professionals significantly contribute—mostly unknowingly—to the many aspects of vulnerability creep-in. Without a doubt, colleagues who fall into this group are an embarrassment to the security profession.
Clueless security professionals need a wake-up call to always remember that a crisis is the product of poor strategic vision and planning and a lack of foresight, coordination, direction, and creative thinking (Tarlow, 2002, pp. 24). In other words, a problem is always a management problem before it becomes an operational problem. These "weak sisters" need to place their problems within a situational context in such a way that executives are able to determine what the risks are for a specific circumstance. Perhaps then these security professionals may achieve some redeeming value in the eyes of others. Three case histories highlight the result of such incompetency:
• More often than not, many of their security programs comprise several activities strung together in a rather haphazard fashion, with little or no coherence at the highest level.
• Often they are authoritative actors who give employees little or no opportunity to use their creative-thinking skills or buy into security improvements. There is no systematic approach to what they do.
• A poor security awareness program leading to employee complacency, poor attitudes and social behavior, and low competency levels.
## Vulnerability Creep-in Just Showed Up—It Wasn't Here Before
Perhaps the greatest challenge I have confronted is those conditions, circumstances, and situations that create the social cancer that eats away at security resilience: vulnerability creep-in (Sullivant, 2007, pp. 162–164).
I can make a strong case that vulnerability creep-in is the product of many years of buildup that, with time and opportunity, spreads throughout all facets of an organization—mostly this occurs unintentionally, unknowingly, and is undetectable. I also contend that the theory of vulnerability creep-in puts forth the notion that the cumulative effects of conditions, circumstances, and situations created by management's actions or inactions affecting security matters directly influence the security organization's ability and capability to perform its critical mission. I further argue that the phenomenon of vulnerability creep-in stems from:
• lack of willpower to pursue practical strategies to correct a problem
• refusal or inability to acknowledge that a problem exists
• fallible decision-making, near-reckless planning, and mostly negligent management
• indecision, poor planning, or the poor execution of security activities
• inexperience, lack of knowledge, and disengagement from the problem-solving process
• arrogance, apathy, complacency, indifference, ineptness, insensitivity, and ignorance
• individuals charged with security decision-making failing to:
• fully grasp the essential principles of security
• recognize the benefits of security dependencies and independencies
• recognize the benefits of operational program and technology integration
• recognize false pretense and incomplete or inadequate research and information
• recognize the difficulty of obstacles that influence security decision-making
• recognize the benefits from lessons learned
• develop a realistic threat profile, asset inventory, and consequences of loss impact
• develop clear security emergency plans and exacting practices
• shun political correctness based on false promises
• demonstrate the wisdom and courage to make midcourse corrections
• management putting its head in the sand and ignoring security issues
All of the above are the cornerstone of predicable failure and should be evident to management.
Experience tells us that many of these conditions exist because of previous executive decisions vetoing recommendations to improve or enhance security, including some staff management resistance to embracing change. Vulnerability creep-in is the gateway through which security weaknesses are manifested. Just like the disease it is, it will eventually drain the energy, strength, and determination out of your people, taking its toll as frustration, disillusionment, and finally "burn out." I describe Vulnerability creep-in as a tsunami wave that never stops and obliterates everything in its wake. Singly and collectively, vulnerability creep-in has the potential to degrade an organization's ability and capability to implement strategic security planning initiatives. Jointly, these actions—if allowed to develop—puncture the very fiber of the corporate risk management framework and architecture, and will eventually lead to the weakening of security resilience whenever reasonable and prudent security measures are not implemented in an orderly, reasonably, prudent, and timely manner. As a security professional, it is your obligation to push back this malignant growth. For some, this may be a horrific challenge of epidemic portions.
## Conclusion
In wrapping up this chapter, I must defend my colleagues and the security profession. It is in some instances extremely difficult for the typical security practitioner to understand and envision the scope, depth, and significance of many of the issues I examine in this book. In fact, the many faces of vulnerability creep-in have eluded even the most seasoned security professionals at one time or another.
Few security professionals possess the insight to uncover systemic conditions from afar. One approach is to use a security consultant with broad experience and expertise in problem solving. These professionals can recognize the telling signs of these repetitive phenomena, which in my view touch the boundaries of negligent management in its greatest form, although of course unknowingly.
Vulnerability creep-in takes a very long time—sometimes years—to mature into an identifiable problem, making it remarkably difficult for an otherwise conscientious enterprise staff and security professionals to recognize the havoc it can create and its subsequent consequence on security resilience. The embryos of this cancer remain in the dark shadows of the organization, hatching undetectably until something happens that prompts the staff or outside parties to start looking for answers. Sadly, when it comes to taking responsibility for security failures, shortcomings, and other related mistakes, some executives are quick to defend corporate actions and slow to admit that improvements and enhancements are appropriate or even necessary.
I find the greatest benefit of being an independent consultant is that I am able to serve the best interests of my clients free from political pressure or influence, and to report my findings to executive management based solely on the facts as I see and understand them—not on conjecture, political correctness, or political favor. This independence of action and thought is contrary to what most governing authorities can or will report on the nature of specific security problems: Why did the problem occur? What has been done to solve the problem? What impediments were encountered in solving the problem? What additional steps need to be taken to prevent reoccurrence? My obligation is to be objective, candid, truthful, and focused, and to give useful and meaning real-time advice. I cannot do this unless I:
• pay attention to the surroundings of those I advise
• ensure executives get the information they need to better judge the present and future
• judge the capabilities organizations and the competencies of those running them
Corporations across America could be equally independent and objective (if they chose to be) in serving the best interests of their clients, customers, stockholders, employees, and the communities they serve. Left unattended, the conditions, circumstances, and situations that create vulnerability creep-in can lead us down the road to "the many faces of vulnerability creep-in." I carry through with this viewpoint in the next chapter by introducing strategies that can save the day.
* * *
1 Presidential Policy Directive 21 (PPD 21): Critical Infrastructure Security and Resilience, The Whitehouse, Washington, DC, 2013.
2 Homeland Security Presidential Directive 8 (HSPD-8): National Preparedness Guidelines, U.S. Department of Homeland Security, Washington, DC, 2011.
3 The term "C-suite" refers to the most important and influential group of individuals within a corporation who make high-stake decisions. C-suite is so named because the titles of top senior executives tend to start with the letter C. For example, CEO, chief operating officer, and chief financial officer. Other designated "chief officers" often vary within and between corporations and may be included in the C-suite group of some corporations. The term "C-suite executives" is also referred to as "C-level executives."
2
# Strategies That Create Your Life Line
## Abstract
This chapter details the elements of seven security strategies for planning the future to enable effective partnerships for implementing a successful corporate security program. It details uniform strategies, guiding principles, and best practices to interface with other business units, and provides general accountability. Further, it introduces a series of key strategies that encompass a series of interwoven "battle plans" to achieve the goal of security resilience.
### Keywords
Authority; Best practices; Compatibility; Constitutional freedom; Information sharing; Interoperability; Partnering; Public confidence; Public safety; Responsibility; Set of uniform security strategies
Strategies push an organization in a forward direction—always into tomorrow and beyond.
John Sullivant
Top Takeaways
• Discover the importance of creating a uniform set of security strategies
• Learn the guiding principles behind security strategies
• Understand the importance of communicating and interfacing with other agencies
## Overview
Strategy provides positive energy that drives business and organizations, guides leadership, and directs people to move in the same direction. Strategy pushes, pulls, and adjusts the security organization in the larger context of its operations, and always in a forward direction—into tomorrow and beyond.
Strategy shapes the future by achieving desirable goals with available resources that ensure long-term success. A useful and meaningful strategy has three parts: (1) a diagnosis that defines or explains the nature of the challenge, (2) a guiding policy for dealing with the challenge, and (3) coherent actions designed to carry out the guiding policy (Rumelt, 2001, pp. 123).
The strategies introduced in this chapter and throughout the pages of this book encompass a series of top-level "battle plans" designed, either singly or collectively, to achieve one or more goals under conditions of uncertainty. Strategies are important because recourses and funding to achieve stated security goals are usually scarce commodities.
## A Need Exists to Create a Set of Uniform Security Strategies
A corporation must recognize the need to establish and maintain a set of uniform security strategies, protocols, and best practices that foster a corporate security culture that optimizes the building of security resilience that is consistent with community service and public safety. The strategies offered in this section achieve this goal and are essential to the integrity, reliability, image, and reputation of any security organization, large or small, public or private. The listing is categorized into two parts.
### Part I: General Security Strategies
• Ensure public safety, public confidence, and services
• Encourage and facilitate partnering internally and externally
• Interface with other corporate programs
• Encourage and facilitate meaningful information sharing
• Safeguard privacy and constitutional freedoms
• Security policy
• Security authority, responsibility, and accountability
### Part II: Special Security Strategies
These strategies are addressed separately in other chapters:
• Chapter 6: Establishing a Security Risk Management Program Is Crucial
• Chapter 7: Useful Metrics Give the Security Organization Standing
• Chapter 8: A User-Friendly Security Assessment Model
• Chapter 9: Developing a Realistic and Useful Threat Estimate Profile
• Chapter 10: Establishing and Maintaining Inseparable Security Competencies
• Chapter 11: A User-Friendly Security Technology Model
• Chapter 12: Preparing for Emergencies
• Chapter 13: A User-Friendly Protocol Development Model
• Chapter 14: A Proven Security Organization and Management Assessment Model
• Chapter 15: Building Competencies That Count: A Training Model
• Chapter 16: How to Communicate with Executives and Governing Bodies
• Chapter 17: A Brighter Tomorrow: My Thoughts
## Security Strategies and Guiding Principles
Implementing security strategies is a never-ending process. It requires a unifying organization, a clear purpose, a common understanding of roles and responsibilities, accountability, and well-disciplined determination. Since a corporation must perform its business mission with diligence and dedication to the communities it serves, all employees—in particular those assigned to and who directly support the staff of the security director—must endeavor to perform at the highest competency levels. These strategies can include one or more of the strategies described in the subsequent sections.
### Ensure Public Safety, Public Confidence, and Services
Anticipate that widespread or large-scale business disruptions will undermine employee and public confidence in the corporation's ability to provide essential services. By making strategic improvements in security and emergency and business continuity planning, a corporation reduces vulnerability from physical attacks, particularly those involving catastrophic consequences. Providing corporate resources and assets with reasonable and prudent protection increases the organization's ability to withstand an attack and reduce the likelihood of sustaining significant losses and consequences. Effective security, emergency preparedness, and business continuity planning make the corporation's resources, assets, and functions more resilient, allowing for the quick restoration of critical services to minimize the detrimental effects to the corporation and the community.
Implementing and exercising a well-developed public safety and confidence strategy includes decision-making activities to:
• develop a risk management framework to guide prevention and protection programs and activities
• identify and regularly update the status of prevention and protection programs
• conduct and update security assessments and the corporate threat estimate profile
• update the security and emergency response plan and associated appendices, as required
• implement new security technologies to enhance and improve the productivity and competency of the security organization
• harden assets to the extent economically feasible to reduce risk exposure
• interdict human threats to prevent potential attacks
• respond rapidly to disruptions to limit the impact on public health and safety and corporate functions
• ensure rapid restoration and recovery from those events that are not preventable
• develop and implement a corporate-wide alert and notification system that notifies employees and others in times of emergency
This strategy is the key to shaping employee and public expectations and instilling confidence in the organization's ability to manage the aftermath of a major terrorist attack, natural disaster, industrial mishap, or weather-related calamity, as well as its capability to restore services in a timely manner.
### Encourage and Facilitate Partnering Internally and Externally
Protection of company resources and assets is a shared enterprise responsibility that entails integration, organization, and collaboration skill sets. Every business disruption is initially a corporate and community problem with potential regional, national, and international repercussions. Corporate leaders should implement preventive and protective measures and emergency response plans to foster an environment in which all employees can better carry out their security responsibilities. Organizing may involve:
• identifying and ensuring the protection of those resources and assets that are most critical in terms of production capacity, economic security, public health and safety, and public confidence. Develop a comprehensive security assessment to prioritize threats and vulnerabilities across the corporation to establish an independent and adequate security budget to facilitate the allocation of security resources, facilities, and equipment.
• providing timely warning and alert notification to ensure that assets receive timely protection against specific or intimate threats.
• ensuring the protection of other resources and assets that may become attractive targets by pursuing specific initiatives and enabling a collaborative environment in which federal, state, and local governments working with the enterprise can better protect those resources and assets. The enterprise should remain cognizant that criticality varies as a function of time, risk, and market changes. Adversaries are known to shift their focus to targets they consider less protected and more likely to yield the desired shock effect at a particular point in time.
• reviewing operations that are critical to the business unit mission to establish security priorities and ensure adequate security and redundancy for all identified critical facilities and services.
• creating and implementing comprehensive multitiered security practices that could include:
• developing essential protocols,
• organizing and coordinating security emergency preparedness and business continuity planning integral to the overall security program,
• developing security protocols for information technology, telecommunications, and cyber security, and
• developing security event–driven emergency response and recovery procedures corresponding to varying ranges and levels of threat and alert conditions.
Successful collaborating activities may involve:
• developing a process to identify and monitor external first responders entering company property
• improving the corporation's ability and commitment to work with federal, state, and local responders and service providers
• exploring potential options and incentives to encourage stakeholders to devise solutions to unique security impediments
• exploring options for incentives to increase the security budget, including government grants, if applicable
• elevating awareness and understanding of threats, vulnerabilities, and risk exposure to corporate critical assets through the promotion of corporate-wide security awareness and other security education programs
• seeking legislation to apply sabotage laws to corporate activities.
### Interface with Other Corporate Programs
Corporate security programs complement and support other major corporate programs such as safety, human resources, business continuity, capital improvement efforts, and the security engineering and design development process. A clear understanding of these relationships and interfaces is vital because there is a degree of common interest and mutually shared responsibility among these programs.
#### Safety Program
In many situations, safety and security protocols complement each other; both emphasize the protection of employees and property. The corporate safety program is an Occupational Safety and Health Administration compliance requirement that protects the workforce. In most instances, safety and security protocols can and do complement each other. For instance, security officers are often in a position to observe compliance with corporate operating protocols and safety procedures. While security officers can help management enforce certain safety compliance issues, they do not direct their entire attention on monitoring employees' behavioral patterns to prevent safety infractions. Instead, their primary focus is to protect employees from injury, death, assault, or attack resulting from the damage or destruction of assets.
Since the rise of terrorism during the 1970s, the primary focus of security has changed from physical asset protection to protection of individuals from thieves and an occasional disturbed assailant to protection from terrorist attacks. When guarding against these evolving threats, security planners and designers need to guard against installing protective materials, barriers, or systems, or establishing protocols that are in direct conflict with existing codes or standards that focus on life safety, fire prevention, and other dangerous hazards. Where a conflict exists between safety and security protocols, the protocol that provides the safest work environment should prevail until the conflict can be resolved.
#### Human Resources and Capital Investment
Human resources are the most important commodities of a corporation. Attracting, recruiting, and keeping good people are solid investment strategies that include:
• hiring practices and attracting, recruiting, and keeping motivated and dedicated people, which helps to reduce risk exposure from the insider threat
• developing corporate-wide criteria for background checks, screening, and positive identification of employees
• developing certification criteria for background screening companies
• participating in the establishment, maintenance, and evaluation of security training programs and certification standards for the security staff
• participating in the development, conduct, and evaluation of a corporate-wide employee security awareness training program
#### Business Continuity Planning
The business continuity planning effort is (or should be) an integral part of the security planning process. Much of the research and data needed for business continuity planning process are based on the framework of the security risk management program, security strategies, and security practices. For example, business continuity planning strategies embrace the same risks, threats, and hazards discovered through a security assessment as well as identified in the corporate threat estimate profile. This research and analysis does not have to be duplicated, but only applied to specific continuity goals and objectives (if they are different from existing security goals and objectives).
#### Capital Improvement Program
Security design architecture must be considered in the planning, design, engineering, and construction of new facilities, systems, networks, and functions early in the developmental phase. The security engineering and design development process must always directly support security operational performance requirements.Explore the hardening of critical facilities against risk exposure with security construction technology, crime prevention through environmental design, and state-of-the-art technology applications.
#### Use Unique Criteria Associated with Protection
Inherent program constraints and limitations must be recognized at the outset. To frame the initial focus of the protection effort, you must be prepared to acknowledge that not all assets that comprise the corporate infrastructure are uniformly "critical" in nature, particularly within a corporate-wide context. Therefore the following suggestions may be helpful in your security planning efforts:
• Priority 1: Identify and ensure the protection of those resources and assets designated as most "critical" to mission operations.
• Priority 2: Identify and ensure the protection of those assets that face a specific, imminent threat.
• Priority 3: Pursue measures and initiatives to ensure the protection of other potential business operations that may become attractive targets.
• Priority 4: Pursue the advancement of concepts, practices, and technologies that increase the security program effectiveness of all resources and assets across all business boundaries.
Such activity may include the following:
• For new or modified facilities, redesign technology-based equipment to significantly lower the costs of existing capabilities.
• Design new facilities that provide cost benefits, state-of-the-art solutions to safety, and security requirements that can benefit all business operations.
• To the extent feasible and practical, use technology that results in better efficiencies such as monitoring, surveillance, and assessment, and the enhanced use of scarce resources.
• Search out technology pilot programs used to solve security problems that have passed the research and demonstration stage, such as the Constellation Automated Critical Asset Management System of the City of Los Angeles, the South Florida Coastal Surveillance Prototype Test Bed, and the National Capital Region Rail Security Corridor Pilot Project in Washington, DC.
#### Exploring Methods to Authenticate and Verify Personnel Identity
The security director should create more effective and positive means of identifying people requiring access to critical assets and functions, including establishing ways and means to control access to and egress from the scene of an emergency, to maintain the integrity of the site boundary, and to protect first responders. This includes a uniform and rapid means of identifying and monitoring first responders reporting to the site of an emergency.
#### Coordinating Interoperability Standards to Ensure Compatibility of Communication Systems
To the extent practical, the security director should strive to create standard communication protocols to enable secure and assured interoperable communications among the various company C3 which stands for Command, Control and Communications centers, security operations centers, and community first responders. Standardized communication systems enhance the security response and promote efficient planning and training at all levels. The ability to establish and maintain efficient communications between security and community first responders is essential to ensure the effectiveness of the response and recovery processes.
#### Security Technologies and Expertise
Science and technology are key elements in protecting resources and assets. A corporation should fully leverage its technological advantages to improve the monitoring of assets and functions to reduce labor-intensive monitoring and surveillance activity. Pooling corporate scientists, engineers, and security professionals can increase the overall understanding of the threat and risk exposure. It also fosters collaboration between the various disciplines and enables the corporation to capitalize on emerging technologies and facilitate security and emergency preparedness planning, decision-making, and resource allocation. This includes, but is not necessarily limited to, coordinating interoperability standards to ensure performance compatibility during both routine day-to-day operations and emergency situations, and implementing best practices.
### Encourage and Facilitate Meaningful Information Sharing
A corporation that participates in the community information sharing process tends to formulate better security policies and protocols, and make informed security investments and decisions in an accurate and timely manner. This includes:
• understanding effective information sharing processes among security partners
• providing protocols for real-time threat and incident reporting, alerting, and warning
• establishing effective coordinating structures among security partners
• enhancing coordination with the local, state, and federal communities
• building public awareness
• analyzing, warehousing, and sharing security assessment data in a secure manner that is consistent with relevant legal requirements and information protection responsibilities
Accordingly, the security director adopts measures to identify and evaluate potential impediments or disincentives to security-related information sharing among business units and between the entity and federal, state, and local governments. This allows for the formulation of appropriate strategies to overcome these barriers and to establish and maintain reliable, secure, and efficient communications and information systems to support meaningful information sharing. This may involve:
• defining security-related information-sharing needs and establishing effective, efficient information-sharing processes to ensure that appropriate users can access needed information in a timely manner
• expanding voluntary security-related information sharing among business units, as well as between federal, state, and local governments and industry
• facilitating the sharing of industry best security practices and processes
• improving processes for the collection and analysis of threat information needed for strategic security planning, prioritization, resource allocation, and budgeting
• improving the company alert advisory system and identifying appropriate actions that correspond to the various threat levels
• ensuring that the public affairs office develops a comprehensive communications plan for notifying the news media and the public of emergency conditions and situations
### Safeguard Privacy and Constitutional Freedoms
Most corporations are a tapestry of diverse races, ethnicities, cultures, religions, and political ideologies. This pluralism and a company's ability to accommodate diversity significantly contribute to its strength as an enterprise. This diversity, however, can also be an inherent vulnerability by possibly exposing employees to propaganda and other influences.
Notwithstanding achieving security, a corporation must accept some level of risk as a persisting condition in the daily lives of the workforce. The challenge is finding the path that enables the corporation to mitigate risk and protect resources, assets, and functions while respecting privacy and the freedom of expression, and upholding federal and state labor laws. The security director collaborates with the director of human resources and other staff agencies, as appropriate, to develop and implement this strategy.
### Security Policy
A corporate security policy commits the organization to protecting its employees and assets from acts that would:
• undermine the corporation's capacity to deliver minimum essential water and power services to the communities it serves,
• undermine the public's morale and confidence in the corporation's capability to deliver services, and
• impair the corporation's ability to ensure the public's health and safety with respect to products and services provided.
To achieve these goals, it is necessary to develop, monitor, and maintain threat-level information and to combine the results of threat analysis information with the elements of security planning, emergency planning, and business continuity planning into a cohesive program in which all elements are compatible and interoperability is achieved across the company.
### Security Authority, Responsibility, and Accountability
All enterprise business units have an important role to play in protecting resources and assets. This necessarily encompasses the mechanisms required to coordinate and integrate security policies, planning, resource management, and performance measurement across the entire spectrum of the company. It includes a coordinated and integrated process for security program implementation that:
• supports prioritization of security programs and activities
• helps to align the resources of the corporate budget to the protection mission
• enables tracking and accountability for the expenditure of allocated security funds
• takes into account federal, state, and local government considerations related to security planning, programming, and budgeting
• draws on expertise across organizational boundaries
• shares expertise and advances in implementing security best practices
• recognizes the need to build a business case based on business and security values
The key component of this strategy is the delineation of security roles, responsibilities, and accountability against established performance expectations.
## Conclusion
A large capital investment is required to acquire and hold onto human resources. Assets are expensive to acquire, install, and maintain, and intellectual property and other confidential and sensitive information is vital to corporate operations. In addition, business operations are dependent on the integrated systems and processes that make up the infrastructure; these can potentially disrupt or shut down operations, turning into unnecessary costs, delays, backlogs, and, in some instances, loss of revenue or disgruntled employees. Finally, the laws and best practices of the industry require the protection of resources, assets, facilities, systems, networks, functions, and information so that if they are compromised, disrupted, injured, damaged, or destroyed, there is the potential for criminal consequences and civil liability.
3
# The Many Faces of Vulnerability Creep-in
## Abstract
This chapter unveils the many faces of vulnerability creep-in, a cancer that hibernates within the bowels of organizations, sometimes for years. The discussion emphasizes that the malignant growth is not limited to security hardware or software technology deficiencies but also spans the entire management culture, stifling creativity, initiative, modernization, and performance, as well as preventing security planning and security enhancements from taking hold. Actual case histories, supplemented by an analysis summary statement of major causes of the observations noted, are provided.
### Keywords
Arrogance; Commitment; Comprehensive; Consequence; Decision; Deficiency; Inadequacy; Leadership; Vulnerability; Weakness
Vulnerability creep-in simply does not happen. It is created! It is a cancer of inexperience, a weak management knowledge base and the inability to grasp the basic but crucial principles and philosophies of security. This cancer hibernates in the bowels of organizations—sometimes for years. It stays dormant and undetected in the darkest corners of a corporation until a major disruptive event occurs.
John Sullivant
Top Takeaways
• Understand management decisions and other actions that influence security resilience
• Understand the implications of weak management and leadership
• Discover the impact deficiencies and weaknesses have on security operations
• Uncover performance weaknesses that influence security abilities and capabilities
• Learn how human and technology performance inadequacies degrade security operations
## Overview
Vulnerability creep-in should never happen, but it does, and it appears throughout the industry with overwhelming regularity. This cancer not only encompasses security hardware and software technology deficiencies but also canvases a management culture that stifles creativity, initiative, modernization, and competency.
## Vulnerability Creep-in Eludes Many Security Professionals
Vulnerability creep-in comes in various disguises and forms. Its many faces shock the very fiber of security practices and make it extremely difficult for many security professionals to recognize and detect its presence, even under the healthiest work relationships with executives and staff. It also defines where security sits on the executive management agenda.
Vulnerability creep-in presents a "triple threat" to security resilience. This axis comprises strategic security deficiencies, programmatic security weaknesses, and security competency inadequacies, as highlighted in Fig. 3.1. The listings represent the most frequently observed frustration-inducing behaviors I have seen in all my years of consulting, staff, and operating responsibilities. I find no industry sector or enterprise to be immune to this phenomenon.
At the very least, vulnerability creep-in holds the promise of damaging an organization's image, brand, and reputation. At the far end of the spectrum, vulnerability creep-in represents wave after wave of degradation of security resilience, and it has had that affect on many security organizations.
The grouping of an activity under a particular category is subjective, and it can easily qualify for placement in any one of the three main categories—as a strategic security deficiency, a programmatic security weakness, or a security competency inadequacy—or appear in more than one category depending on the conditions and circumstances during discovery. There is no doubt that, after reviewing the lists and assessing your own unique organizational business relationships with other business units, you may consider placing selected topics under a different category.
Figure 3.1 Categories of vulnerability creep-in and an executive summary description of less-than-acceptable competencies.
While conventional problem-solving approaches mostly focus on external sources to identify problems, I suggest that in many instances we should turn our focus inward to address crucial factors associated with "insider threat" probabilities. In chapter The Cyber Threat Landscape, I talk about human fallacies. Fallacies may include one or more of the following:
• Processes, protocols, and security practices
• Responsible managers and decision makers who guide, direct, and control the destiny of corporate security
• Individuals who lack the ability to fully grasp the essential principles of security
• Leadership that constantly disengages from the problem-solving process
• Gatekeepers who are bottlenecks to progress and who either delay or block security improvement initiatives or prevent access to chief executives; these gatekeepers often are ignored or discarded as root causes
• Disgruntled, bored, or unhappy employees, and those with a misguided ego, who want to gain attention and demonstrate their capacity to do harm
In the next three major sections I summarize some of the most prominent case histories that directly create tension, uneasiness, and distrust within many security organizations. I have witnessed and reported on these observations throughout my career, counseled executive management on the affect these issues have on security operations and performance, and lectured on these topics at various forums. These topics include:
• strategic security deficiencies, which top the list as the most frequently occurring,
• programmatic security weaknesses, which rank second place, and
• human and technology inadequacies, which place third in the ratings.
## Strategic Security Deficiencies Top the List
Strategic security deficiencies consist mostly of senior management decisions that demonstrate a narrow strategic vision and the exercise of leadership that is not clearly understood by others. They occur more frequently throughout the industry than do the other two categories, which I address shortly. These deficiencies have the potential to degrade security programs and often place enterprises in jeopardy with regulators, governing bodies, stakeholders, the community, or even the courts. Some case histories that fall within this category are described in what follows.
### Some Executives Have No Clue What Security Is About
At several locations, chief executive officers had the perception that the corporate security program was effective, but in reality, these organizations were some of the worst ever seen (lack of understanding or disinterest). At many locations, a number of those in upper management had repeatedly opposed measures to improve various aspects of security initiatives (inexperience or indifference, arrogance). At yet other locations, systemic problems existed for years without executive management intervening to correct the situation. Failure was predictable—and should have been expected by management (poor leadership and management interest, disengagement from the staff and operating managers).
Some enterprises did not have in charge of security anyone with the competencies to bring all elements of a corporate-wide security program to bear. There were no clear lines establishing who was in charge of security (weak leadership, poor management, acceptable business culture, lack of security principles and practices).
The challenge here is to educate C-suite executives, their senior staff, and senior security professionals on the fundamental mission, purpose, and benefit a competent security organization has to offer, reinforcing basic principles of security management and leadership, as well as advanced management theories and best practices.
### Executives Struggle to Grasp Essential Principles of Security Planning
The lack of executive leadership and weak management coupled with too many instances of poor competencies and judgments was sufficient cause to examine some organizations further. Areas preliminarily uncovered included integrity, ethics, subpar oversight of activities and the staff, and poor planning and capability to achieve expectations of what a professional security organization should look like and be (poor management skill sets). Little evidence was found to suggest that the current strategies adopted by several enterprises had or would lead to fundamental improvements to security (poor management oversight, analytical skills).
### Executives Exhibit Little Knowledge of the "Duty to Care Principle"
Across the country, a strong defense team can argue that many enterprises exhibit a disregard for the "duty to care principle."1
Federal and state courts, including the U.S. Supreme Court, hold to this principle. These rulings hold organizations responsible and legally accountable for failing to take measures against acts or omissions that could cause harm, injury, or death within the workplace, thereby failing to provide a safe and secure work environment for employees. The principle not only applies to public and private enterprises alike, but also to individuals such as lawyers, doctors, accountants, police, and engineers, as well as to binding agreements between contracting parties.
The standards of acceptable performance issued by the courts are measured by specific actions taken or not taken by business owners or those in charge of reducing risk exposure from foreseeable threats and hazards. The courts have ruled that the degree of care taken must be reasonable and prudent. Some unacceptable security practices declared by the courts include:
• not enforcing published safety and security guidelines, standards and other directives in a uniform or consistent manner
• providing a false sense of safety and security by posting signs containing false, erroneous, or misleading information
• installing security equipment that provides a sense of a safe and secure environment but is actually an inert component or not in a serviceable condition
• failure to maintain installed security systems to their design performance standard
• not using security equipment as it was intended
Of importance to chief executive officers is being given notice of a security condition by a consultant, auditor, or inspector and failing to take corrective action—until someone was harmed, injured, or killed, or until an employee lodges a complaint against the company; this has often been the basis for many lawsuits. Equally important, courts are increasingly holding corporate officers and even department managers personally liable for neglecting to take a proactive stance in developing and implementing reasonable and prudent measures to protect the workforce. The following paragraphs describe some case histories involving the duty to care principle.
In at least five Fortune 500 corporations, independent and separate consultants completed three to five security assessments and audits within a 5-year period. None of the recommendations received serious consideration by executive management, even though several recommendations from each security consultant were similar in nature (arrogance, indifference, not important to management).
At several locations, corrective actions were not based on complementing security operation–sensitive reporting timelines or on feedback from security practitioners and others having specialized expertise in sound research and security engineering principles (arrogance).
Five years after deferring the implementation of over 300 recommendations presented by 3 separate security consultant firms, one particular enterprise still had no timetable to even start planning and developing a sound security program (indifference, lack of understanding of security needs).
Many enterprises failed to move swiftly to correct previous security deficiencies. Several did not act in earnest until external political pressure was exerted (not important to management).
### The Disruptive Influence of Inexperienced Executives in Security Activities
The inexperience of executive management and many senior staff members in security matters fosters a narrow and perhaps misguided application of security principles, techniques, methods, protocols, and technology. This in turn creates a corporate culture that builds barriers to carrying out effective security strategies. In my view, this situation implants unintentional (and undetectable) gaps in security programs. Here are some case histories to support this perspective.
Bottlenecks created through bureaucratic inefficiencies, insufficient follow-up, and weak management caused delays, slowed things down, and prevented the completion of actions that could have been done in a reasonable time, but were not (poor management, inexperience, indifference).
At some locations, most corrective actions were only symbolic in nature and did not contribute to enhancing security resilience. Other actions were implemented only because of external political pressure from city officials and community groups, and this distracted the enterprise from pursuing practical and workable security solutions (weak management and leadership).
Failure resulting from underestimating the range and difficulty of obstacles that were encountered suggested a lack of strategic vision and expertise to manage security activities at many locations (inexperience, poor planning).
### Many Security Professionals Lead from Behind
At many locations, a clear trend of ineffectiveness, inefficiency, and lack of security leadership became detrimental to the security organization. Many security strategies lack purpose and consistency, and were doomed to fail from the start, which should have been obvious (inexperience, lack of professional development, weak visionary skills).
### Weak Security Managers Must Enhance Skill Sets to Match the Business Environment
I have always had a concern for security directors and security managers who lack the basic skill sets to influence, coach, and teach decision makers and staff, and those who are not fully delegated the authority or given the resources and funding to carry out the corporate security charter. In several instances the security organization's inability to complete actions because of dependent internal departments was a factor contributing to delays in completing many initiatives. In many enterprises a strong, clear, and distinct security policy outlining business unit responsibilities, coupled with executive management support, could have prevented all, if not most, of the findings we reported.
## Programmatic Security Weaknesses Rank Second Place
Programmatic security weaknesses reflect weak leadership, incomplete or poor planning with no vision for program or system integration, and poor decision-making based on fallible, incomplete, or outdated information. Programmatic security weaknesses rank number two as the most frequently reoccurring observations. These weaknesses:
• affect the ability and capability of a security organization to perform its critical operational tasks—deterrence, delay, prevention, protection, detection, assessment, response, and recovery—and contribute to the weakening of security resilience more than any other security activity
• may place entire enterprises in jeopardy with regulators, governing bodies, and the courts or result in stakeholders loosing confidence in an enterprise's ability to provide a safe and secure environment and protect their capital investment
• are often caused by actions that are outside the reach of the security director to resolve without external support and cooperation
### Security Units are Vulnerable to Poor Leadership and Management
I was astonished that so many security organizations lack the ability and capability to fulfill their charter. In general, too many corporate security organizations are a mess, and leadership does not show much resolve to fix things. One particular organization was "in crisis."
• There were numerous management deficiencies in employee discipline, and the simplicity of directions given required improvement.
• Too often, the organization transitioned back and forth between policy fads and the excessive and unnecessary pressuring influence of the "political climate."
### Security Creditability and Competency Hangs in the Balance
Those enterprises without a security leadership element assigned responsibility, authority, and accountability for planning, coordinating, developing, and implementing an integrated security program could not demonstrate the ability and capability to:
• exhibit strong security leadership
• perform adequate security assessments and threat and vulnerability analyses
• design, develop, coordinate, and implement next-generation security strategies
• identify and correct ineffective security practices
• develop and implement workable and practical security emergency response plans
• effectively measure and evaluate security performance
Moreover, these organizations have non-security-type personnel planning, developing, and implementing security programs, including writing security plans, policies, and protocols that do not meet acceptable industry standards. Many of the security missions had become muddled over the years and suffered from poor leadership, a lack of accountability, and an inefficient organizational structure. Strong executive leadership to reestablish credibility could have solved many security problems, both actual and perceived, at these locations.
### High Turnover Rates Take a Toll on Historical Perspective
Change in management or high employee turnover has reached critical mass for many security organizations. It is difficult for these enterprises to hold onto good people for an extended time, and at times it is equally difficult to rid the ranks of subpar performers. With a rush of new blood into an organization, several trends begin to appear.
• One is the gradual loss of corporate memory and experience, or the value of lessons learned.
• Things get lost in the shuffle or forgotten.
• New blood is eager to establish a "stake" in the organization and the focus is on a personal agenda, discarding protocols, processes, and practices that have served organizations well.
The restructuring of several enterprises involving changes in the business culture and its goals, or changes in processes and protocols, may create anxiety, tension, and even mistrust among and between managers and the workforce, and, in particular, between the security organization and other departments.
At several sites, collaborating with the security organization early in the decision-making process would have given the security staff time to evaluate the impact of decisions on preserving the integrity of corporate security, and to design security strategies and solutions to accommodate changes in a timely and orderly manner without jeopardizing overall corporate security.
### Ineffective Planning and Development Plagues Security Organizations
At many locations, improvements had not created the anticipated results, and no midcourse corrective actions were introduced in the hope of finding something else that might work (poor management and planning). In addition, security planning, coordination, development, and implementation were weak or lacking across a wide spectrum of security activity (poor planning).
The security planning effort should be led by a senior security professional who works in concert with operational personnel and those in other disciplines. For large corporations, the enterprise security director should take advantage of the skill sets a qualified security consultant brings to the table. This was not the case in many security organizations. To correct this situation, a security-conscious planning strategy is indispensable to interfacing all the aspects of security enhancements in an orchestrated and deliberate manner. This could have best been achieved if security planning involved:
• the act of viewing or envisioning the physical arrangements and functional interfaces of resources, activities, processes, facility space planning, and security design planning into an integrated whole to support security operations;
• a balanced mix of physical, electronics, information, cyber security, personnel, communications, operations and security principles that encompass prevention and protection techniques, as well as detection, assessment, response, and recovery capabilities; and
• identifying and determining the applicable standards of performance, regulatory mandates, and other obligations enterprises voluntarily subscribe to or are obligated to subscribe to.
These cumulative operational benchmarks are what build the platform on which security design planning2 begins.
### Security Planning, Policies, and Practices Lack Strategic Vision, Balance, and Purpose
At a few locations, some managers spend more time defending the status quo than explaining processes and their rationale; or they take more time to answer questions from or collect data for the investigative team to review, and less time implementing what may be valid recommendations for improving their operations (Broder, 2007, pp. 251).
Recommendations implemented in a piecemeal or indiscriminate fashion rather than in a systematic and logical manner lead to the continuing deterioration of program effectiveness, produce significant cost overruns from original project estimates, and eventually become counterproductive to achieving security strategies, goals, and objectives (Sullivant, 2007, pp. 206).
### Protocols are Poorly Constructed, Poorly Written, and Difficult to Understand
In this category, I most often see obsolete and cumbersome protocols and incomplete and ineffective security plans—particularly security emergency plans—and virtually no formal security event-driven response and recovery procedures (poor management and communications skills). At most locations, security plans and security emergency response plans lack specified actions to be taken (poor management & planning skills).
### Security Compensatory Measures Are Not Widely Used
I am convinced that few industry leaders have no firm grasp of the security compensatory measures concept or the options available to implement them. An experienced security director, however, does (or should) possess this knowledge and knows (or should know) instinctively how to help the corporation benefit from the use of such actions. Whenever security is significantly degraded, corrective actions should be implemented to reduce the vulnerability gap created by such loss.
For example, if automated access controls at a particular entry point malfunction, placing a guard or area representative at the entry checkpoint to verify the identity of persons before they enter the area is a comparable temporary compensatory measure until the system can be repaired. Another alternative may be closing the portal pending equipment repairs and diverting the population to another entry point.
Another example is providing portable emergency lighting systems for high-security areas to compensate for the loss of perimeter or area lighting, should standard backup power supplies or emergency generators not be available. Most sites visited did not have a compensatory measures program (inexperience).
### Security Design, Engineering, and Technology Application Need Improvement
In several instances, in-house engineering departments made unilateral design decisions without the input or the approval of security organizations. After reviewing schematics and other engineering data, and running several functional tests on particular security systems, I am convinced that design teams could have produced reliable, quality designs to support operational needs had design groups "teamed" their way into the final decision-making process, rather than arbitrarily make unilateral design decisions of their own accord. I was shocked to discover the number of security managers who admitted they were not given the opportunity to participate in the design review process or sign off on the design, or who had not seen the design before construction began. In most instances I find that design development and the installation of security systems begin without the benefit of defined formal security system parameters, performance standards, training, and logistics and maintenance considerations (poor management skills, inexperience).
At several locations, the practice of installing security systems in piecemeal fashion, with system integration scheduled to be completed in future years as a retrofit project, was the norm. This strategy—approved by executive management—did not consider the impact this installation approach would have on the ability and capability of the security organization to perform its critical mission. The unilateral decision by the engineering department (without the approval of the security director) placed affected enterprises and security organizations in great jeopardy, ignoring the primary reason for the urgency behind the security upgrades (poor management and planning skills).
### Corporate Management Culture Influences Security Practices and Competencies
Many diversified enterprises practice a management approach in which each division, directorate, or department is a separate operating entity within the corporation, with significant autonomy to conduct its business affairs, including security, as it sees fit. This management approach is sometimes referred to as the "stovepipe mentality" or "silo management" approach.
These organizations are hierarchical in nature and operate in "silos." They seem reluctant to report problems up the chain of command, are skittish about putting security concerns in writing, and have a general bureaucratic resistance to change (corporate business culture).
• Decisions must percolate up the chain of command. These are discussed and analyzed at varying levels of management, and then a decision is handed down. The process is time-consuming and often cumbersome, with little direct interaction between the "doer," the planner, and the decision maker(s).
• Under this management model, security is the inherent responsibility of selected staff members—none of whom are security professionals or have any background in the application of security principles, techniques, methods, or technology. In almost all cases executive management has even less experience and expertise to pass judgment on the staff's security work—a recipe for predictable failure.
• Typically, these corporations have no formal corporate security organization in place with the proper authority, responsibility, and accountability to execute leadership, direction, and oversight of security programs or to provide guidance on security matters to respective business units. Under this management approach:
• The significance of threats are usually minimized or underestimated because there is no corporate threat profile or corporate-wide priorities to establish, develop, and implement security strategies or to prioritize the allocation of resources and funding to protect the most critical assets. Management actions to implement protective measures often are based on incomplete or erroneous information or misguided analysis.
• Security and security-related roles and responsibilities are often blurred and may be duplicated or most likely overlooked, creating cascading ineffective or inappropriate results, including contradictory, conflicting, and confusing guidance.
• Many enterprises require the respective business units to pay directly for security services provided. This approach is often doomed to fail—and this should have been obvious to executive management from the start.
## Human and Technology Inadequacies Rate Third Place
Human and technology inadequacies rank third in the most frequently noted observations. These inadequacies can taint a corporation's brand, stain its image, blemish its reputation, and cause stakeholders to lose confidence in the entity's commitment to excellence. While these inadequacies occur less frequently than strategic deficiencies and programmatic weakness, they do represent the "public face" of a security organization and a corporation. They have a much larger influence in protecting image, brand, and reputation than strategic deficiencies and programmatic weaknesses because they directly influence the overall standing of corporate security programs and relate to operational matters that are easily visible to the public and the news media.
The following sections describe case histories that highlight some of the most prominent inadequacies I have observed.
### Security Force and Other Personnel Shortcomings
In several instances, responsible individuals in the security organization ignore or even cover up security breaches and other inappropriate behavior simply to reduce the need to report incidents and prepare reports (ethical and integrity issues). Office checks completed after hours are either ineffective or are not being performed, even though they were reported as accomplished (poor management oversight).
Several guard service agreements are written in broad general terms and failed to address essential elements of the services to be performed (weak contract administrative and management skills). In addition, many contract guards fail to meet stated minimum employment requirements, including qualifications, education, and competencies to perform to expectations (weak management and leadership skills).
### Security Technologies and Applications Hinder Security Competency
Disparate security systems exist throughout the industry in all business sectors, making detection, assessment, and response difficult, and in many locations making it impossible to accomplish this in a timely manner (budget constraints, poor technical management oversight). At some locations CCTV cameras are not synchronized for call-up and recording when sensors and access control devices are activated (ineffective technical management oversight, poor design).
### Security Design Development Practices are Immature
The goal of the security design phase is to develop sufficient technical and engineering data to demonstrate that the physical features, infrastructure, electronic security systems, and other support elements integral to the security design meet the established system design and performance specifications. These elements include human-factors engineering, technical interfaces, interoperability, supportability, dependability, control room and console layout, and other crucial system features and capabilities such as system integrity and survivability.
The prime objective of security design planning is to ensure that it supports time-sensitive and time-dependent security operational requirements. Security matters are urgent when time is the driving force or is used as one, when the loss of time has real consequences, or when time may be running out. For instance, it is important for senior management and engineering staff to acknowledge that the display, announcement and assessment of alarms create a nonnegotiable, distinct, time-sensitive demand window (3–5 s) for a system operator to react to the validity and severity of an event or transaction that triggers an alarm. This time demand calls for the finite integration of design deployment and technology application that does not hinder, hamper, or slow the capability of a security organization to detect, assess, and respond to security events. Few security systems have this performance capability (poor design & design management).
A qualified engineer with previous experience in developing security designs should lead the design-planning phase. This engineer must work under the guidance and oversight of a security professional and must interact with the security staff.
### Equipment and Facility Shortfalls Degrade Security Capability
Many older security facilities were designed using some combination of volunteer security design criteria, except for compliance with the National Electrical Code and other municipal codes. Most remaining design criteria are based on design features adopted from similar facilities or offered by the security organization and accepted by the design engineer. Newly constructed or recently modified facilities show evidence that designs incorporated information gleaned from open-source general threat statements and appropriate industry facility design criteria.
## Conclusions
Vulnerability creep-in is a cancer of inexperience, a weak management knowledge base, and the inability to grasp the basic but crucial principles of security. It exists for many and varied reasons but mostly results from the cumulative effects of the festering consequences of management's actions:
• Inability to recognize the diversified threat, vulnerability, and the consequences of loss
• Inability to grasp essential principles or prevention and protection concepts, as well as time-sensitive and time-dependent security conditions
• Fallible decision-making and poor or near-reckless security planning
• Exercise of weak or poor security leadership or negligent management
• "Head-in-the-sand syndrome" whereby management ignores security issues or fails to act on security matters
Many factors affect the semblance of vulnerability creep-in: apathy, arrogance, conceit, complacency, indifference, insensitivity, and ignorance, among others. The phenomena of strategic deficiencies occur more frequently throughout the industry than do programmatic weaknesses and performance inadequacies. A major strategic deficiency can degrade a security program and place an enterprise in serious jeopardy with regulators, governing bodies, stakeholders, the community, or even the courts.
Programmatic weaknesses, while equally important, rank as the second most frequently reoccurring observations. Programmatic weaknesses affect the ability and capability of a security organization to perform its critical operational tasks (deterrence, delay, prevention, protection, detection, assessment, response and recovery) and, more than any other security activity, contribute to the weakening of security resilience.
Competency inadequacies rank third among the most frequently noted observations. These inadequacies can taint a corporation's brand, stain its image, blemish its reputation, and cause stakeholders to lose confidence in the entity's commitment to excellence. While these inadequacies occur less frequently than strategic deficiencies and programmatic weakness, they do represent the "public face" of a security organization and a corporation. In many instances, these inadequacies have a much greater impact on protecting image, brand, and reputation than strategic deficiencies and programmatic weakness because they directly influence the overall effectiveness of corporate security programs. Operational matters are easily visible to the public and the news media.
A security-conscious planning strategy is indispensable to interfacing all the aspects of security enhancements in a deliberate manner. The approach involves security planning, facility space planning, and security design planning. Security planning and security design planning are often inappropriately used as synonyms, when in fact each represents different disciplines and education, significant variances in competencies and different responsibilities, as well as authority and accountability.
The challenge for executive management is to remove the barriers and obstacles that impair the modernization of security programs and commit to advancing corporate security, with the aim of providing a more safe and secure work environment for employees, visitors, and the general community.
* * *
1 Because each of the 50 U.S. states is a separate sovereign free to develop its own tort law under the Tenth Amendment, there are several tests in each State for finding a duty of care in United States tort law. Several tests of agreeing or disagreeing with lower court rulings may also be found in U.S. Supreme Court rulings. Employees who have been assaulted on company grounds bring a large amount of lawsuits upon a corporation claiming insufficient or no security was available to provide for a safe and secure environment. Other leading tort actions include malfunctioning security technology, poor lighting, signage, inconsistent security practices and enforcement.
2 Security planning and security design planning are often inappropriately used as synonyms when in fact each represents different disciplines and education, significant variances in competencies and different responsibilities, as well as authority and accountability.
4
# The Evolving Threat Environment
## Abstract
This chapter addresses the dynamics of the changing security landscape, driven by the rising business risk exposure of transnational organized crime, cyber crimes, piracy, and the emerging terrorist capabilities, resulting in adversaries changing tactics and target selection. The crime and terrorist waves are happening on a global basis, as well as across the landscape of our society. These evolving threats have taken many seasoned security professionals and chief executive officers to task in finding practicable and workable solutions to protect the general welfare of corporations and their respective image, brand, reputation, and business interests. Actual case histories are offered throughout the narrative to emphasize the degree of importance these actions have on the threat landscape.
### Keywords
Assassination; Biological; Chemical; Counterproductive; Devastate; Intelligence; Prevention; Protection; Radicalization; Smuggling; Target; Trafficking
Because variables differ from one asset to another, and from one location to another, and from one business interest to another, and from time to time, no one set of security solutions can apply to the protection of all assets.
John Sullivant
Top Takeaways
• Advance your knowledge of the global, national, and local threat environments
• Understand the complexities of an all-hazards threat environment
• Become familiar with threats of significant concern to both the United States and U.S. corporations and other entities
• Distinguish between international, domestic, homegrown, and insider threats
• Recognize the merging threats from transnational criminal organizations and insider threat
• Become familiar with significant modes of attack
## Overview
### Understanding the Business Environment and Its Challenges
In today's risk-averse business world, the dynamics of evolving threats to critical infrastructure and key assets have proven to be daunting. Since businesses have unique characteristics and requirements, they also have unique assets that contribute to business operations. In high-threat environments, these threats are fluid and can worsen rapidly (Sullivant, 2007 pp. 55–84).
### Understanding the Threat Environment and Its Challenges
In the post–Cold War environment, terrorist activity has moved away from government targets and has placed its sights on commercial targets. Business infrastructures and assets are much softer targets than government facilities, and adversaries see them as attractive targets that require little investment but produce massive destructive affects. The economic and psychological impact of destroying the civilian elements of the national infrastructure is more devastating than damaging a single government or military facility. Large numbers of people and business establishments become the victims of a single attack, and cascading collateral damage can be significant (Sullivant, 2007 pp. 19).
Most recently, activists and terrorists minded individuals and groups have selected even softer targets such as elementary schools, college campuses, sports arenas, open plaza's and shopping malls, drive by shooting of restaurants, stores, and other places of public gathering, and even business holiday parties. The only rule these perpetrators have is cause dramatic death and havoc of their choosing, timing and place.
The horrific terrorist attacks in Paris and San Bernardino, Calif., have vaulted terrorism and national security to become the American public's top concern. As the global Islamic Jihad movement expands, Americans continue to fear that the United States is becoming more vulnerable to jihadist attacks. FBI Director James Comey has said the Bureau is investigating ISIS-related activity in all 50 states—and that ISIS is recruiting here "24 hours a day."
### What You Should Know About Terrorist Plots
James B. Comey, Director of the FBI testified before the Senate Committee on Homeland Security and Government Affairs on October 8, 2015 that the threat of terrorism to the United States is diversified and more aggressive as in previous years. Here are some recent examples of uncovered plots.
• Mexico–Texas border: At least 10 Islamic State of Iraq (ISIS) fighters were caught crossing the Mexican border into Texas in October 2014. Four were arrested.1
• A sophisticated international narco-terror ring with national connections from El Paso to Chicago to New York was uncovered in October 2014. Undisclosed numbers were arrested. These men met with two others in Anthony, New Mexico, to discuss the movement of drugs, money, and people in the United States in March 2014. Two men connected to the narco-terror ring had planned in 2009 a Chicago truck bombing that was thwarted. In 2010–2011 they planned two additional bomb plots targeting oil refineries in Houston and Fort Worth. Fellow conspirators at three mosques in El Paso further planned the plots. One of the men smuggled explosives and weapons from Fort Bliss in concert with corrupt U.S. Army soldiers and government contractors.2
• New York: a plot to make explosives was foiled in 2015
• Minneapolis, Minnesota: a local mosque bred homegrown terrorists to fight for ISIS, 2014
• London, England: plot to behead British citizens in public, 2014
• Washington, DC: plot to destroy the capitol building, 2011
• New York City: plot to explode a car bomb at Times Square, 2010
• Detroit, Michigan: plot to blow up Northwest Airlines Flight 253, 2009
• London, England: plot to bomb underground subway and bus, 2005
• Newark, New Jersey: plot to buy a "dirty bomb" and smuggle hand-held missiles into the United States, 2005
• New York City: plot to blow up the subway station at Herald Square, 2004
• New York City: plot to use tourist helicopters to attack city, 2004
• Britain, United Kingdom: plot to attack Heathrow International Airport, 2004
• Madrid, Spain: plot to blow up a high-speed train, 2004
• Madrid, Spain: plot to blow up the city's main subway station, 2002
• Los Angeles, California: plot to attack Los Angeles International Airport during the millennium, 2000
• Los Angeles, California: plot to destroy the U.S. Bank Tower building by aircraft, 1995
• Los Angeles, California: plot to blow up 12 U.S. aircraft over the Pacific, 1995
• Chicago, Illinois: plot to destroy the Sears Tower building by aircraft, 1995
• Paris, France: plot to fly a jet airliner into the Eiffel Tower, 1994
• New York City: plot to blow up tunnels and bridges throughout Manhattan, 1993
### Additional Facts About Other Terrorist Activities (2013–2015)
• The FBI reports that more than 400 Americans are fighting on the battlefield for ISIS.
• ISIS killed 39 on the beaches of Tunisia and another 27 in Kuwait.
• ISIS beheaded two Frenchmen in France.
• Conspirators were arrested in Canada for accessing computer networks of Boeing, Lockheed Martin, and other defense contractors and stealing secret military aircraft and weapons systems data.
• Walter and Christina Liew and retired DuPont engineer Roger Menagerie were convicted of selling DuPont trade secrets; 20 additional defendants pleaded guilty to the same charges.
• Radicals were arrested in London, accused of trying to recruit westerners to join ISIS.
• A 19-year-old woman was sentenced to 4 years for helping a terrorist group.
• Three men were charged with serving as secret agents for Russia.
• A CIA officer was convicted of espionage.
• Yemen fell to terrorist attacks; the president and cabinet members resigned.
• Major portions of Syria and Iraq are occupied by ISIS terrorist insurgents.
• Two New York Police Department officers were killed in a parked patrol car.
• A man with an axe attacked four New York Police Department officers in public.
• A lone gunman shot two Seattle police officers.
• A gunman killed two deputy sheriffs and wounded one in California.
• A Seattle student killed one student, wounded four others, and killed himself.
• Terrorists assassinated French cartoonists and killed several others in Paris.
• Terrorists were arrested in London and Paris.
• Women were beheaded in the workplace by a disgruntled coworker.
• A terrorist was caught at the U.S./Canadian border driving a vehicle loaded with explosives.
• Weapons and explosives were found buried on two nuclear power plant sites.
• A California power grid was attacked by armed adversaries.
In the last month (November, 2015) terror attacks that left 130 dead in Paris and hundreds wounded, 43 dead in Beirut and took down a Russian airliner with 224 people aboard in addition to at least 20 hostages killed and injured numerous in an attack on a luxury hotel in the capital of Mali, Bamako, and most recently San Bernardino, California, have made the entire world horribly aware that the Islamic State does not only seek to establish a caliphate in Syria and Iraq, but also is beginning to export its monstrous savagery across Western civilization.
## The Threat Landscape Is Diversified and Sophisticated
### Protecting Critical Infrastructure and Key Assets Remains a Pressing Concern
During the past three decades security professionals have focused on traditional threats such as joyriding, petty thievery, opportunistic crime, planned criminal activity, the protection of assets and people, and special threats by relying on a token physical security presence backed up by insurance coverage to recoup losses. Since the events of 9/11 and the more recent rise of transnational criminal organizations, activists, extremist and hate groups, terrorist and criminal activities have become more complex, daring and unstable and are a growing threat to our national economy and national security.3
Globalization presents a new dynamic of hard-to-imagine threats: transnational organized crime and domestic crime; domestic and international terrorism, including state-sponsored cyber crimes, cyber terror, and cyber warfare; weather-related catastrophes; and pandemics and civil unrest, to mention a few.4
Today's challenges call for diversified strategies to guard against multiple threats to reduce business risk exposure. Today, the corporate security organization must protect against traditional threats as well as high-technology data and economic information; competitive business strategies and safeguarding proprietary information; and new levels of terror, brutality, and intimidation dominated by chaos, hidden and diverse enemies, and ongoing threats in our society.5 In spite of distinct differences in the nature of threats, knowledge, and experience, proactive and preventative security planning can strengthen resilience in many areas, including the use of effective and enforceable protocols, human factors training, abnormal behavior patterns, and understanding adverse conditions and events. Chief executive officers (CEOs) are counting on their security directors to guide them through inevitable risk-prone situations and offer practical and workable security solutions.
The foundation of all prevention and protection programs is based on the analysis of reliable and dependable intelligence information and professional security experience. This platform is the threat estimate profile (or threat forecast) that essentially guides the decision-making process for selecting mitigation strategies and solutions to counter specific threats. Understanding the threat environment and how it influences the business operating environment is crucial if CEOs are to make the tough choices for their companies.
The FBI and Homeland Security officials predict that the 21st Century will usher in new threats. At this moment, from a national perspective, the two most likely and serious threats are cyber threats and biological and chemical threats.6 In this chapter I talk about biological and chemical threats, as well as other significant threats and share some case histories. In chapter The Cyber Threat Landscape, I talk about cyber threats.
### Biological and Chemical Threats Are a Great Concern to the United States
#### Seized ISIS Laptop Reveals Terrorist Group's Bio Weapons Attack Plan
In 2014, a captured ISIS laptop revealed documents expressing ISIS's biological weapons attack plan.7 Hidden in several folders on the laptop were 35,347 files containing documents and speeches of leading jihadi clerics, videos of Osama bin Laden, and practical training on how to carry out deadly campaigns. The laptop also contained documents about how to build and use biological weapons.
Following the attacks on September 11, 2001, in October and November 2001, anthrax was distributed in envelopes through the U.S. postal system, causing 5 deaths and 21 injuries (Sullivant, 2007, pp. 25). In March 2002, U.S. Special Forces discovered a partly constructed laboratory in Afghanistan, in which al Qaeda planned to develop anthrax and other biological assets, including how to use these as weapons (Sullivant, 2007, pp. 26).
Of special note, the result of a naturally spreading disease and bioterrorism are the same. Most frightening to law enforcement officials is the fact that deadly biological agents can be delivered across international boundaries with little or no chance of detection. A few ounces of smallpox virus—or worse, a genetically altered, highly contagious virus for which there may be no known vaccine—can kill thousands if not millions of people in only days (Sullivant, 2007, pp. 27).
#### Terrorist Groups Want Chemical Weapons Capability
Security analysts have concerns about terrorist groups that continue to seek castor beans to make the poison ricin or obtain sarin, which might be used in subway attacks in America and other countries, and possibly combined with explosives to disperse the toxins.
In 1995, the Aum Shinrikyo Japanese doomsday cult used sarin in a Tokyo subway, killing 13 people and injuring 5,000, causing widespread pandemonium. In 1994 and 1995 the cult used VX to assassinate four enemies of the cult, but only one of the individuals died (Sullivant, 2007, pp. 26). In 2014 Syria used chemical weapons on its own population in the midst of its civil war, and in 2015 ISIS used captured chemical weapons on the Syrian population.
#### Nuclear Weapons May Go to the Highest Bidder
Terrorists continue attempts to acquire the means to make or buy nuclear weapons through their own resources and underground connections (Sullivant, 2007, pp. 26–27).8 In 1993 al Qaeda agents tried repeatedly and without success to purchase highly enriched uranium in Africa, Europe, and Russia, and in particular from Pakistani scientists and a nuclear power plant in Bulgaria.9
The Russian Mafia has masterminded the theft, diversion, transportation, and distribution of nuclear materials outside the former territories of the USSR. Security agents in Turkey, Morocco, and South Africa seized weapons-grade nuclear materials known to belong to Russia. Relaxed border crossing in European countries has made the movement of nuclear materials from former Soviet territories through these nations easier to accomplish and more difficult to detect. Hospitals in Eastern Europe have reported alarming rates of radiation poisoning and death among smugglers trafficking in nuclear materials (Sullivant, 2007, pp. 25).
As early as 1981, Iraq's drive to obtain nuclear weapons was set back when Israeli jets destroyed the Osiris nuclear reactor outside Baghdad. When United Nations inspectors dismantled a revitalized Iraqi nuclear weapons program in 1991, they found that Iraq was probability within 2 to 3 years of having enough highly enriched uranium to build a nuclear bomb (Sullivant, 2007, pp. 25).
In January 2003 British officials found documents in the city of Heart, Afghanistan, that described al Qaeda's nuclear aspirations along with their desire to obtain dirty bombs (Sullivant, 2007, pp. 26).
### International Terrorism
#### ISIS or the Islamic State of Iraq and the Levant
The terrorists known as ISIS—the Islamic State of Iraq and the Levant (ISIL)—are the greatest international terrorist threat the world faces today. ISIS emerged a decade ago as a small Iraqi affiliate of al Qaeda, one that specialized in suicide bombings. Today it is the largest, richest terrorist organization in history. Its rise in Iraq and Syria, Boko Haram in Nigeria, al-Qaeda in the Islamic Maghred (AQIM) in Mali, and al Qaeda in the Arabian Peninsula (AQAP) show that the jihadist movement is a relentless enemy that is constantly finding new ways to cause massive harm and destruction. ISIS is engaged in ethnic cleansing, imminent genocide, dividing captured families, forcing men to choose between conversion and execution, raping women or taking them into slavery, and performing beheadings and mass executions, bank robbery, kidnapping, extortion, and black market oil sales. ISIS followers are ruthless, and their fanatical belief that they are the true leaders of the Muslim world and the head of all jihads makes them a formidable threat in the Middle East and a severe threat to the Western world. They want to create an Islamic state that includes all Muslims as a part of it, covering every aspect of life—a totalitarian project imposing its extreme version of Sharia law on subject populations. They are intolerant of all other views—including al Qaeda's—of how this should be accomplished. Their battleground has been in Syria and Iraq as they—unlike al Qaeda—have conquered and hold land. Their attacks have spread to Africa, Central Europe and the United States.10
#### al Qaeda
After 15 years, al Qaeda is well and still considering attacking America again. Top U.S. intelligence officials warn that al Qaeda poses an even greater challenge today because its franchises are much more globally dispersed and the organization recently has benefited from the massive leaks of U.S. intelligence information. These leaks, created by former National Security Agency contractor Edward Snowden, who is now a fugitive, provided al Qaeda, other terrorist groups and adversaries and Russia insight into U.S. intelligence sources, methods, and tradecraft.11
#### Cells and Sleeper Cells
The ranks of ISIS are filled with thousands of radicals from all over the world and from the remnants of al Qaeda and other terrorist groups who are willing to join their efforts to form an Islamic state, including radicals holding Western passports. At this time, recruitment of these individuals creates the ominous threat of "lone wolves" acting on their own initiative or at the behest12 of ISIS to attack the West, its organizations, and its corporations at home and abroad. We have seen the testaments of this goal in the most recent Paris and San Bernardino attacks. In the wake of U.S. prisoner swaps with the Taliban, militant jihadism has been on the rise worldwide. Expect sleeper cells to get a wake up call. Attacks across the globe are expected, as mentioned in the chapter opening (Sullivant, 2007, pp. 20–22).
Numerous sleeper cells have been discovered in Great Britain, France, and other countries. Over 30 Islamic training compounds exist across the United States. Sleeper cells, consisting of people who have returned home after training with ISIS overseas, and fighting in Iraq and Syria are hiding in all parts of the country. These camps teach jihad against America, harbor fugitives, build weapon stockpiles, and train fighters. It is suspected that the Boston bombers were part of a 12-member terrorist sleeper cell.13
Every major terrorist organization in the Middle East has created significant infrastructure networks across America, Canada, Mexico, Europe, and Asia. The activities of these groups include recruiting, weapons training, bomb making, robbery, extortion, assassination, counterfeiting money and documents, and other criminal activities.14
Currently, the FBI has thousands of individuals in all 50 states either under surveillance or investigation for terrorist activity or for supporting terrorist groups.
### Domestic Extremist Groups
The FBI's top six domestic extremists groups at this time are the Sovereign Citizen Movement, militia groups, white supremacy groups, abortion groups, animal rights groups, and environmental groups.15
#### The Sovereign Citizen Movement
This movement is a loose grouping of American complainants and financial scheme promoters who take the position that they are answerable only to their particular interpretation of common law and are not subject to any statutes or proceedings at the federal, state, or municipal levels. They do not recognize U.S. currency, and they believe they are free of any legal constraints.16–19 They especially reject most forms of taxation as illegitimate.20 Many members of the movement believe that the U.S. government is illegitimate.21
The Southern Poverty Law Center estimates that approximately 100,000 Americans are "hard-core sovereign believers," with another 200,000 just starting out by testing sovereign techniques for resisting everything from speeding tickets to drug charges.22 A 2014 report by the National Consortium for the Study of Terrorism and Responses to Terrorism reported that a survey of law enforcement officials and agencies across America concluded that this movement was the single greatest threat to communities. Islamist extremists and militia/patriot groups round out the top three domestic threats to communities in America.23–26
#### Militia Groups
Militia organizations include paramilitary or similar groups organized to defend their rights and property against a tyrannical government.27 While groups such as the Posse Comitatus existed as early as the 1980s,28 the movement gained momentum after controversial standoffs with government agents in the early 1990s. By the mid-1990s, groups were active in all 50 states, with membership estimated at between 20,000 and 60,000.29
In April 2013 a militia group attacked a power grid in California.30 The group entered an underground facility and vault of a power station through manholes, just off a freeway in San Jose, California. Strategically cutting telecommunications, telephone lines, and Internet cables, their objective was to sabotage communications, which would then delay response by authorities. Thirty minutes later, snipers opened fire on oil-filled cooling systems, and subsequently 17 transformers that funnel power to Silicon Valley began to fail. Electric-grid officials prevented a blackout by rerouting power around the downed station. It took crews a month to repair the station and get it up and running again.
#### White Supremacy Groups
White supremacists believe that white people are superior to people of other racial backgrounds and that whites should politically, economically, and socially govern nonwhites.31 Different forms of white supremacism have different conceptions of who is considered white, and different white supremacists identify various racial and cultural groups as their primary enemy. In the United States the Ku Klux Klan (KKK) and other white supremacist groups such as Aryan Nations, The New Order, and the White Patriot Party are considered antisemitic.32 The groups mentioned above and similar ones reside in the "twilight zone" between a conventional terrorist group and a conventional hate group (Sullivant, 2007, pp. 23).
#### Abortion Groups
The abortion extremist movement consists of a loosely affiliated network of individuals involved in criminal activity or advocating the use of force or violence in the furtherance of an ideology based around the issue of abortion rights and practices.33 Abortion rights movements advocate for legal access to induced abortion services. Groups have demonstrated against clinics, bombed facilities, and killed employees and patients (Sullivant, 2007, pp. 23).
#### Animal Rights Groups
The primary organization leading this movement is the Animal Liberation Front, an international, underground, leaderless resistance that engages in illegal action in pursuit of animal liberation. Activists remove animals from laboratories and farms, destroy facilities, arrange safe houses and veterinary care, and operate sanctuaries where the animals subsequently live. Within the United States, attacks in 2001 included the firebombing of a primate laboratory in New Mexico and a federal horse corral in California (Sullivant, 2007, pp. 23).
#### Environmental Groups: Case Histories
Environmental groups target logging facilities, real estate developers, and other organizations perceived to engage in activities that are detrimental to the environment. In 1998 the Earth Liberation Front firebombed a ski resort in Vail, Colorado, destroying $12 million in property. In 2003 it targeted car dealerships in California, damaging and destroying 125 sport utility vehicles. The Earth Liberation Front is a collection of autonomous individuals who use economic sabotage and guerrilla warfare to stop activities they perceive as exploiting and destroying the environment (Sullivant, 2007, pp. 23).
### Transnational Criminal Organizations
Transnational criminal organizations have infiltrated every fiber of America's infrastructure and most other countries. They are the world's largest illicit social networks and present a clear and present danger to the national economy and national security of all governments. These criminal networks not only are expanding their operations, they also are diversifying their activities, resulting in a convergence of transnational threats that are becoming more complex, explosive, and destabilizing. Transnational organized crime is a cooperative activity between criminal groups in various nations, estimated to be a $2 trillion industry.34
#### Transnational Criminal Organization Structure
Transnational criminal groups include politicians, government officials, and executives who are nothing more than a new bread of sophisticated gangsters, mobsters, thugs, dope dealers, and terrorists who now seek to obtain global power, influence, and monetary and/or commercial gain by illegal means - rather than regional control of territory while protecting their activities through a transnational organizational structure and the exploitation of transnational commerce. The organization comprises countless international executives from varying backgrounds. A representative listing of the organization's membership includes:
• Russian mobsters who emigrated to the United States in the wake of the Soviet Union's collapse
• U.S. criminalheads
• groups from African countries
• Chinese tongs, Japanese boryokudan, and other Asian crime rings
• enterprises based in Eastern European nations such as Hungary and Romania
• Mexican and Columbian drug cartels
Some of their criminal activities focus on:
• attempts to gain influence in government politics and transnational commerce
• buying off corrupt officials. Corruption is any abuse of power for private gain. It includes political wrongdoing, bribery of officials, mispresentation, fraud, procurement manipulation, and wrongful reporting. Bribery, corruption, and other white-collar crimes are not solely legal issues; they can have damaging effects on business organizations. This is why security must be the first line of defense of an organization's image, brand, and reputation.
• forging alliances with corrupt elements of governments to threaten governance
• influencing governments to exploit these relationships to further their interests
• penetrating state institutions to exploit differences between countries
• defrauding millions each year through various stock and financial frauds
• manipulating and monopolizing financial markets, institutions, and industries
• crime–terror–insurgency nexus, intimidation, kidnapping, and assassination
• disguising the pattern of corruption and violence through legitimate businesses
• trafficking drugs, humans, body parts, and endangered species
• trafficking weapons and nuclear materials
• money laundering and prostitution
• stealing intellectual property and cyber crime exploitation
• using power and influence to further criminal activities
• isolating themselves from detection, sanction, and prosecution
### Radicalization Is a Growing Concern
As of this writing, more than 1500 Americans have crossed the threshold of American values to battle in the name of Islam. These American citizens operate under the radar and take on roles as clandestine "lone wolves" or join small groups, giving renewed emphasis to the insider threat. Some of these individuals have committed horrific crimes: killing police officers, beheading an Oklahoma woman, shootings at Fort Hood and in Chattanooga and Huston, and the bombing of the Boston Marathon, to mention only a few.
Since 9/11 more than 50 major plots involving 190 homegrown terrorists with ties to international terrorist groups have been exposed.35 In July 2015, just before the Fourth of July weekend, the FBI reported arresting more than 20 individuals associated with a plan to attack New York City and several other cities. This radicalization process is gaining momentum and represents the greatest current challenge to counterterrorism we face today (Coolsaet, 2011, pp. 85). Most recently, the director of the FBI testified before Congress that the agency has on-going investigations in every state on the radicalization of U.S. citizens and others.
### The Insider Threat
The insider adversary can be any trusted individual filling any position: managers, administrative staff, operations and maintenance personnel, security personnel, vendors, and even part time workers. These persons may be active or passive, violent or nonviolent, and motivated by financial, vengeful, egotistical, psychotic, voluntary, or coercive considerations.36,37
The passive insider adversary commits no acts; he or she merely provides information to outsiders. The active insider adversary may be nonviolent and unwilling to use force against others, or be violent and willing to actively use force. Various insider abilities and capabilities can be used:
• Ability to perform routine tasks or to get authorization to perform special tasks
• Authority to exploit and influence processes, practices, and protocols
• Authorized access to work schedules and employees as sources of information
• Capability to use tools available in the work place
• Characteristics of critical assets, including asset vulnerability
• Supervision of or control of others
• Knowledge of security/control systems, work schedules, and assignments
• Known weaknesses and gaps in security planning, response, and recovery
• Opportunity to choose the time and place to commit an act over a span of time
• Opportunity to recruit and collude with others, both insiders and outsiders
• Specific details of enterprise operations, processes, practices, and policies
## Attack Modes Make Planning and Response a Challenge
In this section I describe some threat modes to consider when planning your security activities as well as your event-driven emergency response and recovery procedures and training.38
### Conventional Attacks Are the Preferred Method to Wreak Havoc
Improvised explosive devices; bomb attacks, assassinations, kidnappings, or ground assault attacks are normally referred to as conventional attacks.
### Nonconventional Attacks Are in Their Embryonic Stage
Nonconventional attacks range from the use of weapons of mass destruction, such as anthrax and radiological materials, to cyber crimes, cyber terror, and cyber warfare. Attacks staged by hostile nation-states are aimed at damaging or destroying economic, trade, currency, and military stability. Transnational groups are bent on controlling the commercial or financial markets, including criminal activities such as corruption, extortion, and fraud.
### Vehicle Bombs
Vehicle bombs are the preferred weapon of use. Terrorists have been successfully using explosives in cars, trucks, and boats for years. In 1995, McVeigh and Nichols used a truck bomb to kill 168 people and injure 680 others in the Oklahoma City bombing. The blast destroyed or damaged 324 buildings within a 16-block radius, destroyed or burned 86 cars, and shattered glass in 258 nearby buildings, causing at least an estimated $652 million worth of damage. Faisal Shazhad attempted to detonate a vehicle bomb in Times Square in 2010.
### Train Bombs
Train bombs have been used successfully in Madrid (2004), London (2005, 2013, 2014, and 2015), Mumbai (2006), and Egypt (2014). Muslims helped to foil a train bomb plot for U.S. Canadian-bound rail lines in 2013. Authorities foiled several suspected bombing plots against New York City subways.
### Airplanes Used as Weapons of Mass Destruction
On September 11, 2001, terrorists hijacked four commercial aircraft and used these planes as weapons of mass destruction against the World Trade Center and the Pentagon. The attacks resulted in more than 3000 deaths and thousands of injuries, catastrophic losses in terms of property destruction and economic effects, as well as profound damage to public morale and the confidence of the nation. In addition to the loss of life and damage and destruction of property and buildings, thousands of vehicles and utility, transportation, telecommunications, and government services throughout the northeastern part of the nation sustained collateral damage. When the seven buildings that made up the World Trade Center complex collapsed, more than 29 surrounding high-rise buildings were either severely damaged or later condemned. Many stand empty to this day. Approximately 34,000 businesses and residences, and hundreds of government agencies, lost the capability to function and communicate for extended periods. The wave of destruction took with it over 300,000 voice lines and over 3 million data lines. Disruption of services occurred because various carriers had equipment collocated at the site that linked their networks to Verizon and other providers. In addition, a considerable amount of telecommunications traffic that originated and terminated in other areas but passed through this location was disrupted. AT&T's local network service in lower Manhattan was significantly disrupted following the attacks, which directly affected the operations of the world financial district, the stock exchange, and international banking operations. Electricity, water, and other services also were knocked out. Satellite links and underground cables were severed, disrupting communications for millions of other users in the northeast and mid-Atlantic states.39
### Piracy
During the 21st century, more than 2000 cases of piracy have been committed on the high seas. A single piratical attack affects maritime security, an economic interest of all nations, including the flag state of the vessel, the various nationalities of the seafarers taken hostage, regional coastal states, owners' states, and cargo destination and transshipment states. Such attacks undermine confidence in global sea lines of communication, weaken or undermine the legitimacy of states, threaten the legitimate revenue and resources of nations, cause an increase in maritime insurance rates and cargo costs, increase the risk of environmental damage, and endanger the lives of seafarers who may be injured, killed, or taken hostage for ransom.
### Kidnapping
Kidnapping for ransom or assassination is a common occurrence across the globe, creating an enormous threat to American citizens and corporate executives. It is believed that in 2013 the Boko Haram was paid nearly $17 million in ransom from the French government. The U.S. Treasury Department estimates that $120 million in ransom flowed to such groups from 2004 to 2012.40 The top countries for kidnapping and ransom are Mexico and Colombia. Mexico City ranks number one in the world, whereas Phoenix, Arizona, takes second place globally. Ransoms have become the main source of funding for terrorist groups.
### Small Aircraft With Explosives
Rural airports are left largely unguarded; great destruction could be caused if airplanes are packed with explosives and flown into crowds or buildings.
### Suicide Bombers
This mode of attack creates fear, panic, and death across the globe. A backpack or vest bomb in a concert, shopping mall, movie theater, restaurant, or other places where large groups gather would cause widespread panic and have a sizable financial impact because people may begin to avoid these destinations. Suicide bombers are a common weapon across the Middle East and bordering countries. This phenomenon, until recently, has not reached the shores of Western countries. During the November attack in Paris, three of the terrorists were suicide bombers, and exploded their vests. The San Bernardino attackers also had in their arsenal suicide vests. I am convinced that this tactic will soon come to the shores of the United States.
### Radiological Bombs
A radiological weapon, or "dirty bomb," combines radioactive material with conventional explosives. Such bombs can be miniature bombs that fit in a suitcase or big bombs that fit in trucks, and they are designed to injure or kill by creating a zone of intense airborne radiation that could extend several city blocks. People in the immediate area would be killed, and radioactive materials would be dispersed into the air and reduced to relatively low concentrations. Jose Padilla, a U.S. citizen who trained in Pakistan with al Qaeda, attempted to build one in 2002. He was convicted of aiding terrorists.
According to a United Nations report, Iraq tested a one-ton radiological bomb in 1987 but gave up on the idea because the radiation levels it generated were not deadly enough. We know that the late Osama bin Laden attempted to purchase several suitcase bombs from contacts in Chechnya and Kazakhstan. Several international intelligence agencies have also reported that about 100 of these dirty bombs disappeared from Russian stockpiles in the early 1990s and have yet to be found.41
### Other Criminal Activity Is Also a Threat
#### Threats to Personnel Safety
There are about two million assault incidents every year. According to the FBI, general assaults account for 42% of all crimes in the United States.42 Every day an estimated 16,400 threats are made against someone in the workplace or against the workplace itself. Every day over 700 workers are attacked on the job—an excess of 200,000 per year. This equates to nearly one worker assaulted every minute. Every day nearly 44,000 workers are harassed, and every year about 1000 workers are victims of a workplace homicide. During the year 2000 there were over 23,000 reported violent acts committed against management-level personnel in all areas of employment in the United States. Here are some targets of assault:
• Executives, officers, or other key personnel who are vulnerable by virtue of their positions and actual or perceived responsibilities, for which some employees, customers, or others find "cause" and attempt to injure or kill them. According to the Justice Department, men are victims of 80% of all workplace violence. Most are executives, managers, or other key personnel.
• Human resources personnel and managers are susceptible because of their role in employment terminations.
• Managers are potential victims of violence connected with personal relationships.
• Women comprise 50 percent of the workforce and share an increasing vulnerability in management positions. Their death in the workplace exceeds the industry index for wrongful deaths.
#### In-house Employee Terminations
Anger or rage is one of the most common sources of workplace violence. "Roller coaster" employment and layoffs can leave discharged employees feeling disrespected and unfairly treated. The combined fear of being unable to support themselves or their families, insult to their capabilities, embarrassment of termination, a question of "Why me, not him or her?," and wondering where and when their next job will come can fester into a strong resentment and a desire for retribution. A discharge for cause can be even more likely to breed resentment, which may result in a violent act against the employer or company representative. The target can be anyone from the CEO to part-time employees.
I believe termination or separation interviews conducted by people trained in dealing sympathetically with both downsizing and for-cause terminations can prevent a large portion of retaliatory assaults against physical or intellectual property or systems. The "clean out your desk while I watch" approach always ignites a firestorm of resentment.
#### Insult and Emotional Trauma
Incidents such as being passed over for promotion or having requests for a transfer to a new position denied can cause deep-seated resentments. More common is the persistent demeaning of an individual by a superior. These conditions can be difficult to discern, frequently continuing for years out of the victim's fear of retaliation or discharge. Skilled interviewers can often unearth these conditions through annual reviews or recognition of frequent requests for transfer. Not only can these conditions become dangerous, but certain behavior such as persistent harassment of one employee by another (especially a superior) is illegal. In these days of frequently impersonal relations between management and workers, the human resources, health and safety, and security divisions would do well to work together to prevent not only legal action but also the potential for violent incidents.
#### Theft of Property
Theft may occur from one of two sources: those within the organization and outsiders. Theft can occur when there is a conspiracy between an insider and someone on the outside. It can be motivated by economic gain, a desire for retaliation, or as a means of gathering information. Corporate theft is a situational, opportunistic, and seasonal phenomenon.
#### Stockroom and Inventory Threat
Stockroom and inventory theft frequently involves more than one individual. Collusion between someone on the inside and someone on the outside is the most common method and may involve criminal partnerships, such as between a cashier and a customer, a receiving clerk and a truck driver, or an employee and someone on a cleaning crew. The types of property in stock or on hand frequently determine the type of thief and the type of crime. Materials that are easily disposed of, such as televisions, computer equipment, weapons, drugs, tires, or cigarettes, and that can be sold on the street are most often stolen by gangs and organized crime groups who have ready outlets for the stolen goods. Weapons, chemicals, or other dangerous substances can be targets of terrorists, extremists, or organized crime groups, as well as professional thieves stealing for pure profit. Common thieves often steal relatively low value items because they are usually easy to steal and remove from the property, and can be easily be discarded if thief is about to be caught attempting to leave the property.
#### Competitors and Espionage
Practiced internally, nationally, and internationally, espionage may involve hiring away a key employee or planting a spy within a company or organization. Activities may include pouring through forms filed with the Securities and Exchange Commission and pirating trade secrets, advertising programs, strategic business plans, football playbooks, music, videos, computer software or hardware, or weapon designs. Espionage, especially economic and competitive espionage, is practiced on a huge scale. Nearly every business enterprise does whatever it can to learn everything possible about its competitors. From a security perspective, however, the release of inside information to a competitor is a real loss and one to be prevented. Most significant losses of this type occur because of someone on the inside selling information for either money or personal gain. Today, given the global use of e-mail, the Internet, fax machines, and scanners, the transfer of a company's confidential or proprietary information can occur in seconds, often not being discovered until it is too late. Stealing, selling, or leaking trade secrets or insider information is an increasing problem in the business world.
#### Vandalism and Sabotage
Security people are just beginning to address the tip of the iceberg in the areas of vandalism and sabotage. Physically booby-trapping computers with explosives or other harmful devices is a frequent strategy of terrorists. While vandalism and sabotage may derive from different intentions, the results are the same: property or operations are destroyed or damaged. Saboteurs have a desire or motive to cause damage. They may not necessarily select a target that would cause the greatest harm, but rather one that seems to afford the greatest chance for success or symbolism. Vandalism, on the other hand, is more often an act of opportunity and may be performed by someone who is merely angry or bored. This person may be a thrill- or power-seeker, whether by wielding a can of spray paint or hacking into a computer. The target may be important only as an opportunity, test, or challenge.
## Conclusions
A big challenge for organizations is prioritizing, understanding, and addressing threats in a business context. The threat of international terrorism remains at a significantly high level, and those with the desire, intent, and means to do us harm continue to demonstrate that they are both highly determined and persistent. Right now, ISIS is the greatest terrorist threat facing not only America, but the entire world. Second to ISIS is al Qaeda. Al Qaeda poses an even bigger challenge today than in previous years because its franchises are "much more globally dispersed," and the organization recently has benefited from the massive leaks of U.S. intelligence information.
The insider threat is by far our greatest challenge. Security measures must aim, in part, to minimize the potential of hiring an adversary and to deter individuals from becoming an adversary once they are hired. Such measures must compel the workforce to do the right thing and cause them to take high risks of exposure to do the wrong thing. If an insider chooses to do the wrong thing, security measures must detect such actions early enough and delay the insider long enough so that a response can interrupt the action before it is completed.
Current threats are escalating faster than we are able to identify, and they know no geographical boundaries. They can occur at any moment, anywhere—in areas from urban centers to Main Street, targeting small businesses and major corporations, and people regardless of age, economic status, or social position, from high-profile individuals to any parent, child, grandparent, friend, or coworker. Corporate America's answer to these threats must be an unyielding resolve to remain relentlessly proactive, followed by reasonable and prudent actions to reduce risk exposure.
The biggest change in industry during the past two decades has been technology. Technology continues to grow and advance beyond our present-day imagination and will do so well into the future. This phenomenon creates an ongoing demand to protect corporate America and its business operations from the rising threats of transnational organized crime and terrorist activities. Change, of course, has always been a management challenge, but change today has taken on an entirely different meaning. Today, it is more rapid and more complex to manage.
The challenge for CEOs is to focus on possessing in a timely manner the whole set of disciplines, expertise, experience, and capabilities to keep up with the fast pace of continual change, while not loosing sight of quality high-performance results within the fog of evolving and emerging security threats. This challenge calls on CEOs to muster a dedicated security organization comprising of staff who are knowledgeable and experienced in dealing with diversified threats, ensuing consequences, and emergency response planning, and who have the expertise to lead prevention, deterrence, and protection initiatives. Lacking this capability, they must seek professional consulting expertise to achieve goals and objectives.
* * *
1 Judicial Watch, Vol., December 20, 2014, Washington, DC.
2 Ibid.
3 The National Strategy for Homeland Security: U.S. Department of Homeland Security, Washington, DC, 2007.
4 Szady, D.W., Vice President, Guardsmark (FBI Assistant Director, Retired), Security Management, April 2014.
5 The National Strategy for Homeland Security: U.S. Department of Homeland Security, Washington, DC, 2007.
6 U.S. Department of Homeland Security, Washington, DC, 2013.
7 Seized ISIS laptop reveals terror group's bio weapons attack plan, August 30, 2014: dnaindia.com.
8 Szady, D.W., Vice President, Guardsmark (FBI Assistant Director, Retired), Security Management, April 2014.
9 Ibid.
10 Lipman, I.A., Founder and Chairman, Guardsmark, The Lipman Report, August 15, 2014.
11 Lipman, I.A. Founder and Chairman, Guardsmark, The Lipman Report, September 15, 2014.
12 Number of Jihadist Fighters Has Doubled Since 2010, Rand Corporation, June 4, 2014.
13 The People, London, England, April 21, 2013.
14 Patterns of Global Terrorism, U.S. Department of State, Washington, DC, 2004.
15 Lipman, I.A., Founder and Chairman, Guardsmark, The Lipman Report, September 15, 2014.
16 <https://www.fbi.gov/news/stories/2010/april/sovereigncitizens_041310/domestic-terrorism-the-sovereign-citizen-movement>.
17 Johnson, Keven, "Anti-government 'Sovereign Movement' on the rise in U.S.", USA Today, March 30,2012.
18 "Sovereign Citizen Suing State Arrested Over Traffic Stop", April 6, 2012, WRTV Indianapolis.
19 <https://en.wikipedia.org/wiki/Sovereign_citizen_movement>.
20 Carey, K., "To Weird for The Wire": How black Baltimore drug dealers are using white supremacist legal theories to confound the Feds," The Washington Monthly, Washington, DC (July 2008).
21 MacNabb, J.J., "Context Matters: The Cliven Bundy Standoff–Part 3," Forbes Magazine, May 16, 2014.
22 MacNab, J.J., "Sovereign Citizen Kane," Intelligence Report. Issue 139, Southern Poverty Law Center. Fall 2010.
23 Parker, J., "Study: Greatest Terrorism Threat In America Not Al Qaeda, It's Right-Wing Sovereign Citizens," addicting info.org, August 3, 2014,
24 Jessica R., "Sovereign citizen movement perceived as top terrorist threat," July 30, 2014, National Consortium for the Study of Terrorism and Responses Terrorism, College Park, Maryland, July 30, 2014.
25 David C., Steve C., Jeremy C., Jack D., "Understanding Law Enforcement Intelligence Processes: Report to the Office of University Programs, Science and Technology Directorate, U.S. Department of Homeland Security," 4 July 2014, National Consortium for the Study of Terrorism and Responses to Terrorism (College Park, Maryland). The Consortium is a grant foundation funded by the U.S. Department of Homeland Security and various other federal agencies, private foundations and universities.
26 The Ku Klux Klan (KKK) or just the Klan is the name of three distinct movements in the United States. They first played a violent role against African Americans in the South during the Reconstruction Era of the 1860s. The second was a very large controversial nationwide organization in the 1920s. The current manifestation consists of numerous small but unconnected groups that use the KKK name. They have all emphasized secrecy and distinctive costumes, all have called for purification of American society and all are considered right wing. All groups are classified as hate groups. It is estimated to have between 5,000 and 8,000 active members as of 2012.
27 Mulloy, D., 2004. American Extremism: History, Politics and the Militia Movement, Routledge, U.K.
28 Pitcavage, M., 2001. Camouflage and Conspiracy: The Militia Movement From Ruby Ridge to Y2K, Institute for Intergovernmental Research. American Behavioral Scientist, <http://abs.sagepub.com/content/44/6/957.abstract>.
29 Berlet, C., Lyons, M., Right-Wing Populism in America: Too Close for Comfort, Guilford, U.K. 2002.
30 FBI Terrorist Task Force, FBI Field Office, Los Angeles, CA, April 2013.
31 Wildman, S.M., Privilege Revealed: How Invisible Preference Undermines America, 87. New York Press, NY.
32 Flint, C., Spaces of Hate: Geographies of Discrimination and Intolerance in the U.S.A. Routledge, London, England, 2004.
33 Abortion Extremism: FBI Domestic Terrorism Operations Unit, Washington, DC, December 12, 2011.
34 Lipman, I.A., Founder and Chairman, Guardsmark, The Lipman Report, April 15, 2013.
35 Szady, D.W., Vice President, Guardsmark (FBI Assistant Director, Retired), Security Management, April 2014.
36 James, P. Chapter 22, "Insider Analysis." The Nineteenth International Training Course for the Physical Protection of Nuclear Facilities & Materials. Sandia National Laboratories & The International Atomic Emergency Agency, Albuquerque, NM, 2006.
37 Murray, D.W., DOD Security System Analysis Department, Sandia National Laboratories, Albuquerque, NM; Biringer, B.E., Security Risk Assessment Department, Sandia National Laboratories, Albuquerque, NM: Defending Against Malevolent Insiders Using Access Controls (contributing authors). Wiley Handbook of Science & Technology for Homeland Security, John Wiley & Sons, NJ. 2008.
38 Szady, D.W. Vice President, Guardsmark (FBI Assistant Director, Retired), Security Management, April 2014.
39 The National Strategy for the Physical Protection of Critical Infrastructure & Key Assets, U.S. Department of Homeland Security, Washington D.C. February 2003.
40 Lipman, I.A., Founder and Chairman, Guardsmark, The Lipman Report, August 15, 2014.
41 Terrorism & National Security, U.S. Department of State, Washington, DC, 2003.
42 Lipman, I.A., Founder and Chairman, Guardsmark, The Lipman Report, August 15, 2014.
5
# The Cyber Threat Landscape
## Abstract
Spies have been damaging U.S. interests since the American Revolution. But today's world makes it easier to commit espionage because of the increase in the number of people who now have access to sensitive information, the ease of transmitting information, and the growing demand for sensitive information from end users. This chapter highlights some of the high-profile adversaries who have crossed the lines to perpetrate the most damaging U.S. counterintelligence and business failures. Actual case histories are offered throughout the narrative to emphasize the degree of importance these actions have on the threat landscape.
### Keywords
Awareness; Breaches; Capability; Espionage; Insider; Intelligence; Malicious; Response; Risk; State-sponsored; Training
The cyber threat has pushed security planning and protection from an operational concern of corporate security and IT departments onto the strategic agenda of CEOs and Boards at many enterprises across America. But many Board directors are dissatisfied with both the quantity and quality of information offered [to] executive decision-makers about cyber security and cyber risk. These executives want changes in how security oversight responsibility is invoked, improved incident response means and competency that stop breaches.
John Sullivant
Top Takeaways
• Discover who is behind all the data breaches and who is being targeted and why?
• Understand the perceptions of executive management, information technology security professionals, and employees
• Uncover the truth about employee dependability, reliability, and trustworthiness
• Gain an understanding of constraints in dealing with, detecting, and responding to breaches
• Determine the effectiveness of cyber protocols, budgets, and training
## Overview
Spies have been damaging U.S. interests since the American Revolution. But today's world makes it easier to commit espionage because of the increase in the number of people who now have access to sensitive information, the ease of transmitting information, and the growing demand for sensitive information from end users.
Some of our most trusted people have crossed the line to perpetrate the most damaging U.S. counterintelligence failures. In each case these individuals had exhibited the identifiable signs of being a traitor, but those signs went unnoticed or unreported for years because of the unwillingness or inability of colleagues and managers to accept the possibility of treason. Another reason is the fear of being sued for defamation of character. Insiders convicted of stealing information had been doing so for a long time before being caught. Here are five important case histories:
• Army PFC Bradley Manning leaked the largest cache of classified documents in U.S. Army history when he disclosed restricted military records to the Wikileaks website. He was sentenced in 2013 to 35 years in prison.1
• Former National Security Agency (NSA) contractor Edward Snowden perpetrated the biggest NSA intelligence leak in U.S. history. In 2011 Snowden leaked millions of documents to the Wikileaks website, revealing numerous NSA global surveillance programs. He devastated the entire country and its national security, degrading the United States' capability to gather intelligence information.2
• Former FBI counterintelligence agent Robert Philip Hansen provided highly classified national information to Russia and the former Soviet Union. Hansen provided the KGB and its successor agency, the SVR, with top secret and "code word" documents from 1985 through 2001.3
• The biggest espionage leak in U.S. Navy history was the Walker family spy ring. This group gave the Soviets information from 1968 to 1985, which allowed the Soviets to access weapons data, naval tactics, and surface, submarine, and airborne readiness capabilities. It was later discovered that the Walkers' activities enabled North Korea to seize the USS Pueblo and capture a significant amount of classified information. The information cache shared by the Walkers with the Soviets enabled the Soviets to build replicas and gain access to U.S. naval communications systems, which continued into the late 1980s.4 North Korea still has possession of the USS Pueblo.
• Daniel Ellsberg, a senior research associate at the Massachusetts Institute of Technology's Center for International Studies, strengthened public opposition to the Vietnam War in 1971 when he leaked the Pentagon Papers to the New York Times. The documents contained evidence that the U.S. government had misled the public and Congress regarding the country's involvement in the war, including the years leading up to the war.5
While terrorism continues to dominate our national discourse, the global threat landscape has been transformed, with terror networks using new technologies and strategies to carry out attacks at home and abroad. The cyber terror threat has become more sophisticated and more deadly with the advent of social media and mobile networks.
## Who Is Responsible for Today's Cyber Attacks?
Threats come from terrorists, hackers, disgruntled employees, individuals specifically engaged in corporate and economic espionage, professional spies, state-sponsored terrorists, and transnational organized crime operations. The expertise of cyber attackers varies from small-time hackers with minimal capabilities to national intelligence agencies with thousands of software engineers exploiting the latest techniques. Experts divide cyber culprits into four categories based on their capabilities.6
• Group 1 consists of "hacktivists," such as Anonymous, and terrorist groups such as al Qaeda, Hezbollah, Hamas, and ISIS.
• Group 2 consists of cyber criminals. The capabilities of these criminals vary, but their motivation is primarily financial gain. Their goal is not destruction but acquisition of information.
• Group 3 is nation-states performing cyber espionage for technology transfer. These adversaries are infinitely more insidious and damaging to the U.S. economy than cyber criminals, hacktivists, or terrorists, and include China, North Korea, Russia, and Iran.
• Group 4—the most formidable group—is destructive foreign military operatives. Their goal is to shut down the systems of national critical infrastructures. Such attacks would cause widespread chaos and damage, and diminish the country's capability to defend the nation from an all-out military invasion. Agents from China, North Korea, Russia, and Iran are among this group.
## The Cyber Threat Continues to Devastate the U.S. Economy and National Security
Cyber intrusions into corporate networks, personal computers, and government systems are occurring every day by the thousands. Cyber attacks include cyber crime, cyber terror, and cyber warfare.7
• Cyber crime involves phishing, extortion, fraud, theft, and other crimes. This crime is rampant and is growing in scale and sophistication.
• Cyber terror involves attacks on critical computer-controlled infrastructure such as water, energy, telecommunications, transportation, and banking. Cyber terror is also expected to grow in scale and sophistication.
• Cyber warfare involves the theft of sensitive information and espionage used by one nation-state against another. China and Russia have engaged in cyber warfare on at least two occasions: China's reprisals against U.S. government information networks after the May 1999 accidental bombing of the Chinese embassy in Belgrade, and Russia's distributed denial of service attacks against Estonian computer networks in May 2007—though both countries deny involvement.8
The cyber threat is not defined by a single event such as an attack on an electric grid; rather, it is the ongoing onslaught and the transfer of wealth from our economy and national security—thus a cyber "death by a thousand cuts."
Computers and servers in the United States are the most aggressively targeted information systems in the world. These attacks threaten the nation's public works, communications systems, computer networks, and commerce. Cyber crime is emerging as one of the most daunting threats faced by the nation today. More than 100 countries, including some major U.S. allies, are deeply involved in cyber espionage and have been for several decades. Examples of such threats include:
• shutting down systems or simply generating fear
• altering air traffic, train, and subway data and controls to create mid-air collisions and crashes
• causing havoc with financial institutions, creating bank and credit fraud
• disrupting communication and transportation systems and services
• disrupting power grids, gas and oil pipeline flow, and water and sewer supplies
• disabling or hacking into sensitive computer systems
• making services unavailable to users
• manipulating computers to cause explosions or environmental contamination
• violence against persons or property
• sending a wireless virus out to computers and phones, rendering them useless
• stealing money, intellectual and proprietary information, and identities
Cyber espionage is intensifying in frequency and severity, doing horrendous damage to our national economy and security. Iran, China, North Korea, and Russia are the leading international cyber hackers.9
Hackers have penetrated, taken control of, damaged, and/or stolen sensitive personal and official information from computer systems at many government departments and agencies10:
• Commerce | • Justice
---|---
• Commodity Futures Trading Commission | • Labor
• Environmental Protection Agency | • NASA
• Defense | • National Weather Service
• Energy | • Nuclear Regulatory Commission
• Federal Reserve | • Office of Personnel Management
• Food & Drug Administration | • States
• Homeland Security | • U.S. Copyright Office
We know that China operates the largest covert electronic espionage spy network in the world. They have been spying on the United States and stealing our secrets since the early 1970s. French companies have been stealing American trade secrets since the early 1960s.
Thousands of prominent U.S. corporations have also been penetrated, systems damaged, and proprietary, sensitive, and confidential information stolen. In fact, in 2013 the FBI notified more than 3000 U.S. companies that they had been hacked.11 That number reflects only a fraction of the true scale of cyber intrusions into the private sector by criminal groups and foreign governments and their proxies—particularly China, Iran, North Korea, and Eastern Europe; it is impossible to detect all such breaches. Here is a sampling of some of the corporations penetrated:
• Automatic Data Processing | • JPMorgan Chase & Company
---|---
• Boeing Aircraft Company | • Lockheed Martin
• Citigroup | • Major government contractors12
• CrowdStrike Company | • Michael's
• Dairy Queen | • NASDAQ
• EMC Corporation | • Sony
• Epsilon Data Management | • Target
• Home Deport | • Wal-Mart
|
• U.S. Investigative Services (USIS)13
It is not surprising to discover that 80 percent of most U.S. companies have experienced at least one breach, with most of them achieving "veteran status" for numerous attacks. It is equally disturbing to learn that most of the breaches are not reported to the government. And, 40 percent of these companies do not interact with the FBI, U.S. Secret Service, or other agencies on such cyber breaches. Their reasoning is that they will lose market share, stock prices will drop, prosecutions will make their trade secrets public, and they do not want to be embarrassed.14
## Trusted Insiders Bear Watching
Of all the methods for obtaining a company's intellectual and proprietary information or classified government information, the most effective is the use of the trusted insider—one who volunteers or is successfully recruited or sent by an intelligence service or corporation. 93 percent of U.S. organizations are vulnerable to such insider threats.15 While businesses are growing increasingly aware of insider threats, they still lack enforcement controls to stop perpetrators and the will to punish them. Businesses take little action to mitigate the insider threat.
### Motivational Factors Shed Insight on Undesirable Employee Behavior
Many motivational factors explain why an employee would decide to steal a company's intellectual or proprietary information, or sensitive or classified government information, and give it to a competitor or another organization. Lipman identifies 16 factors, and a good account of these motivational factors is given in "The Lipman Report" of March 15, 2014.
• Alienation | • Organizational drift
---|---
• Drugs | • Money
• Emotional involvement | • Messiah complex
• Family problems | • "My generation"
• Hatred and revenge | • National pride
• Hostage situation | • Sense of adventure
• Idealism and beliefs | • Threat/blackmail
• Ingratiation | • Weak ego
Some actions that may suggest an individual is involved in unauthorized, illegal, or unethical activities may include:
• accessing restricted websites
• a disregard for policies on installing personal software or hardware
• asking to use others' passwords
• doing unauthorized work at home
• downloading documents that are unrelated to their responsibilities
• indifference to coworkers or supervisors
• suspicious personal contacts with competitors or unauthorized people
• unexplained affluence
• unreported foreign contacts
• use of a personal computer at work
• working odd hours
### We Can Learn From Our Mistakes and Bad Experiences
One of the legacies of Edward Snowden's treason16 is that many companies are now concerned about the insider threat more than they have ever been, but fewer are taking any serious action to do something about it.
• Snowden demonstrated that a trusted person with the most stringent security measures could devastate an entire organization, or in Snowden's case the entire nation.
• While technology and security practices should have caught Snowden, there is also the realization that his coworkers and managers should have noticed indications of unusual behavior.
• The damaging leakage of national top secret information by Snowden serves as a wake-up call not only for government agencies but private employers as well.
• Snowden's actions provide a clear example of what can happen, even for some of the most security-conscious organizations, when the insider threat is not taken seriously.
A legacy of betrayals by the Walker family, Hansen, Ellsberg, and Manning is that people with boundless access to sensitive data present the greatest risk of misusing that privilege. Wrongdoers are able to cover their actions very well, but the reality is that just about every malicious insider shows some indications of their intent. Managers and coworkers are in the best position to see those indications.
## State-Sponsored Cyber Attacks Create Havoc With Our Economy and National Security
Sponsored cyber attacks17 are becoming the method of choice for foreign governments to infiltrate and steal information and intelligence from the U.S. government and American businesses, and we are unprepared to stop them. We have suffered breaches involving:
• credit card information18
• critical national infrastructure intelligence19
• employer data20
• patient health records21
• personal financial information22
Collectively, these breaches demonstrate both the diversity of targets and their shared vulnerabilities. Here are three case histories of major concern to our national security:
• USIS23 is the largest government contractor conducting background investigations for the U.S. Department of Homeland Security. A single USIS data breach involved the theft of personnel information for 25,000 federal employees and contractors seeking clearance for access to U.S. government classified information. While this breach represents a second black eye for USIS—it was the firm that performed the background check for Edward Snowden and the U.S. Navy Yard shooter—the broader implications of this attack are serious and highly concerning. Experts advise that this type of attack is usually intended for the purposes of identifying potential recruitment candidates for intelligence purposes. By collecting such information, the sponsors behind this attack can identify which members of the U.S. security clearance population might be suitable for targeting by a foreign power.
• The Nuclear Regulatory Commission24 suffered three major attacks in as many months. These breaches seem to have been designed to gather information on the capabilities of U.S. nuclear assets and to probe the cyber readiness of the Commission's workforce.
• A U.S. defense contractor who smuggled classified F-35 design plans for China. This theft remained undetected until the design architecture was noticed on China's stealth bomber.
58 percent of senior information technology (IT) security professionals believe the industry is losing the battle against state-sponsored attacks. 30 percent say they are not even confident that foreign state-sponsored hackers have not breached their own corporate network. 96 percent believe that the hacking landscape is going to get worse over time.25
## Cyber Practices and Incident Responses Need Improvement
No corporation or government is exempt from cyber attacks, yet many organizations are not clear-eyed about their cyber security resilience. Several prominent research firms and institutions report a telling story about America's cyber security capabilities and the character of those charged with planning, development, implementation, and monitoring for success. Security practitioners, executive management, and governing boards that face cyber security challenges can greatly benefit from understanding the impact of cyber crimes on their organizations and act accordingly.
Below is a selection of case histories from recent surveys, which will give you a sense of the magnitude of the problem, including system vulnerability, that security professionals face on a daily basis. This information can be a useful tool for developing prevention and protection strategies, emergency response plans, cyber incident response plans, and protocols to strengthen cyber security operations. This information can also offer insight into fostering business relations, establishing and maintaining dialog with upper management, and structuring awareness training programs. The case histories are divided into five groups:
• Perceptions of executives, IT security professionals, and employees
• Employee dependability, reliability, and trustworthiness
• Capability to detect and respond to breaches
• Usefulness of cyber policies, plans, and procedures
• Budget, time, and training
### Executives, IT Security Professionals, and Employee Perceptions Are Cause for Alarm
A recent Cisco study revealed that complacency, ignorance, and low levels of security awareness among corporate senior management staffers contributed to major insider threat vulnerabilities. The study found that staff were becoming a big part of the insider threat problem.26 58 percent of staffers were aware of security threats and the risk they pose to corporate information. Disturbing as this finding is, one would hope that, upon reading the report findings, C-suite executives took immediate steps to change the attitudes and behavioral work habits of their senior staff members or, lacking success in that, found quality replacements who really understand and demonstrate their individual responsibilities about security. It seems that neither action was taken.
Similar survey findings suggest that the biggest cyber security threat firms face is not state-sponsored, geopolitical, or clandestine, but much closer to home: employees. Internal security breaches, including accidental ones, are caused by careless employees, and results are indicative of noncompliance, misunderstanding of protocols, and failure to communicate effectively with security departments.
• 55 percent of Department of Defense officials surveyed identified careless and untrained insiders as the greatest source of (IT) security threats at their agencies.27
• One study reported that almost all (91 percent) of the companies surveyed had at least one external breach in the past 12 months.28
• Another study addressed management's knowledge of security vulnerabilities and attacks. In this study, 35 percent of the respondents said that they had experienced an insider attack, whereas 34 percent indicated that the threat was not even a management priority.29
• Yet another survey30 of 240 senior IT decision makers found that hackers were present on a network for an average of 229 days before being discovered. This is more than 7 months.
While most C-suite executives agree that protecting their company's confidential data and trade secrets from the prying eyes of competitors is important, 55 percent of senior IT security executives said they had discovered an insider taking information from the company's computer systems to use in a competing business.31
Other studies show similarly disturbing results32:
• 40 percent of CEOs believe they are making the wrong level of security investment or are unsure whether their investment is appropriate.
• 30 percent of board members understand or are aware of specific cyber security threats.
• 27 percent of CEOs cite cyber criminals as the most prominent threat.33
• 12 percent of CEOs cite state-sponsored cyber attacks as the greatest threat.34
• 8 percent of CEOs cite competitors as the biggest single security peril.35
One particular study focused on workforce behavior patterns and CEOs' confidence level regarding their employees:
• 75 percent of CEOs consider data leaks or malicious behavior by insiders as their number 1 risk.36
• 53 percent of CEOs say the main risk to corporate data and computer systems is human error, carelessness, or ignorance among their own employees.37
• 50 percent of CEOs worry more about their own employees turning rogue than about external cyber threats.38
Despite this, 61 percent of companies breached take no disciplinary action against employees.39
• When questioned, 79 percent of employees admit that their illegitimate actions had never been discovered.
• 47 percent of the workforce admits to removing confidential files and information from the workplace.
• 41 percent of employees admit to giving their password to coworkers and family friends.
• Of those employees who were caught:
• 67 percent said they were spoken to but no action was taken, and no report of their behavior was entered in their personnel file.
• 25 percent said nothing happened.
Other surveys revealed other statistics:
• 50 percent of security experts said their agency was likely to be a target of a denial-of-service attack in the next 12 months.40
• 40 percent of IT professionals said the increase in breaches had not changed the level of attention CEOs give to security or any budget increase for additional resources to handle the influx of hackers.41
• 36 percent believe employees can access or steal confidential information.42
• 32 percent of IT security professionals said they had never spoken to their CEO. Of those who did, 23 percent say they speak to the CEO only once a year.43
• 30 percent of U.S. CEOs said they are prepared to meet the growing threat of a major cyber attack.44
Few would argue that many companies are blind to data breaches, are complacent in their security measures, and have little or no contact with board members, local law enforcement, or the FBI regarding these matters.
### Employee Dependability and Reliability Cannot Be Trusted
Human error looms large. From misconfigurations and poor patch management practices to the use of insecure or default credentials and the loss of equipment to the disclosure of sensitive information through careless mistakes—human error accounts for 95 percent of security incidents.45
The cyber threat from within is the number 1 concern of most chief executives. Surveys reveal many telling conditions among the workforce. A study of breaches, commissioned by Cisco, revealed that many employees deliberately fail to adhere to security policies because of a lack of understanding and poor communication from their security department. A complementary study by Xerox also found that 54 percent of employees did not always follow their company's security polices, leaving the security of sensitive data at heightened risk.46
• 49 percent of employees said security breaches are caused by a lack of user compliance.47
• Another 49 percent of employees said compromises occur when other employees bypass security measures.48
• 36 percent of employees said breaches result from employee errors.49
• 25 percent of employees said breaches are caused by malicious insider behavior.50
Within the U.S. government, the biggest source of cyber threats is inept coworkers, rather than intentional leakers.51
• Careless or poorly trained employees account for 53 percent of security breaches.
• Foreign governments account for 48 percent of cyber invasions.
• General hacking accounts for 35 percent of security breaches.
• Terrorists account for 31 percent of security breaches.
• Employees bypassing security measures create 40 percent of security breaches.52
Employee dependability and reliability will continue to be a challenge for CEOs until they take responsible action to implement clear and distinct guidance regarding employee behavior and have the courage to consistently enforce violations of security practices.
### Ability to Detect and Respond to Breaches Requires Significant Improvement
No doubt, CEOs take a dim view of people who damage the company's image, brand, and reputation. I argue that inadequate qualifications, training, and budgets are the lead contenders responsible for performance ineffectiveness and inefficiencies. A recent study by the Sans Institute53 found that poor or no integration between security products had a tendency to negatively affect a response to cyber attacks. IT security professionals said they needed better, more compatible tools and a faster response to defend against cyber attacks. Key results of this study found that broad definitions of an incident place a strain on incident response (IR) teams, and that a lack of formalized IR plans and dedicated IR staff plagues most organizations.
Another Sans Institute study54 found that:
• 62 percent of responders said there is no time available to review and practices procedures.
• 60 percent of responders said key impediments hinder an effective response.
75 percent of responders indicated they did not have the ability to detail the human behavioral activities of an insider threat.55
The Ponemon Institute study found that 47 percent of IT security professionals felt frequently disappointed with the level of protection their security program offered their customers.56
A Meritalk survey concluded that detecting and responding to breaches requires significant improvement, whereas overall attitudes seem to indicate a high degree of overconfidence among many IT security practitioners.
• 95 percent of IT security professionals in these organizations are in agreement that they can detect a breach of critical systems within a week, but nearly all publicly disclosed breaches go for months without detection.57
• In that same Atomic Research study, 85 percent of IT security professionals report that point-of-sale intrusions take 2 weeks to discover.58
• 60 percent of IT security professionals believe their systems have been hardened enough to prevent breaches.59
• 43 percent of IT security professionals report that Web attacks take months to discover.60
• 40 percent of cyber security professionals said ensuring a user-friendly experience is a priority.61
• 35 percent of IT security professionals said it takes 2–3 days to discover a breach.62
Other studies report similar types of statistics:
• 74 percent of IT security professionals said their agency is not ready to support secure access from mobile devices.63
• 74 percent of IT security professionals said preventing theft of information is their top priority.64
• 67 percent of IT security professionals said their agency is not ready to fend off hackers.65
• 60 percent of IT security professionals are confident that security controls protect individuals' account information.66
• 38 percent of the IT security professionals surveyed said they do not have, or know of, any systems in place to stop employees from accessing unauthorized data.67
In another survey, 60 percent of IT security professionals indicated they are not prepared to respond to insider attacks.68
In yet another survey, 30 percent of U.S. companies reported that they have no system in place to stop employees from accessing unauthorized data. 48 percent of the companies said they changed passwords to stop former employees from gaining access to their systems.69
Based on survey findings, it might be in the best interests of these organizations to consider performing a formal assessment of their cyber security programs against these survey findings to enhance security resilience.
### Cyber Security Protocols Lack Clarity, Substance, and Usefulness
In Chapter A User-Friendly Protocol Development Model I talk about the many facets that contribute to poor clarity, consistency, and organization and, often, ineffective protocols. In that chapter I also emphasize that most protocols are cumbersome, outdated, and not user friendly.
Several Meritalk, Atomic Research, and Forrester studies reveal telling employee concerns regarding the effectiveness and user-friendliness of IT security guidance.
• 80 percent of users said security protocols distract from productivity.70
• 66 percent of employees viewed security directives as time restrictive.71
• 66 percent of users said security protocols are burdensome and time-consuming, and they cannot complete their work because of the security measures.72
• 60 percent of employees said work takes longer because of security protocols.73
• 54 percent of users said they struggle to keep track of their passwords.74
• 51 percent of IT professionals are somewhat confident in their security plan.75
• 36 percent of IT professionals had no confidence in their security plan.76
• 50 percent of employees said they were not aware of their company's current security protocols.77
• 48 percent of 1000 IT professionals included in a LogRhythm survey regularly changed passwords to stop former employees from gaining access.78
While protocols have their place, they are of little value unless employees understand their responsibilities and the rationale behind the rules, and are properly trained to use them quickly when responding to a cyber breach, or detecting it and stopping further future damage. Study findings strongly point out that security protocols do not meet these expectations.
So, how do you make sure that your organization's information assets are protected? The first line of defense is to develop clear, distinct, and user-friendly protocols with employee buy-in. The second line of defense is employee awareness. A more security-aware workforce can mean the difference between an employee preventing the next data breach and an employee becoming the next breach. The third line of defense is proper training and quality management oversight of workforce behavior trends.79
### Users Say Budget, Time, Resources, and Training Are Insufficient to Thwart Cyber Threats
• In a 2013 survey, Global Corporate IT Security Risks reported 60 percent of IT decision makers believe they are not given enough time or funding to develop effective IT security policies. 49 percent said they did not feel they had organized, systematic processes to deal with IT risks.80
• 28 percent of educational institutions said they are confident they had sufficient investment. In this same survey, only a third 34 percent of government and defense organizations said they have enough time and resources to develop security protocols.81
• 52 percent of the companies surveyed did not provide cyber security education to their employees.82
• 42 percent of employees said they receive adequate training.83
• Another study reported that respondents attributed their failure to respond to insider attacks to both a lack of training (55 percent) and budget (51 percent).84
Providing an adequate budget, resources, and time to prepare procedures and train personnel in these procedures must be a high priority of every CEO. Without this support from upper management, nothing will ever be accomplished.
### Monetary Consequences of Cyber Crime Have Reached a New High
The United States averages 5.7 million cyber attacks annually, and those are only the breaches we know about. Here is some interesting cost data that may make you raise your brows:
• The FBI estimates that American companies have lost a staggering $1.2 trillion (roughly $100 billion more than drug trafficking or heroin, cocaine, and marijuana) to theft of intellectual and proprietary information over the past decade. Currently, the FBI is prosecuting over 50 economic espionage cases a year and has seen a 300 percent increase in economic espionage investigations over the past 5 years.85
• Daily attempted or actual cyber attacks number in tens of thousands, costing corporations an average of $1.5 million a day in lost revenue.86
• System repairs resulting from cyber attacks exceed $130.1 million per year.87
• Only 3 percent of total breaches are classified as "noteworthy" (meaning significant). These breaches account for 75 percent of the total costs for security incidents and 95 percent of all costs related to image, brand, and reputation damage.88
• Costs to repair damage to image, brand, and reputation average $5.3 million per substantial event.89
• Those surveyed say a serious security incident costs large companies an average of $649,000 and small to medium-sized companies an average of $50,000.90
• In 2013, the U.S. government spent $11.6 billion to protect classified information.91
• The estimated cost to US companies and consumers to defend against cyber attacks is up to $100 billion annually.92
• The growing cost of cyber crime on the global economy is $575 billion a year—more than the value of many countries' economies.93
• The average cost of cyber attack clean up after each serious breach is $1 million.94
• The average cost of cyber crime is 11.6 million per US company.95
• Breaches and damages caused by employees reach $3 million to $4 million per year,96 yet, as reported earlier, insiders who threaten the entire corporation are seldom disciplined, fined, demoted, or fired from their jobs.97
## Conclusions
Today, more information is carried or sent out the door on removable media in a matter of minutes than the sum of what was given to America's enemies as hard copies throughout history. Consequently, the damage done by malicious insiders and hostile nation states will likely continue to increase unless we create effective threat detection programs and enforce the implementation of such programs so cyber threats can be proactively identified and mitigated before they fully mature.98
### Public and Private Sectors Struggle to Build Security Resilience
Our understanding of cyber threats is limited because available statistics on cyber security are poor, contradictory, and sporadic at best. Compilations of cyber attacks and violations within the private sector rely on voluntary reporting and surveys. Interviews with chief information officers and other security officials indicate a widespread reluctance to report most intrusions, even attempted ones. Unfortunately, CEOs and other decision makers have the tendency to look at cyber security as just another expense. From a risk-management perspective, many CEOs simply do not see cyber protection as a bottom-line activity.99
However, costly and devastating cyber attacks continue to plague both public and private sectors and individuals, suggesting that the present cyber security strategies are not very effective.100 As a nation, our cyber security responses have failed to address the extent and nature of cyber threats. Even though we have the technology to eradicate the problem, the politicians in Washington view political correctness as a sound strategy. This is a good example of politicians (from both parties) not doing what they are elected and paid to do.
### We Are Dealing with Outside Experts and Cunning Insiders, Not a JV Team
Well-funded and businesslike adversaries using extremely sophisticated, targeted attacks dominate the cyber threat landscape,101 as do malicious and negligent employees who victimize their own organizations by continuing to put them at grave risk.
The increase in foreign state-sponsored cyber breaches illustrate an important and alarming shift in the cyber threat landscape as these global adversaries increasingly leverage cyber strategies to exploit vulnerabilities to further their own national interests. State-sponsored data breaches should serve as a wake-up call for organizations of all sizes and in all industries, public and private, to act in a responsible manner to preserve and protect not only their current investments, but also future aspirations to grow and prosper.
### Our Approach Is Not Working: We Need to Change Our Strategy
While companies and governments spend billions on technology solutions to deter, detect, and deflect unauthorized access and network intrusion, breaches keep happening. Why? Clearly, our efforts are not working. We are not keeping pace with the threats we face. We need to change how we think about and approach cyber security. We need to think outside the box, abandon self-interest and personal agendas, and start thinking "total quality management" 102 for the betterment of the entire organization and the nation. I encourage the reader to consider these ideas when developing your cyber security plan.
• Stop thinking about data breaches as external threats. More than 90 percent of all reported breaches are attributed to the actions of a trusted insider, and 90 percent of those could have been prevented if established protocols were in place and management did its job.103 It is time to design a better-quality workforce.
• We need an in-depth screening process. While organizations work to screen out applicants with specific stability issues, the absence of these traits does not ensure that the individual is not predisposed to compromise national security after being hired. Those who act because of conscience issues and moral ambiguity—traits that are not so easily detected—demonstrate this. Current investigation techniques and even polygraphs can only bring to the surface past nefarious behavior. They cannot predict future malicious behavior. The best weapon to ferret out undesirable and unethical employees, in addition to an intensive background investigation, is a penetrating interview to detect personality traits that would lead one to question whether the individual can be entrusted with serious secrets.104 However, industry leadership is not yet ready to "intrude" on potential hires in this manner.
• Conscientious and quality supervision must include enjoining supervisors and managers at all levels of hierarchy to monitor employee anomalies and, when necessary, take immediate reasonable and prudent steps to safeguard business investment and interests. Such intrusiveness is viewed by many as "spying" on employees rather than overseeing social behavior and work patterns.
• While we must accept that traditional IT security measures are essential, it is also time to embrace a more comprehensive philosophy that views security through a holistic lens that incorporates the physical, technical, and administrative risks across the entire organization, including third-party threats and the insider threat lurking within. Only through this approach can we identify vulnerabilities and prevent a serious data breach from occurring in the first place.
• Organizations must create a security culture and encourage vigilance across the entire spectrum of the company. Every employee, from the janitor to the CEO, must receive frequent, up-to-date security awareness training. Specialized cyber training for employees on phishing attacks, anomaly detection, and other techniques used by hacker groups is essential so they can perform their jobs more efficiently.
Since most data breaches occur because of inept, careless, or resentful employees, an "insider threat program" must include:
• continuous monitoring and evaluation of personnel
• procedures for reporting anomalous behavior
• assessment of individuals' reliability and trustworthiness
• establishment of an integrated capability to monitor and audit computer network user activity
• implementation of the "two-person rule" for access to the greatest level of sensitive information and system activity
Today's harsh realities require organizations to have comprehensive cyber IR plans ready to execute at a moment's notice. IR plans, in concert with the other security emergency response plans and procedures that are custom designed to meet the security needs of each organization, are undeniably a critical component of an organization's security strategy to establish and maintain security resilience.105
### American "Exceptionalism" Is Disappearing: We Must Take It Back
Corporate espionage is the highest that it has ever been in the history of the United States, and cyber intruders are using every unethical and criminal means to acquire data that will give them a competitive or financial advantage over their competitors. Cyber spies are stealing valuable trade secrets, intellectual property, and confidential business strategies. Top-secret defense information and other U.S. classified information have been stolen over the past decade, and this crime is spiraling at a rapid pace. Despite the efforts of corporations and the government, cyber attacks and cyber espionage continue to grow at an exponential pace, and cyber intrusions into corporate networks, personal computers, and government systems are occurring every day by the thousands. The threat of state-sponsored attacks is extremely serious for all entities, public and private, with attacks being launched on a regular basis, 24/7. And the trusted insider who wishes to steal information is in a key position to obtain it.
### Human Fallacy Is Our Greatest Weakness: Let Us Do Something About It!
One of the greatest challenges CEOs face is managing the human side of the enterprise. Today there are more threats, more vulnerabilities, more portable storage devices, and increased mobility. That means that educating employees about security is more difficult, demanding, and necessary than ever before. Employees are the weakest link in the security chain because they are not trained to be security-conscious, are not responsible and accountable for their actions, and are not properly supervised. A report by Ernst & Young found that "security awareness programs at many organizations are weak, half-hearted and ineffectual." As a result, employees ignore them.106 The best strategy is to teach employees on a continual basis the perils of human error and inattention to security protocols (Sullivant, 2007, pp. 14–44).
### We Must Act Responsibility and Be Accountable for Our Actions
Chief executives can no longer ignore the possibility of cyber attacks. Five critical elements are essential in establishing a successful cyber security program.
1. CEOs must aggressively enforce a vigorous information and cyber security program.
2. CEOs must allocate the necessary resources and funding to support the program.
3. Everyone from the CEO down must get involved and buy in to the program.
4. All individuals must be adequately trained and their performance continually monitored.
5. No program can be successful without the collaboration of security, legal, human resources, and the user departments.
Companies have gone out of business because of economic espionage, and large companies are losing billions of dollars. The economic espionage problem is serious, and corporations have a responsibility to deal with it in a responsible manner.
### Only Our Willingness Stands in the Way of the Sharing of Intelligence Information
Not only are thieves learning to steal millions of credit card numbers and email addresses, they have access to elaborate pieces of malware that are capable of spying on whole organizations for long periods of time, capturing computer screens, key strokes, and data, and transmitting it all to distant servers without being detected.107
Because of this emerging threat, federal agencies, particularly the FBI, now believe sharing information with the public is more important than ever before. The FBI recently announced that it cannot fight this new cyber threat effectively without help from the private sector, and it is looking to share threat information with companies and to get companies to share intelligence from their product divisions and from their general employee population.108
### We Must Gain Executive Management's Trust, Get in Front of the Issues, and Stay There
In the world of IT security, threats are constantly evolving and shifting. It is critical to stay abreast of the current emerging threat landscape. Keeping up to date with security threats helps you to mount defenses that are more effective and to educate your users. User education is important, yet is an often-overlooked element of IT security. Users must avoid being easy prey, especially in the case of phishing fraud.
### CEOs Face Great Challenges and Must Rise to the Occasion
The challenge for CEOs is formidable. They must:
• recognize emerging cyber threats and allocate sufficient resources, training time, procedural development time, and funding to stay ahead of new threats
• create an awareness of the company's weaknesses and the insider threat through enhanced security awareness training
• make cyber security risk management decisions based on the corporation's best interest to advance the bottom line, with no guarantee of being successful
• establish rules of behavior, codes of conduct, and ethic principles for the workforce
• acquire, equip, and train a staff that is technically and professionally skilled to design, develop, and implement cyber security measures, or, lacking that capability, seek professional security consulting expertise to achieve these goals and objectives
• foster a culture of security awareness throughout the company
The challenge for security professionals is equally formidable. They must:
• develop comprehensive yet simple cyber security procedures and incident response procedures and then train the workforce to use them effectively and efficiency
• adhere to best practices and hold employees accountable for their actions
• foster a culture of security awareness throughout the company
Employees must also accept inherent challenges, such as:
• complying with all security procedures
• accepting individual responsibility and accountability for their actions, particularly when they willfully ignore standards and acceptable practices or stray from fundamental and time-honored principles of security
• participating in fostering a culture of security awareness throughout the company and reporting security violators to supervisors
* * *
1 United States versus Manning, August 21, 2013.
2 <https://en.wikipedia.org/wiki/Edward_Snowden>.
3 FBI National Press Office Release, Washington, DC, February 21, 2001.
4 <https://en.wikipedia.org/wiki/John_Anthony_Walker>.
5 <https://en.wikipedia.org/wiki/Daniel_Ellsberg>.
6 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, September 2013.
7 See footnote 7.
8 See footnote 7.
9 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, May 2014.
10 The Federal Government's Track Record on Cybersecurity and Critical Infrastructure. A Report Prepared by the Minority Staff of the Homeland Security & Government Affairs Committee. Senator Tom Coburn, MD, Ranking Member (3), February 4, 2014.
11 <https://www.washingtonpost.com/world/national-security/2014/03/24/74aff686-aed9-11e3-96dc-d6ea14%20c099f9_story.html>.
12 Thousands of companies having prime contracts, many classified are continuing targets of espionage spying by China, North Korea, Iran and other countries.
13 Retrieved from: <http://www.reuters.com/article/2014/08/22/us-usa-security-contractor-cyberattack-idUSKBNOGM1TZ20140822>.
14 The Lipman Report, March 15, 2014, Exclusively for Management; <http://www.guardsmark.com/files/crime/TLR_Mar_14.pdf>.
15 <https://www.nsi.org/Security_NewsWatch/NewsWatch/1.21.15.html>.
16 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html>.
17 Retrieved from: <http://venturebeat.com/cagtegory/security/>.
18 Ibid.
19 Retrieved from: <http://venturebeat.com/2014/09/03/victim-to-a-mysterious-cyber-attack-home-depot-struggles-to-find-out-what-went-wrong?/>.
20 See footntoe 21.
21 Retrieved from: <http://venturebeat.com/2014/08/18/hackers-stole-data-from-4.5-million-u-s-patients/>.
22 Ibid.
23 Retrieved from: <http://www.com/azrticle/2014/08/22/us-usa-security-contrazctor-cyberattack-idUSKBNOGMITZ20140822>.
24 Retrieved from: http://venturebeat.com/2014/07/30/Canda-Says-China-Guilty-Of-Cyber-Attack-On-To Research-Organization/.
25 Lieberman Software Corporation, Black Hat USA 2013 Conference, Las Vegas, NV. E&T Magazine, September 14, 2013. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.4.14.html/>.
26 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/1.14.15.html/>.
27 SolarWinds Survey, 2015. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/1.25.15.html/>.
28 eSecurityplanet.com. Retrieved from: http://nsi.org/SecurityNewsWatch/NewsWatch/6.4.14.html/, (accessed 02.09.14.).
29 Retrieved from: <http://venturebeat.com/2014/09/03/victim-to-a-mysterious-cyber-attack-home-depot-struggles-to-find-out-what-went-wrong?/>.
30 Itgovernance.com.uk/boardroom-cyberwatch.aspx. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.9.14.html/>.
31 Courion Corporation, Annual User Conference, May 2014, Boston, MA. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.4.14.html/>.
32 IT Governance's Boardroom Cyber Watch 2013 Survey. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.10.13.html/>.
33 Ibid.
34 Ibid.
35 Ibid.
36 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.23.14/>.
37 IT Governance's Boardroom Cyber Watch 2013 Survey. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.10.13.html/>.
38 Ibid.
39 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html/>.
40 Meritalk surveyed 100 cyber security professionals and 100 employees within the federal government. Survey results are indicative of noncompliance and failure to communicate effectively. Meritalk.com/cyber-security-experience-register.php. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
41 Atomic Research surveyed 102 financial organizations and 151 organizations in the United Kingdom, all of which process card payments. Government Security News, June 25, 2014. Retrieved from: <http://nsi.or/SecurityNewsWatch/NewsWatch/6.25.14.html/>.
42 LogRhythm survey of 1000 IT professionals. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html/>.
43 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.23.14/>.
44 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.13.14.html/>.
45 2014 Cyber Security Intelligence Index, IBM, NY, 2014.
46 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/9.13.14.html/>.
47 Meritalk.com/cyber-security-experience-register.php. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
48 Meritalk study. Retrieved from: <http://nsio.org/SecurityNewsWatch/NewsWatch/8.21.14.html/>.
49 Ibid.
50 Forrest study. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch.8.21.14.html/>.
51 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.3.14.html/>.
52 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
53 Threat Intelligence & Incident Response: A study of U.S., Europe, Middle East and Africa (U.S. & EMEA) Organizations, Sans Institute, IL, August 2014. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.18.14.html/>.
54 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.14.14.html/>.
55 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/9.1.14.html/>.
56 Ponemon Institute surveyed more than 160,000 security professionals in 15 countries to determine the challenges they face in dealing with cyber security threats. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.23.14.html/>.
57 Atomic Research surveyed 102 financial organizations and 151 organizations in the United Kingdom, all of which process card payments. Government Security News, June 25, 2014. Retrieved from: <http://nsi.or/SecurityNewsWatch/NewsWatch/6.25.14.html/>.
58 Ibid.
59 Meritalk study. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.21.14.html/>.
60 Ibid.
61 Meritalk surveyed 100 cyber security professionals and 100 employees within the federal government. The survey results indicate noncompliance and a failure to communicate effectively. Meritalk.com/cyber-security-experience-register.php. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
62 Ibid.
63 Meritalk.com/cyber-security-experience-register.php. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
64 Ibid.
65 Ibid.
66 Ibid.
67 LogRhythem survey of 1000 IT professionals. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html/>.
68 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/9.1.14.html/>.
69 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html/>.
70 Meritalk.com/cyber-security-experience-register.php. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.17.13.html/>.
71 Meritalk study. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.21.14.html/>.
72 Ibid.
73 Meritalk study. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.21.14.html/>.
74 Ibid.
75 Atomic Research: Government Security News, June 25, 2014. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.25.14.html/>.
76 Ibid.
77 Forrester study. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/8.21.14.html/>.
78 LogRhythem survey of 1000 IT professionals. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html>.
79 Retrieved from: http://nsi.org/Securitysense/what-is-security sense.shtml.
80 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, December 2013.
81 eSecurityPlanet.com. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.4.14.html/>, (accessed 02.09.13.).
82 Ponemon Institute surveyed more than 160,000 security professionals in 15 countries to determine the challenges they face in dealing with cyber security threats. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.23.14.html/>.
83 LogRythem survey of 1000 IT professionals. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/4.16.14.html/>.
84 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/9.1.14.html/>.
85 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, May 2014.
86 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/3.27.14%20html/>.
87 See footnote 88.
88 2014 Cyber Security Intelligence Index, IBM, NY, 2014.
89 Ibid.
90 eSecurityplanet.com. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/6.4.14.html>, (accessed 02.09.14.).
91 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.9.14%20html/>.
92 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/3.27.24.html/>.
93 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/1.14.15.html/>.
94 Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/10.10.13%20html/>.
95 Ibid.
96 Ibid.
97 Lipman, Ira, A., Founder & Chairman, Guardsmark. The Lipman Report (pp. 2–5), March 15 2014.
98 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, December 2013.
99 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, May 2014.
100 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, April 2013.
101 2014 Cyber Security Intelligence Index, IBM, NY, 2014.
102 Total quality management presents a dramatic rethinking about how decisions are made, how work is evaluated, and how communication is conducted in the workplace. Schmidt, Warren, H. and Finnigan Jerome, P. Finnigan, TQ Manager, Jossey-Bass Publishers, San Francisco, 1993.
103 <http://nsi.org/SecurityNewsWatch/NewsWatch/1.21.15.html/>.
104 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, April 2013.
105 <http://nsi.org/SecurityNewsWatch/NewsWatch/1.14.15.html/>.
106 Szady, David, W., FBI Assistant Director, Retired. Security Management, The Time for Urgency Is Now, May 2014.
107 See footnote 108.
108 WSJ.com, <http://nsi.org/SecurityNewsWatch/NewsWatch/9.17.14.html/>, (accessed 15.09.14.).
6
# Establishing a Security Risk Management Program Is Crucial
## Abstract
This chapter zeros in on the criticality of establishing and maintaining a realistic and practical risk management program that can demonstrate to chief executives how well the security organization is performing and determine the significant shortfalls organizations confront is achieving competencies and expectations, as well as the challenges organizations face to correct deficiencies, weaknesses, and inadequacies. A security risk management framework and architecture platform is offered for adoption. Actual case histories are offered throughout the narrative to clarify or emphasize a particular point made.
### Keywords
Detect and assess; Deter and delay; Effectiveness, efficiency, and productivity; Measurement and evaluation; Performance; Probability versus likelihood; Response and recover; Responsibility and accountability; Risk metrics; Security resilience; Self-appraisal
Where no performance measurement standard exists, there can be no meaningful evaluation of mission ability and capability, and mission effectiveness, efficiency and productivity. Without these measurement criteria to baseline an endeavor, any investigative process such as a security assessment, audit, or inspection is just an exercise in the waste of time, money and resources, producing embarrassing personal opinions and speculation rather than objective analysis, defendable facts and professional judgments.
John Sullivant
Top Takeaways
• Learn the purpose and need for a risk management program
• Learn how to measure security organizational performance
• Understand how measurement and evaluation establish organizational creditability
• Learn how to use a successful risk management framework and architecture platform
## Overview
Did you know that nearly two-thirds of upper management believes that security is stronger than it actually is, whereas only less than a quarter of top executives are aware of their company's true security resilience posture?1 Costly cyber attacks are not almost routine for businesses, but while many organizations are focusing on external attackers, companies may want to know that the largest single cause of confidential data loss is due to employees—more than 42%. Nearly three out of four companies have suffered an insider threat event. According to the "IT Security Risks Survey" conducted by Kaspersky Lab and B2B International, 73% of companies have been affected by both intentional and unintentional internal information security incidents. Out of those, more than 21% of companies also lost valuable data that subsequently had some sort of negative effect on their business. Fraud committed by employees is a major issue. The survey found that 15% of organizations encountered situations where company resources were used by employees for their own purposes. The losses caused by these incidents exceeded the damage caused by confidential data leaks for enterprises by outsiders. As you will recall, in both Chapters The Evolving Threat Environment and The Cyber Threat Landscape, I talked about the perceptions of several chief executive officers (CEOs) many years before the survey cited above was conducted. My findings, and those of many of my colleagues, refute the majority of CEO beliefs expressed in that survey. I find it astounding that almost two-thirds of the nation's top CEOs are in the dark about the true security readiness2 of their corporations. This gap in perceptions, knowledge, and understanding of the strengths and weaknesses of a security organization by respectable top management should be great cause for alarm. It is time for executive management and top security professionals to bridge the gap between "what is" and "what is not," and to earnestly work together to develop an executive and securisty management communications plan to narrow this gap. Nothing is more discouraging than having your ideas ignored, your presence taken for granted, or failing in your attempt to be successful (Schmidt and Finnigan, 1994, pp. 1). The secret to being successful is picking yourself up when you fall, picking up the pace should you slow down, and believing in yourself when others do not.
Risk management is a strategy of security activity and the cornerstone of security governance. It is important for every security organization to have in place a realistic risk management program that can show executive management how well the security organization is performing its prime mission or, conversely, where the organization fails to perform to expectations. The goal of a security risk management program is to help security organizations become more productive; to determine the effectiveness of security policies, procedures, practices, and security measures; to ascertain the readiness of critical operational abilities and capabilities; and to determine the quality of management, leadership, staffing, and training while reducing the level of risk exposure.
To be of value to an entity, the security risk management program must be based on a set of acceptable performance standards, rules of behavior, and expectations that service the security organization, with a focus on those areas that matter most to C-suite executives. In sum, risk management is the process of constructing, measuring, evaluating, selecting, implementing, and monitoring actions to alter the presence of risk.
## Risk Management Measures and Evaluates Risk Exposure and the Ability to Deal With Threats
The management of risk requires effective measurement and understanding of what effect vulnerability has on the level of risk. Both risk and vulnerability constantly change in response not only to threats and hazards but also to the business objectives. Organizations need a mature risk and vulnerability identification, measurement, and management process. In Appendix A, I highlight a proven strategy and model that can be adopted by any security organization.
A well-orchestrated security risk management program reflects the culture and character of the corporation and its security organization. To determine the effectiveness of security abilities and capabilities, as well as performance expectations, measurement and evaluation must be grounded in critical security functions. A reliable and valid measurement and evaluation program permits you to speak to corporate leadership in a familiar business language.3 A sound program is vital to any security organization and is an important element of overall security management responsibility and accountability. Measurement and evaluation play key roles in examining the effectiveness, efficiency, and productivity of security performance. Without a compelling program, security professionals and budgets will never achieve aspiring goals and objectives.
### Purpose and Need for a Security Risk Management Measurement Program
Executive management has a right and need to know how effective, efficient, and productive his or her security organization is, but what does this really mean? Do you really understand the significance of this commitment and how it affects your organization? In a risk-based environment, a business-oriented audience wants to know:
• How well are things going? If not well, how long have conditions existed?
• What are our risks? What is our posture? What do we do about it?
Communicate well the answers to those questions and you have won the battle. Articulate what works and what does not work, and you have won the war.
### Identifying Security Successes and Failures Is Crucial
Evaluating performance effectiveness simply identifies gaps in the security organization's ability and capability to accomplish its mission. It also helps to build a foundation for developing and implementing prioritized solutions (Sullivant, 2007, pp. 159). Such an effort may include any or all of the following:
• Analyze policies, processes, practices, protocols, training, prevention, and protection measures to determine the effectiveness of the security program, including its dependency partners, in preventing undesired security and risk-based events and their consequences from occurring.
• Identify the strengths and weaknesses of the security organization, its leadership, and staffing, as well as any corporate culture barriers that degrade performance.
• Analyze data collected, conduct interviews, and perform selected tests and exercises, including testing security systems.
The process focuses on answering the following questions and must be all-encompassing:
• What is the mission and overarching goals of the security organization?
• What assets, functions, and resources need to be protected?
• What threats, hazards, accidents, and disasters does the corporation face?4 To identify these conditions, risk management and risk analysis must be all-encompassing. What I mean by that is that it should include all reasonable threats and hazards; not all security- and safety-related events might pose the greatest risk or the greatest opportunities for risk mitigation. Many risk mitigation actions can reduce the consequence of many threats and hazards and must be evaluated on that broader basis.
• Which physical, cyber, and procedural security measures must the inside/outside adversary defeat to successfully penetrate a sensitive area, reach a targeted asset, carry out the mission objective, and affect an escape?
• How well do enterprise institutional drivers and performance strategies contribute to the effectiveness of the overall security program?
• How well has the enterprise integrated its program, system, and operational capabilities into its routine?
• What are the restrictions, limitations, and constraints of protection?
• Who is imposing such obstacles or what circumstances and conditions threaten performance?
## Subscribing to a Security Risk Management Program
Few security organizations adequately measure and evaluate performance, processes, and outcomes. Most have no clue how to accomplish this. The reoccurring deficiencies, weaknesses, and inadequacies I talk about in Chapters The Evolving Threat Environment and The Cyber Threat Landscape are testimonials to the inability of most organizations to measure and evaluate their own performance and to do so in an independent and objective manner. The consequences of not measuring or incorrectly measuring and evaluating security activity can be detrimental to an organization for various reasons. It could inhibit:
• Meaningful measurement and evaluation of the enterprise's security capability
• Executive management from holding the security organization accountable for effective performance and productivity
• The ability of security management to remain accountable for effective, efficient, and productive performance
These consequences could potentially create a management problem of the most fundamental nature; many security organizations do not formally measure performance because the resources, expertise, knowledge, and funding needed to do so are not readily available. Always remember that all problems are management problems before they become operating problems. Those measurement and evaluation programs that do exist are mostly presented at the conceptual level, with little or no guidance on how to effectively use them, how to ascertain what exactly needs to be measured, how to obtain measurements, and when and how measurement should be used. Two reasons exist for this condition.
First, there is no industry-wide standard for measuring and evaluating security organizations. Certainly, management is not in favor of allocating funds and resources for a noncompulsory program. Throughout the industry are several volunteer standards that have been developed by professional associations such as the American Society of International Security and the National Institute of Standards Technology, but few security organizations subscribe to these guidelines. Instead, they hazardously attempt to design their own programs, inventing the rules as they go along.
• At the very least, organizations typically pick and choose segments of these volunteer standards in an area of particular interest and attempt to perform in-house spot checks, convincing themselves they have properly measured and evaluated their security operations. However, they generally fail to separate critical activity from noncritical activity and to prioritize the most crucial functions.
• The regulated industries, such as energy, chemical, seaports, and civil aviation, have good measurement and evaluation programs, but these efforts fall under the purview of the regulators. Under this concept, the enterprise's and security organization's contribution to the overall process is to correct noted deficiencies or, alternatively, refute the findings. Few security organizations expend the energy, time, resources, and money to challenge a regulator's findings. Political correctness often embraces the status quo to maintain the peace with the regulatory agency and corporate senior management.
The second reason is that measuring and evaluating a security organization is time-consuming and requires unique talent and skill sets that are not normally available within a typical security organization. Most organizations simply fill out a checklist and file it. There are hundreds of checklists available—many are thorough and comprehensive, yet few are useful tools for measuring and evaluating performance. When the applicable blank sections of these checklists are filled in, one has only a document that shows compliance or noncompliance with a particular regulatory requirement, standard or code, or best practice. Checklists seldom touch on the human side of the enterprise. To find the answers you really need, more information and additional investigation are needed:
• Why particular items on the checklist were marked "NO"?
• How long have these conditions existed? Why do they exist in the first place? Why were these conditions not discovered earlier and are only now surfacing?
• Who approved these conditions and why? What are the root causes of the ratings?
• What actions could or should have been taken to prevent these unsatisfactory conditions?
• What was (or is) the impact of the unsatisfactory condition on up- and downstream operations, including dependencies and the supply chain?
• What security enhancements and improvements are needed? What steps are needed to prevent reoccurrence?
• Who needs to get involved in program fixes? Who needs to approve program fixes?
The crux of the matter is that you need more than a completed checklist to determine the performance effectiveness, efficiency, and productivity of any security organization. Unfortunately, many security professionals lack the time, expertise, or experienced staff to measure and evaluate their organization. Seeking outside consulting expertise can be extremely beneficial. For instance, a thorough and comprehensive performance, management, or financial audit could significantly increase your management knowledge base and minimize the damaging consequences of inadequate performance. It also offers opportunities to:
• Enhance corporate brand, image, and reputation
• Improve security management and leadership skills
• Improve work force performance, enhancing productivity and synergy
• Establish coherent, clear and distinct practices, and improve accountability
## A Risk Management Program Establishes Creditability
### What Are the Fundamental Aspects of a Risk Management Program?
Three of the many key aspects of risk management are performance, productivity, and risk.
• Performance is the measurement of the enterprise's ability and capability to achieve its critical operational objectives, usually stated in terms of accomplishment, such as planning and executing; the ability and capability to deter, delay, detect, prevent, protect, assess; security emergency planning; and the development of event-driven response and recovery procedures; as well as developing the capability to master these tasks.
• Productivity is the effort evolved and the cost incurred in achieving outcomes, usually stated in dollars or operational benefits, both tangible and intangible.
• Risk is the potential for injury or loss of life, or the damage or destruction of assets, functions, and other property. Risk has two parts: the likelihood of something happening and the consequence(s) of it happening.
You can do four things to improve and enhance the credibility and standing of your security organization: ensure quality service and performance, develop relationships, build teams, and continuously improve performance. Let us see how you might benefit from adopting each of these approaches.
### Quality Service and Performance Must Be Your Number One Priority
In the overall scheme of things, your customers—both internal and external—are the people and organizations you service and perform for. You are responsible and accountable for setting the ultimate criteria for quality service. Satisfying the needs of your customers, including upper management, is your top priority. Lest the service you provide has slipped your mind, please recall that you engage in the greatest of tasks: the saving of life and the protection of critical facilities and assets through the successful application of risk management principles, exceptional execution of security management oversight and leadership, and the dedication to advance the profession.
### Developing Relationships Is a Key Condition for Success and Your Second Priority
Your second priority is to establish and maintain a business climate of openness and trust. When a problem occurs, it is time to honestly state the facts. There is no time for hidden agendas. What should be in question is whether the root causes of the problem have been correctly identified and whether the fix is the right solution. Any other issues are secondary in nature; often they are not important enough to detract you from fixing the problem. Where trust is high, ideas and communications flow easily. Barriers between divisions and departments and people are minimized. More work is done in teams, many of which may be interdepartmental and multidisciplinary. Most important, teams view errors and problems as opportunities for learning, rather than blunders to be punished. Where trust is low, however, everything becomes more complicated. People hesitate to point out problems, suggest new ideas, or take responsibility for mistakes or omissions. The most critical element, of course, is the solid commitment of top management to embrace and participate in open communications and trustful professional relationships.
### Building Teams for Creative Thinking and Achievement Is Priority Three
Priority three is to acquire new skill sets as well as to refine your current skill sets. The way of doing business as a "loner" has long passed—if ever it existed in the first place. There is no room in today's business world for the self-centered leader who expects sole recognition for all accomplishments, whether performed by others or not. Successful leaders seldom receive public recognition, and most of us seem to be fine with that. An occasional pat on the back, however, is nice. As an alternative, praise your people and recognize their contributions to the organization. Executive management will notice them, and you.
To be successful, build teams: Building skill sets is crucial to problem solving, planning, and learning. If workers are expected to behave differently, they have to be trained differently. They must feel comfortable with new protocols, processes, and practices, and understand their significance in a healthy work environment. When groups work well they provide a level of satisfaction and expertise that energizes and inspires others. When a team solves a problem, every member of the team is recognized. When a group achieves its goal, everyone celebrates. There is little doubt that the exhilaration that comes from being part of a successful team is different from the satisfaction that comes from individual achievement. Setbacks or disappointments are also easier to manage as a member of a team.
### Continuously Improving Performance Is Priority Four
The quest to learn and improve performance is a work in progress—it never stops. Priority four is to keep up with industry and enterprise changes, and new practices and technologies. You cannot settle for just getting by. As long as things are not perfect, there is room for improvement. The singular standard operating procedure you should follow is that on the plaque hanging on your office wall behind your desk: "Keep doing better." If all things are perfect, then your standard operating procedure is to make sure they stay that way.
## When to Measure and Evaluate Performance
One of the goals of any security assessment is to analyze (that is, to measure and evaluate) security performance. Such as assessment should be conducted at least every 24 months, or more frequently, when:
• Operational requirements or business goals and objectives change significantly
• Capital improvement efforts call for the security review of new facility security designs
• The level of threat, hazards, accidents, and disaster conditions change significantly
• A threat advisory notice calls for the assessment of security abilities and capabilities
• Existing processes, practices, and security technologies are no longer practicable
• A significant amount of the security workforce rotates or transitions to another organization, or its leadership element is no longer functional.
Inspections and audits are typically performed as mandated by law or industry standards, or to ease management and board anxieties to ensure operations are accomplishing their intended purpose. Measurement and evaluation can be accomplished either internally by the organization as a self-appraisal, or externally by a qualified security consultant.
While self-appraisals can be a good management tool, they have limited application and usefulness. I am not a fan of self-appraisals; they seldom produce intended results because they are generally biased, lack objectivity and independence of thought, and are usually influenced by "working politics."
Second, such appraisals are usually constraint by time and the availability of qualified resources. Since self-appraisals measure and evaluate one's own performance, in-house resources conducting them may not be clear about the root causes of any of the deficiencies, weaknesses, or inadequacies they observe, or they may be hesitant to document and report factual information that could embarrass the boss. When these conditions prevail, self-appraisals have a tendency to give executive management incomplete, outdated, or erroneous information. One can expect that such results often project a false sense of security and potentially lead to vulnerability creep-in downstream.
Conversely, an evaluation performed by a qualified security consultant could easily perform an in-depth, independent, and unbiased examination of the security organization that results in objective judgments free of any internal or external influences, including working politics. The metrics these professionals use have scientific merit and value to the organization, focus on the enterprise's risks and goals, and consider operating reasonableness. The results of such professional services show promise of significantly enhancing and improving security resilience. These services can entail all aspects of a security organization or be an endeavor focused on a particular area of interest to senior management. A clear and distinct request for a proposal and statement of work is the vehicle to use to obtain such services.
## A Risk Management Program Is Key to Performance Success
Appendix A describes a proven integrated framework and architecture design that resonates with executive management. It can produce results. The framework consists of measurement and evaluation processes, and the relationship between measurement and evaluation. The architecture platform consists of risk-based metrics5 that involve performance analysis,6 risk analysis,7 and diagnostic analysis,8 as well as the evaluation tools used most by security organizations. The risk framework and architecture is not a one-size-fits-all solution using all elements, all the time. Tailoring the framework to a selected assessment methodology for a specific application can be useful in combining or eliminating tasks (for example, moving from a conceptual approach to a procedural one), providing clarity and detail to certain tasks. Conceptual frameworks may or may not explicitly specify an order for task activity or the flow of information between tasks, and they do not specify techniques or provide specifics with respect to data and measures. Procedural frameworks are more detailed and structured than conceptual frameworks and do indicate the order of tasking and the flow of information, and specify the techniques used to perform each task. They may or may not specify the data and measures used.
## Executives Need Compelling and Persuasive Information to Make Sound Business Decisions
Chief executives need compelling and persuasive information to help them determine whether the security organization possesses the ability and capability to perform its critical task—information that tells them whether, and in what important ways, the security program or activity is working well or poorly, and why. Attachment 1 further outlines some of the functional areas CEOs, boards, community governing bodies, and emergency response agencies have expressed an interest in over time. This listing is not all-inclusive, nor is it static. I offer these topics as a "straw man" tool to help you tailor your own listing to meet the specific reporting requirements that matter to senior management, boards, and community governing bodies. To honor the total measurement philosophy, you may wish to measure and report all areas to management, but this is usually not possible, practical, or desirable. Ideally, you should close the gap as much as possible between what must be measured and what is desirable to be measured. The narrower this gap is, the more comprehensive measurement and evaluation program you have. Despite any appreciation that might exist for the total measurement philosophy, the scope of measurement is not usually governed by a commitment to this ideal, but rather by a combination of factors unique to your corporate culture. The most influential are likely to be:
• The desire to remain fully accountable
• The cost of measuring and evaluating "all" activity versus "indispensable" activity
• The degree of enthusiasm for and resistance to further measurement and evaluation
• The intensity of external pressure for more comprehensive measurement
In the final analysis the scope of measurement is likely to be a compromise between that which you would like to undertake and that which you can and must afford, financially and politically.
• The first step in the process is to determine which areas are to be measured.
• Then identify the activities not to be measured and document the rationale for your decisions.
• Prioritize the listing based on your mission statement and commitments.
• Add critical areas that may not be included in any program documentation.
• When you narrow down the listing to meet your specific needs, have a one-on-one sit-down session with your boss and the CEO to review the list. They will let you know what matters to them.
As mentioned earlier, the listing is not static. It often is seasonal and situational, depending on circumstances, conditions, and business activity.
## Conclusions
A comprehensive measurement and evaluation program can identify and significantly reduce security deficiencies, weaknesses, and inadequacies. Experience shows that most litigation could be avoided with proper management foresight in planning and executing proactive security measures to minimize risk exposure.
One cannot expect either executive and security management decision makers to make sound security decisions if they are hampered by the lack of good information or lack of a solid management knowledge base. Decisions based on validated and reliable facts are usually the right choices.
## Appendix A: Risk Management and Architecture Platform
### Frameworks
#### Measurement
Measurement monitors productivity outcomes that support business goals and advance the security organization's progress in accomplishing its mission. It has value when an outcome is defined in absolute terms, not subjective or ambiguous descriptions. There are occasions, however, where outcomes such as "detect," "assess," and "respond" may be measured in relative terms because human behavior deals with abstract conditions, circumstances, and situations of uncertainty, the outcome of which is outside the control of, for example, a responding force. It supports policy decisions that improve security resilience. It can also serve as an early warning system to management and as a vehicle for advancing accountability. Measurement may address activities conducted (process), the products and services delivered (outputs), or the results of those products and services (outcomes).
#### Evaluation
Evaluation examines how well a program is working or not working. Evaluation examines the achievement of objectives in the context in which they occur; may assess a program's effects beyond its intended objectives or compare the effectiveness of alternative programs aimed at the same objective; and supports resource allocation and other policy decisions to enhance and improve productivity and security resilience.
## Relationship Between Measurement and Evaluation
Measurement focuses on whether mission objectives, expressed as an acceptable measurable performance standard, have been achieved. Evaluation examines security operations, or factors in the operational environment that may impede or contribute to its success, or help to explain the linkages between security inputs, outputs, and outcomes.
## Architecture Platform
The platform is made up of risk-based metrics and evaluation tools. Metrics establish the margin of expected human, technology, and process performance to achieve mission goals and objectives. Strategies address those critical areas requiring improvement or compliance that are most important to executive management.
Risk-based metrics measure security performance effectiveness and efficiency, and the productivity9 of critical security activities and critical security programs. The means used to achieve these results is met using performance analysis, risk analysis, and diagnostic analysis—all key elements of a comprehensive security assessment. The areas described in what follows may provide value.
### Performance Analysis
Performance analysis metrics measure the degree of effectiveness of various activities:
• Blast-resistant and fire-resistant structures
• Built-in security design for new or modified facilities and sites
• Capital improvement initiatives affecting security
• Compliance/noncompliance with regulatory requirements and other commitments
• Command, Control & Communications C3 capabilities and coordination and interaction with others
• Cyber security effectiveness
• Effort/time spent on primary/secondary responsibilities
• Electronic security application, deployment, performance, and maintenance
• Emergency response forces (eg, police, fire, medical, mutual assistance agreements)
• Filtering air against known pathogens and chemicals
• Human resource capital investment and social behavioral issues
• Interface/coordination with local, state, and federal law enforcement/security agencies
• Management, leadership, organization structure, staffing, experience, and expertise
• Next-generation security systems and architecture
• Obstacles that hinder processes, practices, and performance
• Platform for making better security decisions and shortening the decision-making process
• Policies, plans, protocols, practices, and process progress or lack thereof
• Secured corporate-wide web for crisis management analysis, response, and recovery
• Security design and engineering strategy
• Security force qualifications/certifications
• Security management knowledge base and leadership
• Security systems, communications, equipment, and facilities
• Security system downtime and compensatory security measures
• Security training
• Threat estimate profile
• Supporting major HAZMAT accidents and disasters
• Synergy with senior staff, business units, and external organizations
• Time-sensitive assessment capabilities
• Time-dependent delay, detection, deterrent, prevention, and protection capabilities
• Time-sensitive assessment and, event-driven responses, and recovery capabilities
• Topics of which management has insufficient knowledge
• Work performance and termination standards
### Risk Analysis
Risk analysis metrics measure the probability that something will happen:
• Criticality of threats, vulnerabilities, and assets10,11
• Dedicated backup power systems for security facilities and security systems
• Dedicated network for security system is ensured
• Emerging technologies that enhance security posture
• Emerging threats and vulnerabilities
• Consequences of losing critical assets and resources
• Incidents affecting image, brand, reputation, safety, health, and security
• Increased insurance premiums/negative press resulting from occurrences
• Likelihood of insider threat
• Likelihood of security system success or failure
• Likelihood of successful adversary engagement
• Likelihood of a threat, hazardous condition, accident, or disaster occurring
• Methodologies to accurately identify and predict actors perpetrating cyber attacks
• Predictable paths and methods of currently undetectable food, water, and air alteration
• Prevention and protection measures
• Security force's ability and capability to respond to and recover from risk-based events
• Repeat findings of noncompliance/failure to meet performance expectations
• Residual risk tolerance versus consequence impact
• Results of most recent security assessments, audits, inspections
• Risk tolerance versus consequence impact of "no decision"
• Severity of threats, vulnerabilities, and consequences of loss
### Diagnostic Analysis
Diagnostic analysis metrics measure the impact of functions:
• Business impact/performance costs
• Common business unit security areas that compliment/augment business activity
• Cost against budget/cost and risk reduction/performance/return on investment
• Cost–benefit analysis and cost estimating
• Employee and security force turnover rates and terminations
• Finance security impact on the bottom line
• Human and technology performance
• Prioritizing the allocation of resources and funding
• Prioritizing mitigation solutions
• Rank ordering of critical assets, processes, or functions
• Rank ordering of the criticality of threats, vulnerabilities, and consequences of loss
• Revising land use to compliment emergency planning
• Root causes of events or trends in activity
• Self-diagnosing and self-healing security systems
• Spatial clustering of critical infrastructures and assets
• Trends affecting critical business operations, risk, threats, vulnerabilities and consequences
## Evaluation Tools Mostly Used Within Security Organizations12
### The Physical Security Assessment
The physical security assessment is the forensic holistic evaluation of the "state of operational security readiness." It centers on the protection, robustness, and assurance of mission continuity and workforce protection essential to mission execution. Activities may include:
• Analyze threats and vulnerabilities that attract adversaries
• Analyze the consequences of asset loss against threats
• Assess program effectiveness of proposed mitigation solutions
• Benchmark program effectiveness
• Communicate program risks to build understanding of and confidence in the results
• Conduct interviews, review program documentation, and collect and analyze data
• Define project boundaries and scope of analysis
• Deliver draft/final report
• Determine circumstances and conditions influencing performance
• Determine political and social tolerance for acceptable residual risk exposure
• Evaluate personnel and training
• Evaluate plans, protocols, processes, and practices
• Help decision makers make informed decisions to reduce program risk exposure
• Help to monitor system mitigation solutions for effectiveness and continual improvement
• Identify asset criticality
• Identify program performance strengths and weaknesses
• Identify project goals and objectives
• Perform a cost–benefit analysis of the proposed program mitigation options
• Perform gap analyses
• Perform key client orientation
• Plan and coordinate project activities
• Prepare cost estimate of mitigation solutions and milestone schedule
• Present briefings to management
• Produce prioritized suggestions to reduce risk and improve performance
• Select mitigation solutions to reduce risk exposure
### The Cyber Security Assessment
The cyber security assessment is the forensic investigation of computer systems and networks. Cyber security assessments focus on the protection of system integrity from unauthorized access, misuse, or manipulation of hardware, software, and human interaction. Activities may include:
• Analyze the results of service denial or other consequences
• Analyze system threats and vulnerabilities that are attractive to adversaries
• Assess the acceptability of residual system risk exposure
• Assess the performance effectiveness of the proposed system mitigation solutions
• Benchmark system effectiveness
• Communicate system risks to build understanding of and confidence in the results
• Conduct interviews
• Define project boundaries and the scope of analysis
• Determine equipment change out, software updates
• Determine political and social tolerance for loss of data or services
• Determine system design modifications or acquisition of new systems
• Evaluate personnel and training
• Evaluate the physical and electronic security architecture
• Examine root causes of system breaches
• Help decision makers make informed decisions to reduce system risk exposure
• Help management monitor system mitigation solutions for continual improvement
• Identify critical cyber assets
• Identify project goals and objectives
• Identify system performance strengths and weaknesses
• Perform briefings
• Perform a cost–benefit analysis of the proposed system mitigation options
• Perform key client orientation
• Perform technical gap analyses of system controls, incident reports, and recovery plans
• Plan and coordinate project activities
• Prepared cost estimate of mitigation solutions & milestone schedule
• Produce prioritized suggestions to reduce risk and improve system performance
• Review system documentation and collect and analyze data
• Select mitigation solutions to reduce system risk exposure
### The Security System Technical Assessment
The security system technical assessment is the forensic technical assessment of a security system. The technical analysis centers on system performance, features, and human interfaces. Activities may include:
• Analyze backup systems, redundancy features, and fail-safe capability
• Analyze the results of service denial or other consequences against threats
• Analyze man–machine interfaces
• Analyze technology constraints and cascading effects stemming from system failures
• Analyze system threats and vulnerabilities
• Assess the performance effectiveness of the proposed system mitigation solutions and the acceptability of residual system risk exposure
• Assess system reliability, maintainability, and interoperability characteristics
• Assess the availability of qualified system operators to acknowledge and assess the severity of the incident, to make the appropriate decision to "up-channel" the report, and to dispatch a response team that is capable of handling the situation
• Benchmark performance, including human engineering considerations and usability
• Calculate the speed in which transactions and detection devices activate, signal transmissions to a monitoring console, and acceptable time delay for camera call-up after sensor activation plus the time the video transmission takes to reach a monitoring location
• Collect and analyze data
• Communicate system risks to build understanding of and confidence in the results
• Conduct interviews
• Define project boundaries and scope of analysis
• Determine equipment change-out, software updates
• Determine political and social tolerance for weak system performance
• Determine system design modifications or acquire new systems
• Evaluate personnel and training, and recommend improvements to training program
• Evaluate system technology application and deployment
• Examine root causes of system breaches
• Help decision makers make informed decisions to reduce system risk exposure
• Help management monitor system for continual improvements
• Identify dependencies and interdependencies between subsystem components
• Identify project goals and objectives
• Identify system performance strengths and weaknesses
• Perform a cost–benefit analysis of the proposed system mitigation options
• Perform key client orientation
• Perform technical gap analyses of system controls, system management, and cyber security plan, and coordinate project activities
• Produce prioritized suggestions to reduce risk and improve performance including milestone schedule
• Present briefings
• Recommend prioritized mitigation solutions
• Review system specifications and plans
• Select mitigation options to reduce system risk exposure
### The Technical Surveillance Countermeasures Inspection Review
The technical surveillance countermeasures inspection review is the technical forensic examination of selected offices, meeting areas, conference rooms, and other locations used to discuss highly sensitive business activities or confidential, proprietary, competitive-sensitive information; trade secrets and patients; and scientific data. The process uses technical sophisticated equipment to detect and find:
• Audio sounds and frequencies emitted by computerized technology
• Computer-related threats
• Electromagnetic spectrum, radiofrequency signals
• Hidden eavesdropping devices
• Hot spots inside walls
• Magnetic fields and electrical noise
• Objects inside walls
• Presence of technical surveillance devices
• Residual heat of a bug or power supply
• Technical security weaknesses
• Visual, electronic, and physical evidence of bugging
• Written report of findings, cost estimate of mitigation solutions and milestone schedule
### The Organization and Management Review
The organization and management review is the forensic examination of the organization's ability and capability to perform its critical mission. The review:
• Analyzes management leadership and use of resources, staffing, and budget
• Analyzes what does and does not work
• Benchmarks performance
• Communicates organizational strengths and weaknesses to build understanding
• Determines political and social tolerance for acceptable performance
• Examines the mission statement
• Examines individual and group performance effectiveness, efficiency, and productivity
• Examines processes, practices, and protocols
• Evaluates organizational synergy and customer satisfaction
• Evaluates personnel qualifications, experience, and certifications
• Examines training programs to determine performance effectiveness
• Helps management to monitor system mitigation solutions for continual improvement
• Produces prioritized suggestions to enhance and improve organizational performance
• Performs a cost–benefit analysis of proposed recommendations
### The Inspection Review
The inspection review is the forensic examination of a security organization to verify compliance with pre-established security standards and practices as described in policy and regulations in an effort to help maintain its security posture. Inspection teams use checklists to compare an organization's compliance with that outlined by an authoritative or regulatory body, the results of which are detailed in after-action reports provided to the responsible party. The inspection review:
• Determines whether program objectives, controls, processes, procedures, practices, and management are in place and report accordingly
• Examines plans, policies, and procedures
• Recommends corrective actions to be taken
• Reviews criteria to establish, check, maintain, and improve the management system against predetermined standards
• Tracks the status of improvements and their completion in a timely manner
### The Compliance Audit
The compliance audit is the forensic examination of a security organization's compliance or noncompliance with regulatory requirements and adherence to protocols, standards, codes, and other commitments to better the understanding of costs and benefits. The audit:
• Compares "what is" with "what should be" and provides feedback for corrective action
• Examines activity to ensure that fundamental, task-unique conditions for success are met
• Identifies any looming impediments that might slow down, hold back, or delay progress
• Identifies the effectiveness and efficiency of operations, facilities, equipment, protocols, management, and leadership
• Recommends correct actions
### The Special Study
The special study focuses on a concept of operation or the feasibility of an idea, process, or technology to support a broader range of goals and objectives. Research, development, test, and evaluation (RDT&T) activity is usually involved.
## Quality Assurance: Zero Defects
The cornerstone of this framework and architecture platform is ZERO DEFECTS. This removes the emphasis on statistical quality controls used for hardware and software, and places responsibility and accountability for quality performance in the hands of those delegated the authority to oversee the various segments of a security mission on a personal basis.
The concept of zero defects:
• Aims at stimulating individuals and groups to care about accuracy and completeness, to pay attention to detail, and to improve work habits and social norms
• Emphasizes personal motivation and instills pride of work ownership
• Emphasizes reducing errors and omissions to Z-E-R-O
For ZERO DEFECTS to be of value, the measurement and evaluation process must:
• Have clear, concise, and distinct objectives that define value
• Identify exacting activity, process, practice, and protocols that capture the interest of decision makers and stakeholders
Goals and objectives must have value and meaning to decision makers and stakeholders. SMART goals accomplish this.
S| Specific| Clear and unambiguous language understood by management
---|---|---
M| Measurable| Visible to quality performance, progress, and productivity over time
A| Attainable| Realistic, practical, and reachable; reliable, dependable, and creditable
R| Relevant| Operating reasonableness, which is linked to business goals and objectives as well as business risk
T| Time-bound| Clear start and end points; have final closure
* * *
1 <https://www.nsi.org/Security_NewsWatch/NewsWatch/11.18.15.html>.
2 "Readiness" and the terms "ability" and "capability" are often used interchangeably and have the same meaning. Refer to Appendix A, Security Risk Management & Architecture Platform.
3 "Persuading senior management with effective, evaluated security metrics". Research funded by the American Society for Industrial Security (ASIS) Foundation 2014: Alexandria, VA.
4 Threats are intentional manmade acts to harm and injury persons or damage and destroy property. Hazards and accidents are unintentional occurrences such as fire, explosions, oil spills, and production failures. Floods, tornados, hurricanes, earthquakes, and tsunamis are examples of weather related calamities and are a natural phenomenon, usually referred to as natural disasters.
5 Risk-based metrics gauge the value of both human and technology performance.
6 Performance analysis examines the effectiveness, efficiency, and productivity of human, and technology performance, including compliance to laws, industry standards or other guidelines.
7 Risk analysis is the process of dividing risk into its component parts: threat, vulnerability, and consequences. Risk analysis describes the nature and magnitude of risk exposure to critical assets from threats and hazards, and the likelihood of an occurrence and its consequences, including the relevant uncertainties.
8 Diagnostic analysis examines route causes of events, trends, conditions and circumstances; analyzes the criticality of threats, hazards, and consequences and the rank orderings respective criticalities; and examines the technical interfaces and dependencies of security systems.
9 Effectiveness, efficiency, and productivity standards or expectations differ among security organizations and are dependent on the specific mission, regulatory requirements, and the expectations of upper management.
10 Asset criticality and loss consequence are fundamental factors that weight on the types of solutions management considers, including prioritizing the allocation of resources and funding to those areas that require security the most.
11 In determining the threat environment, Probability of Occurrence (PA) is an important factor in the analysis and decision-making process.
12 While audits and reviews are typically performed on a standalone basis, we have seen a trend whereas many security organizations consolidate particular aspects of a management audit or review into the statement of work for conducting a comprehensive security assessment, including a security technical assessment. This approach may be cost-effective because it eliminates duplication of research, interview, and analysis time, which would be required in all instances for independent reviews, audits, and some inspections. Regardless of the cost savings realized, many organizations prefer to keep these activities independent of each other, while other organizations are mandated by regulatory or industry standards to keep them separate. Absent the need to keep audits, reviews, and inspections as separate entities, a holistic approach to identify performance effectiveness, efficiency, and productivity is recommended whenever feasible and practicable.
7
# Useful Metrics Give the Security Organization Standing
## Abstract
This chapter presents a series of risk-based metrics that are designed to facilitate decision making and improve performance and accountability. When integrated into the overall risk management program and used correctly, they can form the basis for long-term capital improvements. The chapter emphasizes how risk-based metrics can be used to measure the effectiveness of critical security activity, including performance capability; how well an organization can secure the enterprise against threats; and the effectiveness of its security emergency planning and response. The metrics presented here are risk-based, quantifiable, and qualitative measurements of a particular aspect of a security program, system, individual or group or unit—or the entire entity—that will help an organization protect its people, infrastructure, assets, and information. Using these metrics allows you to measure results that correlate objectives, risk, and investment and to speak to leadership in a familiar business language. A metrics framework and architecture platform is offered for adoption.
### Keywords
Accountable; Characteristics; Consequence; Manipulation; Performance effectiveness; Probability theory; Relevance; Reliability; Risk-based metrics; Timeliness; Validity
Not having metrics to measure our progress and competencies is frustrating in proving our value to executive management.
John Sullivant
Top Takeaways
• Develop solid metrics that defend solutions
• Minimize when you or your boss is wrong or surprised
• Save time while increasing accuracy and reducing mistakes
• Help executive management make the right decisions
• Use risk-based metrics to measure critical security functions
• Protect against cognitive bias that leads to mistakes
• Justify your arguments and recommendations
• Use practical risk-based metrics that resonate with management
• Use metrics that are persuasive and matter to executive management
## Overview
The basic security concept accepts the reasoning that no amount of security can keep a corporation or agency safe from every possible threat, hazard, accident, or disaster, and that all resources, assets, facilities, processes and practices cannot be given the same level of protection from such events. In other words, there is no such thing as perfect security, and there will never be such a scenario. Using risk-based metrics, C-suite executives can focus on key drivers and indicators of change to improve rigor, enhance understanding, and avoid pitfalls—always recognizing, acknowledging, and accepting the fact that there will always be a degree of residual risk, vulnerability, and consequences to deal with. We then enter the arena of prioritizing our prevention and protection actions, our detection and response and recovery capabilities, and our competencies.
Stakeholders in the information technology (IT)1 parts of the business must also make these decisions and not leave it up to IT professionals to assume this awesome responsibility. Doing so perpetuates the notion that IT risks relate only to IT. They do not. IT risks are only a portion of a much larger corporate integrated security risk management program.
Because of the diversity of security and its effect on the entire corporation or agency, security directors must adopt a provocative approach across the entire spectrum of security activity to determine the strengths and weaknesses of their organization. By default, this effort must focus on the capability of a corporation in general and a security organization in particular to perform its indispensable tasks—deterrence, delay, prevention, detection, protection, assessment, and response to and recovery from an adverse event—encompassed by the process of saving life and protecting assets. No other security mission task is more important than these. Embracing a set of risk-based metrics to address risk exposure and the performance effectiveness of these critical activities is fundamental to the creditability of a security organization.
## Risk-based Metrics Are Often Underestimated
The vastness of security issues that need to be dealt with and the limited amount of resources and funding available make it critical that the security practitioner choose wisely how to manage risk and not be managed or influenced by it. I have found that most organizations have an array of operational metrics that they use to report basic law enforcement activity, such as the number of criminal acts, traffic accidents, traffic violations, personal assistance calls, population and vehicle throughputs, and a myriad of other behavioral social activity. While operational metrics can be of value internally to a security organization, they seldom resonate with chief executives because they are neither linked to, aligned with, or part of the larger enterprise risk process or corporate business goals and objectives, nor do they directly contribute to saving life and protecting critical infrastructure and key assets.
Conversely, risk-based metrics help executive management drive business and security decisions and behavior, and form the basis for long term capital improvements. They enable policies, processes, and practices to influence collaboration for corporate-wide benefits, drive investment decisions, and guide strategic and profit center alignment.
Measuring the performance of a security organization also identifies opportunities to help chief executive officers (CEOs) achieve company goals. Integrating security risk-based metrics into the corporation's overall risk management program offers a CEO and the leadership team a viewpoint from a different company perspective. This effort helps senior management to further understand security's contribution to the corporation and the important role it plays (Sullivant, 2007, pp. 72–73).
Here I deliberately avoid operational metrics and instead focus on presenting security risk-based metrics that address a security organization's ability and capability to perform its prime mission: saving life and protecting critical infrastructure and assets. Some elements of the management team may find this to be a provocative strategy foreign to the current culture. One can expect these forces to resist change, attempt to hold on to their own "turf" rules, and argue the basis of "old school" principles. A risk-based strategy fosters and promotes team building and shared security responsibility that provide a road map for change.
## Setting the Metric Framework and Architecture Foundation
Sharing security responsibility punctures the "old school" concept and abandons the myth that responsibility is the internal province of the security organization. A well-designed metric can promote both a driving force and a starting point in determining the level of organizational security responsibility, and it can demonstrate how various organizations contribute to overall corporate security resilience.
## Well-Designed Risk-based Metrics Resonate with CEOs
Embracing a set of risk-based metrics is fundamental to a security organization's credibility, reputation, and ability to perform. Risk-related metrics serve executives exceptionally well, but risk-based metrics are only an indicator, not an absolute value for measuring. They serve as the first step in guiding security professionals to meet acceptable competency standards and are a vehicle through which security programs can demonstrate their measurable influence on a company's strategic, organizational, financial, and operational risks and profits.
Risk-based metrics can gauge the effectiveness, efficiency, and productivity of the most critical security activities, programs, and competencies that are of interest to management. Such metrics may be quantitative or qualitative measurements, or a combination of both. Risk-based metrics focus on the actions (and results of those actions) that security organizations take to manage the risk of image, brand, and reputation; the protection of people, assets, and information; and conditions and circumstances that affect the well-being of the workforce, business operations, and corporate survivability. When a company uses these metrics to formulate conclusions, the decisions made are more likely to be the right ones since they are grounded in scientific merit, strategic relevance, and operational reasonableness.
Appendix A, "Metric Framework and Architecture Platform," illustrates how these characteristics create the foundation for meaningful and useful metrics that are simple and quick to complete, provide results that are easy to explain to senior management, and, most important, address those factors that matter most to C-suite executives. The framework and architecture are also important because they provide a roadmap to communicate with executives in a language they understand and embrace. I dedicate Chapter How to Communicate With Executives and Governing Bodies, to this very important topic.
Security organizations can effectively use two categories of measurement: the theory of probability and the theory of performance. This chapter focuses on the theory of probability, whereas the theory of performance is the main theme of chapter A User-Friendly Security Assessment Model, chapter Establishing and Maintaining Inseparable Security Competencies, chapter Preparing for Emergencies, chapter A User-Friendly Protocol Development Model, and chapter A Proven Organization and Management Assessment Model.
## Theory of Probability
Probability theory is applied to the inseparable risk-based elements of the security risk management process (Sullivant, 2007, pp. 66–67):
• Serious damage to company assets, management, and business activities occurs.
• The life or the safety of the body or personal rights of management or employees is endangered by an incident or accident.
• The reputation of the company or the confidence in a brand is seriously damaged.
• Threat and vulnerability analysis is the probability that a specified threat, hazard, accident, or disaster may happen and the rank order of each outcome.
• Consequence impact analysis is the probability that an asset, facility, function, process, or resource may be injured, damaged, destroyed, or lost by a threat, hazard, accident, or disaster, and the rank order of the impact of each loss outcome.
• Competency analysis is the probability that a corporation possesses the ability and capability to perform its inseparable operational tasks to deter, delay, prevent, protect, and detect specified threats and other security-related functions; and to assess, respond to, and recover from such activity in a successful and timely manner.
• Shareholders, customers, business partners, and the public are seriously affected.
Probability is used to quantify some proposition, the truth of which we are not certain of. Certainty is described as a numerical measure, between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Thus the higher the probability of an occurrence, the more certain we can be that it will happen; it is thereby deserving of greater attention from management. While a lower rating also needs management's attention, it is not to be used as a tradeoff candidate for a higher rating. A proposition with a lower rating typically is considered for mitigation action as budgets and resources become available or is considered as residual risk tolerance.
This standard is useful in determining the degree to which critical infrastructures and assets need to be protected in an all-hazards environment that may affect business operations, should an incident occur. Here I offer a useful guideline for determining the process of ranking events and the protection of assets.
### Probability of Occurrence (PA) Criteria
Probability of occurrence (PA) criteria introduce planning variables into the decision-making process and add credibility to the analysis process (Sullivant, 2007, pp. 76–81). Fig. 7.12 graphically displays its integrated component parts.
Figure 7.1 Business consequence analysis. Source: Sullivant, J., 2007. CFC, CSC, CHS-IV, CPP, RAM-W, Diplomate, ABFET. Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving (Exhibit 7.7 Example Worksheet 18-Malevolent Acts & Undesirable Events by Los of Consequences and Probability of Occurrence (PA) page 150). Wiley & Sons, New Jersey.
In Fig. 7.1, the likelihood that something will happen is ranked in column 1 as high, moderate, low, not likely, and undetermined. Columns 2 and 3 transcribe the likelihood rating into both numerical and narrative values. The numerical designation is helpful if you desire to measure the range in quantitative terms, whereas the abbreviated narrative value is helpful if you want to measure the ranges in qualitative terms. Caution is in order when using a quantitative measurement for security matters that are largely uncertain predictions as they could give executive management a false sense of security risk conditions. My rationale for this judgment is offered in the paragraph that follows. Objective (or quantitative) probability considers the relative frequency of the occurrence, whereas subjective (or qualitative) probability includes expert knowledge as well as quantitative data considering an occurrence. Column 4 describes the risk exposure occurrence measurement in narrative form.
Determining a realistic PA is an important factor in the decision-making process. In the realm of security operations, analytical results, however, need not be based on the precision of a classical probability equation. As such, PA contains wide latitude for variation. The advantage of using PA is that absolute precision is not important nor desired. What is important is to identify specific threats, hazards, accidents, or disasters and associate their level of severity to business accomplishment or the consequences of business failure. Risk, then, is determined by applying a probability rating using accurate historical information; acceptable actuarial tables; established policy, standards, specifications, and procedures; and acceptable professional judgment. From a business perspective I have never been able to fully convince executive management that there is a 0.9 or 0.7 percent chance that something bad may happen. I learned that approach has little or no meaning or value to management, and it is difficult to ask management to allocate resources and funds to such a proposition. What has worked for me is building a business case on a "High" or "Moderate" likelihood that a specific event could occur, verified by a realistic forecast of potential business loss consequences. I have found management can relate to revenue loss, and if significant will act on any reasonable request to reduce business risk exposure.
When considering the effective performance of an electronic security system, determining the probability of security system success (PS)3,4 is based on quantitative measurement only. What I mean by this is that security hardware and software either works or it doesn't work. There is no room for shades of grey for technology to work only occasionally. When measuring technology performance and system capability you are addressing a simple pass/fail criteria. Nothing else is an acceptable alternative. Nothing else matters. As such, PS encompasses the cumulative effect of the following activities measured against specified standards of time constraints and performance levels.
• Probability of detection is the activation of an intrusion detection sensor.
• Probability of CCTV camera call-up is the activation of one or more cameras integrated with a sensor, card reader, door, or other security device.
• Probability of communications is the time it takes for a signal to transmit from the sensor to the monitoring station, possibly through one or more control panels.
• Probability of video display is the time it takes a signal takes to display on the designated monitor.
• Probability of assessment is a human measurement function and is the degree of speed and accuracy with which an individual can respond to an alarm, which includes reacting to an announced alarm, performing an initial assessment, and notifying a responding unit of the crisis.5
• Probability of response force encompasses a combination of human and technology attributes that examine the ability and capability of the response force to act. This involves arriving on the scene within a specified time; tactically deploying adequately and in a timely manner; using available technical and human expertise to effectively contain or neutralize the adversary; and prevent him or her from achieving a targeted objective or completing his or her mission.6
Figure 7.2 Business consequence analysis (CA). Source: Sullivant, J., 2007. CFC, CSC, CHS-IV, CPP, RAM-W, Diplomate, ABFET. Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving (Exhibit 7.7 Example Worksheet 18-Malevolent Acts & Undesirable Events by Los of Consequences and Probability of Occurrence (PA) page 151). Wiley & Sons, New Jersey.
• Probability of backup response force is the ability and capability of a backup response force to arrive on the scene and tactically deploy in a timely manner within specified response times, and to assist the response force team leader (or on the scene commander) as directed.7
• Probability of event recording is the activation of software protocols to document system transactions and alarms in real time, including archive retrieval capability.
• Probability of backup systems is the activation of backup systems when the primary system fails.
• Probability of emergency power supplies is the activation of emergency power supplies when primary power fails.
#### Business Consequence Analysis Criteria
I also offer a model for helping you develop a cardinal rank order of consequence loss (Sullivant, 2007, pp. 81–82). Fig. 7.2 may be useful in your decision-making process to allocate adequate resources and funding to protect those resources and assets that need special protection against damage or loss.
The likelihood of a consequence rating (column 1) shows the probable severity of loss inflicted in a descriptive context. The numerical rating (column 2) illustrates the range of loss in quantitative terms, whereas the narrative rating (column 3) shows the ranges in qualitative terms. The consequence analysis (CA) (column 4) represents the potential magnitude of damage or destruction that could be sustained given specific threat parameters, such as the means8 usually used to carry out an attack and the site or facility conditions, including population density margins, physical configuration of assets, and the asset's proximity to other hazardous areas, as well as other critical factors. Objective and subjective probability analysis, including expert knowledge, and the measurement cautions discussed under probability of occurrence (PA) above equally apply to CA. The following factors play a crucial role in determining the criticality of loss:
• Human cost: the physical and psychological harm to employees, customers, clients, and other stakeholders resulting from a loss.
• Environment impact: the degradation of the quality of the environment or harm to endangered species.
• Economic loss: impacts on the national, regional, and local economy and reduction in the net tax base of the local jurisdiction.
• Corporate image cost: loss of reputation and standing in the community and industry, negative press, loss of customer or client base; damage to image, brand, and reputation; loss of confidence among stockholders, customers, clients, stock market, regulators, and the community in corporate leadership's ability to return enterprise to "normal."
• Asset criticality: the cardinal rank ordering for business impact that provides the necessary supporting rationale to defend the prioritization of a particular asset loss; looked at singly and collectively, including life-cycle costs, redundant systems, backup units, and the logistical capability to restore or replace a damaged or destroyed asset in a reasonable timely manner.
• Financial cost: equipment and property repair or replacement and downtime; overtime pay, stock devaluation, loss of sales; reduced cash flow, insurance costs, potential lawsuits, and regulatory fines and/or penalties.
## Benefits of Using Risk-based Metrics
Risk-based metrics answer business questions regarding security, which facilitate strategic decision making by the organization's highest level of governance. Key benefits of value to executive and security management are numerous. Metrics show:
• Compliance with legislation, regulations, standards, policies, and procedures. They benchmark specific performance levels and help to guide security decisions by showing when, where, and how security competency moves out of the expected range of performance expectations, and by demonstrating adherence to decisions already made with respect to performance expectations.
• Where the security organization is meeting its performance expectations or where improvement is needed. Metrics allow the organization to adjust its readiness capability while continuing to build upon strengths and correct weak performance. Metrics help to resolve disagreements and nonconformities, or to define when a process or protocol has not achieved the desired results, without pointing fingers at individuals. Metric results make it about correcting the process or practice rather than personality.
• CEOs and governing bodies that they can pilot the security organization like all other organizations in the company and acknowledge its "financial contribution" to the corporation through the protection of critical infrastructure and assets. This means recognizing security activity as a production center rather than a cost center.
• Key business areas that demonstrate signs of high-risk exposure. Metrics offer strategies that show promise for reducing business risk.
• The root causes of security deficiencies, weaknesses, and inadequacies. Metrics identify security trends, both within and outside the organization's control, and guide decision makers in adjusting processes, practices, and protocols, and in allocating reasonable resources and funding to those areas that need greater prevention and protection measures. Metrics can also show the utilization of security resources and expenditures and help develop the security budget.
• Estimate risk exposure associated with various ways of conducting business.
• Uniformity to specified security measures, providing economies of scale and measurably adding to employee well-being.
• The effectiveness of the risk mitigation and regulatory compliance program and how the security organization contributes to the bottom line.
• Operational or human failure costs: cyber threats, theft, fraud, waste and abuse, workplace violence, and other major activity. These costs are immense, and they cannot be adequately planned or budgeted for except under a special contingency budget. Cumbersome and inefficient processes, poor practices, and substandard performance are high-cost areas but are more predictable.
• The productivity of human and technology performance. Metrics allow the organization to monitor performance over time to make midcourse corrections, if necessary.
• C-suite executives why security measures should be implemented to reduce business risk. The direct linkage between identified risk exposure to business goals and operations, and lack of security measures and mitigation solutions makes a compelling case for the need to reduce business risk. Metrics help to define problematic threats, vulnerabilities, and loss consequences. Metrics speak to the hearts and minds of executives by focusing on areas of business risk that are important to them.
• Executive management the level of business risk so they can understand and make informed decisions on the level of residual security risk exposure they are willing to accept.
Valid and reliable risk-based metrics lead to conclusions that are more accurate and more persuasive communication with senior management. They help to identify the success or failure of existing security measures and proposed security solutions.
## Conclusion
### A Historical Perspective
Historically, corporate management has viewed security as a cost center rather than a production center and security metrics as merely measuring routine activity, not critical mission tasking that has meaning, value, and usefulness. Under this viewpoint, it is difficult for security professionals to measure security benefits against the service benefits of profit centers. This "old-school thinking" must end. We must make change a high-priority goal to be accomplished. It is not a question of whether this change is necessary, but rather how to persuade executive management that such change is in the best interests of the corporation. Certainly, this is an excellent opportunity for all security professionals to join forces in this crusade.
### Useful Metrics Span a Wide Area of Interest
Security metrics measure a wide variety of issues, from human and technology performance to the effectiveness, efficiency, and productivity of processes, practices, and protocols to the ability and capability of an organization to perform its critical tasks. Metrics are not intended to be models of perfection—they cannot be. Rather, they are guidelines that security professionals and executive management should use to help the decision-making process move along. Organizations that use metrics coupled with an analytical process are more likely to make the right decisions. Security metrics allow organizations to hold individuals accountable for specified results and goals. They are a vehicle through which critical security operations and programs can demonstrate their measurable impact on an organization's strategic, organizational, financial, and operational risks and profits. Therefore, it is paramount to advance the understanding of these metrics and knowledge of how to effectively use and communicate metrics, as well as what it takes to make a better metric. Chapter How to Communicate with Executives and Governing Bodies focuses on these important topics.
### Balancing Business Innovations and Risk Exposure
The dynamics of the threat environment means that a security director is forced into a state of continuous conflict between the business wanting to drive innovation and the security team needing to rein in risk exposure. Executive decision makers want to know that the business is adequately protected against risk, but they need to weigh the risks of yesterday and today against the opportunities of tomorrow. A win–win situation exists when the senior management team and the security team work hand-in-hand to develop safeguards that allow the chief executive to carry out the corporation's strategic business vision.
### Align Security Goals with Company Goals
Metrics should be aligned with the organization's objectives and risks and should measure specific activity, performance or issues that matter to senior management. Presenting metrics that meet measurement standards, are aligned with the organization's objectives and matter to management, and tell a compelling story tailored to the audience; communicating based on risk exposure and over time; using meaningful graphics; keeping presentations short; and presenting metric data at regular intervals will enhance your communication with C-suite executives.
### Metric Creditability
Creditable metrics possess scientific validity, organization relevance, reliability, return on investment, and practicality characteristics. At a high level, this strategy can help security practitioners better understand how to effectively communicate metric meaning and value to executives. If a metric is not reliable or valid, then the conclusions drawn from it will be inaccurate. Drawing inaccurate conclusions and communicating misinformation undermines your attempt to describe your point of view, which in turn drives management to further underestimate the importance of security metrics.
### Measurement Provides Feedback
Security leaders continue to use metrics mainly to guide budgeting and to make the case for new technology investments. In some cases, they use measurements to help develop strategic priorities for their security organizations. Leaders need to focus on finding the delicate balance between developing a strong, holistic security, and risk management strategy, while implementing more advanced and strategic capabilities to achieve their primary security mission.
### Closing Thoughts
In this chapter I have presented an opportunity to advance your capability to measure performance and productivity. The framework is grounded in scientific merit, strategic relevance, and operational reasonableness. This process, in turn, enhances your ability to communicate effectively with upper management in a user-friendly language they understand. Numerous security organizations have successfully measured and evaluated their effectiveness using this approach, and it can work for you and your boss, as well.
## Appendix A: Metric Framework and Architecture Platform
### Scientific Merit or Value
#### Reliability
Reliability is the long-term ability of metrics to yield consistent results with little or no variability in reporting in the face of disturbances and that are unaffected by sources of measurement error. There is no over- or under-collecting. Data are collected carefully in real time from actual occurrences, official records, field interviews, and conditions observed while performing security assessments, audits, or inspections, and they are highly reliable and predictable. Repeated measurements using the same method, as well as alternative methods, should achieve the same results.
#### Validity
Results are based on theory and research that support drawing conclusions from the metric. For example, there is a direct relationship between security intervention and a reduction in business risk exposure. Data are collected from official documents, resources, and observations. Previous uses have validated the metrics.
#### Generalizability Theory
Conclusions are based on quantitative or qualitative analysis, professional judgment, expertise, and best practices. Conclusions drawn are consistent and applicable across different settings, organizations, or circumstances, including comparisons with similar external organizations.9
## Strategic Relevance
### Organizational Relevance
Metrics gauge the ease or difficulty of operations and provide useful and meaningful information and insight that matter most to C-suite executives, enabling them to carry out their responsibilities better. Metrics are linked to specific organizational missions, objectives, goals, assets, risks, threats, or vulnerabilities. The linkage is strong and of high relevance to the organization.
### Communication
The combined metrics provide insights into the strengths and weaknesses of security activities. Metrics point out areas that may need strengthening or support areas for continual improvement. Metrics, their purpose, and their results can be communicated easily. Privacy concerns are strictly maintained.
### Return on Investment
Return on investment (ROI) can be used to demonstrate cost savings or the consequence of loss in relation to relevant security spending.10 This involves expressing the following in terms of dollars or some other unit that is relevant to decision makers:
• Cost of security intervention
• Effects of security intervention and unintended consequences related to the intervention
• Investment in security technology that improves effectiveness and productivity
ROI can show the relationship between a security action and practice and the benefit it provides. The relationship between security measures' costs and benefits gained is readily measureable. A sample formula is offered for determining general ROI:
ROI=profitorbenefitgain(orlossesavoided)duetosecuritymeasures−costofsecurity×100Costofsecurity
You may use the above sample or one preferred by your own organization—whichever best suits your needs.
ROI considers quantitative factors, such as dollar amounts, and qualitative factors, such as anticipated operational efficiency improvements. ROI should focus on three factors: regulation, revenue, and reputation.
• Regulation refers to being in compliance with relevant laws.
• Revenue references profit.
• Reputation refers to the reactions and beliefs that key stakeholders may form and share with others should security failure occur.
## Operational Reasonableness
### Manipulation
Data cannot be coached, guessed, or faked by individuals collecting the information.11 Measurements are based on official records, actual measurements, and practices that are not easy to fake. Quality assurance reviews ensure the authenticity of collected data and maintain the integrity of metrics. Data are highly likely to be correct and current.
### Timeliness
Data are gathered in a timely fashion, are up to date, and reflect conditions at the time of collection. Data are collected during a security assessment, audit, or management review. Measurement is straightforward and could be quickly applied by different people over time. It is highly unlikely that any calculations would be out of date. Data derived in this way could be used for drawing conclusions and making real-time decisions.
### Cost
There are usually no development costs. Metrics have already been developed and tested, and are ready for use.12 Administering metrics is a process of management accountability in conducting regular business and is not costly. Little or no training of administrators is required. Obtaining data and calculating results does not offend employees or customers, or disrupt business operations.
* * *
1 International Organization for Standardization (ISO) / International Electrotechnical Commission (IEC) 27,001 is a widely used, best practice certification that outlines mandated information technology security requirements surrounding the range of threats and vulnerabilities for cyber security, including related metrics.
2 The application of Fig. 7.1 is shown in Chapter Developing A Threat Estimate Profile.
3 Few organizations, if any, have the technical expertise, time and technical resources available to perform a formal PS specification test of their electronic security system to determine an exacting level of system performance to original equipment manufacturer specifications or a formal system acceptance test performed as part of the system turnover process during the acquisition phase. Rather, many organizations perform self-tests at the start of each shift and at other times, such as when maintenance on the system is performed. Such tests may include any or all of the following:
• A system diagnostic test to check for anomalies, system malfunctions, or inoperative alarm points.
• A physical inspection of visible system components to check for visible damage or tampering.
• Testing detection sensors for general operability but no formal Pd testing.
• Testing CCTV and communications for general operability but no technical testing.
• Testing of automated and manual barrier systems for general operability.
• Other system functions as applicable to user needs.
4 Depending on the complexity of the system and mandated regulatory performance requirements, additional probability elements can be added to the representative listing to meet any unique local demands that may need to be addressed.
5 Measurement involves a level of performance effectiveness and efficiency and other factors such as visibility, weather conditions, operation of equipment, and distractions.
6 Measurement involves a combination of factors such as knowledge of route or routes to take, traffic congestion, weather conditions, condition of transport mode used, potential for being ambushed on the way to the scene, and other factors such as tactical knowledge, experience, and leadership.
7 Ibid.
8 The preferred means of most attacks is the use of explosives, the effect of which is dependent on the amount used, its placement, the quality of control devices, and the expertise of the adversary.
9 Not all external organizations are willing to share similar data collected, thus attempting to benchmark particular results with many external organizations may not be possible. In those instances, existing security effectiveness may be used as a benchmark to internally measure the improved effectiveness of proposed mitigation actions.
10 Some executives do not consider security risk to be a major component of the overall corporate risk effort, so ROI is not of interest to them. For other CEOs, ROI is a vehicle to justify budgets and can help in examining financial inputs and outputs of selected security activities. I point out that in many instances, the actual financial ROI may be difficult to fully calculate. This is because ROI claims may not be available or able to make the case for greater security investment. This may require extended research, analysis, and independent conclusions to make a persuasive business case. When available, however, ROI can serve as a road map to where a security organization has been, where it presently stands and where it needs to go to achieve mission objectives.
11 People could conceivably fake data, but that would mean lying about verifiable facts. Equally important, self-appraisals are not generally objective or reliable because they lack independence of thought and action. They have a tendency to under report or not report on particular areas to "protect" the boss and/or the establishment. Conversely, external security consultants are objective, independent, and free of any conflict of interests and the influences of "work politics." These professionals have no incentive to fake data, or to under or over report or ignore compliance issues, other non-conforming matters or best practices. For these professionals, reporting false or inaccurate data may subject them to criminal prosecution, revocation of certification standing, fines, suspension of business license, or any combination of the above.
12 Minimal costs may be associated with inserting the description category of topics to be measures in selected metrics.
8
# A User-Friendly Security Assessment Model
## Abstract
This chapter emphasizes the importance of embracing a proven security assessment methodology. The model enables authorities to create building blocks for threat, vulnerability, and consequence integration that allows officials to determine which areas of the corporation are at most risk so appropriate investments can be made to protect critical infrastructure, operations, and processes from damage or destruction, and resources from harm, injury, or loss. It provides a proven user-friendly security assessment model and metrics that can be fitted to any security organization of any size to measure performance effectiveness and competency.
### Keywords
Consequence analysis; Continual improvement; Critical sensitive information; Criticality analysis; Mitigation strategies; Prioritize action plan; Risk and uncertainty; Risk assumptions; Risk treatments; Security assessment model; Security resilience; Threat and vulnerability analysis
The security assessment helps identify security organization strengths and weaknesses, and channels mitigation actions to reduce security vulnerability and increase security resilience.
John Sullivant
Top Takeaways
• Analyze and evaluate performance and behavioral triggers
• Evaluate probability, business risk exposure, and consequence loss
• Conduct a comprehensive security assessment
• Customize an assessment model to fit your particular needs
• Use risk-based metrics to measure and evaluate performance
## Overview
In this chapter I present a security assessment model that resonates with executive management because it offers a tool to increase the capability of an enterprise to prevent injury or death to resources, the damage or destruction of assets, or the disruption of business operations. While it is desirable to achieve a perfect and absolutely risk-free environment, the reality is that this goal is unattainable. Therefore a priority for executives, the security director, and stockholders early in the security planning process is to agree on what is or is not acceptable risk so effective security planning can take hold (Sullivant, 2007, pp. 45–49).
Interestingly though, many industries and companies have no regulatory requirement to conduct formal security assessments. But many companies acknowledge the value of doing so as part of prudent business practices, as well as their "duty to care" obligation. These companies know that security assessments take them from where they are to where they need to be. Companies that regularly conduct security assessments are more prepared for crisis and respond to it more effectively, not to mention the likely probability of enjoying lower corporate insurance premiums for implementing and enforcing workable mitigation solutions.
Absent a proven management tool that delivers strategies for synthesizing integrated solutions, or failing to ensure reasonable security solutions are implemented, a corporation has little assurance that its security program is aligned with business goals, is in compliance with regulatory requirements, is capable of addressing the likely threats and hazards it will face or its implementation is effective. Insurance companies have been known to force substantial management and organizational changes on companies with insufficient security measures and programs. There are better ways to improve security—ways that you have total control over—than bureaucratic insurance mandates.
## A Reliable Security Assessment Model That Resonates with C-Suite Executives
Fig. 8.1 A user friendly security assessment model, (Sullivant, 2007, pp. 55–84) provides specialized, customized, and tailored research and analysis methodology with laser-like focus by identifying program strengths and weaknesses and developing mitigation analyses to strengthen the security posture and to enhance practices whereby risk and uncertainty can be objectively identified and reduced. The model has applicability in the private, not-for-profit, nongovernmental, and public sectors, and in any size organization.
The model, which is discussed in detail in my book Strategies for Protecting National Critical Infrastructure Assets, uses a holistic approach to measurably reduce risk through a combination of threat, vulnerability, and consequence analysis; deliberate mitigation treatments; and prioritization actions that bring value and meaning to C-suite executives. It offers a detailed road map that can help enterprises that are in denial of risk to raise security standards and embrace a new set of strategies to improve security resilience (Sullivant, 2007, pp. 4–5).
At the outset, it is important to note that the model1 shown is an all-inclusive analytical process. Such a comprehensive analysis may not be suitable for your company at a particular time. In designing the model I made certain that the basic architecture was sufficiently flexible to allow the freedom to define personalized assessment boundaries, and I encourage you to select the dimensions that are most suitable to your immediate needs.
Recognizing the desire to focus on specific problem areas, rather than a general perspective, I created several independent lower tier models that can also be tailored to meet specific needs. I address these models in the following chapters:
• Chapter 9, "Developing a Realistic and Useful Threat Estimate Profile"
• Chapter 10, "Establishing and Maintaining Inseparable Security Competencies"
• Chapter 11, "A User-Friendly Security Technology Model"
• Chapter 12, "Preparing for Emergencies"
• Chapter 13, "A User-Friendly Protocol Development Model"
• Chapter 14, "A Proven Organization and Management Assessment Model"
### Why Security Assessments Should Be Important to You
Security assessments are important from both a local and national planning perspective in that they enable authorities at all levels to create building blocks for threat, vulnerability, and consequence integration, and allow officials to determine areas and operations of a corporation are at most risk so appropriate investments can be made to protect targeted critical infrastructures, key assets, and resources (Sullivant, 2007, pp. 5).
Figure 8.1 A user-friendly security assessment model. Source: Sullivant, J., CFC, CSC, CHS-IV, CPP, RAM-W, Diplomate, ABFET, 2007. Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving. Reprinted with permission from John Wiley & Sons, NJ.
### How to Effectively Use the Model
The model allows chief executives and boards to use a proven framework architecture to develop thresholds for future standards for preemptive or protective actions and to set priorities to build a safe, more secure, and more resilient company through the protection of assets and resources against threats and hazards that could (Sullivant, 2007, pp. 16):
• impair its ability to perform essential services and ensure the public's health and safety
• undermine its capacity to deliver minimum essential services and products
• damage its ability and capability to function
• challenge the public's confidence in its capability to deliver services
• weaken its image, brand and reputation
The model (and all the tailored models) resonates with executives because it is a risk-based measurement and evaluation process that gives specific local meaning to an entity, the goal of which is to systematically (Sullivant, 2007, pp. 61–70):
• characterize the business and operational environment, including critical activities, services, processes, practices, partnerships, dependencies, and stakeholder relationships, and the potential consequences related to a disruptive incident based on realistic risk scenarios
• identify legal, regulatory, and other obligations to which the organization subscribes, and how these commitments influence protecting assets and resources in an all-hazards environment
• develop an operational needs analysis, a compliance analysis or voluntary commitment analysis
• characterize significant threats, hazards, industrial mishaps, natural disasters, and weather-related calamities influencing the workforce and business operations
• reduce threat, vulnerability, and consequence to critical assets through the process of identifying, analyzing, and prioritizing:
• the likelihood that critical assets may be attractive targets selected for disruption, damage, or destruction based on the intent and capability of an adversary
• the vulnerability characteristics of assets, processes, functions, and locations that make them susceptible to destruction, incapacitation, or exploitation by mechanical failures, natural hazards, and malicious acts
• consequences of any disturbance, damage, or destruction to critical assets, taking into account health, economic, psychological, and governance impacts.
• formulate, analyze, and prioritize risk treatments and identify acceptable levels of residual risk exposure
• manage risk through the creation of strategies that mitigate the effects of risk exposure—including preventive and protective capabilities such as deterrence, detection, defense (delay and denial), assessment, reporting, response, and recovery—as well as through continual improvement based on objective measurement and evaluation
• evaluate risks and consequences within the context of changes within the organization or that are made to the organization's operating environment, processes, practices, partnerships, and dependencies
• evaluate the effectiveness of protocols, practices, training and qualifications, security organization, management and leadership, security management knowledge base, and corporate leadership support for security programs
• evaluate the value of security programs, operations, and technology and best practices for effectiveness, efficiency, and productivity
• evaluate the inseparability of physical security, cyber, information, and technology architecture to maximize the effectiveness, efficiency, productivity, and costs of security resilience
• measure and evaluate both the existing performance effectiveness (PE1) and the effectiveness of proposed risk treatments (PE2).
## Measuring and Evaluating Performance Effectiveness
### Security Analysis Framework
The model provides the framework for conducting specialized, customized research and analysis. It identifies requirements to help an organization develop and implement policies, objectives, and programs, taking into account legal requirements and other commitments to which the organization subscribes, and information about significant threats, hazards, accidents, and weather-related calamities that may have an influence on business operations and the protection of critical assets. It applies to risks (and their consequences) for which an enterprise needs to integrate management, technology, facilities, processes, and people into a resilient security culture. The extent of the application depends on factors such as risk assumptions, risk uncertainty, threat, vulnerability, consequence analysis, and risk tolerance; policy and practices; the nature of activities, products, and services; and the location where, and the conditions in which, it functions.
The model uses metrics (Sullivant, 2007, pp. 73–84) to calculate factors that:
• may cause temporary or permanent loss or degradation of business operations
• measure the effectiveness, efficiency, and productivity of security operations and programs, and the security organization's ability and capability to protect assets and resources against specific threats and crises
• determine security capabilities and abilities to safeguard a corporation against likely threats that may lead to the formulation of strategies and programs to enhance security resilience, objectives, targets, and practices
### Theory of Performance Effectiveness
Performance as a theory can be applied to the performance effectiveness (PE) of critical security activity, security programs, and the actions taken to enhance and improve security resilience. The goal of PE is to benchmark activity against legal, regulatory, and other commitments that organizations subscribe to and how these standards of conformance and expectations, as well as principles, strategies, processes, and best practices, influence the capability of an organization to perform its prime security mission (Sullivant, 2007, pp. 73–84).
PE measures the strengths and weaknesses of a security organization. It determines gaps in competency expectations, standards, and requirements, and establishes a starting point for developing mitigation strategies and solutions to correct noted deficiencies, weaknesses, and inadequacies.
The PE analysis process involves the complete understanding of operations, procedures, methods, techniques, and constraints associated with the security organization and the analytical ability to distinguish between and isolate conditions, circumstances, objects, activities, and relationships that are capable of producing ineffectiveness, inefficiencies, safety conditions, and cost overruns. This includes identifying, examining, and recording data, conditions, circumstances, and events that can contribute to unacceptable outcomes.
To achieve total quality measurement and evaluation, PE must be reflected as PE1 and PE2, which are outlined below.
#### PE1: Existing Effectiveness
PE1 (Sullivant, 2007, pp. 83) is the "before" analysis that measures actual security conditions and the ability and capability of the security organization to perform its mission. PE1 answers the question, "How well prepared are you?" PE1 represents the effectiveness, efficiency, and productivity of existing protective measures (physical, electronic, cyber, information, personnel, and procedural) and protocols, processes, practices, competencies, management, leadership, and the organization to deliver a reasonable deterrence, delay, denial, prevention, protection, detection, assessment, and response and recovery ability and capability to defend against threats, risk exposure, or vulnerability.
#### PE2: Proposed Effectiveness
PE2 (Sullivant, 2007, pp. 83) represents the effectiveness, efficiency, and productivity of proposed risk mitigation treatments to identified deficiencies, weaknesses, or inadequacies to reduce vulnerability and risk exposure—including the acceptability of residual vulnerability—to enhance overall security resilience. PE2 sets priorities for implementing security enhancements and improvements, and helps to establish the budget, milestone schedule, and the allocation of resources to execute operational needs. PE2 also offers a road map for monitoring continual improvement actions that may be necessary to achieve security mission goals and objectives. PE2 tells you what you have been waiting to hear: how well prepared you should be.
Fig. 8.2 performance effectiveness (PE) metric and calculation criteria shows how the concept of PE works. It resonates with chief executives because it focuses on those topics of most interest to them: the security organization's ability and capability to perform its indispensable operational tasks: deterrence, delay, denial, prevention, protection, detection, assessment, response to, and recovery from adverse events in the course of saving lives and protecting assets. No other security mission task is more important than this.
The example illustrates an overall PE1 effectiveness rating of 0.41—far below the effectiveness rating of 0.90 preferred within the industry. In this example the strategies and mitigation solutions developed should all focus on correcting the observed deficiencies, weaknesses, and inadequacies rated <0.90, with an overarching goal of achieving an effectiveness rating of at least 0.90. Most certainly, the goal is achievable, but it requires hard work, determination, and executive management's commitment to achieve positive change.
Figure 8.2 Performance effectiveness (PE) metric and calculation criteria.
You would use the identical template to measure and evaluate the proposed mitigation solutions (PE2). The gap between the findings for PE1 and PE2 provides security analysts an avenue to develop mitigation options, and decision makers with the ability to make the correct choices to improve security resilience.
## The Benefits Management Enjoys from Using a Risk-Based Model
The model is important to planners and executive decision makers because it produces a professional, candid, independent, and objective analysis of enterprise security strengths, weaknesses, and vulnerability in order to measure the effectiveness of existing protective measures, evaluate the current status of the security operations and sensitive programs, and identify gaps in the security process (Sullivant, 2007, pp. 47–53).
• The model enables executive management to ask questions before making a decision. It represents a concise, consistent, uniform, and deliberate security management action plan that focuses on enhancing an enterprise's security posture from a systems-level perspective.
• The model provides to the organization and its customers trust and confidence that the organization is able to establish and sustain a safe and secure environment that fulfills organizational and stakeholder requirements.
• The model offers a deliberate means for analysis from a holistic systems-level perspective. It provides a road map to developing resilient strategies to reduce risk through deterrence of, prevention of, detection of, protection against, and mitigation of attempts to damage or destroy infrastructure and assets, incapacitate or exploit human resources and physical, virtual, and tangible and intangible assets; response and recovery planning; security training; and continual improvement.
• The model produces a comprehensive, systematic, and defensible analysis that drives integrated business risk reduction options. It does more than address criminal activities and terrorist threats; by using an all-hazards approach, security assessment activities allow for a more complete suite of integrated business risk-reduction options for various critical business functions.
• The model offers strategies and solutions that can reduce insurance premiums, and these savings often match or exceed the costs of many security upgrades.
• The model teaches what needs to be protected and from whom. It integrates physical measures, processes, practices, information, people, facilities, and equipment, as well as their dependencies and interdependencies with other critical program elements such as safety; ethics; integrity; social and work rules of behavior; human resources capital investment; the security force's experience, expertise, qualifications, training, and certifications; and corporate support of security activities.
• The model helps management rank assets that are most critical to business operations, assets facing imminent threat, and other assets that may be attractive targets so they can gauge corporate priorities for changes to enterprise designs, infrastructure, or policies, processes, and practices.
• The model allows decision makers to channel scarce resources and funding into those areas that need it most. It brings together the right balance of people, information, facilities, operations, processes, and systems to deliver cost-effective solutions, which, when applied and integrated into practice, lead to improved security resilience.
• The model gives management a framework for continual improvement to increase the probability of enhancing and improving security readiness and preparation, response and recovery, and continuity.
## Conclusions
The challenges ahead call for the thorough evaluation of security operations and programs. Embracing a process approach to solving security problems allows decision makers to benefit from the relationships between risk, threats, severity analysis, and risk treatment options that address the most critical issues first. The program requires the cooperation and support of management at all levels, working to establish and maintain protective measures, emergency planning, and business continuity initiatives that are appropriate to the needs of a corporation.
Missing this opportunity can lead to bad decisions followed by poor practices. Assessment and threat analysis outcomes bring together:
• concepts and techniques to improve operations
• best practices to overcome inadequate performance
• state-of-the-art technologies to increase system performance and capability
The security assessment process is the road map that brings together information so security planners can "connect the dots" and decision makers can make the right choices. Strategic security planning begins with specialized customized research and analysis to:
• uncover the root causes of operational and technology weaknesses and deficiencies
• identify potential threats, vulnerabilities, and consequences
• uncover archaic, obsolete, and cumbersome protocols, processes, and practices
While identifying strategic deficiencies, programmatic weaknesses, and performance inadequacies is a good philosophy for ensuring conformance to regulatory requirements, industry standards, and best practices, it is only the first step in a series of steps that ultimately lead to successful strategies and security mediation solutions. The measurement and evaluation process continues with delivering a catalog of suggested treatments aimed at reducing threat attractiveness, such as designs that:
• embed hazard resistance and harden critical facilities and assets
• enhance physical, information, personnel, and technology security measures
• build in network resiliency
• resolve system technical performance levels
• converge new technologies and emerging technology measures
• use diverse hot standby and redundant systems
• create policies, processes, practices, procedures, and emergency response plans
• respond to and recover from crisis
• build a culture of security and train employees to act securely and responsibly
Using a proven security assessment model such as the one presented here prevents waste, ensures a thorough analysis, and offers constructive, cost-effective, strategic advice for solving unique security problems. It is a fundamental tool for security practitioners: it bolsters business cases for improving and enhance security resilience—process changes, technology advancements, best practices, additional resources, and adequate funding. Poorly conducted assessments become a waste of time and resources and can lead enterprises to take action that is ineffective, giving the CEO and board a false sense of security.
* * *
1 As of this writing, I have customized and tailored the general Model to fit the Banking & Finance, Food & Agriculture, Energy, including Gas, Oil & Pipeline, Telecommunications, Civil Aviation and Water Sectors. It can also be customized to meet the need of any one of the national critical infrastructure sectors not mentioned, as well as any other unique business operations.
9
# Developing a Realistic and Useful Threat Estimate Profile
## Abstract
This chapter addresses the urgency for developing a realistic and useful threat estimate profile that has value and meaning to chief executives. The discussion focuses on identifying the range and levels of threats against specific assets and modes of attack; characterizing assets, facilities, and processes; and translating these elements into an understandable forecast that enables action. Metrics are introduced to identify threats and hazards, and suggestions are put forth to determine the rank order of assets, loss, consequences, and the probability of an event occurring. Without a completed and up-to-date threat estimate profile, an organization will never know where to effectively allocate resources and funding to protect those assets that need it the most.
### Keywords
Adversary planning considerations; Bottom-line performance; Collateral damage; Consequence loss; Economic impact; Investment strategies; Preparedness initiatives; Probability of occurrence; Threat estimate profile
Yesterday's threat is history. Tomorrow is where we confront threat head-on. We will never know the truth until after it happens. We can only estimate its being based on analysis and experience. The analyst is therefore concerned about a string of future conditional probabilities.
John Sullivant
Top Takeaways
• Risk exposure and asset protection
• Complexities of the threat environment
• Develop a meaningful and useful threat estimate profile
• Analyze and assess threats, risk exposure, consequences, and probability of occurrence
## Overview
You probably think that chief executive officers (CEOs) want to know what threats can harm their company, the consequences of those threats, and what is being done to protect their people and assets. But when it comes to security preparedness, many CEOs are on the "dark side of the planet."
In Chapters The Evolving Threat Environment, and The Cyber Threat Landscape, I introduced the fundamental aspects of the threat environment security professionals face on a daily basis. Here, I draw upon those threat elements to address the importance of formulating a realistic and useful threat estimate profile that has value and meaning to chief executives.
Few would disagree that a corporation requires a comprehensive threat estimate profile if its business is to survive. The risks facing the organization and the way in which threats are profiled and quantified provide a solid foundation for the development of security programs and strategies. This holistic approach involves people, technology, and processes.
## Providing Meaningful Strategic Threat Advice to Executive Management Is Essential
As mentioned previously, 60% of upper management believes that security is stronger than it actually is, whereas only 22% of top executives are aware of their company's true security readiness. It is astounding that almost two-thirds of the nation's CEOs say they are in the dark about the true security status of their corporation. This should raise significant concern both in the C-suite boardroom and within the halls of the security organization.
At almost every site visited I found the lack of a prepared threat estimate profile to undermine an enterprise's ability to prioritize deterrence and delay techniques, preventive and protective measures, and the allocation of resources and funding to secure those assets that are most critical to business goals and objectives. Based on my findings, I argue that few corporations invest any effort in developing a threat estimate. In my many years of conducting threat and vulnerability studies, I found little evidence to suggest that corporate-wide security emergency planning—and the development of such plans and response and recovery procedures—was based on a current and meaningful threat estimate profile. In fact, many organizations had not even performed a formal security assessment to identify unit strengths and weaknesses, identify vulnerabilities and risk exposure, and determine the effectiveness of security performance. The few organizations that had a useable and meaningful threat estimate profile seldom kept it up to date, making it too outdated to be useful in updating any of the emergency plans and procedures reviewed. Other organization threat profiles had no local meaning and utility, or served little value in preparing security emergency plans and event-driven response and recovery procedures (more on this topic in Chapter: Preparing for Emergencies).
Only by understanding the range and level of threats, and the potential harm they can cause a company, can C-suit executives make informed judgments to more effectively control security risk. CEOs expect the security director to lead them "out of darkness" and help them not only to make informed risk management decisions in order to increase bottom-line performance, but also to report the true status of the security organization's capability and ability to perform its essential critical mission: deterring criminal and unauthorized activity/intent, preventing easy targets, denying unauthorized access, protecting resources and assets, delaying effort, detecting an act, assessing the threat, responding accordingly to an event, preventing damage, and delaying or stopping an adversary's escape.
In this role, corporate security is both a strategic and operational activity, and the security director must distinguish between these layers. However, research has found that too often the corporate security strategy is not aligned with the corporate business strategy. The consequences of this knowledge gap means that the security organization is likely to be marginalized. Aligning security strategies with business strategies ensures that corporate security programs are in harmony with the company's priorities and places the security director and chief executive on the same page. The threat estimate profile helps achieve this goal.
## Threat Planning Relies on the Development of a Useful Threat Estimate Profile
Jack F. Williams Professor of Law, Georgia State University advocates that threat is best understood as the product of an adversary's capability, intent, and authority. He argues threat is also strongly influenced by an adversary's culture and constituencies, and requires a "cultural awareness" of an adversary. Williams advocates that threat analysis is the art of wasting information, that is, the art of peeling away layers of irrelevant information, incorrect information, and disinformation to expose relevant and credible information related to the threat interest of a corporation.
Sources of information that flush out threat include classified, unclassified, and open-source material, as well as expert judgment. It is well accepted and understood among analysts and security professionals that the best sources of information are classified information and hands-on experience, followed far behind any open-source material, much of which contains only bits and pieces of factual information; thus the latter is mostly based on speculation and opinion of the conditions and circumstances reported.
There is no question that solutions to protecting critical infrastructures and assets must be based on a thorough security assessment that accounts for the review and update of an existing threat estimate, or the creation of one where one does not exist. Fig. 9.1 highlights the elements that make up a comprehensive threat estimate profile (Sullivant, 2007, pp. 131–155). A completed threat estimate profile answers these questions – before significant funds and resources are made available:
Figure 9.1 Threat estimate profile. Source: Sullivant, J., 2007 (CFC, CSC, CHS-IV, CPP, RAM-W, DABFET). Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving (Exhibit 7.1 Composition of Design-Basis Threat Profile, page 134). Wiley & Sons, New Jersey; 2007.
• What are the consequences of specific attacks on specific assets in terms of business economic impact, health and welfare, damage (including collateral damage), and destruction?
• What points of infrastructure or asset failure (and their location) could have extensive cascading consequences?
• What are the highest-risk areas from a business perspective incorporating consequence, vulnerability, and threat?
• What investment strategies can an enterprise pursue that will have the most effect in reducing overall risk?
As shown above, the threat estimate profile comprises a national threat assessment perspective, a regional or sector-level threat assessment, and a local or site-specific threat assessment, all of which use, to some degree, the elements of the lower-tier platform that brings together numerous inputs from a variety of resources:
• Threat characteristic and parameters
• Range of potential threats and hazards
• Adversary group planning considerations
• Adversary organization and command
• Threat consequences and probability of occurrence
The threat profile offers a systematic forum to judge how well security performance goals are achieved. Strategic security planning therefore begins with:
• conducting a comprehensive security assessment that produces a realistic threat estimate profile so effective, reasonable, and prudent security measures to safeguard business interests, operations, investments, and resources, and to explore gaps in ineffective performance or omission of performance, can be examined
• developing prudent and reasonable security measures, and clear and distinct processes, practices, and protocols—particularly exacting emergency preparedness and continuity planning—to protect against natural and manmade disasters, industrial mishaps, and criminal activity through the development of specific event-driven security response and recovery procedures
Strategic planning continues with:
• examining training needs, identifying competency gaps, and developing training programs
• diligently testing and exercising plans
• improving the capability to respond to crisis
• achieving continual measurement and evaluation of performance
Without proper planning, preparation, and training, employees will lack the guidance and confidence necessary to perform their duties during an emergency, whether a terrorist attack, criminal act, natural disaster, industrial mishap, or other catastrophic event.
## Suggested Composition of a Threat Estimate Profile
At the corporate level, there can be three major sections to a threat estimate profile: the national threat assessment, the regional threat assessment, and the local threat assessment, as applicable to a specific industry sector or business.
### The National Threat Assessment
At the national level, the national threat assessment is prepared by the U.S. Department of Homeland Security with significant input from the nation's intelligence community and the FBI; the assessment is approved by the president of the United States. This statement focuses on the most critical economic security, national security, and national defense threat considerations affecting America's global interests.
A U.S. corporation with a significant national presence or that is a major government/defense contractor should consider preparing a national threat assessment that addresses its global business interests, including its attractiveness as a target, if appropriate. Four U.S. government policy directives offer broad guidance for preparing national threat statements:
• Presidential Policy Directive 21: Critical Infrastructure Security and Resilience
• Presidential Policy Directive 8: National Preparedness
• The National Infrastructure Protection Plan (NIPP), which outlines how government and private-sector participants in the critical infrastructure community work together to manage risk and achieve security resilience outcomes
• The National Strategy for Protection of Critical Infrastructure and Key Assets, which identifies a clear set of national goals and objectives that outline the guiding principles that underpin efforts to secure infrastructures and assets vital to national security, governance, public health and safety, the economy, and public confidence. It establishes a foundation for building and fostering a cooperative environment in which government, industry, and private citizens can carry out their respective protection responsibilities
### The Regional/Corporate Threat Assessment
Each federal agency, known as a sector-specific agency, leads a collaborative effort for critical security within the 16 national critical infrastructure sectors identified within the NIPP. Each agency develops and implements a sector-specific plan, which details the application of the NIPP to the unique characteristics and conditions of the industry sector. The sector-specific agency, in concert with industry participants through private industry sector coordinating councils, prepares a sector or regional threat statement. This government–industry collaboration helps industry to prioritize protection and preparedness initiatives and investments within and across sectors.
## The Local/Site-Specific Threat Assessment
Local or site-specific threat estimate profiles are prepared by a corporate entity and tailored to local circumstances, conditions, and situations. Local threat estimates are the most relevant estimates because they focus directly on unique problems confronting corporations, giving the threat statement local meaning and value to the chief executive. This threat estimate brings together relevant, essential information from multiple sources to help security decision makers set priorities to apply resources where they offer the most benefit for mitigating risk by lowering vulnerabilities, deterring threats, and minimizing the consequences of attacks and other incidences.
A comprehensive threat profile serves as the benchmark for further strategic security policy development and direction, emergency preparedness, and business continuity planning. The threat estimate profile is a "living document" and therefore a crucial element of the overall planning process; its development and upkeep should be a priority initiative for every chief executive.
Without this essential threat estimate, it is difficult to determine what the highest-priority activity should be when planning and coordinating security operations and initiatives. Outputs may be misguided and ineffective, and more than likely mimic a false sense of accomplishment, leading to excessive and counterproductive labor efforts, less-than-satisfactory performance results and expectations, and wasteful expenditures.
Several national strategy programs (which complement the NIPP) offer a wide array of guidance for developing threat parameters and protective measures at the local level:
• Aviation transportation industry
• Border controls
• Cargo security
• Chemical manufacturing industry
• Chemical, biological, radiological materials
• Commercial and government facilities
• Countering violent extremism
• Critical manufacturing industry
• Dams and energy facilities
• Emergency services
• Food and agriculture industry
• Gas, oil, and pipelines
• Maritime transportation industry
• Money laundering | • National defense
• Natural disasters
• Nuclear power plants
• Nuclear reactors, materials, and waste
• Pandemic flue
• Ports and harbors
• Rail and truck transportation industry
• Trafficking in human, body parts, weapons, and drugs
• Telecommunications industry
• Water and wastewater treatment plants
• Weapons of mass destruction
---|---
## Identifying the Range of Potential Threats and Hazards Is a Critical Planning Process
A valid threat profile contains all potentially postulated, probable, and emerging threats and hazards that could realistically apply to a corporation. The list of threats and hazards can be short or long, depending on factors such as the industry, location, and other considerations. Regardless, it should be sufficiently detailed to provide to security planners the information necessary to formulate effective security measures to guard against such threats.
Fig. 9.2 Range of Potential Threats and Adversary Characteristics (Appendix A) is a representative sampling of potential postulated, probable, and emerging threats. The listing is categorized by a series of adversary characteristics, which give security planners and analysts insight into possible adversary planning considerations and intentions to commit particular acts. Adversary planning and execution capabilities are divided into operational, technical, and logistical capabilities and authority (Clark, 2004, pp. 66–173).
• Operational capability focuses on leadership structure, command and control, intelligence, financing, recruitment, experience, expertise, training and education, social outreach, communications, political influence, territory, and infrastructure to operate and provide sanctuary to its members, whether they be terrorist groups, domestic extremist groups, organized crime, transnational criminal groups, or any other criminal element and recognized authority.
• Technical capability focuses on having either internal or external access to the instruments needed to carry out activity.
• Logical capability focuses on having local, regional, or global capability to demonstrate a threat capability.
• Authority refers to internal authority to operate, recruit, and replenish forces, equipment, and supplies and external permission to carry out approved operations.
You can populate the listing by placing a checkmark within the appropriate "bins of capability" as they apply to the specific range of potential threat.
The breakout helps security planners to distinguish which threats and capabilities are more suitable to deterrence, prevention, detection, and protection measures. The analysis also has merit when planning for emergencies because criminal elements and crowd behavior patterns do take advantage of a crisis to commit criminal activity and other unauthorized acts—thus the need for protecting a scene and preserving evidence, as well as the need for law enforcement to safeguard the general community from looters and rioters.
One cannot understand threat without understanding the culture within which an adversary operates. Such factors may include any or all of the following:
• Alliances
• Communications network
• Geography
• Ideology
• Legality
• Legitimacy of a higher authority to grant permission to act and to discipline
• Philosophy
• Political infiltration
• Relationship with other criminal or terrorist groups
• Religion
• Social values
• Sociopolitical and religious attributes, including universe of operation and influence
Failing to recognize the culture space within which an adversary lives, operates, and retains authority can lead to analytical drift, subconscious projection, and superficial threat analysis. Analysts need to pay attention to performance signs for clues about potential targets and attack means.
"Bins" of capability, intent, and authority help to evaluate credibility, reliability, relevance, inferential force, and an adversary's purpose. From an analyst's perspective, credibility is the measure of belief and authenticity, reliability is the measure of consistency and coherence, relevance is the measure of fit, inferential force is the measure of weight, and adversary purpose is the measure of intent. Both the list of threats and adversary characteristics can easily be customized to fit your unique planning parameters, giving utility and meaning to your senior management.
## Consequence Analysis and Probability of Occurrence for Threats and Hazards
Fig. 9.3 Consequence Analysis (CA) and Probability of Occurrence (PA) of Threats and Hazards (Appendix B) takes the data presented to the next level of threat analysis. It brings together the results of consequence analysis (CA) and probability of occurrence (PA) for each threat and hazard and puts them into perspective relative to organization characteristics. This involves establishing a linkage between CA and PA in the legend of Figure 9.3 to analyze the relationship between threat and hazard conditions and the vulnerability of each critical asset to determine mitigation selection and evaluation, with the understanding that not all risks can be addressed and not all assets can be protected because of limitations of resources and funding, and practicality. Accordingly, security risk characterization forms the basis for deciding which actions are best suited to mitigate security risk.
Using the legend CA criteria presented in Figure 9.3, each listed threat and hazard is given a consequence severity rating based on the narrative that describes the potential harm that could develop should an event occur. For illustrative purposes, the narrative is presented in general terms, offering a wide range of application to various infrastructures and assets. To achieve better utility and local meaning, threats, hazards, and the narrative can easily be modified to fit the particular configuration and structural makeup of specific critical assets and other site conditions.
Once you have assigned a CA rating from the legend in Figure 9.3—F, VS, MS, SS, or SU—to each threat and hazard, you can determine the realistic PA, taking into consideration factors that would influence your decision making. Use the legend PA presented in Figure 9.3 to complete this analysis by assigning each threat and hazard a PA rating of H, M, L, or I.
Once you have completed the CA and PA analysis, you are ready to start the next steps in the strategic planning process: validating mitigation risks, selecting mitigation actions, and evaluating the potential of residual risk exposure. Together, these data provide decision makers with sufficient crucial information to prioritize risk, consequences, and probability to ensure that resources and funds are used where they are most needed. Because some threats are less likely to occur than others, ranking or prioritizing each threat according to the likelihood of occurrence against the criticality of a particular asset, and against the consequence of asset loss should an event actually happen, is essential to sustaining critical business operations (Sullivant, 2007, pp. 109–129).
## Benefits of Having a Threat Estimate Profile
When the elements of threat, vulnerability, and consequence are combined, they form the risk associated with critical infrastructures and assets. The result is a comprehensive systematic and defensible analysis of an asset's criticality that drives integrated risk reduction activities. The threat estimate profile allows decision makers to:
• define the level and range of a natural disaster, weather-related calamity, industrial mishap, criminal activity, or other major catastrophic event
• determine the probability and consequences of threat occurrence
• understand an adversary's capabilities, operations, tactics, and support mechanisms
• provide insight into strategic, tactical, and operational planning; countermeasures development; program implementation; and staffing needs by reducing threat attractiveness, vulnerability, and the ensuing consequences of loss
• formulate strategies to protect assets against and mitigate the effects of threats, vulnerabilities, and consequences
• channel scarce resources and funding into those areas that need it most by bringing together the right balance of people, information, facilities, operations, processes, and systems to deliver cost-effective solutions, which, when applied and integrated into practice, lead to improved awareness, preparedness, prevention, response, and recovery from events—whether manmade crisis, accidents, or natural disasters.
## Conclusions
Too often, corporate security strategies are not aligned with corporate business strategies. Aligning security strategies with business strategies can ensure that corporate security programs are in harmony with company priorities and can place the security director and chief executive on the same page. A valid threat estimate profile helps to achieve this goal. A threat estimate profile helps planners and decision makers to:
• define the level and range of natural disaster, weather-related calamity, industrial mishap, criminal activity, or other major or catastrophic event
• determine the probability and consequences of threat occurrence and understand an adversary's capabilities, operations, tactics, and support mechanisms
• provide insight into strategic, tactical, and operational planning; countermeasures development; and program implementation
• determine staffing needs
The information that makes up the threat profile is never static. The threat profile is a "living document" that requires constant review and updating as the threat environment changes. It should always be used as a backdrop to developing corporate security strategies, planning, and direction.
Not having a reliable, useful, and meaningful threat profile makes it difficult to determine what the highest-priority activity should be when planning and coordinating security operations and initiatives. Any analytical effort would certainly be misguided and ineffective, and more than likely mimic a false sense of accomplishment, leading to excessive and counterproductive labor efforts, less-than-satisfactory performance expectations, and wasteful expenditures.
## Appendix A
Figure 9.2 Range of potential threats and adversary characteristics.
## Appendix B
Figure 9.3 Consequence analysis (CA) and probability of occurrence (PA) of threats and hazards. Source: Sullivant, J., 2007 (CFC, CSC, CHS-IV, CPP, RAM-W, DABFET). Strategies for Protecting National Critical Infrastructure Assets: A Focus on Problem-Solving (Exhibit 7.7 Example Worksheet 18-Malevolent Acts & Undesirable Events by Loss of Consequences and Probability of Occurrence (PA) page 151). Wiley & Sons, New Jersey.
10
# Establishing and Maintaining Inseparable Security Competencies
## Abstract
This chapter introduces the concept of inseparable competencies and describes the value and meaning the competencies have in supporting business goals and objectives. A security organization has only one mission: to deter, delay, prevent, protect, assess, respond to, and recover from any significant security event that influences the operation or survivability of the corporation. Any other activity performed by a security organization is secondary. This chapter emphasizes the importance of strategic and tactical planning vision and insight to preserve life and safeguard assets. It calls for a strong commitment to sustain a degree of care and diligence, or to face the consequences of failure. Actual examples of operational requirements are offered throughout the narrative.
### Keywords
Chain reaction relationship; Delay/penetration resistance; Detection and assessment processes; Intangible strategy; Operational competencies; Performance outcomes; Prevention and protection techniques; Principle of timeliness; Response and recovery
Deterrence, delay, prevention, protection and detection are meaningless capabilities unless you have the ability to assess, respond to and recover from a major threat event.
John Sullivant
Top Takeaways
• Importance of executing ability and capability
• Criticality of detect, prevent, protect, assess, response and recovery
• Integrating the principles of timely security reactions
• Reality of dealing with potential failure
• Importance multitasking and multidisciplinary competencies
## Overview
The concept of "inseparable security competencies" is characteristically embedded in any security organization, regardless of size, whether public or private. Few chief executives I interviewed, however, expressed any understanding of the true value and meaning these concepts have in supporting their business goals and objectives. The capabilities concept contains two major segments that permeate every aspect of an enterprise. The first element entails the strategic vision and tactical insight to effectively plan and develop strategies to deter, delay (or deny), prevent, protect, detect, assess, respond to, and recover from any attempt to disrupt, damage, or destroy an entity's resources, critical infrastructure, and key assets as well as classified, sensitive, and propriety information. The second element involves the timely strategic and tactical integration of human and technology performance to direct and carry out those actions necessary to contain, neutralize, or defeat a wide array of threats. Here, I emphasize the importance of establishing, distinguishing, and maintaining these competencies.
## Are Your Security Competencies a Top Priority?
It is noteworthy to report once again that a security organization has only one primary security mission: to deter, delay, prevent, protect, detect, assess, respond to, and recover from any significant security or security-related event that affects the operation or the survivability of the corporation. Any other activity performed by a security organization is secondary (Sullivant, 2007, pp. 165–169).
These indispensable competencies call for a security organization to have the necessary strategic and tactical planning vision and insight to preserve life and safeguard assets, prevent unauthorized access to critical areas and information, achieve agreed upon involvement and commitment, and ensure the ability and capability to perform to regulatory requirements, industry standards, best practices, or management expectations. Moreover, it calls for the creation of integrated processes, policies, and protocols, and to obtain and sustain the necessary resources, facilities, operations, and technologies to achieve overall security resilience.
Unless and until you commit to establishing and maintaining the necessary degree of care and diligence expected (or required), achieving the ability and capability to perform your primary mission is doubtful. Therefore it is essential that you understand and recognize the significance of these abilities and capabilities because this knowledge directly influences how seriously you take the task of measuring and evaluating these critical security competencies, and accepting their performance outcomes (Sullivant, 2007, pp. 169).
Fig. 10.1 Eight Inseparable Security Competencies illustrates the relationship, interdependency, and suitability of these capabilities in a highly reactionary industry in both planning and execution.
The processes of deterrence, delay, prevention, protection, detection, assessment, response, and recovery are by default time-sensitive and time-dependent functions that vary from one situation and set of circumstances to another and under varying threat conditions. The operational significance of this chain reaction relationship is that to be effective, the ability of the security organization to detect, assess, and respond to a given event is measured not in hours or minutes, but in almost real time, spanning only 5–8 s under the greatest-severity threat conditions. Any hesitation on the part of a security organization to react outside this window could be catastrophic for the enterprise. Understanding the integrated role these competencies play in strategic security planning is essential to carrying out your prime security mission. These security techniques, means, and methods—when planned, designed, and applied properly—create a formidable prevention and protection strategy that can serve an organization well in reducing risk exposure, while improving and enhancing organizational and security resilience. I discuss each strategy in the subsections below.
Figure 10.1 Eight inseparable security competencies.
### Deterrence Is Mostly an Intangible Strategy
Deterrence is a by-product of the various security strategies embraced by a security organization. Deterrence may encompass administrative processes, protocols, practices, and security awareness, as well as physical and technological measures and techniques aimed at protecting critical infrastructure and key assets from an array of threatening conditions.
• Administrative measures may involve the redesign of suitable security systems, changes in protocols and practices, more emphasis on employee security awareness, and an increase in intelligence-gathering activities.
• Physical measures may be natural or manmade barriers or facility architectural design.
• Technology measures may include alternative materials and processes, interoperable communications and information networks, and advanced and emerging security technologies.
The goal of deterrence is to create conditions that make it more difficult for an adversary to carry out a threatening activity, thus presenting an unacceptable risk to the adversary in inflicting harm, injury, or death to resources or in damaging or destroying critical assets and other properties. When an adversary perceives an unacceptable risk, the effectiveness of deterrence can influence the adversary to adjust or change the mode of penetration, attack, tactic, and weapons used, as well as increase the time it takes the adversary to complete a particular mission. Deterrence aids delay, prevention, protection, detection, assessment, response, and recovery, and it provides to employees, governing authorities, and the community a level of confidence that a safe and secure work environment exists.
### Delay Channels the Population
Physical barriers are used to restrict, channel, deny, delay, or prevent an adversary from gaining access to a protected area and reaching an intended target. Barriers can be natural, such as mountains, deserts, water obstacles and rivers, cliffs, ditches and canyons, seas, or other natural features that are difficult to traverse; they can also be structural, such as fences, floors, walls, vaults, barricades, fences and gates, grills, roofs, bars, barbed wire, and other structures or vast open space and distances of travel. Delay is also designed to slow down the adversary in reaching a vulnerable point or asset until a response force capable of defeating the adversary can arrive at the scene. For example, conditions that determine how long it would take an adversary to reach an objective is dictated by such factors as:
• perceived strength and capability of the security organization and its response elements
• configuration of the area
• site or facility hardness and standoff distances
• types and quantity of physical barriers to be crossed
• distance to targeted area
• expertise and tactical skill sets
• types of tools, weapons, and equipment the adversary must use
• a safe escape route and time required to depart the area
Penetration resistance time is measured from the moment of detection, typically at the boundary of the property or restricted area housing critical assets, to the moment the adversary reaches a targeted asset. Ideally, the time it takes a response force to reach or connect with the adversary should not exceed the time an adversary, once detected, would need to reach a targeted asset. Few security organizations incorporate this time-sensitive response capability into their emergency planning or practice sessions. Even fewer exhibit a willingness to expend resources and funding to acquire this capability.
Much of the regulated security industry, however, mandates some degree of delay/penetration and response time requirements. Some industry standards address volunteer delay/penetration and response times as well.
• The facility delay/penetration criterion can vary based on the characteristics of particular infrastructures and assets, their mission, regulatory mandates or industry standards, and whether national, regional, or local security interests are at stake.
• Some operational security requirements call for a 5-min delay/penetration time to be built into the security design. Under this architectural standard, the in-place security response force is expected to maintain the ability and capability to respond and engage an adversary within that 5-min window—preferably before the adversary reaches a targeted asset and has time to cause harm, injury, damage, or destruction.
• Other criteria can range from 15- to 30-min delay/penetration resistance times for high-value assets such as commercial nuclear power stations, power generation plants and dams, water treatment and waste plants, and other critical infrastructures, such as defense manufacturing and research, development, test, and evaluation centers.
• For Department of Defense and other national critical assets, stringent delay/penetration resistance time may exist for such assets as high explosives, ammunitions, and weapons.
• Military strategic and tactical weapons systems and personnel on alert also have stringent delay/penetration resistance requirements, as do national intelligence facilities, telecommunications systems, space satellite systems, and National or Military Command, Communications and Control C3 facilities.
• The protection of nuclear weapons and the assurance that they remain continuously within the custody of the U.S. government, whether deployed on land, on sea, or in the air, have special security measures and delay/penetration timelines.
Notwithstanding the various delay/penetration and response times evoked throughout the private and public sectors, one thing is clear. The more critical a particular asset is to the interests of U.S. national security or the economic survivability of a corporation, the greater the delay/penetration time—and the more security resources with greater abilities and increased capabilities need to be allocated to protect the asset. This results in a higher capital investment and higher operational and training costs to secure these special assets.
Typically, within the private sector, such abilities and capabilities are rare. The authority, responsibility, and accountability to protect the most critical assets and operations affecting national security or corporate survivability within the content of national defense RDT&E or production are generally assigned to special security organizations that possess the necessary skill sets, knowledge base, expertise, training and qualifications, logistics, and resources to engage in such special mission assignments under industry and government special agreements. Delay/penetration resistance techniques help the deterrence, prevention, protection, detection, assessment, and response processes, giving the security organization time to assemble and react to a given threat condition in a timely manner.
### Prevention
Prevention has various collective meanings, all aimed at achieving the same outcome. I define prevention as:
• specific operations aimed at deterring, preempting, interdicting, or disrupting illegal activity
• protecting lives and providing for the general well-being of the workforce
• assessing and analyzing conditions to determine the full nature and source of the threat to reduce risk exposure
• means and techniques to avoid, preclude, or limit the impact of a disruption; eliminate, deter, or prevent the likelihood of a disruptive incident and its consequences; remove human or physical assets or their lockdown location; or help stop something from happening or arising, thus significantly reducing risk exposure.
• increasing security operations, heightening inspections, and improving surveillance operations
• applying intelligence and other information to a range of activities and sharing information, warning, and alert notices with others
Prevention helps the deterrence, delay, protection, detection, and assessment processes.
### Protection
Protection involves those capabilities necessary to shield, preserve, and secure resources and assets, keeping resources safe from injury or death and assets safe from damage or destruction.
• Protective measures can include the integration of resources, processes, practices, protocols, and facility designs to guard against malevolent attacks such as terrorism and sabotage, criminal activity, disasters, and loss of services or injury from system or equipment failures.
• Protective measures may include the removal of hazardous materials, relocation of operations and resources, or the total lockdown of a facility or site, and providing increased security patrols and fixed posts, as well as implementing special security compensatory measures.
• Standoff distances are also a means of shielding that helps to reduce or minimize the effects of an explosive charge placed at or near the boundary of an area or facility, or collateral damage sustained from a nearby asset or facility under attack.
Protection helps the deterrence, delay, prevention, and detection processes.
### Detection
Detection measures are designed to expose the presence of intruders, unauthorized weapons, explosives, and other contraband; criminal behavior; and any compromises in security system integrity. Detection monitors the validity of access controls, circulation controls, and behavior patterns, and communicates an alarm. Ideally, detection should take place as far away as possible from the critical assets requiring protection.
Detection techniques help the prevention, delay, protection, assessment, and response processes.
### Assessment
Assessment is the evaluation of unusual events such as security breaches, criminal behavior, or unauthorized activity. Humans, technology, or a combination of both can perform assessment. Assessment may require the strategic deployment and use of area patrols and fixed posts complimented by security technology such as CCTV cameras that activate in conjunction with sensors in alarm status. Other means can also contribute to the assessment process:
• Employee security awareness and reporting of incidents
• Procedural checks and balances such as passwords and code words
• The "buddy system," or "two-person" rule
• Verification and authentication systems
• Environmental control systems
• Management information systems
• Supervisory control and data acquisition systems
• Supervisory oversight of any combination of the above
With all these techniques in the "security toolbox," a security organization—in concert with other business units—can maintain a reasonable ability and capability to perform detection and assessment through direct human observation; enforcement of protocols, processes, and practices and security awareness, assisted by technology.
The use of technologies also enhances the safety and effectiveness of first responders and reduces the need for expensive use of patrols and fixed posts to perform the assessment function. Security lighting and advanced infrared technology also enhance surveillance and assessment capabilities.
The use of remotely dispersed intrusion detection and surveillance devices creates the need for a security organization to be aware of the validity, severity, and nature of an event that triggers an alarm. Beyond the technical capability to visually announce an alarm and to use video to surveil areas, the responsibility to assess and analyze developing situations and conditions rests solely with the expertise and experience of the system operator, as well as the leadership and experience of the security management team. This team must direct and carry out a response capable of containing, neutralizing, or stopping an undesirable event. For security incidents, the window of this initial assessment is extremely time-critical and time-sensitive.
### Response
The security response addresses the short-term, direct effects of an incident. Response activities may include:
• operations aimed at preempting, interdicting, or disrupting illegal or unauthorized activity
• prioritizing assignments for normal posts and patrols
• increasing or expanding security operations and continuing investigations into the nature and source of the threatening incident
• applying intelligence and other information and actions to lessen the effects or consequences of an incident
• providing area and perimeter security and strict access control during a widespread pandemic that may involve the isolation or quarantine of personnel pending transportation to medical facilities
### Recovery
Once response actions are complete, recovery addresses those actions that are required to get the security force and corporation back to normal business operations:
• Maintaining the security of the area affected, preserving evidence and controlling access to the scene during the initial stages of rescue operations and investigation
• Maintaining the security of the area during construction to repair and/or replace lost facilities, infrastructure, and assets based on the criticality of business operations
• Determining what short-term and long-term compensatory measures will be required and the resources, facilities, and equipment needed to sustain such operations
• Providing assistance to return the affected area back to normal business operations by shifting security priorities while still maintaining a high state of alert
• Planning the reestablishment of normal security operations for the affected area(s) while supporting other areas of the corporation on an extended work schedule
• Adjusting the corporate threat alert notification system based on the severity of the threat event and corporate vulnerability exposure to circumstances, conditions, and situations created by the initial threat condition
• Evaluating security conditions during and after the event to determine the need to reduce or expand security operations, to determine additional resources and logistical support needed to continue security operations, and to identify lessons learned.
## Timely Interdependencies of Security Capabilities
There can be no doubt that the principle of timeliness is crucial to effective security operations (Sullivant, 2007, pp. 169–172). In the realm of security operations, deterrence, delay, prevention, protection, detection, assessment, and response are critical time-sensitive and time-dependent capabilities that cannot be ignored unless executive management takes on the awesome responsibility of accepting the consequences of residual risk exposure without approving the continuation of reasonable security compensatory measures. I discuss each of these principles below.
### Principle of Timely Security Deterrence Should Focus on "Curb Appeal"
The principle of timely deterrence refers to attractiveness as a target (or, in real-estate terms, its "curb appeal") the enterprise demonstrates to its customer or client base, community and governing bodies, as well as adversaries. The architecture of the corporation should display strength, confidence, and leadership. Its configuration and layout should give an adversary cause to pause and assess the probability of a successful breach or, conversely, the consequences of failing to successfully complete an attack. The goal of timely deterrence is to lead the adversary to the conclusion to "shop elsewhere."
### Principle of Timely Security Delay
The principle of timely delay introduces a series of strategic obstacles and nuisances into the path of an adversary; these are aimed at increasing the time it takes the adversary to reach a protected asset or activity, thereby increasing the risk of unnecessary exposure while permitting time for an adequate response to develop and take hold. Overcoming obstacles and processes to achieve an objective requires the adversary to have more resources, logistical support, communications and equipment, and an equal amount of assistance to ensure an escape route and find a safe heaven immediately afterward. If the technical delay mechanisms used are ineffective, an aggressor could trip one or more lines of detection, open or bypass one or more portals to gain access to an area, or circumvent several protocols to complete the assignment and leave the area before the response force arrives. Or an aggressor could seal off a series of alarms in the system and still take the time needed to complete the mission, knowing that the response will be inadequate.
### Principle of Timely Security Prevention
The principle of timely prevention is the continuing link of security measures in progress. Its aim is to introduce integrated safeguards and physical barriers, processes, administrative procedures, and building architecture and layout designs that reduce an adversary's attraction to critical infrastructures and key assets.
### Principle of Timely Security Protection
The principle of timely protection takes into consideration built-in architectural design safeguards such as explosive and penetration resistance technologies; heating, ventilation, and air-conditioning protection screens and filters; physical barriers and safe havens and other means and mechanisms to minimize injury or safe life, or damage or destroy property until a response force capable of engaging and neutralizing an adversary arrives on the scene.
### Principle of Timely Security Detection
The principle of timely detection requires that the penetration of a protected area or asset be detected as far as possible from the facility, system, or function and before the adversary reaches the intended target. A security program's detection capability is only as good as the security force, employee security awareness, and the properly deployed and integrated security systems that perform to expectations or standards.
### Principle of Timely Security Assessment
Real-time assessment includes the immediate actions taken to react to security and security-related events in real time. Real-time assessment involves the processing of critical information and potentially harmful conditions in sufficient time to be useful in the formulation of a timely response. The goal of timely assessment is to provide the security organization with a real-time assessment capability to observe and evaluate situations and conditions, to track the aggressor(s), and to provide the necessary direction to the response force to control, contain, or neutralize the threat in almost real time. An effective assessment capability has two elements: event identification and event tracking.
#### Event Identification
Assessment must be able to distinguish between normal acceptable activity and behaviors and any deviation from these norms. Human assessment can accomplish this (in part) through a motivated and dedicated workforce, security awareness training, security patrols and fixed posts, and the reporting of unusual activity or behavior. But the critical aspect of human assessment mostly rests with the security system operator and supervisor within the security monitoring station. When human assessment is complemented by video technology, the application of cameras must provide for near-real-time activation of a detected event to distinguish clearly the severity of the threat (including, if possible, the identity of the perpetrator(s)) to determine a proper response. Where integrated security systems are deployed, a tripped alarm should announce and display at a remote monitoring station in 1 s or less. Where CCTV components are integrated into the detection system, camera activation and display of the alarmed zone at the monitoring station should occur in 1.5 s or less. This combined transmission time accounts for a 2.5-s lapse before the system operator can even interact with the system to perform a "human assessment" of the conditions, circumstances, and situations that caused the alarm. In most instances a qualified and certified security system operator can digest the scene and recognize what is happening in 3 s. It can take the operator an additional 3 s to notify and dispatch an in-house response force to the scene. This brings the total time lapse up to this point to at least 8.5 s—more than enough time (a skilled aggressor needs 5 s)1 for a skilled adversary to clear an 8-foot chain link fence or other barrier, move out of the footprint of a camera, and blend in with the surrounding environment.
#### Tracking the Adversary and Activity
For the safety of the response force and standby observers, it is crucial that the security force know the exact status of conditions at the scene as well as the capability and activity of the aggressor(s) if it is to effectively contain, neutralize, or defeat the adversary. This can be accomplished only through proper human assessment. To achieve this goal, the security system must have the capability to track the sequence of events and the movements of the perpetrator(s). Once the aggressor(s) is out of a camera's view, the system operator must expend additional time and energy searching for and tracking the intruder(s) before he or she can guide the response team toward the aggressor(s) by reporting the intruder's activity, and in determining the severity of the penetration, if possible.
#### The Muddied Water
The situation becomes more complicated when the security organization must rely on receiving information from employees and others; from operations, communications, and other centers that monitor activities; or by communicating with one or more local law enforcement agency. Under these circumstances and conditions People get caught up in the moments surrounding excitement, uncertainty, and often fear. Some people loose their thoughts, others speculate what they actually heard or saw. Others want to feel important and either exaggerate or lie about the events that happened. Here are some examples:
• First reports and information received from employees and others could take several minutes after an occurrence. Experience reveals that such initial reports are always fragmented, incomplete, and even contradictory. This often delays the initial assessment process and the response team from getting to the scene in a timely manner. It may also limit the usefulness of the response team once the team arrives on the scene.
• Making contact with law enforcement agencies and explaining the threat situation could take several minutes, usually followed by an undetermined amount of time for them to arrive on the scene. Although many police departments (and other law enforcement agencies) have an exceptional record of responding to incidents within the private and public sectors Fox News recently reported that the average national response time for law enforcement is 11 minutes. I have tested many law enforcement agencies and have clocked their response time between 5 to 10 minutes, although some agencies can take up to 30 min or more to show up, depending on available patrols, distances and traffic conditions, and other public service priorities. Additional time is usually expended after law enforcement units arrive at the scene because they often require a briefing of the circumstances and conditions that caused the call for assistance, as well as safety issues that could impede their response. Being escorted by corporate security personnel to where the adversary(s) is or was last sighted can also delay the law enforcement response.
### Principle of Timely Security Response
The principle of timely response involves the immediate actions that prevent loss of life or property and provide emergency assistance to others. For security it involves the ability to demonstrate a timely, gradual, and flexible response that is sufficient to prevent, control, contain, or neutralize the event that justified the call and that can react to more than one event-driven threat scenario simultaneously. The makeup of the response force is not important—what is important is the ability and capability of the response force to react under the time constraints imposed upon it. The response may involve the ability and capability to:
• carry out its function of saving lives and protecting assets
• neutralize or contain a threat
• establish and secure the perimeter of an area
• preserve the integrity of an area and control access
• assist in the evacuation of an area or building
• guide and assist external first responders such as police, firefighters, and medical personnel to the scene
• report conditions, circumstances, and situations to management
### Principle of Timely Recovery
In times of crisis and danger a security organization must possess the ability and capability to:
• expand and contract its shifting resources and changing priorities, and to disperse and work individually and as a group
• coordinate and work with affected internal business units and with external emergency service agencies, law enforcement officials, and other governing agencies, as the situation calls for
• continue protecting the scene, control access, perverse evidence and help remove injured personnel
• recall off-duty personnel, brief them on conditions, and make assignments
• manage on-duty personnel and shift their mind-set from normal security operations to one or more emergency crisis while potentially transitioning into a 12-h shift
• remove from duty and replace security personnel who may have been injured or lost in the line of duty; replace others who would need to be relieved to eat, rest, and sleep, and then return for another extended shift
• transition the staff back to normal security operations while maintaining an emergency security posture for as long as necessary to support enterprise recovery operations
• gradually withdraw the expanded security force from the area when corporate restoration operations are completed
## Conclusions
Inseparable security operational competencies are an characteristic inherent in any security organization, regardless of size. Equally important is the effective planning and deployment, and timely execution of these crucial capabilities. Without them, a security organization cannot perform its prime mission.
### Deterrence
The principle of timely deterrence aims at giving an intruder cause to pause. It is the visual evidence that a security program and commitment by management will induce some perpetrators to look to attack other facilities where exposure would be less risky for them.
### Delay
Delay slows an adversary in his or her attempt to reach a targeted asset so a response force capable of containing, neutralizing, or defeating the adversary can interrupt the intrusion.
### Prevention
Prevention methods are used to avoid, preclude, or limit the impact of a disruption; eliminate, deter, or prevent the likelihood of a disruptive incident and its consequences; remove human or physical assets to their lockdown locations; and help to stop something from happening or arising.
### Protection
Protection shields, preserves, and keeps resources from injury or death and assets from damage or destruction.
### Assessment
Security technology plays a vital support role when systems are programmed to respond to specific hazardous stimuli. For instance, when a harmful contaminant is released within a research laboratory, the monitoring system may be programmed to sound an alarm when the agent is detected. The response may include sealing the portals and utility openings and releasing neutralizing agents to sanitize the area through a secondary and protective ventilation system, followed by a human response to remove personnel from the affected area when it is safe to enter. As such, the overall technical solution to a security response must assist—never hinder—the security organization when executing a human response to an incident.
### Response
Deterrence, delay, detection and assessment are meaningless unless the security organization has the ability and capability to respond to the scene and to neutralize or contain an adversary. The capability to response is operationally dependent on a human function, as is visual assessment and surveillance. A security organization must maintain the capability to intercept, contain, and neutralize an aggressor before he or she can reach the intended target.
### Recovery
Recovery is the ability of the security organization to operate well enough to meet its obligations to protect the life/safety of employees, and protecting property in any given emergency while transitioning back to normal security operations is essential while business units concentrate on restoring business and revenue capacity. More attention needs to be given to security recovery operations to effectively support corporate recovery efforts, to prevent security force "burnout" from working extended shifts for prolonged periods, and to avoid staff shortages.
### Closing Thoughts
A security organization must maintain the capability to detect, assess, and track the sequence of events and the movements of a perpetrator(s) from the start of the engagement through the conclusion of the incident. Security organizations that fail in detecting, assessing, and tracking security events and in initiating an appropriate response within 5–8 s are substandard performers. These security organizations cannot adequately perform their prime security mission. A technical audit or assessment of a security system is an excellent risk management tool to measure and evaluate the performance parameters of a security system, to determine mitigation solutions that are necessary to bring an existing system up to par with industry standards, or to determine to replace it with state-of-the art technology.
* * *
1 Sandia Laboratory has completed reliable and validated penetration tests of 6-foot, 7-foot, and 8-foot fences and other barrier systems under various weather conditions. Fences and barriers were cleared in 3–5 s on successive successful tests.
11
# A User-Friendly Security Technology Model
## Abstract
This chapter details the elements that are crucial to developing a technical security strategy. It discusses security planning and security design, and engineering planning from a systems-level perspective. It addresses the purpose and benefit of conducting a technical security analysis. It outlines the ramifications of the technical security planning process, highlighting a concept of technology application; the development of system performance factors; the importance of having quality maintenance, inspection, and testing programs; the need to establish and maintain the capability to respond to system failures; and the importance of implementing security compensatory measures. Actual case histories highlighting system deficiencies and ineffective technology applications and poor maintenance practices are presented.
### Keywords
Concept of technology application; Human factors engineering; Inspection and testing; Maintenance and logistics concept; Preventive maintenance; Quality performance factors; Security design and engineering planning; Security planning; System integration; Technical security assessment
Security technology was never intended to replace or reduce the security force, but to make it easier for them to focus human attention on assessment, analysis, decision making, and accountability. The application and configuration of security technology, therefore, must always complement security operations and never hinder, hamper, or slow down the security organization from carrying our its critical security mission.
John Sullivant
Top Takeaways
• Create a technical security strategy
• Interdependencies of the technical security planning and security design planning processes
• Significance of technology application and system configuration considerations
• Criticality of system quality performance parameters
• Quality maintenance and logistics support capability
• System failures and the need for compensatory measures
• Inspection and testing of security systems
• Selected case histories
## Overview
Security operations are becoming increasingly computerized and rely more and more on the finite performance standard of electronic capabilities to improve the effectiveness and efficiency of the security organization. When security technology is properly pulled together and correctly applied to protect critical assets and processes, the result is a functionally integrated security system that offers capabilities that are unmatched and unachieved by a human attempting to perform the same functions.
This demands we know how well security systems perform and what actions we must take to correct deficiencies, weaknesses, and nonconformities to performance expectations or specification standards. The application of system availability, readiness, reliability, maintainability, supportability, and survivability, as well as technology application and human factors engineering, are crucial elements that significantly contribute to achieving security mission requirements.
## A Dire Need Exists to Embrace a Technical Security Strategy
The execution of a sound technical security strategy requires extensive research, thorough planning, comprehensive understanding of the critical issues and risks inherent in any security system upgrade or new procurement undertaking, and exhaustive teamwork between the security organization, the engineering unit, executive management, the procurement division, and other business units.
The demand for developing a technical security strategy stems from poor technology performance and the lack of a strategic vision to correct the problem, and a lack of understanding the fundamental mission of security technology. Appendix A - Selected Security Technology Deficiencies and Weaknesses graphically illustrate selected histories that tell a compelling story about the widespread security technology conditions and circumstances that exist throughout the industry. One approach to developing a technical security strategy is to pool enterprise resources with technology designers and system integrators to help advance an overall understanding of technology performance, system capabilities and limitations, application theory, and life cycle care. The security director must assuredly orchestrate this umbrella strategy, lead the nurturing of team-building skills, and embrace the use of advanced techniques that ensure timely detection of, assessment of, and response to security events.
## The Technical Security Planning Process Is Often Misunderstood and Underestimated
As can be seen in Fig. 11.1 \- An integrated technical security planning process: a unifying umbrella strategy, An integrated technical security planning process: a unifying umbrella strategy, functional areas of responsibility are divided yet interwoven between the security organization and the design and engineering unit. The figure illustrates in the most general terms the exchange of management and engineering excellence necessary to carry out the overall technical planning process.
Figure 11.1 An integrated technical security planning process: a unifying umbrella strategy.
At its highest level, the division of planning activities is convenient for the purposes of this discussion. In its simplest form, security planning and security design planning merge to become a management and engineering analysis process. The former falls within the realm of security operational competencies, whereas the latter draws on architecture and engineering aptitudes to support operational needs. To successfully deliver a functional security system, the security organization and the engineering unit must work hand in hand. Early technical decisions have a profound effect on the delivery of a functional system with matching performance expectations. Appendix A: Security Technology Deficiencies and Weaknesses Case Histories clearly bring this point to the forefront.
### The Technical Security Analysis Provides a Road Map to Decision Making
The first step in the technical planning process is to characterize the configuration and performance capability of an installed security system, if one exists. The security director, in concert with the engineering department, is responsible for conducting this technical analysis or ensuring that a qualified security consultant performs one. Fig. 11.2 \- Security system technical analysis methodology, a security system technology analysis model, illustrates the investigative process from a systems-level perspective (Sullivant, 2007, pp. 179, 273). The model is flexible and can be customized to fit the unique needs of any security organization, large or small.
#### Purpose of the Technical Analysis
The technical analysis measures the strengths and weaknesses of in-place security technologies, identifies limitations and gaps in application and performance, and evaluates the consequences of system ineffectiveness. The security technology analysis aims to:
• characterize system objectives, technology application, performance parameters, and mission
• characterize quality factors and system capabilities
• characterize human factor engineering dependencies between man–machine interfaces
• determine time-sensitive and time-dependent characteristics
• identify gaps in system performance and protective features
• analyze system deficiencies, vulnerabilities, weaknesses, and consequences
• determine the system's life expectancy
• increase system performance and capability in an all-hazards environment
• build in network resiliency
• introduce improvements to strengthen performance, safety, integrity, and survivability
• evaluate the system operator's knowledge base and competency
• identify gaps between existing training and training needs
The process emphasizes a total quality systems approach to problem solving that contributes to determining mitigation solutions that are acceptable to executive management.
Figure 11.2 Security system technical analysis methodology.
#### Benefits Derived from the Technical Analysis
Decision makers can benefit from the analysis because it helps them understand:
• how systems can best be deployed, how integration increases the performance capabilities of the security organization, and their relationship with and dependency on other security program activities
• system vulnerabilities and weaknesses and the technology's effectiveness, efficiency, and productivity for detecting, deterring, assessing, and responding to security-related events in near real-time
• the consequences of their decisions about system usage and performance, how to steer long-term planning needs for facility and space use, and how to channel scarce resources and funding into those areas that need it most
• what remedies work best to strengthen system performance and enhance the integrity of system operations and survivability
• how effective use and careful handling of the equipment and its proper maintenance as called for by the manufacture protects the warranty and extends the life cycle of the entire system
### The Role of Security Technology Planning
The security director assimilates the technical analysis and feeds the findings into the overarching technical security planning process. In this role, the director collaborates with scientists, technology developers, system integrators, unit engineers, and others to:
• solve system technical issues using a systematic approach and develop mitigation actions from a business and management perspective
• ensure regulatory compliance
• train the organization to achieve its inherent operational effectiveness
## Embracing The Challenges of New Technology Advancements
When no system exists, the director has the option of starting a technical analysis review process by researching and analyzing data, and performing a competitive analysis of the initial platform to develop a preliminary design document that characterizes system performance, maintenance, logistics, training, and other important characteristics. Or, the director may opt to a unit engineer, or have a security consultant perform this task. Regardless of the party performing the analysis, it is crucial that the design document serves to communicate system performance expectations to the engineering group responsible for creating the engineering drawings and delivering a functional and acceptable system to the security director. Preparing a design is a complex task and includes, but is not necessarily limited to, the following substrategies. The design document or system specification must define:
• The goals and objectives of the security system.
• Critical system operational capabilities and abilities that must be performed and by whom.
• Critical processes and best practices, including system self-healing features.
• Realistic event-driven response and recovery scenarios.
• Critical time-sensitive and time-dependent activities that are important to the design.
• System fail-safe and integrity features.
• Quality performance standards, safety and human factors engineering.
• Life cycle logistics, maintenance, and depot support needs.
• Failures that would call for implementing security compensatory measures.
• Inspection and testing requirements.
• Training and certification requirements.
In the design document or specification it is crucial to describe clearly, in unambiguous terms, all critical system performance characteristics, requirements, and standards that must be met, including any acceptable design alternatives and constraints or limitations that may influence the design.
### The Role of Security Design and Design Engineering
The lead engineer is responsible for developing an acceptable technical design and is responsible to the security director for delivering a functional and workable design and associated integrated plans. Security design planning begins early in the security planning stages, starting with the results of the technical analysis and a preliminary design concept. As the design matures, and with guidance furnished by the director, engineers resolve technical and human interface considerations, perform trade-off analyses, assist in verifying performance expectations, and capabilities, and perform a series of design reviews with stakeholders. Typically, three design reviews are called for: the preliminary design, the detailed design, and the installation design.
A significant goal of design planning is to ensure time-sensitive and time-dependent security operational needs and performance standards specified by regulations, industry best practices, and local operational requirements are met. Another design goal is to ensure system configuration and performance complement security operations, and never hinder, hamper, or slow down, the security organization in carrying out its ability and capability to perform its critical mission: deter, delay, prevent, protect, detect, assess, respond to and recover from one or more security events or other emergencies in near-real time.
Also, the application of security technology is not intended to replace or reduce the security force, but to make it easier for them to focus on incidents, events and threats, and exchanges with other persons. Under this concept, security technology helps realign the security force so human skills can be applied to critical decision-making tasks such as reporting conditions, assessing circumstances, investigating incidents, and determining the type of responses. Proper security response requires strategic and tactical planning, agreed-upon involvement, and capability to perform to expectations. Throughout the design process, engineers must work hand in hand with the security director and security staff to:
• identify the characteristics of hardware, software, facilities, data, personnel, and training
• translate operational needs into technical performance characteristics
• define system technical performance capabilities, including system integrity features
• integrate technical compatibility of physical, functional, and program interfaces
• integrate quality factors into the engineering process to meet operational objectives
• clarify complex technical interdependencies, synergies, and trade-offs
#### Quality Factors and Safety Features
Experience has repeatedly demonstrated that emphasis on quality factors (readiness, suitability, availability, reliability, maintainability, supportability, and survivability) and safety concerns must start during the earliest planning activities to ensure the characteristics of the system are dealt with and established at the front end of the security planning and system engineering and design cycles.
Retrofitting quality factors and safety features after the design is complete and the procurement process has begun can be a costly "mistake" and often cost prohibitive to correct, forcing the security director to accept a poor design, weak system performance, and accept substandard performance from the security workforce. Retrofitting security into the design after the fact can increase costs anywhere from 30% to over 300% from the original cost estimate. I cannot emphasize enough the importance of you not falling into this trap. You will never be able to recover from engineering flaw.
### What Does Integration Mean to the Security Professional?
System integration is the bringing together of a set of component subsystems into one arching system and ensuring that all components function together as an integrated whole throughout the system's life cycle. This means that design management and engineering analysis for system performance and technology enhancement is a work in progress always measured against the changing mission requirements.
As security integrators, we must have a deep understanding of the prime security mission and its capabilities, and we cannot be ambiguous about what that is. Security organizations operate under a tremendous amount of scrutiny—always under the microscope of politicians, special interest groups, regulators, government agencies, and the public.
That opens up a lot of visibility about how a security organization operates and how it responds to security threats, which is just one area that it needs to react to. These threats come in all shapes and forms, ranging from intentional threats from misguided youth, trespassers, insider threats, hardened criminals, domestic and international threats, transnational organized crime, illness and disease, including threats from natural and manmade disasters, industrial accidents, and weather-related calamities.
## Technology Application Has High-Visibility Challenges
Security systems can be deployed in almost any area, serving multipurpose objectives. The security director also has the awesome responsibility of establishing quality factors and safety and performance parameters to ensure systems are designed to perform under various conditions and circumstances.
## Importance of a Quality System Maintenance Program
### Maintenance Concept
A good security maintenance program meets three objectives: reduce equipment downtime caused by equipment failure or malfunction, ensure the equipment operates on a continual and uninterrupted basis, and extend the service life of equipment to a reasonable level.
A sound maintenance program includes a clear maintenance concept; the type and level of maintenance necessary to support the system; categories of equipment to be serviced, when, and the type of service; maintenance and logistics needs; organizational responsibilities; support equipment, tools, consumables, and spares; and the records and reports used in implementing maintenance.
The maintenance concept must be clear and describe the broad planned approach to sustaining a simplistic maintenance program for the life of the system. Areas to consider include:
• the level of maintenance necessary to sustain levels of readiness, suitability, availability, reliability, maintainability, human factors, safety, supportability, and survivability requirements
• the concept of "pull and replace" and exceptions thereto. This means system components must be readably accessible for inspection and servicing without major disassembly or reassembly, and without disconnecting primary and secondary power sources.
Within the commercial marketplace there are typically three levels of maintenance: preventive maintenance, corrective maintenance, and depot support.
### Preventive Maintenance
Preventive maintenance keeps a security system in top shape and performing to expectations. It calls for scheduled maintenance checks and services (usually on a quarterly basis) to offset the effects of the environment and normal equipment wear, and to preclude the premature malfunction or failure of equipment.
Preventative maintenance is typically performed on equipment while the system is online and generally without the need to disassemble/reassemble equipment or disconnect power. For those rare instances when it may be necessary to shut down a portion of the security system for safety reasons, it may also be necessary to plan for the extent and type of security compensatory measures that may need to be implemented to maintain a level of security comparable to that provided by the failed component or that part of the system power has been shut down. More on this topic in a moment.
### Corrective Maintenance
Corrective maintenance includes all actions performed to restore failed equipment to its specified condition. At the unit level, system availability can best be achieved when failed equipment is simply removed from service and replaced by a new or refurbished spare part. The "pull and replace" concept minimizes system downtime as well as costly security compensatory measures. Under this concept:
• failed equipment is replaced online and may require the brief disconnection of power
• failed equipment is returned to the depot for analysis and the determination to repair or replace the failed unit
The exception to a pull and replace policy applies to such components as vehicle gate tracking systems, gate operators, automated vehicle drop-arms, vehicle crash barriers, fences and gates, and lighting, to name a few. These components are usually repaired on site and may require disassembly and reassembly, including shutting off the power source(s) at some time during the repair process.
A good practice for the maintenance group to embrace before they begin performing any type of corrective maintenance is to notify the security organization so the unit can plan for necessary security compensatory measures and put them in place before maintenance begins. The security organization must also be notified when corrective maintenance is completed so the system can be tested before maintenance crews are released, and security compensatory measures can be terminated in an orderly and timely fashion and security resources reallocated to other activities.
### Depot Support
The depot augments on-site maintenance capabilities on an on-demand basis. Depot support may include product and service warranty, hardware and software troubleshooting, consultation and diagnostics support, logistical support and spare replacements, and on-site technical assistance and training. Maintenance agreements generally spell out service and support requirements.
## Embracing Inspections and Tests Extends the System Life Cycle
Inspection and testing programs have significant long-term value because these activities validate that the system continuously performs as designed and intended throughout its life cycle. They also provide a vehicle for reporting to design teams, through the development of fact-based test reports, any unusual difficulties, deficiencies, or questionable conditions for further review and potential action, as necessary.
Once the system is operational and ownership has transferred from the installation contractor to the end user, it is in the best interests of the security organization to embrace a continuing program of self-inspection and operational tests for the life cycle of the system. These inspections and tests ensure system integrity against tampering, damage, or destruction and continual reliable performance and minimize system downtime. This activity includes physical inspections, system diagnostic tests, operational tests, and performance tests.
### Always Conduct Physical Inspections at the Start of Each Shift Change
• Walk down the fence line of restricted areas to inspect the fence fabric for cuts, other damage, or signs of tampering on gate locks.
• Examine electrical panels and other hardware such as sensors, cameras, barriers, and gates for damage or signs of tampering.
• Check doors, windows, and other openings to ensure they are secured and/or locked and for signs of forced entry.
• Check general areas for suspicious persons and packages.
### Always Conduct System Diagnostic Tests at the Start of Each Shift Change
Whenever system operators change shifts, conduct a system self-diagnostic test to verify the integrity of system features, circuit continuity, and the activation and working order of all alarm points. System diagnostic testing may also be programmed to automatically run during specific times, including after a power loss.
### Always Conduct Weekly Operational Tests
Once a week test:
• fence sensors by tapping the fence fabric
• area sensors by walking, running, jumping, and crawling through the detection zone
• doors and windows that are alarmed by opening and closing them
• tamper-switch alarms by opening and closing circuitry panel doors
• automated vehicle barrier systems and vehicle gates for operability
• the camera footprint to verify whether any shift in the camera field of view has occurred. Walk the outer edges of the camera zone, validating results against preset plots or recordings of previous walk tests performed. Conduct this test both during daylight hours and in darkness.
Tests need not be completed in one sweep. Rather, you can schedule them throughout the week by assigning designated zones to the various shifts.
Shift leaders are the ideal supervisors to schedule operational tests and to ensure the results are captured within the retrieval system or entered into the system transaction/activity log. The off-going shift leader briefs the incoming shift leader of inspection and test deficiencies, as well as the status of any maintenance issues and the tests completed during the shift, including any maintenance and tests pending or scheduled to be performed.
### Maintenance Performance Tests
It is crucial to test the security system after corrective maintenance is performed, after each inoperative state,1 and when necessary—such as during severe weather conditions or a major industrial accident that affects system operations. Only those functions directly affected by maintenance activities need to be tested.
During maintenance, it may be necessary to place some portions of the system in the ACCESS mode. In the ACCESS mode, a single sensor or group of sensors or access control devices, vehicle gates, and barriers may be shunted, which would preclude the announcement of an alarm or advisory notice.2
### Seasonal Performance Tests
Perform these tests on a quarterly basis to measure the variance in system performance resulting from seasonal temperatures and changes in weather conditions. Moreover, a thorough performance test should be conducted at least 30 days before the system or any equipment warranty expires to take advantage of any warranty services and products that may be necessary.
### Test Plans and Test Procedures
Test plans and test procedures guide and control test activity. Test plans outline roles and responsibilities, performance standards, safety precautions, and test limitations and constraints, as well as the records and reports required to be maintained.
Test procedures provide systematic instructions to verify system performance and protective features. Procedures identify the specific test trials to be performed; the pass/fail criteria to be applied; the test population, methodology, and equipment used; safety considerations for each test trial; and the test logs to be used to record test results.
### Collection and Composition of Test Data and Test Logs
One method of computing data and examples of test logs are offered in Appendix B - Sample Test Logs. You may use these test logs as designed or modify them to meet your particular testing and reporting requirements.
## System Failure Modes and Compensatory Measures
It is essential the security director develop contingency event-driven response and recovery procedures that addresses specific implementing security compensatory measures for the lost capability of failed equipment or system failure.
Whenever system performance is degraded or lost, it is prudent to implement security compensatory measures that are comparable to the affected performance lost in order to overcome any security vulnerability created by such failure. When spare parts are not stocked on site, implementing compensatory measures becomes a crucial consideration, particularly in instances when such measures may need to remain in place for extended periods until spare parts can be ordered, received, and installed and performance testing be satisfactorily completed. Fig. 11.3, security system failure modes and compensatory measures illustrates the three potential system failure modes important to security operations: catastrophic, major, and minor. The matrix is not all inclusive but only represents a sampling of the most common system failures and outlines a suggested decision-making process to implement security measures.
Figure 11.3 Security system failure modes and compensatory measures.
## Conclusion
When stand-along security equipment or disparate systems prevail, they provide little or no security protection and often provide a false sense of security to executive management, governing authorities, and the workforce.
This perception is quickly dispelled when security equipment is configured into meaningful interoperable segments that can create the potential for total system integration. However, quality hardware and software integration greatly depends on the reliability, dependability, and quality expertise of the modified and dedicated people who are responsible for operating and maintaining the system. Only then can there be true system integration.
## Appendix A: Selected Security Technology Deficiencies and Weaknesses
### Background Information
This information reviews relevant case histories. This information is shared to provide a better understanding of the scope of problems security directors face on a daily basis and for further research for the interested reader. The information represents eye-witness accounts and personal observations noted and reported as I performed security assessments, audits, and inspections, and as I participated in one-on-one interview sessions with numerous chief executive officers, chief operating officers, and other corporate senior officials; directors of security and their respective staff members; and other company employees.
## Overview of Selected Case Histories
• At almost every site I visited within the private sector (except for regulated locations) I found the total absence of a formal test, inspection, and maintenance program for installed security systems. Management at these locations could not produce convincing evidence these activities were being accomplished, or whether these systems were performing to acceptable industry levels. (Poor planning and supervision, lack of a system maintenance program)
• When testing security systems, many had a probability of detection (Pd) ratio below 0.803 and no better than just an opportunity to detect or witness an event by chance. Security organizations that are saddled with such weak system performance could not demonstrate their ability and capability to detect intrusions and assess penetrations, thereby being unable to demonstrate an adequate response to security events. (Poor or no maintenance program, lack of understanding of system performance characteristics)
• In most locations (including some regulated sites) exterior CCTV cameras were not deployed to provide maximum utilization or adequate coverage. Other cameras were not synchronized for call-up when sensors or access control devices were activated, lacking the capability for immediate real-time assessment and response to security alarms. Several cameras were not always monitored, and I found monitors and cameras that were turned off. Site officials could not provide an adequate explanation of the intent and purpose of specific cameras or why some monitors and cameras had been turned off. Neither could system operators or security managers provide any reasonable explanation for the noted conditions. (Poor planning and understanding of system applications)
• In most instances, I found that the design development and installation of security systems had started without defining formal system parameters, requirements, performance standards, or operations, maintenance, logistical, and training considerations. (Poor leadership planning, coordination, and decision making)
• Many security systems lacked their own independent and dedicated uninterruptable power supply. Existing backup power supplies were insufficient to support most system operations. (Poor security design planning)
• At one location, batteries for most card readers were outside specification standards. These batteries were corroded and leaking acid. The shelf life of these batteries had expired 5 years earlier, and site officials could not determine when the batteries were procured. A review of the system database revealed that backup power systems had never been tested. The first recorded transition of the system was February 9, 1998, suggesting that the system (including the batteries) were procured and installed around that time. During our visit in 2008, no other record of inspection or testing of batteries could be found, and site maintenance officials could not recall every serving the batteries during the 10-year period in question. (Poor system integration planning, installation management, and maintenance program)
• For many corporations, outsourcing of the design and installation of security systems is difficult to pursue, particularly when a unionized labor force of engineers, electricians, maintenance workers, and other disciplines were available and potential layoffs were looming. Even when not influenced by the union, many corporations adopted a "go-it-alone" mentality despite the lack of expertise or experience in strategic security planning, security engineering, or the installation of complex security systems. Under this concept of operation, several procurements reduced system parameters under the guide of cost savings; installation attempts had resulted in poor workmanship and deployment gaps; misguided attempts at system integration; and erroneous programming of software parameters that in effect, degraded system performance from the start. This vulnerability was predicable and both executive and security management should of known it. (Failure to understand and recognize limitations of in-house capability and expertise in security design planning, procurement, and installation; poor engineering leadership decision-making capability)
• Security design recommendations implemented in a piecemeal or indiscriminate fashion, rather than in a systematic and logical manner, led to the continuing deterioration of program effectiveness, producing significant cost overruns from original project estimates and eventually becoming counterproductive to achieving security strategies, goals, and objectives. (Inexperience, limited knowledge of technology performance and application)
• Legacy systems abide across the security industry in both the public and private sectors. Most of these systems cannot be upgraded in a cost-effective manner and require complete replacement with state-of-the-art systems to support today's security needs. Moreover, most systems were not really "systems" at all. Rather, they consisted of individual stand-alone components operating independently of each other. For instance, access control devices, sensors, and CCTV cameras were not configured into an integrated system, nor did they provide for the operational capability for real-time detection of, assessment of, and response to security alarms. At many locations components were not fully programmed, making detection and assessment extremely difficult and in some instances even impossible to perform. Inadequate communications often contributed to the ineffectiveness of the security response force. (No system integration, poor planning, and poor budget forecasting)
Generally, not having a clear and distinct design document or functional system specification that spelled out the mission of the system, its performance characteristics and expectations, its technical interfaces, and its measurement and evaluation tools led to poor security design planning, system configuration, and technology deployment as well as weak emergency planning at all the sites visited. This fallacy was predicable, and both executive and security management at each independent location should have known it.
## Appendix B: Sample Test Logs
### General Information
The test logs listed below are offered for informational purposes only in helping you document the performance testing of your security system (Figs. 11.4–11.13).
In each test log, "P" indicates pass and "F" indicates failure. The measurement emphasizes a "GO" "NO-GO" result, meaning that equipment either works or it doesn't. This type of testing does not recognize a range of failure. While only a single line item for each test sample is shown, it is recommended you perform at least 10 test trials for each alarm point or device tested.
Enter "N/A" in any area that does not apply to a particular test log entry.
Figure 11.4 Fence-mounted sensor test log.
Figure 11.5 Exterior microwave sensor test log with zone plot.
Figure 11.6 Door contact sensor test log.
Figure 11.7 Card reader/keypad test log.
Figure 11.8 Contraband detection equipment test log.
Figure 11.9 Interior motion sensor test log.
Figure 11.10 Equipment enclosure test log.
Figure 11.11 Closed-circuit TV controls test log.
Figure 11.12 Uninterruptible power supply (ups) test log.
The test director (usually a security supervisor) oversees and manages test team members and authorizes the retest of any alarm point that registers below the accept/reject criterion of 0.90% probability of detection or 0.90% probability of performance. A rating of <0.90% in any test trial category constitutes a failure of the item tested, which must be scheduled for retesting at the earliest possible opportunity.
Figure 11.13 Backup battery test log.
## Safety Information
Only qualified security or maintenance personnel should conduct test trials on intrusion detection sensors, contraband detection equipment, access control devices, and console and CCTV controls. Only qualified maintenance personnel should conduct test trials on equipment enclosure tampers, UPS and backup batteries, line supervision, power loss, and voltage reading test trials.
Only qualified system operators monitor the announcement and display of alarms, collect data, and document test trial results on test logs. One observer should witnesses the conduct of each test trial performed in the field to verify that testing was conducted in accordance with the approved test procedure. A second observer should witnesses the alarm data reporting process, visual display of test trials, the functioning of CCTV controls, as well as the reactions of the system operator when responding to test trial events.
* * *
1 An inoperative state exists when power is disconnected to perform maintenance or for any other reasons, when both primary and backup power sources fail to provide power, or when power applied to equipment has failed to kick-in.
2 Placing the system in the ACCESS modes does not constitute an inoperative state unless accompanied by or followed by any of the stated conditions.
3 While no universal mandate for commercial security systems exists, most corporations pursue a probability of detection (Pd) of 0.90 or greater (Sullivant, 2007, pp. 194). A good design, quality selection of components and subsystems, and quality installation by an experienced system integrator can easily achieve this detection ratio.
12
# Preparing for Emergencies
## Abstract
This chapter takes on the ambitious goal of bridging the gap between how prepared we are, how prepared we need to be, and how we prioritize efforts to close this gap. It highlights significant deficiencies, weaknesses, and inadequacies in planning for security emergency operations. Significant emphasis is given to response and recovery actions, which are by far the greatest weaknesses in the total chain of security preparedness. Actual case histories are offered throughout the narrative to illustrate the significance of the problem.
### Keywords
Event-driven recovery procedures; Event-driven response procedures; Preparing for security emergencies; Prevention; Prioritizing security response; Protection; Reporting and alerting system; Security emergency planning considerations; Threat condition levels; Triggering response events
We always jump at the idea of protecting ourselves from industrial accidents and weather-related calamities. But many leaders take a step back when it comes to terrorism, criminal activity and other incidents initiated by those who wish to do us harm, particularly psychopaths, the mentality ill, hate groups, or disgruntled persons, content to have local law enforcement address these issues. At the highest level of strategic planning we ignore our duty to care principal—and we are responsible and accountable for the consequences.
John Sullivant
Top Takeaways
• Leadership and communications
• Security emergency operations
• Creating a security emergency response plan
• Creating event-driven security response and recovery procedures
## Overview
In this chapter I talk about the ambitious goal of bridging the gap between how prepared we are and how prepared we need to be, as well as how to prioritize efforts to narrow this gap? The answer to these and more questions lies somewhere between a completed security assessment that includes the preparation of a vulnerability analysis and the development of a realistic threat estimate profile. Throughout the pages of this book I have persistently mentioned that early detection and identification of security problems at the source is not the strong suit of many executives or security professionals, or, at the very least, it does not seem to be a priority that is high on their agenda.
What I reveal here and elsewhere relative to security emergency planning and response and recovery capabilities is that too many executives and security professionals seem to be "asleep at the switch." Too many security professionals demonstrate their inexperience when it comes to developing comprehensive and useful security response plans and response and recovery protocols. I have witnessed too many instances of vague and ambiguous statements of intent rather than commitment, and when tested (as I have done on numerous occasions) the results support my conviction that many security organizations simply fail when it comes to responding to and recovering from a crisis. I have found that little or no thought is given to strategic planning vision, as evidenced by poor performance in carrying out emergency security operations. When executives disengage from the security planning process, they must equally share in the responsibility and accountability for dismal security performance.
Here I continue the chronicle of business risk exposure to individuals who wish to do us harm or to accidental or natural destructive events, and their potential affects on the welfare of a corporation, its resources, and its assets.
## Security Emergency Planning Is Critical to Organizational Survival
Security emergency planning is subject to a wide range of social, economic, and technical factors. In his book "Emergency Response Planning for Corporate and Municipal Managers", Paul A. Erickson, PhD (2006, pp. 13), advocates that we should collaboratively and holistically embrace the process of security emergency planning, coordination, development, and implementation. This calls for chief executive officers to step up and take responsibility for the safety and security of the workforce and the corporation against the potential risks that their operations face. Meeting this executive responsibility requires the execution and testing of security response plans that detail:
• strategic planning and the prioritization of assets, resources, funding, and training to build required competencies
• specific steps to be taken to prevent or respond to an emergency
• necessary corporate coordination and liaison with competent local, state, or even national authorities
## Planning for Prevention, Protection, Response, and Recovery
While many executives and corporations have a good record of accomplishment in planning for and responding to natural disasters and industrial accidents, they are less accomplished in preparing for other crisis. With so much attention on crisis planning, response, and recovery, one might suspect that corporate America is as prepared as it can be, but unfortunately this is not the case.
### Security Survey Looks at Capability Through Plan Development and Training
Steelhenge Consulting of London, England conducted an international survey of companies in 2014 in the U.S., Canada, Central and South America, Africa, Middle East, Australia, New Zealand, Asia, Europe, and the U.K. All economic sectors were represented as were all parts of the world, with the exception of Russia. Significant highlights of the survey1 reveal that:
• 76% of companies surveyed lack a basis crisis management plan. 45% felt having one was not important or necessary.
• 56% of companies surveyed have not conducted crisis drills, tests, or exercises.
• 50% of the companies surveyed have ineffective or incomplete security emergency response plans or no plans at all that address manmade crisis and incidents. 28% of these companies waited for a brutal experience of a crisis to occur before creating a plan.
• 50% of the companies surveyed who out source security responsibilities have little confidence in the provider's ability to provide adequate protection or delivered promised services.
• 50% of the crisis management plans are based on operational need and senior management direction. Very few are prepared to meet regulatory compliance.
• 81% of the companies that had plans, did not define roles and responsibilities; 24% lacked effective communications support; 50% reviewed or audited their plans after an exercise,crisis, or "near-miss", but 40% had no program to review or conduct training, or exercises; and 13% had done no preparation at all.
### Highlights of Industry Standing From a Global Perspective
Survey summary results include:
• 47% of the companies were very well prepared and had a structured program for crisis management and emergency response plan review, staff training and exercises, with a good staff awareness.
• 40% of the companies were prepared and had a crisis management or emergency response plan but no regular program of reviews, training, exercises, and little staff awareness.
• 8% of the companies were not well prepared. They were aware of the potential impacts of a crisis but no formal plan or program in place for training and exercising, and very little staff awareness.
• 4% of the companies were ill prepared. They had no resources committed to crisis management or emergency planning and minimal or no staff awareness.
Prevention and protection strategies are pre-event work in progress planning activities that take place in a highly dynamic and evolving (threat and work) environment and are performed before an event occurs. Prevention and protection actions include strategic planning activities that help to reduce risks:
• Assessment and vulnerability analysis
• Likelihood of event occurrence
• Mitigation processes and procedures
• Infrastructure and facility protective measures
• Prioritizing actions, resources, and funding
• Training
Deterrence against threats and hazards is also work in progress and begins with properly planning and implementing effective security measures to minimize risk exposure. The process continues with appropriate training of people, the diligent exercise of plans, and the capability and leadership to resolve actual crisis. Without determination and proper planning, preparation, and training, employees will lack the guidance and confidence necessary to perform their duties during any emergency, whether a terrorist attack, criminal activity, a natural disaster, a weather-related calamity, or other catastrophic event.
Response and recovery strategies are work in progress actions implemented after an event. Response activities are done immediately following an event to save lives and minimize damage or loss of assets. Recovery involves those actions that are necessary, once response functions are completed, to begin restoration and rebuilding business and security operations, and to get people and the corporation back to their pre-incident situation as soon as possible.
## Alert Notification Systems Serve as Triggering Mechanisms to Carry Out Security Planning Considerations
Another disturbing issue is that not all U.S. companies subscribe to an alert notification system. Security planners associated with companies that do embrace an alert notification system are more likely to have sufficient advanced warning to review security strategies and agree on timely, reasonable, and prudent response actions. Companies that fail to subscribe to an alert notification system are more likely to make uninformed decisions, wrong decisions, or decisions that lead to chaotic results.
Fig 12.1, illustrates a few examples of potential crises that could qualify as triggers to increase a change in the corporate security posture. I offer these tips because they may be helpful in your security planning endeavors.
A corporate alert notification system, such as the one illustrated, offers a means to analyze and prioritize information regarding the potential risk exposure to the corporation based on verifiable and reliable intelligence. By using such a system, in conjunction with implementing corporate security response plans, decision makers have the options available to increase the protection of known targeted assets in order to make it more difficult for an adversary to harm or damage those assets. Therefore, it is important for an enterprise to clearly define what it can and must do in the event of an incident or event and to coordinate capabilities and activities with partner organizations in order to carry out necessary response actions. The system also uses any error in timing or coordination that could occur during an adversary's attempt to carry out an attack. A significant security incident at one location or apparently unrelated incidents at several locations could be rapidly communicated up or down channels, across the industry, or internally within the corporation to determine an appropriate security response or series of integrated responses.
An alert notification system can also help security decision makers deliberately plan for the increased security of other critical assets because of an imminent threat or actual attack against a particular asset. Such actions could be based on predetermined event-driven response procedures designed to minimize disruptive consequences that may themselves interact in ways that could create additional vulnerabilities. For instance, efforts to develop and implement compensatory measures to include equipment, additional security personnel, and special actions necessary to ensure that the effectiveness of electronic security systems are not affected by power failure or infrastructure damage or destruction. Virtually all threat alert notifications have the potential to cause the security organization either to increase its security posture in anticipation of an event occurring or to provide immediate response to cope with a specific event for an indefinite period of time.
Figure 12.1 Corporate alert notification system and potential triggering incidents that may affect a corporate threat level.
C-suite executives, directors and managers of business operating units, and the director of security can then agree on the prioritization of response actions such as those highlighted in Fig. 12.2. This figure takes the alert notification triggering metric to the next logical planning and decision-making level: What do we do? When do we do it? Who does what? Fig. 12.2 depicts a proposed top-level sequence of activity by level of threat condition and by specific event-driven tasks by those responsible for carrying out assigned actions. It represents a top-level guideline of roles, responsibilities, authority, and accountability to protect the corporation, its resources and assets, and its critical business interests. Together, Figs. 12.1 and 12.2 are a formidable management toolbox for planning and executing specific event-driven response and recovery operations discussed next.
Figure 12.2 Emergency planning considerations in preparing respective event-driven response and recovery procedures.
## Planning for Security Event-Driven Response and Recovery Operations
The enormity and complexity of the security mission and the uncertain nature of events make the effective implementation of security response and recovery efforts a great challenge. The concept of security response and recovery stems from an irreversible commitment to possess the ability and capability to protect corporate resources and assets under uncertain conditions, with exceptional performance outcomes. The concept implicitly advances the notion that a security organization must maintain the flexibility to transition from normal security operations to uncertain emergency security operations without jeopardizing critical business operations, while concurrently responding to varying and specific undesirable events. Fig 12.3 graphically displays this revolving process. It also merges the projected corporate alert notification system and its integral event-driven response and recovery options into actionable decision-making activities.
### Normal Security Post Instructions and Procedures
Security post instructions and procedures provide day-to-day guidance for carrying out security activities. Deviations from these instructions generally require the approval of security supervision or management.
### Event-Driven Security Response Procedures
Event-driven security response procedures contain techniques, tactics, methods, and practices to use when confronting threatening situations. These are general guidelines that are subject to modification and adjustment because of uncertainty, an adversary's actions, and other conditions and circumstances. These actions are internal to the security organization. All security response and recovery procedures contain sensitive security information, which must be published and maintained separate from other corporate emergency plans and guidance.
Figure 12.3 Event-driven security emergency response and recovery matrix.
Event-driven response procedures outline actions that are required to cope with possible threat scenarios and prescribe uniform measures to be taken to address the range and level of threat conditions. Here are some additional helpful tips to use when developing security response procedures:
• Prepare a response procedure for each event that is likely to occur, as stipulated in the company-approved corporate threat estimate profile. I discussed this strategy in Chapter Developing a Realistic and Useful Threat Estimate Profile.
• Make sure each response procedure is a self-contained stand-alone event-driven guidance.
Some examples of event-driven security response procedures that may be useful to your organization include, but are not necessarily limited, to the following:
• Account for security personnel
• Airborne, Chemical, biological, radiological contamination or attack
• Assault
• Assist disturbed persons
• Assist handicapped persons
• Augment operational centers
• Lockdown buildings or entire campus
• Bomb explosion—conventional
• Bomb explosion—dirty bombs
• Bomb explosion—nuclear
• Bomb threat caller
• Bomb threat search and evacuation
• Child care center protection
• Communications failure | • Hostage situation
• Hurricanes and Tornados
• Implement mutual assistance packs
• Implement positive identification measures
• Increase general security posture
• Increase patrols
• Increase security at designed areas
• Inspect personal protective equipment
• Intruder—breaking and entering
• Intruder—robbery in progress
• Intruder—trespassing
• Intruder—vandalism
• Kidnapping and extortion
• Lightening storm
---|---
• Civil disturbance and demonstration
• Clear gathering areas
• Duress alarm activation
• Earthquake—building damage
• Earthquake—area damage
• Emergency security staff relief
• Emergency safe haven
• Equipment shutdown
• Evacuate area/building
• Executive protection | • Malicious destruction of property
• Medical help for injury and illness
• Officer down alert
• Power failure
• Protect deployed crews from sniper fire
• Recall off-duty security personnel
• Sabotage of critical assets
• Search persons, vehicles, materials
• Search and clear areas
• Shooter incident
• Explosion or fire
• Extended monitoring and surveillance
• Find missing persons
• Form additional response teams
• Floods & heavy rains
• Frontal attack on area or facility
• Hazardous material incidents
• Help evacuate injured persons | • Substance abuse and alcohol use
• Tampering with systems
• Test security systems
• Termination of employee for cause
• Threatening communications
• Use of supporting forces
• Workplace violence
### Event-Driven Security Recovery Procedures
It has been my experience that security recovery from any event is the most overlooked factor in security planning. Eyewitness accounts and studies confirm that few executives and security planners pay attention to security recovery during the planning stage. Those I have personally interviewed and surveyed say there are too many unknown variables to effectively plan recovery. I totally reject this notion and I am disappointed at the lack of strategic vision exhibited by so many of my colleagues.
Make this mistake no more! Recovery is a crucial planning consideration for any response before an incident occurs. Simply put, recovery is nothing more than an "exit strategy." How can you charge head-on into uncertainty, without investing in a parachute that works? It only makes sense that you understand what you are doing, what you can expect, and when and how you plan to withdraw or regroup from a given situation. Surely you must understand the lives of your people and others are at stake. When do you plan for scheduling, relief, rest, and looking after the troops? When do you plan for logistics? In the course of responding to any crisis, how do you maintain the security of corporate business operations? How, when, and by whom are these resources, equipment, supplies, and other needs put in place? Surely, planning for recovery is not something you would after you commit an entire organization to a particular crisis. If you are of this mind-set, my advise is to get out of the security business because not only you are a danger to yourself, but to your organization, the entire corporation, and the rest of the profession—who I am certain are not eager to make your acquaintance or share the same foxhole with you.
As a responsible security professional in a leadership role, security recovery must receive your explicit attention. Get rid of the notion that you can take care of logistics and other matters after you engage a crisis. When you realize you are in trouble, it is too late. Without an exist strategy you cannot operate well enough to protect the lives and safety of the workforce or property in any given crisis as executive management expects. When General Dwight D. Eisenhower was the Supreme Allied Commander of Europe during WWII, he told his multi-national staff that once the battle begins, all plans far apart, but planning for the battle is everything. I believe this wisdom is still valid today.
Security recovery operations involve two basic multitrack tasking assignments: First, it calls for the immediate intervention by the security organization to help the corporation minimize further losses brought about by an event so executive management can begin the process of corporate recovery, including activities and programs designed to reassemble the workforce and restore critical business functions to an acceptable condition as soon as possible. In addition to normal security operations that must be maintained, special security operations required to protect corporate assets during the recovery process are in themselves works in progress that cannot be ignored. Second, it requires the exercise of flexibility because the security organization is required to reorganize, adjust, shrink, or expand as necessary to meet concurrent threats without jeopardizing the security and safety of the corporation, as well as the remaining business activities unaffected by events, including security activity at remote domestic and international corporate sites. This is also a concurrent security work in progress.
At the corporate level, recovery activities include damage and impact assessments, prioritization of critical processes to be resumed and return to normal operations, and reconstitution of operations to a new condition and standard. Steps may include any or all of the following:
• plans and processes to bring the enterprise out of the crisis that resulted in an interruption of business operations
• those actions necessary to rebuild interim and long-term infrastructure, including security systems, supervisory control and data acquisition systems, data management systems, and management information systems
• activities, resources, and priorities to support the reconstitution of business operations and services to an acceptable level
• implement measures for social, political, environmental, and economic restoration
• incorporate mitigation measures and techniques, as feasible
• evaluate the crisis to identify lessons learned
• report after the incident
• develop initiatives to mitigate the effects of future incidents
At the security organization level, recovery involves short- and long-term activities: the short term activity is to provide the business side of the entity security protection to achieve the above goals, while protecting normal on-going business activity, the long term activity involves transiting the security organization from its current state of emergency operations back to its normal operating posture without jeopardizing the integrity of the corporate recovery effort while performing services to support both business recovery operations and transitional activities. Security recovery actions to support corporate recovery efforts may take months or even years to complete, and cannot even begin until the business side of the enterprise has healed from its wounds, and has recovered to normal operations.
By the very nature of its mission, security recovery operations involve assessing injury or loss of any members of the security staff and any damage or destruction sustained to security facilities, equipment, and communications resulting from a particular crisis. As a security planner you must consider the following in assessing your security organization's recovery capability:
• A security organization would probably experience casualties and the damage or destruction of security facilities, equipment, and communications during a direct attack by an adversary or a major disaster.
• A direct attack or disaster will certainly impair the reporting to duty of a significant portion of the security staff, or prevent those on duty from receiving relief or being able to go home to their families.
• Collateral damage can conceivably be brought about by a nearby attack involving conventional explosives against other high-risk corporate entities in the near vicinity that could impair a security organization's capability to function. The partial or total destruction of security and other facilities, the shutdown of operations, the disruption of vehicular traffic and mass transportation, the demand on lost utilities, the unavailability of emergency services, the closure of streets, and the establishment of security corridors around a large area could directly affect security and business operations for an indefinite period. Never lose sight of the emergency response and recovery lessons learned from the 9/11 attacks. Recovery of the World Trade Center and surrounding affected areas has taken more than 14 years. Some reconstruction efforts are still on-going at this writing.
## Strategies for Integrating and Prioritizing Security Response and Recovery Operations
A common error committed by security professionals is the failure to embrace security emergency preparedness and planning as a holistic discipline (Erickson, 2006, pp. 29–61). For security to succeed, it must not loose site of its purpose, that is, to perverse life and limit the loss of life and personal injury; to protect resources, assets, facilities, and information; to limit damage and destruction of property in the support of business goals and objectives; and to continue supporting business units while concurrently responding to a crisis. All these factors must work together and must be interconnected to provide maximum benefit.
Fig 12.4 graphically illustrates how security response and recovery priorities must match the priorities of the corporate business services. The figure outlines a basic water and power utility and demonstrates the multitasking responsibilities it would undertake, including the direct and indirect support role the security organization would be expected to maintain and sustain, not only during normal security operations but also during a crisis. The only reason security exists is to support the enterprise's business goals, objectives, and productivity, even during times of crisis. Enterprise recovery is important to a security organization because it cannot even plan to transition from a recovery mode back to normal security operations until all business operations affected by the crisis have first returned to normal.
Figure 12.4 Corporate strategy for prioritizing security response and recovery during a crisis.
During uncertainties, it is imperative that security management maximizes the use of available security officers, irrespective of rank or seniority, to perform critical life-saving tasks. Under such circumstances and conditions, union agreements (where they exist with respect to seniority or bid assignment) should be suspended during the crisis until such time that sufficient security staff members are able to report to duty and the situation permits the orderly realignment of the security work force to a more stable schedule. The suspension of any union agreements should remain in effect only as long as necessary; in no event should it last beyond the completion of the security recovery transition period for the declared emergency. A good management/labor relationship effort is crucial to carrying out this emergency workforce policy.
## Security Emergency Response Plan
The security response plan provides the framework and authority to plan, coordinate, develop, and carry out necessary security actions. Sharing security responsibilities and delegating authority to act are key components of the successful implementation of any security response (Erickson, 2006, pp. 65–91).
### The Wavering Complexities of Security Emergency Planning
Effective security emergency planning emphasizes protecting corporate resources and assets from the full range of plausible threats, not just those that are most frequently reported or considered to be the most likely to occur. To achieve this it is necessary to develop, monitor, and maintain threat level information and to combine the results of threat analysis into the elements of security and emergency preparedness into a cohesive program in which all elements are compatible and operational ability is maintained across business unit boundaries. This drives the need to develop proactive event-driven response and recovery procedures for specific undesirable events on a continuous basis as business operations adjust, modify, or change approaches to achieving business goals.
In addition, the response plan details hazards that are relevant to the direct impacts, disruptions, and cascading effects of natural disasters and industrial mishaps. Moreover, it calls for strategies, plans, policies, and procedures to prepare for, mitigate, respond to, and recover from a variety of undesirable events in an all-hazards context. This focus includes:
• a user-friendly and meaningful comprehensive corporate threat estimate profile that identifies the range and levels of threats and modes of attacks, and determines the criticality of assets, consequences of loss, and the probability of occurrence, as well as natural disasters and industrial mishaps
• a security organization and coordinating structure to enable effective partnerships across the corporation and between and among governing agencies and community responders
• an integrated approach to enhancing protection of the physical, cyber, and human elements in which individual protective measures complement one another
• the development and use of tools to help from effective risk-mitigation solutions in an all-hazards context
Not doing so is irresponsible. The emphasis is on preparing levels of capabilities to address a wide range of realistic threats and hazards. Risk can be managed through developing readiness priorities of capabilities to address a range of scenarios, analyzing intelligence information, understanding capabilities, and effectively using resources.
### Critical Elements of a Security Response Plan
At a minimum, a security emergency response plan should address the following critical elements:
• Security mission, security emergency organization and staffing, crisis management and leadership, and continuity of command. Security is a reactionary business that requires exhaustive research and coordination, continuous strategic planning and development and the commitment to respond to security emergencies. To effectively achieve this posture those individuals with security responsibilities use the same organization, technology, resources, and basic skill sets for both normal security operations and emergency response situations. There can be no proper security planning or response without the existence of strong leadership and an on-site chain of command. Equally important is the assignment of security responsibilities to all organizations and individuals for carrying out specific actions at projected times and places during an emergency; these often exceed the routine responsibility of any one business unit and set forth lines of authority, accountability, and organizational relationships during an emergency.
• Intelligence, rumor control, and communications control. Coordinating with intelligence sources and liaising with the media distills misinformation, incomplete information, or distorted information. Communication plays a vital role in both the prevention of a security emergency and the emergency itself.
• Ability and capability to carryout event-driven response and recovery activities.
• Maintain internal and external dependencies, including mutual agreements and reenforcement capabilities and support. The plan must identify steps to address mitigation concerns during security response and recovery activities.
• Ability and capability to transition from normal security to an emergency security posture. Both normal and emergency security operations call for the exercise of strong leadership over physical security, electronics security, cyber security, information security, personnel security, and corporate-wide security emergency planning that gains the continual confidence and support of the CEO and other C-suite executives. Transitioning from a day-to-day security posture to an emergency security configuration must happen as smoothly, efficiently, and effectively as possible because such a shift in momentum directly affects the entire enterprise. This includes executing post and patrol priorities; determining extended work hours and relief capabilities; prioritizing asset protection and implementing security compensatory measurements; maintaining the security of the perimeter and area; controlling access to the scene; preserving evidence; and providing security escorts and executive protection, as necessary. The plan must show how all actions will be coordinated and describe how people and property will be protected during emergencies, disasters, and accidents.
• Planning for and providing logistical support: transportation, mobilization, and mobility (air, sea, and land); evacuation logistics and security; medical assistance and evacuation; reliable backup communications; food service, lodging, maintenance; and security facilities and equipment, including prepositioned emergency supplies, materials, and equipment. The plan must also identify personnel, equipment, facilities, supplies, and other resources that are available for use during security response and recovery operations
• Providing for the well-being of the security workforce: personal affairs and counseling; family assistance, comfort, and counseling; and financial assistance
• Emergency budget and capability to procure emergency supplies, materials, equipment, and security consulting services
• Security training and exercises. A security response plan is only as good as the training given to the personnel who must implement the plan. Practice drills are essential for refining individual and group skill sets and for updating the security response plan and procedures.
### Security Planning Constraints and Limitations
To be sure, there are inherent planning constraints and limitations that must be recognized at the outset. As mentioned previously, it is not practical or feasible to protect all resources, assets, systems, networks, functions, and information against every possible threat nor are. All are all assets uniformly "critical" in nature; therefore, a risk-based security strategy enhanced by intelligence and information analysis and reporting provides the basis for an effective security response strategy. While complete protection against all potential threats is not possible (particularly the threat of explosion and those dangers imposed by chemical, biological, and radiological attacks), applying best practices can reduce vulnerability and consequences. For example, emergency response planning actions must consider the following security priorities:
• Priority 1: Respond to prevent further injury or loss of life.
• Priority 2: Respond to those assets, systems, networks, and functions designated as most critical to the mission and other business interests.
• Priority 3: Respond to those assets, systems, networks, and functions that face a specific, imminent threat
• Priority 4: Respond to other assets that may become potential targets to terrorists or criminal elements over time. Advance warning of potentially vulnerable assets, systems, networks, and functions is crucial. This fosters a proactive approach to enhance decision-making processes and response to the various levels of threat.
The security challenge goes beyond most corporate-level emergency response plans. Today's threats call for an ongoing, dynamic, and interactive process that ensures the continuation of a security organization's core activities before, during, and—most important—after a major crisis. Proactive planning and preparation by the security organization for potential security- and safety-related incidents and disruptions diminish both the impact and duration of the disruption and help to avoid or minimize the suspension of critical security activities, thereby allowing a return to normal security operations as rapidly as possible (Sullivant, 2007, pp. 157–176).
## Conclusions
The attacks on September 11, 2001, thrust disaster planning into the spotlight, and subsequent crises—hurricane Katrina, outbreaks of infectious disease, the earthquake in Japan, and the devastating tsunami, as well as piracy, kidnapping, assassinations, beheadings, bombings, and other attacks—are tragic reminders that extraordinary events that affect businesses and our daily lives are all to ordinary.
The fact that a number of large organizations do not have crisis management/emergency plans, and the majority do not run a program to develop response capabilities is frightening to say the least. Any readers that are still doubters as to the value of crisis management and emergency planning and preparation only have to speak to organizations who have suffered a crisis.
New organizational community threats are beginning to escalate in probability, breadth, and severity. By recognizing these emerging patterns, astute security professionals can be in a position to begin preparedness measures in the early stages of threat development. But identifying those new risks is only half the equation.
In performing my work, I frequently observed how personnel and bureaucratic rivalries among senior officials had taken precedence over effective security emergency planning and response to emergencies. Before any serious discussions of correcting security emergency planning and response begin, management needs to accept responsibility for the damaged relationships among the staff and start repairing interpersonal communications, build a team/clientele, and focus on the critical need to improve and enhance security emergency planning response capabilities when such an intense atmosphere prevails.
While complete protection against all potential threats and hazards is not possible, we can apply a series of integrated security strategies, protocols, and prevention and protection measures to reduce risk exposure to an acceptable level. Security response and recovery protocols that are not predicated on or guided by the results of a threat assessment and vulnerability analysis and mitigation strategies are at best guesswork and usually incomplete, ultimately off target, and produce no results when they are needed most.
Make no mistake about it: the threat is real, and it consists of more than mere terrorism. It will continue to increase in frequency, severity, and lethality. It can take many forms and affect anyone at any time and at any location. Most security consultants, including myself, agree that our greatest threat and weakness lie within: the insider threat. Security precautions and preparations to minimize risk exposure must turn inward; we must take a closer in-house look at the people who are charged with planning, developing, coordinating, approving, directing, and carryout security policies, plans, protocols, and measures and enforcing guidelines, standards, and specifications, least we bread a new "Walker family, NSA contractor Edward Snowden, FBI agent Robert Hansen, MIT professor Daniel Elllsberg, and PFC Bradley Manning."
## Appendix A: Case Histories: Security Emergency Planning Fallacies
### Background Information
This information is a review of relevant case histories. The information is shared for a better understanding of the scope of problems security directors face on a daily basis and for further research for the interested reader.
Source: The information represents eyewitness accounts and personal observations that I noted and reported in the course of performing security assessments, audits, and inspections, and during one-on-one interview sessions with numerous chief executive officers, chief operating officers, and other corporate senior officials, directors of security and their respective staff members, and other company employees.
### Security Emergency Planning Lacks Strategic Insight and Determination: Selected Case Histories
Significant shortcomings in the development of functional security response plans, including event-driven response and recovery procedures, exist throughout the industry. Most plans lack organization and clear presentation of critical information (poor planning, management, and communications skills).
I found little evidence to suggest security emergency planning, or to suggest that the development of such plans and response and recovery procedures was based on a validate threat estimate profile or any other threat assessment tool. The few organizations that had threat profiles of file seldom kept them up to date. The majority of these threat profiles were too outdated to be useful in updating any of the plans reviewed (poor planning).
• Few security response plans exist. When they do, most are weak in identifying security responsibilities and actions.2 Time-critical, time-sensitive, and time-dependent security actions lacked specificity. Procedures failed to identify particular security event-driven actions, including dependency support (poor planning and experience).
• We found no visible evidence of a Command, Control and Communications C3 structure in security plans to demonstrate that key leadership exists to direct security emergency operations. Many corporate emergency response plans were written in generic terms with respect to roles, responsibilities, and authority (poor planning and leadership).
• No security event–driven response procedures or checklists existed at most locations to address system malfunctions or catastrophic failures, including actions to take in the event of power or communications failures or degradation of system performance. Commensurate security compensatory measures are almost nonexistent across the entire industry (poor planning and management).
• There were no security event–driven response procedures or checklists in many Command, Control and Communications C3 centers describing what actions to take when an emergency occurs (poor management).
• The lack of professional security leadership at several sites underscores the immaturity and weakness of published corporate and security response plans. Immature policies, standards, and procedures often confuse and distort information rather than provide effective guidance. These security organizations could have prevented many predictable security events (or at least minimized their effect) by developing clear event-driven response and recovery protocols, conducting appropriate security training, and performing adequate management oversight of activities.
• Many enterprises failed to demonstrate adequate capabilities to respond to a crisis at nearly every level of security emergency preparedness.
• One organization failed utterly in preparing for and responding to a disaster that was long predicted and imminent for days. I wonder how much more profound the failure would have been if a disaster—such as a gas/oil/chemical explosion and the subsequent fires, collateral damage, and loss of life and injuries—was to take them totally by surprise.
• None of the security organizations I visited had planned for security recovery operations or had any functional and user-friendly recovery procedures (poor planning).
* * *
1 Preparing for Crisis - Crisis Management Survey 2014 Report (distributed Internationally in February and March 2014). Steehenge Consulting, 16 St Martin's Le Grand, London ECIA 4EN.
2 Security operations and response actions to security events and other emergencies are normally considered "sensitive security information". In some instances, such operations and response actions are even classified. Generally, corporate-wide emergency response plans are shared with local governing authorities and emergency response entities. Generally, they are not exempt from public disclosure. Some states mandate by law that such plans be public documents and must be available to the public on demand. To protect the integrity of security operations and specific security response actions, it is in the best interest of the corporation not to include security responsibilities and actions in the corporate-wide response plan, but only give reference to its existence as a separate document. The contents of such security response plans and procedures are protected under state and federal laws, and other regulations. Their content and access to such plans and procedures is based on a right and need to have access to the information for the official duties.
13
# A User-Friendly Protocol Development Model
## Abstract
This chapter addresses the importance of having rules to channel behaviors and outcomes. A strategy for determining the value and contribution of protocols to the organization; detecting gaps, duplications, and omissions from protocols; and improving upon their purpose and usefulness is offered. Actual case histories provide insight into the weaknesses of major security publications and how the entire security industry is affected by the many shortfalls uncovered.
### Keywords
Accountability; Authority; Conflicting requirements; Counterproductive; Emergency preparedness planning; Evaluation criteria; Manage tension; Organizational resilience; Performance standard; Responsibility; Risk-based platform; User friendly
Shortfalls in the development of protocols exist throughout all industry sectors and within most security organizations.
John Sullivant
Top Takeaways
• Protocols that are right on target
• Value of written communications in passing on critical information
• Management becomes easier with clear and distinct guidance
• Measure and evaluate the effectiveness, efficiency, and productivity of protocols
• Gain insight from protocol case histories
## Overview
Nobody likes regulations. In our business, however, everyone recognizes that some uniform guidance is necessary and essential for a security organization to provide consistency and clarity to security policy, protocols, and practices. Equally important is to remove and dismiss regulations that are outdated, duplicative, or even counterproductive. Unnecessary or poorly targeted regulations do not help employees or improve security, but they do cost entities time and money. They also obstruct the innovation and connections needed to make security programs more resilient.
The challenge is to build a security culture that can effectively eliminate outdated rules and regulations and ensure that new ones are properly coordinated to develop practicable and workable guidance, and instructions that are meaningful, clear, necessary and enforceable. Most security organizations work hard to provide quality service and make good use of scarce resources. Management needs to work equally hard to produce reasonable and manageable protocols. Any protocol that fails to meet this simple test should never be written.
## Adopting a Protocol Strategy Is Crucial to Quality Performance
Since every document you write is a reflection of your organization and your people, you must acquire communication skills that produce professional results, perfect content and clarity, and appropriate organization, grammar, usage, punctuation, and sentence structure in your writing.
A protocol strategy has meaning and purpose only if it focuses on desirable characteristics that are common to all technical and professional publications, in which the goal is to communicate instructions, guidelines, standards, specification requirements, and direction and where noncompliance or failure to follow the protocol, or omission and vague context, could result in serious consequences. Consequences could be such activities as safety and security violations, activities that may lead to personal injury or loss, damage or destruction to equipment and assets, or financial loss resulting from inattentiveness or careless work habits, including the potential loss of proprietary or classified information (Sullivant, 2007, pp. 165, 169).
Protocols communicate rules, directions, and guidelines that control behaviors and outcomes that are agreeable to the leaders who are involved in carrying out their intent and purpose. Within the realm of security activity a representative sampling of protocols consist of:
• Policies, regulations, and directives
• Business unit security instructions
• Security reports
• Alert notification notices
• Security system O&M instructions
• Inter/intra agency correspondence
• Security management plans
• Security operations plans
• Standard operating procedures
• Crime prevention literature
• Security system design specifications | • Engineering drawings and plans
• Security threat profile
• Facility evacuation and fire plans
• Post orders and special orders
• Security contracts and statements of work
• Security mutual assistance agreements
• Shutdown and startup procedures
• Training materials
• Security emergency plans
• Event-driven recovery and recovery procedures
---|---
Jeffrey Hunker1 (2009, pp. 15–17) of Carnegie Mellon University argues that there is value in looking at instances in which protocol strategy evolves to provide an ongoing and sustaining framework for better security execution, such as matching protocol needs with the opportunity to improve processes, practices, and work habits. According to Hunker, Some themes for improving protocol development include:
• Threats should prioritize policy | • Implementation matters
---|---
• Managing tension | • Leveraging lessons learned
• Better measurement tools | • Delegating authority, responsibility, and accountability
### Threats Should Prioritize Security Policy
I previously brought to light the consequences of not developing a useful and meaningful corporate threat estimate profile that could be used in making security decisions, including the development of sound protocols. Without a valid threat estimate profile, policy development is hindered by the inability to fully identify and understand the threats that surround the business environment. This uncertainty has three significant consequences (Hunker, 2009, pp. 15–17; Sullivant, 2007, pp. 92–96):
• At its highest level, security policy defines the investment interests of a corporation. Lower-tier instructions relate to more immediate actions, and without clarity and understanding of threats and policy, lower-tier protocols become blurred and overall policy implementation suffers.
• With multiple and indiscriminate threats not clearly defined, various business units within a corporation are prone to form their own perception of security, rather than address or follow corporate strategic security needs.
• The prioritization of policy goals is impeded. The lack of clearly linking threats to business goals and operations weakens your ability to channel resources and expenditures to the activity of greatest importance.
Unless you embrace these issues and address their resolution, you will not able be to create a sound platform for better security protocols, practices and processes.
### Managing Tension
As an element of good protocol development, management needs to control tension between excessive controls, omission, and gaps, and between contradicting guidance and conflicts of interest within the policy framework.
### Better Measurement Tools
Most security professionals are unaware that metrics do not always have to measure direct impacts; they can also serve to address dependencies and interdependences within multiple functional areas. In some instances they can be proxies for specific outputs that are inherently difficult to identify and measure. For example, maintaining a secure and safe workplace is not only a laudable goal in itself, it drives major performance and productivity improvements. It reduces fraud, waste and abuse, and other criminal activity; creates an awareness of health and safety concerns that focus on reducing injuries to the general workforce; and can lower insurance rates and workman's compensation expenses (Sullivant, 2007, pp. 104, 106).
### Implementation Matters
While management defines the basis for action, the execution of policy depends on the actions of those who are responsible for developing the plans, procedures, and other protocols necessary to implement the policy, including management oversight and monitoring for continual improvement in the areas of effectiveness, efficiency, and productivity.
### Leveraging Lessons Learned
As the theme of this book explicitly suggests, our greatest, predictable failing is that we consistently and repeatedly duplicate the same mistakes. Condoning or accepting the theory of "vulnerability creep-in," as described in Chapter The Many Faces of Vulnerability Creep-in, reinforces this behavior.
### Delegating Authority, Responsibility, and Accountability
As a student who has studied the art of protocol creation, I am troubled by some of the observations I have witnessed and reported over the years (see Appendix A for highlights of selected case histories). For instance, all too often it remains unclear who knows what to do during a crisis, who manages or drives the security agenda, and who is responsible and accountable for decision making and carrying out orders. To remove the cloud of doubt, chief executives and other leaders need to establish exacting lines of delegated authority, responsibility, and accountability, and to permit the respective staffs and business unit managers to consistently enforce protocols and remain within those boundaries. This is particularly an important management tool for the security organization (Sullivant, 2007 pp. 207–212).
## Need for Protocols
At the highest level, policy creation sets the direction for achieving security goals and objectives. Policy then becomes the acceptable norm adopted by an organization. For example, when policy states that "employees will adhere to security performance standards," the general goal or behavior pattern will not change over time. Policy does not state what the security performance standards or behaviors are, or how management will enforce such standards. Rather, lower-tier publications such as regulations, directives, plans, and procedures are used to carry out the intent of formal policy which can easily be modified and updated as necessary, without having to adjust the original policy statement. Policy decision makers should also ensure that policies and lower-tier protocols do not contain conflicting requirements, guidance, or behavior. When such conflicts exist, management must take prompt action to resolve any conflict or contradiction in carrying out the protocol. Without a strong connection between a policy statement and its respective implementation protocol, it is very likely that there may be a mismatch between the intent of the policy and the interpretation of carrying out its strategy.
## Purpose of Protocol Reviews
A critical review of security protocols offers management the essential information it needs to (Sullivant, 2007, pp. 92–94, 104–212):
• Establish reliable direction and guidance that fosters organizational resilience that are consistent with the standards a corporation subscribes to, in accordance with the organization's overall business goals and objectives. In many instances these commitments are indispensable to the boundaries of the security organization, its mission, and it goals, obligations, legal responsibilities, and other requirements that are consistent with its commitment to protect and preserve human life and property, support corporate business goals, and protect its brand, image, reputation, integrity, and relationships with stakeholders and the community.
• Identify inconsistencies, omissions, and other discrepancies that may lead to the revision of existing protocols or the creation of new guidance that replaces outdated or unworkable instruction, bringing the security organization into alignment with management's expectations, regulatory requirements, legal requirements, and industry best practices.
A protocol strategy that addresses the full range of measures at its disposal protects the enterprise and its workforce, assets, and facilities. Such a strategy must be embraced and enforced by all divisions of the company. When fully integrated into a comprehensive security program, protocols enhance the effectiveness and efficiency of security resilience through the joint efforts of all corporate division chiefs and subordinate branch managers by using the combined technical, professional, and management resources available across the entire corporation.
## Quality Review Process for Essential Security Protocols
A major administrative goal of management is to deliver a specific collection of protocols that help to guide security organizations to carry out security activity in a uniform and efficient manner. Fig. 13.1 Publication Quality Assurance Review Methodology illustrates a user-friendly metric scale that gauges the organization, presentation, and content of documents that warrant measurement and evaluation. Seven measurement indicators are used: management, planning, coordination, operations, logistics, administration, and finance.
These indicators play a key role in the protocol development process. They are desirable quality assurance characteristics common to all technical and professional publications in which the goal is to communicate instructions, guidance, standards, specifications, and direction where noncompliance or failure to follow protocol could result in serious consequences such as injury or loss of life, damage or destruction of equipment or property, or financial losses.
Three rating levels, ranging from "meets evaluation criteria" (GREEN) to "addresses most or some evaluation criteria" (YELLOW) to "fails to address regulatory competency requirements or acceptable industry standard" (RED), are used to evaluate the acceptability of a publication. These indicators are important because they show a clear and distinct separation between:
• a document that satisfies all the stated evaluation criteria and requires no rework
• one that addresses some of the evaluation criteria but needs redesign and revision to meet acceptable best practices
• one that fails to meet standards and requires major rework to make it compliant with industry practices
I use a top-down, bottom-up evaluation technique to examine the scope, purpose, content, and organization of publications. The process allows for a better understanding of the vertical and horizontal interfaces between publications, as well as information dependencies between internal business units and external organizations, that may affect business operations, security activities, and their contributions to performance effectiveness.
Figure 13.1 Publication quality assurance review methodology.
The review process also identifies whether the absence of specific information within a particular protocol could lead to deviations from compliance and the application, safety, security awareness, user-friendliness, and usability of the guidance.
## Benefits Derived from Protocol Analysis
The goal is to revise or remove guidance that does not contribute to the wellness, effectiveness, efficiency, and productivity of the organization. Specifically, the analysis must:
• ensure compliance exists with security measures
• determine which security measures need to be revised, and those that should be removed from service because they are archaic, obsolete, and cumbersome practices
• identify existing instruction that requires updating or correction, or create new rules of behavior that reduce costs and improve overall workforce effectiveness, efficiency, and productivity for consistency as a new generation of employees joins the company
Such guidance is a good management tool that helps effective practices outlast the person who developed them.
## Conclusions
Well-developed protocols provide distinct value and meaning to those affected by their creation.
• They delineate authority, responsibility, accountability, and succession of leadership.
• They establish a command structure with effective leadership.
• They offer a set of actions predicated on goals and objectives guided by the threat profile.
• They set the standard for interfaces, dependencies, reporting relationships, and communications.
• They identify and allocate resources, facilities, and equipment to accomplish the mission.
• They establish evaluation and measurement tools to benchmark performance.
• They define training requirements and qualifications.
• They provide a quality assurance feedback loop to correct program deficiencies.
Protocols must always be designed to enhance overall security activity and to reduce exposure consistent with the threat. Improving policies, procedures, and other directives also contributes significantly to the protection of resources, assets, facilities, systems, functions, and products that are vital for many reasons—most of which are based on economic considerations and industry best practices. Having this clear and distinct exchange of communications is important to any business enterprise because:
• Resources require a large capital investment to acquire, train, maintain, and retain.
• Assets, facilities, systems, and products are expensive to acquire, install, and maintain.
• Intellectual property and other confidential and sensitive data directly affect the corporation's competitive edge and are vital to the efficiency and effectiveness of business operations.
• Finally, laws and best practices call for the safeguarding of resources, assets, facilities, systems, and functions so that if they are compromised, disrupted, injured, damaged, or destroyed, there is potential for criminal consequences and civil liability.
Another important aspect of formal protocols is that decision makers, planners, and writers must be cognizant of is the use of the terms "shall," "should," "may," and "will"—all of which have specific legal meaning as well as liability considerations.
While the commitment to rules, processes, and procedures is not to be overlooked, initiative, discretion, training, and experience need to prevail in situations that are not covered by formal instruction and when a situation accelerates out of control and scope of performance expectations involving the perception of danger, decision making, or inaction beyond operational and procedural tolerances.
## Appendix A
### Protocol Case Histories
#### Background Information
This information is a review of relevant case histories. The information is shared for a better understanding of the scope of problems security directors face on a daily basis, and for further research for the interested reader.
Source: The information represents eyewitness accounts and personal observations I have noted and reported in the course of performing security assessments, audits and inspections, and one-on-one interview sessions with numerous chief executive officers (CEOs), chief operating officers, and other corporate senior officials, directors of security and their respective staff members, and other company employees.
#### Overview of Selected Case Histories
The mission, responsibilities, authority, and accountability of many security monitoring stations or security communications, command, and control (C3) centers is not described in any of the documents reviewed (poor planning and management).
Security procedures, post instructions, and operating orders for special events require significant revisions to provide clear, user-friendly guidance (poor written communication skills).
During entry briefings, several CEOs acknowledged that most security policies were issued by executive decree because not all group leaders would sign off on the policy. During the interview process, it was evident that this unilateral action created friction between the staff and the security organization, notwithstanding that the decree was issued by the CEO without security advice and consent (ineffective team-building skills).
The purpose of many procedures, including roles and responsibilities, reporting relationships, and accountability, were not clearly delineated. These sections are written in such general terms that they lack specificity, particularly where internal and external dependencies, community interfaces and jurisdiction, and mutual assistance played a significant role in the response. In the protocols I reviewed it was difficult to determine who or what department is accountable for implementing or supporting many of the procedures (poor planning and management skills).
The clarity and presentation of important ideas and the message were confusing and difficult to grasp. In many instances the guidance was ambiguous and vague (Poor communication skills).
Clear and distinct security protocols are lacking at many locations, even though these deficiencies were identified and reported to those organizations on numerous previous visits (poor management and leadership skills).
Distinguishing between policy statements and mission statements, and the details associated with the execution of procedures that describe the systematic actions to take, was and remains a challenge. In many instances, "applicability" and "responsibilities" were scattered throughout the body of the protocols, making for difficult reading and understanding of purpose (poor communication skills).
At most locations visited, security plans required significant clarity to address and integrate key program elements influencing the capability and ability to deter, delay, prevent, protect, detect, assess, and respond to criminal activity and other events (poor communication skills).
Many facility access and circulation control protocols were loosely implemented. On several occasions, I noticed that established security practices were being completely ignored (poor planning, ineffective enforcement).
At most locations, the human resources division did not address a security work standard within the employee manual to measure employees' conformity to security rules, practices, and behavior (poor planning and work habits).
Continuing research suggests that most corporations have little insight into their security protocols, making them more complacent about threats and more easily targeted. Burying one's head in the sand may be a good security strategy for ostriches. However, there can be no arguing that it is not for security organizations.
* * *
1 Hunker was the founding director of the Critical Infrastructure Assurance Office (which was later merged within the Department of Homeland Security), a member of the National Security Council, Senior Director for Critical Infrastructure, a member of the Council of Foreign Relations, and dean of the Heinz College at Carnegie Mellon University.
14
# A Proven Organization and Management Assessment Model
## Abstract
This chapter speaks to the importance of having strong, effective security management skill sets and the leadership character and conviction to move a security organization forward through the creation and implementation of strategic security programs, and to provide management oversight of important security activities that resonate with C-suite executives. Actual case histories highlight significant management and leadership shortfalls.
### Keywords
Body of knowledge; Governance; Human side of enterprise; Management and leadership characteristics; Organizational structure; Policies and protocols; Responsibility and accountability; Social behavior patterns; Traits and attributes; Work and social interactions
A security organization that fails to focus on total quality management, fails in everything it does.
John Sullivant
Top Takeaways
• use a management assessment model to audit organization competency
• complexities of organization and management reviews
• use risk-based metrics to measure and evaluate performance
• chief executive officer's perspective
## Overview
It is a grave mistake to presume to understand executive management better than they understand themselves unless you have walked in their shoes. Perhaps the best advice this old soldier can give you is to understand them as people who, by their own account, carry the corporation on their shoulders, while you carry only the burden of proof to exercise security change. There is no doubt that internal debate about the merits of change will frequently surface between C-suite executives, the senior staff, and the security organization. But such debate may evolve into healthy constructive discussion, with each side giving in a little; thus such differences could be a good thing, giving rise to positive resolution.
This chapter speaks to maintaining a functional and viable security organization that is capable of performing its critical mission: deterrence, detection, prevention, protection, assessment, response, and recovery. I also emphasize the importance of effective security management and strong leadership to create and implement security strategies, and to provide oversight of security activities that resonate with C-suite executives.
In my view, the goal and objective of a security organization is to establish and maintain a family of corporate-wide security strategies that are acceptable to the chief executive. Such an organization provides the necessary framework for the coordination of prevention and protection efforts at all levels of management and across all aspects of corporate business operations. Lest we forget: security is a shared responsibility, and executive management and the senior staff are a key ingredient in the successful implementation of an overall corporate security program.
Security, however, is a reactionary function that requires exhaustive research, coordination, continuous strategic planning and development, and the commitment to respond to security uncertainty. To effectively achieve this posture, those individuals with security responsibilities use the same organization, technology, resources, and basic skill sets for both normal security operations and emergency response situations. As such, transitioning from a day-to-day security posture to an emergency security configuration must happen smoothly, efficiently, and effectively, because such a shift in momentum directly affects the entire enterprise.
Both normal and emergency security operations call for the exercise of strong leadership over such areas as physical security, electronics security, cyber security, information security, personnel security, and corporate-wide security emergency planning that gains the continual confidence and support of the chief executive officer (CEO), other C-suite executives, and the senior staff.
## Embracing the Mission of the Security Organization
In accomplishing the security mission, a security director faces complex challenges in a diversified high-threat and volatile environment—and always under ambiguous, uncertain, and rapidly changing circumstances, situations, and conditions. With the concurrence and support of the CEO, the security organization serves as the nucleus of corporate strategic security planning. In this decisive leadership role, the security director establishes broad security strategies; sets basic policy, protocols, and best practices; oversees security management from the position of stakeholders and the CEO; and engages in decision making. Security managers and supervisors are responsible for the overall execution of security policies, plans, protocols, and security activities and also provide feedback and insight to the director on all matters relating to security, including policy and best practices. The director is the single point of coordination for all security matters within the corporation and between federal, state, and local governments for all law enforcement and homeland security matters. Given the dynamic nature of the threat environment, the director continuously monitors corporate security programs and develops a strong business case for security investment, and investigation when the occasion arises.
Security goals and objectives that complement corporate business strategies are achieved through the exercise of management principles; security best practices; collaboration with C-suite executives, other company managers, and division chiefs; with the approval of the chief executive. Under the leadership of the director, functional responsibilities assigned to a security organization are varied and diversified; they could include one or more of the following:
• Offer strategic advice to the CEO, other C-suite executives, and division managers in implementing policy, processes, and practices, including emergency planning responsibilities.
• Assist division chiefs in promoting security strategies and security awareness, and in developing and implementing business unit security guidance consistent with the policies and practices stipulated within the corporate security plan.
• Promulgate security policies, plans, and protocols, and enforce security practices designed to reduce business risk exposure.
• Sponsor programs and measures that contribute to the objectives of diversified security programs, and maintain the currency of the security plan and related protocols.
• Organize, direct, and coordinate physical, electronic, cyber, information, and personnel security programs for a wide range of assets that are owned, operated, maintained, or leased by the company.
• Apply unified criteria for determining criticality and prioritizing security investments.
• Direct staff who are engaged in security and emergency preparedness planning activities to eliminate or mitigate business risk exposure.
• Develop security restoration and recovery plans for implementation in the aftermath of an attack, industrial accident, or natural disaster.
• Coordinate security emergency activities throughout the company to promote effective event-driven response and recovery procedures that support business unit operations, as well as business unit response and recovery activities.
• Maintain liaison with city, state, and federal law enforcement agencies and the state-level Department of Homeland Security.
• Participate in information sharing analysis centers, InfraGuard meetings, joint task forces, commissions, and groups involving antiterrorism strategies, threat advisories, and joint planning operations.
• Represent the security interests of the company at external security meetings and conferences.
• Present briefings to executive management and governing authorities.
• Develop and maintain current the corporate threat estimate profile (or Threat Forecast) using a uniform methodology for prioritizing critical assets, threats, hazards, and consequences.
• Gather and analyze threat intelligence information and threat advisory notices.
• Set priorities for strategic security planning to reduce business risk exposure.
• Approve security and security-related training programs for company employees and specialized security seminars for senior managers, designated staff members and security supervisors.
• Evaluate the effectiveness of security emergency preparedness planning activities to respond to and recover from emergencies and disasters; and make midcourse corrections to reduce or remove identified program deficiencies and weaknesses.
• Approve security design criteria and system performance standards; play a key leadership role in the strategy acquisition of physical and electronic security, cyber and information technology hardware and software, personnel security and related products, and management consultant services; influence the development of statements of work and bid specifications; and judge proposals and cost estimates for security projects.
• Establish action plans, milestone schedules, and outcome measurements to achieve security goals and objectives.
• Work with outside consultants as appropriate for independent security services.
• Analyze security requirements, establish and develop performance standards, and measure program effectiveness consistent with value and industry best practices.
• Review corporate emergency preparedness and business continuity plans for consistency and interoperability, and to ensure that security emergency response and recovery actions directly support business-critical emergency operations. Provide crisis management support to the corporate crisis management center.
• Participate in the exercise and testing of the emergency preparedness plans and, in particular, security operational capabilities.
• Prepare contract guard requirements, participate in contract negotiations, measure, evaluate performance, and continuously monitor service enhancements, improvements, and contract management and leadership.
• Collaborate with the corporate public affairs division in performing liaison duties with the media and other public relations functions.
## A Reliable Organization and Management Assessment Model That Resonates with CEOs
Fig. 14.1, A Proven Organization and Management Assessment Model, graphically displays the critical elements of investigating organization, management, and leadership characteristics.
## Purpose of Measuring Organization and Management Competency
The model offers an independent judgment of the unit's capability to perform its mission against established criteria, to comply with regulations, or to ease anxieties among executive management or the board. Security appraisals can be operational, management, performance, or compliance reviews, or any combination of these, depending on the client's desire for productivity output. The process may lead to the redesign of the organization, staffing adjustments, or change management.
Operational and management reviews enhance the entity's effectiveness, efficiency, and productivity by identifying what does and does not work, and by identifying candidate areas for improvement. Performance (or competency) and compliance reviews ensure that programs and specific projects accomplish their intended purpose and contribute to a better understanding of costs and benefits.
The model helps to:
• examine the human side of the enterprise to determine individual and group characteristics, interpersonal communications, working relationships, social behavior patterns, work and social interactions, attitudes, perceptions, and expectations; roles, responsibilities, and authority; mission awareness; the effectiveness, efficiency, and economy of managing the security workforce; performance proficiencies, qualifications, experience, expertise, and capabilities; and leadership and management traits and attributes
• review the organization's design, makeup, structure, and governance to determine the strengths and weaknesses of the organization and identify what areas require continual improvement to make important business-related decisions on where to use scarce resources and funds
• formulate or modify the organization design and strategic planning framework that integrates governance and management performance improvement, identifies unworkable measures, and provides enterprise-wide solutions to enhance organization productivity, including change and people strategy, and change management, when appropriate
• uncover root causes of ineffectiveness, inefficiencies, and excessive costs; inadequate internal controls; unworkable measures, practices, and norms; weak accountability; and the mismanagement of operations, programs, or resources
Figure 14.1 A proven organization and management assessment model (Sullivant, 2007, pp. 55–84).
• evaluate how the security organization operates today and its capability to meet the needs of the company tomorrow, and to provide decision makers with an understanding of how best to manage the security organization and those areas needing special attention
• accelerate performance by integrating and aligning security processes, protocols, people, and information systems with enterprise business strategy, goals, and objectives; to implement a system of management improvements, internal controls, and performance parameters to overcome unit deficiencies, weaknesses, and inadequacies
Unresolved problems can create dysfunctional relationships in the workplace. Ultimately, they become impediments to flexibility and in dealing with strategic change in an open-ended and creative way. Intervention offers the promise of continually improving security activities by mending dysfunctional units; bringing them into line with regulatory compliance standards or expected performance and best practices; rebuilding organizations to improve performance and regain confidence and trust; and in getting startup organizations up and running to their full potential at the earliest possible time.
## Measuring Security Management and Leadership Competencies
For the purposes of this chapter, let us agree that security management is the art of overseeing the efforts of people, and it comprises planning, organizing, coordinating, controlling, and directing activity to accomplish security goals.
• Planning involves deciding what needs to happen in the future and generating policy, plans, and protocols for action.
• Organizing is the process of making sure human and technology resources and logistical support are put into place.
• Coordinating involves creating a structure through which goals can be accomplished.
• Controlling is the monitoring of activity and progress against plans, protocols, goals, and objectives, including milestones.
• Directing determines what must be done in a situation and getting people to do it right the first time.
Security directors, managers, and other security professionals in responsible positions have the authority and responsibility to make decisions to carry out the security mission, and they are accountable for that. As previously discussed in Chapter A User-Friendly Security Assessment Model, performance effectiveness metrics resonate with chief executives because they focus on topics of most interest to them. Fig. 14.2, Management and Leadership Performance Effectiveness (PE) Metric and Calculation Criteria, follows suit with this concept. The metric may be used for both the "before" evaluation (existing performance effectiveness, PE1) and "after" mitigation implementation (effectiveness of proposed risk treatments, PE2), as discussed in Chapter A User-Friendly Security Assessment Model.
Appendix A, "Case Histories: Management and Leadership," illustrates some examples of management and leadership incompetency that directly influence individual and group productivity.
Figure 14.2 Management and leadership performance effectiveness (PE) metric and calculation criteria.
## Benefits of an Operational and Management Audit
Realized benefits can include:
• transforming low-performance or dysfunctional organizations to new heights
• introducing best practices specific to organizational needs
• transferring knowledge that is needed to smoothly implement customized strategies and solutions
• determining what improvements are needed to make important business-related decisions on where to invest scarce resources and funds
• accelerating performance by aligning security organizational processes, people, and information systems with enterprise strategy
• implementing a system of management improvements, internal controls, and performance parameters to overcome the root causes of ineffectiveness, inefficiency, excess costs, and the mismanagement of operations and programs
## Conclusions
CEOs dictate the direction and tone of the security organization and set the climate for security performance and accomplishment. The key role of any CEO is to take prudent and reasonable action to prevent harm to human resources and damage or destruction to assets that support critical business operations. These actions, though simple, are not always cheap. But let us not confuse "cheap" and "expensive" with "cost-effective." Within the realm of business survivability, deterrence, delay, prevention, protection, detection, assessment, response and recovery from both a corporate and security organization level are considered cost when the cost to implement and maintain a security program is significantly less than the expected cost of losing corporate image, brand and reputation and/or assets, resources, productivity, and revenues, including downtime, restoration, recovery, training, and start-up costs.
The model promotes accountability of strategies, processes, and practices. It evaluates performance, management efficiency, and compliance; examines qualifications, experience, and the expertise of the security workforce; assesses capabilities to achieve goals, objects, and targets; and looks at social behavior and working relationships internally and with external organizations.
The challenge, then, is to commit to obtaining the body of knowledge, skill sets, and expertise to pursue the saving of lives and the protection of assets from those who wish to do them harm, as well as from hazards and weather-related calamities, and translate these elements into profound outcomes that create opportunities to deal effectively with ambiguous security challenges. CEOs must view the safety and security of their people as a nonnegotiable requirement. CEOs must also assert genuine leadership, communicate to employees what needs to be done, and make pragmatic policy decisions to empower others to make responsible security-related and business decisions, take appropriate action, and be responsible and accountable for their behavior. It will require courage, shared sacrifice, and a willingness to compromise and make the tough choices that are essential to setting a new course for the security organization.
## Appendix A: Case Histories – Management and Leadership
### Background Information
This information is a review of relevant case histories. The information is shared for a better understanding of the scope of problems security directors face on a daily basis, and for further research for the interested reader. Source: The Information represents eyewitness accounts and personal observations I noted and reported in the course of performing security assessments, audits, and inspections, and during one-on-one interview sessions with numerous CEOs, chief operating officers, and other corporate senior officials, directors of security, their respective staff members, and other company employees.
## Overview of Selected Case Histories
At sites where executive management showed little or no interest in security planning, there was noticeable frustration among the general staff and the security organization with the pace of implementing security enhancements (poor management and leadership skills, poor planning and strategic vision).
One CEO acknowledged during the exit briefing that, in retrospect, having realistic priorities would have been beneficial in achieving security goals (executive leadership to correct the program was absent).
Another CEO at a different company told me that strategic security priorities generally were not met because there were too many, all had equal importance, and there were no funding or resources allocated to implement the plan (leadership inexperienced in managing and overseeing programs).
A few officials acknowledged that most problems stemmed from turf battles between executive management and their direct reports over delegated authority to run operations free of executive interference versus expert belief they had the experience and judgment to exercise their duties and responsibilities. Here, improved coordination and shared responsibility would have prevented most, if not all, of the problems at this location (lack of leadership confidence in staff performance, authoritative management style, and no team-building skills).
Several security organizations were found to be severely stressed because of workload, extended work periods, shortage of personnel, high turnover, and other factors that affect morale and motivation. Poor leadership skills—including not caring for people—precipitated failed performance. The mood of these organizations often switched from frustration and disillusionment to open self-loathing (weak management and leadership attributes, poor communication skills, not caring).
At several enterprises, many business units were hostile toward the security organization and working at cross-purposes for several years without executive management intervening. Relationships between the security organization and other departments were to the point where loathing among the staff had drained talent, time, and money from the enterprise's business operations (poor executive leadership, communication skills, and interpersonal relationships; total absence of professionalism).
In several instances I found upper management guilty of lax oversight of employees and ethical lapses in running the company. Management also failed to heed clear warning signs and take reasonable and prudent actions to resolve ineffective and inefficient operations across a wide spectrum of security activity (arrogance and mismanagement).
At many locations, a clear trend of ineffectiveness, inefficiency, and lack of strategic vision to implement the complexities of a comprehensive security program were found (poor security management, leadership, and vision).
At many locations, security planning, coordination, development, and implementation were weak or lacking across a wide spectrum of security activity (weak security management and leadership, inexperience).
At several security organizations there was a lack of focus, vision, leadership, structure, and discipline. Officers neglected to properly investigate complaints or incidents, or to write reports. Although security management did an excellent job maximizing the talents and skill sets of selected officers by assigning them to special projects, management failed to share with the general security workforce the scope and purpose of these special projects and their results, or to identify the officers working on these projects. This created tension and resentment among the security workforce and the perception that the security director was engaging in favoritism (poor management, bad work habits).
At one location the security organization had strayed so far from the path of responsible management that the concept of leadership had no meaning for the security force. At this same site there was squabbling between various supervisors and the security manager in the presence of security officers and contract guards, including myself as an invited security consultant to help resolve their management and leadership problems. The security manager, although a certified protection professional (CPP)—did not exhibit the skills necessary to bring all elements of a corporate-wide security program to bear (inexperience, inability to effectively communicate, very poor "people skills").
At several locations, the lack of strategic threat analysis, asset vulnerability, and loss of consequences undermined the organization's ability to effectively provide security to assets that needed it most (inexperience, lack of understanding the importance of strategic threat analysis). This entity will continue to face difficulties in trying to implement security programs that have undefined unified parameters and risk-based metrics to measure and evaluate progress, performance, and productivity. At this location, the lack of professional security leadership experience and expertise serves to underscore the immaturity of and weakness of the single corporate security strategy developed (lack of strategic vision, inexperience).
15
# Building Competencies That Count
## A Training Model
## Abstract
The discussion in this chapter highlights weak training indicators and concentrates on the need to adopt a reliable training model that revitalizes security training across the entire spectrum of security operations, as well as how to effectively use it when planning, developing, and implementing revised or new training programs. The value of training, its importance, and its benefits are emphasized. A comprehensive training model highlights the types of training programs and instructional methods often used for carrying out localized training activity. Actual case histories highlighting major training concerns are offered to support the judgments within the narrative.
### Keywords
Competency; Course design; Drills and exercises; Instruction; Job performance criteria; Objectives and tests; Security awareness training; Special security training; Trained personnel requirements; Training methodology; Training needs analysis
Training, a motivated and disciplined workforce and exercising leadership competencies is the only way to achieve corporate security goals and objectives—anything else is a waste of time, effort and money.
John Sullivant
Top Takeaways
• importance of building competencies
• perform a training needs analysis
• reliable research data to validate training requirements
• use selective effective learning techniques to get your point across
• evaluate and measure training outcomes
• planning and practicing scenarios to respond to incidents
## Overview
Over the years, security awareness training programs have produced little in terms of motivating the workforce, enhancing security, safeguarding classified information, or defending against cyber crimes, cyber terrorism, and cyber warfare. For the most part, these programs have been underfunded, conducted by overzealous or inexperienced trainers, and often do not appeal to the values and ethics of most employees who receive such training. A major weakness of these programs is they are given only upon the initial hiring, for which about 15 min of a 3-day program are allocated to the general topic of security with little or no specificity. Moreover, recurring security awareness training is seldom provided. Specialized security training for the security force fairs somewhat better than employee security awareness training but requires much improvement to meet the demands of today's challenges. Although security training is slowly gaining attention in the boardroom, it does not reflect a genuine management priority in all instances.
On the bright side, organizations are doing a much better job of collecting and analyzing risk-based performance data, and are keeping management better informed of the wellness of employee security education, as well as the security organization's performance effectiveness, efficiency, and productivity standing. Because much of the enhancement effort depends on changing beliefs, attitudes, and the behavior of individuals and groups, it follows that embedding policies, protocols, practices, and training is a good idea in helping organizations understand the best way to work with people to achieve corporate security goals and objectives.
## Why Security Training Is Important
Five reasons stand out regarding why security training is important. First, many executives view training as a "nonproductive" activity, meaning that training takes people away from their jobs, and that costs money. At the highest end of the spectrum, it goes against the grain for some executives to pay personnel for nonproductivity, unless there is a visible, tangible return on investment. To overcome this setback, one needs to build a case for training that focuses on reducing turnovers, increasing organizational resilience, attracting quality people, saving time and money, and creating opportunities for higher profit margins, which will—within a realizable time frame—return the investment through increased productivity, less absenteeism, and fewer accidents and losses.
Second, security training is important because it establishes a continuing attitude that can motivate an individual to report otherwise unnoticeable actions of others and report security vulnerabilities that could, if allowed to hibernate within the bowels of the organization, cause injury or loss of life, or damage and destruction to critical assets, as well as damage to the company's brand, image, and reputation.
Third, competency training is very important; it is designed to yield specific behavioral learning outcomes that support successful job performance, productivity, and safety. I define "competency" as a group of related individual skills and attributes that influence a major job function, indicate successful performance and proficiency, are measurable against standards, and are subject to continual improvement through training and experience.
Fourth, training enables organizations to create benchmarks by assessing the current level of competency in comparison to preset performance expectations. Exposure to competency training offers every person in the organization something of value. Most leaders know workers on the front lines are the people who are most likely to have occasion to notice something out of the ordinary that may flag a vulnerability or threat to the entity. Therefore, a major theme of all security and security-related training programs should be to motivate individuals to bring potential issues to the attention of management in a timely manner without retribution, so problems can be fixed while they are still manageable. This approach helps reduce vulnerability creep-in
Last, and most important, training increases the ability to reappraise stressful situations, decrease rumination, and increase emotional intelligence and mindfulness. According to the New Hampshire Technical Institute Business Training Center in Concord, New Hampshire employees become less judgmental after quality training, and others perceive them as more personable and approachable. Increased mindfulness has been shown to help people sustain attention, increase working memory, improve immune system function, reduce stress and anxiety, reduce depression, and increase focus, clearer thinking, and judgment.
Because security training affects and influences various operations in different ways, its orientation must take on a different meaning for each corporation, business unit, manager, and employee.
## Goals and Value Are Drivers of Effective Training
Security careers span diverse industries in every sector of the global economy, ranging from positions with small and medium-sized businesses to leadership roles that are essential to protecting every aspect of an enterprise. The security industry is changing swiftly and growing rapidly, relying more than ever on workforce innovation, productivity, training, education, and professional development and growth to be successful. You should capitalize on these emerging trends to benefit your organization and the development of your people.
• Training focuses on the job that an individual currently holds.
• Education focuses on the new skill sets that an individual may require in a future position, learned through formal accredited courses of instruction.
• Professional development focuses on the activities that an individual may participate in (in the future) through professional courses or seminars.
## A Reliable Training Model Resonates With Chief Executive Officers
Fig. 15.1 Meaningful and Useful Training Development Model, resonates with executives because it highlights a practical systematic process to identify job performance standards and competency demands, and to develop course objectives, outlines, and instruction that can withstand the test of both professional scrutiny and academic certification.
Figure 15.1 A meaningful and useful training development model.
The model has meaning and value to executives because it is sufficiently flexible to fit any security organization, large or small, public or private. It can be used to review existing courses or develop new acceptable training programs (Sullivant, 2007, pp. 185). This model has proven its value because is has shifted the compass of educational psychology from the traditional approach, which uses multiple types of questions to measure learning, to a balanced nexus of knowledge and performance-based measurement. Past and present innovative course designers, including myself, have continually advocated this approach for years, only to be set back by limited budgets or rebuked by superiors who lack an understanding of the full benefits and return on investment such a training approach can deliver.
## Independent Research and Credence of the Model
Today, new evidence vindicates those who have demonstrated this vision. Many industry leaders are now benefiting from adopting this form of analytical analysis in training development. Two recent events can be credited with changing the learning landscape.
First, several recent security surveys report that most security violations, cyber breaches, theft, and noncompliance incidents occur because of ineptness, carelessness, resentfulness, non compliance, ignorance, and other employee motivational factors that contribute to low levels of proficiency and poor-quality work. These surveys show that:
• 62% of those surveyed say their behavior and performance had a low to moderate affect on security.1 48% of the employees surveyed claim that security policies did not apply to their job function.2 49% of the employees surveyed thought security was not their personal responsibility.3
• 58% of employees say they receive inadequate or poor training on the job.4 52% of the companies surveyed say they did not provide cyber security education to their employees.5
• A separate survey reported that 55% of government officials identify carless and untrained employees as the greatest source of security threat and low productivity at their agencies.6
• 53% of chief executive officers surveyed say the main risk to corporate America is human error, carelessness, ignorance, poor training of employees, and weak supervision.7 The same number of chief executive officers also say accidents, security violations, and compliance issues result from undisciplined employees.8
Second, an independent security industry survey of risks and professional competencies performed by the ASIS Foundation, in conjunction with its parent organization, ASIS International, and the University of Phoenix (2014), profoundly compliments the reliability of many of the case histories I report throughout the pages of this book, as well as my training needs analysis model. Survey results add further credence to the concept of "vulnerability creep-in" presented in Chapter The Many Faces of Vulnerability Creep-in.
When the ASIS Foundation invited 483 members of ASIS International who hold executive or senior-level positions to participate in a survey to identify security risks, challenges, and professional competencies, they performed a great service to the security profession. The ASIS Foundations partner, the University of Phoenix, provided an even greater service when the university system validated the survey findings with quantitative data, thus helping to verify and prioritize the identified security risks, challenges, and critical competencies.
Challenges identified by the University of Phoenix include, but are not limited to, the following:
• Aging workforce and loss of management knowledge base
• Managing issues and limited budgets
• Managing scarce resources
• Use of security technology or information technology
The purposes of this book, critical competencies are those skill sets needed by security professionals—particularly senior officials—who are placed in a position of trust to:
• advance corporate goals and objectives
• provide advice to executive management and the senior staff
• exhibit leadership traits in all settings
• train others to the proficiency levels demanded by the mission, regulatory guidance, and other obligations
With respect to senior security professionals, the University of Phoenix analysis validated and prioritized 22 critical security competencies. I summarize these leadership competencies and their management categories, as reported by the University of Phoenix, in Fig. 15.2. Security Competencies
Based on survey results documented by those individuals surveyed, the University of Phoenix then ranked the competencies and divided them into the three categories shown in Fig. 15.2: most critical, medium critical, and least critical. The listing does not represent my order preference. I contend that the particular industry sector and the affected security organization would determine the meaningful value and criticality of each competency when measured against the importance of its particular mission goals and objectives. For instance, I suggest that:
• "Technological excellence," although rated least critical, would certainly carry significant weight in a national research, development, evaluation, and test environment, placing it in the most critical category. I served more than ten years in a national and international Research, Development, Test and Evaluation (RDT&E) arena working with the National Nuclear Security Agency under the START Treaty and at the Air Force Test & Evaluation Center having an active security management responsibility for the Space Shuttle Program.
Figure 15.2 Security competencies. Source: University of Phoenix, Security Industry Survey of Risks and Professional Competencies, ASIS Foundation (2014).
• "Business financial literacy," rated medium critical, would command a most critical rating for those associated with the banking and financial industry or involved in investigating financial fraud, waste, and embezzlement. My experience in banking and financial security projects has taught me that the business lexicon is an essential communications tool, not only in the banking and financial industry but in every industry. I emphasize communicating with executive management in chapter Effectively Communicating with Executives and Boards.
• Last, in a high-risk, highly visible international security arena, "multicultural versatility" and "international multicultural competence" would play an important role in sensitive multicultural business and government environments, being noteworthy of a most critical rating in most international settings. While serving on the United States Air Forces Command Staff along side my NATO staff peers, I worked closely with representatives of all NATO countries in highly visible and uncertain environments and situations. I also was involved in several private enterprise projects in South Korea, Zambia, Greece and Turkey. The exercise of diplomacy and discretion in dealing with cultural diversity, including respective national customs, traditions and norms coupled with uncertainty and highly visible political exposure in all international assignments was crucial. I am convinced that one cannot perform well in this type of environment without understanding and being sensitive to culture diversity when leading and working with ethically diverse teams, including high government officials.
Criticality of competencies can also take on a very different meaning and value when analyzed in light of a security organization's critical operational competencies, such as deterrence, delay, prevention, protection, assessment, responding to, and recovering from a terrorist act, criminal activity, industrial mishap, manmade or natural disaster, or weather-related calamities. These activities call for leadership traits necessary to direct security forces and other company employees in times of crisis, saving lives and further preventing damage or destruction to assets.
These competencies are discussed later in the chapter. For now, it is important to know that in navigating through the model, the experienced analyst needs to have advanced knowledge of the risks that might cause harm or loss to the enterprise, the challenges that might impede security's development, cohesiveness and effectiveness in responding to risks, and the political-social sensitivity of the work environment.
A good means for determining training needs for senior security professionals is to review the research accomplished by the University of Phoenix9 and other fine research institutions with your own independent research, and adopt the results to fit your needs. While there never is a single solution for all expectations, survey findings do perform a very important function. Survey results can act as a benchmark to measure the existing performance of senior security professionals by identifying gaps in their performance effectiveness. Corporations can fare well by developing industry-aligned academic and training programs that adequately prepare security professionals, security workforce members, and enterprise employees for security risks, challenges, and competencies.
To date, however, there exists no agreed-upon, complete set of competencies used across all roles and levels of the security force. Nor do binding, uniform educational guidelines for organizations exist to develop these competencies. This training model, tailored to fit your needs, can address these deficits by subscribing to guidelines that meet your day-to-day requirements as well as emergency needs. Whenever your thinking and planning are in doubt, applying the duty to care principle (discussed in Chapter The Many Faces of Vulnerability Creep-in) may offer you a reasonable and prudent solution to a practical problem.
Performing a training needs analysis as the first step in the training developmental process. This involves four tasks: identify job performance criteria, identify trained personnel requirements, analyze existing training programs, and design the curricula.
### Identify Job Performance Criteria
This involves researching the sources that create the job activity. Sources can be regulatory requirements, legal commitments, company policy that addresses the specific aspects of job activity (eg, why, when, where, how), job descriptions, and results of independent studies and case histories embedded through this book, including the competency study by the University of Phoenix. This research and analysis results in baseline training requirements that are subject to identifying trained personnel requirements and training limitations and constraints.
### Identify Trained Personnel Requirements
This involves researching how the regulatory, legal, or policy requirements for the job activity directly affect specific performance needs at the job level. Not all aspects of a particular job require formal training, and those tasks need to be filtered out of the course curricula. In many instances filtered tasks are better suited for on-the-job training rather than a formal academic setting. (More on this topic in a moment.)
### Analyze Current Training Programs
The purpose of evaluating security training is to:
• identify deficiencies and gaps in the proficiency of the security workforce
• determine the adequacy and usability of instruction given
• identify training needs against requirements to determine what modifications or new training programs are necessary to provide skill sets and knowledge base to meet the demands of the job
• assess emerging training needs to develop on-target, "just-in-time" training programs that meet the needs of the security organization
• function as a platform for developing and validating new training needs
### Design the Curricula
The architecture of a sound training program comprise curricula course charts, course outlines, student populations, facility requirements, and training materials. The best training approach is one that provides student-centered instruction that presents the knowledge and skills that are essential to perform the current job or proficiency training oriented toward preparing individuals for a future promotion or job. Regardless of the training goal, training programs should focus on building a culture of security to act securely and responsibly.
An effective means for accomplishing these goals is to:
• conduct a training analysis to identify job performance criteria against trained personnel requirements
• design and deliver training facilities and training aids and materials to support training objectives
• design and validate the course and conduct instruction
• continually evaluate the effectiveness, efficiency, and productivity of training and make mid-course adjustments to enhance and improve training to keep current with the business environment, including new processes and practices
## Types of Security Awareness Training Programs
Building security awareness means creating a corporate-wide appreciation for how security is fundamentally integrated into day-to-day business operations. A focused security awareness program reduces risk exposure and enhances personal protection. Corporate security awareness programs may consist of, but are not necessarily limited to, the following topics.
### The Employee Security Awareness and Emergency Response Training Program
Employees want to feel safe and secure in the workplace. Employee security awareness training should be given to all new and transferring employees. To have meaning and value, training should be directed toward security policies, procedures, and requirements that are particular to the general workforce. At a minimum, everyone should have a general knowledge of:
• threats facing the corporation
• the threat alert notification system
• assigned emergency response responsibilities
• how to report security incidents or unusual occurrences
• what to do in the event of emergency
Persons granted unescorted entry into restricted or controlled areas should:
• receive orientation training on entry control procedures
• understand methods to verify someones right and need to be in the area
• understand the responsibilities and duties of an escort official
• understand methods used to gain unauthorized entry to such areas
### Specialized Security Training for Designated Enterprise Employees
Selected middle managers, first-line supervisors, and other persons should receive training designed to maintain proficiency and keep this group apprised of threats, security practices, protocols, and mission changes that affect corporate business security goals. First responders should receive additional comprehensive training to effectively carry out their assigned responsibilities with assurance that their personal security will not be jeopardized. The sections below describe some sample courses.
#### Emergency Operations Center Responder Training
This training prepares employees assigned to the corporate crisis management center to perform assigned duties.
#### Emergency Preparedness Training
This training provides to corporate first responders training to respond to varying threat scenarios, such as a bomb threat, active shooter fire, explosion, environmental contamination medical emergency, and building evacuation.
#### Cyber Security Training
This training provides designated employees training to safeguard the information technology network and telecommunications systems.
#### Security Alert Status and Security Reporting Protocols
This training provides managers and operators of command centers and control rooms the interrelationship of critical time-sensitive and time-dependent security reporting requirements and actions to take that are associated with the threat alert notification system.
#### Contamination Detection and Surveillance
This training provides designated engineers, scientists, laboratory technicians, and field personnel with the training necessary to use and test environmental monitoring devices, analyze and interpret results, and take appropriate emergency response actions, as needed.
### Executive Management Security Awareness Seminars
This training is for corporate officers and other decision makers who must be aware of the security programs from a business perspective. Security awareness training for this group focuses on strategic issues. For them to fulfill their responsibilities, it is essential that they have a clear, concise, and unambiguous understanding of the threat, its consequences, security planning strategies, and security operations. Security training courses for the senior management staff could include, but are limited to, the following:
#### Crisis Management Training for Staff Members
This training provides orientation training to decision makers with respect to assigned crisis management roles and responsibilities.
#### Security Strategies and Security Planning Seminar
This training provides to decision makers a clear, concise, and unambiguous understanding of relevant and effective security strategies that will foster public confidence. It can include security emergency and business continuity planning to sustain business operations, and the application of integrated security, security-related, and safety principles.
#### Executive Protection Seminars
This training provides to executive management an overview of protective requirements against kidnapping, hostage taking, personal assault, and mobility vulnerabilities. It may also include preventive and protective measures for the protection of self and family members, within the residence as well as in other locations.
## Specialized Security Staff Training Program
Formal training and certification requirements for the security staff are vital in building a stable security force culture and operational capability. The purpose of this training is to develop specific skills and capabilities that the person being trained will regularly use on the job. Here are some samples.
### Security Officer Training
This training, performed when an employee is initially hired, provides security officers with administrative orientation and training to qualify for basic security duties and responsibilities.
### Flight, Seas Coast, or River Observer Training
Where corporate aviation and water security assets and resources are used to support security operations, this training provides selected security officers with the necessary skill sets to conduct security air and water surveillance operations to determine the status of ground conditions, the ability to direct responding ground forces to the location requiring a specific security response, and to call in additional responders as required.
### Workplace Violence Training
This training provides security officers with an understanding of basic tactics and methods to use when responding to workplace violence incidents on corporate property or when assisting the human resources office in processing disgruntled or hostile terminated, or other potentially dangerous employees.
### Emergency Security Response Procedure Training
This training provides security officers and security supervisors with proficiency-level certification training for responding to varying event-driven scenarios. This training may include intelligence gathering, analyzing the scene, field tactics, fields of fire, self-defense techniques, and communications.
### Security System Operation, Maintenance, and Testing
This training provides proficiency (certification) training to security force members who are responsible for operating, maintaining, and testing integrated security systems. Training include how to override selected system parameters, temporarily block individuals enrolled in the system from gaining access to restricted areas, generating security management information reports, and performing critical system functions necessary to protect the integrity of the system or safety of personnel.
### Security System Enrollment Training
This training provides designated security members with proficiency (certification) skills to prepare and issue identification credentials, to enroll personnel in the system with approved access levels, and, when necessary, to remove individuals from the system when given the proper authorization to do so.
### Special Security Event Training
This training provides designated security members with training required to support special corporate activities such as open houses, social events, or other gatherings, usually on a one-time or infrequent basis.
### Security Management Training
This training provides security supervisors with the means to distinguish the severity of a threat, apply deductive analysis, and effectively determine the appropriate tactics and methods to use when responding to a threat scenario.
### Security System Administration Training
This training provides designated security staff members with proficiency (certification) skills to adjust system parameters and perform detailed diagnostic testing.
## Course Design Brings Instruction to Life
Designing a course in collaboration with the corporate human resources division ensures the continuity of learning concepts, operations, requirement, practices, responses to security incidents, and security alert conditions and actions, as well as the uniformity of quality instruction. Training new employees—particularly security officers—can be a scheduling challenge. Obstacles such as availability, work priorities, and overtime pay can directly affect the quality of training and learning. You must plan, develop, and implement training needs in a manner that is cost-effective to your organization. The following instructional techniques and methods are beneficial management tools to use for course planning and design consideration.
### Classroom Instruction
The lecture method is a common method for sharing information and facts, particularly for large groups. This approach is mostly used to address basic general training topics.
Instruction, coupled with other learning techniques, can be effective when the instructor, students, education tools, and the learning environment are closely integrated with the use of audiovisual aids such as charts, graphs, slides, videos, chalk boards, and models. Instruction may be conducted during any shift or at other times such as a scheduled training day. This training includes:
• theory and application of principles
• new protocols, processes, and practices
• problem-solving exercises
### Computerized and Programmed Instruction
This instruction can be modular and self-paced, and can be scheduled at any time based on work priorities, availability of resources, and just-in-time training objectives. Both computerized and programmed instruction are effective one-on-one learning tools.
Through the use of a computerized self-paced design, learning materials can be repeated as often as necessary so the student can master the material at his or her own pace. This method of instruction can take place on the job, during all shifts, 24/7. The approach is cost-effective because no special training day for an individual or group is required, only a time frame, such as 30 days, to complete the lesson. Using a corporate-provided network, trainees can access information for any subject matter, any time. Tests can easily be administered at the end of the learning presentation, with the trainee instantly knowing how well he or she did. Should the results of the learning effort be unsatisfactory, the system provides instructions on what to expect next. Results are recorded instantaneously in the trainee's personnel file, with a summary printout provided to the trainee's immediate supervisor.
Programmed instruction is presented in written form. This instruction follows the same path as computerized instruction but is completed more slowly because it requires more reading time to cover the course material. The material is presented in a series of carefully planned and interdependent learning modules. The trainee controls the process and moves ahead only after learning and understanding each previous step. Programmed instruction, as with computerized instruction, does not present a scheduling problem. It can be accomplished independently and on the job. The supervisor or training manager provides immediate feedback and offers tutorial assistance for any problem area that may be encountered by the trainee, and records the results of training in the trainee's file.
### Correspondence Study/Training Bulletins
This method of instruction consists of passing on information during guard mounts and posting information on bulletin boards or at specific post assignments that are affected by the material. Personnel are empowered to read the training bulletins during the work shift, as time permits. It is a quick and effective way to distribute a new process or procedure that significantly affects security operations. This method is time sensitive, and its implementation requires immediate execution. To ensure the protocol is understood, supervisors, under this training concept, make regular (but unscheduled) visits to each post and:
• ask specific questions about the new protocol
• observe the security officer in an actual situation involving protocol application
• set up a hypothetical situation requiring the security officer to demonstrate his or her working knowledge of the protocol
### Seminars
This learning technique is effective for small groups and combines presentation, visual aids, materials, and participation across a broad spectrum of learning objectives. It offers the opportunity to enhance team-building skills, professionalism, social behavior, and decision-making competencies. Materials are often distributed to attendees before the start of the seminar so they can be prepared to participate in the session based on the review of the material. Discussion involves theories, concepts, and their effective application through demonstrative planning problem-solving skills.
### On-the-Job Training
On-the-job training (OJT) is performed on the job. OJT involves learning by doing, watching and listening while actually working the job in the actual work environment under actual work conditions. It also involves a trainer or the supervisor observing and monitoring the physical skill-sets learned and the degree of associated knowledge gleamed from performing the job. Such training increases a security officer's skills and knowledge, measures his or her understanding and application of both existing and new practices and processes, tests new skills and knowledge, and permits the supervisor to make immediate midcourse adjustments to correct noted weaknesses and deficiencies in understanding or in applying skill sets. One-on-one or group OTJ occurs when the supervisor observes the ongoing performance of the security officer and provides immediate feedback in response to situations that were not correct or where the security officer hesitates or appears unsure or confused.
### Field Training (or Drills and Exercises)
This approach is used to demonstrate motor skills, critical thinking, and team-building skill sets during a crisis. It may include such competencies as:
• assault line
• AWAT or combat tactics
• building and area search techniques
• command, control, and communications
• coordination with internal and external agencies
• fields of fire and suppression fire
• force protection
• ground intelligence
• leadership
• map and compass reading
• patrolling and blocking forces
• perimeter control
• preservation and control of the affected area
• response techniques
• retrograde maneuvering and withdrawal techniques
• tactical deployment techniques
• terrain association
Practical exercises demonstrate the application of theories and concepts through appropriate event-driven actions. Realistic exercises serve several purposes. They allow management to:
• assess plans and procedures to determine their feasibility under actual conditions
• assess whether personnel understand their emergency response functions and duties
• identify areas for continual improvement
• enhance coordination, communication, and proficiency among the participants
• enhance the ability of management and the staff to respond to crisis
• use results of exercises as lessons learned
Field training exercises are used to present employees with situations that might actually be experienced on the job but cannot readily taught or performed by any other learning technique. Attendees are expected to take actions that would actually be executed during an actual encounter with an adversary or hostile force under real-time conditions. The advantage of such training is that time can be compressed and long periods of delay can be telescoped into the amount of time allocated for the exercise. Participants learn from simulation and imitation experience without paying the price of making wrong decisions or taking incorrect actions in an actual encounter with a hostile individual or group. Experience gained and errors committed during field training exercises offer valuable insights to the planning process and build strong individual and group bonds and levels of confidence. Drills and exercises also serve to enhance the public image of the corporation and increase the confidence level of employees, management, and the community.
#### Objectives and Scope of Security Field Training and Exercises
Drills and exercises are an integral part of the overall corporate emergency planning effort. To the extent feasible and practical, security exercises should always be incorporated within corporate-wide exercises. The security director, however, usually conducts field-training exercises independent of other corporate business units. Security exercises provide the opportunity to test skills and knowledge in order to identify strengths and weaknesses; learn new skills; practice decision-making, techniques, and communications; and determine gaps in existing plans, procedures, and practices. Four types of learning can be achieved by performing training exercises:
• learning by doing
• learning through imitation
• learning through observation and feedback
• learning through repeated trials
• learning through video replay of actions and direct critique
#### Planning Security Field Training and Exercises
Planning considerations include:
• individual and group safety, including equipment safety
• use of equipment and communications used on the job
• participation in the actual work environment and under simulated threat conditions
• the ability to control the environment to bring about conditions that will obtain desired responses from participants
• immediate direct feedback to a decision a participant might make
The security director works with other staff members and local community authorities to determine the type of field training and exercises to be performed, the scope of involvement, and exercise limitations. Exercises are structured and organized in a manner in which results can measure performance in the following areas:
• capability to implement extended work schedule
• crisis management organization and leadership
• evaluation of response time
• inspection of equipment and demonstrated knowledge of its care and usage
• interaction and coordination within defined groups
• dependency groups internal and external to the security organization and the corporation
• mobilization of personnel and equipment in response to an emergency
• response tactics and decision making
• safety and force protection
• supportability of other divisions' emergency response actions
• timeline to provide expanded security coverage and duration of coverage
#### Developing Security Field Training and Exercise Scenarios
Developing security exercise scenarios requires an extensive knowledge of adversaries' modes of attack, their capabilities, and previous activities. It involves a great deal of research, planning, and coordination; strict controls; and approval from all levels of management. Serious effort is made to combine the appearance of reality with training controls so that the transfer of learning to the job is optimized. The security director, supported by other members of the security and corporate staff, develops realistic preplanned drills, condition simulations, field problems, and scenarios.
The goal of planning field exercises is threefold. First, and most important, a key ingredient of planning, developing, and implementing security drills and exercises is to prevent placing exercise personnel and those who are on duty but not involved in the exercise at risk of injury. Any and all scenarios must refrain from carrying out any action that confronts on-duty security officers, contract guards, members of a support force, or other employees with deceptions, which can:
• interfere with actual security operations in progress
• distract them from performing their assigned security mission
• be interpreted as a hostile act
• jeopardize the safety of individuals or the security of assets
• induce the use of deadly force
• instill in employees performing routine duties a sense of fear or uncertainty that a real attack may be occurring
Forcible breaches of a boundary barrier, failure to heed a security challenge, and similar overt actions are examples of prohibited deceptions.
Second, scenarios must be designed to demonstrate how well the security organization can perform its critical operational mission to deter, detect, delay, assess, respond to, and recover from a variety of threatening security or security-related events, while concurrently supporting corporate business goals.
Third, scenarios must capture how security leaders demonstrate critical competencies such as decision making, oral communications, critical thinking, maximizing the performance of others, persuasive influencing, and other important competencies under stressful conditions.
Inherent in exercising these competencies is the effectiveness of command, control, and communications among all participants. Equally important is the public relations department announcing company-wide exercises within the community in advance to alert the public (and government) of the training exercise. Fig. 15.3 graphically illustrates a suggested approach to measuring security performance during field training or drills and exercises. Since the threat situation is not a static entity, neither should its measurement metric. In Fig. 15.3, Scenario 1 offers security management the flexibility to add to the metric any of the threats previously discussed in earlier chapters, or to accommodate any unique threat area(s) of meaningful value to the executive management team. This simple tailoring process allows you to measure the results of any threat scenario that may be important to you at a particular time.
Figure 15.3 Critical operational capabilities and competency under stressful engagement with adversary.
In Fig. 15.3, Scenario 2 equally is not a static activity. This metric addresses a large-scale event that calls into play several independent yet inseparable critical competencies that could determine the outcome of a given security event beyond the execution of actual tactical movements, deployment techniques, or other battle formations and engagement activities.
#### Conducting Exercises
Typically, three types of exercises are used by the industry: tabletop, limited, and full-scale. Tabletop exercises involve the review of plans, maps, charts, diagrams, drawings, protocols, checklists, and processes to ensure clarity and purpose of execution. These reviews should be performed using the guidelines offered in Chapter A User-Friendly Protocol Development Model. The review also includes emergency response plans and event-driven response and recovery procedures. A good idea is to walk through the various scenarios with key participants to determine their understanding and knowledge of the subject matter, as well as their rationale for selecting a course of action in response to a particular threat scenario and to give personnel the opportunity to ask questions. Tabletop exercises help to build confidence in both the management staff and in those individuals who are expected to respond to crisis.
Limited security exercises are activities internal to the security organization. They serve as training sessions and planning for corporate full-scale exercises scheduled in the future. These exercises allow the security organization to run practice drills during security operations with available on-duty security personnel.
Full-scale security exercises are conducted in concert with corporate-wide drills and exercises. It is highly recommended that a full-scale corporate exercise involving a bomb explosion or a chemical, biological, and radiological attack, or any incident that requires the evacuation of a building or major complex, the establishment of an emergency safety area, or the participation by community first responders, be conducted at least annually.
#### Lessons Learned
It is important that security organizations evaluate their vulnerability posture after each major security incident, disaster, industrial mishap, and field-training exercise to help improve practices, confidence, and response capabilities. In addition, the lessons learned process should be used to identify new security priorities and investment, take advantage of emerging approaches and new technologies, and perpetuate a proactive security culture throughout the corporation.
## Professional Development Is Key for Security Planners
For all practical purposes, except for attending an accredited university security management program—such as that at the University of Phoenix or other equally fine universities—this training may only be able to be applied through self-imposed research, reading, correspondence courses, observation of other leaders, and learning to excel in using the critical competences discussed in this chapter.
## Benefits Management Enjoys by Adopting the Model
The benefits of training help to improve security organizational performance and individual and group proficiency, while increasing security awareness; unit effectiveness, efficiency, and productivity; and security resilience. This model leads to the solid development of training programs that encompass just-in-time training involving individuals, groups, and agencies that personnel work with in real incidents in the actual work environment.
## Conclusions
To create an overall effective security organization, including a useful and meaningful training program, it is important to create first a security culture that is curious about error, or unsatisfactory performance, rather than one that has a "shoot the messenger" mentality where retribution and punishment are expected, and thus reporting is avoided.
Curiosity is a sign of willingness to learn why things are not as they seem and is a starting point for change. Training widens the understanding of human performance and social behavior, and the workplace environment, and reinforces practical skills and important reminders, such as lessons learned from previous exercises and drills.
It is important to note that the complexity of the subject matter being taught largely guides the method of instruction. Other course design considerations include class size and student background; learning objectives and level of proficiency to be obtained; quality and expertise of the faculty; adequacy of facilities, equipment, and training aids; and available training time.
When carried out according to its intensions, training strengthens organizational values and attitudes; improves individual and group proficiency; and builds confidence in the workforce, security management, executive management, boards, and, where appropriate, regulators and other governing bodies. Training therefore serves as a platform to implement change solutions to operational and behavioral problems.
* * *
1 SolarWinds Federal Cyberfsecurity Survey Summary Report, March 26, 2014, Chantilly, VA 20151: <http://docplayer.net/2500018-Solarwinds-federal-cybersecurity-survey-summary-report.html>
2 SolarWinds Federal Cybersecurity Survey Summary Report 2015, Chantilly, VA 20151: <http://www.solarwinds.com/resources/surveys/solarwinds-federal-cybersecurity-survey-summary-report-2015.aspx.webloc>
3 Ibid
4 <http://www.businesswire.com/news/home/20150420006379/en/LogRhythm-Survey-Finds-Employees-Place-Organizations-Risk>
5 Ponemon Institute surveyed more than 160,000 security professionals in 15 countries. Retrieved from: <http://nsi.org/SecurityNewsWatch/NewsWatch/7.23.14.html/>. Ibid
6 SolarWinds Federal Cybersecurity Survey Summary Report 2015, Chantilly, VA 20151: <http://www.solarwinds.com/resources/surveys/solarwinds-federal-cybersecurity-survey-summary-report-2015.aspx.webloc>
7 IT Goverance's Boardroom Cyber Watch Survey <https://virtualizationandstorage.files.wordpress.com/2013/02/cyber-watch-survey-report-final.pdf>
8 SolarWinds Federal Cybersecurity Survey Summary Report 2015, Chantilly, VA 20151: <http://www.solarwinds.com/resources/surveys/solarwinds-federal-cybersecurity-survey-summary-report-2015.aspx.webloc>
9 Security Industry Survey of Risks & Professional Competencies, University of Phoenix, 2014.
16
# How to Communicate with Executives and Governing Bodies
## Abstract
This chapter stresses that communicating with executives and governing bodies is perhaps the most important skill set one should possess or strive to acquire. The chapter's focus is on knowing what executives expect from a security professional: the ability to translate his or her body of knowledge in clear terms that have meaning and value and in a language that matters to the chief executive officer. Presentation, control of time, organization, and useful graphics are emphasized. Actual case histories highlight poor attempts to communicate with executives and board members.
### Keywords
Build a business case; Candid; First impressions count; Management language; Management perspective; Message delivery; Process thinking; Professional; Risk-based versus operational metrics; Security terminology; Strategic thinking; Trustworthy; Value and meaning; Verbal visionary
The only thing more difficult than talking is listening, and most of us rarely are good at doing either, particularly when the topics are security, safety or the budget. Always say things that matter and speak in a language management understands.
John Sullivant
Top Takeaways
• objectivity and perception in the security world
• formulate a proactive relationship with executive management
• fact-finding and effectively communicating ideas
• think and speak in a language executives understand
• communicate with the C-suite and gain their buy-in
• CEOs need value information from you
• deliver powerful persuasive presentations
• build and defend a business case before executive management
• deliver meaningful options and alternatives the CEO can use
• listening and responding to questions
## Overview
Chief executive officers (CEOs) reveal the corporate vision and then encourage, cheerlead, direct, and organize the company to work toward goals and objectives. Successful CEOs focus on things that matter, communicate constantly, have limited objectives, finish projects or stop those that need to be stopped, and support people. To achieve these goals, CEOs expect their senior security professional to focus on tomorrow rather than on yesterday by providing substantive updates, realizing that not all news is good news, always saying things that matter and that executives and governing bodies do not already know, and speaking to them in the language they understand, care about, and can act on.
## Why Would a CEO Ever Ask You for Help?
Executives need advice from people who see the world from their perspective. They have a great need for a trusted source of unbiased information, to hear hard truths quickly, and should not be the last to know what is happening. As an executive's senior security professional, your perspective matters if problem solving is about tomorrow, even if the topic is about yesterday's mistake; you need to use time wisely and say things that matter in a brief, candid, and powerful way.
To be of value to your CEO you must have at your fingertips important security-related business knowledge that helps the business run. This calls for the ability to extract wisdom and useful conclusions from unrelated information and facts at a moment's notice. It calls for developing expertise beyond your security responsibilities and to understanding the broader issues the company faces. This includes providing advance warning plus options for solving (or at least managing) trouble or opportunity, and the unintended consequences both bring to the table. This also means helping with the dynamics of dealing with the board of directors with respect and preserving the corporation from realistic threats. You must also understand the pattern of events and issues that matter to the business so you can plan for them. How can you do this? The answer is simple: know what executives are trying to accomplish, what motivates them, what matters to them, the problems they face, how they think and make decisions, and how they achieve success. Do these things and you will gain management's attention, trust, confidence, and loyalty.
CEOs also expect you to respond through real-time, face-to-face communications between C-suite executives, the board of directors, managers, and subordinates. However, face time with the CEO matters only when the advice you give matters, and only if such advice can help the CEO run the company better, thereby making tomorrow better. For example, show how security initiatives contribute to the corporation keeping money, making money, and saving money. If you can do these things well, you will gain the respect and trust of C-suite executives and others.
## Why Should a Chief Executive Listen to You?
Right from the start, first impressions tell the story of your upbringing, education, demeanor, dependability, and reliability. Taint any one of these personal attributes and your image, brand, and reputation can begin to falter. CEOs look for these attributes in their senior security professional because they are fundamentally important to effective decision making based on uncertainty, oral communications, critical thinking, structured brain storming, conceptual analysis, maximizing other's performance, and persuasive influencing.
CEOs communicate verbally and talk in the future tense about tomorrow and beyond, and often about territory no one yet owns or occupies. It is up to the staff to digest and translate the CEOs vision into a narrative that can be shared by the board of directors and those tasked with implementing that vision. That is the purpose of having a trusted staff. As security director, you fill a major trusted advisory role on this staff.
As a security professional in a key leadership role, you wear two hats in which you must be equally competent. You are an operational line manager as well as a trusted senior advisor to executive management. In the former position you manage and direct security operations. In this role you oversee activities that range from enforcing security practices to offering related services such as patrolling, crime prevention, site and facility protection to responding to and investigating incidents. In the latter position—which is still in its infancy in many organizations—you fulfill a corporate staff management role with great potential for becoming an influential voice in executive management's ear. In this role you focus on the strategic vision, planning, developing, and implementing policies and best practices, and cohesively integrating the various security programs that enhance and improve corporate security resilience. Some organizations have recognized the value and benefit of this capability and have propelled the security director into a " trusted consulting role" providing advice directly to the CEO, other C-suite executives, and the board of directors. Other corporations are holding back in making this change.
By default, you are the point person for all security matters, with the awesome responsibility to brief and update the CEO, senior staff, and the board of directors. And you must use the language they understand, care about, and can act on. You will gain the attention of the CEO as long as:
• you think, act, and talk security strategy from a business perspective
• the CEO trusts your advice
• the CEO believes you have a sense of what it takes to achieve success
As you move up in responsibility, authority, and accountability, this trust becomes increasingly crucial. Here are some tips that can help you be successful:
• Speak the language executives understand, care about, and can act on.
• Impressions count: focus on the future and develop a management perception.
• Be a verbal visionary. Be that window for tomorrow.
• Be trustworthy, candid, and professional. Give advice constructively.
• Build a solid business case. Know when to pull your parachute cord.
Let me briefly summarize each of these tips.
## Speak the Language Executives and Board Members Understand, Care About, and Can Act On
You must learn to blend security terminology sparingly with management's language to get your message across in a clear and simple manner. If you can master management's language and apply its usage to your organization, you will receive a very positive reception when dealing with the executive team.
### Communicating With Executives and Board Members Is a Work in Progress
Communications is not a one-time adventure. It is a continuous journey with no end. Every time you write a memo, every time you talk on the phone or speak one-on-one or to a group—it is a continuous saga. To be successful in your communications with executives and board members, you must never bother this group with detail or trivia, Always keep your message, simple, short and to the point, and logically organized. When you offer too much information, or overly complicate the goal you are trying to achieve, or exhibit poor organization skills-sets, your message becomes confusing and distorted, making it hard to relate your topic to wider business strategies that do not relevant to executive and board decision making.
### Use Terms Management Understands and Can Act on
So, how do you speak to management in ways that are valuable and useful or strategic? First, seek to learn before speaking. Second, when you do speak, speak the language management uses because that is what they understand. While they may be familiar with some general security terms, they may not understand most professional and technical terms you customarily use when communicating with other security professionals. Saturating your message with security language when communicating with executives will not get that message across. Below is a short list of terms that resonate with executive management.
• Alternatives
• Asset protection
• Best practices
• Business strategic vision
• Capital investment
• Competitive intelligence
• Cost-effective
• Crisis consulting
• Crisis management
• Customer loyalty management
• Customer reengineering
• Downstream impact analysis
• Exposure management
• Financial exposure and protection
• Image, brand, and reputation
• Internal/external dependencies
• Link analysis
• Management development
• Mid-stream adjustments
• Motivation strategy
• Operating capital
• Operationally focused
• Operational review and analysis
• Options
• Partnering | • Perspective
• Process strategy
• Productivity
• Profitable deployments
• Profit margin
• Quality assurance
• Quality controls
• Return on investment
• Risk avoidance
• Risk reduction
• Risk exposure
• Risk management
• Risk transfer
• Staff development
• Stay the Course
• Strategic planning
• Supply chain impact
• Team building
• Total quality management
• Troubleshooting
• Trusted agent
• Unintended consequence
• Upstream impact analysis
• Validation
---|---
For some, learning to communicate with executives using a nonsecurity vocabulary may be a new experience, but if you want management to listen to and understand your message, you must step up to the challenge by learning management's lexicon. A good source for finding business terms relevant to your corporation and industry is the language used throughout corporate plans, policies, directives, general correspondence, financial and marketing literature and formal conversations.
To be useful, for example, security information must have value and meaning to the CEO and be presented in a business context: What is the risk exposure? What do we do if? Where do we stand on security performance? productivity? What about our profit margin? One way to get your message across to management is to demonstrate how security values complement business values: express these relationships in business context, and explain how security activities contribute to making money, keeping money, saving money, and protecting the corporation's investments.
## Impressions Count
Getting your message across to management involves not only substance but also appearance and demeanor; style and body and facial language; speech and voice; and image, brand, and reputation creditability. Lets take a moment to review each of these attributes.
### Appearance and Demeanor
First impressions are lasting impressions. Clothes and personal appearance send powerful messages before you even say a word. Clothing and accessories indicate who you think you are and what others think of you. Clothes help you fit in as well as stand out. Dress according to your company's dress code and what is customary for the occasion. The better you appear the better impression you will make.
### Style and Body and Facial Language
Style, facial expressions, eye contact, smiles, and gestures add a distinct personality to your message and inspire understanding and confidence. Posture and gestures reveal what you think of yourself and your audience. Rigidness communicates anxiety and insecurity. Be alert but not tense. Be relaxed but not too relaxed. Be self-aware. Use gestures to convey a feeling or to emphasize a point.
### Speech and Voice
Choose words that create a favorable impression with the listener. Eye contact and a quality voice pitch make for enthusiasm, informality, humor, and sincerity. Good volume, tone, and pitch add variety to your message. A monotone will bore your listeners. Speaking too slowly or too quickly may make your listeners uncomfortable. To emphasize an important sentence, for example, say the first part in a normal voice, then pause and whisper the last two words, and pause again before speaking. A pause gives you time to think. It gives the listener an opportunity to absorb and retain what you said.
### Image, Brand, Reputation Credibility
Your audience wants to know who you are—your image, brand, and reputation—and why they should listen to you: because of your experience, expertise, and authority in the field. If the audience does not know you, establish your credibility at the very start of your presentation. Tell a brief but exciting story about a profound experience you had.
## Tips That Will Help You Get Your Message Across
Executives are creatures of habit and social norms. They expect you to be persuasive and acceptable in presenting your case. This section describes tips that can help you resonate.
### Preparing Your Message for Delivery
Use the experience and knowledge of your "number 2" and staff members to help you gather the information you need to make your point. Update metrics. Always remember your goal: to get your message across using clear, distinct, and powerful language your CEO understands, cares about, and can act on. A good "A-team" can do that for you. Always bring your number 2 and (if seating permits) at least two subject matter experts in the area you will be talking about to any management presentation you give. The prime responsibility of your subject matter experts is to take key notes that require follow-up action, to observe the body language of those in attendance while you are speaking, to help with visual aids and distribute handouts, and to participate in the question-and-answer period (only if you call on them for support). Having your number 2 help to prepare the message and be present provides him or her with useful insight into the senior management decision-making process and experience to give future presentations in your absence.
Practice your approach in front of your staff and seek their candid advice to improve and refine the presentation. At the onset, it will be natural to use your notes or script to practice, but do not get too dependent on these. You must put them aside when the curtain goes up.
Giving strategic advice to executives has as much to do with image, trust, and confidence as it does with words, knowledge, and expertise. Nothing will tarnish your image, stain your trust, or lower your confidence level among your audience than if you memorize or read your message.
#### Memorizing Is a No-No
You cannot be effective in a memorization mode. What happens if you are interrupted with a question from the audience or distracted by some nearby activity that causes you to mentally loose your place or forget the last words you spoke? When you memorize, the material controls you. Instead, you need control of the material. A good policy is to practice your message using your notes until you master the material and are able to speak with authority on the issues without hesitation. Practicing your lines is similar to what actors do. They rehearse scenes over and over again until the director is satisfied he or she has captured their best performance with the camera lenses. The main difference between you and actors is that when you are on center stage, it is a live performance. I often rehearse presentations a dozen times or more. I do not stop until I am comfortable with what I have to say. I consistently make adjustments and refine the content of my message before the presentation. Often, I even change it while speaking.
#### Reading Too Is a No-No
When you read, your notebook and podium stand between you and the audience. You lose any opportunity for naturally using eye contact, gestures, facial expressions, and tone of voice to attract and keep the attention of the audience. In fact, reading your message can cause you to lose your audience. It is your job to keep their interest in what you say. On a personal note, another reason I do not like reading is that I have to wear glasses to read the script or have it typed at a 20- to 24-point font size. Then I have to remove my glasses so I can make eye contact with the audience. All that movement becomes a distraction to the listener.
One last thought on memorizing or reading your message. Once you begin to speak, everything human falls away. Remember, you are not there to give a speech or lecture, or to explain complex or technical information. You are there to establish trust, confidence, and rapport; to demonstrate character and integrity; to showcase your knowledge of the topic you are talking about; and to persuade your listeners to give you want you want. It is difficult—if not impossible—to achieve these objectives by burying your nose in a notebook. That works for ostriches, not serious-minded persons. The audience is not in your notebook; they are in front of you, and they want you to be personable. They want to see the whites of your eyes and sense that you acknowledge their presence. You must reach out and touch their sensitivity so they can relate to you and your value system.
## Think Strategically
Always focus on the future whether you speak, write or even think about what you want to do. Don't waste time and energy dwelling on the past. Always look forward into the future.
### Strategic Thinking
The most fundamental task for a CEO and board of directors is to set the right goals so the organization can establish strategic objectives and processes that lead to success. Strategic thinking helps you understand how executives approach problems. Strategic thinking is the vision of the future, but too often we are bogged down in what happened yesterday, last week, or last month. We spend far too much time and energy figuring out how we got to where we are and who is to blame for getting us here. We should instead focus on how to move forward in an organized and judicious fashion and how to learn from our experiences. Know where you have to go. Show your audience how you are going to get there. Be constructive: give insightful and perceptive analysis and advice. Focus on the future.
### Process Thinking
Most CEOs prefer to use process thinking. Process thinking is a problem-solving approach that divides issues into symmetrical local, sequential segments so problem solvers can proceed to work and think in an orderly, logical, and incremental fashion. Process thinking incorporates an integrated systematic approach to problem solving that offers a range of recommended options plus the assumptions and rationale that support them. It focuses on executive goals, perceptions, and vision, providing substantive intensity (Sullivant, 2007, pp. 213–216). All the strategy models presented in this book embed the process thinking approach.
### Risk-Based Metrics Resonate with Executives
Metrics have no value unless they are tied to, aligned with, or part of the larger organizational risk process and a continuous improvement program. Metrics that are tied directly to the organization's security strategies—the corporate business plan, security plan, security emergency plan, crisis management plan, and associated security protocols—can have a direct relationship with compliance or nonconformance to those guidelines, as well as performance effectiveness, efficiency, and productivity; they can also warn of worsening security risk situations. All areas matter to executive management.
## Develop a Management Perspective
People in staff functions tend to believe that their recommendations and big ideas will save the day for management. But CEOs give more credence to recommendations and ideas that come from operating managers. This distinction is so important it bears repeating. In Chapter Introduction I talked about why most CEOs prefer not to be briefed by staffers. Earlier in this chapter I talked about you wearing two hats. As an advisor, it is crucial that you talk and write about your staff's functional responsibilities in operational management terms rather than just in the terms of staff security expertise. Always write in language that is meaningful and useful to management. Express solutions in management language, rather than in staff language. The failure to align activities and solutions with management goals and objectives is often the reason most staffers are considered less important than the operations team. Get your message across as an operating manager, not a staffer.
### Think in Terms of Business Operations and Business Risk Exposure
You should always see things from the CEO's point of view. Credibility requires that you speak to risk exposure in both your oral and written communications, providing advance warning plus options for solutions and managing trouble or opportunity, and unintended consequences and risk reduction, in a business and financial context. Be curious: investigate and master new and less-well-understood information. Question all assumptions and validate or seek alternative viewpoints. Develop a business management mind-set, behavior pattern, and attitude that attracts management's attention to give you standing and a pathway to occasional visits to the CEO's inner circle of advisors other than giving formal presentations (Lukaszewski, 2008, pp. 40).
### Carve Out Recommendations in a Business Context
Let me put things into perspective: management's job is to run the business; your job is to help management do theirs. This is why it is important you know what the business is about. To truly act in the best interests of the business, you must bring in important and useful security-related business knowledge—beyond that already known by the CEO—to run the business. Management generally looks for these types of feedback:
• Strategies, mistakes, and successes: Where does security stand on performance effectiveness, efficiency, and productivity? Where does it stand on best practices?
• Emotional intelligence about the temperament of the workforce: What should executives know? Do employees feel they have a safe and secure workplace?
• Threats and exposure, unplanned visibility, and organizational forecasting: What should executives worry about today, tonight, and tomorrow morning? What can be deferred?
### Offer Constructive Options
Be a force for prompt, positive, and forward thinking. Be reflective, but take only useful, positive lessons from the past. Seek out relevant patterns and experiences to formulate new insights for the future. Solving security problems using a systematic/process approach and developing mitigation actions from a business and management perspective is a step in the right direction. Always focus on team success and leadership to achieve useful, important, and positive outcomes.
## Be Trustworthy, Candid, and Professional
### Do Others Perceive You as Trustworthy?
Executives must trust you before they will act on your advice. You must gain their confidence in your judgment, integrity, and reputation or they will turn to others for security advice. You must be unconditionally honest from the start and demonstrate your value system in all words and deeds. Your standing as a trusted agent only counts when combined with kept promises, careful talk, self-control, truthfulness, and confidentiality.
The stakes are always high in the relationship dynamics between a trusted security director and the C-suite executives who relay on that security director for results. Trust is one of the important reasons people are promoted. Losing trust is also a primary reason people are ignored, demoted, or even fired. Having the boss trust you gives you access to information, meetings, and the influence over others (provided that they trust you as well). Trust requires truth; truth requires understanding and recognition of the viewer's point of reference as he or she sees it (Lukaszewski, 2008, pp. 59). Lukaszewski advocates that trust involves five critical ingredients:
• Candor is truth with an attitude, insight, and honest perspective. A candid person interprets and clarifies information in ways that are obviously helpful and avoids being self-serving.
• Credibility is the acceptance by others of your behavior, record of accomplishment, and delivering what you promise.
• Integrity is the inclination to do the right or most appropriate thing at the first opportunity or whenever there is a choice to be made. A person with integrity is someone you can count on to steer you in the right direction or help you make the normally correct decision, often on the spot, every time.
• Loyalty is a genuine affection for an individual or circumstance. It is willingness to go anywhere, do most anything, follow the lead given, and spontaneously speak up for an individual or circumstance.
• Competence is the ability to apply special knowledge, experience, and insight to resolve issues, questions, and problems, putting the power of your intellect and expertise to work.
According to Lukaszewski (2008, pp. 60, 61), six elements are needed to establish and maintain trust.
• Provide advance information whenever you can. Providing advance information is important because its absence can have a negative impact on a trust relationship. Executives expect to be warned of danger, damning decisions, or threats and disloyalty.
• Seek the leader's input. Asking for input is the second most powerful element of trust. It gets others involved, lets them know where you are coming from and where you want to go, and demonstrates your team-building and leadership skills. Taking action without asking for or seeking input is considered arrogant and not empathetic.
• Listen carefully. Learn to listen before you speak. Trust depends on careful listening from every side.
• Implement change based on what you hear. Changing announced actions, behaviors, and outcomes is a reflection of what is heard.
• Stay engaged. This requires you to take the first step to initiate, maintain, or keep moving the relationship.
• Engage others. The most powerful gesture you can make to build trust is to invite those affected by your decisions and authority into the decision-making process.
Lukaszewski (2008, pp. 61–63) also contends that trust is not everlasting. He has a top-ten list of the most frequent and most easily avoided trustbusters.
• Arrogance presumes you have permission to make unilateral decisions without input from others.
• Broken promises means you are not able to meet or do not want to keep commitments.
• Chest beating is a self-validating and condescending behavior that puts distance between those who want to trust and those who need to be trusted.
• Creating fear usually occurs when one party damages or threatens to damage another, creating feelings of dread, helplessness, even betrayal of the relationship.
• Deception is intentionally misleading through acts of omission, commission, negligence, or incompetence, which can create feelings of separation, distance, and disappointment.
• Denial is failing or refusing to come forward and acknowledge mistakes and errors in judgment or blame shifting.
• Disparagement is shifting blame to others or faulting conditions, circumstances, and outcomes.
• Disrespect is trivializing or degenerating the reputation of an individual, product, or organization.
• Holding back is deliberately withholding information, support, administration, cooperation, or collaboration.
• Underestimating events or danger fails to accurately identify faulty thinking that can lead to mistakes, errors, and bad behaviors.
For the security professional, this is a list of warning signs that could indicate that the trusted relationship between you and executive management may be on the path toward demise.
### Do Others Perceive You as Being Candid in Your Dealings With Them?
Executives expect you to offer unvarnished and candid advice.
• Be straightforward about risk and uncertainties.
• State your position clearly and persuasively.
• Disclose setbacks and other bad news early and openly to avoid or preempt worsening problems. Act in real time to solve problems before they become unmanageable.
• Resist the temptation to "protect the boss" by withholding important information and facts, or by under reporting or over reporting, as this practice erodes trust.
• Obtain and report the facts within the context of their discovery and the investigation of the facts.
Lose any self-imposed false impression you may have that the more time you spend with the boss, the more likely he or she will call on you for future advice. Never lose site of the fact that time with executives is always limited, focused, and operationally oriented. Anything else is unproductive and could be disastrous for your career.
### Always Project a Positive Image in Your Business Affairs?
Executives expect you to be professional and transparent in all your business affairs. Some desirable qualities that can project a positive image and brand include, but are not necessarily limited to, the following (listed in alphabetical order):
• Act in real time to address real problems. Always have honest introspection.
• Actions should be unchallengeable and explainable. Exhibit a sense of reality.
• Anticipate and identify problem areas early, while they are still manageable.
• Apply critical thinking skills and act decisively. Focus on the ultimate outcome.
• Attract other leaders. Provide strategic, insightful advice. Nourish team building.
• Provide clear and decisive judgment in making critical decisions in the face of uncertainty.
• Empower subordinates to give you candid advice. Listen to those around you.
• Exercise strong leadership, even under uncertain and visible circumstances.
• Preserve and uphold the highest standards of ethics and professionalism.
• Relentlessly clarify the record, correct mistakes, and issue an apology for wrongdoing.
• See critical issues as executive management sees them.
• Translate strategies into meaningful measurable activity and workable solutions.
• Cultivate trust relationships and build confidence with executives.
• Demonstrate consistency, confidence, and competency.
• Launch aggressive drives against ineffectiveness and inefficiency, and slash unproductiveness.
• Stimulate team problem-solving initiatives to their full potential.
• Regard differing views as opportunities for understanding and personal growth.
• Address every concern or question and avoid judging the questioner.
• Always be open, accessible, and willing to help management tackle issues.
• Avoid whining, bickering, and arguing. Leave your ego at the nearest exit.
• Develop followers, even in the face of aggressive negativity, anger, or arrogance.
• Dump any cynicism you might have about management and others.
## Be a Verbal Visionary
CEOs drive and lead organizations by what they say. You must be prepared to engage in fast-paced discussions in real time, which requires strong verbal skills, and to do so in the territory of the executive, which is the future toward which the boss is steering the organization. Your greatest responsibility of leadership is to identify the vision for the security organization and get others to contribute willingly to achieving that goal. Your second-greatest responsibility is to get the resources and funding needed to move ideas forward.
### Use Risk-Based Metrics to Develop a Telling Story and Tailor It to the Audience
Risk-based metrics ensure that you have a measurable means of communicating risk to executives. Using a metric provides objectivity that helps you and decision makers resolve conflicts about the process or procedure rather than personality.
• Put your ideas together in a logical way, and practice being concise and vivid.
• Speak like someone you would like to listen to.
• Say important things. Say things that matter.
• Speak to the facts, not speculation or opinion.
• Ground your vision in a reality that attracts your audience.
• Use your strong sense of identity to share your goals, objectives, and sense of destiny.
• Remain one step ahead of everyone—anticipate problems, and opportunities, and have a plan.
Find a way to tell a persuasive story or give compelling examples of your experiences and personal history that tend to blunt people's feelings or emotions, and about realistic risk and what you did to reduce it, so they let you continue talking and so they listen.
• Talk specifically about business and security objectives.
• Make the story compelling by naming actual business resources threatened, the value of those resources, and the consequences of loss should an event occur.
• Use positive, direct, and powerful language to get the audience's attention and keep it.
Comparisons help people see the right and wrong side of a situation, and the right question at the right time can open minds to help people recall ideas well after your presentation is over.
Tell the story in plain, positive language. Ensure the story has a moral, a lesson, or a reason for being told that the listener can immediately relate to. Say things that you know people will remember and will want to pass on to others. A good story can have a great influence on listeners. Speak in simple terms to keep people better focused on what you are saying. It forces them (sometimes against their will) to take notes. People who take notes usually come back to ask questions and to open a dialog with you, and that is what you want them to do.
### Operational Metrics Fail to Resonate With Executives
In telling your story, refrain from using operational metrics—metrics for example that simply identify the number of attempt criminal acts, traffic accidents, traffic violations, or other non-risk activities. These metrics tend to be based on invalid and unreliable data because they rely on voluntary reporting of activity. One cannot draw accurate risk-related conclusions from this information. Such data do not resonate well in the boardroom because they are not linked to, aligned with, or part of a larger risk process. Executives fail to understand their meaning in a business risk context. Use operational metrics only for your own background information and within the security organization, or to develop a case history to support security- and risk-related metrics or the productivity of processes or practices.
## Be That Window for Tomorrow
### Measuring Tomorrow's Results
Problems are always about tomorrow, even though you may be fixing yesterday's mistakes. CEOs need help getting tomorrow right, so focus your advice there. Learn from your own experiences and those of others, then translate outcomes into lessons learned that executives need to hear. Focusing on the future will help you build these strengths:
• Gain experience and important knowledge of the business that can make you more effective and efficient.
• A knowledge of patterns can tell you which strategies to use to avoid problems. Focus on the ultimate outcome and use the right patterns to make your comments and writing more memorable.
• Understand strategic patterns so you can be an intelligence forecaster of circumstances, conditions, and reactions.
Information about the past can be useful if you can analyze and learn from patterns, then apply their meaning to tomorrow. These insights can help you understand better the situations your CEO confronts.
### Measuring and Communicating Risk-Based Metric Results Over Time
This allows comparisons that can be a useful vehicle for communicating risk-based metric values and results. Metrics that show progress toward meeting specific strategic goals can tell a compelling story through the unfolding of events over time. Distinguishing metrics that are time-sensitive from those that provide value over time can also enhance the overall value of your presentation.
## Give Constructive Advice
Always offer clear, constructive, and accurate strategic and tactical advice that is practical, pragmatic, purposeful, and focused, on the spot, 24/7.
### Always Be Professional and Display a Positive Image
Always be positive in your approach, mannerisms, and comments. Never criticize anyone or make a negative comment about any failure or shortcoming you are presenting. Never exhibit arrogance or a condescending attitude. Bickering, arguing, and failing to listen may lead to explosive confrontations followed by bitter relationships. Never burn a bridge behind you. Because most of us remember the negative sting of criticism, the CEO may shut you down on the spot and reject you as an advisor. Should this happen, your ability and opportunity to contribute to the corporation may end. Instead, make constructive suggestions so that you are heard, and put your energy to positive use enhancing and improving the situation.
### Select a Beneficial Approach That Resonates with Your Audience
There are many approaches to delivering a message, and many corporations and agencies have developed their own style and format for briefing executives. These tailored-made templates serve these corporations well in terms of information flow and sequence, and you should have no problem tailoring your briefing to this format. Few, however, emphasize time constraints and attention span. Personally, I favor the approaches created by two different men: Milo O. Frank and James E. Lukaszewski. Frank and Lukaszewski both address time and attention span. Both approaches resonate with audiences and could help you develop powerful presentations. Both concepts are simple and direct. Both have powerful attention-getter elements.
Frank (1986, pp. 9–119) designed an attention-getter approach, which he coined "30 s or less." The approach emphasizes presenting a business case in segments of 30 s or less. The bases for Frank's 30-s rule rest on two compelling reasons why 30 s is the ideal length of time to get your point across: time constraints and attention span. People tend to loose interest in a topic after 30 s, and their minds start to wonder to other things.
Lukaszewski (2008, pp. 25–84) designed a similar approach referred to as the "3-min drill." His concept organizes a business case into segments of 30, 60, or 150 words to address topics in 3-min intervals, as well as to gain listener attention and retention. Lukaszewski's approach calls for a word count to be eventually translated into a measured unit of time.
I prefer Frank's approach (modified slightly) over Lukaszewski's approach because, for me, it is easier to manage the topic and control my time by restricting my comments to 30-s segments rather than counting words. The editing process then is simplified. Another reason I like Frank's concept is that each bullet point can be a separate and distinct 30-s message. This keeps the visual aid neat and clean, and me on track and moving forward. I am convinced that the best way to keep the interest and attention of an audience is to do and say something new and interesting every 30 s.
I encourage you to review and practice each concept, then select the approach you feel at ease with. You may prefer to pick and choose the best aspect from each approach to further develop your own particular comfort level, as I have.
#### Staying within Time Constraints Helps Win the Battle
CEOs are tough. They do not have time to wait for you to get your point across; they will not listen to you for long. Neither will the senior staff, board of directors, or community governing bodies. Use time wisely. The operative rule is to say less but make it more important, and to write less but make it more powerful. One powerful element of communications is to be concise and to the point. Say what you have to say once, and end your message quickly—in 10 min or less.
The first few words you speak form a positive or negative image in the minds of those in the audience. Your closing must also resonate with your audience. It determines whether you get what you asked for. Everything between your opening remarks and closing statements must be one powerful attention-getter after another, each in less than 30 s.
#### Capturing the Attention Span of Your Audience Helps Win the War
Attention span and attention-getting bullet points go hand in hand. At the onset—even before you start developing the content, sequence, and organization of your message—you must recognize that the attention span of an average individual is only about 30 s. That's how long people will pay attention to what you have to say without drifting off to think about what they are going to do after the meeting, where they plan to go tonight, or what they plan to wear tomorrow. The movie and TV industries and the media all have mastered the 30-s rule; you know it as the 30-s commercial, which attracts interest, keeps attention, and sells millions of product lines. With practice, you can sell your idea to executive management in 30 s or less.
## Build a Solid Business Case
Most colleagues agree that less is more. So do I. Always be brief, clear, and to the point. This is worth repeating. Talk less but make it more important; write less but make it more powerful. Keep your presentation to 10 min. Here is a six-point approach that can help you deliver your message:
• Report the facts.
• Set a course for the future.
• Identify business impact.
• Introduce pathways to achieving your goal.
• Pick a preferred path.
• Close out.
### Point 1: Report the Facts
Describe the nature of your business, problem, or situation in 30 s or less.
• Be careful not to under- or over report. Both can have harmful affects.
• Introduce a clear objective that captures the interest of your audience.
• Know your topic and present it as concisely and memorably as possible.
• Present bullet points that include only top-level information.
• Stay on track toward achieving your objective.
• Present important data and facts, but always recognize that they are debatable.
• Tell a story or personal experience that will keep the audience on the edge of their seats.
• Personalize your story so it has meaning to your listeners.
Put to work strategic tools such as meaningful graphics to express your ideas clearly and memorably in 30 s or less.
• Use risk-based metrics in a clear and concise manner that energizes the CEO.
• Create a simple dashboard slide that attracts the attention of management.1
• Risk charts (but not too many) resonate with senior management.
• Simple graphics and powerful words make your message memorable.
• Use clear, simple language that your listener will understand.
• Show the probability and severity of potential events.
• Allow executive management to make the decision you want them to make.
### Point 2: Set a Course for the Future
Tell executive management what you want and where you want to go in 30 s or less.
• Offer unvarnished and candid advice. Keep executives firmly grounded.
• Be straightforward about risk and uncertainties. Be reasonably free of bias or manipulation that can distort the facts you report.
• CEOs do not like to be given ultimatums. Too many security professionals unknowingly do this. Be alert to this pitfall and stay clear of it. Offer a limited range of constructive options in a preferred sequence that the CEO can act on.
### Point 3: Introduce a Pathway to Achieving Your Goal
Always credit management with knowing more than you do, even if you think they do not. Believe me when I say they need to know far less than you think they do to make a decision. Keeping your message free of confusing details helps management better understand your objective. And, because management knows there are many ways to achieve a goal or objective, they expect a short, concise menu of decision options to consider. The goal is to have several ideas to choose from rather than being stuck on one option.
• Always propose three options—one of which is to do nothing.
• Introduce the do nothing option first and highlight its business impact in 30 s or less. Doing nothing is a provocative strategy and often the most appealing for many executives because it gives them time to reflect by postponing a decision. To be noticed, mention doing nothing first—before the boss, other executives, or lawyers mention it.
• Present the remaining two options (in order of preference) and why they are acceptable in 30 s or less. To keep your image, brand, and reputation, as well as your trustworthiness and creditability, intact, never present an idea that you cannot do or do not want to carry out. Setting these priorities establishes a sense of urgency for the CEO. Do not distract him or her from focusing on your priorities.
### Point 4: Pick Your Path
Suggest the option you believe to be the best and state its benefits in 30 s or less.
### Point 5: Identify Business Impact
Put yourself in the boss's shoes and explain how your idea may threaten the company, why it matters, and available opportunities to strengthen business operations. Do all this in 30 s or less. Identify positive and negative consequences that could arise, including collateral damage related to your choice, if applicable, and why mitigation actions reduce risk while improving and enhancing security resilience—and do this in 30 s or less. Shy away from such conclusions as speculative fear, the "only solution syndrome," and an easy "cookie-cutter solution" in your presentation. They never work.
A good CEO has the ability to accept, absorb, and apply the advice you are giving. To ensure you do your part in helping the boss be a better decision maker, allow your presentation to enable him or her to do just that.
### Point 6: Close Out
When you tell the CEO what you want and why, that is your cue to get off the stage.
• Conclude your briefing by summarizing your risk mitigation strategy in 30 s or less.
• Provide a cost estimate summary and a milestone schedule showing major activity in 30 s or less.
• Anticipate issues that your listeners might raise and answer any questions in 30 s or less. Offer positive answers on the spot or promise to give an answer as soon as possible after the meeting.2
Be prepared to answer constructive as well as confrontational questions. Managerially relevant questions foster productive discussion and the exploration of ideas. These questions and your answers to them give the boss a more critically essential understanding. Confrontational questions presented by the staff may be perceived to demean, malign, or murder your ideas and advice. Those in the room, particularly the CEO, always remember this type of questioning and who in particular among the staff is pursuing this type of questioning. For whatever reason, these staffers persist and resurface at the worst possible times. Answer these questions with the same objectivity and professionalism you used when answering relevant management questions.
At the end of the question-and-answer period, thank everyone for their interest and the time taken away from their busy day. Now you can really relax—you're done, until the next time. Wait to be excused or for the CEO to adjourn the meeting.
## Know When to Pull Your Parachute Cord
Even the best of professional athletes do not win every time, but they always return to try to win the next game. Even with all the hard work and diligence you put into your proposal, be prepared for the possibility of your idea being rejected by the senior staff and disapproved by the boss. Some reasons for this decision may stem from:
• the idea not being part of management's strategic interest or focus. You should have known this before hand, in which case you should have never given the briefing.
• the idea being developed without input from the boss or someone the boss trusts, not being staffed properly or sufficiently coordinated with all divisions, or usurping the legitimate territory of others. Rework the presentation, do your homework, and return to the table later.
• management not supporting or participating in the effort. Timing is off, resources and funding are not available, or the message was not convincing enough. Come back again better prepared.
• the idea falling short of adequately addressing the business side of the enterprise. Go back to the drawing board and come back later.
• the idea being too advanced for the time and not really understood by the staff. More research is needed before introducing the idea again in the future.
Disappointments such as these happen often, and you must be able to recover from such defeat. In the case histories mentioned above, your trust and confidence may have been tarnished; people may question your management and leadership skills, or perhaps your ability to work hand in hand with the staff on critical issues needs to be refined. Regardless of the reason for failing, pick yourself up, dust yourself off, heal any wounds with the staff that may exist, and discuss the shortfalls of the presentation with your number 2 and your security staff. Listen to what they have to say and heed their advice. Have them review the contents of the briefing, handouts, and notes. Ask your number 2 to comment on your approach and demeanor. Ask the staff for candid advice on what you could have done better. Learn from your mistakes and move on.
## Present Program Results Regularly
Present selected metrics monthly, quarterly, semiannually, or annually to various audiences and at different intervals. Tailor the content of each briefing to fit the particular audience and their area (s) of interest.
Keep in mind that data age over time and can become historical and less actionable, and thus potentially less valuable. For example, some threats and hazards are seasonal or even situational. You can blend in the appropriate topic at selected briefing intervals if the information is relevant and current. Distinguishing metrics that are time-sensitive from those that provide value over time enhances the overall value of your recurring presentation. Here are some tips for tailoring your briefings to specific audiences:
• C-suite executives, the senior management staff, boards, and community governing bodies are interested in only top-level metrics about significant corporate-wide problems affecting image, brand, and reputation; security performance strengths and weaknesses; threats, vulnerabilities, and anticipated improvements; costs to facilitate executive decision making; investments; and profit margin.
• Maintenance and operations staffs focus on the detailed aspects of their particular areas of expertise and responsibility. They want to know how good or bad things are, and what it takes to improve their areas of responsibility or to fix mechanical problems as soon as possible.
• Regulators, consultants, inspectors, and auditors are interested in the root causes of ineffectiveness, inefficiency, and lack of productivity within the scope of their review charter. They look to correcting management, leadership, ad logistics issues that affect compliance performance and productivity.
Multilevel tailored metrics—each geared toward the particular audience—best serve the interest of the security organization as well as the corporation. You can layer slides and metrics to organize your thoughts, establish relationships, and set priorities for each audience you address.
## Conclusions
### Work Hard to Establish and Maintain Trust and Respect
If you can put yourself in the boss's shoes and look at things from a business perspective; talk the language management understands, cares about, and can act on; think and make recommendations using management's process approaches; and then apply what you know, you will be respected and have influence with the CEO and other executives.
### Collaborate to Narrow the Communication Gap
Staff functions exist and are funded by executives to address challenges and to help executives do their jobs. But this desire to fix things can become a difficult task if the right team is not in place. When executive management, the staff, or security leadership creates circumstances, conditions, and behavior patterns that lead to problem situations, the complexity of problem solving can create greater challenges and sometimes tough working relationships between executive management and the security organization.
In earlier chapters, I mentioned that the greatest majority of security problems stem from:
• inappropriate, weak, or poor security measures
• inadequate security policies, processes, and practices
• poor security awareness and ineffective security training programs
• human fallacies and technology deficiencies and breakdowns
• barriers and obstacles that contribute to ineffective and inefficient security performance
• weak or poor management and leadership practices, and poor decision-making
These issues deserve executive management's attention, or they will never be resolved. It is crucial that the communication gap between the CEO and the security organization be closed. The effort calls for trust, confidence, maturity, professionalism, strong working relationships and leadership, and a strategic vision that focuses on the best interests of the corporation. There is no doubt that such a drastic change in a single organization can create chaos and bring about resistance and turf maneuvering, but these challenges must be met and hurdles overcome. A corporation that embraces the concept of total quality management and team building (Schmidt and Finnigan, 1994, pp. 10–29) can overcome many of the barriers and obstacles that exist.
Last, the security profession has been partially successful at recognizing systemic security deficiencies, weaknesses, and inadequacies, but less successful in acknowledging, identifying, and addressing the root causes of these systemic problems. Properly designed risk-based metrics offer a focused analysis of why conditions repeatedly arise and of opportunities to explore strategies to address root causes. One of the greatest challenges CEOs face is the commitment to acknowledge the route causes of such problems and to fix them quickly.
### Focus on the Ultimate Outcome
Achieving success and obtaining goals only happens in the future, never in the past. Stay focused on the future and what you know you can accomplish based on where you have to go.
### Making a Business Case
In 30 s you can deliver a powerful and memorable message. In 30 s you can communicate effectively, persuasively, and concisely, and you can capture your audience's attention, keep its interest, tell a wonderful story, and ask for (and get) what you want. The right message enables you to get your point across and keep it where it belongs: in the mind of your listeners. If you wish to keep the interest and attention of your audience, say something important every 30 s. I suggest you do it in 10 min or less.
### How Will You Know if You Are Successful?
The best way to get a CEO to accept your ideas is to offer advice that is simple, sensible, positive, and practical. Use your competency to become an important and influential resource to your CEO 24/7. Work to make this relationship effective. You will know you have succeeded when:
• people continue to tell your stories
• you are quoted in other meetings and seminars, or even when you are in the room
• meetings are held up until you arrive
• the boss and others routinely suggest that ideas, concepts, plans, and policies be run by you early in and at the end of the process
• others have respect for you and hold you and your ideas in high regard
• leaders tell you and others how you've helped them, and your insights become evident in their decisions, actions, beliefs, and strategies
Success does not require you to have a seat at the executive table, only an invitation to visit the corner office and the boardroom when needed. To get there you have to be sought out by the boss or someone the boss totally trusts. If you offer value, and if the boss knows of that value and has respect for your critical thinking, you will be noticed. Once accepted, you will be expected to contribute something positive, useful, and of value, from the boss's perspective.
### Much Work Remains to Improve Communication with Executives
During the past decade, the security profession has made great advances in connecting with chief executives. As the importance of security and the significance of diversified threats expand, so must your ability to communicate effectively with executive management. One of the greatest challenges you will face is not how to reduce risk, but how to convey the benefits of risk reduction in language executive leaders understand and care about. Much work remains to improve communication skills in this regard.
* * *
1 dashboard containing multiple charts and graphs may be useful internally within the security organization for briefing other groups but for presentation to senior management, a single graphic with powerful data on one side of one sheet of paper can be worth at least a notebook full of words and tabs.
2 If formal minutes of the meeting are taken, it is an acceptable protocol to provide a memo to the secretary of the meeting answering or clarifying any issues that were brought out during the question and answer discussion. Typically, the contents of the memo can be inserted into the minutes or added to the minutes as an addendum. The contents of such a memo explaining or answering a particular question can then be reviews by all present when the minutes are distributed. Objectives can be immediately responded to. In some instances the topic may even be brought up again for discussion at the next regular meeting. Most CEOs, however, prefer the parties to get together before the minutes are final and the next meeting is scheduled.
17
# A Brighter Tomorrow
## My Thoughts
## Abstract
This chapter speaks to the importance of effectively assigning and delegating appropriate security authority, responsibility, and accountability across the entire corporate structure. It highlights the criticality of keeping executive management advised of security operations, programs, and capabilities, including emergency response planning, and the need for executive management to be approachable and sensitive to security needs. The importance of establishing and maintaining strong security leadership throughout the entire corporation, and gaining the full support and confidence of C-suite executives in the security decision-making process, are also emphasized. Only with a better understanding of the root causes of vulnerability creep-in; the background/history associated with safeguarding against threats, vulnerabilities, and consequences of loss; and a thorough definition of how effective the recommended strategies can be will the reader have a real appreciation for the information presented in this chapter and book. Actual case histories provide a perspective of general industry capabilities.
### Keywords
Accountability; Authority; Change management; Ethics; Future leaders; Human fallacies; Integrity; Leadership; Management; Responsibility; Security emergency planning; Training; What works?
Where trust is high, and ideas flow freely, much work can be accomplished. Finger pointing on the other hand stifles creativity and is a leadership fallacy best left at the doorstep.
John Sullivant
Top Takeways
• embrace a brighter tomorrow
• apply strategic visionary thoughts
• preserve the corporate image, brand, and reputation
• strategic planning is everything
• leadership traits for the next generation
## Overview
The deficiencies, weaknesses, and inadequacies unveiled throughout the pages of this book have been reoccurring for a very, very long time. I and many of my colleagues have been witnessing and reporting on these conditions for over five decades. With hindsight, my view is that this phenomenon has always existed but has seldom been noticed because previous evaluation practices have focused on security hardware and software performance. Only within the last two decades have consultants been asked to investigate the "human side" of the enterprise and report the status of adequacy of training and policies, social behaviors, work habits, attitudes, interrelationships, or the mind-set and security knowledge-base of both executive and security management.
It is time to plan for the future by reflecting on the past and the present and to recognize our successes and failures, accounting for the areas we must grow in: better communications with C-suite executives, better synergy with the senior staff, forward-looking leadership skills, and the development of advanced competencies for the emerging generation of security leaders.
## A Perspective for the Future
The mere existence of conditions, circumstances, and situations that help to create a vacuum for potential deficiencies, weaknesses, and inadequacies is unacceptable and certainly should not to be condoned by any responsible leader. This is a pervasive problem, and I believe its mere presence needs to be eradicated by both executive and security management wherever it crops up.
But changing a cultural mind-set can be a bit more complicated than changing engrained policies and behavioral patterns. This calls for an enlightening experience in new concepts, ideas, approaches, and technologies, followed by a continuing internship in planning, coordinating, developing, and executing first-class security operations and programs. No doubt this is work in progress, and all of us have a tremendous amount of hard work ahead of us.
As early as chapter Introduction, I was unflinching in stating that some decision makers—security professionals among them—do not fully understand or grasp the essential principles of security or the criticality of their interconnectivity. Many have difficulty recognizing the holistic benefits of embracing security programs and system integration means and techniques, including the importance of the criticality to deter, delay, prevent, protect, detect, assess, respond to, and recover from security events in a timely manner. I make no apology for these eyewitness accounts and my subsequent analysis of my observations. My only regret is not being able to share with you all my findings, timing and expense to address all the issues being prohibited. My representative introduction of five decades of experience is sufficient to grasp the tapestry of my work.
I am not yet suggesting the security industry is doomed, only that it is approaching a pivotal point in our history that will soon challenge us to renew our business relationships and practices, and embrace new technologies that are shifting from proprietary databases and hardware to open wireless architecture with published specifications and new management and leadership characteristics yet to be developed or recognized. It is time for a major change in our thinking of uncertainty and unwillingness, and in our priorities to push for professional and technical development to meet a brighter tomorrow.
And let us not lose sight of the opportunities that executives have and the challenges inherent in today's business and threat environments by exercising the necessary leadership to prevent the usual delays and bottlenecks associated with building security resilience. Understanding the magnitude of this crisis is both urgent and important.
The time has come to reflect on the past and the present and look to the future. It is time to account for your successes and failures, and that in turn focuses your energy on those areas in which you can nurture and grow. An easy first step is to share this book with your boss and chief executive and have a real dialogue about the tough security issues executives have been hesitant to talk about. Perhaps it may be time to ask your chief executive the toughest question of your career: How can I help you be a better security decision maker? A second easy step is to share the contents of this book with your staff and members of your security organization. The next step is somewhat harder - its getting a concensus from your peers and others that the theme of this book has value and is on target, and mobilizing resources to make behavioral changes suitable to your enterprise in general and in particular to your organization, and the security industry, to deliver a better tomorrow. Some tips that will help make a better tomorrow are the focus of this closing chapter.
## The Evolving Business and Threat Landscape
### Business Environment
Until corporate culture changes, security organizations will continue to face difficulties in trying to carry out programs that have undefined parameters and standards of performance, as well as measurement and evaluation criteria that are not meaningful or useful to executives. Having a clear understanding of how to relate security goals and objectives to business goals and objectives remains a significant challenge for most security organizations. Many have an inclination that things are not what they should be, but have no idea where or how to start addressing potential problems. Such organizations could benefit greatly from the knowledge and expertise of an independent security consultant. A clear understanding and use of the basic principles of a security risk management framework and its measurement and evaluation platform are essential to program success. Get aboard and embrace these principles as part of your daily routine.
### Threat Environment
New threats are escalating in probability, breadth, and severity. By recognizing these emerging patterns, you will be able to develop preparedness measures in the early stages of security planning. But identifying and understanding new threat conditions is only half the equation. Prioritizing threats, vulnerabilities, and assets; developing mitigation strategies and solutions; formulating action plans; and monitoring the effectiveness of approved actions are the second part of the equation that requires strategic thinking and steadfast determination.
Many companies believe they know what their security problems are and have the solutions ready to be implemented. But experience has proven that such conclusions are mostly based on incomplete and inadequate information, and sometimes speculation leading to poor decision making and often to a false sense of security. Many of these same companies and others are not fully aware of, nor do they understand the significance of, the threat landscape. This is because most companies see little value in developing a threat profile to use to identify and prioritize threats, vulnerabilities, and the protection of assets. My work has shown that threat analysis is a useful tool in establishing priorities, but none of the strategies I reviewed over the years seemed to be preceded or guided by such threat analyses. This is a void of great consequence and we must have the fortitude to change the mind-set of executives who resist meaningful and useful intelligence that would help them make the right security choices in saving lives, protecting property, and sustaining company brand, image and reputation.
Corporate governance also has enormous concerns about protecting intellectual property, yet it does little to safeguard its information, processes, and secrets, or punish employees who violate protocols and norms and ignore security practices. At the 25th Annual Global Fraud Conference, Held in San Antonio, Texas, in June 2014, keynote speaker and former FBI Director Louis Freeh urged 3,000 people in attendance to use tougher security measures to protect their intellectual property. During his presentation he emphasized financial. Institutions in particular are more vulnerable and are hacked more often than any other business sector. Financial institutions soon may be required to beef up their internal protection of intellectual property1 through the application of new federal regulations. Other regulated industries such as utilities, energy, telecommunications, transportation, and public health will soon face new security standards as well.
With the constant threat of disasters, both natural and manmade, security professionals must be proactive, incorporating plans as a fundamental part of any security operation. Preparedness begins with understanding the business's goals and objectives, followed by knowing corporate commitments, obligations, regulatory requirements, management knowledge base, and the corporate culture.
The ability to keep up with evolving threats, coupled with the operational and performance demands imposed on security organizations and the rapid pace of regulatory changes, is a major challenge for many security directors. The increasing number of security concerns has forced many organizations to place company survivability and security resilience on par with each other, including placement on the agendas of corporate chief executive officers (CEOs) and their boards.
## Corporate Image, Brand, and Reputation Hang in the Balance
Companies spend billions of dollars investing in their corporate image through trade, brand name identification, and image to establish and maintain their reputation at almost any cost. The value of this ongoing campaign possibly represents a corporation's largest inventory (Broder, 2006, pp. 233). It is no wonder good corporate leadership does not look kindly upon any business unit—particularly safety, security, and compliance groups—that place its image, brand, or reputation in jeopardy. Moreover, an organizational culture that applauds innovation and flexibility rather than suppressing it, gives security directors and other managers the freedom to take risks, and praises people for recognizing and owning problems, rather than chastising them for reporting problems, is the leader of the pack.
### The Challenge of Exposing Vulnerability Creep-in
Vulnerability creep-in is a malignant product that has to stop being used as an excuse for not moving forward. It has to be cleaned up, swept away, and never allowed to return. An independent objective security assessment or audit can determine the range of security enhancements that may be used to remove or minimize the root causes of ineffectiveness and inefficiency created by vulnerability creep-in. This examination process breaks down each site, facility, system, and function into the smallest segments possible to make the investigative process manageable. The profile proceeds to identify weaknesses in the corporation's ability and capability to deter, prevent, protect, detect, delay, assess, respond to, and recover from specified threat conditions.
### Security's Weakest Link: Human Fallacies
It is common knowledge across the security industry that human weakness, not processes, protocols, practices, or technology, put organizations most at risk. Apparently, however, this is not common knowledge throughout the executive management sphere of influence. Or, perhaps they know but fail to acknowledge it.
A recent survey2 by Secure World in June 2014 found that 56% of workers have not received any security awareness training. Another study3 found 95% of the breaches traceable to human error. Despite this fact, security awareness training is still ignored by many organizations. If there is a common thread that all security experts agree on, it's that poor training and unaware employees lie at the root of most of all, cyber security breaches.
In the past, disgruntled staff lacked the tools to easily steal secrets or cause serious harm. Now, virus toolkits are available to provide inside attackers with a cheap and easy way to cost companies millions of dollars and ruin organizations' reputations. What, then, can be done to protect corporate interests?
• Have a systematic approach to monitoring employees' access to the computer network and, in particular, what they are downloading.
• Monitor people who ignore or bypass procedures to ensure that they are not acting illegally.
• Deny computer access when a person goes on vacation or is notified of his or her termination.
• Ensure that the person being let go does not exit with sensitive documents or have access to computer systems.
• Provide sufficient budgets for cyber security countermeasures designed to protect systems from attacks initiated from inside or outside the company.
The first (and best) line of defense is employee and management awareness. The more people understand and care about how their behavior affects the company's security posture, the better off the company and employees will be.
### Cyber Incident Response Capabilities
Overall, organizations are not ready to handle their mandated incident response requirements. Having a plan in place to address incidents enables organizations to counter issues and breaches when they do arise. But only 43% of all U.S. companies have formalized incident response plans, while 53% do not have formal incident response teams.4 Both of these situations lead to a disjointed approach to managing and remediating incidents, resulting in delayed or incorrect responses.
10% of U.S. companies have effective incident response capabilities. Only 26% of the companies report dissatisfaction with their incident response capabilities, citing lack of time and resources to review and practice procedures (62%) and lack of budget (60%) as key impediments to effective response.5
### Cyber Security Threat Gains Executive Management's Attention
The increasing frequency, sophistication, and business impact of many cyber attacks have pushed cyber security planning and protection from an operational concern of corporate security and information technology (IT) departments to the agenda of boards and CEOs at many organizations across America.6
Senior executives face an information gap that makes it difficult for them to align investments in risk protection with the true strategic value of an organization's digital assets. Every organization that has suffered a recent security breach also has already had some form of cyber security in place. Beyond that, too many organizations fail to align IT security capabilities with larger corporate security goals and overall risk appetite.
## Measuring and Evaluating Performance and Productivity
Most security programs lack risk-based metrics to measure and evaluate their effectiveness.
### Prioritizing
One of the biggest challenges organizations have is prioritizing, understanding, and addressing vulnerabilities in a business context, including placing a monetary value on the worth of an asset, as well as on the loss of the asset if it is damaged or destroyed. Some CEOs, staff, and employees, and even some security organizations, underestimate the threat and do not understand the implications or consequences of losing critical infrastructure and assets. A major goal for a security director must be to clearly communicate security dangers and mitigate risk exposure in language that is meaningful to executives but without making "fearful" statements that may lead to workforce panic or unrest.
My past work in reviewing various strategies and mitigation solutions has revealed the importance of identifying and prioritizing issues that require immediate attention. While many organizations have developed strategies that identify some top priorities, an equal number of strategies contain more priorities of seemingly equal importance that cannot be realistically achieved. The development of a threat estimate profile is the vehicle to use to accomplish this priority goal.
### Protocols and Practices
Security policies have their place, but they are of little value if they fall short on results and employees do not understand the rational behind the rules. Many employees fail to adhere to security policies because of a lack of understanding and poor communications from their security department, or they do not always follow their company's security policies.7
Many security contracts and agreements are written poorly. Most contract guard forces lack tactical response and search-and-rescue expertise, as well as adequate training to meet the demands of the security mission. In many instances I have observed "response" to be the purview of local law enforcement, while site contract guards stand by and watch, contributing nothing to the response—not even checking the area to make sure it is secure.
Many security protocols are poorly written and have been successfully challenged under litigation. Protocols must be crafted to pass the test of legal review and must be clear, distinct, and brief. But brevity does not equate to losing site of a publications' meaning and purpose for the sake of reducing the page count. Protocols must outline authority, responsibility, and accountability for implementation and identify the fundamental aspects of a process.
## Security Design Performance and Program Integration
Understanding the security design process is critical for every stakeholder responsible for security resilience. Before you begin talking about security solutions, you have to understand the process and key players involved. Security experts will define the steps in a proven process: from establishing the need for security, through asset and risk assessment, to the development of functional requirements and mitigation solutions.
Years ago, little (if any) thought was given to building security into the design of a facility. The experts of those days considered such an idea unnecessary because if security were needed in the future they would simply add it. Then came along some bright developers and enlightened owners and entrepreneurs who recognized that building security into the facility design process was more cost-effective than adding it onto a project as an afterthought (Broder, 2006, pp. 252).
As a consultant to the US. Army Corps of Engineers in the early 1980s, my team introduced this engineering concept to the Department of Defense. It eventually became Department of Defense policy for all new military construction projects, and over the years it has saved U.S. taxpayers billions of dollars in design, engineering, and construction costs (Sullivant, 2007, pp. 57–61).
The moral of this story is that the security director—not engineers, designers, accounts, or even CEOs—set the ultimate criteria for security design quality and security system performance. There is no room in this business for an engineer, designer, or some other individual to exhibit a "take it or leave it" attitude. This person is not helping you solve your security problem: he is the security problem, and a major contributor to vulnerability creep-in. Stay clear of accepting or signing off on a security design that falls short of specification expectations under the guise that it will be modified and upgraded later. This seldom happens, if ever. This rationale, often presented to you by the design and engineering group and supported by the accountant, is typical of how vulnerability creep-in sets in.
### System Reliability, Dependability, and Availability
In today's business world, corporations that have management information systems, control systems, security systems, and other systems that are unavailable and people who are unproductive for hours, days, or longer can be disastrous. Companies cannot afford to be without the technology and information necessary to conduct their business affairs. It is not just manmade threats, such as criminal activity and acts of terrorism, or weather-related calamities and industrial accidents that have upper management's interest. It is common events such as system failures, equipment malfunctions, and lack of system protection features. Redundancy and backup systems can increase system reliability and dependability. Newer self-healing systems can also increase system survivability parameters.
### Technology and Other Protective Measures Avoid Paying in the Courtroom
Violent incidents continue to occur at businesses where cameras and other security technologies are used but not functioning and where there are no logs, incident reports, or security personnel records. It is not a coincidence that criminals select these soft targets and repeatedly target these businesses and prey on their customers and employees. Businesses that ignore security system maintenance and fail to keep performance standards end up paying for such negligent security management. Businesses with cost-effective security programs and the use of state-of-the-art proactive measures to minimize exposure have successfully defended themselves in liability litigation alleging security inadequacies.
### Integrating Physical and IT Security, Business Continuity, Crisis Management, and Emergency Planning
During the past decade, much discussion and some action have taken place to converge physical security and IT security. What has been overlooked and is now gaining attention from senior management is the convergence of crisis management, business continuity, emergency planning, and organizational (and security) resilience. The integration of these separate but related disciplines is crucial to the synergy of emergency response and business recovery. Eliminating the duplication of effort, reducing ineffective use of resources, and narrowing the gap of inefficiency and productivity are key benefits to placing these activities under a single leadership umbrella—preferably that of the corporate security director.
## Training Programs Need a Major Uplift
People are the weak link in any organization. Because people are a major capital investment and the most important asset of any corporation or agency, it would greatly benefit management to properly train employees to become more proficient and productive. Realistic training increases the motivation of the workforce. It provides for greater unity among the workforce and frees supervisors to provide quality oversight of their teams' performance. For all these reasons and many more, training programs—particularly security awareness training—need to mature as the evolving threat becomes more intense and complex and consumes more resources and funding not readily available.
In Chapter Building Competencies That Count: A Training Model, I mentioned typical security awareness programs in the public and private sectors are weak, half-hearted, and ineffective. In most cases, new employees receive some security awareness training when they join a company, but typically that training is not reinforced on a regular basis. As a result, employees ignore and even undermine security programs. Even excellent security awareness programs associated with highly sensitive and compartmentalized information do not seem to deter those who have crossed the line to do others and their country harm. The Snowden's and Manning's of this country are examples.
While billions of dollars each year are spent on security hardware and software, most data breaches and information losses are based on the weak link in the security chain: people. Yet very little time and money are spent giving effective security awareness training to employees whose primary responsibility is to protect information. People can either make or break information and cyber security programs—and the entire corporation. Employees are the weakest link in the security chain because they are vulnerable, vindictive, often misguided, and greedy. Only a few are adequately trained to be security-conscious. Most people receive little or no training that would help prevent many of the losses companies sustain.
Too many enterprises plan and develop training programs from a tabula rasa instead of using experience, history, and common sense as a starting point. This is the reason so many security awareness and security orientation training programs, although designed with the best of intensions, fall flat on their proverbial faces. All to often the result is a complete "epic fail" because course designers and course-approving officials forget, ignore, or simply do not know what most security experts know does not work. Because of the emerging threats that we face today, the design and content of security awareness and security orientation programs should be tailored to help attendees perform their jobs today and for the near future.
## Security Emergency Plans and Response/Recovery Procedures
Of all the deficiencies noted, poor security emergency planning and lack of organizational readiness capability and ability are rampant throughout most of the industry, but some enterprises, such as nuclear power plants and chemical facilities, have excellent programs that meet or exceed regulatory performance expectations.
## Communicating with Executives and Governing Bodies
### Accepting Responsibility
A new trend is emerging: security is no longer a cause of embarrassment. It is a matter of management accountability. The CEO has always been responsible for the overall growth, safety, and security of his or her corporation. But the dynamics of the diversified threat, and in particular the cyber threat, now make security a fundamental bottom-line issue that can no longer be ignored or swept under the rug by executives. There is no argument that the cost of investing in adequate security is significantly lower than the cost of responding to and recovering from a major security event, disaster, or major cyber breach.
### Communicating and Interacting with Executives and Governing Authorities
Many security directors and IT security professionals continue to struggle with expressing their ideas to executive management and the board. The greatest challenge they face is not how to reduce risks but how to convey to leadership the benefits of security risk management. Their situation gets even tougher when they are in a state of continuous conflict between the business wanting to drive innovation and the security team needing to rein in risk. Executive decision makers want to know the business is adequately protected against risk but need to weigh the risks of yesterday and today against the opportunities of tomorrow.
Join the many security directors who have taken the lead and are driving the security dialogue with the CEO and the board, changing the conversation so that security and risk can be considered alongside other risks that boards oversee. Security strategy and security risk can now fit comfortably with other strategies and risks the board addresses.
### Reporting the State of Security Readiness
It is a god idea to report the "state of security readiness" to CEOs, their staff, boards, and other governing bodies or community groups on a regular basis. I recommend using this schedule as a guide:
• CEOs and senior staff: monthly or quarterly
• Boards: semi-annually, annually, or as circumstances and conditions warrant
• External governing bodies or community groups: annually or as deemed necessary
Such presentations may be beneficial whenever special circumstances arise, such as an increase in the threat condition by the local government, after there occurs a major security event or incident that could dangerously affect public health and safety, or whenever business goals, objectives, or operations significantly affect existing security capabilities and abilities to support corporate initiatives.
## Security Leadership Needs a Touch Up
### Executive Management in the Shadows
Too many chief executives are on the dark side of the planet when it comes to protecting resources, assets, facilities, functions, and processes. Ignoring a problem with the hope that a security event or incident may never occur is wrong (Broder, 2006, pp. 250). It is making a life and death decision that no CEO has the legal or moral authority to assume. Everyone makes mistakes. The issue is not necessarily that mistakes happen, but rather why they happen, how we plan for them happening, and, when they do occur, how we recover from their impact. Once a strategy is put into motion, CEOs need to know whether the strategy is doing what it is supposed to do. If not, immediate midcourse corrective action must be introduced to address the discovered issues. A quality performance measurement and evaluation program that focuses on continual improvement would allow the organization to keep up with business changes, new security practices, and technology advancements.
### Security Management Is Holding on
The future of security management is shifting away from individual facility security toward enterprise security management. This involves the integration of environmental controls, information systems, and security systems to operate more efficiently and, in some environments, merge into a new technology platform. Once developed and fielded, these capabilities can translate into effective, efficient, and productive gains.
A wise and experienced security director can demonstrate how security, when properly planned, coordinated, developed, and executed, and with proper oversight, can hold down costs across the broad and show a reasonable return on investment. Effective security and safety practices also foster leadership accountability.
### Slippage of Leadership, Foresight, and Execution of Responsibilities
The security professional has more challenges to face than he or she may be capable of handling. This means that the consequences of failure can be more devastating than ever before, particularly when dealing with the establishment if it consumes a large portion of your time on a reoccurring basis. Security professionals are great at identifying deficiencies, weaknesses, and inadequacies and fixing the symptoms. What they struggle with is recognizing and addressing the root causes behind recurring activity. The security director's job, then, is to keep substance from forming into a basis for a crisis and, if such a crisis should occur, to contain its effects. This puts the security director in a very difficult position if the basis for a crisis turns out to be the workings of executive management (Tarlow, 2002, pp. 58). However, professionalism demands that you always be prepared for such an exchange of the highest order (Sullivant, 2007, pp. (56–109).
### Management Is Losing Ground on Oversight Responsibility
When an organization identifies a weakness in security, it is standard industry practice (when mandated by regulators) for management to record the problem, find a way to fix it, and assign a deadline for completion. As management makes progress and the weakness is eventually remedied, corporate records are then updated. Organizations then provide progress reports to the governing bodies that are responsible for overseeing security matters. Without this basic evaluation system in place, it is impossible for the organization to tell whether problem areas or compliance matters are being addressed.
While such a corrective action program does not exist for unregulated industries, many corporations have adapted this approach. It makes good business sense to adopt a comprehensive performance measurement and evaluation program. Yet just about every aspect of this essential measurement and evaluation process is either missing or had broken down at several organizations I visited: problems were identified but never fixed, fixes were scheduled but not completed, and fixes were recorded as complete when they were not. These breakdowns were reported during previous visits, yet monitoring the progress of corrective efforts relative to known weaknesses was not effective, and nothing had changed to bring most of the organizations around to good business practices. An accurate measure of security program effectiveness will never be achieved at these locations unless the corporate culture changes its management practices.
The challenge CEOs face is to commit to obtaining the body of knowledge, skill sets, and expertise to save lives and protect assets from those who wish to do them harm, as well as from environmental hazards and weather-related calamities, and to translate these into profound outcomes that create unparalleled opportunities to deal effectively with ambiguous security challenges. CEOs must view the safety and security of their people as a nonnegotiable requirement. CEOs must also assert genuine leadership, communicate to employees what needs to be done, and make pragmatic policy decisions to empower employees to make responsible decisions, take appropriate action, and be accountable for their behavior. This requires courage, shared sacrifice, and a willingness to compromise and make the tough choices essential to setting a new course for the organization.
### Management is Either Ignoring Issues, Covering Them Up, or Has No Clue What's Going on
Another disturbing issue deals with the perception some CEOs have about security performance. Some executives see their organization's security program as far more mature than do those at the managerial level and below. Experience tells us that these perception gaps stem from poor communication and collaboration among the different roles involved in planning, developing, and implementing security operations. Weak or no performance measurement and program evaluation criteria, and a combination of incomplete or inadequate reporting, add to the dilemma.
The challenge for CEOs is to assert genuine leadership in cultivating communications among the senior staff, the security organization, and employees, with the goal of raising awareness about the importance of listening to reasonable and prudent arguments for accepting cost-effective strategies. Equally important is the crucial need to establish and maintain a solid business relationship between the security director and CEO that fosters candid decision, mutual respect, and trust in enterprise security matters. CEOs must have candid and factual information if they are expected to make sound security policy decisions.
### Management Social Behavior and Ethics Need Polishing
An equally important challenge to building security resilience is removing sheer arrogance, complacency, indifference, apathy, ignorance, and fear, followed by fallible decision making, near-reckless planning, and negligent management. We also face another challenge: management putting its head in the sand over many issues that should receive their attention and failing to act in a responsible manner. Also, let us not forget that management's ignorance or failure to act in a reasonable and prudent manner often is responsible for liability injuries caused by third-party crime. A wise leader will do everything within his or her power to prevent such an embarrassment to the company's image, brand, and reputation, yet litigation cases are on the rise across the nation. If allowed to flourish, these factors can directly and indirectly contribute to the weakening of security resilience in many ways. Work conditions can affect your well-being and livelihood. Circumstances can influence your status and judgments, and situations often temper your objectivity.
The challenges for CEOs, then, are to:
• establish and maintain a proactive security mentality
• identify and remove obstacles that stifle and impair modernizing the security program
• continue individual and group development to build self-confidence
• research and explore new possibilities to bring home new ideas
• seek outside consultation and strategic advice from qualified independent consultants
• expand their knowledge base through lessons learned reporting
• meet with security management and review the "state of security" on a regular basis
Through your influential leadership, you must make CEOs recognize the benefits of a corporate commitment to advancing security in the throngs of a rapidly and dynamically changing business world, advancing technology, and a shifting threat environment. You must be the pillar that stands between management and the wholesale scuttling of the integrity of security.
## Change Management in the Wind
CEOs, staff members, employees, and the security organization must be on the same team and work together to achieve common business and security goals and objectives. When this relationship breaks down, governing boards may impel corporations to call for new leadership.
### Corporate Boards Are Pressuring C-Suite Executives to Demonstrate Leadership
Chief executives who hinder the buildup of security resilience will either take the initiative to improve their company's security program or can expect shareholders to demand their removal. Security experts agree that companies of all sizes are imperiled by diversified threats, and executive leadership must institute a culture change that values security as a foundation of doing business.8
### Security Directors and Managers Are Under the Gun to Produce
Security directors and managers may also lose their jobs if a major security event or cyber incident takes place without well-crafted security response plans and realistic event-driven response procedures.9 Security professionals who want to keep their jobs must develop clear and distinct security policies, emergency security response plans, and event-driven response procedures, including comprehensive cyber security incident response procedures, as well as explicit security training programs that focus on preparing employees to do their jobs. There is no excuse for not training and, where appropriate, certifying personnel to perform their duties and responsibilities. This includes general security awareness training for all employees; information and cyber security awareness training for employees who have access to sensitive and classified information and use computer systems; general and specialized training for the security force; and educating executive managers, senior staff, board members, and governing bodies on the company's state of security readiness and other security matters.
### Chief Information Security Officers Are Corporate Scapegoats
Chief information security officers (CISOs) are not faring well with executives. According to a recent report issued by Threat Track Security, in August 2014, many CEOs view them as scapegoats.10 This report highlights that:
• 75% of C-suite executives do not view CISOs as part of the business's leadership team.
• 66% of CEOs say CISOs do not have a broad awareness of organizational goals and business needs outside of data security.
• 44% of CEOs say they would blame CISOs for any data leaks.
• 25% of CEOs would blame their cyber security decisions for hurting the financial strength of the company.
CEOs and CISOs remain far apart on how to best address cyber threat issues. The problem is further exacerbated by the lack of communication between the offices of the CEO and CISO.11 36% of CEOs say that the CISO never reports to them on the state of IT infrastructure security, as opposed to 27% of CEOs who say they receive updates on a somewhat regular basis.
CISOs are pointing the finger directly at the workforce as the primary concern, citing that a lack of employee education and diligence represents the greatest threat to the security of the corporate IT infrastructure. CEOs disagree, believing that external phishing attacks represent the largest threat to the organization, and that companies have sufficient time and resources to adequately train and educate their employees to effectively mitigate threats. This division between CEOs and CISOs should be a wake-up call for every organization to demand better alignment between the executives charged with protecting their most vital assets. The gap between how these encampments view threats to IT infrastructure security needs to be resolved quickly before it becomes detrimental to the nation's economic security and national security interests.
## What Does Work May Surprise You
### Successful Security Programs Integrate People, Processes, Best Practices, Technology, Strategic Vision, and Strong Leadership
Successful security programs require the right mix of people, processes, best practices, and technology at a quintessential level of integration with strategic vision, strong security leadership, and insight.
### Integrated Security Risk Management
Security assessments for critical infrastructure have traditionally followed four paths: a distinct separation from IT security, physical security, business continuity, and emergency management. The gap between all paths is slowly closing under the umbrella of a single integrated security resilience assessment model, such as the one presented in Chapter A User-Friendly Security Assessment Model.
A thorough security assessment should be a top priority for a corporation's management team. A security assessment should be conducted at least every 18–24 months; whenever a major change in mission occurs; when business operations are relocated; when facilities are retrofitted or modified, or when new facilities are planned; and after each major emergency. Security assessments, including penetration testing by trusted third-party security consultants, are now just as important as marketing new business and delivering quality products and services (Sullivant, 2007, pp. 55–84).
### Mitigating Risks to a Company's Image, Brand, and Reputation
Risk to a company's image, brand, and reputation is a relevant component of any security risk management program. Should any of these risks occur, it could rapidly cascade throughout the enterprise and produce adverse affects on value, supply chain relationships, market position, revenue, employee moral, and stakeholder confidence. Mitigating the risks to company image, brand, and reputation is a responsibility shared by the entire business.
### Developing Relationships of Openness and Trust is a Key Condition for Success
Where trust is high, ideas and communications flow easily. Where trust is low, everything becomes foggy. People hesitate to point out problems, suggest new ideas, approve ideas, or take responsibility for their mistakes or actions. They go to great lengths to create a paper trail to protect their position just in case things go wrong. Many corporations have learned the hard way about wasted energy that goes into unproductive memos, superfluous copies, and defensive conversations (Schmidt and Finnigan, 1994, pp. 9). Whenever one-on-one talks with upper management or governing bodies take place, a better business relationship may come out of it, but past experiences suggest that nothing substantial will change until individuals start being held accountable for their actions.
### Making a Business Case for Security Investment
One of the greatest challenges facing security directors is rationalizing funding for security investments. A focus on "how to get the money" is starting in the wrong place. Understanding how security aligns with the company's goals and how it fits into the corporate-wide risk management picture is essential. That starts with asking pertinent questions (Sullivant, 2007, pp. 199–218): What is security's role in protecting corporate image, brand, and reputation? What are we protecting and why? How is security relevant to protecting those assets? What are the true measurements of success?
While many in the upper echelon are paying more attention to security, they are still not spending enough to protect the organization against diversified threats, hazards, mishaps, and major business disruptions. While 60% Cyber Information Security Officers plan to increase the security budget. The Threat Track Security survey also cited 65% of the CEOs as saying insufficient funds was their number 1 challenge to operating at the security level expected by their company.12
### Security Transparency
Security abilities, capabilities, and policies should be transparent to all business units and upper management. This approach enables business units to be more clear and distinct in communicating their security requirements and unique differences to the security organization, as well as helping business units to support security practices. There exists an urgent need to show and demonstrate accountability, transparency, and uniformity of security performance standards.
## Characteristics of Future Security Leaders
Security leaders are increasingly being called upon to address broad security concerns, and as a result are becoming a strategic voice within their organizations. The constantly evolving threat landscape, emerging technologies, and budgetary constraints are requiring security leaders to play a more active role in communicating with C-suite executives and with their boards, as the increase in security incidents affect corporate brand, image, and reputation and customers' trust in them.
Tomorrow's security leaders have a tremendous vault of historical information and experience to pioneer new security horizons. You must build your career through informed experience, success at each stage of development, and continual advancements in education. To be successful, you must progress in your career not by chance, but through deliberate planning and creating opportunities. As a member of this select group of security leaders, you will experience a transition from a seasoned profession to a new generation of leaders who will not only be security executives but business leaders as well. This transition actually began more than two decades ago, but it has been slow in catching on across the entire security industry. I predict it will take another decade to really gain a foothold throughout the industry. It is this generation that I believe will gain the greatest benefit from using this book. By understanding the past and utilizing the strategies for building security resilience outlined in it, you will be able to lead the next generation of cultured security professionals to new heights of competency and excellence.
In climbing the ladder of success, decision making, oral communications, critical thinking, maximizing other's performance, and persuasive influencing are among the core competencies I believe you will be required to successfully perform. You must also acquire:
• a strong business vision, strategy, and policies with comprehensive risk management, and effective business relations skill sets
• an in-depth understanding of the concerns of C-suite executives. This is critical as more seasoned security leaders meet regularly with their board and C-suite leaders. Today, the top trends they discuss include:
• identifying and assessing risks (59%)
• resolving budget issues and requests (49%)
• deploying new technology (44%)
• building the trust of the C-suite and board in strategic decision making that is of vital interest to the corporation tomorrow, if not today
Beyond internal relationships, developing relationships with law enforcement, industry partners, and legislators is vital in fostering greater public and private communications.
## My Parting Thought
The overarching goal of my message throughout the pages of book has been to inform you, the reader, of the numerous security deficiencies, programmatic weaknesses, and human and technology inadequacies I have uncovered so that you may be able to establish a partnership with upper management and tear down the barriers and remove the obstacles that breed vulnerability creep-in and incompetency within your organization. Achieving this goal will contribute significantly to advancing the security profession as well as organizational resilience.
It's up to you to make change happen. I know you can do it. Now go do it, and God speed.
My warmest regards to every one of you.
John Sullivant.
* * *
1 <http://www.fraudnewsamerica.com/fraud-news-now/louis-freeh-speaks-acfe-conference/>.
2 <https://www.secureworldexpo.com/56-workers-may-not-receive-any-security-awareness-training>.
3 <https://www.duosecurity.com/blog/human-error-accounts-for-over-95-percent-of-security-incidents-reports-ibm>.
4 <https://www.sans.org/press/sans-institute-releases-results-of-survey-incident-response-how-to-fight-back.php>.
5 Ibid.
6 <http://www.reuters.com/article/ny-bain-company-idUSnBw055053a+100+BSW20140305>.
7 <https://www.nsi.org/Security_NewsWatch/NewsWatch/7.9.15.html>.
8 Talking points offered by the Armed Forces Communications and Electronics Association (AFCEA) International Symposium, held June 24–25, 2014, in Baltimore, MD. <http://www.afcea.org/cyber/>.
9 <http://www.fierceenterprisecommunications.com/story/poorly-handled-data-breach-could-cost-ciso-his-or-her-job-warns-gartner/2013-06-12>.
10 <http://www.threattracksecurity.com/resources/white-papers/chief-information-security-officers-misunderstood.aspx>.
11 <http://www.coresecurity.com/content/CEOs-Lack-Visibility-Into-Origin-and-Seriousness-of-Security-Threats>.
12 <http://www.networkworld.com/article/2224389/cisco-subnet/cisco-sees-big-plans-for-big-data.html>.
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# Index
'Note: Page numbers followed by "f" indicate figures.'
A
Abortion groups, 41–42
Alert notification systems
corporate alert notification system, , 167f
emergency planning considerations, 167–168, 168f
potential triggering incidents, , 167f
Al Qaeda,
Animal rights groups, 41–42
Anthrax,
ASIS Foundation,
B
Backup battery test log, 161f
Biological weapons,
Building security resilience
C-suite executives,
Homeland Security Presidential Directive (HSPD) 8,
Presidential Policy Directive (PPD) 21,
threat environment,
Business consequence analysis (CA) criteria, 96f, 97–98
Business continuity planning,
Business environment, challenges, ,
Business financial literacy,
C
Capital improvement program,
Card reader/keypad test log, 157f
Chemical weapons capability,
Chief information security officers (CISOs), 256–257
C-level executives,
Closed-circuit TV controls test log, 159f
Consequence loss analysis (CA), , 124f–127f
Contamination detection/surveillance,
Contraband detection equipment test log, 158f
Corporate security programs,
business continuity planning,
capital improvement program,
coordinating interoperability standards, 15–16
exploring methods,
human resources and capital investment,
safety program, 13–14
security technologies and expertise,
unique criteria, with protection,
C-suite executives, , 106f,
Cyber crime/criminals, 52–53
Cyber incident response capabilities,
Cyber security threat,
Cyber security training,
Cyber terror,
Cyber threats, 67–70
build security resilience, 66–67
challenge for CEOs, 70–71
corporations penetrated,
cyber crime/criminals, 52–53
cyber culprits, categories,
cyber practices and incident responses
budget, time and training, 64–65
capability to detect and respond to breaches, 61–63
employee dependability and reliability, 60–61
IT security professionals and employees, 58–60
monetary consequences, 65–66
perceptions of executives, 58–60
plans and procedures, 63–64
trustworthiness, 60–61
usefulness of cyber policies, 63–64
cyber terror,
cyber warfare,
government departments and agencies,
hacktivists,
mistakes and bad experiences,
outside experts and cunning insiders,
sharing of intelligence information,
sponsored cyber attacks, 56–57
undesirable employee behavior, 55–56
Cyber warfare,
D
Delay channels, 130–132
Deterrence,
Domestic extremists groups,
abortion groups and animal rights groups, 41–42
environmental groups,
militia groups, 40–41
Sovereign Citizen Movement,
white supremacy groups,
Door contact sensor test log, 157f
E
Emergency operations center responder training,
Emergency preparedness training,
Emergency security response procedure training,
Environmental groups,
Equipment enclosure test log, 159f
Event-driven security recovery procedures, 171–172
Event-driven security response procedures, 169–170, 169f
Executives/governing bodies, communication, , 239–240,
accepting responsibility, 251–252
business affairs, 232–233
business operations,
business risk exposure,
carve out recommendations,
chief executive officers (CEOs), 222–224
communicating and interacting,
communications gap,
constructive advice, 235–237
impressions count, 226–227
learn to use terms management, 225–226
maintain trust and respect,
measuring and communicating risk-based metric results over time,
measuring tomorrow's results, 234–235
message preparation, delivery
memorizing, 227–228
number 2,
reading,
offer constructive options,
process thinking,
risk-based metrics,
solid business case, ,
achieving your goal,
close out,
course for future,
identify business impact,
pick your path,
report the facts,
state of security readiness,
strategic thinking, 228–229
trust
avoided trustbusters,
candor,
competence,
credibility,
integrity,
loyalty,
maintain trust,
ultimate outcome,
verbal visionary, 233–234
work in progress, 224–225
Exterior microwave sensor test log, zone plot, 156f
F
Fence-mounted sensor test log, 155f
Field training/exercises,
conducting exercises, 219–220
development, 217–219
lessons,
objectives and scope, 216–217
planning field training,
Financial institutions, 245–246
Flight observer training,
G
General security strategies,
H
Hacktivists,
Homeland Security Presidential Directive (HSPD) 8,
Human and technology inadequacies,
equipment and facility shortfalls degrade security capability, 30–31
security design development practices,
security force and personnel shortcomings, 29–30
security technologies and applications hinder security competency,
I
Impressions count, 226–227
Inseparable security competencies, 138–140
assessment, 133–134
delay channels, 130–132
detection,
deterrence,
eight inseparable security competencies, , 129f
prevention,
protection, 132–133
recovery,
security response,
timely interdependencies, 134–138
Interior motion sensor test log, 158f
International multicultural competence, 207–208
International terrorism
al Qaeda,
cells and sleeper cells,
ISIS,
Islamic State of Iraq and the Levant (ISIL),
Islamic State of Iraq (ISIS),
Islamic State of Iraq and the Levant (ISIL),
L
Local/site-specific threat assessment, 117–118
M
Measuring/evaluating performance and productivity
practices, 248–249
prioritizing,
protocols, 248–249
Militia groups, 40–41
Misguided executive decision-making, 6–7
Multicultural versatility, 207–208
N
National Security Agency (NSA),
National threat assessment,
New Hampshire Technical Institute Business Training Center in Concord,
Nuclear weapons, 37–38
P
Penetration resistance time,
Performance effectiveness (PE)
existing effectiveness,
goal of,
proposed effectiveness, 109–111, 110f
Poison ricin,
Presidential Policy Directive (PPD) 21,
Probability of occurrence (PA), 93–98, 94f, , 124f–127f
Probability theory
business consequence criticality criteria, 96f, 97–98
certainty,
probability of occurrence (PA) criteria, 93–98, 94f
Program integration, 249–250
Programmatic security weaknesses, 24–25, 27–28
corporate management culture influences security practices and competencies, 28–29
high turnover rates,
ineffective planning and development plagues security organizations, 26–27
poor leadership and management,
security compensatory measures, 27–28
security creditability and competency,
Protocol strategy
benefits,
better measurement tools,
case histories, 188–189
delegating authority,
implementation matters,
improving protocol development,
leveraging lessons,
managing tension,
needs,
publication quality assurance review methodology, 185f
purpose of, 183–184
quality review process, 184–186
responsibility and accountability,
security activity protocols,
threats,
Proven organization/management assessment model, 194f
benefits,
case histories,
with CEOs,
management and leadership performance effectiveness, 196f–197f
measuring security management and leadership competencies,
purpose of measuring, 193–195
security mission, 191–193
Q
Quality system maintenance program
corrective maintenance, 148–149
depot support,
maintenance concept,
preventive maintenance,
R
Realistic and useful threat estimate profile
chief executive officers (CEOs),
consequence loss analysis (CA) and probability of occurrence (PA), , 124f–127f
corporate security,
C-suit executives,
local/site-specific threat assessment, 117–118
potential threats and hazards, 118–120, 122f–123f
threat estimate profile, 115–116, 115f
benefits, 120–121
cultural awareness, 114–115
national threat assessment,
regional/corporate threat assessment,
strategic security planning,
Response/recovery procedures,
Return on investment (ROI),
Risk-based metrics,
align security goals with company goals,
balancing business innovations, 99–100
benefits, 98–99
chief executive officers (CEOs), 91–93
closing thoughts,
measurement provides feedback,
metric creditability,
metric framework and architecture foundation,
operational reasonableness,
probability theory
business consequence criticality criteria, 96f, 97–98
certainty,
probability of occurrence (PA) criteria, 93–98, 94f
risk exposure, 99–100
scientific merit/value,
strategic relevance, 101–102
wide area of interest,
Russian Mafia,
S
Sector-specific agency,
Security alert status,
Security awareness training programs,
designated enterprise employees, 210–211
and emergency response training program,
executive management security awareness seminars, 211–212
Security design performance, 249–250
Security directors and managers,
Security emergency planning, , ,
alert notification systems
corporate alert notification system, , 167f
emergency planning considerations, 167–168, 168f
potential triggering incidents, , 167f
corporate strategy, , 173f
critical elements, 175–176
event-driven security recovery procedures, 171–172
event-driven security response procedures, 169–170, 169f
normal security post instructions and procedures,
prevention and protection strategies, 164–166
recovery capabilities, 169f
response and recovery, 164–166
security planning constraints and limitations,
wavering complexities, 174–175
Security leadership, 253–254
characteristics, 258–259
ethics need polishing,
executive management, 252–253
management social behavior,
oversight responsibility, 253–254
security management,
Security management training,
Security officer training,
Security professional experience,
Security reporting protocols,
Security risk management program
American Society of International Security,
architecture platform,
diagnostic analysis, 84–85
performance analysis,
risk analysis,
building teams,
checklists,
conceptual frameworks,
continuously improving performance, 78–79
developing relationships,
evaluation tools
compliance audit, 88–89
cyber security assessment,
inspection review,
organization and management review,
physical security assessment,
security system technical assessment, 86–87
special study,
technical surveillance countermeasures inspection review, 87–88
zero defects,
frameworks,
goal of,
identifying security successes and failures, 74–75
measure and evaluate performance, 79–80
vs. measurement and evaluation,
National Institute of Standards Technology,
performance,
procedural frameworks,
productivity,
purpose and need,
quality service and performance,
risk,
sound business decisions, 80–81
Security strategies/principles,
accountability, 17–18
constitutional freedoms,
corporate security programs,
business continuity planning,
capital improvement program,
coordinating interoperability standards, 15–16
exploring methods,
human resources and capital investment,
safety program, 13–14
security technologies and expertise,
unique criteria, with protection,
meaningful information sharing, 16–17
partnering internally and externally, 12–13
public safety and confidence,
safeguard privacy,
security authority and responsibility, 17–18
security policy,
services, 11–12
Security's weakest link,
Security system administration training,
Security system enrollment training,
Security toolbox,
Sleeper cells,
Smallpox virus,
Sovereign Citizen Movement,
Specialized security staff training program, 212–213
Special security event training,
Special security strategies,
Sponsored cyber attacks, 56–57
Strategic relevance, 101–102
Strategic security deficiencies, 21–22,
disruptive influence of inexperienced executives in security activities, 23–24
duty to care principle, 22–23
struggle to grasp essential principles of security planning,
weak security managers, business environment,
T
Technical security planning process,
road map to decision making, 143–145, 144f
role of,
security design and engineering, 146–147
unifying umbrella strategy, 142–143, 142f
Technological excellence,
Threat environment, 245–246
airplanes used, mass destruction,
biological weapons,
challenges, 33–34
chemical weapons capability,
competitors and espionage,
conventional attacks,
domestic extremists groups,
abortion groups and animal rights groups, 41–42
environmental groups,
militia groups, 40–41
Sovereign Citizen Movement,
white supremacy groups,
in-house employee terminations, 47–48
insider threat, 43–44
insult and emotional trauma,
international terrorism
al Qaeda,
cells and sleeper cells,
ISIS,
Islamic State of Iraq and the Levant (ISIL),
kidnapping,
nonconventional attacks,
nuclear weapons, 37–38
piracy,
protecting critical infrastructure, 36–37
radicalization process,
radiological bombs, 46–47
small aircraft with explosives,
stockroom and inventory threat,
suicide bombers,
terrorist activities, 2013-2015,
theft of property,
threats to personnel safety,
train bombs,
transnational criminal organizations, 42–43
uncovered plots,
vandalism and sabotage,
vehicle bombs,
Threat estimate profile, 115–116, 115f
benefits, 120–121
cultural awareness, 114–115
national threat assessment,
regional/corporate threat assessment,
strategic security planning,
Timely recovery principle,
Timely security assessment principle,
adversary and activity,
event identification, 136–137
muddied water,
Timely security delay principle,
Timely security detection principle,
Timely security deterrence principle,
Timely security prevention principle,
Timely security protection principle, 135–136
Timely security response principle,
Training development model, 250–251
benefits,
competency training,
continuing attitude,
course design,
classroom instruction,
computerized and programmed instruction,
correspondence study/training bulletins, 214–215
field training, 215–220
on-the-job training,
seminars,
critical operational capabilities and competency, 219f–220f
goals and value,
independent research and credence
analyze current training programs,
ASIS Foundation,
competencies,
curricula design,
job performance criteria identification, 208–209
trained personnel requirements identification,
University of Phoenix, , 206f–207f
nonproductive activity,
professional development,
reliable training model, 203–204, 203f
security awareness training programs,
designated enterprise employees, 210–211
and emergency response training program,
executive management security awareness seminars, 211–212
specialized security staff training program, 212–213
Transnational criminal organizations, 42–43
U
Uniform security strategies, 10–11
general security strategies,
special security strategies,
Uninterruptible power supply (ups) test log, 160f
University of Phoenix, , 206f–207f
User-friendly security assessment model
benefits,
with C-suite executives, 106f
goal of,
security assessments, 105–107
performance effectiveness (PE)
existing effectiveness,
goal of,
proposed effectiveness, 109–111, 110f
security analysis framework,
User-friendly security technology model
deficiencies and weaknesses,
quality system maintenance program
corrective maintenance, 148–149
depot support,
maintenance concept,
preventive maintenance,
sample test logs
backup battery test log, 161f
card reader/keypad test log, 157f
closed-circuit TV controls test log, 159f
contraband detection equipment test log, 158f
door contact sensor test log, 157f
equipment enclosure test log, 159f
exterior microwave sensor test log, zone plot, 156f
fence-mounted sensor test log, 155f
interior motion sensor test log, 158f
uninterruptible power supply (ups) test log, 160f
system failure modes and compensatory measures, 151–152, 152f
system life cycle,
diagnostic tests,
maintenance and seasonal performance tests, 150–151
physical inspections, 149–150
test data and test logs,
test plans and test procedures,
weekly operational tests,
technical security planning process
road map to decision making, 143–145, 144f
role of,
security design and engineering, 146–147
unifying umbrella strategy, 142–143, 142f
technical security strategy,
technology application,
V
Vulnerability creep-in,
categories, 19–20, 20f
challenge of exposing,
human and technology inadequacies,
equipment and facility shortfalls degrade security capability, 30–31
security design development practices,
security force and personnel shortcomings, 29–30
security technologies and applications hinder security competency,
phenomenon, 7–8
programmatic security weaknesses, 24–25, 27–28
corporate management culture influences security practices and competencies, 28–29
high turnover rates,
ineffective planning and development plagues security organizations, 26–27
poor leadership and management,
security compensatory measures, 27–28
security creditability and competency,
strategic security deficiencies, 21–22,
disruptive influence of inexperienced executives in security activities, 23–24
duty to care principle, 22–23
struggle to grasp essential principles of security planning,
weak security managers, business environment,
triple threat, 19–20
W
White supremacy groups,
Wikileaks website,
Workplace violence training,
# Table of Contents
1. Cover image
2. Title page
3. Table of Contents
4. Copyright
5. Dedication
6. About the Author
7. Foreword
8. Preface
9. Acknowledgments
10. 1. Introduction
1. Overview
2. Building Security Resilience and Developing Relationships
3. Watch Out for Stumbling Blocks
4. Vulnerability Creep-in Just Showed Up—It Wasn't Here Before
5. Conclusion
11. 2. Strategies That Create Your Life Line
1. Overview
2. A Need Exists to Create a Set of Uniform Security Strategies
3. Security Strategies and Guiding Principles
4. Conclusion
12. 3. The Many Faces of Vulnerability Creep-in
1. Overview
2. Vulnerability Creep-in Eludes Many Security Professionals
3. Strategic Security Deficiencies Top the List
4. Programmatic Security Weaknesses Rank Second Place
5. Human and Technology Inadequacies Rate Third Place
6. Conclusions
13. 4. The Evolving Threat Environment
1. Overview
2. The Threat Landscape Is Diversified and Sophisticated
3. Attack Modes Make Planning and Response a Challenge
4. Conclusions
14. 5. The Cyber Threat Landscape
1. Overview
2. Who Is Responsible for Today's Cyber Attacks?
3. The Cyber Threat Continues to Devastate the U.S. Economy and National Security
4. Trusted Insiders Bear Watching
5. State-Sponsored Cyber Attacks Create Havoc With Our Economy and National Security
6. Cyber Practices and Incident Responses Need Improvement
7. Conclusions
15. 6. Establishing a Security Risk Management Program Is Crucial
1. Overview
2. Risk Management Measures and Evaluates Risk Exposure and the Ability to Deal With Threats
3. Subscribing to a Security Risk Management Program
4. A Risk Management Program Establishes Creditability
5. When to Measure and Evaluate Performance
6. A Risk Management Program Is Key to Performance Success
7. Executives Need Compelling and Persuasive Information to Make Sound Business Decisions
8. Conclusions
9. Appendix A: Risk Management and Architecture Platform
10. Relationship Between Measurement and Evaluation
11. Architecture Platform
12. Evaluation Tools Mostly Used Within Security Organizations
13. Quality Assurance: Zero Defects
16. 7. Useful Metrics Give the Security Organization Standing
1. Overview
2. Risk-based Metrics Are Often Underestimated
3. Setting the Metric Framework and Architecture Foundation
4. Well-Designed Risk-based Metrics Resonate with CEOs
5. Theory of Probability
6. Benefits of Using Risk-based Metrics
7. Conclusion
8. Appendix A: Metric Framework and Architecture Platform
9. Strategic Relevance
10. Operational Reasonableness
17. 8. A User-Friendly Security Assessment Model
1. Overview
2. A Reliable Security Assessment Model That Resonates with C-Suite Executives
3. Measuring and Evaluating Performance Effectiveness
4. The Benefits Management Enjoys from Using a Risk-Based Model
5. Conclusions
18. 9. Developing a Realistic and Useful Threat Estimate Profile
1. Overview
2. Providing Meaningful Strategic Threat Advice to Executive Management Is Essential
3. Threat Planning Relies on the Development of a Useful Threat Estimate Profile
4. Suggested Composition of a Threat Estimate Profile
5. The Local/Site-Specific Threat Assessment
6. Identifying the Range of Potential Threats and Hazards Is a Critical Planning Process
7. Consequence Analysis and Probability of Occurrence for Threats and Hazards
8. Benefits of Having a Threat Estimate Profile
9. Conclusions
10. Appendix A
11. Appendix B
19. 10. Establishing and Maintaining Inseparable Security Competencies
1. Overview
2. Are Your Security Competencies a Top Priority?
3. Timely Interdependencies of Security Capabilities
4. Conclusions
20. 11. A User-Friendly Security Technology Model
1. Overview
2. A Dire Need Exists to Embrace a Technical Security Strategy
3. The Technical Security Planning Process Is Often Misunderstood and Underestimated
4. Embracing The Challenges of New Technology Advancements
5. Technology Application Has High-Visibility Challenges
6. Importance of a Quality System Maintenance Program
7. Embracing Inspections and Tests Extends the System Life Cycle
8. System Failure Modes and Compensatory Measures
9. Conclusion
10. Appendix A: Selected Security Technology Deficiencies and Weaknesses
11. Overview of Selected Case Histories
12. Appendix B: Sample Test Logs
13. Safety Information
21. 12. Preparing for Emergencies
1. Overview
2. Security Emergency Planning Is Critical to Organizational Survival
3. Planning for Prevention, Protection, Response, and Recovery
4. Alert Notification Systems Serve as Triggering Mechanisms to Carry Out Security Planning Considerations
5. Planning for Security Event-Driven Response and Recovery Operations
6. Strategies for Integrating and Prioritizing Security Response and Recovery Operations
7. Security Emergency Response Plan
8. Conclusions
9. Appendix A: Case Histories: Security Emergency Planning Fallacies
22. 13. A User-Friendly Protocol Development Model
1. Overview
2. Adopting a Protocol Strategy Is Crucial to Quality Performance
3. Need for Protocols
4. Purpose of Protocol Reviews
5. Quality Review Process for Essential Security Protocols
6. Benefits Derived from Protocol Analysis
7. Conclusions
8. Appendix A
23. 14. A Proven Organization and Management Assessment Model
1. Overview
2. Embracing the Mission of the Security Organization
3. A Reliable Organization and Management Assessment Model That Resonates with CEOs
4. Purpose of Measuring Organization and Management Competency
5. Measuring Security Management and Leadership Competencies
6. Benefits of an Operational and Management Audit
7. Conclusions
8. Appendix A: Case Histories – Management and Leadership
9. Overview of Selected Case Histories
24. 15. Building Competencies That Count: A Training Model
1. Overview
2. Why Security Training Is Important
3. Goals and Value Are Drivers of Effective Training
4. A Reliable Training Model Resonates With Chief Executive Officers
5. Independent Research and Credence of the Model
6. Types of Security Awareness Training Programs
7. Specialized Security Staff Training Program
8. Course Design Brings Instruction to Life
9. Professional Development Is Key for Security Planners
10. Benefits Management Enjoys by Adopting the Model
11. Conclusions
25. 16. How to Communicate with Executives and Governing Bodies
1. Overview
2. Why Would a CEO Ever Ask You for Help?
3. Why Should a Chief Executive Listen to You?
4. Speak the Language Executives and Board Members Understand, Care About, and Can Act On
5. Impressions Count
6. Tips That Will Help You Get Your Message Across
7. Think Strategically
8. Develop a Management Perspective
9. Be Trustworthy, Candid, and Professional
10. Be a Verbal Visionary
11. Be That Window for Tomorrow
12. Give Constructive Advice
13. Build a Solid Business Case
14. Know When to Pull Your Parachute Cord
15. Present Program Results Regularly
16. Conclusions
26. 17. A Brighter Tomorrow: My Thoughts
1. Overview
2. A Perspective for the Future
3. The Evolving Business and Threat Landscape
4. Corporate Image, Brand, and Reputation Hang in the Balance
5. Measuring and Evaluating Performance and Productivity
6. Security Design Performance and Program Integration
7. Training Programs Need a Major Uplift
8. Security Emergency Plans and Response/Recovery Procedures
9. Communicating with Executives and Governing Bodies
10. Security Leadership Needs a Touch Up
11. Change Management in the Wind
12. What Does Work May Surprise You
13. Characteristics of Future Security Leaders
14. My Parting Thought
27. References
28. Index
# List of Figures
1. Figures in 3
1. Figure 3.1
2. Figures in 7
1. Figure 7.1
2. Figure 7.2
3. Figures in 8
1. Figure 8.1
2. Figure 8.2
4. Figures in 9
1. Figure 9.1
2. Figure 9.2
3. Figure 9.3
5. Figures in 10
1. Figure 10.1
6. Figures in 11
1. Figure 11.1
2. Figure 11.2
3. Figure 11.3
4. Figure 11.4
5. Figure 11.5
6. Figure 11.6
7. Figure 11.7
8. Figure 11.8
9. Figure 11.9
10. Figure 11.10
11. Figure 11.11
12. Figure 11.12
13. Figure 11.13
7. Figures in 12
1. Figure 12.1
2. Figure 12.2
3. Figure 12.3
4. Figure 12.4
8. Figures in 13
1. Figure 13.1
9. Figures in 14
1. Figure 14.1
2. Figure 14.2
10. Figures in 15
1. Figure 15.1
2. Figure 15.2
3. Figure 15.3
# List of Tables
# Landmarks
1. Cover image
2. Title page
3. Table of Contents
1. i
2. ii
3. iii
4. iv
5. v
6. xiii
7. xiv
8. xv
9. xvi
10. xvii
11. xviii
12. xix
13. xx
14. xxi
15. xxii
16. xxiii
17. xxiv
18. xxv
19. xxvi
20. xxvii
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| {
"redpajama_set_name": "RedPajamaBook"
} | 6,978 |
Q: Validate href inside a div I have this type of markup:
<div class="box" href="pic-gallery/img01.jpg">
<div>----------</div>
</div>
Now as I am going to validate this it is showing error as href inside a div is not allowed. So how to validate this error? I had used:
<div class="box" onclick="href='pic-gallery/img01.jpg'"></div>
but it is not opening the image as picture is coming through the fancybox. So please help me out. Any help and suggestions will be highly appreciated.
A: href isn't a valid attribute for div, just a and area. Your best bet is to use an actual link (an a element). You can use styling (display: block) to make it shown as a block on modern browsers (not, sadly, on some older versions of IE), and since its content model is transparent, you could put a div inside it. All of the examples on the Fancybox howto page show using an a element, not a div.
So perhaps
<a class="box" href="pic-gallery/img01.jpg">
<div>----------</div>
</a>
...where the "box" class includes display: block. Or if you use that class places where you don't want block display, break out the display: block and apply it separately (via another class or inline style attribute).
A: With fancybox, you can show your images by putting their path inside links:
<a class="box" href="pic-gallery/img01.jpg"></a>
This will be identified by fancybox based on link's class eg box and will be opened by fancybox.
A: This is expected - the href attribute is not valid on a <div> element. As T.J. said above, it would be best to use an actual <a> element to do this - it makes more semantic sense. You could even nest the <a> inside the outer <div> and hide it with CSS, so non-JS enabled users don't see redundant markup.
A: Instead of this code.
<div class="box" onclick="href='pic-gallery/img01.jpg'"></div>
Try this
<script type="text/javascript">function open_win(){window.open("pic-gallery/img01.jpg");}</script><div class="box" onclick="javascript:open_win();"></div>
But how do you want to open the image?
A: I know this is unusual but you could still open an image (or any other type of content) in fancybox adding the onclick attribute to the <div> (or any other tag other than the <a> tag) and without using the href attribute.
You may have this (valid) html:
<div class="box" onclick="openFancybox('pic-gallery/img01.jpg');">
<div>whatever here</div>
</div>
and use this script:
<script type="text/javascript">
function openFancybox(url){
$.fancybox({
'href': url,
'type': 'image' //select the proper type of content
});
}
</script>
what you are doing is passing the url to the function instead of using href
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,009 |
\section{Introduction}
\subsection{Recurrence rate and Lagrange constants}
We study recurrence of maps of the unit interval that preserve Lebesgue measure.
Let $T\colon [0,1)\to [0,1)$ be a measurable map of the unit interval into itself.
The recurrence rate of $T$ at $x\in [0,1)$ is defined as
\[
r(T,x) = \liminf_{n \to \infty}\ n\, |T^n x-x|\in[0,\infty].
\]
Denote by $R_\alpha: [0,1) \to [0,1)$ the rotation by the angle $\alpha\in\mathbb{R}$,
that is
$R_\alpha(x) = x+\alpha \pmod 1$.
Since the group of such rotations acts transitively on $[0,1)$ by local isometries (apart from at $x=0$), we note that \mbox{$r(R_\alpha,x)=r(R_\alpha, \frac12)$}, for all $\alpha$ and $x \not= 0$.
Set $r(R_\alpha):=r(R_\alpha, \frac12)$.
One verifies that, for every $\alpha\in\mathbb{R}$,
\[
r(R_{\alpha})=\liminf_{q\to+\infty\atop q\in\mathbb{Z}}\ q\,\DZ{q\alpha},
\]
where $\DZ{t}=\min_{n\in\mathbb{Z}}\limits|t-n|$ stands
for the distance of $t\in\mathbb{R}$ to the nearest integer.
We will provide two generalizations of the following well known result.
\begin{theorem}[Hurwitz \cite{Hurwitz}] \label{thm:Hurwitz_rotation}
For any real number $\alpha$ we have $r(R_\alpha) \leq \frac{1}{\sqrt{5}}$.
Moreover, $r(R_\alpha) = \frac{1}{\sqrt{5}}$ if and only if the continued
fraction expansion of $\alpha$ is eventually constant and equal to $1$.
(In particular, $r(R_\beta)=\frac{1}{\sqrt{5}}$ for
$\beta = \frac{\sqrt{5}-1}{2} = [0; 1, 1, 1, ...]$).
On the other hand, if $r(R_\alpha) \not= \frac{1}{\sqrt{5}}$ then $r(R_\alpha) \leq \frac{1}{2 \sqrt{2}}$.
\end{theorem}
In other words, the inequality $r(R_{\alpha},x)\leq\frac1{\sqrt5}$ holds
for all rotations $R_\alpha\colon [0,1) \to [0,1)$ and $x\neq0$.
Note that Hurwitz \cite{Hurwitz} also proved that the inequality $q\, \DZ{q\alpha}<\frac1{\sqrt5}$
has infinitely many solutions in integers $q\geq1$.
\emph{The Lagrange constant of} $\alpha\in\mathbb{R}$ is defined as follows:
\begin{equation} \label{eq:lagrange_rot_dim1}
L(\alpha) = \frac1{r(R_{\alpha})}=\limsup_{q \to \infty}\ \frac{1}{q\,\DZ{q\alpha}}
\in\big[\sqrt5,\infty\big],
\end{equation}
and \emph{the (classical) Lagrange spectrum} is defined as the set of possible
finite Lagrange constants
\[
\mathcal{L}_1 := \big\{L(\alpha):\, \alpha \in [0,1) \big\}\setminus\{+\infty\}.
\]
An equivalent way of stating Hurwitz's Theorem (Theorem~\ref{thm:Hurwitz_rotation}) is
\begin{equation}\label{eq:LagSp1}
\mathcal{L}_1 \cap \big[0, 2\sqrt2\big) = \big\{\sqrt5\,\big\}.
\end{equation}
\subsection{Two generalizations of Hurwitz's Theorem}
The first proposed generalization is that the inequality $r(T,x) \leq
\frac{1}{\sqrt{5}}$ in Hurwitz's Theorem actually holds almost surely for all
Lebesgue measure preserving transformations $T\colon [0,1) \rightarrow [0,1)$
(and not just for the rotations $T=R_{\alpha}$).
\begin{theorem}\label{thm:rec01}
Let $T\colon [0,1) \rightarrow [0,1)$ be a measurable map of the unit interval
which preserves the Lebesgue measure~$\mu$.
Then, $r(T,x) \leq \frac1{\sqrt5}$, for $\mu$-almost every $x \in [0,1)$.
\end{theorem}
The above theorem provides the optimal constant in the quantitative recurrence
result in~\cite[Theorem 2.1]{Boshernitzan-recurrence} where, under the
conditions of Theorem \ref{thm:rec01}, a weaker inequality was
established (see Theorem \ref{thm:rec2} below).
Note that quantitative Poincar\'e recurrence results are possible in the more
general settings of transformations of arbitrary metric spaces having finite
Hausdorff dimension: see \cite{Boshernitzan-recurrence}
and the discussion following Theorem~\ref{thm:rec2} below.
\bigskip
Our second generalization of Theorem~\ref{thm:Hurwitz_rotation}
is related to interval exchange transformations.
An \emph{interval exchange transformation} (or \emph{i.e.t.} for short) is a bijection
from an interval to itself that is a piecewise translation on finitely many intervals.
More precisely,
given a permutation $\pi \in S_k$ and a vector $\lambda \in \mathbb{R}_+^k$,
we define a $k$-i.e.t. $T_{\pi,\lambda}$ as
\[
T_{\pi,\lambda}(x) = x - \sum_{j < i} \lambda_j + \sum_{\pi(j) < \pi(i)} \lambda_j,
\quad \text{ if \ $x \in [\lambda_1 + \ldots + \lambda_{i-1}, \lambda_1 + \ldots + \lambda_i)$}.
\]
Note that rotations are exactly the 2-i.e.t.s with permutations $\pi=(2,1)$.
The \emph{singularities} of $T$ are the points $x_i = \sum_{j \leq i}
\lambda_j$ for $i=1,\dots,k-1$. An i.e.t. $T_{\pi,\lambda}$ is said to be \emph{without connection} if there is
no pair of singularities $x$ and $y$ of $T$ such that $T^n x = y$ for some $n \geq 1$. It
was shown by Keane~\cite{Keane1975} that this condition implies the minimality
of the transformation $T$.
Given an i.e.t. $T = T_{\pi,\lambda}$ that satisfies the Keane condition, its
$n$-th iterate $T^n$ is also an i.e.t. but on $(k-1)n+1$ intervals. Let
$\varepsilon_n(T)$ be the smallest length of any of the intervals of $T^n$. In particular
$\varepsilon_0(T) = 1$ and $\varepsilon_1(T) = \min \lambda_i$. Note that the
number $\varepsilon_n(T)$ can alternatively be defined as the minimum distance
between the $n$-th first preimages of the singularities together with $0$ and $1$.
For $T=T_{\pi,\lambda}$ we define
\[
\mathcal{E}(T) := \liminf_{n \to \infty}\, \frac{n \varepsilon_n(T)}{|\lambda|}
\quad \text{where } \ |\lambda| = \lambda_1 + \ldots + \lambda_k.
\]
The value $L(T) := \mathcal{E}(T)^{-1}$ is called the \emph{Lagrange constant} of $T$.
It generalizes the Lagrange constant for the rotations $R_\alpha$. We also
recall that if $\pi \in S_k$ is \emph{irreducible} (or \emph{indecomposable})
then for Lebesgue-almost every $\lambda$ the Lagrange constant of
$T_{\pi,\lambda}$ is infinite.
The Lagrange spectrum of i.e.t.s was introduced by S.~Ferenczi
in~\cite{Ferenczi-lagrange} under the name \emph{lower Boshernitzan-Lagrange spectrum}. It
was then further studied by P. Hubert, L. Marchese and C. Ulcigrai in~\cite{HubertMarcheseUlcigrai}.
The \emph{Lagrange spectrum} of the $k$-i.e.t.s is the following set of values:
\[
\mathcal{L}_{k-1} = \{L(T)\colon\ \text{$T$ is a $k$-i.e.t. satisfying the Keane condition and $L(T) < \infty$}\}.
\]
Because $T^n$ is made of $(k-1)n+1$ intervals, $\inf\mathcal{L}_{k-1} \geq k-1$.
In~\cite{HubertMarcheseUlcigrai}, the better bound
$\inf\mathcal{L}_k \geq \frac\pi2 k$ is established.
We prove the following.
\begin{theorem} \label{thm:lagrange}
There exists a constant $\varepsilon_0 > 0$ such that for any $d \geq 1$
\[
\mathcal{L}_d \cap \left[0,\ d \sqrt{5} + \frac{\varepsilon_0}{d}\right] = \left\{d\sqrt{5}\right\}.
\]
Moreover, for any permutation $\pi \in S_{d+1}$ such that $\pi(1) = d+1$, the length
vector $\lambda = (\frac{\sqrt{5}+1}{2},1,1,\ldots,1)$ is such that
$T_{\pi,\lambda}$ satisfies the Keane condition and $L(T_{\pi,\lambda}) = d\sqrt{5}$.
\end{theorem}
The proof of Theorem \ref{thm:lagrange} will be given in
Section~\ref{sec:lagrange_iet}. We will actually completely characterize the
$(d+1)$-i.e.t.s $T$ such that $L(T) = d \sqrt{5}$. Note that the case $d=1$ is given
by Hurwitz's theorem (see in particular~\eqref{eq:LagSp1}) and that the case $d=2$ was proven
in~\cite[Theorem~4.10]{Ferenczi-lagrange}.
\bigskip
The common tool in the proofs of Theorems~\ref{thm:rec01} and~\ref{thm:lagrange}
is Theorem~\ref{thm:delta_estimate_in_convex} concerning an unconventional packing problem
in $\mathbb{R}^{2}$ (see Section \ref{sec:pack} for precise setting), which determines the relevant
optimal constant $\frac1{\sqrt 5}$. Section~\ref{sec:interval_recurrence} is
dedicated to the proof of Theorem~\ref{thm:rec01}. And in
Section~\ref{sec:lagrange_iet} we provide the proof for
Theorem~\ref{thm:lagrange}.
\subsection{Further Comments}
\subsubsection*{The Classical Lagrange spectrum}
There are many results about the Lagrange spectrum $\mathcal{L}_1$ (of rotations), including the following.
\begin{enumerate}
\item $\mathcal{L}_1$ starts with a discrete sequence $\sqrt{5}$, $2\sqrt{2}$, $\sqrt{221}/5$, \ldots with an accumulation point at $3$ \cite{Markov},
\item $\mathcal{L}_1$ contains the half line $[c,+\infty)$ where $c = \frac{2221564096 + 283748 \sqrt{462}}{491993569} \simeq 4.528$, and
this half line is maximal (i.e. $\mathcal{L}_1$ does not contains a half-line $[c',+\infty)$ with $c' < c$) \cite{Hall47}, \cite{Freiman75},
\item $\operatorname{Hdim}(\mathcal{L}_1 \cap [0,t]) = 0$ if and only if $t \leq 3$ and $\operatorname{Hdim}(\mathcal{L}_1 \cap [0, 2\sqrt{3}]) = 1$ \cite{Moreira}.
\end{enumerate}
The interval exchange Lagrange spectrum $\mathcal{L}_d$ contains $m \mathcal{L}_{d'}$ if $d = m d'$. In particular
$\mathcal{L}_d$ contains $d \mathcal{L}_1$, from which some properties follow (such as the existence of a half line).
But nothing as precise as the three above items for $\mathcal{L}_1$ is known in general for $\mathcal{L}_d$.
\subsubsection*{Lebesgue-preserving maps on subsets in $\mathbb{R}^{n}$ of finite volume}
Recall that quantitative Poincar\'e recurrence (almost everywhere) results
are possible in more general settings of transformations of arbitrary
metric spaces having finite Hausdorff dimension,
see~\cite{Boshernitzan-recurrence}. In particular,
the following result holds.
\begin{theorem}[\cite{Boshernitzan-recurrence}, Theorem~1.5]\label{thm:rec2}
Let $(X,d)$ be a metric space and let $\mu$ be a probability measure on it
which coincides, for some $\alpha\in(0,\infty)$, with the $\alpha$-Hausdorff
measure on $(X,d)$.
Then, for any transformation $T\colon X\to X$ which preserves the measure $\mu$, we
have
\[
\liminf_{n \to \infty} n^{1/\alpha} d(x, T^n x) \leq 1,
\qquad \text{for $\mu$-almost every $x \in X$.}
\]
\end{theorem}
Now, denote by $\mu_{d}(\cdot)$ the Lebesgue measure on $\mathbb{R}^{d}$ where $d\geq1$.
Let also $\rho$ be a norm on $\mathbb{R}^d$ and $B_\rho$ be the unit ball for this norm.
Let $X \subset \mathbb{R}^d$ be a measurable set of finite non-zero measure and let
$T\colon X \to X$ be a transformation which preserves $\mu_d$.
Then Theorem~\ref{thm:rec2} implies that for almost every $x \in X$ we have
\[
\liminf_{n \to \infty} \ n^{1/d}\rho({x} - T^n{x})\leq
2\left(\frac{\mu_{d}(X)}{\mu_{d}(B_{\rho})}\right)^{1/d}.
\]
In the particular case when $X = [0,1)^d$ is the unit cube,
the above inequality takes the form
\[
\liminf_{n \to \infty} \ n^{1/d}\rho({\bf x} - T^n{\bf x})\leq
2\ \mu_{d}(B_{\rho})^{-1/d}.
\]
In the even more special case where $X = [0,1)$ and $\rho$ is
the absolute value, we obtain a weaker version of Theorem~\ref{thm:rec01}
with the constant $1$ instead of $\frac1{\sqrt5}$. The technique we use in this
article to determine
the optimal constant $\frac1{\sqrt5}$ for $X = [0,1)$ does not seem to extend to
higher dimensions; not even for the square $X=[0,1)^2$.
\subsubsection*{Singular vectors and the Dirichlet spectrum}
We have seen one extension of the Lagrange constant of 1-dimensional rotation
to interval exchange transformations. It can also be defined for higher-dimensional
rotations as follows. Given $\alpha \in \mathbb{R}^d$ we define, similarly to~\eqref{eq:lagrange_rot_dim1},
\[
L(\alpha) = \limsup_{q \to \infty}\ \frac{1}{q^{1/d}\,\DZ{q\alpha}}.
\]
where $\DZ{x}$ denotes the Euclidean distance to the nearest integer lattice point. In
both contexts, the Lagrange constant also has a natural $\liminf$ counterpart
that we discuss next.
Given $\alpha\in \mathbb{R}^d$ we define its \emph{Dirichlet constant} $D(\alpha)$ as
\[
D(\alpha) = \liminf_{n \to \infty} \frac{1}{n^{1/d} \varepsilon_n(\alpha)}
\qquad \text{where} \qquad
\varepsilon_n(\alpha) = \min_{1 \leq k \leq n} \DZ{k \alpha}
\]
Recall that a vector $\alpha$ is called \emph{singular} if $D(\alpha) = +\infty$
(such vector only exists if $d \not= 1$). The set of singular vectors is known
to be of zero measure in any dimension, and its Hausdorff dimension has recently
been computed by N. Chevallier and Y. Cheung~\cite{ChevallierCheung}. Recall
that for the Lagrange constant, a vector $\alpha$ such that $L(\alpha) < +\infty$
is called \emph{badly approximable}. For a Lebesgue generic $\alpha$ we have
$D(\alpha) = c_d$ and $L(\alpha) = +\infty$, where $0 < c_d < +\infty$ is a
constant that only depends on the dimension.
Similarly, if $T$ is an i.e.t. that satisfies the Keane condition we define
its \emph{Dirichlet constant} as
\[
D(T) = \liminf_{n \to \infty} \frac{1}{n \varepsilon_n(T)}.
\]
The \emph{Dirichlet spectrum}\footnote{
In~\cite{Ferenczi-lagrange} the Dirichlet spectrum is called the \emph{upper
Boshernitzan-Lagrange spectrum}. The reason for this is that M. Boshernitzan
proved that for i.e.t. the condition $D(T) < +\infty$ implies unique
ergodicity~\cite{Boshernitzan-uniqueergodicity}.} is the set of possible
Dirichlet constants for a given class of systems
(i.e., a dimension for rotations, or a number of intervals for i.e.t.s, are fixed).
For rotations (or 2-i.e.t.s), the Dirichlet spectrum has a structure similar to
the Lagrange spectrum: that is, it starts with a discrete sequence and contains
an interval (see the discussion and references in the introduction
of~\cite{AkhunzhanovShatskov2013}). But the situation changes dramatically when
one goes to higher dimensional situations. For instance, for both the
2-dimensional rotations~\cite[Theorem~1]{AkhunzhanovShatskov2013} and 3-i.e.t.s
\cite[Theorem~4.14]{Ferenczi-lagrange} the Dirichlet spectrum is an interval.
Nothing seems to be known about the structure of Dirichlet spectrum
for rotations in $\mathbb{R}^3$ or 4-i.e.t.s.
\section{An unconventional packing problem in $\mathbb{R}^{2}$}\label{sec:pack}
Denote by $\mathbb{C}$ the set of complex numbers. Given $z = x + iy$ we define
$\operatorname{\bf N}(z) = \sqrt{|xy|}$ (and $\operatorname{\bf N}^2(z) = (\operatorname{\bf N}(z))^2 = |xy|$). The
function $\operatorname{\bf N}$ can be thought as a
generalization of a norm whose unit ball is the region delimited by the
hyperbolas $xy = \pm 1$. Unlike with a genuine norm, the unit ball of $\operatorname{\bf N}$, namely
$\{z\colon \operatorname{\bf N}(z) \leq 1\}$,
is not convex. However, it is still star shaped, and satisfies $\operatorname{\bf N}(tz) = |t| \operatorname{\bf N}(z)$
for all real $t$.
Given a polygon $P$ with vertices $z_1$, $z_2$, \ldots, $z_n$, we define
its $\operatorname{\bf N}$-perimeter as $\displaystyle p(P) = \sum_{i=1,\ldots,n}\limits \operatorname{\bf N}(z_{i+1} - z_i)$ (where indices are taken modulo $n$).
Our main tool in the present paper is given by the following result.
\begin{theorem}[\cite{Smith}] \label{thm:delta_estimate_in_convex}
Let $\Gamma$ be a finite set of points in $\mathbb{C}$ such that $N(x-y) \geq 1$
for every pair of distinct points $(x,y)$ of $\Gamma$.
Let $C$ be its convex hull. Let $A$ and $p$ be respectively the area and
$\operatorname{\bf N}$-perimeter of $C$. Then
\[
\# \Gamma \leq \frac{1}{\sqrt{5}} A + \frac{p}{2} + 1.
\]
Moreover, if equality holds, then the set $\Gamma$ is a subset of a golden
lattice.
\end{theorem}
In the case of norms (i.e.,~when the unit ball is convex) the above result
was a conjecture of H.~Zassenhaus, which was proven in full generality by N.~Oler~\cite{Oler}.
\begin{theorem}[\cite{Oler}] \label{thm:delta_euclidean}
Let $\rho$ be a norm in $\mathbb{R}^2$ and let $\Gamma$ be a finite set of points
such that $\rho(x-y) \geq 1$ for all pairs $(x,y)$ of points of $\Gamma$.
Let $C$ be the convex hull of $\Gamma$, $A$ the area of $C$ and $p$ the
$\rho$-perimeter of $C$. Then
\[
\# \Gamma \leq \Delta(\rho) A + \frac{p}{2} + 1
\]
where $\Delta(\rho)$ is the critical determinant of the unit ball of $\rho$.
\end{theorem}
The \emph{critical determinant} $\Delta(C)$ of a centrally symmetric convex body
$C$ in $\mathbb{C}$ is defined as follows. A lattice $\Lambda \subset \mathbb{C}$ is said to be
$C$-admissible if $C \cap \Lambda = \{0\}$. Then
\[
\Delta(C) := \min \{\det(\Lambda):\ \text{$\Lambda$ is $C$-admissible}\}.
\]
In Theorem~\ref{thm:delta_estimate_in_convex} the constant $\frac{1}{\sqrt{5}}$ is
also a critical determinant (for a star but non-convex body). This constant is achieved
exactly by the golden lattices. These two facts are just a reformulation of
Hurwitz Theorem (Theorem~\ref{thm:Hurwitz_rotation}).
The rest of this section is devoted to the proof of Theorem~\ref{thm:delta_estimate_in_convex}.
A complete proof is given in the PhD thesis of N.~E.~Smith (a student of
H.~Zassenhaus), see~\cite{Smith}. Our proof uses the same path except that a delicate
induction is avoided by using Delaunay triangulations.
\begin{remark}
As pointed out in the review paper~\cite{Zassenhaus} a weaker version of
Theorem~\ref{thm:delta_estimate_in_convex} can be derived
from Theorem~\ref{thm:delta_euclidean} as shown in the PhD thesis
of Sr. M. R. von Wolff~\cite{vonWolff}. Namely, we always have
$N(z) \leq \rho(z)$ where $\rho(z) = (|x|+|y|)/2$. Hence
if $N(z) \geq 1$ then a fortiori $\rho(z) \geq 1$ and
Oler's result applies. Luckily the critical determinants are
the same for $N$ and $\rho$ equal to $1/\sqrt{5}$, though in the error term
the $\rho$-perimeter is generally larger than the $N$-perimeter.
Note that this weaker result would have been enough for our applications but we
prefer to include a self-contained and short proof of
Theorem~\ref{thm:delta_estimate_in_convex}.
\end{remark}
\begin{remark}
It would be tempting to conjecture that Oler's result actually holds
for centrally symmetric bodies. But this is actually false. Sr.\ M.\ R. von Wolff provided
a counterexample in her PhD thesis~\cite{vonWolff}.
\end{remark}
\subsection{Admissible triangles}
Given a triangle $(p,q,r)$ in $\mathbb{C}$, it is always inscribed in a smallest rectangle,
namely the rectangle $R(p,q,r) = [x^-, x^+] \times [y^-,y^+]$ defined by
\[
\begin{array}{l@{\qquad}l}
x^- = \min(\operatorname{Re}(p),\operatorname{Re}(q),\operatorname{Re}(r)) & x^+ = \max(\operatorname{Re}(p),\operatorname{Re}(q),\operatorname{Re}(r)) \\
y^- = \min(\operatorname{Im}(p),\operatorname{Im}(q),\operatorname{Im}(r)) & y^+ = \max(\operatorname{Im}(p),\operatorname{Im}(q),\operatorname{Im}(r)).
\end{array}
\]
\begin{definition}
We call a triangle $(p,q,r)$ in $\mathbb{C}$ \emph{admissible} if the three points $p,q,r$
are on the boundary of the minimal rectangle $R(p,q,r)$ and no two of them are on the same side.
\end{definition}
\begin{remark}
One can alternatively define admissible triangles as triangles for which the sign of the slopes
of the sides are not all the same. This is the definition proposed in~\cite{Smith} on
page 7 in which admissible triangles are called \emph{type (a)}.
\end{remark}
Let $(p,q,r)$ be an admissible triangle. On the rectangle $R(p,q,r)$ exactly one vertex is in a corner.
By convention we always label the sides $a,b,c$ so that the two sides $a,b$
are adjacent to that corner and $a$, $b$, $c$ are taken in counter-clockwise
order. (See Figure~\ref{fig:admissible_vs_nonadmissible} above.)
\begin{figure}[!ht]
\begin{center}
\includegraphics{admissible_triangle1.pdf} \hspace{1cm}
\includegraphics{admissible_triangle2.pdf} \hspace{1cm}
\includegraphics{nonadmissible_triangle.pdf}
\end{center}
\caption{Two admissible triangles and one non-admissible triangle.}
\label{fig:admissible_vs_nonadmissible}
\end{figure}
Recall that $\operatorname{\bf N}\colon \mathbb{C} \to \mathbb{R}$ is the function defined by $\operatorname{\bf N}(x+iy) = \sqrt{|xy|}$.
The main ingredient of the proof of Theorem~\ref{thm:delta_estimate_in_convex} is
the following lemma which establishes the fact that the area of an
admissible triangle is completely determined by the $\operatorname{\bf N}$-length of its sides.
\begin{lemma} \label{lem:formula_area_triangle}
Let $a,b,c$ be three sides of an admissible triangle
$\Delta$ and let
\[
\alpha := \operatorname{\bf N}(a)^2, \quad \beta := \operatorname{\bf N}(b)^2, \quad \gamma := \operatorname{\bf N}(c)^2.
\]
Then
\begin{equation}\label{eq:abcd}
\operatorname{\bf area}(\Delta) = \frac{ \sqrt{\alpha^2 + \beta^2 + \gamma^2 - 2\alpha\beta +
2\alpha \gamma + 2\beta \gamma}}{2}.
\end{equation}
\end{lemma}
\begin{proof}
Applying $g_t$ and an homothety of $1/\sqrt{\gamma}$ we can assume
(up to symmetry) that $c=(1,-1)$ as shown
in the picture below.
\begin{center}
\includegraphics{area_triangle.pdf}
\end{center}
Then we have \
$\alpha=x(y+1)$,
$\beta=y(x+1)$,
$\gamma=1$ \
while \ $\operatorname{\bf area}(\Delta) = \frac{1+x+y}{2}$, and
the validation of the formula~\eqref{eq:abcd} becomes straightforward.
\end{proof}
\begin{corollary} \label{cor:area_triangle}
Let $\Delta$ be an admissible triangle with $a$, $b$, $c$, $\alpha$, $\beta$, $\gamma$
as in Lemma \ref{lem:formula_area_triangle}.
Let $m = \min \{\alpha,\beta,\gamma\}$ and $M = \max \{\alpha,\beta,\gamma\}$.
Then
\[
\frac{\sqrt{5}}{2} \ m \leq \operatorname{\bf area}(\Delta) \leq \frac{\sqrt{m^2 + 4M^2}}{2} \leq \frac{\sqrt{5}}{2} \ M.
\]
If moreover $\operatorname{\bf area}(\Delta) \leq \sqrt{2}\ m$ then
\[
\frac{\sqrt{M^2 + 4m^2}}{2} \leq \operatorname{\bf area}(\Delta).
\]
\end{corollary}
\begin{proof}
Let us set $m=\min(\alpha,\beta,\gamma)$ and $M=\max(\alpha,\beta,\gamma)$.
By symmetry we can assume that $\alpha \geq \beta$.
Let $f(\alpha,\beta,\gamma) = \alpha^2 + \beta^2 + \gamma^2 - 2 \alpha\beta + 2\alpha\gamma + 2\beta\gamma$.
From Lemma~\ref{lem:formula_area_triangle} we have $\operatorname{\bf area}(\Delta) = \sqrt{f(\alpha,\beta,\gamma)}/2$.
As $\alpha^2 + \beta^2 \geq 2\alpha\beta$, we have
\[
f(\alpha,\beta,\gamma)
\geq \gamma^2 + 2\alpha\gamma + 2\beta\gamma
\geq 5 m^2
\]
which proves the lower bound. For the upper bound, if $M=\alpha$ then we can use the fact that $-2 \alpha \beta + 2 \beta \gamma \leq 0$. If $M = \gamma$ then we use
\[
f(\alpha,\beta,\gamma)
= (\alpha-\beta)^2 + \gamma^2 + 2\alpha\gamma + 2\beta\gamma
\leq (\gamma-\beta)^2 + \gamma^2 + 2\alpha\gamma + 2\beta\gamma
\leq 4M^2 + m^2.
\]
To prove the last statement we analyze the function $f(\alpha,\beta,\gamma) = \alpha^2 + \beta^2 + \gamma^2 - 2 \alpha\beta + 2\alpha\gamma + 2\beta\gamma$. For each possibility of maximum and minimum, we just analyze $f$ as a one-variable function. The values of the extrema can be computed by elementary calculus. We summarize this information in the following array.
\[
\begin{array}{l|cccc}
\text{order on $\alpha,\beta,\gamma$} & \operatorname{argmin}(f) & \min(f) & \operatorname{argmax}(f) & \max(f) \\ \hline
m = \beta\ \text{and}\ M = \gamma & \alpha=m & 4Mm + M^2 & \alpha=M & m^2 + 4 M^2 \\ \hline
m = \beta\ \text{and}\ M = \alpha & \gamma=m & M^2 + 4 m^2 & \gamma=M & 4 M^2 + m^2 \\ \hline
m = \gamma\ \text{and}\ M = \alpha & & & & \\
\alpha/\gamma \leq 2 & \beta=m & M^2 + 4m^2 & \beta=M & m^2 + 4M m \\
2 \leq \alpha/\gamma \leq 3 & \beta=M-m & 4M m & \beta=M & m^2 + 4Mm \\
3 \leq \alpha /\gamma & \beta=M-m & 4M m & \beta=m & M^2 + 4m^2 \\
\hline
\end{array}
\]
In the two first cases $m=\beta, M=\gamma$ or $m=\beta, M=\alpha$ we have the lower bound $f(\alpha,\beta,\gamma) \geq 4m^2+M^2$.
In the case $m=\gamma, M=\alpha$, the condition $\operatorname{\bf area}(\Delta) \leq \sqrt{2}\ m$ implies that $\alpha/\gamma \leq 2$. Indeed,
if we had $M/m > 2$ then $\operatorname{\bf area}{\Delta} \geq \sqrt{4Mm}/2 > \sqrt{2}\ m$. And
in the case $\alpha/\gamma \leq 2$, the lower bound $M^2 + 4m^2$ is valid.
\end{proof}
Note that the gap between $\sqrt{5}/2 \simeq 1.118$ and $\sqrt{2} \simeq 1.4142$ is not large. But having this gap is essential as it will allow us to get lower bounds from upper bounds in Section~\ref{sec:lagrange_iet} via the following lemma.
\begin{corollary} \label{cor:distorsion_from_area}
Let $\Delta$ be an admissible triangle with $a$, $b$, $c$, $\alpha$, $\beta$, $\gamma$
as in Lemma \ref{lem:formula_area_triangle}.
Let $m = \min \{\alpha,\beta,\gamma\}$ and $M = \max \{\alpha,\beta,\gamma\}$.
Assume that
$\operatorname{\bf area}(\Delta) \leq \left(\frac{\sqrt{5}}{2} + \varepsilon\right)m$,
for some\, $\varepsilon$, $0 < \varepsilon < \sqrt{2} - \frac{\sqrt{5}}2$.
Then $M \leq (1 + (2\sqrt{2} + \sqrt{5})\varepsilon) m$.
\end{corollary}
\begin{proof}
Because $\varepsilon < \sqrt{2} - \frac{\sqrt{5}}2$ the second half of Corollary~\ref{cor:area_triangle} holds: $M^2 + 4m^2 \leq 4 \left(\operatorname{\bf area}(\Delta)\right)^2$.
Using the hypothesis, we get
$M^2 + 4m^2 \leq 4 ( \frac{\sqrt{5}}2 + \varepsilon)^2 m^2$ and hence
$M^2 \leq (1 + 4\sqrt{5} \varepsilon + 4\varepsilon^2) m^2 <
(1 + 4(\sqrt{2}+\frac{\sqrt{5}}2)\varepsilon) m^2$. Taking square roots in this last inequality and applying the inequality $\sqrt{1+x} \leq 1+x/2$, which is valid for all $x > 0$, we get the result.
\end{proof}
\subsection{$L^\infty$-Delaunay triangulations}
For a general reference on Delaunay triangulations we refer the reader to~\cite{Okabe-tessellations}.
\begin{wrapfigure}{R}{0.45\textwidth}
\centerline{\includegraphics{delaunay.pdf}}
\caption{An $L^\infty$-Delaunay triangulation with one of the maximal squares $S$.}
\label{fig:delaunay}
\end{wrapfigure}
Let $\Gamma \subset \mathbb{C}$ be a finite set of points. A \emph{triangulation} of
$\Gamma$ is a set of triangles with disjoint interiors whose vertex set is
contained in $\Gamma$. Note that we have no maximality assumption here.
The $L^\infty$-\emph{Delaunay triangulation} of $\Gamma$ is defined as follows:
a triangle with vertices $p,q,r \in \Gamma$ belongs to that triangulation
if and only if there exists a square $S \subset \mathbb{C}$ with horizontal and vertical sides
such that $S \cap \Gamma = (\partial S) \cap \Gamma = \{p,q,r\}$. An example of a
Delaunay triangulation is provided in Figure~\ref{fig:delaunay}.
In some cases, there might be more than three points on the boundary of a
square. We will implicitly exclude the case where two points $z$ and $z'$
of $\Gamma$ are on the same horizontal or vertical line, as these
correspond to $\operatorname{\bf N}(z - z') = 0$. Assuming that
$\displaystyle \min_{\stackrel{z,z' \in \Gamma}{z \not= z'}} \operatorname{\bf N}(\Gamma) > 0$,
there are either three or four points on maximal squares. In the latter case, there is an
ambiguity as there are two different ways of making two triangles out of these
four points. We will abuse the terminology and still speak about \emph{the}
Delaunay triangulation for one of the triangulations obtained after making
a choice in each quadruple of points in a maximal square.
\begin{lemma} \label{lem:Linfinity_Delaunay_properties}
Let $\Gamma \subset \mathbb{C}$ be a finite set that contains at least three
points and is such that no pair of points are on the same horizontal or vertical
line. Let:
\begin{itemize}
\item[\em(a)] $C$ be the convex hull of $\Gamma$;
\item[\em(b)] $T$ be the finite collection of closed triangles determined by
the $L^\infty$-Delaunay triangulation of $\Gamma$ (the interiors
of these triangles are disjoint);
\item[\em(c)] $U=\bigcup_{\Delta\in T}\Delta$ be the union of all these triangles.
\end{itemize}
Then the following statements hold.
\begin{itemize}
\item[\bf1.] The $L^\infty$-Delaunay triangulation $T$ contains only admissible triangles.
\item[\bf2.] The set $U$ is simply connected.
\item[\bf3.] The $\operatorname{\bf N}$-length of $\partial U$ is smaller than the $\operatorname{\bf N}$-length of $\partial C$
(where $\partial U$ and $\partial C$ stand for the boundaries of $U$ and $C$, respectively).
\end{itemize}
\end{lemma}
\vspace{1pt}
\begin{proof}
The first statement is immediate from the definition. Indeed, each triangle of $T$
is inscribed in a square with its three vertices on the sides (by definition of
the Delaunay triangulation) and since no pair of points of $\Gamma$ are on the same
horizontal or vertical line, they belong to different sides.
The segments $[p,q]$ on the boundary $\partial U$ of $U$ are the ones such that there
exist arbitrary large squares $S$ with $S \cap \Gamma = \{p,q\}$. Such a segment
needs to be on the boundary.
For the third statement, let $\gamma=[p,q]$ be an edge of the convex hull $C$
of $\Gamma$ that is not an edge of a triangle in $T$. (Thus $\gamma\in\partial C$ but
$\gamma\notin \partial U$).
The line through $\gamma$ separates the plane into two regions, and one of them
contains all points of $\Gamma$ except $p$ and $q$.
Without loss of generality we assume that $\operatorname{Re}(p) < \operatorname{Re}(q)$, $\operatorname{Im}(p) < \operatorname{Im}(q)$ and that
the points of $\Gamma$ are above the line through $p$ and $q$ as in the following picture.
\begin{center}
\includegraphics{boundary_length.pdf}
\end{center}
The segment $\gamma$ is not an edge of a triangle in $T$ if and only if there are points
in the square $S$ which admits $\gamma$ as a chord.
Let $\Gamma_0$ be the set
of points in the interior of $S$ that are different from $p$ and $q$.
Let $p_1$ be the point in $\Gamma_0$ with lowest imaginary part.
Now we proceed inductively until \ $\Gamma_n$ \ by defining
\[
\Gamma_n := \{x \in \Gamma_{n-1} \mid \operatorname{Re}(x) > \operatorname{Re}(p_n) \quad \text{and} \quad
\operatorname{Im}(x) > \operatorname{Im}(p_n)\}.
\]
and, if $\Gamma_n\neq\emptyset$, we continue with picking\, $p_{n+1}\in \Gamma_n$ with
the lowest imaginary part.
Let $p_1,\ldots,p_n$ be the points selected in the above way when the process stops
(i.e., when $\Gamma_n=\emptyset$). By adding two more points $p_{0}=p$ and $p_{n+1}=q$,
we end up with the $(n+2)$ points
$p_0=p,p_1,\ldots,p_n,p_{n+1}=q$, with the edges $[p_{k},p_{k+1}]$,
$0\leq k\leq n$, forming the contour $\phi_{p,q}$ of $\partial U$
between $p$ and $q$.
Now, we claim that $\operatorname{\bf N}(q-p) \geq \sum_{i=0}^n \operatorname{\bf N}(p_{i+1} - p_i)$. This is to say
that the triangle inequality is actually reversed! It follows from the fact
that $\operatorname{\bf N}$ restricted to the positive quadrant is concave.
This completes the proof of Lemma \ref{lem:Linfinity_Delaunay_properties}.
\end{proof}
\subsection{Proof of Theorem~\ref{thm:delta_estimate_in_convex}}\label{sec:proofpack}
Let $\Gamma \subset C$ be a finite set of cardinality $s$ and $C$ its convex hull.
Let $T$ be the $L^\infty$-Delaunay triangulation of $\Gamma$ and let
$U$ be the union of the closed triangles in $T$ (notations just as in
Lemma~\ref{lem:Linfinity_Delaunay_properties}). Next, we establish
a lower bound (see \eqref{eq:bound-on-n}) on the number $n$ of triangles in $T$.
The set $\Gamma$ can be partitioned into the
three subsets $\Gamma=\Gamma_2\cup\Gamma_{bad}\cup\Gamma_{good}$
as follows:
\begin{enumerate}
\item The set $\Gamma_{2}$ of $2$ \emph{special} points that lie on the extreme left and extreme right of $\Gamma$,
\item The set $\Gamma_{bad}=(\Gamma\cap\partial U)\setminus\Gamma_2$ of
$s_{bad}$ points that lie on $\partial U$ but not in
$\Gamma_2$,
\item The set $\Gamma_{good}=\Gamma\setminus(\Gamma_2\cup\Gamma_{bad})$ of remaining $s_{good}=s-2-s_{bad}$ points that lie in the interior of $U$.
\end{enumerate}
Since the $\operatorname{\bf N}$-distance between any two points of $\Gamma$ is at least 1 we
have that $s_{bad} + 2$ is smaller than the $\operatorname{\bf N}$-perimeter of $U$. But
from Lemma~\ref{lem:Linfinity_Delaunay_properties} we know that the $\operatorname{\bf N}$-perimeter
of $U$ is actually smaller than that of $C$. Hence $s_{bad} + 2 \leq p$.
Next, with each triangle $\Delta$ of $T$, we associate a point in $\Gamma$ as follows. There is
exactly one vertex of $\Delta$ for which the vertical line through that point
intersects the interior of the triangle as in the following pictures:
\begin{center}
\includegraphics{triangle1.pdf} \hspace{1cm} \includegraphics{triangle2.pdf}
\end{center}
It is easy to see that
\begin{enumerate}
\item for the (two) points in $\Gamma_{2}$, there are no associated triangles,
\item for each of the $s_{bad}$ points in $\Gamma_{bad}$ there is exactly one associated triangle,
\item for each of the $s_{good}$ points in $\Gamma_{good}$ there are exactly two associated triangles.
\end{enumerate}
In other words, the number of triangles in $T$ is given by the formula $n = 2
s_{good} + s_{bad}$. Now, substituting $s_{good} = s-2-s_{bad}$ and taking into
account the inequality $s_{bad}+2 \leq p$ we obtain
\begin{equation}\label{eq:bound-on-n}
n = 2 s_{good} + s_{bad} = 2s - s_{bad} - 4 \geq 2s - p - 2
\end{equation}
By Corollary~\ref{cor:area_triangle}, each of the triangles in $T$ has area
at least $\frac{\sqrt{5}}{2}$. So
\[
A \geq \frac{\sqrt{5}}{2}\, n \geq \frac{\sqrt{5}}{2} \left(2s - p - 2 \right),
\]
and the inequality claimed in Theorem~\ref{thm:delta_estimate_in_convex} follows.
\subsection{The rectangular case}
The special case where $C\subset \mathbb{R}^{2}=\mathbb{C}$ is a rectangle with sides parallel to the
coordinate axes is addressed by the following result. It is in this form that our packing
result will be used in Section~\ref{sec:interval_recurrence}.
\begin{theorem} \label{thm:rectangular}
Let $C=[x^-,x^+]\times[y^-,y^+]\subset\mathbb{R}^{2}$ be a rectangle of area
$A = (x^+ - x^-)(y^+-y^-)$, and let $\Gamma \subset C$ be a finite subset
of cardinality $s\geq2$.
Set \ $\delta = \min_{\substack{x,y\in C\\ x\neq y}}\limits\, \operatorname{\bf N}(x-y)$ and $A' = A/\delta^2$. Then
\vspace{-2mm}
\begin{equation}\label{eq:rect1}
s\leq \frac{A'}{\sqrt 5}+ \sqrt{2 A'} + 1.
\end{equation}
In particular, for a given $\varepsilon>0$, we have
\begin{equation}\label{eq:rect2}
s\leq\left(\frac 1{\sqrt 5}+\varepsilon\right)\cdot A'
\end{equation}
provided that either $A'$ or $s$ are large enough.
More precisely, for\, $0<\varepsilon<1/2$, each of the following two conditions
\begin{equation}\label{eq:twoconditions}
\text{either \quad {\bf(c1)}}\ A'>\tfrac4{\varepsilon^2},\hspace{12mm} \text{or \quad {\bf(c2)}}\
s>(\tfrac3\varepsilon+1)^2,
\end{equation}
suffices for the inequality \eqref{eq:rect2} to hold.
\end{theorem}
\begin{proof}
We show how to deduce Theorem~\ref{thm:rectangular} from
Theorem~\ref{thm:delta_estimate_in_convex}.
We adopt the notation used in these two results.
By Theorem \ref{thm:delta_estimate_in_convex}, we have
$
s \leq \frac A{\delta^2 \sqrt 5}+\frac{p}{2\delta}+1
$
where $p$ is the $\operatorname{\bf N}$-perimeter of the convex hull of $\Gamma$.
As all quantities in the above inequality are invariant by the linear
action of the diagonal flow $x+iy \mapsto e^t x + i e^{-t} y$ we can
assume that $C$ is a square with side length $\sqrt{A}$. The $\operatorname{\bf N}$-perimeter
is always smaller than $\sqrt{2}/2$ times the euclidean perimeter (since the
euclidean ball of radius $\sqrt{2}$ is contained in the $N$-ball of radius
$1$). Moreover, if $C_1 \subset C_2$ are two convexes, it is well known that
the euclidean perimeter of $C_1$ is smaller than the one of $C_2$. Hence $p
\leq 2\sqrt{2}\, \sqrt{A}$. The equation~\eqref{eq:rect1} follows.
It remains to check the inequality $\frac{\sqrt{2A}+1}A<\varepsilon$, assuming
that $0<\varepsilon<1$ and that at least one of the conditions in
\eqref{eq:twoconditions}, either ({\bf c1}) or ({\bf c2}), holds.
The condition {\bf(c1)}, $A>\frac4{\varepsilon^2}$, implies that $\frac1{\sqrt A}< \frac1{2}$, and
then $\frac{\sqrt{2A}+1}A< \frac{2}{\sqrt A}<\varepsilon$.
The condition {\bf(c2)}, $s>(\frac2\varepsilon+1)^2$, implies that $s\geq25$,
and then~\eqref{eq:rect1} implies
that $s\leq(\sqrt A+1)^2$. We obtain $\sqrt A\geq\sqrt s-1>\frac2\varepsilon$,
and then $A>\frac4{\varepsilon^2}$. Thus
{\bf(c2)} implies {\bf(c1)}, the case already established.
This completes the deduction of Theorem~\ref{thm:rectangular} from Theorem~\ref{thm:delta_estimate_in_convex}.
\end{proof}
\section{Recurrence in the interval} \label{sec:interval_recurrence}
This section is dedicated to the proof of Theorem~\ref{thm:rec01}. In the first
part we prove a technical step involving an estimation
of the measure of points with a lower bound on the rate of recurrence. This proposition uses
the unconventional packing result of Theorem~\ref{thm:delta_estimate_in_convex} (in
its form given in Theorem~\ref{thm:rectangular}) and basic ergodic theory. In a second part we derive
Theorem~\ref{thm:rec01} using the Lebesgue density theorem.
\subsection{An estimate for the measure of badly recurrent points}
The following estimate is used in the proof of Theorem~\ref{thm:rec01}.
\begin{proposition}\label{prop.Vr}
Let \ $T\colon [0,1) \rightarrow [0,1)$ be a measurable map which
preserves the Lebesgue measure $\mu$. \\
Let \ $V\subset [0,1)$ be a non-empty open subinterval.
Set
\[
\rho(x,V)=\inf_{\substack{n\geq1 \\[.4mm] T^nx\in V}} \ n\cdot|T^n(x)-x|\quad
\text{\em(for } \ x\in V),
\]
and for $r > 0$ define the subsets $V_r=\{x\in V\mid \rho(x,V)\geq r\}\subset V$.
Then $\displaystyle \mu(V_r)\leq\frac{\mu(V)}{r\sqrt 5}$.
\end{proposition}
The above proposition is trivial for $r\leq\frac1{\sqrt 5}$
(because then it follows immediately from the inclusion $V_r\subset V$).
Note also that one can recover the recurrence rate $r(T,x)$ from $\rho(x,V)$ as
\[
r(T,x) = \liminf_{\varepsilon_1,\varepsilon_2 \to 0} \rho(x, (x-\varepsilon_1,x+\varepsilon_2)).
\]
\begin{proof}
Let $S\colon V\to V$ be the first return map on $V$ induced by $T$.
Thus
\[
S(j)=T^{F(x)}(x) \quad \text{(for a.a. $x\in V$)},
\]
where $F(x)$ is the minimal integer $n\geq1$ such that $T^n(x)\in V$.
By Kac's lemma, the function $F\colon V\to\mathbb{N}$ is defined almost everywhere and
$\int_{V} F(x)\,dx\leq1$. For $n\geq0$, we have
\[
S^n (x)=T^{F_n(x)}(x), \quad \text{where }
\ F_n(x)=\sum_{k=0}^{n-1} F(S^k x) \quad \text{(for a.a. $x\in V$}).
\]
By the Birkhoff Ergodic Theorem, the pointwise convergence
\begin{equation}\label{eq:individ1}
\lim_{n\to\infty}\frac{F_n(x)}n=G(x) \quad \text{(for a.a. $x\in V$)},
\end{equation}
to some integrable function $G(x)\geq1$ takes place, and
\begin{equation}\label{eq:integralG1}
\int_{V}G(x)\,dx=\int_{V} F(x)\,dx\leq1.
\end{equation}
Denote by $V'$ the subset of those $x\in V$ for which all the values $S^n(x)$,
$F_n(x)$ for all $n \geq 0$ and $G(x)$ are defined and~\eqref{eq:individ1}
holds. Clearly, $\mu(V')=\mu(V)$.
Fix $x\in V'$ and let $\{z_{n}\}_{n\geq0} = \{x_n+ iy_n\}_{n\geq 0}$ be
the sequence in $\mathbb{C}$ defined by the formula
\begin{align*}
x_n&=\operatorname{Re}(z_n)=F_n(x)\in\mathbb{N}\cup\{0\}, \\
y_n&=\operatorname{Im}(z_n)=T^{x_n}(x)=T^{F_n(x)}(x)=S^n(x)\in V.
\end{align*}
(Thus $\{x_n\}$ is a strictly increasing sequence of integers,
with $x_0=0$, $z_0=it$). For an integer $q\geq 1$, let
\begin{align*}
\Gamma_q=\Gamma_q(x)&=\{z_n\mid n\in[0,q-1]\}=\{z_0,z_1,\ldots,z_{q-1}\},\\
\Gamma'_q=\Gamma'_q(x)&=\big\{z_n\mid n\in[0,q-1], \ \text{\small and } \operatorname{\bf N}^{2}(z_n-z_m)\geq r, \
\forall m\in [n+1,q-1]\}\big\} \subset \Gamma_q,\\
\Gamma''_q=\Gamma''_q(x)&=\Gamma_q\setminus\Gamma'_q=\{z_n\mid n\in[0,q-2], \ \text{\small and }
\exists m\in [n+1,q-1] \ \text{\small \ such that } \operatorname{\bf N}^{2}(z_n-z_m)<r\}.
\end{align*}
Let also $C_q(x)=[0,x_q] \times V$ and $A_q(x)=\operatorname{\bf area}(C_q(x))=\mu(V)\,x_q$. Given $\Gamma \subset \mathbb{C}$ as
the one defined above, we set
\begin{equation} \label{eq:delta_definition}
\delta(\Gamma) = \min_{z,z' \in \Gamma} \operatorname{\bf N} (z - z').
\end{equation}
Next we establish the following inequality:
\begin{equation}\label{eq:ineqGpq}
M_x\colon\!=\limsup_{q\to\infty}\limits \frac {|\Gamma'_q(x)|}q\leq\frac{\mu(V)\,G(x)}{r\sqrt5} \quad \ \text{(for $x\in V'$).}
\end{equation}
Let us fix $x\in V'$ and chose an increasing sequence of positive integers $\{q_n\}_{n \geq 0}$ so that
\begin{equation}\label{eq:mt}
M_x=\lim_{n\to\infty}\limits \frac {|\Gamma'_{q_n}|}{q_n}.
\end{equation}
Let us also fix $\varepsilon>0$. Then the inequality
\[
|\Gamma'_{q_n}|\leq \frac{A_{q_n}}{\delta^{2}(\Gamma'_{q_n})}\left(\frac1{\sqrt5}+\varepsilon\right)
\]
holds for all large $n$, in view of \eqref{eq:rect2} in Theorem~\ref{thm:rectangular} and where $\delta$ is defined
by~\eqref{eq:delta_definition}.
(Note that $\Gamma'_q\subset C_q$ and $\lim_{n\to\infty}\limits|\Gamma'_{q_n}|=\infty$ because otherwise $M_x=0$ and~\eqref{eq:ineqGpq} becomes trivial).
Since $\delta^{2}(\Gamma'_q)\geq r$ (in view of the definition of $\Gamma'_q$) and $\varepsilon>0$ is arbitrary, we get \
$
\limsup_{n\to\infty}\limits \ \frac {|\Gamma'_{q_n}|}{A_{q_n}}\leq
\frac 1{r\sqrt5}
$
\ and hence \
$
\limsup_{n\to\infty}\limits \frac {|\Gamma'_{q_n}|}{x_{q_n}}\leq \frac{\mu(V)}{r\sqrt5}
$
\ (as $A_q=\mu(V) x_q$).
Taking in account \eqref{eq:mt} and that \
$\lim_{q\to\infty}\limits\frac{x_q}q=\lim_{q\to\infty}\limits\frac{F_q(x)}q=G(x)$, \
we obtain
$
M_x=\limsup_{q\to\infty}\limits \frac {|\Gamma'_{q_n}|}{q_n}\leq\frac{\mu(V)\,G(x)}{r\sqrt5},
$
and the inequality \eqref{eq:ineqGpq} follows.
Next we observe the inclusions $V_r\cap \Gamma_q(x)\subset \Gamma'_q(x)$
(see the definition of $V_r$ in Proposition~\ref{prop.Vr}) and conclude that
\begin{equation}\label{eq:1vdsum}
\sum_{n=0}^{q-1}\limits 1_{V_r}(S^n(x))=|V_r\cap \Gamma_q(x)|\leq|\Gamma'_q(x)|
\quad \ \text{(for $q\geq2$)}
\end{equation}
where $1_{V_r}$ stands for the characteristic function of the set $V_r$.
Since the map $S\colon V'\to V'$ is measure preserving, integrating~\eqref{eq:1vdsum} results in the inequality
\[
q\mu(V_r)=\int_{V'}\Big(\sum_{n=0}^{q-1} 1_{V_r}(S^n(x))\Big)\,dx
\leq \int_{V'}|\Gamma'_q(x)|\,dx,
\]
whence
\[
\mu(V_r) \leq \int_{V'}\frac{|\Gamma'_q(x)|}q\,dx \leq
\int_{V'}\Big(\sup_{p\geq q}\frac{|\Gamma'_p(x)|}p\Big)\,dx.
\]
Passing to the limit $q\to\infty$, we get
\[
\mu(V_r) \leq \int_{V'}\!\Big(\limsup_{q\to\infty}\frac{|\Gamma'_q(x)|}q\Big)\,dx \leq
\int_{V'} \frac{\mu(V)\,G(x)}{r\sqrt 5}\,dx\leq\frac{\mu(V)}{r\sqrt 5},
\]
in view of \eqref{eq:integralG1} and \eqref{eq:ineqGpq}.
This completes the proof of Proposition \ref{prop.Vr}.
\end{proof}
\subsection{Derivation of Theorem \ref{thm:rec01} (from Proposition \ref{prop.Vr})}
\label{sec:derivation}
\begin{proof}[Proof of Theorem~\ref{thm:rec01}]
Let $r>\frac1{\sqrt5}$ be given. Let $\Phi_N$
be the finite collections of subintervals of $[0,1]$ defined as below
\[
\Phi_N=\big\{[\tfrac nN, \tfrac {n+1}N]\mid 0\leq n\leq N-1\big\} \quad (\text{for }N\geq2).
\]
Each $\Phi_N$ partitions
the unit interval $[0,1]$ into $N$ subintervals of equal lengths $\tfrac1N$ (up to their boundaries).
Recall that for every subinterval $V\subset [0,1]$, the inequality
$\mu(V_r)\leq\frac {\mu(V)}{r\sqrt 5}$ \
holds (by Proposition \ref{prop.Vr}). In particular,
\[
\mu(V_r)\leq\tfrac 1{Nr\sqrt 5}, \quad \text{for any } V\in \Phi_N.
\]
Next we introduce two sequences of sets
\[
W_N=\!\!\bigcup_{V\in\Phi_N}\limits \!\!V_r; \qquad W'_N=\bigcap_{n\geq N}\limits \! W_n
\qquad \text{(for } \ N\geq2),
\]
and two additional sets
\begin{align}
W=&\bigcup_{N\geq2}W'_N= \liminf_{N\to\infty} \ W_N=
\big\{x\in[0,1]\ \big|\ x\in W_N, \ \text{\small for all $N $
large enough}\big\},\label{eq:W}\\
U=&\ [0,1]\!\setminus\! W= \{x\in[0,1] \mid x\notin W_N, \
\text{\small for infinitely many $N$} \big\}.\label{eq:U}
\end{align}
Every subinterval $J\subset[0,1]$ can be covered by $[\mu(J)N]+2$ subintervals
from the collection $\Phi_N$, so
\[
\limsup_{N\to\infty}\ \mu(W_N\cap J) \leq \limsup_{N\to\infty}
\big(\tfrac{[\mu(J)N]+2}{Nr\sqrt 5}\big)
=\tfrac1{r\sqrt 5}\cdot\mu(J),
\]
and hence, for every $N\geq2$,
\[
\mu(W'_N\cap J) \leq
\liminf_{n\to\infty}\,\mu(W_n\cap J)\leq \tfrac1{r\sqrt 5}\cdot\mu(J).
\]
Since $J\subset[0,1]$ is arbitrary and $\tfrac1{d\sqrt 5}<1$, the sets $W'_N$ cannot have Lebesgue density
points, thus $\mu(W'_N)=0$, and hence $\mu(W)=0$.
It follows that $\mu(U)=\mu([0,1]\!\setminus\!W)=1$.
Next fix $x\in U$ and set $H_x=\{n\geq2\mid x\notin W_n\}\subset\mathbb{N}$. By definition
of $U$ (see \eqref{eq:U}), the set $H_x$ is infinite.
Fix $N\in H_x$. Observe that \ $x\in V$,
for some $V\in\Phi_N$ (as $\bigcup_{V\in\Phi_N}\limits \!\!V=[0,1]$),
while \ $x\notin V_r$ \ (as $x\notin W_N$). It follows that
\[
\rho(x,V)=\inf_{\substack{n\geq1 \\[.4mm] T^nx\in V}} n\cdot|T^n(x)-x|<r.
\]
We obtain (in view of the implication \
$\{x,T^nx\}\subset V\in \Phi_{N}\!\implies\! |T^nx-x|\leq\frac1N$) \ that
\[
\inf_{\substack{n\geq1 \\[.4mm] |T^nx-x|\leq\frac1N}}\!\! n\cdot|T^n(x)-x|< r, \qquad
\text{for all } \ N\in H_x.
\]
Taking in account that $H_x$ is infinite, one concludes that $r(T,x)=\liminf_{n\to\infty} \ n\,|T^n(x)-x|\leq r$.
As the selection $x \in U$ and $r>\frac1{\sqrt5}$ are arbitrary and $\mu(U)=1$, the proof
of Theorem~\ref{thm:rec01} follows.
\end{proof}
\section{Lagrange constants of interval exchange transformations}
\label{sec:lagrange_iet}
Our proof of Theorem~\ref{thm:lagrange} uses translation surfaces that can be thought
as suspension flows of interval exchange transformations. The Lagrange spectrum
of an interval exchange transformation will now be studied through the
$\operatorname{\bf N}$-norm of edges that are part of some specific triangulation.
\subsection{From interval exchange transformations to translation surfaces}
First, we define translation surfaces. For more details, we invite the reader to
consult the survey by Masur and Tabachnilov~\cite{MasurTabachnikov}.
A \emph{translation surface} is a surface that is obtained from gluing
$2d$ euclidean triangles by identifying their edges by translation. The simplest example
are tori $\mathbb{C} / \Lambda$ where $\Lambda$ is a lattice. The torus $\mathbb{C} / \Lambda$
with $\Lambda = \mathbb{Z} u \oplus \mathbb{Z} v$ is obtained by gluing together the two triangles
with sides respectively $(u, -u+v, -v)$ and $(v, -u, u-v)$. In that case we have $d=1$.
(See Figure~\ref{fig:torus}).
\begin{figure}[!ht]
\begin{center}\includegraphics{torus.pdf}\end{center}
\caption{The fundamental domain of the torus seen as the gluing of two
euclidean triangles by translations.}
\label{fig:torus}
\end{figure}
Equivalently, a translation surface is a compact surface $X$ endowed with an
atlas defined on $X$ minus a finite (non-empty) set of points $\Sigma \subset
X$ with values in $\mathbb{C}$ such that coordinate changes are translations. (We assume
that the atlas is maximal for sake of uniqueness). It is easy to see that a
surface glued from euclidean triangles has such a geometric structure. Conversely,
on a translation surface there always exists a triangulation whose edges are flat
segments, and therefore the two definitions are equivalent.
Two translation surfaces $(X,\Sigma)$ and $(X',\Sigma')$ are isomorphic if
there exists a homeomorphism $\phi:X \to X'$ such that $\phi(\Sigma) = \Sigma'$
and for every chart $g: U \to \mathbb{C}$ of $X'$, $g \circ \phi$ is a chart of $f$. If the two
surfaces are given by a triangulation, the surfaces are isomorphic if and only if
one can pass from one to the other using edge flips (that is, we are
allowed to paste two triangles together and cut the resulting quadrilateral
along the other diagonal).
A point in the surface that is not a vertex of a triangle is
called a \emph{regular point}. The (image of the) vertices in the surface are called
the \emph{singularities}. As there are identifications, there can be fewer singularities
in the surface than vertices. Around each singularity, there is a well defined angle that
is a multiple of $2\pi$. If a translation surface $X$ is made of $2d$ triangles
then the set of conical angles of the singularities $2k_1 \pi, 2k_2 \pi,
\ldots, 2k_n \pi$ satisfies the relation $d = k_1+k_2+\ldots+k_n$. In the torus
of Figure~\ref{fig:torus}, we have $d=1$, $n=1$ and $k_1=2\pi$.
A translation surface inherits a translation structure: that is, given a point $p$ on the surface
and a vector $v \in \mathbb{C}$ one can define $p + v$ on the surface unless the segment
$p + tv$ contains a vertex for some $t$ with $0 \leq t < 1$. In general, we do not have $p + (v+w) = (p + v) + w$.
The \emph{(vertical) translation flow} on $X$ is the flow defined (almost everywhere) by
$\phi_t(p) = p + t \sqrt{-1}$.
A \emph{saddle connection} in a translation surface is a straight-line segment
that joins two singularities.
An horizontal segment $I$ in $X$ is \emph{admissible} if the orbits of its left and
right extremities under the translation flow have the following property: either
in the past or in the future, the orbit hits a singularity before returning to
the interval.
\begin{proposition}
Let $X$ be a translation surface made of $2d$ triangles and $I \subset X$ an admissible
horizontal interval.
The first return map $T$ of the flow on $I$ is an interval exchange
transformation. Furthermore, if $X$ has no vertical saddle connection then $T$
satisfies the Keane condition and the number of subintervals in $T$ is $d+1$.
\end{proposition}
In the case of the torus ($d=1$) the first return maps on admissible intervals are rotations
or 2-i.e.t.
We will denote by $\mathcal{C}(d)$ the set of translation surfaces obtained by
gluing $2d$ triangles \footnote{In Teichm\"uller theory, $\mathcal{C}(d)$ is just the
finite union of strata of translation surfaces with given dimension. For example one
has $\mathcal{C}(2) = \mathcal{H}(0)$, $\mathcal{C}(3) = \mathcal{H}(0,0)$, $\mathcal{C}(4) = \mathcal{H}(0,0,0) \cup \mathcal{H}(2)$
and $\mathcal{C}(5) = \mathcal{H}(0,0,0,0) \cup \mathcal{H}(2,0) \cup \mathcal{H}(1,1)$.}.
\subsection{Lagrange constants, best approximations and Delaunay triangulations}
Now we explain how Lagrange constants of interval exchange transformation can be computed
from the $\operatorname{\bf N}$-norm of holonomies of saddle connections.
Let $X$ be a translation surface. To a saddle connection can be associated a
vector in $\mathbb{C}$ that is called its
\emph{holonomy}. It corresponds to the displacement induced on the translation
structure while traveling along this segment. Given a translation surface $X$
we denote by $V(X) \subset \mathbb{C}$ the set of holonomies of saddle connection in
$X$.
\begin{theorem}[\cite{Vorobets}, \cite{HubertMarcheseUlcigrai}]
\label{thm:a}
Let $X$ be a translation surface. We define
\[
\operatorname{a}(X) := \liminf_{\stackrel{v\in V(X)}{\operatorname{Im}(v) \to \infty}} \frac{\operatorname{\bf N}^{2}(v)}{\operatorname{\bf area}(X)},
\]
where $\operatorname{\bf N}(v) := \sqrt{|\operatorname{Re}(v)|\ |\operatorname{Im}(v)|}$, for vectors $v \in \mathbb{C}$.
Let $T$ be an interval exchange transformation that is the induced map of the
translation flow of $X$ on some admissible horizontal interval.
Then $\mathcal{E}(T) = \operatorname{a}(X)$.
\end{theorem}
In the above theorem, the minimum is taken over all saddle connections in
$V(X)$. We will show in Lemma~\ref{lem:best_approx_vs_delaunay} that it is enough to restrict the $\liminf$ to
a subset of edges. Then we show that this subset of edges is exactly
the set of edges of the Delaunay triangulations of some deformations
of $X$.
We first need to introduce "quadrants" of saddle connections
from~\cite{Marchese-Khinchin} and~\cite{DelecroixUlcigrai}. Let $X$ be a
translation surface. Given two segments with the same starting point they
have a well defined angle. If the starting point has a total angle
$2k\pi$ then the angle between the segments is between $0$ and $2k\pi$.
Let us consider the vertical half lines that start from the singularities
in direction $\sqrt{-1}$. Up to a change of orientation, a saddle connection can
always be made to start with an angle in $[-\pi/4,\pi/4]$ with respect
to one of these outgoing vertical separatrices. Let us fix a numbering
of these half lines from $1$ to $d$. We associate to each of them
a pair $V^i_\ell(X)$ and $V^i_r(X)$ of subset of saddle connections
that are the one with angle respectively in $[-\pi/4,0]$ and $[0,\pi/4]$
with the corresponding vertical.
A saddle connection is called a \emph{best approximation} if it is the diagonal
of an immersed rectangle in the surface whose boundary edges are horizontal and
vertical. Equivalently, $\gamma \in V^{i}_s(X)$ where $i \in \{1,2,\ldots,d\}$
and $s \in \{\ell,r\}$ is not a best approximation if there exists $\eta \in
V^{i}_s(X)$ (the same quadrant) so that $|\operatorname{Re}(\eta)| < |\operatorname{Re}(\gamma)|$ and
$|\operatorname{Im}(\eta)| < |\operatorname{Im}(\gamma)|$.
We will denote by $V_{ba}(X)$ the set of holonomies of best approximation on $X$. From its definition
it follows that
\[
\operatorname{a}(X) = \inf_{v \in V_{ba}(X)} \operatorname{\bf N}(v) = \inf_{v \in V(X)} \operatorname{\bf N}(v)
\]
where $\operatorname{a}(X)$ is defined in Theorem~\ref{thm:a}.
We now show that best approximations can be seen as the edges of some Delaunay
triangulations.
The group
$\operatorname{SL}(2,\mathbb{R})$ acts on the set of (equivalence classes) of translation surfaces
through its linear action on $\mathbb{R}^2$. The subaction of the diagonal subgroup
$\displaystyle g_t = \begin{pmatrix}e^t & 0 \\ 0 & e^{-t}\end{pmatrix}$ is
called the \emph{Teichm\"uller flow}. Note that this action is also well
defined on points and segments (that is, given a pair $(X,p)$ (or $(X,\gamma)$)
made of a translation surface and a point, or a segment, and a matrix
$m$, the image of $p$ (or $\gamma$) in $m \cdot X$ is well defined).
As in the case of the plane, one can define the Delaunay triangulation of a
translation surface $X$ by considering maximal immersed squares. The following
two lemmas are elementary.
\begin{lemma}
Let $X$ be a translation surface with neither a horizontal nor a vertical saddle
connection. Then for all $t \in \mathbb{R}$, $g_t X$ has a well defined Delaunay
triangulation except for a discrete set of times $t_n$ for which some quadruple
of singularities are on the boundary of an immersed square (in which case
there is no uniqueness of Delaunay triangulation).
\end{lemma}
\begin{lemma} \label{lem:best_approx_vs_delaunay}
Let $X$ be a translation surface. For a saddle connection $\gamma$ in $X$ the following are equivalent:
\begin{enumerate}
\item $\gamma$ is a best approximation,
\item there exists $t \in \mathbb{R}$ such that the $L^\infty$-Delaunay triangulation of $g_t X$ contains $g_t \gamma$ as an edge.
\end{enumerate}
\end{lemma}
\begin{proof}
We just need to remark that any rectangle immersed in $X$ can be turned into a square using the $g_t$ action.
\end{proof}
\subsection{At the bottom of the Lagrange spectrum are golden surfaces}
Let us introduce the surfaces that will be shown to be exactly the ones that
minimize the quantity $\operatorname{a}(X)$ of Theorem~\ref{thm:a}. Let $\Lambda$ be the lattice
$\Lambda = \mathbb{Z} (-1,1) \oplus \mathbb{Z} (\phi-1, \phi)$ where $\phi = (\sqrt{5}+1)/2$ is
the golden ratio. We call any lattice in the family $g_t \Lambda$ a
\emph{golden lattice} and the associated quotients $\mathbb{C} / g_t \Lambda$ a
\emph{golden torus}. We also call any parallelogram generated by a basis of
$\Lambda$ a \emph{golden parallelogram}. A \emph{golden surface} in $\mathcal{C}(d)$ is
a translation surface obtained by gluing together $d$ identical golden
parallelograms (each obtained by gluing $2$ triangles). In geometric terms, such
surface is a ramified covering of degree $d$ of a golden torus.
In this section we prove the following result
\begin{theorem} \label{thm:lagrange_surface}
There exists $\varepsilon_0$ such that the following holds.
If $X$ is a translation surface in $\mathcal{C}(d)$ such that
\[
\inf_{v \in V(X)} \frac{\operatorname{\bf N}^{2}(v)}{\operatorname{\bf area}(X)} \geq \frac{1}{d\sqrt{5}} - \frac{\varepsilon_0}{d^2}
\]
then $X$ is a golden surface.
\end{theorem}
Together with Theorem~\ref{thm:a}, Theorem~\ref{thm:lagrange_surface} implies~Theorem~\ref{thm:lagrange}.
In order to simplify notation in the proof, we will from now on always deal with surfaces such that $\operatorname{\bf area}(X) = d$. That
way the mean area of a triangle is $1/2$ independently of $d$.
\begin{lemma} \label{lem:low_to_up_bound}
There exist constants $\varepsilon_1 > 0 $ and $C_1 > 1$ such that the following holds.
For any area $d$ translation surface $X$ in $\mathcal{C}(d)$ such that for some $\varepsilon < \varepsilon_1 / d$
we have
\[
\inf_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v) \geq \frac{1}{\sqrt{5}} - \varepsilon.
\]
Then
\[
\sup_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v) \leq \frac{1}{\sqrt{5}} + C_1 d \varepsilon.
\]
\end{lemma}
\begin{proof}
Let us consider a translation surface $(X,\omega)$ of area $d$ and let $\varepsilon < \varepsilon_1/d = \frac{2\sqrt{2} - \sqrt{5}}{20d} \simeq \frac{0.03}{d}$.
Assume that
\[
\inf_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v) \geq \frac{1}{\sqrt{5}} - \varepsilon.
\]
As a consequence of Corollary~\ref{cor:area_triangle}, we have for any translation surface
\begin{equation} \label{eq:bound_triangle}
\inf \{\operatorname{\bf area}(\Delta): \text{$\Delta$ admissible triangle in $X$}\}
\geq
\frac{\sqrt{5}}{2} \inf_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v)
\geq
\frac{\sqrt{5}}{2} \left( \frac{1}{\sqrt{5}} - \varepsilon \right).
\end{equation}
Let us consider the $L^\infty$-Delaunay triangulation $T$ of the surface $X$
and let $\Delta_0$ be one triangle in $T$. Using the fact that
the sum of the areas of the $2d$ triangles from $T$ is $\operatorname{\bf area}(X) = d$ we have that
\[
\operatorname{\bf area}(\Delta_0) \leq d - (2d-1)\ \min_{\Delta \in T} \operatorname{\bf area}(\Delta).
\]
Now, using~\eqref{eq:bound_triangle} we obtain that
\begin{align*}
\operatorname{\bf area}(\Delta_0)
& \leq d - \left(2d-1\right) \frac{\sqrt{5}}{2} \left(\frac{1}{\sqrt{5}} -\varepsilon\right) \\
& \leq \left(\frac{1}{\sqrt{5}} - \varepsilon \right)
\left( \frac{\sqrt{5}d}{1 - \sqrt{5} \varepsilon} - d\sqrt{5} + \frac{\sqrt{5}}{2}\right) \\
& \leq \left( \frac{1}{\sqrt{5}} - \varepsilon \right)
\left( \sqrt{5} d (1 + 2\sqrt{5} \varepsilon) - d \sqrt{5} + \frac{\sqrt{5}}{2} \right) \\
& \leq \left( \frac{1}{\sqrt{5}} - \varepsilon \right)
\left( \frac{\sqrt{5}}{2} + 10 d \varepsilon \right)
\leq \left( \frac{\sqrt{5}}{2} + 10 d \varepsilon \right) \inf_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v).
\end{align*}
Here we used the inequality $1/(1-\sqrt{5}\varepsilon) \leq 1 + 2 \sqrt{5} \varepsilon$ which is valid since $\sqrt{5}\varepsilon < 1/2$. From our assumption, $10d\varepsilon < \sqrt{2} - \sqrt{5}/2$, and we can apply Lemma~\ref{cor:distorsion_from_area} and get that
\[
\sup_{v \in V_{ba}(X)} \operatorname{\bf N}^{2}(v) \leq \left(1 + \frac{\sqrt{5}+1}{2} 10 d \varepsilon \right) \left( \frac{1}{\sqrt{5}} - \varepsilon \right)
\leq \frac{1}{\sqrt{5}} + C_1 d \varepsilon
\]
where $C_1 = 10 ( 2\sqrt{2} + \sqrt{5}) + 1/2 \leq 52$.
\end{proof}
Let us define the following distance between vectors
\[
\operatorname{\bf dist}((x_1,y_1),(x_2,y_2)) =
\left\{\begin{array}{ll}
1 & \text{if $\operatorname{sgn}(x_1) \not= \operatorname{sgn}(x_2)$ or $\operatorname{sgn}(y_1) \not= \operatorname{sgn}(y_2)$}\\
\max\left( \left|\log\left(\frac{x_1}{x_2}\right)\right|, \left|\log\left(\frac{y_1}{y_2}\right)\right|\right) & \text{otherwise}
\end{array} \right.
\]
Note that $\operatorname{\bf dist}$ is invariant under the action of diagonal invertible matrices: in other words, for any nonzero real numbers $\alpha$ and $\beta$ we have
\[
\operatorname{\bf dist}((\alpha x_1, \beta y_1), (\alpha x_2, \beta y_2)) = \operatorname{\bf dist}((x_1,y_1),(x_2,y_2)).
\]
Let also $\tau$ be the linear map defined by
\[
\tau(x,y) = (-x/\phi, \phi y), \qquad \text{where \ $\phi = \frac{1+\sqrt{5}}{2}$}.
\]
Note that the only lattices satisfying $\tau(\Lambda) = \Lambda$ are the golden lattices.
\begin{lemma} \label{lem:parallelogram}
There exist constants $\varepsilon_2 > 0$ and $C_2 > 1$ such that for any $\varepsilon < \varepsilon_2$
and any $\zeta_\ell = (x_\ell, y_\ell), \zeta_r = (x_r, y_r), \zeta = (x,y) \in \mathbb{C}$, if the conditions
\begin{itemize}
\item $x_\ell < 0$ and $x_r > 0$,
\item $0 < y_\ell < y_r < y$,
\item all of $\operatorname{\bf N}^2(\zeta_\ell)$, $\operatorname{\bf N}^2(\zeta_r)$, $\operatorname{\bf N}^2(\zeta)$, $\operatorname{\bf N}^2(\zeta_\ell - \zeta_r)$, $\operatorname{\bf N}^2(\zeta - \zeta_\ell)$ and $\operatorname{\bf N}^2(\zeta - \zeta_r)$
are in between $1/\sqrt{5} - \varepsilon$ and $1/\sqrt{5} + \varepsilon$,
\end{itemize}
hold, then all of $\operatorname{\bf dist}(\zeta_r,\, \zeta-\zeta_\ell)$, $\operatorname{\bf dist}(\zeta_\ell,\, \zeta-\zeta_r)$, $\operatorname{\bf dist}(\tau(\zeta_\ell), \zeta_r)$, $\operatorname{\bf dist}(\tau(\zeta_r),\, \zeta-\zeta_r)$, $\operatorname{\bf dist}(\zeta_\ell, \tau(\zeta-\zeta_\ell))$ are smaller than $C_2 \varepsilon$.
\end{lemma}
\begin{proof}
Up to rescaling we can assume that $x_\ell = -1$. Once $x_\ell$ is fixed, the maps
\[
(y_\ell, x_r, y_r) \mapsto (\operatorname{\bf N}^2(\zeta_\ell), \operatorname{\bf N}^2(\zeta_r), \operatorname{\bf N}^2(\zeta_r - \zeta_\ell))
\quad \text{and} \quad
(y_\ell, x, y) \mapsto (\operatorname{\bf N}^2(\zeta_\ell), \operatorname{\bf N}^2(\zeta), \operatorname{\bf N}^2(\zeta-\zeta_\ell))
\]
have invertible derivative at the point
\[
y_\ell = \frac{1}{\sqrt{5}},\ x_r = \phi - 1,\ y_r = \frac{\phi}{\sqrt{5}},\ x = \phi - 2,\ y = \frac{\phi^2}{\sqrt{5}}.
\]
Moreover, the above point is the unique solution of $\operatorname{\bf N}^2(\zeta_\ell) = \operatorname{\bf N}^2(\zeta_r) = \operatorname{\bf N}^2(\zeta) = \operatorname{\bf N}^2(\zeta-\zeta_\ell) = \operatorname{\bf N}^2(\zeta-\zeta_r) = \frac{1}{\sqrt{5}}$. One concludes using the inverse function theorem.
\end{proof}
Recall that $V_{ba}(X)$ denote the holonomies of best approximations. Given a
quadrant $i$ in $X$ we denote by $V_{ba}^{(i)}(X)$ the set of holonomies of
saddle connections restricted to the $i$-th quadrant.
\begin{lemma} \label{lem:ba_far_appart}
There exist constants $\varepsilon_3 > 0$ and $C_3 > 0$ such that if $X$ is any area $d$ surface in $\mathcal{C}(d)$ such that
\[
\forall v \in V_{ba}(X),\quad \frac{1}{\sqrt{5}} - \varepsilon_3 < \operatorname{\bf N}^2(v) < \frac{1}{\sqrt{5}} + \varepsilon_3
\]
then in any quadrant $i$ of $X$ we have
\[
\forall u,v \in V^{(i)}_{ba}(X), u \not= v, \qquad \operatorname{\bf dist}(u,v) > C_3.
\]
\end{lemma}
\begin{proof}
Choose an $\varepsilon_3$ so that we can apply Lemma~\ref{lem:parallelogram}. In a given fixed quadrant $i$
holonomies can be identified with saddle connections. Lemma~\ref{lem:parallelogram} implies that
best approximations are far apart.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{thm:lagrange_surface}]
Let $d \geq 1$ and $\varepsilon > 0$ be such that
\[
\varepsilon < \min\left(\frac{\varepsilon_1}{d}, \frac{\varepsilon_2}{C_1 d},\ \frac{\varepsilon_3}{C_1 d},\ \frac{C_3}{C_1 C_2 d^2}\right).
\]
Let $X \in \mathcal{C}(d)$ be a translation surface so that
\[
\inf_{v \in V_{ba}(X)} \operatorname{\bf N}^2(v) \geq \frac{1}{\sqrt{5}} - \varepsilon.
\]
We will show that $X$ is actually a golden surface. Because $\varepsilon <
\varepsilon_1 / d$ we can apply Lemma~\ref{lem:low_to_up_bound}. Denoting
$\varepsilon' = C_1 d \varepsilon$ we have that
\begin{equation} \label{eq:all_sc_close}
\forall v \in V_{ba}(X), \quad \frac{1}{\sqrt{5}} - \varepsilon' \leq \operatorname{\bf N}^2(v) \leq \frac{1}{\sqrt{5}} + \varepsilon'.
\end{equation}
Morever $\varepsilon'$ satisfies
\[
\varepsilon' < \min\left(\varepsilon_2,\ \varepsilon_3,\ \frac{C_3}{C_2 d}\right).
\]
We now show that any best approximation is part of a triangulation close to a golden
triangulation. In a moment we will use a fixed point argument to show
that $X$ is itself a golden surface.
A quadrilateral $q$ in $X$ is called \emph{admissible} if there exists an
immersed rectangle $R$ with horizontal and vertical sides such that there is exactly
one vertex of $q$ on each side of $R$. It is easy to see that an admissible
quadrilateral can be decomposed into two admissible triangles in two ways by
adding either of the two diagonals of $q$. The two diagonals of an admissible
quadrilateral $q$ will be called left-right and top-bottom diagonals. Given an
admissible quadrilateral, we can identify each side by its position: bottom
right, bottom left, top right, top left. The slopes of the bottom right and top
left sides are positive and following~\cite{DelecroixUlcigrai} we will say that
they are \emph{right slanted}. Similarly the bottom left and top right sides
are \emph{left slanted}.
\begin{figure}[!ht]
\begin{minipage}{0.3\textwidth}
\centerline{\includegraphics{pil_pir.pdf}}
\subcaption{An admissible quadrilateral $q$. The sides $\zeta_{b\ell}$ and $\zeta_{tr}$ are left slanted
while $\zeta_{br}$ and $\zeta_{t\ell}$ are right slanted.}
\label{fig:pil_pir}
\end{minipage}
\hspace{0.1\textwidth}
\begin{minipage}{0.6\textwidth}
\centerline{\includegraphics{left_move.pdf} \hspace{1cm} \includegraphics{right_move.pdf}}
\subcaption{A left move followed by a right move on a golden parallelogram. The initial quadrilateral has blue right slanted and
green left slanted sides. The top-bottom diagonals are in red. The sides of the new quadrilateral are dashed.}
\end{minipage}
\caption{Quadrangulations and diagonal changes.}
\label{fig:quad_and_moves}
\end{figure}
Let $Q$ be a quadrangulation of $X$. We denote by $E_\ell(Q)$ and $E_r(Q)$ the left
slanted and right slanted sides of $Q$. We measure how $Q$ is close to a quadrangulation
into golden parallelograms with the following function
\[
g(Q) = \max \left(
\max_{\zeta \in E_r,\zeta' \in E_r} \operatorname{\bf dist}(\zeta, \zeta'),\,
\max_{\zeta \in E_\ell,\zeta' \in E_\ell} \operatorname{\bf dist}(\zeta, \zeta'),\,
\max_{\zeta \in E_r,\zeta' \in E_\ell} \operatorname{\bf dist}(\tau(\zeta), \zeta'),\,
\right).
\]
It is clear that $g(Q) = 0$ if and only if $Q$ is a golden quadrangulation.
Let $\varepsilon'' = d C_2 \varepsilon'$.
\textbf{claim 1:} Let $\zeta_0$ be a right slanted best approximation in $X$. Then there exists a
unique quadrangulation $Q_0$ of $X$ into admissible quadrilaterals that admits $\zeta_0$ as one
of its sides and so that $g(Q_0) < \varepsilon''$.
Since $\varepsilon' < \varepsilon_2$, it follows from Lemma~\ref{lem:parallelogram}
that $\zeta_0$ is the bottom right side of a unique quadrilateral so that its bottom left side $\zeta_{b\ell}$, its top
left side $\zeta_{t\ell}$ and its top right side $\zeta_{tr}$ satisfy that all of $\operatorname{\bf dist}(\zeta_0, \zeta_{t\ell})$,
$\operatorname{\bf dist}(\zeta_{b\ell}, \zeta_{tr})$ and $\operatorname{\bf dist}(\tau(\zeta_0), \zeta_{b\ell})$ are smaller than $C_2 \varepsilon'$.
We denote this quadrilateral by $q(\zeta_0)$.
Similarly, given a left slanted best approximation $\zeta$ one can also build a
unique quadrilateral so that its bottom left side $\zeta_{b\ell}$ is
$C_2\varepsilon'$-close to $\tau^{-1}(\zeta)$.
Using these two rules we can build step by step a quadrangulation of $X$. More precisely, starting from $q_0$ we consider
its top sides and construct new quadrilaterals from these two. Then we repeat the operations with the newly created sides.
By construction, either the newly created top side will coincide with an
already constructed bottom side of another quadrilateral, or
we will have some non-trivial intersection between two constructed
parallelograms. Let us show that this second case cannot happen. Let us
consider a chain $q_0, q_1, \ldots, q_k$ of adjacent quadrilaterals such
that the bottom sides of $q_0$ and $q_k$ belong to the same bundle of $X$ and
the bundles of $q_i$ for $i=0,\ldots,k-1$ are disjoint. Necessarily $k \leq d$,
and hence the bottom sides of $q_k$ are $k C_2 \varepsilon'$-close to those of
$q_0$. As $k C_2 \varepsilon' \leq \varepsilon'' \leq C_3$,
Lemma~\ref{lem:ba_far_appart} implies that $q_0 = q_k$. This finishes the proof of the claim.
We will now use claim~1 to show that the surface $X$ is itself a golden
surface. In order to do so, we analyze how the different quadrangulations of
claim~1 are related to each other. The relation between the various
quadrangulations correspond to a particular case of the so called
Ferenczi-Zamboni induction~\cite{Ferenczi-induction} (see also~\cite{DelecroixUlcigrai}
for a particular case related to quadrangulations).
Given two admissible quadrangulations $Q$ and $Q'$ of $X$ we say that $Q'$ is obtained from $Q$ by a
\emph{left move} if the left slanted sides of $Q$ and $Q'$ are equal and the right slanted
sides of $Q'$ are the top-bottom diagonals of quadrilaterals of $Q$. We define right moves similarly. See also Figure~\ref{fig:quad_and_moves}.
By the uniqueness in claim~1, there exists a biinfinite sequence of
quadrangulations of $X$ into admissible quadrilaterals \ldots, $Q_{-1}, Q_0,
Q_1, Q_2, \ldots$ each of them satisfying the claim, and such that $Q_{n+1}$ is
obtained from $Q_n$ by a left move followed by a right move.
Recall that the bundles in $X$ are numbered. Hence each quadrilateral also
inherits a number given by the bundle it belongs to. We say that two
quadrangulations $Q$ and $Q'$ are \emph{combinatorially equivalent} if
for each $i \in \{1,\ldots,d\}$, the labels of the quadrilaterals
on the top left and top right of the quadrilateral labeled $i$ are the same
for $Q$ and $Q'$.
It is easy to see that there are finitely many possible combinatorial types
of quadrangulations. Moreover, if $Q'$ is obtained by a left or right move
from $Q$ then the combinatorial type of $Q'$ is only determined by the
combinatorial type of $Q$. We refer the reader to~\cite{DelecroixUlcigrai}
or~\cite{Ferenczi-induction} for these two elementary facts. Combining these
two facts, we see that the sequence of combinatorial types of the quadrangulations $(Q_n)_{n
\in \mathbb{Z}}$ is periodic for some period $p$. Since a left or right move operates as a linear
transformation on the holonomies of the sides, there exists a $2d \times 2d$ matrix $A$
with non-negative integer coefficients so that the holonomies of the sides of $Q_p$ are the images
of the side of $Q_0$ by $A$. Let $v_0$ be the holonomy of $\zeta_0$. Let $Q'_0$ be
the quadrangulation with the same combinatorics of $Q_0$ but such that all right
slanted sides have holonomy $v_0$ and all left slanted sides have holonomy $\tau(v_0)$.
The quadrangulation $Q'_0$ is a golden quadrangulation of another translation surface.
By construction, the real and imaginary parts of holonomies of $Q'_0$ are eigenvectors
of $A$ (namely real parts are multiplied by $\phi^{-2p}$ and imaginary parts by $\phi^{2p}$).
Applying the Perron-Frobenius theorem to the real and imaginary parts of the holonomies
we obtain the uniqueness of the fixed point (up to scalar multiples). Hence, $Q'_0 = Q_0$ and $X$
is a golden surface.
\end{proof}
\bibliographystyle{amsplain}
| {
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The Puppy Episode is een dubbellange aflevering van de Amerikaanse televisieserie Ellen, die uitgezonden werd op 30 april 1997 (vierde seizoen, nr. 22/23). Het scenario was van de hand van Ellen DeGeneres, en Gil Junger was verantwoordelijk voor de regie. Deze aflevering is bijzonder omdat het titelpersonage Ellen Morgan erin uit de kast komt. Twee weken daarvoor was Ellen DeGeneres zelf uit de kast gekomen. Het was een novum voor Amerikaanse televisie dat een homoseksueel hoofdpersonage door een openlijk homoseksueel acteur werd gespeeld. Deze controversiële aflevering van Ellen behoorde tot de beste bekeken (42 miljoen kijkers in de V.S.) en best gewaardeerde afleveringen van de serie. De aflevering werd bekroond met een Emmy Award voor 'Outstanding Writing in a Comedy Series', een GLAAD Media Award en een Peabody Award.
Rolverdeling
Naast de vaste bezetting van Ellen DeGeneres (Ellen), Joely Fisher (Paige), Jeremy Piven (Spence), David Anthony Higgings (Joe), Clea Lewis (Audrey) en Patrick Bristow (Peter), spelen Laura Dern, Steven Eckholdt en Oprah Winfrey belangrijke gastrollen, respectievelijk de vrouw op wie Ellen verliefd wordt, Ellens oud-studiegenoot en Ellens psychotherapeut. Daarnaast zijn er vele cameo's van bekende lesbiennes (Melissa Etheridge, k.d. lang en Jenny Shimizu), Ellens moeder (Betty DeGeneres) en Hollywoodacteurs die Ellens coming-out steunden (Gina Gershon, Demi Moore, Billy Bob Thornton en Dwight Yoakam). Onder de figuranten zijn voor de oplettende kijker nog meer lesbische bekendheden te ontdekken, zoals Leisha Hailey (toen de partner van k.d. lang) en Judy Wieder (hoofdredacteur van The Advocate). De samenstelling van de uitzending geeft aan dat men zich ervan bewust was dat met The Puppy Episode televisiegeschiedenis werd geschreven.
Synopsis
Deel 1
Ellen gaat uit eten met een oud-studiegenoot, Richard (Steven Eckholdt), die op doorreis in L.A. is. Hij stelt Ellen voor aan zijn collega Susan (Laura Dern) en tussen hen blijkt het te klikken. Op zijn hotelkamer doet Richard een versierpoging, maar Ellen is daar niet van gediend en gaat snel weg. Op de gang komt ze Susan tegen, die haar uitnodigt op haar kamer. Ellen lucht haar hart over Richards gedrag en vraagt of Susan en Richard ooit iets hebben gehad. Daarop vertelt Susan dat ze lesbisch is en dat ze in de veronderstelling was dat Ellen dat ook was. Ellen schrikt en ontkent in alle toonaarden. Ze ontvlucht Susans kamer en klopt bij Richard aan om alsnog op zijn avances in te gaan. De volgende dag schept Ellen tegen haar vrienden op over haar avontuurtje met Richard, maar tegenover haar therapeut (Oprah Winfrey) biecht ze op dat seks met Richard op niets is uitgelopen, omdat ze niet de juiste gevoelens voor hem heeft. Op de vraag van haar therapeut of ze die gevoelens weleens voor iemand anders heeft gehad, bekent Ellen dat ze verliefd is op Susan. In de veronderstelling dat Richard en Susan de volgende dag beide vertrekken, gaat Ellen naar het vliegveld om Susan te vertellen dat ze gelijk had en inderdaad lesbisch is.
Deel 2
Ellen bespreekt haar gevoelens voor vrouwen met haar therapeut en de wijze waarop daar in het algemeen door de maatschappij (discriminerend) op gereageerd wordt. De therapeut dringt er niettemin op aan dat Ellen haar vrienden over haar geaardheid vertelt. De vrienden reageren verrast en met variërende mate van enthousiasme. Ook blijkt dat ze onderling al lang over haar geaardheid hadden gespeculeerd. Ellen is verliefd op Susan, maar zij blijkt al een vriendin te hebben. Susan vertrekt en laat Ellen gedesillusioneerd achter. In een poging Ellen op te vrolijken en hun acceptatie te tonen, nemen haar vrienden haar mee naar een lesbisch koffiehuis. In no time probeert een jonge vrouw (Jorja Fox) Paige te versieren, waaruit blijkt dat er in feite helemaal niets veranderd is (Paige heeft namelijk ook over aandacht van mannen nooit te klagen). Ellen vertelt haar therapeut dat het uit de kast komen tegenover haar vrienden een zware last van haar schouders heeft genomen. De therapeut maakt haar wel duidelijk dat er nog een lange weg is te gaan voor ze haar leven echt op orde heeft.
Achtergronden
Ellen Morgans liefdesleven
Toen de voorbereidingen van de serie in 1992 begonnen, werd al overwogen om Ellen Morgan lesbisch te laten zijn, maar dat idee werd snel verworpen. De producers wilden niet dat haar seksualiteit alle aandacht zou opeisen. Bovendien hadden ze er weinig vertrouwen in dat productiemaatschappij ABC met het plan in zou stemmen. Ellen DeGeneres vond dit geen probleem, want zij was er zelf ook nog niet aan toe om uit de kast te komen. Volgens medewerkers van de serie was zij er zelfs bijzonder op gebrand om alles wat ook maar enigszins homoseksualiteit kon suggereren, te vermijden. Tegelijkertijd begon zij zich na verloop van tijd, toen zij meer invloed kreeg en uitvoerend producent werd, meer en meer te storen aan Ellen Morgans dates met mannen. Redenerend dat er genoeg vrouwen zijn die weinig uitgaan, gooide zij verschillende scenario's in de prullenbak. Uiteindelijk leidde dit ertoe dat Ellen Morgan een aseksuele identiteit kreeg wat de schrijvers aanzienlijk beperkte in hun mogelijkheden.
Codenaam
Het idee om Ellen Morgan lesbisch te maken bleef echter steeds spelen. Het was volgens sommige medewerkers dé manier om van de show meer te maken dan een dertien-in-een-dozijn komedie over een hechte vriendengroep. In de zomer van 1996 werden de mogelijkheden serieus verkend en begonnen in het geheim onderhandelingen daarover met ABC. Om aan het project te kunnen refereren werd gesproken over de aflevering 'waarin Ellen een puppy krijgt'. De titel 'The Puppy Episode' slaat op die geheimhoudingsstrategie en heeft dus niets met een jong hondje te maken. Ondanks pogingen om het idee binnenskamers te houden en ondanks het feit dat ABC pas in maart 1997 het groene sein voor de verhaallijn gaf, lekte het al in september 1996 uit. Geruchten over een op handen zijnde coming-out van beide Ellens deden maandenlang de ronde en deze opwinding werd gevoed door verschillende hints in de aan The Puppy Episode voorafgaande afleveringen en uitspraken van DeGeneres zelf in verschillende media.
Coming-out van Ellen DeGeneres
De op handen zijnde coming-out van het personage Ellen Morgan noodzaakte Ellen DeGeneres om zelf ook uit de kast te komen. Er was al lang over haar geaardheid gespeculeerd en geroddeld, en het zou ongeloofwaardig zijn als ze het zou blijven verzwijgen. Twee weken voor de uitzending van The Puppy Episode haalde haar coming-out de omslag van TIME Magazine onder de kop Yep, I'm Gay (1997, nr.15, pp. 66–71). Het interview was tegelijkertijd een onverhulde promotie van de bewuste aflevering. Eind april schoof ze samen met haar toenmalige partner Anne Heche aan bij een galadiner in het Witte Huis en op de dag dat The Puppy Episode werd uitgezonden verscheen ze samen met Anne in de talkshow van Oprah Winfrey.
Reacties
Dankzij de grote hoeveelheid voorpubliciteit behaalde The Puppy Episode met 42 miljoen aanzienlijk hogere kijkcijfers dan de serie normaal gesproken had. Slechts een van de vaste sponsors, te weten Chrysler, weigerde reclametijd rond en tijdens de aflevering te kopen. De aflevering werd met verschillende prijzen bekroond, waaronder een Emmy voor het scenario.
Hoewel DeGeneres veel geprezen werd om haar moed, waren er ook vele minder positieve reacties. Conservatief-religieuze groeperingen protesteerden tegen ABC en het moederbedrijf The Walt Disney Company, die in hun ogen homoseksualiteit promootten. Een aantal rechts-religieuze antihomoconservatieven tekende een open brief waarin The Puppy Episode werd gekarakteriseerd als een 'klap in het gezicht van Amerikaanse gezinnen'. Nadat de kijkcijfers van Ellen in het vijfde seizoen verder terugliepen en de sponsors zich een voor een terugtrokken, werd de serie door ABC stopgezet. DeGeneres had daarna een paar jaar moeite om opnieuw televisiewerk te krijgen en keerde daarom terug naar het theater- en stand-upcircuit. Hoewel in mindere mate kon ook tegenspeelster Laura Dern na haar gastoptreden als Ellens 'love interest' enige tijd moeilijk werk vinden.
Lange termijn
The Puppy Episode en het daarna volgende vijfde seizoen van de komedieserie heeft de deur geopend voor andere televisieseries met homoseksuele hoofdpersonages. Met name Will & Grace en The L Word worden onmogelijk geacht zonder het baanbrekende effect van The Puppy Episode.
Sommige acteurs durven dankzij Ellens coming-out en het feit dat ze nog steeds (of eigenlijk weer) succesvol is, zelf ook uit de kast te komen. T.R. Knight (Grey's Anatomy) bijvoorbeeld refereerde bij zijn coming-out in oktober 2006 expliciet aan haar.
In 2002 werd de website AfterEllen.com over lesbische en biseksuele vrouwen in de media en de entertainmentindustrie opgericht, die uitgroeide tot de bestbezochte 'lesbische' site op het Internet. Deze website beschouwt The Puppy Episode en DeGeneres' coming-out als een mijlpaal en het startpunt van de verbetering van de zichtbaarheid van lesbiennes en biseksuele vrouwen in films, boeken en op televisie. Dat is de reden dat de site in haar naamgeving (vert. Na Ellen) aan dit moment refereert.
Externe links
A.J. Jacobs (1996) Out? In: Entertainment Weekly, nr 346-47, 27 september 1996.
Melinda Lo (2005) Back in the Day: Coming Out With Ellen In: AfterEllen.com, april 2005.
Puppy Episode
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Will Clothing Rental Make Its Way to Promotional Apparel?
NEW YORK, NY - OCTOBER 18: General atmosphere at WeWork x Rent The Runway Partnership Launch Event on October 18, 2018 in New York City. (Photo by Thos Robinson/Getty Images for WeWork) | Credit: Thos Robinson
By Hannah Abrams
Rent the Runway was the first major company to launch the clothing rental model. The concept is simple: Shoppers pick out an apparel item they like, choose the size, select the dates they need the outfit, pay a fee, and the item is sent to their door. After the purchaser has worn the outfit, she sends it back.
In this era, many people are gravitating toward this model because it gives them a chance to expand their wardrobe without paying a premium. If someone is attending a wedding and they need a dress that they have no intention of ever wearing again, a model like this is ideal.
Now that Rent the Runway has proven its success in the marketplace, other retailers are getting in on the rental game. According to AdWeek, Express announced it launched Express Style Trial where shoppers can spend $69.95 a month to rent three pieces from the brand. New York & Co announced the launch of NY&C Closet for $49 a month for a similar three-product rental. And Ann Taylor launched a service called Infinite Style, which gives purchasers access to unlimited clothing rentals for $95 a month.
It's too early to say whether or not this model will extend to promotional apparel any time soon, but we think there's some potential there. It seems like it could be a fit for brands that are already upping their branded merchandise offering and want to target younger audiences with a fun spin on the sharing economy. A Taco Bell apparel rental program doesn't seem so farfetched given the brand's other forays into merchandise.
Obviously, it would be a little difficult to apply this model to branded merchandise as a whole. However, there might be a recyclable initiative that could be applied for companies that know they will only use the apparel items once.
E Hannah Abrams Author's page
Hannah Abrams is the senior content editor for Promo Marketing. In her free time, she enjoys coming up with excuses to avoid exercise, visiting her hometown in Los Angeles and rallying for Leonardo DiCaprio to win his first second Academy Award.
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This Apparel Line Is Designed to Fix Your Posture For You
How to Sell Blazer Programs to Uniform-Free Schools | {
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UGA CLASSICS STUDY ABROAD IN ROME
May 24-July 2, 2019
Now accepting applications for Summer 2020
Watch the full video, Roma Amor by Alan Flurry, about UGA Classics Study Abroad in Rome HERE!
Watch the full video, Filmed by Anna Conti, Summer 2016 HERE!
Watch the full video, Filmed by Alan Flurry, Summer 2014 HERE!
Information on the Rome Program
Location: Rome, Italy, founded in 753 B.C.
Institution: The University of Georgia Department of Classics.
Student Body: Approximately 15-20 students per summer.
Housing: At the Hotel Ercoli at the northeast end of the Quirinal hill (via Collina, 48), just inside the ancient Aurelianic Wall, where the group has stayed each summer since 1975.
Orientation in Athens in March.
Courses: CLAS 4350 (Ancient Rome), CLAS 4400 (The Art of Rome), and CLAS 4305 (The Urban Tradition of Rome) or LATN 4405 (The Latin Tradition of Rome).
Activities: Most participants take three upper level courses in ancient Roman civilization, all of which center around regular group field trips and explorations in the city. Some coverage of later periods (medieval, renaissance, baroque, fascist) will be included.
Day trips outside the city include visits to the Etruscan sites of Tarquinia and Cerveteri, Hadrian's villa and the Villa d'Este at Tivoli, and other venues. The group takes a multi-day trip to the Bay of Naples to visit Pompeii and other ancient sites buried by the eruption of Mt. Vesuvius, the Naples National Archaeological Museum, the Greek temples at Paestum, and other ancient remains in Campania.
Academic Calendar: Six weeks from late May to early July.
Faculty: Dr. Elena Bianchelli (UGA) is the Program Director, responsible for recruiting and financial arrangements; Dr. Chris Gregg (George Mason University) is the Professor-in-Charge, who will teach most of the courses and lead the group in Rome and Campania.
Program Fees: See the fees HERE. PROGRAM COSTS DO NOT INCLUDE AIRFARE OR TUITION. Students who are not residents of Georgia or do not attend a University System of Georgia school will pay an additional $250 out of state fee. UGA tuition and fees will be charged to the student account, just as if the student were taking classes on campus, and must be paid before the departure for Rome.
**PLEASE NOTE: This program is physically strenuous. Participants must be able to climb hills and walk several miles a day over uneven terrain.** | {
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{"url":"https:\/\/www.deepdyve.com\/lp\/springer_journal\/creating-maximally-entangled-states-by-gluing-l60dcDldCC","text":"# Creating maximally entangled states by gluing\n\nCreating maximally entangled states by gluing We introduce a general method of gluing multi-partite states and show that entanglement swapping is a special class of a wider range of gluing operations. The gluing operation of two m and n qudit states consists of an entangling operation on two given qudits of the two states followed by operations of measurements of the two qudits in the computational basis. Depending on how many qudits (two, one or zero) we measure, we have three classes of gluing operation, resulting respectively in $$m+n-2$$ m + n - 2 , $$m+n-1$$ m + n - 1 , or $$m+n$$ m + n qudit states. Entanglement swapping belongs to the first class and has been widely studied, while the other two classes are presented and studied here. In particular, we study how larger GHZ and W states can be constructed when we glue the smaller GHZ and W states by the second method. Finally we prove that when we glue two states by the third method, the k-uniformity of the states is preserved. That is when a k-uniform state of m qudits is glued to a $$k'$$ k \u2032 -uniform state of n qudits, the resulting state will be a $$\\hbox {min}(k,k')$$ min ( k , k \u2032 ) -uniform of $$m+n$$ m + n qudits. http:\/\/www.deepdyve.com\/assets\/images\/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals\n\n# Creating maximally entangled states by gluing\n\n, Volume 16 (3) \u2013 Feb 9, 2017\n16 pages\nLoading next page...\n\n\/lp\/springer_journal\/creating-maximally-entangled-states-by-gluing-l60dcDldCC\nPublisher\nSpringer US\nCopyright\nCopyright \u00a9 2017 by Springer Science+Business Media New York\nSubject\nPhysics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics\nISSN\n1570-0755\neISSN\n1573-1332\nD.O.I.\n10.1007\/s11128-017-1535-9\nPublisher site\nSee Article on Publisher Site\n\n### Abstract\n\nWe introduce a general method of gluing multi-partite states and show that entanglement swapping is a special class of a wider range of gluing operations. The gluing operation of two m and n qudit states consists of an entangling operation on two given qudits of the two states followed by operations of measurements of the two qudits in the computational basis. Depending on how many qudits (two, one or zero) we measure, we have three classes of gluing operation, resulting respectively in $$m+n-2$$ m + n - 2 , $$m+n-1$$ m + n - 1 , or $$m+n$$ m + n qudit states. Entanglement swapping belongs to the first class and has been widely studied, while the other two classes are presented and studied here. In particular, we study how larger GHZ and W states can be constructed when we glue the smaller GHZ and W states by the second method. Finally we prove that when we glue two states by the third method, the k-uniformity of the states is preserved. That is when a k-uniform state of m qudits is glued to a $$k'$$ k \u2032 -uniform state of n qudits, the resulting state will be a $$\\hbox {min}(k,k')$$ min ( k , k \u2032 ) -uniform of $$m+n$$ m + n qudits.\n\n### Journal\n\nQuantum Information ProcessingSpringer Journals\n\nPublished: Feb 9, 2017\n\n## You\u2019re reading a free preview. Subscribe to read the entire article.\n\n### DeepDyve is your personal research library\n\nIt\u2019s your single place to instantly\ndiscover and read the research\nthat matters to you.\n\nEnjoy affordable access to\nover 12 million articles from more than\n10,000 peer-reviewed journals.\n\nAll for just $49\/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It\u2019s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### DeepDyve Freelancer ### DeepDyve Pro Price FREE$49\/month\n\n\\$360\/year\nSave searches from Google Scholar, PubMed\nCreate lists to organize your research\nExport lists, citations\nAccess to DeepDyve database\nAbstract access only\nUnlimited access to over\n18 million full-text articles\nPrint\n20 pages\/month\nPDF Discount\n20% off","date":"2018-05-20 11:55:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.49388790130615234, \"perplexity\": 1417.7120658228328}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-22\/segments\/1526794863410.22\/warc\/CC-MAIN-20180520112233-20180520132233-00524.warc.gz\"}"} | null | null |
{"url":"http:\/\/mymathforum.com\/elementary-math\/346231-how-many-motorcyclists-were-served.html","text":"My Math Forum How many motorcyclists were served?\n\n Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion\n\n April 18th, 2019, 09:01 AM #1 Senior Member \u00a0 \u00a0 Joined: Jan 2012 Posts: 741 Thanks: 7 How many motorcyclists were served? During fuel scarcity, a fuel station served fuel to motorist and motorcyclist in the ratio 1:4. How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters? The only meaning I can make from the problem is that if 3 000 litres of fuel is served to motorcyclist such that each motorcyclist collect 30 litres then the number of motorcyclist served is (3000)\/30 = 100 Again, another understanding I have from the ratio 1:4 given, for each one litre a motorcyclist, a motorist get 4 litresApart this two meanings, I don't seem to get any relationship between the ratio 1:4 and 3 000 litres of fuel and when each motorcyclist collect 30 litres Thank you\n April 18th, 2019, 09:44 AM #2 Newbie \u00a0 \u00a0 Joined: Oct 2018 From: USA Posts: 29 Thanks: 15 Math Focus: Algebraic Geometry So if the ratio for motorists:motorcyclists is 4:1, if motorcyclists get 30 then motorists should get 120. Where $x$ is the number of motorists and $y$ is the number of motorcyclists: $\\displaystyle 120x+30y = 3000$ $\\displaystyle y = 100-4x$ But i'm not sure where to go from here since there isn't any information on the number of motorists that showed up. Thanks from Chikis\nApril 18th, 2019, 10:26 AM \u00a0 #3\nMath Team\n\nJoined: Jul 2011\nFrom: Texas\n\nPosts: 2,923\nThanks: 1518\n\nQuote:\n During fuel scarcity, a fuel station served fuel to motorist and motorcyclist in the ratio 1:4. How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters?\nThe given ratio of motorist to motorcyclist = 1:4 $\\implies$ the 3000 L of fuel was dispensed in a 600:2400 ratio, motorists to motorcyclists\n\nIf each motorcyclist received 30 L, then 2400\/30 = 80 motorcyclists were served.\n\nApril 18th, 2019, 11:09 AM \u00a0 #4\nSenior Member\n\nJoined: Jan 2012\n\nPosts: 741\nThanks: 7\n\nQuote:\n How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters?\nI think the problem I had here was that I did not know that 3 000 litres of fuel was served to both motorists and motorcyclist. Initially, I thought the 3000 litres of fuel was only served to motorcyclist. But in your own judgement of wording or grammar, do you think How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters? mean that only motorcyclists were served 3 000 litres of fuel as I thought initially or it means both motorists and motorcyclists were served the same litres in the same ratio?\n\nLast edited by Chikis; April 18th, 2019 at 11:16 AM.\n\n April 18th, 2019, 11:18 AM #5 Math Team \u00a0 \u00a0 Joined: Jul 2011 From: Texas Posts: 2,923 Thanks: 1518 I interpreted the 3000L to be the total fuel dispensed to both motorists & motorcyclists, otherwise, the problem is trivial division ... why bother with the ratio information? Last edited by skeeter; April 18th, 2019 at 11:36 AM.\n April 18th, 2019, 11:49 AM #6 Senior Member \u00a0 \u00a0 Joined: Jan 2012 Posts: 741 Thanks: 7 Thanks for the interpretation. Your interpretation is very correct! But let's face the fact. Do you think the author is wrong in the wording of the problem?\n April 18th, 2019, 04:04 PM #7 Math Team \u00a0 \u00a0 Joined: Jul 2011 From: Texas Posts: 2,923 Thanks: 1518 Not wrong ... maybe he\/she could have worded it better. Last edited by skeeter; April 18th, 2019 at 04:07 PM.\n April 19th, 2019, 07:16 AM #8 Global Moderator \u00a0 Joined: Dec 2006 Posts: 20,623 Thanks: 2076 The problem states that there is fuel scarcity and that the fuel is served (rather than sold) to motorist and motorcyclist in the ratio 1:4. This wording suggests that the fuel station is implementing a rationing policy, namely that each motorist will be served 1\/4 as much fuel as each motorcyclist. As each motorcyclist is served 30 l of fuel, that would mean that each motorist is served 7.5 l of fuel. The above seems to be a reasonable interpretation of the problem, but it means that more information would be needed to solve it, as the only equation available would be $30x + 7.5y = 3000$, where there are $x$ motorcyclists served and $y$ motorists served (and each variable is a positive integer). This allows $x$ to be any integer from 1 to 99, and $y$ correspondingly to be $400 - 4x$.\n\n Thread Tools Display Modes Linear Mode","date":"2019-05-21 14:50:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.835451602935791, \"perplexity\": 3346.2850159773957}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232256426.13\/warc\/CC-MAIN-20190521142548-20190521164548-00285.warc.gz\"}"} | null | null |
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The Dusty Baker is officially invited to be a destination in Welcome Competitor. We hope you're in! | {
"redpajama_set_name": "RedPajamaC4"
} | 9,035 |
Q: Angular/Firestore Sum the values of an Array of Objects inside a document I have a document inside a firestore collection with several key-values, one of them is an array of objects and i want to calculate the sum of all the values of key "orders" inside the array "sessions" for that id.
{
id: "asdSDWESHGawhadah",
name: "John",
lastName: "Doe",
age: "20",
sessions: [
{
orders: 1
date: 2019 - 11 - 24
},
{
orders: 5
date: 2019 - 11 - 26
},
{
orders: 4,
date: 2019 - 11 - 29
},
],
}
I haven't been able to show the result of the sum ( 10 in this case) in the HTML.
I tried to do it in the typescript of the component where i call the service that gives me the document, but the variable is an Observable with my Interface so i cant use map or reduce, i know there is a way using RxJs, i can't find a good example to understand, its to complex for my knowledge.
Is there an easy way to obtain the sum result from Firestore directly?
constructor(
private fbservice: FirebaseService,) { }
ngOnInit() {
this.fbpatient$ = this.fbservice.getOnePatient(idPatient);
}
The getOnePatient method brings me the data that contains all of the sessions with the values i want to sum
but as i said i cant work with fbpatient$ like a normal javascript object cause of the Observable.
Thank you
A: You could solve this by using the RXJS map operator, something like this:
mySumObservable$ = this.fbservice.getOnePatient(idPatient).pipe(
map(patient => {
return patient.sessions.reduce((sum, session) => sum + session, 0);
})
);
Then you could get the sum out of the mySumObservable$ either by subscribing to it in your code, something like:
mySumObservable$.subscribe(sum => this.patientSum = sum);
Or by subscribing with the async pipe in your html:
<div>{{ (mySumObservable$ | async) }}</div>
A: Thanks to user SnorreDan i came up with this solution, it works for me altough i dont know if it's the best way or the best practice. Then i subscribe in the HTML as SnorreDan suggested with {{mySumObservable$}}
let sum = 0;
this.mySumObservable$ = this.fbservice.getOnePatient(idPatient).pipe(
map((patient) => {
patient.sessions.forEach((patient) => {
sum = sum + patient.orders;
});
return sum;
})
) as any;
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,085 |
\section{Introduction}
Since its discovery, superconductivity has long been a rich environment for understanding the quantum nature of our universe. Superconductors themselves are macroscopic condensates of paired electrons that owe their coherence to quantum mechanics. It is no surprise then that superconductivity in disordered two-dimensional thin film materials has proven to be a rewarding playground for studying quantum phase transitions (QPTs).\cite{hebard1990,shahar1992,goldman1998,adams2004,sambandamurthy2004,steiner2005,stewart2007,gantmakher2010} These QPTs are driven by quantum fluctuations between two competing phases of matter at zero temperature tuned by a non-thermal parameter $g$.\cite{sachdev}
For the superconductor-insulator transition (SIT) in thin films, theory\cite{ghosal1998,ghosal2001,bouadim2011} and experiment\cite{sacepe2008,sacepe2011,mondal2011,sherman2012} have both shown that the single-particle gap in the superconductor persists into the insulator. While the local amplitude remains finite and the single-particle density of states shows a robust gap, the coherence peaks become diminished and global superconductivity is lost. This suggests that Cooper pairs do not break up in the insulator, and in fact superconductivity is destroyed by the loss of global phase coherence between pairs on different islands. The SIT, then, is predominantly driven by quantum phase fluctuations.
We therefore use a bosonic description of a thin film superconductor in terms of a Josephson junction array (JJA) of superconducting islands, the Hamiltonian of which is related to the quantum XY model.\cite{wallin1994,sondhi1997,swanson2014} Here, amplitude fluctuations are ignored and we directly simulate the phase degrees of freedom using quantum Monte Carlo (QMC). This gives us access to quantum phase fluctuations, which have have been experimentally observed in global measurements\cite{crane2007,sherman2015,poran2017} but have only recently been imaged locally using scanning SQUID techniques.\cite{kremen2018}
In this paper we calculate local two-particle quantities such as compressibility, two-particle local density of states (LDOS), and local diamagnetic susceptibility in order to highlight their importance in observing local quantum fluctuations. Local spectroscopies have previously played an important role in identifying a variety of physical phenomena, including the use of scanning tunneling spectroscopy (STM) to map spatial inhomogeneities in high-$\mathrm{T_c}$ cuprates,\cite{howald2001,pan2001,lang2002} local compressibility measurements to observe electron-hole puddles in graphene,\cite{martin2008} and a combination of STM and spin-polarized STM to detect a possible signature of Majorana fermions in ferromagnetic chains on a superconductor.\cite{nadj-perge2014} Here we make predictions for experimental measurements that can be performed using scanning Josephson spectroscopy (SJS)\cite{randeria2016} and compressibility probes, which can be used to visualize quantum phase fluctuations.
The number-phase uncertainty principle that is at the heart of the SIT is also emerging as a paradigmatic model in quantum information. The ``quantum phase slip" qubit describes a state with a well-defined flux in which number fluctuations introduce phase slips. The dual ``Cooper pair box" is a qubit with well defined number of Cooper pairs in which Josephson tunneling creates number fluctuations.\cite{mooij2006} We discuss below how the qubit evolves across the SIT and connect these concepts to our results on spectroscopies.
Our main results are as follows:
\noindent (1) The global two-particle DOS $P(\omega)$ is peaked at $\omega = 0$ in the superconducting phase due to the presence of a Cooper pair condensate. As the SIT is approached, this peak diminishes and the spectrum becomes gapped at the critical point, signaling a transition to a Cooper pair insulator. The global two-particle compressibility $\kappa$ is also finite in the superconducting phase where Cooper pairs are free to tunnel and vanishes at the critical point where they become localized.
\noindent (2) The local compressibility $\kappa(\mathbf{r})$ in a disordered system captures the onset of quantum fluctuations as the SIT is approached. In the superconducting phase, increasing phase fluctuations create pockets of localized Cooper pairs where the compressibility is small. The LDOS $P(\mathbf{r}, \omega)$ in these regions exhibits an $\omega = 0$ peak that is strongly suppressed whereas $P(\mathbf{r}, \omega)$ outside of these pockets resembles the global $P(\omega)$ of a superconductor. As $g$ is increased toward the SIT, fluctuations of $\kappa(\mathbf{r})$ increase mirroring the presence of increasing phase fluctuations. Thermal fluctuations obfuscate the presence of these insulating pockets instead of increasing them in size, providing an easy way to separate quantum fluctuations from thermal fluctuations.
\noindent (3) The local diamagnetic susceptibility $\chi(\mathbf{r})$ also shows increasing fluctuations as the SIT is approached from the superconducting side. As a function of $T/T_c$, the standard deviation of $\chi(\mathbf{r})$ is peaked only in a narrow region around $T_c$ for $g$ deep in the superconducting phase. As $g$ is increased toward the critical point, this peak broadens around $T_c$, indicating that fluctuations of $\chi(\mathbf{r})$ are appearing well-below $T_c$. The fact that these extra fluctuations exist far below $T_c$ provide evidence that they are indeed of quantum origin.
\section{Model and Methods}
A useful model for understanding quantum fluctuations across the SIT is the 2D JJA model with Hamiltonian
\begin{equation}
\label{eq:ham}
\hat{H} = \frac{E_C}{2}\sum_i \hat{n}_i^2 - E_J \sum_{\left<ij\right>} \cos(\hat{\theta}_i - \hat{\theta}_j)
\end{equation}
where $\hat{n}_i$ and $\hat{\theta}_i$ are canonically conjugate Cooper pair number and phase operators, respectively, that satisfy the commutation relation $\left[\hat{\theta}_i,\hat{n}_j\right]=i\delta_{ij}$. $E_J$ links phases on nearest neighbor sites via a Josephson coupling while $E_C$ represents the charging energy of Cooper pairs on each site. When $E_J$ is large, the phases align and the system is in a coherent superconducting phase. When the $E_C$ term dominates, the system favors a well-defined number eigenstate, leading to quantum phase fluctuations that destroy the superconducting order and transition the system to a bosonic insulating phase. Thus we use the ratio $g = E_C/E_J$ as a knob to tune the system across a QPT between a superconductor and an insulator. It is important to emphasize that loss of global phase coherence is responsible for destroying superconductivity in our model. We assume that fluctuations of the superconducting amplitude are small and that we are working at temperatures well below the pair-breaking scale $T^\ast$ of the superconducting island.
\begin{figure}[!tb]
\includegraphics[width=0.5\textwidth]{model.pdf}
\caption{(a) We simulate the JJA Hamiltonian by mapping to two separate classical actions: XY and integer current model ICM. (b) Schematic phase diagram of the SIT along the $g$-$T$ plane. At zero temperature, the JJA can be tuned through an SIT at $g = g_c$. At finite temperature, both the superconducting and insulating phases transition to normal states with increasing $T$. In-between there is a quantum critical regime.}
\label{model}
\end{figure}
We simulate this model using QMC two different ways as shown schematically in Fig.~\ref{model}a. In both cases we use a quantum-classical mapping to map the quantum JJA Hamiltonian to a classical action.\cite{wallin1994,sondhi1997} First we map the 2D JJA to a (2+1)D XY model of classical phases, a language that is well suited for calculating the two-particle DOS $P(\omega)$ and compressibility $\kappa$. Simulations of the (2+1)D XY model are performed using a Wolff cluster algorithm\cite{wolff1989} on system sizes $64\times64$ for global calculations and $24\times24$ for local calculations. To calculate diamagnetic susceptibility $\chi$, we instead map the JJA to a (2+1)D integer current model (ICM) because the current basis is more natural for exploring the fluctuations of diamagnetic currents. We simulate the ICM using a worm algorithm\cite{prokofev2001} on a $64\times64$ lattice for both global and local calculations. See Appendix A for more details on these mappings.
It is important to note that simulations calculating local quantities require a small amount of disorder to be introduced in order to create structure. Without disorder, local structure is washed out by Monte Carlo averaging. We introduce a small amount of disorder in the spatial bonds of each model by randomly removing a fraction $p = 0.1$ of Josephson couplings $E_J$ throughout the lattice. This creates regions where insulating sites can nucleate and be detected by our local probes. There have previously been studies on disorder-tuned SITs,\cite{bouadim2011,swanson2014} however we emphasize that the disorder in our model is static and the fluctuations we see are ultimately caused by tuning $g$, not disorder.
Both the global $P(\omega)$ and local $P(\mathbf{r},\omega)$ are calculated by analytically continuing imaginary time data to real frequencies using the Maximum Entropy Method (MEM).~\cite{gubernatis1991,sandvik1998} The procedure is delicate and we have performed extensive tests, including checking sum rules, to ensure the validity of our results (see Appendix B for more information).
\section{Results}
\subsection{Bosonic spectral function}
\begin{figure*}[!tb]
\includegraphics[width=\textwidth]{global.pdf}
\caption{Global density of states and energy scales across the SIT: (a) Global two-particle DOS $P(\omega)/\omega$ obtained from analytic continuation of the imaginary time Green's function $G(\tau)$ shown as a function of $g$. For $g < g_c \sim 4.26$ the DOS shows a zero energy peak corresponding to the Cooper pair condensate. As $g$ increases, this weight shifts toward finite energy modes and for $g > g_c$ the system forms a gap characterized by the energy scale $\omega_{\mathrm{gap}}$, signaling the transition to an insulating state. (b) Cuts of $P(\omega)/\omega$ plotted for $g = 3$ (superconducting) and $g = 6$ (insulating) highlighting the difference in two-particle spectra between the two phases. (c) Energy scales near the SIT. The superfluid stiffness $\rho_s$ and compressibility $\kappa$ are finite in the superconducting phase but go soft at $g_c$. Similarly, on the insulating side, the two-particle gap scale $\omega_{\mathrm{gap}}$ is finite and approaches zero as $g_c$ is approached. Note that the error bars are the size of the data points here. (d) We show how the spectral weight in $P(\omega)$ shifts from $\omega = 0$ to finite energy modes with increasing $g$. At small $g$, most of the weight is centered around zero energy, however as $g$ increases past the SIT this weight decreases to zero and increasingly shifts to finite energy states.}
\label{global}
\end{figure*}
The bosonic Green's function in imaginary time is given by $G(\mathbf{r}, \mathbf{r}'; \tau) = \left< \hat{a}^\dagger (\mathbf{r}',\tau) \hat{a}(\mathbf{r},0) \right>$ where $\hat{a}$, $\hat{a}^\dagger$ are Cooper pair raising and lowering operators. In the language of the JJA we can rewrite\cite{fisher1989} the raising operator in terms of its amplitude and phase as $\hat{a}^\dagger (\mathbf{r},\tau) = \sqrt{\hat{n}(\mathbf{r},\tau)}e^{i\hat{\theta}(\mathbf{r},\tau)}$, but since we are ignoring on-site amplitude fluctuations we can write the Green's function purely in terms of the phase variable as
\begin{equation}
\label{eq:green}
G(\mathbf{r}, \mathbf{r}'; \tau) = \left< e^{i\left(\hat{\theta}(\mathbf{r}',\tau) - \hat{\theta}(\mathbf{r},0)\right)} \right>
\end{equation}
which is a spin-spin correlation function in the classical XY representation.
The real frequency spectral function $P(\mathbf{k},\omega)$ is the imaginary part of the corresponding real frequency Green's function $G(\mathbf{k},\omega)$
\begin{equation}
P(\mathbf{k},\omega) = - \frac{1}{\pi}\mathrm{Im} G(\mathbf{k},\omega).
\end{equation}
However, since we are working with imaginary time in our QMC, we need a way to analytically continue $G(\mathbf{k},\tau)$ to a real frequency spectral function. This leads to the following relation between $G(\mathbf{k},\tau)$ and $P(\mathbf{k},\omega)$
\begin{equation}
\label{eq:laplace}
G(\mathbf{k},\tau) = \int_{-\infty}^\infty \frac{d\omega}{\pi} \frac{e^{-\tau\omega}}{1-e^{-\beta\omega}} P(\mathbf{k},\omega).
\end{equation}
Solving this equation for $P(\mathbf{k},\omega)$ amounts to inverting a Laplace transform. However, performing this procedure on QMC data of $G(\mathbf{k},\tau)$ with error bars is non-trivial and requires the use of numerical analytic continuation techniques. In our work, we use MEM to obtain $P(\mathbf{k},\omega)$ from $G(\mathbf{k},\tau)$ and have validated our results by checking relevant sum rules.
We are particularly interested in the DOS which is the sum over momentum of the spectral function
\begin{equation}
P(\omega) = \sum_{\mathbf{k}} P(\mathbf{k},\omega) = A(|\mathbf{r}-\mathbf{r}'| = 0,\omega)
\end{equation}
This amounts to performing MEM on $G(|\mathbf{r}-\mathbf{r}'|=0,\tau)$ data. In Fig.~\ref{global}a we plot $P(\omega)/\omega$ as a function of $g$ across the SIT. Since the form of (\ref{eq:laplace}) requires $A(-\omega) < 0$, we plot $P(\omega)/\omega$ to obtain a quantity that more closely resembles an experimentally measured DOS. We see that $P(\omega)/\omega$ is strongly peaked at $\omega = 0$ in the superconducting phase, corresponding to the existence of a Cooper pair condensate. As the SIT is approached, spectral weight shifts from the central peak to the finite energy modes on either side of $\omega$ until the system forms a gap for $g>g_c$. We plot the shift of this spectral weight from zero energy to finite energy modes in Fig. \ref{global}d. In Fig. \ref{global}c we plot the size of this gap $\omega_{\mathrm{gap}}$ as a function of $g$ along with other energy scales including the superfluid stiffness $\rho_s$ and the compressibility $\kappa$ (described in the next section). As we expect, $\rho_s$, $\kappa$, and $\omega_{\mathrm{gap}}$ go soft at $g_c$ from their respective sides of the transition.
\subsection{Compressibility}
The global compressibility $\kappa$ is a quantity that characterizes fluctuations of the Cooper pair number density operator $\hat{n}$. We can define the average current along a generic spacetime bond $b$ in the XY representation as
\begin{equation}
\braket{j_b} = -\frac{\partial \ln Z}{\partial A_b} = \braket{K_b\sin(\partial_b \theta - A_b)}
\end{equation}
where $Z = \Tr e^{-\beta \hat{H}}$ is the partition function, $A_b$ is the element of an externally applied vector potential along bond $b$, and $K_b$ is the coupling constant along that bond. We can then identify the average density $\braket{n}$ with the current along \textit{temporal} bonds $\braket{j_\tau}$.\cite{wallin1994}
The generalized electromagnetic response tensor
\begin{equation}
\Upsilon_{bb'} = \frac{\partial \braket{j_b}}{\partial A_{b'}}
\end{equation}
describes the response of a current $j_b$ along a spacetime bond $b$ to an externally applied vector potential $A_{b'}$ along a bond $b'$. While the superfluid stiffness $\rho_s$ can be obtained from the static, transverse long wavelength limit of the spatial response function $\Upsilon_{xx}$, the compressibility is given by the static long wavelength limit of the temporal response function $\Upsilon_{\tau\tau}$~\cite{kubo2003}
\begin{align}
\Upsilon_{\tau\tau}(\mathbf{r},\mathbf{r}';\tau,\tau') &=\frac{\partial \braket{j_\tau (\mathbf{r},\tau)}}{\partial A_\tau(\mathbf{r}',\tau')}\\
\label{eq:comp}
&= \left<-k_\tau(\mathbf{r},\tau)\right>\delta(\mathbf{r},\tau) - \Lambda_{\tau\tau}(\mathbf{r},\tau)
\end{align}
where $\left<-k_\tau(\mathbf{r},\tau)\right> = \left<K_\tau \cos(\partial_\tau\theta(\mathbf{r},\tau))\right>$ and the temporal current-current correlator $\Lambda_{\tau\tau}(\mathbf{r},\tau) = \left<K_\tau^2 \sin(\partial_\tau\theta(\mathbf{r},\tau))\sin(\partial_\tau\theta(0,0))\right>$. Note that since we are performing linear response we take the limit $A_\tau \rightarrow 0$, and we make use of translational symmetry in the second line.
The compressibility $\kappa$ is then the static, long wavelength limit of $\Upsilon_{\tau\tau}(\mathbf{r},\tau)$
\begin{equation}
\kappa = \lim_{\mathbf{k}\rightarrow 0} \Upsilon_{\tau\tau}(\mathbf{k},i\omega_n=0).
\end{equation}
Note that this amounts to calculating the response of the pair number density $\braket{n} \sim \braket{j_\tau}$ with respect to an externally applied electric potential $\phi \sim A_\tau$, which is the usual definition of compressibility.
In Fig. \ref{global}c we show $\kappa$ as a function of $g$. $\kappa$ is finite in the superconducting phase where Cooper pairs are phase coherent and are able to tunnel across the system. $\kappa$ decreases as $g_c$ is approached and vanishes in the Mott insulating phase where Cooper pairs become localized by phase fluctuations.
\subsection{Local quantities}
We next turn our attention to calculations of the LDOS $P(\mathbf{r},\omega)$ and local compressibility $\kappa(\mathbf{r})$. $P(\mathbf{r},\omega)$ is related to the local Green's function (\ref{eq:green}) at $\mathbf{r}=\mathbf{r}'$ by inverting (\ref{eq:laplace}) once again
\begin{equation}
G(\mathbf{r},\tau) = \int_{-\infty}^\infty \frac{d\omega}{\pi} \frac{e^{-\tau\omega}}{1-e^{-\beta\omega}} P(\mathbf{r},\omega).
\end{equation}
The local compressibility $\kappa(\mathbf{r})$ is given by the local response function $\Upsilon_{\tau\tau}(\mathbf{r},\tau)$ in (\ref{eq:comp})
\begin{align}
\kappa(\mathbf{r}) &= \Upsilon_{\tau\tau}(\mathbf{r},i\omega_n=0) = \lim_{A_\tau\rightarrow 0} \frac{1}{\beta}\sum_{\mathbf{r}',\tau,\tau'} \frac{\partial j_\tau(\mathbf{r},\tau)}{\partial A_\tau(\mathbf{r}',\tau')} \\
&= \frac{1}{\beta}\sum_{\mathbf{r}',\tau,\tau'}\left(\left<-k_\tau(\mathbf{r},\tau)\right>\delta(\mathbf{r}',\tau') - \Lambda_{\tau\tau}(\mathbf{r},\mathbf{r}',\tau,\tau')\right).
\end{align}
\begin{figure*}[!tb]
\includegraphics[width=\textwidth]{localDOS.pdf}
\caption{Local compressibility and LDOS in a disordered system near the SIT. (a) Map of the local compressibility $\kappa(\mathbf{r})$ on a $24\times24$ lattice at $g = 3.6$, near the SIT. We introduce a small amount of bond disorder ($p=0.1$) to produce local structure in our QMC data. We see that while the majority of system has finite $\kappa$ (superconducting), the local $\kappa(\mathbf{r})$ map picks out large dark regions with $\kappa$ near zero (insulating), as we would expect for a system exhibiting strong quantum fluctuations. This is reflected in the two-particle LDOS $P(\mathbf{r}, \omega)/\omega$ shown in (b). In the compressible region highlighted in blue, we see that $P(\mathbf{r}, \omega)/\omega$ has a peak at $\omega = 0$ characteristic of a superconductor. On the other hand, the incompressible region highlighted in red exhibits a peak that is highly suppressed at $\omega = 0$, indicating that this region is approaching an insulating regime. The global $A( \omega)/\omega$ is shown in purple for comparison.}
\label{localDOS}
\end{figure*}
In order to extract local structure from our QMC simulations, we break translational symmetry by introducing a small fraction of bond disorder. In Fig. \ref{localDOS}a we show a local map of $\kappa(\mathbf{r})$ at $g=3.6$, near the SIT. We see that the system forms puddles where $\kappa(\mathbf{r})$ is significantly suppressed. These incompressible regions are locations where a large density of bonds have been cut, resulting in the formation of insulating islands. In Fig. \ref{localDOS}b we plot the corresponding $P(\mathbf{r},\omega)$ in two representative regions. We see a strong spatial correlation between the strength of $\kappa(\mathbf{r})$ and the distribution of low-energy spectral weight. The superconducting region highlighted in blue is highly compressible and has most of its spectral weight peaked strongly around $\omega = 0$, reflecting the strength of the superconducting condensate. The behavior of $P(\mathbf{r},\omega)$ in this region matches that of the global $P(\omega)$ shown in purple, which reflects that of a globally phase-coherent superconductor. On the other hand, in the region highlighted in red with small compressibility, we see that the $\omega = 0$ peak in $P(\mathbf{r},\omega)$ is highly suppressed . Here we can see evidence of a two-particle gap beginning to form as spectral weight shifts from $\omega = 0$ to finite energy modes, indicative of an emerging Cooper pair insulator.
\begin{figure*}[!tb]
\includegraphics[width=\textwidth]{localKappa.pdf}
\caption{(a) Maps of the local compressibility $\kappa(\mathbf{r})$ on a $24\times24$ lattice as a function of $g$ and temperature $T$ on the superconducting side of the transition. We see that as the transition is approached with increasing $g$, fluctuations of the compressibility also increase. Interestingly, with increasing $T$ we see that fluctuations in $\kappa(\mathbf{r})$ actually become smoothed out due to increasing number fluctuations. Since the behavior of $\kappa(\mathbf{r})$ as we evolve tuning $g$ or $T$ is different, we can separate the effects of thermal fluctuations from quantum fluctuations. (b) Distributions of $\kappa(\mathbf{r})$ for various maps. We see that as $g$ increases for fixed $T$, the distribution of $\kappa(\mathbf{r})$ broadens significantly and the standard deviation $\sigma$ increases. However, with increasing $T$ and fixed $g$, the distribution only changes slightly and actually becomes narrower.}
\label{localKappa}
\end{figure*}
It is important to emphasize that the emergence of insulating islands shown in Fig. \ref{localDOS}a is caused by quantum phase fluctuations due to proximity to a quantum critical point. To illustrate this, in Fig. \ref{localKappa}a we also plot $\kappa(\mathbf{r})$ as a function of $g$ and temperature $T$. As $g$ increases toward the SIT, fluctuations in $\kappa(\mathbf{r})$ increase, leading to an increase in the size and prevalence of incompressible islands. Interestingly, as $T$ increases the fluctuations in $\kappa(\mathbf{r})$ become smoothed out and the insulating islands become smaller. This is due to the fact that $\kappa$ is sensitive specifically to number fluctuations. While quantum number fluctuations are expected to decrease as $g$ increases, \textit{thermal} number fluctuations increase as $T$ increases due to higher energy number states becoming available. This is clearly seen in Fig. \ref{localKappa}b, where the distribution of $\kappa(\mathbf{r})$ broadens significantly with increasing $g$, but narrows slightly with increasing $T$. This difference in behavior as $\kappa(\mathbf{r})$ evolves with $g$ and $T$ provides a way to distinguish quantum fluctuations from thermal fluctuations. We propose that an experiment that measures $\kappa(\mathbf{r})$ across the SIT will be able to directly image the presence of quantum fluctuations. The fact that these fluctuations are in fact \textit{quantum} phase fluctuations is further confirmed by our results on the diamagnetic susceptibility.
\subsection{Diamagnetic susceptibility}
\begin{figure*}[!tb]
\includegraphics[width=\textwidth]{dia.pdf}
\caption{(a) Local maps of the diamagnetic susceptibility $\chi(\mathbf{r})$ obtained on a $64\times64$ lattice as a function of $g$ and $T$ using the ICM representation. We see that for small $g$, $\chi(\mathbf{r})$ is large and uniform until the system approaches $T_c$, as expected of thermal fluctuations. However, as $g$ is increased toward the SIT, fluctuations in $\chi(\mathbf{r})$ begin to appear well below $T_c$, suggesting that these additional fluctuations are quantum in nature. In (b) we plot the standard deviation of $\chi(\mathbf{r})$ for each value of $g$ as a function of temperature. We see that while the standard deviation is always peaked around $T_c$, this peak broadens as the SIT is approached, pointing to the increasing importance of quantum phase fluctuations in this regime.}
\label{dia}
\end{figure*}
Phase fluctuations increase both as a function of temperature and a function of $g$. The question becomes how to separate thermal phase fluctuations from quantum phase fluctuations. A well-known property of a superconductor is the fact that it generates diamagnetic supercurrents in the presence of a magnetic field. In general the magnetization generated by an external field is related to the free energy by
\begin{equation}
\braket{M} = \frac{\partial (T\log Z)}{\partial B}
\end{equation}
where $-T\log Z$ is the free energy in terms of the partition function $Z$ and $B$ is an external applied magnetic field. We can calculate the corresponding local diamagnetic susceptibility $\chi(\mathbf{r})$, which is sensitive to phase fluctuations, from linear response using a Kubo formula
\begin{equation}
\chi(\mathbf{r}) = -\frac{\partial \braket{M(\mathbf{r})}}{\partial B} = \left<M(\mathbf{r})M\right>.
\end{equation}
The local diagmagnetic susceptibility is the response of a \textit{local} induced magnetization $M(\mathbf{r})$ to a \textit{global} applied magnetic field $B$. This amounts to calculating the correlator between the local magnetization $M(\mathbf{r})$ and the global magnetization $M$. To obtain $\chi(\mathbf{r})$, we perform QMC simulations in the dual ICM representation of the quantum JJA model. This representation is more suited to calculating quantities involving the supercurrent since the QMC configurations themselves are given in terms of integer currents (see Appendix A2).
\begin{figure*}[!htb]
\includegraphics[width=\textwidth]{IV.pdf}
\caption{(a) Evolution of the Cooper pair spectral function $P(\omega)$ across the SIT tuned by $g=E_c/E_J$, the ratio of charging energy to the Josephson energy. (b) The first cut shows a ``Quantum phase slip" qubit whose behavior is consistent with a finite current at zero voltage, if we interpret the y-axis as the current and the x-axis as the voltage. In the second cut, we approach the transition described by a finite slope around $\omega=0$, consistent with a finite resistance. The final cut describes a ``Cooper pair box" qubit whose behavior is consistent with zero current until a critical voltage is reached.}
\label{IV}
\end{figure*}
In the language of the ICM, we can write the total magnetization, assuming a uniform $B$-field in the $\hat{z}$-direction, as
\begin{equation}
\braket{M} = \frac{1}{2\beta}\sum_{\braket{ij},\tau} (x_i y_j - x_j y_i)j_{ij}^\tau
\end{equation}
where $j_{ij}^\tau$ is an integer current on a spatial bond connecting sites $i$ and $j$ on timeslice $\tau$. The spatial pattern that $j_{ij}^\tau$ is summed along comes from the corresponding vector potential of the uniform $B$-field, $\mathbf{A} = \frac{B}{2}(-x,y,0)$. $M(\mathbf{r})$ is calculated from the discrete analog of the magnetization current $\mathbf{j}(\mathbf{r}) = \Delta\times\mathbf{M}(\mathbf{r})$ where $\mathbf{j}$ are the integer currents. Inverting this for $M_z(\mathbf{r}) = M(\mathbf{r})$ gives us
\begin{equation}
M(\mathbf{r}) = \int d\mathbf{r}' \cdot (\hat{z} \times \mathbf{j}(\mathbf{r}')).
\end{equation}
In Fig. \ref{dia}a we show local maps of $\chi(\mathbf{r})$ as a function of $g$ and $T/T_c$. Here, $T_c$ is the temperature at which the superconductor transitions to a normal state but still contains pairs; it should not be confused with the pair-breaking transition, that occurs at a much higher temperature. As expected, we observe that fluctuations of $\chi(\mathbf{r})$ increase with $T/T_c$ due to thermal fluctuations. Similarly, fluctuations of $\chi(\mathbf{r})$ also increase with increasing $g$. In both cases we see pockets with near-zero susceptibility beginning to form as phase fluctuations destroy the ability for coherent supercurrents to exist. However, interestingly, as $g$ increases the fluctuations in $\chi(\mathbf{r})$ appear at lower values of $T/T_c$. The fact that fluctuations appear well below $T_c$ when the system is near a quantum critical point suggests that the fluctuations with increasing $g$ are predominantly caused by \textit{quantum} phase fluctuations.
This shows up as a broadening of the standard deviation of $\chi(\mathbf{r})$ across $T/T_c$ as shown in Fig. \ref{dia}b. For small $g$, the standard deviation is peaked mainly around $T_c$, suggesting that only thermal fluctuations are relevant in this regime. However as $g$ increases the temperature range where standard deviation is large broadens to include temperatures well below $T_c$ reflecting the importance of quantum fluctuations. This broadening of the temperature range of $\chi(\mathbf{r})$ fluctuations was recently observed in scanning SQUID experiments of the thin film superconductor NbTiN.\cite{kremen2018} In the experiment, a scanning SQUID was used to directly image the local $\chi(\mathbf{r})$ and the corresponding standard deviation as a function of temperature and film thickness was found to qualitatively match that of theory. Importantly, this was the first time quantum fluctuations were directly imaged in an experiment.
\section{Conclusion and Outlook}
We have presented three different calculations of local two-particle response functions across the SIT: density of states $P(\mathbf{r},\omega)$, compressibility $\kappa(\mathbf{r})$, and diamagnetic susceptibility $\chi(\mathbf{r})$. We have shown how these quantities can be used to probe the local structure of fluctuations across the SIT. Particularly, for both $\chi(\mathbf{r})$ and $\kappa(\mathbf{r})$ we see an increase in local quantum fluctuations as the system approaches the critical point from the superconducting side, independent of thermal fluctuations
Our aim is to connect these calculations to spectroscopic measurements that can be performed in an experiment. We have already discussed how $\chi(\mathbf{r})$ can be measured using scanning SQUID techniques. We next turn our attention to measurements of $P(\omega)$ and $\kappa(\mathbf{r})$. It has previously been shown that it is possible capture the local structure of the superconducting order parameter using a combination of scanning tunneling spectroscopy (STM) and scanning Josephson spectroscopy (SJS) using a superconducting Pb tip.\cite{randeria2016} There, a suppression of the zero-energy peak measured in the SJS conductance was found on impurity sites, similar to our results on disorder sites of the JJA. We propose an experiment that uses SJS in conjunction with local compressibility measurements\cite{martin2008} to map out the evolution of quantum fluctuations across the SIT as we have done in Fig.~\ref{localDOS} and \ref{localKappa}.
We are also interested in connecting with recent developments in quantum information and quantum computing. As emphasized earlier, the essence of the SIT is the number-phase uncertainty principle. This can be used to define two types of dual qubits based on whether the phase dominates with quantum phase slips (QPS) disrupting that order (``QPS" qubit) on the SC site or whether the number of Cooper pairs is well-defined with Cooper pair tunneling disrupting the order (``Cooper pair box" qubit) on the insulating side.\cite{mooij2006} The behavior of the Cooper pair spectral function in Fig.~\ref{IV} tracks the evolution of the qubit across the SIT .
\noindent {\it QPS qubit:}
The QPS qubit is dominated by the inductive energy $E_J=\Phi_0^2/{(2L)}$, where $L$ is the inductance of the loop and $\Phi_0=h/{(2e)}$ is the SC flux quantum. The charging term mixes states with different fluxoid number $f=\Phi/\Phi_0$ where $\Phi$ is the flux through the loop and lifts the degeneracy at half-integer values of $f$. A current biased Josephson junction can be modeled as the dynamics of the phase in a slanted washboard potential. The phase is trapped in one of the minima yielding a zero voltage state, a superconductor, until the current exceeds a critical value.
\noindent {\it Cooper pair box qubit:}
In the dual regime, the insulator has a fixed number of Cooper pairs on each island and is dominated by the charging scale $E_C=(2e)^2/{(2C)}$ where $C$ is the capacitance of the island. Josephson tunneling mixes states with $n$ and $n+1$ Cooper pairs on an island and lifts the degeneracy at half integer values. In the voltage-biased configuration, charge is trapped in a potential minimum resulting in a zero current state, an insulator, for voltages below a critical value.
Once we understand how a qubit behaves in different regimes, it in fact becomes a device to measure and quantify the degree of fluctuations, both thermal and quantum, across QPTs. We expect these ideas will motivate developments in quantum measurement.
\section*{Acknowledgements}
H.K. would like to acknowledge support from the Israel US bi-national foundation grant no. 2014325. N.T. acknowledges support from the DOE-BES grant DE-FG02-
07ER46423. We would like to thank Yen Lee Loh for helpful discussions.
| {
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{"url":"https:\/\/math.stackexchange.com\/questions\/1581154\/matrix-multiplication-and-exponents","text":"# Matrix multiplication and exponents\n\nLet's say I have $3\\times3$ matrix $A$, which is known. I'm given $A^x$ and $A^y$. The goal is to determine $A^{xy}$. $x$ and $y$ are unknown. Is it possible?\n\n\u2022 If the matrix is diagonalizable powers are easy. Do you know if you can diagonalize your matrix? Dec 18, 2015 at 15:25\n\u2022 @Wintermute Does that mean if the matrix can be Gauss-Jordaned so that everything outside the main diagonal is 0? Dec 18, 2015 at 15:27\n\u2022 @CaptainCodeman no, this is matrix similarity, not row-reduction (\"Gauss-Jordaning\"). Dec 18, 2015 at 15:30\n\u2022 Euh...A brute-force solution: since the characteristic polynomial of A is of degree $3,$ we can always compute explicitly (at least theoretically) the powers $A^n,$ so we can conversely obtain the values of $x$ and $y$... Of course this is not what you want. :P Dec 18, 2015 at 15:30\n\u2022 @CaptainCodeman I'm not quite sure what you mean by Gauss-Jordaned. A matrix is diagonalizable if you can write it $A=P^{-1}DP$ for some diagonal matrix D. Then we have the nice result $A^x=P^{-1}D^xP$, which is great because it's easy to raise a diagonal matrix to a power. Dec 18, 2015 at 15:32","date":"2022-08-19 21:41:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8018116354942322, \"perplexity\": 334.2535260230923}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882573760.75\/warc\/CC-MAIN-20220819191655-20220819221655-00558.warc.gz\"}"} | null | null |
{"url":"http:\/\/mathhelpforum.com\/calculus\/92037-triple-integral-volume-problem.html","text":"1. triple integral volume problem\n\nI need to find the volume of region bound by z = x + y z = 10 and the planes x= 0 and y = 0\n\nI set up an integral from 0 to 10 then from 0 to 10 - x and from 10 to x + y dzdydx with the function being one dzdydx\n\nI get an answer 5 times the amount I should. Could someone please tell me if I miscalculated the bounds on one of my integrals??? Thanks so much for the assistance, Frostking\n\n2. Here, $z=x+y$ is a plane sloping diagonally upward along the $x$- and $y$-axes that forms a tetrahedron with the planes $x,\\,y=0$ and $z=10$. We can always use the formula for the volume of a cone:\n\n$V=\\frac{1}{3}Bh,$\n\nwhere $B$ is the base area, here $50$. You are correct that the integral to evaluate is\n\n$\\int_0^{10}\\int_0^{10\\,-\\,x}\\int_{x\\,+\\,y}^{10}dz\\,dy\\,dx.$\n\nCarrying out two steps, we find that this equals\n\n\\begin{aligned}\n\\int_0^{10}\\int_0^{10\\,-\\,x}(10-x-y)\\,dy\\,dx &=\\int_0^{10}\\left[10y-xy-\\frac{y^2}{2}\\right]_0^{10\\,-\\,x}\\,dx\\\\\n&=\\int_0^{10}\\left(10(10-x)-x(10-x)-\\frac{1}{2}(10-x)^2\\right)\\,dx\\\\\n&=\\int_0^{10}\\left(100-10x-10x+x^2-\\frac{x^2}{2}+10x-50\\right)\\,dx.\n\\end{aligned}","date":"2017-10-22 00:12:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 10, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8322868347167969, \"perplexity\": 234.79614295546085}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187824899.75\/warc\/CC-MAIN-20171021224608-20171022004608-00881.warc.gz\"}"} | null | null |
Cut through brush at the campsite or on the trail with a Coleman® 18-in. Steel Machete. The durable hardened steel blade will stand up to tough treatment. Wherever your adventure takes you, keep the machete close in the canvas sheath that attaches to both a traditional belt and a military-style belt.
18-in. Steel Machete is rated 3.0 out of 5 by 1. | {
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Best Self Storage Units in Lansing, Michigan of 2023
In order to pick the top 9 storage units companies in Lansing, we looked at all 86 facilities in the area, including an in-depth review of each company's amenities, features, and customer reviews.
Airport & Grand River Self Storage
AllSafe Storage
AXS Storage
Charlotte Mini Storage
Delta Self-Storage
Michigan Storage North
Mullins Self Storage
MySpace Self Storage
Storage Sense™
U-Stor-It
Our goal is to connect people with the best local storage facilities. We analyzed every single storage facility in the area and rated them based on 30 different variables to pick the best storage unit facilities in Lansing.
shape-1 9
The 9 Best Storage Facilities in Lansing
4400 Millwood Road Lansing, MI 48906
Conveniently located close to the Capital Region International Airport and the Royal Scot Golf Course, Airport & Grand River Self Storage touts itself as a "space station" for tenants' extra belongings. The fully fenced facility offers 24/7 access via personalized keypad codes at the secured gate. Tenants can choose monthly leases or long-term leases at a discount with online auto-payment available. The facility is protected by security camera monitoring, and outdoor parking for boats, RVs, and cars is available. Military discounts are available. ...Read More
2416 West Willow Street Lansing, MI 48917
Family owned and operated for the past 15 years, AllSafe Storage is located just 3 miles to the east of Lansing Mall and prides itself on offering low prices and friendly service. The fully fenced facility features recorded computerized entry that allows tenants to visit during gate hours from 6 a.m. to 10 p.m. daily. Each unit on the premises has its own alarm system and the fully lit facility also utilizes video surveillance. In addition, there is a 24/7 manager on site able to troubleshoot any problems that arise. All units are rented on a monthly basis, but long-term discounts can be worked out. ...Read More
11373 South Old U.S. 27 Dewitt, MI 48820
AXS Storage is located right off of Old U.S. 27 and offers 24/7 access to units via an electronic gate. The fenced-in facility features a variety of storage units that all offer drive-up access for easy move-in and move-out. Large aisleways easily accommodate a moving truck, and video surveillance is used to secure the premises. Reservations can be made online along with bill pay for contactless service. Units are leased on a monthly basis, but discounts are available for long-term contracts. Free locks are offered with every rental. ...Read More
2440 Lansing Road Charlotte, MI 48813
Located just 15 minutes away from downtown Lansing, Charlotte Mini Storage offers a variety of outdoor storage units that range in size from 10 x 10 to 40 x 60. In addition, outdoor parking is available for RVs, boats and autos. All units offer drive-up access and large rolling doors. As an authorized U-Haul dealer, moving trucks can be rented from the self-storage facility, and moving supplies are available for purchase in the office making the storage center a one-stop moving solution. Aisleways at the fenced facility are large enough to allow semi-truck access, and security surveillance is in place. 24/7 access is allowed via an electronic gated entryway. ...Read More
746 Knights Inn Drive Lansing, MI 48917
Situated right off the I-96 expressway in West Lansing, Delta Self Storage offers standard and climate-controlled self-storage units for rent on a monthly basis. 24/7 gate access is allowed via a computerized entry gate so that business, commercial and residential clients can easily get to their units as needed. In addition, RVs, vehicles and boats can also be stored on the premises. All units offer drive-up access and are protected by state-of-the-art video equipment. Motion-activated lights and fencing aid in security, and a backup generator is on the property to ensure all climate-control units remain safe during power outages. ...Read More
14485 S. Old U.S. 27 DeWitt, MI, 48820
Situated right off Old U.S. 27 next door to the Sunbelt Rentals, Michigan Storage North offers outdoor standard storage solutions. All units can be reserved online and offer drive-up access with large paved aisleways that allow moving trucks to back in for easy move in. The gated self-storage facility offers 24/7 access via a personalized keypad code. Units range in size from 5 x 10 to 10 x 20 and are available on a monthly or long-term basis. Registration includes a lock and key, and online payment is available. ...Read More
6381 Lansing Avenue Jackson, MI 49201
Located in between the Grand River and state route 127, Mullins Self Storage is a self-storage facility that offers standard outdoor storage units with drive-up access. There are a variety of clean units available in many sizes, and each unit has its own secure lock. Reservations can be booked online, and tenants can pay their bills online to create contactless service. Office hours are on weekdays from 7 a.m. to 5:30 p.m. and on Saturday from 9 a.m. to 1 p.m. ...Read More
5814 South Pennsylvania Avenue Lansing, MI 48911
MySpace Self Storage is just a few minutes away from I-96 and is within close proximity to a handful of restaurants and shops. The self-storage facility offers standard and climate-controlled units as well as floor units that offer drive-up access. State-of-the-art security is in place to protect belongings around the clock, and moving supplies are available for purchase in the office. Monthly rent can be paid online for contactless service. ...Read More
708 East Cesar E. Chavez Avenue, Lansing, MI 48906
South Creyts Road Location:4724 South Creyts Road, Lansing MI 48917
North Aurelius Road Location:5600 North Aurelius Road, Lansing MI 48911
Storage Sense is a full-service rental company, that's secured and gated to limit the entry of the allowed individuals into the facility. The company has temperature-controlled units in sizes ranging from 5x5 to 61x100. The drive-up units help to lessen the workload for the tenant when they're moving in or out. Additionally, online payment options are available in the facility. There is indoor temperature-controlled vehicle parking, and the indoor loading and unloading area is easily accessible. ...Read More
3625 W Saint Joseph Street Lansing, MI 48917
Locally owned and operated, U-Stor-It sits right off I-496, making it a convenient stop for residential and commercial storage needs. The self-storage facility offers outdoor units in a variety of sizes that all have roll-up doors and drive-up door access. Large aisleways make it easy to maneuver through the well-lit parking lot. Access is available 24/7 via electronic gate entry, and the fully fenced facility is protected further by the presence of an on-site manager. Security deposits are not required, and online payments and reservations are accepted for easy contactless service. Deliveries can be accepted by the front office, and discounts are available for the military. ...Read More
The Cost of Self Storage in Lansing, MI
The average costs of storage units in Lansing are above with the state and national averages for the most common storage unit sizes. Storage unit costs will vary depending on the various amenities the facility offers, so shop around to make sure you're only paying for what you need.
The average cost of storage units in Lansing compared to state and national averages
How to Store Your Book Collection
Do You Need Storage Unit Insurance?
How to Store Art and Jewelry | {
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Celso José Marranzini Pérez (born 11 January 1952, Santo Domingo) is an economist and businessman from the Dominican Republic. He was the Vice President of Corporación Dominicana de Empresas Eléctricas Estatales (CDEEE, "Dominican Corporation of State Electrical Companies"); former chairman of Consejo Nacional de la Empresa Privada (CONEP, "National Council of the Private Enterprise").
He was born to Constantino Marranzini Risk (the son of Liberato Marranzini, an Italian immigrant from Santa Lucia di Serino, and Amelia Risk Assis, a Lebanese immigrant) and María Altagracia Pérez Pintado (the daughter of Celso Pérez, a Spanish industrialist from Asturias, and Carmen Pintado, who was born in Puerto Rico to Spanish parents).
References
People from Santo Domingo
Dominican Republic people of Italian descent
Dominican Republic people of Lebanese descent
Dominican Republic people of Spanish descent
Dominican Republic people of Asturian descent
People of Campanian descent
Dominican Republic businesspeople
Dominican Republic economists
1952 births
Living people | {
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Q: Doing CallOrder of Fake on itself with argument validation How do i do a call order verification of a fake with argument validation in sinon.js?
It is the same fake which is called multiple times with different arguments...
something like below
let someFake = sinon.fake();
someFake(1);
someFake(2);
someFake(3);
sinon.assert.callOrder(someFake.calledWith(1), someFake.calledWith(2),
someFake.calledWith(3));
A: You are essentially using the wrong API for the job, so it's no wonder you are not getting the expected results :) If you look at the docs for callOrder you will see that the signature is using spy1, spy2, .., which indicates that it is meant to be used by more than one spy. A fake is implementation wise also a Spy, so all bits of the Spy API also applies to a Fake. From the docs:
The created fake Function, with or without behavior has the same API as a sinon.spy
A sidenode, that is a bit confusing, is that the docs often use the term "fake" to apply to any fake object or function, not functions created using the sinon.fake API specifically, although, that should not be an issue in this particular case.
With regards to your original question, the Spy API has got you covered since Sinon 1.0 here. You use getCall(n) to return the nth call. There are lots of interactive examples in the docs for this, but essentially you just do this:
// dumbed down version of https://runkit.com/fatso83/stackoverflow-66192966
const fake = sinon.fake();
fake(1);
fake(20);
fake(300);
sinon.assert.calledThrice(fake);
assertEquals(1, fake.getCall(0).args[0])
assertEquals(20, fake.secondCall.args[0])
assertEquals(300, fake.lastCall.args[0])
function assertEquals(arg1,arg2){
if(arg1 !== arg2) {
throw new Error(`Expected ${arg1} to equal ${arg2}`);
}
console.log(`${arg1} equal ${arg2}: OK`)
}
<script src="https://cdn.jsdelivr.net/npm/sinon@latest/pkg/sinon.js"></script>
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Q: Impossibility to show in a label the text of an object My objective is to show in a label the text of an object of a custom class called Files. Here is Files.h :
#import <Foundation/Foundation.h>
@interface Files : NSObject
@property (nonatomic, retain) NSString *title;
@property (nonatomic, retain) NSString *text;
@end
This is Files.m :
#import "Files.h"
@implementation Files
@dynamic title;
@dynamic text;
@end
Here is the .h file of my app. the label is called trackName:
#import <UIKit/UIKit.h>
#import "Files.h"
@interface FirstViewController : UIViewController
{
Files *plainpalais;
}
@property (weak, nonatomic) IBOutlet UILabel *trackName;
-(Files*) chooseFile;
@end
This is the .m file of the app:
#import "FirstViewController.h"
@interface FirstViewController ()
@end
@implementation FirstViewController
@synthesize trackName;
-(Files*)chooseFile
{
return plainpalais;
}
- (void)viewDidLoad
{
[super viewDidLoad];
plainpalais.text=@"hello";
plainpalais.title=@"plainpalais";
trackName.text=plainpalais.title;
// Do any additional setup after loading the view, typically from a nib.
}
- (void)viewDidUnload
{
[self setTrackName:nil];
[super viewDidUnload];
// Release any retained subviews of the main view.
}
- (BOOL)shouldAutorotateToInterfaceOrientation: (UIInterfaceOrientation)interfaceOrientation
{
if ([[UIDevice currentDevice] userInterfaceIdiom] == UIUserInterfaceIdiomPhone) {
return (interfaceOrientation != UIInterfaceOrientationPortraitUpsideDown);
} else {
return YES;
}
}
@end
The problem is that the label trackName doesn't show plainpalais...
Thanks for help !
PS: I'm a beginner so this is probably a basic mistake.
A: You have used @dynamic in your Files.m implementation which tells the compiler that you'll provide getters/setters for these properties at a later time, i.e. using the Objective-C runtime.
I suspect you want to use @synthesize rather than @dynamic. For example,
#import "Files.h"
@implementation Files
@synthesize title;
@synthesize text;
@end
Also you haven't actually created a Files object in the code you have given us. The chooseFile method appears to be returning a nil object (assuming you haven't initialised plainpalais somewhere else). Perhaps you should initialise plainpalais in an init method, e.g.
- (id)init {
self = [super init];
if (self) {
plainpalias = [[Files alloc] init];
}
return self;
}
Don't forget to release this object in dealloc (if you aren't using ARC).
| {
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\section{Introduction}
In a series of papers \cite{FOCS2007,FOCS2007journal,Galesietal,BGL-SAT,BGLR} a program of \emph{parameterized proof complexity} is initiated and various lower bounds and classifications are extracted. In \cite{FOCS2007}, parameterized proof complexity is given as a program to gain evidence that $\W[2]$ is different from $\FPT$, while in \cite{FOCS2007journal} the program is recast as searching for evidence that $\WSAT$ is different from $\FPT$. The reason for the discrepancy between the conference and journal versions of that paper is that the latter formulation allows for a cleaner model-theoretic interpretation of the gap theorem which is the paper's principal mathematical result.
Several parameterized proof systems are discussed in \cite{FOCS2007,FOCS2007journal}. The subject of half of the paper is \emph{parameterized tree-Resolution} which is proved to not be \emph{fpt-bounded} in the process of developing a gap theorem for the propositional translations of fo-contradictions in the manner of Riis's well-known gap theorem \cite{complexity_gap}. The system of \emph{parameterized Resolution} is mentioned in the last part of that paper, together with methods to embed parameterized proof systems in classical proof systems. These parameterized proof systems are designed to refute \emph{parameterized contradictions} $(\mathcal{F},k)$, \mbox{i.e.} propositional formulae $\mathcal{F}$ with no satisfying assignment of weight \textbf{$\leq k$}. No lower bounds were given for parameterized Resolution in \cite{FOCS2007,FOCS2007journal} and the first published lower bounds for this system appeared for the \emph{pigeonhole principle} in \cite{Galesietal}. However, the non-fpt-boundedness of parameterized Resolution (and a fortiori of parameterized tree-Resolution) is in fact a trivial observation as the parameterized contradictions
\[ (\Theta_{m,k},k) := \ \ (v^1_1 \vee \ldots \vee v^m_1) \wedge \ldots \wedge (v^1_{k+1} \vee \ldots \vee v^m_{k+1}) \]
are readily seen to require size $\geq m^{k+1}$ to refute (see the forthcoming Observation~\ref{obs:1}).\footnote{This example $(\Theta_{m,k},k)$ seems to have originated independently with Neil Thapen and the present author. It then appeared variously in private communications and it is explained and attributed explicitly to an anonymous referee in \cite{BGLR}.} The most interesting of the further systems discussed in \cite{FOCS2007,FOCS2007journal} we will call \emph{embedded $\W[2]$-parameterized Resolution}. It involves the adding of pigeonhole axioms to directly axiomatise the fact that no more than $k$ of the propositional variables may be evaluated to true. No lower bounds are currently known for this system (in particular the $(\Theta_{m,k},k)$ admit fpt-bounded refutations in this system).
In this note we explore the possibility of a program of parameterized proof complexity that gains direct evidence that $\W[1]$ is different from $\FPT$ (note that the program of \cite{FOCS2007,FOCS2007journal} could be recast anywhere between $\W[2]$ and $\WSAT$, but not lower in the W-hierarchy). Of course, the separation of $\W[1]$ from $\FPT$ is harder than $\W[2]$ from $\FPT$, but we might still wish to attack it directly. Here we seek to refute \emph{weighted parameterized contradictions in $3$-CNF} \mbox{i.e.} propositional $3$-CNF formulae $\mathcal{F}$ with no satisfying assignment of weight \textbf{$= k$}. We go on to explore lower and upper bounds. The trivial lower bound of $(\Theta_{m,k},k)$ no longer applies, and we are forced to look for an alternative. However, the alternative we provide -- although simple -- also gives a lower bound for the new version of \emph{embedded $\W[1]$-parameterized Resolution}.
Another interesting thing about our \emph{$\W[1]$-parameterized Resolution} is that all weighted parameterized contradictions $(\mathcal{F},k)$ created from actual contradictions (\mbox{i.e.} in which $\mathcal{F}$ is a contradiction) become fpt-bounded. This contrasts sharply with the case for parameterized proof systems for $\W[2]$ and above. Indeed, the authors of \cite{BGLR} even suggest to restrict attention to so-called ``strong parameterized contradictions'' $(\mathcal{F},k)$ in which $\mathcal{F}$ is a contradiction itself -- though this is largely in response to the problems posed by $(\Theta_{m,k},k)$. Owing to this, the gap theorem of \cite{FOCS2007,FOCS2007journal} does not fit naturally in this framework, although it can be forced in -- rather as it is in \cite{FOCS2007journal}.
Aside from $(\Theta_{m,k},k)$, the state-of-the-art for parameterized contradictions (coming from actual contradictions) involves non-fpt-boundedness of the pigeonhole principle in $\W[2]$-parameterized bounded-depth Frege in \cite{BGLR}. Similar lower bounds had been derived for $\W[2]$-parameterized tree-Resolution in \cite{FOCS2007} and for $\W[2]$-parameterized Resolution in \cite{Galesietal}.
The paper is organised as follows. After preliminaries and known results, we explore $\W[1]$-parameterized Resolution, with lower bounds in Section \ref{sec:3.2} and upper bounds in Section \ref{sec:3.2}. Finally, we explore lower bounds for embedded $\W[1]$-parameterized Resolution in Section \ref{sec:3.3}.
\section{Preliminaries}
A \emph{parameterized language} is a language $L\subseteq \Sigma^* \times \mathbb{N}$; in an instance $(x,k) \in L$, we refer to $k$ as the \emph{parameter}. A parameterized language is \emph{fixed-parameter tractable} (fpt - and in \FPT) if membership in $L$ can be decided in time $f(k).|x|^{O(1)}$ for some computable function $f$. If FPT is the parameterized analog of P, then (at least) an infinite chain of classes vye for the honour to be the analog of NP. The so-called W-hierarchy sit thus: $\FPT \subseteq \W[1] \subseteq \W[2] \subseteq \ldots \subseteq \WSAT$. For more on parameterized complexity and its theory of completeness, we refer the reader to the monographs \cite{DowneyFellows,FlumGrohe}. Recall that the \emph{weight} of an assignment to a propositional formula is the number of variables evaluated to true. Of particular importance to us is the parameterized problem \textsc{Weighted-3CNF-Sat} (resp., \textsc{Bounded-CNF-Sat}, \textsc{Bounded-Sat}) whose input is $(\mathcal{F},k)$ where $\mathcal{F}$ is a formula in $3$-CNF (resp., CNF, unrestricted) and whose yes-instances are those for which there is a satisfying assignment of weight $=k$ (resp., $\leq k$, $\leq k$). \textsc{Weighted-3CNF-Sat}, \textsc{Bounded-CNF-Sat} and \textsc{Bounded-Sat} are complete for the classes $\W[1]$, $\W[2]$ and $\WSAT$.\footnote{For proofs of latter two completeness results see \cite{FOCS2007,FOCS2007journal}, respectively.} Their respective complements (modulo instances that are well-formed formulae) we call \textsc{PCon}, \textsc{PCon-CNF} and \textsc{W-PCon-3CNF}, complete for the classes co-$\W[1]$, co-$\W[2]$ and co-$\WSAT$. For example, \textsc{PCon} is the language of \emph{parameterized contradictions}, $(\mathcal{F},k)$ \mbox{s.t.} $\mathcal{F}$ has no satisfying assignment of weight $\leq k$; and \textsc{W-PCon-3CNF} contains all $(\mathcal{F},k)$ \mbox{s.t.} $\mathcal{F}$ has no satisfying assignment of weight $= k$.
A \emph{proof system} for a parameterized language $L \subseteq \Sigma^* \times \mathbb{N}$ is a poly-time computable function $P:\Sigma^* \rightarrow\Sigma^*\times \mathbb{N}$ \mbox{s.t.} $\mathrm{range}(P)=L$. $P$ is \emph{fpt-bounded} if there exists a computable function $f$ so that each $(x,k)\in L$ has a proof of size at most $f(k).|x|^{O(1)}$.
These definitions come from \cite{Galesietal,BGL-SAT,BGLR} and are slightly different from those in \cite{FOCS2007,FOCS2007journal} (they are less unwieldy and have essentially the same properties). The program of \emph{parameterized proof complexity} is an analog of that of Cook-Reckow \cite{Proof_Complexity_start}, in which one seeks to prove results of the form co-$\W[x]\neq$co-$\W[x]$ by proving that parameterized proof systems are not fpt-bounded. This comes from the observation that there is an fpt-bounded parameterized proof system for a co-$\W[x]$-complete $L$ iff $\W[x]=$co-$\W[x]$.
\emph{Resolution} is a refutation system for contradictions $\Phi$ in CNF. It operates on clauses, by the \emph{resolution} rule in which from $(P \vee x)$ and $(Q \vee \neg x)$ one can derive $(P \vee Q)$ ($P$ and $Q$ are disjunctions of literals), with the goal being to derive the empty clause. The only other permitted rule in weakening -- from $P$ to derive $P \vee l$ for a literal $l$. We may consider a Resolution refutation to be a DAG whose sources are labelled by initial clauses, whose unique sink is labelled by the empty clause, and whose internal nodes are labelled by derived clauses. As we are not interested in polynomial factors, we will consider the \emph{size} of a Resolution refutation to be the size of this DAG. Further, we will measure this size of the DAG in terms of the number of variables in the clauses to be resolved -- we will never consider CNFs with number of clauses superpolynomial in the number of variables.
We define the restriction of Resolution, \emph{tree-Resolution}, in which we insist the DAG be a tree.
The version of parameterized Resolution given for $\WSAT$ in \cite{FOCS2007journal} is a bit awkward in that involves converting non-CNFs to CNF, so we will stick to that in \cite{FOCS2007}. The system of \emph{$\W[2]$-parameterized Resolution} seeks to refute the parameterized CNF contradictions of \textsc{PCon-CNF}. Given $(\mathcal{F},k)$, where $\mathcal{F}$ is a CNF in variables $x_1,\ldots,x_n$, it does this by providing a Resolution refutation of
\begin{equation}
\mathcal{F}\cup \{\neg x_{i_1}\vee \ldots \vee \neg x_{i_{k+1}} : 1 \leq i_1 < \ldots < i_{k+1} \leq n \}.
\label{equ:W[2]}
\end{equation}
Thus, in $\W[2]$-parameterized Resolution we have built-in access to these additional clauses of the form $\neg x_{i_1}\vee \ldots \vee \neg x_{i_{k+1}}$, but we only count those that appear in the refutation.
In \emph{$\W[1]$-parameterized Resolution}, we seek to refute the weighted parameterized $3$-CNF contradictions of \textsc{W-PCon-3CNF}. Given $(\mathcal{F},k)$, where $\mathcal{F}$ is a $3$-CNF in variables $x_1,\ldots,x_n$, we do this by providing a Resolution refutation of
\begin{equation}
\begin{array}{ll}
\mathcal{F} & \cup \{\neg x_{i_1}\vee \ldots \vee \neg x_{i_{k+1}} : 1 \leq i_1 < \ldots < i_{k+1} \leq n \} \\
& \cup \{ x_{i_1}\vee \ldots \vee x_{i_{n-k+1}} : 1 \leq i_1 < \ldots < i_{n-k+1} \leq n \}.
\end{array}
\label{equ:W[1]}
\end{equation}
Note that we may consider any refutation system as a $\W[2]$- or $\W[1]$-param- eterized refutation system, by the addition of the clauses given in (\ref{equ:W[2]}) or (\ref{equ:W[1]}), respectively.
Let $[n]:=\{1,\ldots,n\}$. The \emph{pigeonhole principle} will play a role in the paper. Its negation, PHP$_{n+1,n}$, is a contradiction most easily given by the clauses $\neg p_{i,j} \vee \neg p_{l,j}$ ($i\neq l \in [n+1]$ and $j \in [n]$) and $\bigvee_{\lambda \in [n]} p_{i,\lambda}$ ($i \in [n+1]$). PHP$_{n+1,n}$, and its variants, provide contradictions that are ubiquitous in proof complexity, especially since Haken proved an exponential lower bound for it in Resolution \cite{Haken's_classical}.
\subsection{Known Results}
There is a canonical way to translate first-order (fo) sentences $\phi$ to sequences of CNF formulae $\langle\Phi_n\rangle_{n \in \mathbb{N}}$ such that $\Phi_n$ is satisfiable iff $\phi$ had a model of size $n$ (see \cite{FOCS2007} based on \cite{complexity_gap}). When $\phi$ has no finite models, then $\langle\Phi_n\rangle_{n \in \mathbb{N}}$ is a sequence of contradictions ripe for a refutation system. Note that the size of $\Phi_n$ is polynomial in $n$. The famous theorem of Riis goes as follows.
\begin{thm}[Riis 2001 \cite{complexity_gap}]
For an fo-contradiction $\phi$, either: 1.) $\langle\Phi_n\rangle_{n \in \mathbb{N}}$ is refutable in tree-Resolution in size $n^{O(1)}$, or 2.) exists $\epsilon>0$ \mbox{s.t.} every tree-Resolution refutation of $\langle\Phi_n\rangle_{n \in \mathbb{N}}$ is of size $>2^{\epsilon n}$. Furthermore, Case 2 prevails precisely when $\phi$ has some infinite model.
\end{thm}
\noindent In the parameterized setting one might hope for a finer classification of Case 2, and indeed that is what was given in \cite{FOCS2007}.
\begin{thm}[Dantchev, Martin and Szeider \cite{FOCS2007}]
For an fo-contradiction $\phi$ with an infinite model, either: 2a.) $\langle(\Phi_n,k)\rangle_{n \in \mathbb{N}}$ is refutable in $\W[2]$-paramet- erized tree-Resolution in size $\beta^k n^{\alpha}$ ($\alpha$ and $\beta$ constants depending on $\phi$ only), or 2b.) exists $\gamma>0$ \mbox{s.t.} every $\W[2]$-parameterized tree-Resolution refutation of $\langle(\Phi_n,k) \rangle_{n \in \mathbb{N}}$, for $n>k$, is of size $>n^{k^\gamma}$. Furthermore, Case 2b prevails precisely when $\phi$ has a model without a certain kind of finite dominating set.
\end{thm}
\noindent Since Case 2b can be attained, for example when $\phi$ expresses the negation of the pigeonhole principle, it follows that $\W[2]$-parameterized tree-Resolution is not fpt-bounded. The same principle in fact yields a sequence that proves that $\W[2]$-parameterized Resolution is not fpt-bounded \cite{Galesietal}, though this latter fact is somehow trivial in light of the following. Recall $(\Theta_{m,k},k)$ involving $n:=m.(k+1)$ variables.
\begin{observation}
\label{obs:1}
$(\Theta_{m,k},k)$ requires size $\geq m^{k+1}$ (\mbox{i.e.} $\geq \left( \frac{n}{k+1}\right)^{k+1}$) to be refuted in $\W[2]$-parameterized Resolution.
\end{observation}
\noindent This is because we need all $m^{k+1}$ clauses of the form $\neg v^{a_1}_1 \vee \ldots \vee \neg v^{a_{k+1}}_{k+1}$, $a_1,\ldots,a_{k+1} \in \{1,\ldots,m\}$ (comprising the set $\Gamma$), for $\Theta_{m,k} \cup \Gamma$ to be a logical contradiction. That is, for $\Gamma'$ a strict subset of $\Gamma$, $\Theta_{m,k} \cup \Gamma'$ is satisfiable.
If we considered $\W[2]$-parameterized depth-2 Frege (see \cite{Krajicek's_Book} for additional definitions), then $(\Theta_{m,k},k)$ would technically remain not fpt-bounded, because of the large number of additional axioms needed from (\ref{equ:W[2]}). But, those $n^{k+1}$ additional axioms (recall $n:=m(k+1)$) could be coded as a single axiom in depth $2$ -- thus $(\Theta_{m,k},k)$ would essentially become easy. One might reasonably complain, however, that the size of that axiom would be $n^{k+1}$.
\section{Properties of $\W[1]$-parameterized Resolution}
\label{sec:3}
\subsection{Lower bounds}
\label{sec:3.1}
Since $(\Theta_{m,k},k)$ is not a $3$-CNF, it does not provide a trivial reason for $\W[1]$-parameterized Resolution to not be fpt-bounded. However, there is a canonical way to turn CNFs to $3$-CNFs by the use of extension variables, where each clause $(v^1_i \vee \ldots \vee v^m_i)$ becomes, e.g., the conjunction of $(v^1_i \vee v^2_i \vee \neg z^1_i)$, $(z^1_i \vee v^3_i \vee \neg z^2_i)$, \ldots, $(z^{m-4}_i \vee v^{m-2}_i \vee \neg z^{m-3}_i)$, $(z^{m-3}_i \vee v^{m-1}_i \vee v^m_i)$ (where $z^1_i,\ldots,z^{m-3}_i$ are new variables). This or variants thereof is the standard method to reduce SAT to $3$-SAT, known as standard nondeterministic extension in \cite{AlekhnovichBRW02}. Suppose we thus transform the CNF $(\Theta_{m,k},k)$ to the $3$-CNF $(\Theta'_{m,k},k)$. It is easy to see by the method of a Boolean decision tree solving the search problem, that $(\Theta'_{m,k},k)$ admits $\W[1]$-parameterized \textbf{tree}-Resolution of size $\leq 7^{k+1}$. Of course, this is due to the extra variables we have added and the way in which they contribute to the weight.
Therefore, we must look elsewhere: for $n$ even, define
\[ \Psi_{n,k}:= \ \ \{v_1\leftrightarrow v_2, v_3 \leftrightarrow v_4, \ldots , v_{n-1} \leftrightarrow v_n \}, \]
where $v_i \leftrightarrow v_{i+1}$ abbreviates $(v_i \vee \neg v_{i+1}), (v_{i+1}\vee \neg v_i)$. Note that $(\Psi_{n,k},k)$ is not a parameterized contradiction, but is a weighted parameterized contradiction.
\begin{lem}
For $k$ odd, $(\Psi_{n,k},k)$ requires size $\geq \left(\frac{n}{2}\right)^{k/2}$ to be refuted in $\W[1]$-parameterized Resolution.
\end{lem}
\begin{pf}
The argument is similar to that for Observation~\ref{obs:1}. We need at least $\left(\frac{n}{2}\right)^{(k+1)/2}$ clauses of the form
\[\neg v_{2a_1-1} \vee \neg v_{2a_1} \vee \ldots \ldots \vee \neg v_{2a_{(k+1)/2}-1} \vee \neg v_{2a_{(k+1)/2}},\]
(comprising the set $\Gamma$), for $\Psi_{n,k} \cup \Gamma$ to be a logical contradiction. That is, for $\Gamma'$ a strict subset of $\Gamma$, $\Psi_{n,k} \cup \Gamma'$ is satisfiable.
\end{pf}
\subsection{Upper bounds}
\label{sec:3.2}
In the world of $\W[1]$-parameterized Resolution, we have the agreeable situation that non-parameterized contradictions, in $3$-CNF, are always easy to refute (something that does not happen for the $\W[2]$ or $\WSAT$ versions).
\begin{lem}
\label{lem:upper-bound}
Let $\Phi$ be a contradiction in $3$-CNF and let $k$ be arbitrary) then $(\Phi,k)$ has fpt-bounded refutations (of size $\leq 3^{k+1}$) in $\W[1]$-parameterized tree-Resolution.
\end{lem}
\begin{pf}
Prove that $\Phi$ has no satisfying assignment of weight $\leq k+1$ by recursive branching over positive clauses. The positive clauses will not be used up in this process because if they were, this would witness a satisfying assignment for $\Phi$.
\end{pf}
\noindent This means that for lower bounds, one must look at \emph{proper} parameterized contradictions, that \textbf{do} have some satisfying assignments, just not of weight $k$. Our terming of this ``agreeable'' is in sharp contrast to the situation for $\W[2]$, in which the authors of \cite{BGLR} suggest -- as mentioned before -- to restrict attention purely to parameterized contradictions derived from actual contradictions.
\subsection{Embedding into Resolution}
\label{sec:3.3}
We may consider any $3$-CNF weighted parameterized contradiction augmented with pigeonhole clauses enforcing the condition that precisely $k$ variables may be evaluated to true. In this manner, we obtain the system of \emph{embedded $\W[1]$-parameterized Resolution}. A similar system -- \emph{embedded $\W[2]$-parameterized Resolution} -- was presented in \cite{FOCS2007,FOCS2007journal} for parameterized contradictions.
Given a weighted parameterized contradiction $\Phi_n$, in variables $x_1,\ldots,x_{n}$, we construct $\Phi'_n$ with additional variables $r_{x_1,j},\ldots,r_{x_n, j}$ ($j \in [k]$) and $s_{x_1,j},\ldots,s_{x_n,j}$ ($j \in [n-k]$). The clauses of $\Phi'_n$ are those of $\Phi_n$ augmented by the following pigeonhole clauses.
\[ \mbox{$\neg x_i \vee \bigvee_{l=1}^{k} r_{x_i,l}$ and $\neg x_i \vee \neg
r_{x_i,j} \vee \neg r_{x_{l},j}$ for $i\neq l \in [n]$ and $j \in [k]$.} \]
\[ \mbox{$x_i \vee \bigvee_{l=1}^{n-k} s_{x_i,l}$ and $x_i \vee \neg
s_{x_i,j} \vee \neg s_{x_{l},j}$ for $i\neq l \in [n]$ and $j \in [n-k]$.} \]
$\Phi'_{n}$ is an ordinary contradiction ripe for an ordinary refutation system (it is no concern that $\Phi'_{n}$ itself is not $3$-CNF).
Let $\Psi'_{n,k}$ be the CNF generated from the $3$-CNF $\Psi_{n,k}$ by this method. Seeing the two asymmetric pigeonhole principles lurking within $\Psi'_{n,k}$, the following will not be a huge surprise.
\begin{lem}
\label{lem:simple}
Let $k$ be an odd number. Then for no function $f$ and positive integer $c$, can $\Psi'_{n,k}$ be refuted in Resolution in size $f(k).n^c$.
\end{lem}
\begin{pf}
We know from \cite{Haken's_classical} that PHP$_{n+1,n}$ is a family of contradictions without polynomial-size Resolution refutations. Consider the family $\mathcal{P}_{n,k}$ of CNF contradictions in variables $c_1,c_2$, $p_{i,j}$ $(i \in [n]; j\in [k])$ and $s_{i,j}$ $(i \in [n]; j\in [n-k])$, with clauses:
\[
\begin{array}{ll}
\neg c_1 \leftrightarrow c_2 \\
\neg c_1 \vee \neg p_{i,j} \vee \neg p_{l,j} & i \neq l \in [n]; j \in [k] \\
\neg c_1 \vee \bigvee_{\lambda \in [k]} p_{i,\lambda} & i \in [n] \\
\neg c_2 \vee \neg q_{i,j} \vee \neg q_{l,j} & i \neq l \in [n]; j \in [n-k] \\
\neg c_2 \vee \bigvee_{\lambda \in [n-k]} q_{i,\lambda} & i \in [n] \\
\end{array}
\]
\noindent This contains twin pigeonhole principles and is at least as hard to refute as the hardest of these two. To see this, one may consider the decision DAG model with forced assignments to $c_1$ (and therefore $c_2$). The so-restricted decision DAG would then give a refutation of PHP$_{n,k}$ ($c_1$ true) and a refutation of PHP$_{n,n-k}$ ($c_1$ false). In fact, there are never polynomial refutations of $\mathcal{P}_{n,k}$ for any fixed $k$ (as PHP$_{n,n/2}$ is known to be hard \cite{Razborov_WPHP}). However, we need only consider $k=1$ and the fact that $\mathcal{P}_{n,k}$ can therefore not be refuted in Resolution in size $f(k).n^c$ (for any $f$ and $c$).
To complete our proof, we will now reduce $\mathcal{P}_{n,k}$ to $\Psi'_{n,k}$ in order to translate lower bounds of the former to the latter. Using the reduction $x_i := \neg c_2$, $r_{x_i,j}:= p_{i,j}$ and $s_{i,j}:=q_{i,j}$, we claim we can derive in Resolution, in a linear number of steps, the clauses of $\Psi'_{n,k}$ from the clauses of $\mathcal{P}_{n,k}$, whereupon the result follows.
To settle the claim, note that all instances of $v_i \leftrightarrow v_{i+1}$ come from $\neg c_1 \leftrightarrow c_2$. $v_i \vee \neg s_{v_i,j} \vee \neg s_{v_{i'},j}$ and $v_i \vee \bigvee_{l=1}^{n-k} s_{v_i,l}$ are immediate. And $\neg v_i \vee \bigvee_{l=1}^{k} r_{v_i,l}$ and $\neg v_i \vee \neg r_{v_i,j} \vee \neg r_{v_{i'},j}$ involve a series of resolutions with $c_1 \vee \neg c_2$.
\end{pf}
\begin{cor}
Embedded $\W[1]$-parameterized Resolution is not fpt-bounded.
\end{cor}
\noindent We conclude this note with the recollection that the fpt-boundedness of embedded $\W[2]$-parameterized Resolution remains unknown.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,047 |
Q: Generated SQL query with "WHERE (1 <> 1)" condition I'm trying to query a many-to-many relationship using the Gorm ORM for Go.
I have two structs: User & Address.
type User struct {
// gorm.Model
UUID string `gorm:"type:uuid;primary_key;auto_increment:false"`
Firstname string
// ...
Addresses []Address `gorm:"many2many:useraddresses"`
}
// Address represents the Postgres SQL address model
type Address struct {
UUID string `gorm:"type:uuid;primary_key;auto_increment:false"`
Line1 string
// ...
}
I took inspiration from the many-to-many example shown here in the documentation, (except I used a slice of users []User instead of a single user).
var u []User
var a []Address
If I query just using the users as a Model, all users are returned (sends sql query SELECT * FROM "users"):
db.Model(&u).Find(&u)
However, if I include related Addresses, surgeons are returned, but no Addresses:
db.Model(&u).Related(&a, "Addresses").Find(&u)
This creates another sql query that precedes the first:
SELECT "addresses".*
FROM "addresses" INNER JOIN "useraddresses" ON "useraddresses"."address_uuid" = "addresses"."uuid"
WHERE (1 <> 1)
Of course, the where false condition prevents any addresses from being returned.
Can anyone shed light on how I can include the addresses using the db.Model method of Gorm?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,660 |
{"url":"http:\/\/math.usf.edu\/research\/colloquia\/","text":"USF Home > College of Arts and Sciences > Department of Mathematics & Statistics\n\nMathematics & Statistics\nColloquium Archive\n\n# Colloquia \u2014 Spring 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nSerguei Denisov\n3:00pm-4:00pm\nCMC 130\nE. A. Rakhmanov\n\nAbstract\n\nTBA\n\n## Friday, April 29, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nAbdenacer Makhlouf\nUniversit\u00e9 de Haute Alsace\n3:00pm-4:00pm\nCMC 130\n\nAbstract\n\nTBA\n\n## Friday, April 22, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nYukio Matsumoto\nUniversity of Tokyo\n3:00pm-4:00pm\nCMC 130\nMasahiko Saito\n\nAbstract\n\nTBA\n\n## Friday, April 15, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nKaren Keene\nNorth Carolina State\n3:00pm-4:00pm\nCMC 130\nMil\u00e9 Kraj\u010devski\n\nAbstract\n\nTBA\n\n## Friday, April 8, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nMichael A. H\u00f6gele\nBogot\u00e1, Colombia\n3:00pm-4:00pm\nCMC 130\nYuncheng You\n\nAbstract\n\nTBA\n\n## Friday, April 1, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nKeqin Feng\nTsinghua University\nBeijing, China\n3:00pm-4:00pm\nCMC 130\nXiang-dong Hou\n\nAbstract\n\nTBA\n\n## Friday, March 25, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nPolytopes of Stochastic Tensors\nFuzhen Zhang\nNova Southeastern University\nFort Lauderdale\n3:00pm-4:00pm\nCMC 130\nWen-Xiu Ma\n\nAbstract\n\nA square matrix is doubly stochastic if its entries are all nonnegative and each row and column sum is 1. A celebrated result known as Birkhoff's theorem about doubly stochastic matrices states that an $$n\\times n$$ matrix is doubly stochastic if and only if it is a convex combination of some $$n\\times n$$ permutation matrices (a.k.a. Birkhoff polytope).\n\nWe study the counterpart of the Birkhoff's theorem for higher dimensions. An $$n\\times n\\times n$$ stochastic tensor is a nonnegative array (hypermatrix) in which every sum over one index is 1. We study the polytope ($$O$$) of all these tensors, the convex set ($$L$$) of all tensors with some positive diagonals, and the polytope ($$T$$) generated by the permutation tensors. We show that $$L$$ is almost the same as $$O$$ except for some boundary points. We also present an upper bound for the number of vertices of $$O$$.\n\n## Friday, March 11, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nConstanze Liaw\nBaylor University\n3:00pm-4:00pm\nCMC 130\nAlan Sola\n\nAbstract\n\nTBA\n\n## Friday, February 26, 2016\n\nTitle\n\nSpeaker\n\nTime\nPlace\n\nCavitation of spherical bubbles with surface tension and viscosity and connection with FRW cosmological equations\nStefan C. Mancas\nEmbry-Riddle Aeronautical University\n3:00pm-4:00pm\nCMC 130\nRazvan Teodorescu\n\nAbstract\n\nIn this talk an analysis of the Rayleigh-Plesset (RP) equation for a three dimensional vacuous bubble in water is presented. When the e ects of surface tension are neglected we find the radius and time of the evolution of the bubble as parametric closed-form solutions in terms of hypergeometric functions. By including capillarity we show the connection between RP equation and Abel's equation, and we present parametric rational Weierstrass periodic solutions for nonzero surface tension. When viscosity is present we present only numerical solutions. We also show the connection between the RP equation and Einstein's field equations for spatially curved FRW cosmology.\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTBA\nThomas Banchoff\nBrown University\n3:00pm-4:00pm\nCMC 130\nMil\u00e9 Kraj\u010devski\n\nAbstract\n\nTBA\n\n## Friday, February 12, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nTiling and spectral are equivalent in $$\\mathbb{Z}_p^2$$\nAzita Mayeli\nQCC and the Graduate Center, CUNY\n3:00pm-4:00pm\nCMC 130\nArthur Danielyan\n\nAbstract\n\nThe equivalence relation between tiling and spectral property of a set has its root in the Fuglede Conjecture a.k.a. Spectral Set Conjecture in $$\\Bbb R^d$$, $$d\\geq 1$$. In 1974, Fuglede stated that a bounded Lebesgue measurable set $$\\Omega\\subset\\Bbb R^d$$, with positive and finite measure, tiles $$\\Bbb R^d$$ by its translations if and only if the Hilbert space $$L^2(\\Omega)$$ possesses an orthogonal basis of exponentials. A variety of results were proved for establishing connection between tiling and spectral property for some special cases of $$\\Omega$$. However, the conjecture is false in general for dimensions $$3$$ and higher.\n\nIn this talk, we will define the tiling and spectral sets $$E\\subseteq\\Bbb Z_p\\times\\Bbb Z_p$$, $$p$$ prime, and show that these two properties are equivalent for $$E$$. In other words, we prove that the Fuglede Conjecture holds for $$\\Bbb Z_p\\times \\Bbb Z_p$$.\n\n## Friday, February 5, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nThe phenomena of heavy tails in physical models including random matrices\nPaul Jung\nUniversity of Alabama at Birmingham\n3:00pm-4:00pm\nCMC 130\nSeung-Yeop Lee\n\nAbstract\n\nWe will discuss a toy model of heavy tails and show how this does not follow central limit behavior. We will then see how this relates to models in physics including random matrices. In the random matrix setting, we equate limiting spectral distributions (LSD) to spectral measures of rooted graphs. The LSD result also includes matrices with i.i.d. entries (up to self-adjointness) having infinite second moments, but following central limit behavior. In this case, the graph is the natural numbers rooted at one, so the LSD is well-known to be the semi-circle law.\n\n## Friday, January 29, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nGraph Polynomials motivated by Gene Assembly\nHendrik Jan Hoogeboom\nUniversity of Leiden\nthe Netherlands\n3:00pm-4:00pm\nCMC 130\nNata\u0161a Jonoska\n\nAbstract\n\nThe interlace polynomial was discovered by Arratia, Bollobas, and Sorkin by studying DNA sequencing methods. Its definition can be traced from 4-regular graphs (the Martin polynomial), to circle graphs and finally to arbitrary graphs.\n\nOur interest in these polynomials came from the study of ciliates, an ancient group of unicellular organisms. They have the remarkable property that their DNA is stored in two vastly different types of nuclei. The two representations of the versions of the gene can be elegantly modelled using a 4-regular graph.\n\nWe give an overview of the polynomials involved, their basic properties, and their relation to the Tutte polynomial. Joint work with Robert Brijder, Hasselt Belgium.\n\nTitle\nSpeaker\n\nTime\nPlace\n\nLocal Gaussian process approximation for large computer experiments\nRobert B. Gramacy\nUniversity of Chicago\n2:00pm-3:00pm\nCMC 130\nLes\u026baw Skrzypek\n\nAbstract\n\nWe provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built-up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, GPUs, and cluster computing, while at the same time allowing for a non stationary modeling feature as a bonus. We demonstrate our method on examples utilizing designs sized in the tens of thousands to over a million data points. Comparisons are made to the method of compactly supported covariances, and we present applications to computer model calibration of a radiative shock and the calculation of satellite drag.\n\n## Friday, January 22, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nMinimal Energy and Maximal Polarization\nEdward B. Saff\nVanderbilt University\n3:00pm-4:00pm\nCMC 130\nVilmos Totik\n\nAbstract\n\nThe work to be discussed has its origins in research conducted at USF some twenty years ago. It concerns minimal energy configurations as well as maximal polarization (Chebyshev) configurations on manifolds, which are problems that are asymptotically related to best-packing and best-covering.\n\nIn particular, we discuss how to generate $$N$$ points on a $$d$$-dimensional manifold that have the desirable qualities of well-separation and optimal order covering radius, while asymptotically having a given distribution. Even for certain small numbers of points like $$N=5$$, optimal arrangements with regard to energy and polarization can be a challenging problem.\n\n## Friday, January 15, 2016\n\nTitle\nSpeaker\n\nTime\nPlace\n\nOn the Complexity of Conjugacy Problem in certain Metabelian Groups\nDelaram Kahrobaei\n3:00pm-4:00pm\nCMC 130\nDima Savchuk\n\nAbstract\n\nWe analyze the computational complexity of the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most exponential. For a subfamily of groups we prove that the conjugacy search problem is polynomial. We also show that for some of these groups the conjugacy search problem reduces to the discrete logarithm We also provide experimental evidence which illustrates our results probabilistically. This is a joint work with Conchita Martinez and Jonathan Gryak.\n\nPolycyclic and Metabelian groups have been proposed as platform for Cryptography by Eick and Kahrobaei some years ago. The results I am presenting will have potential applications in Cryptography. The interesting question would be whether such cryptosystems are resistant against quantum algorithms.\n\nTitle\nSpeaker\n\nTime\nPlace\nCombinatorialists use the probabilistic method to construct impossibly large graphs and study their properties. 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News and Publications > Articles
Will New Children's Center Change Pediatric Medicine at Hopkins?
Realizing the Promise in the Bloomberg Children's Center
The Charlotte R. Bloomberg Children's Center and, at left, neighboring Sheikh Zayed Tower.
On the evening of April 12th, the Mayor of New York City stood before more than 1,400 dignitaries, donors, and doctors. They had all gathered for the dedication of The Charlotte R. Bloomberg Children's Center, and His Honor, Charlotte's son, Michael Bloomberg, was in fine form. In tones both hopeful and bar-setting, Bloomberg spoke of the promise of the impressive new 12-story edifice. "If this center will bring the youngest and most vulnerable patients the kind of care and comfort that they need; if it will increase the knowledge and experience of the greatest doctors and teachers; if it will inspire other institutions to do more and do better," said Bloomberg, "then we all will be happy." So what will it take to make all those 'ifs' go away? And how far can a new Children's Center take Hopkins down that path?
Consider what may eventually be called, simply, "The Choice." When the history of this clinical building is written in a few generations, of all the decisions that will have woven its hopefully successful tale, perhaps none will have been more critical than the judgment to integrate the new children's hospital into the existing East Baltimore campus.
The choice of whether to go free¬standing or remain physically part of the medical community was a matter of lengthy debate. According to Children's Center Director George Dover, several off-campus sites were on the table, including a potential "Super Center" that would have combined the institutional knowledge and experience of both Hopkins and the University of Maryland in a central downtown location.
Dover well understood the allure and prestige of a move to a freestanding structure. He notes that many of the country's finest care centers for children have stand-alone status, including Children's Hospital of Philadelphia (CHOP), D.C.'s Children's National Medical Center, and Wilmington's (DE) Nemours/DuPont Hospital for Children.
Dover could have pushed in that direction, but feared that achieving breakaway status would negatively impact the kind of visionary medicine he felt bore the Hopkins stamp. In Dover's mind, it came down to a single priority: Be the best, or be the biggest. From that vantage point, the call practically made itself. "We never designed this place to be the biggest," says Dover. "In fact, the number of beds in this building is smaller than D.C. Children's, CHOP, and DuPont, our major competitors. We didn't even try to get where they were."
Dover says limiting size directly affects quality of care, both now and in the future. Pushing up the bed count strictly to pump up the volume of patients could, in Dover's opinion, fundamentally alter the Children's Center's century-old mission. "If we hired faculty to serve those additional beds, and they were working 100 percent of the time, clinically, they wouldn't be innovating, they'd just be keeping up with the clinical demands," Dover says. "We still want to hire physicians who can do both research and clinical work, but if we grow too big, our faculty won't have the time to do both."
To Dover, freestanding status would have limited the fertile ground for seeding such breakthroughs, the research equivalent of moving from a beautiful botanical garden to a rooftop herbal planter. Dover cites the thoughts of the last Children's Center director who opened a new hospital, Robert Cooke. In 1964 Cooke, in his dedication speech, worried that moving into the larger CMSC could trigger rapid growth, create silos, and weaken pediatrics' long-standing reputation for collegiality with their adult medicine counterparts. "(Cooke said) that the culture depended upon people being close to each other, bumping into each other," to create and nurture ideas, says Dover. "That without this closeness, the 'aura' around pediatrics could be threatened." That concern resonated a half-century later as Dover contemplated the Children's Center's path. He decided to stay on the road well traveled.
"The most important structural thing that will allow us to continue to innovate is being connected to the rest of the hospital," he says. "Those eight stories that bridge the children's tower and the adult tower; the fact we're sitting on the same parcel as the Dome, across the street from the School of Public Health, down the block from the basic sciences and the School of Medicine, across the street from the new Armstrong Education building, and the fact that we stayed in this environment is the major thing that will allow us to innovate. Sometimes it's not what you do that's important, but what you don't do."
This continuing connection and sharing with adult medicine can be seen literally at the new hospital's front door, where the Pediatric and Adult Emergency Departments stand side-by-side. But there's more than symbolism at work here; there's a direct benefit to pediatric emergency cases.
"We put CT scanners, MRIs, and trauma bays between the Adult ED and the pediatric unit," says Dover. "We don't have enough patients coming solely to the pediatric unit to justify that, but when you combine the adult patients and pediatric pa¬tients it makes sense. So we can actually take some of the present technology and bring it closer to the bedside because we're willing to share it with our adult colleagues."
The structure also offers a unification of sorts, which could well amp-up synergies between pediatric specialties. Between the modern David M. Rubenstein Child Health Building, opened in 2006, and the bridge-connected Bloomberg Children's Center, nearly all of the pediatric clinical services have been joined together, or as Dover puts it, consolidated in a more focused fashion.
"When you decide to build a building across the street exclusively for pediatric outpatients (Rubenstein), when you decide to build a tower exclusively for pediatric inpatients, one of the things you do is bring the pediatric community even closer together," Dover says. "Giving a sense of identity to pediatrics which will attract all these wonderful people into our building is a great idea, and because we're so close to the adult side, we're not separating ourselves. Once we made that choice, we began to see the opportunity to do some remarkable things."
In 2001, just as plans for the new Children's Center were in their embryonic stages, the Institute of Medicine laid down a formidable gauntlet. Their report entitled: Crossing the Quality Chasm: A New Health System for the 20th Century, didn't mince words. It condemned American medicine for being unresponsive to patient needs, uncoordinated in its application of care, and unnecessarily unsafe.
The IOM's report challenged institutions to improve in six areas and created a new buzzword for hospital administrators and faculty: Patient-Centered Care, or as the IOM put it, "providing care that is respectful of and responsive to individual patient preferences, needs, and values, and ensuring that patient values guide all clinical decisions."
To say that the phrase—adapted to the more universal "Patient- and Family-Centered Care"—has become the single guiding principle of the design and function of the new Children's Center would be neither understatement nor hyperbole. There's a microeconomics term called "The Second-Mover Advantage," which may best explain where the Bloomberg Children's Center stands as it opens its doors. Though Hopkins never claimed to be the first institution to practice patient- and family-centered care, they've used their "second-mover advantage" to learn from others' successes (and mistakes) in the field. Pediatric faculty, staff, and administrators made numerous trips to facilities across the country, gleaning a multitude of ideas and creating a master "wish-list" of patient-centered initiatives.
The result at this moment may well be the gold standard of patient-and family-centered care. Beautiful? Yes, so far as that term can apply to any structure made of concrete, steel, and glass. Lots and lots and lots of light-giving glass. But what's most impressive, from its outer skin to its inner wiring, is how form and function com¬bine to create a third, far more powerful element: Opportunity.
It's impossible to discuss the new building with faculty and not have words such as "opportunity" and "promise" pepper their conversation. To a person, they see the structure through their professional prism and glimpse new ways of healing. Call it the potential beyond the amenity, but it's everywhere one looks. For Child Life Director Patrice Brylske, those playful, oversized sculptures, the hundreds of pieces of fascinating art that dot the walls, the colorful playrooms on each floor, are more than just a delightful aesthetic; each is a potential conversation starter with a child, an entree for building trust and taking fear out of the hospital experience, which leads to better healing.
"The old building restricted a lot of the lovely things we wanted to do for patients and families, but this environment is so stimulating, so rich, it feels so freeing," says Brylske. "Now we have to challenge ourselves to use what's in this beautiful building to support our work."
Part of her vision involves using the Great Room—a two story gym-size facility on the 11th and 12th floors—and other open spaces to expand Child Life's creative arts program. "We have such diverse space now that we can accommodate a menagerie of artists, from music and art to dance, poetry and drama, elements that we didn't have the space for before, to have that quality interaction with patients and families."
Brylske also mentions the private rooms that are the standard accommodations as being of great benefit to engaging children in play, especially those who aren't mobile. The 205 private rooms are cited time and again by staff as perhaps the key central element in improving all aspects of patient care. Many are quick to point out the family-friendly details such as on-demand room service, family lounges with microwave ovens and overnight beds. Pleasing amenities to be sure, but purposeful as well; keeping families on-site longer and close to their loved ones has numerous ancillary benefits.
Sally Radovick, Director of Pediatric Endocrinology, sees the private rooms as offering the ideal educational space for parents who suddenly have to cope with a child's life-changing illness. She points to children admitted because of life-threatening diabetic ketoacidosis, often the first sign that they have Type 1 Juvenile Diabetes.
"An important aspect, during the acute phase, is to begin teaching (chronic disease management)," says Radovick. "Learning about insulin dosing, what type I diabetes is, nutritional support…it's critical for this initiation of self-care for the chronic state. Now, parents can stay with their child in a single room round the clock, and they can learn from the nursing staff and diabetes educators how to take care of this child, how to give the insulin injection, and participate in carbohydrate counting each meal, which was potentially more difficult to do in a room with two or more children."
Director of Pediatric Nephrology Barbara Fivush also credits the private rooms for fostering better staff-family/patient conversations. In just the short time the hospital has been open—the official start date was May 1st—Fivush says she can see and hear the change.
"Our service has many chronically impaired patients with complicated emotional problems…the conversations can get pretty detailed, and I think we felt un¬comfortable (in multi-family rooms) talking about their care," Fivush says. "Now we have the privacy to really get to spend time with our families, which promotes the ability to communicate better because you don't have to be concerned about who is listening and who else is in the room."
She adds, "I've just been on service in the new hospital this week, but I'm very impressed with the conversations we're having, about non-adherence, why they got kidney failure from a certain drug, why that drug was given to them in the first place…so many topics that are not naturally easy to discuss unless the environment is open to that."
Private rooms also increase patient safety, a key element of the IOM's pivotal report. "With private rooms, you don't worry about cross-infection from roommates," says pediatric pulmonologist Beryl Rosenstein, former long-time vice president for Medical Affairs at Johns Hopkins Hospital. In the old building, "we had to move patients around because of infection control issues. Now it's simple; every patient is in their own little cocoon."
And many systems have been built around preserving the sanctity and safety of that little cocoon. Marlene Miller, director of the Division of Quality and Safety, notes that drug delivery has been completely revamped from stem to stern. The pediatric pharmacy is five times larger than its predecessor, there are separate rooms with separate pass-throughs for IV meds, and quiet space for the pharmacists to do their dosage calculations without being disrupted. Also, the medication distribution system has been redesigned with more frequent delivery of meds, more frequent removal of the discontinued meds, and bedside delivery of medication so there's less distraction for the nurse.
"She's not in a med room with five other nurses all getting meds for their patients," says Miller. "Her patient's meds are right by the bedside."
Keeping the nurse with their patients, especially those who are critically ill, is a win-win result of another amenity, Clinical Customer Service Representatives (CCSR). In the past, PICU and NICU nurses would often be called away from their patients to meet families and instruct them on proper safety protocols before entering the rooms. Now, they can stay by the bedside, as the CCSR staff greet families at the entrance to each unit and prep them for their visit.
"The CCSR is going to welcome the family in, show them how to wash their hands, and walk them down to the patient room," says NICU nurse Christy Richter. "It's what we've always wanted to do, but in the past it wasn't ideal; you had to have somebody else watch your patient while you got the parent. That wasn't really welcoming for anyone. But now their anxiety level will already be lower when they enter the room. And their hands will already be washed so we can get right to 'here's what's going on with your baby.' The continuity is just going to be better."
Continuity. Safety. Quality of care, notably Patient- and Family-Centered Care. Modern medicine lives by these buzzwords; together they form the mantra by which the new Bloomberg Children's Center will attempt to create a standard of care that would make the IOM proud.
That's as of today. But what about medicine 10, 20, 50 years from now? Will the new Bloomberg Children's Center still be going strong when our children have children, or will time have passed it by? Put another way, will the faculty and staff have made their mark on medicine in Bloomberg Children's Center, much as they did in the CMSC and Harriet Lane? Or could this next era for the Children's Center become a grand experiment that ultimately yields disappointing results? If history is any indication, it's hard to imagine the latter, especially given the thousands of planning hours put into envisioning the future of pediatric medicine. Still, playing clairvoyant is a daunting task.
"You go into it with a lot of humility and insecurity, really, about where the world is going, but you learn lessons for the future from the lessons from past experiences," admits veteran pediatrics administrator Ted Chambers. "One of the advantages Dr. Dover and I have is that we've been here for some time, so we've built up experiences that lead you to how you would shape the building and the future of the Children's Center."
Indeed, a consulting group hired early in the process strongly suggested that Hopkins build a far smaller inpatient children's hospital than what Dover and Chambers eventually delivered. The consultants based their recommendation on national data which showed pediatricians across the country were doing a better job at keeping kids from getting sick, and inpatient admissions were dropping.
They thought they were seeing the big picture; Dover and Chambers thought otherwise. Pediatric cases, especially chronic ones, were getting more complicated. Numerous specialists and services were required, often beyond the scope and resources of most pediatric centers, but not Hopkins. So, by their thinking, while many centers will be seeing fewer inpatients in the years to come, Bloomberg Children's Center will thrive by offering top-notch care to the most complex of cases.
Physically that means having a building with the flexibility to handle those cases now and in the future. Expanded dedicated pediatric OR suites, designed to fit the specific needs of subspecialties including neurosurgery and cardiology, are both state-of-the-current-art and adaptable to technology that at least has been glimpsed on the horizon.
"We're going to be able to integrate robots into the system; the rooms are made to accommodate those kind of advances," says neurosurgeon Ben Carson. "The only reason we don't use robots right now in neurosurgery is they're not quite fine enough. But once they become fine enough and delicate enough, the kinds of things we'll be able to do will be mind boggling."
Even the air that's breathed throughout the hospital has the future in the mind. "The whole building is HEPA (high-efficiency particulate air) filtered. The air is cleaned in a way we never had in the old building," says Chambers. Such filtering not only lets immune-compromised children stay safer, but it's vital to emerging therapies.
"The way the air handling system works, you can administer a drug in a certain room and it doesn't leak out into the corridor or other areas," Chambers says. "With gene transplantation, one of the lessons we learned is we needed a very special air handling system to administer the gene, because you didn't want these genes just floating around anywhere."
There's little doubt that as technology evolves, so too will the concept of the traditional children's hospital. Expertise that is regionally based is on the verge of having a national and global reach, and Bloomberg Children's Center is set up for that emerging world of telemedicine. Cardiologist Philip Spevak has built a NASA-esque imaging command center that coordinates numerous imaging modalities both in-house and to satellite sites to come.
"This lab is really set up with good hardware and software that has the capacity of seeing an image anywhere, at any time, from anyone," says Spevak. "That's important in clinical care because expertise varies from center to center and pediatric cardiology program to program, and you even have expertise here in say, congenital heart cardiac imaging. So we can be an expert consultation service (to other centers) in a minute. We're also using our center to train technologists at other hospitals."
Ben Carson sees a similar technological outreach from OR to overseas coming down the road: "The new operating rooms are very technologically advanced. I did nine cases last week, and to be able to record what you're doing, with just a simple maneuver, have it sent to a central source where you can then upload it to your computer in your office, make slides, do various presentations, makes access to this information to other people much greater, so now it's not just what you're learning, it's what you're able to transmit to others… the fact that we'll be able to communicate with medical centers in Nigeria, in Israel, in Dublin, in South America, in New Zea-land, this is the wave of the future."
Guaranteeing that future will take equal parts money and new faculty, and the new Children's Center may well play a key role in attracting both researchers and trainees.
"The National Institutes of Health is extremely pleased we have this new opportunity," says Pediatric Allergy & Immunology Division Chief Robert Wood."They now know we have the space and resources to conduct our studies in the best possible environment, which can only help to secure new funding opportunities."
"The opportunity to show current and future residents that the space in which they would be caring for patients conveys the high level of respect that this building does for patients is a wonderful message for us to be sending to applicants," says Julia McMillan, vice chair for Education and director of the Pediatric Residency Program. "And for the residents who are here, now (through the transition from the CMSC) it says we knew the old space didn't convey the respect we felt for our patients, and we fixed it. It took us a while, but now we've fixed it; it isn't just something we talk about, it's something we actually did."
It's a change that could make history.
Johns Hopkins' medical concierge services offer complimentary assistance with appointments and travel planning. Request free assistance:
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"""
Linear and logistic regression including regularization.
Currently, only L2 regularization is available.
Includes closed form, gradient descent, and SGD solvers.
"""
import numpy as np
from descentmethods import gradientdescent
class BaseRegression:
"""Base Class for implimenting Linear Regression"""
def __init__(self):
"""
Attributes::
_learned (bool): Keeps track of if Linear Regression has been fit
_weights (np.ndarray): vector of weights for linear regression
"""
self._learned = False
self._weights = np.NaN
@property
def learned(self):
return self._learned
@property
def weights(self):
return self._weights
@learned.setter
def learned(self, value):
self._learned = value
@weights.setter
def weights(self, value):
self._weights = value
class LinearRegression(BaseRegression):
"""Class for implimenting Linear Regression"""
def predict(self, X):
"""
Args:
X (np.ndarray): Test data of shape[n_samples, n_features]
Returns:
np.ndarray: shape[n_samples, 1], predicted values
Raises:
ValueError if model has not been fit
"""
if not self.learned:
raise NameError('Fit model first')
# Add column of 1s to X for bias
X = np.asarray(X)
X = np.column_stack((np.ones(np.shape(X)[0]), X))
prediction = np.dot(X, np.transpose(self.weights))
return prediction
def grad(self, X, y, weights):
"""
Computes the gradient (needed if using gradient descent).
Args:
X (np.ndarray): Training data of shape[n_samples, n_features]
y (np.ndarray): Target values of shape[n_samples, 1]
weights (np.ndarray): Optional use of gradient descent to
calculate weights.
if False, uses closed form solution to calculate weights.
Returns:
np.array: the gradient of the linear regression cost function
"""
hypothesis = np.dot(X, weights) - y
gradient = np.dot(np.transpose(X), hypothesis) / np.size(y)
return gradient
def fit(self, X, y, gradient=False, reg_parameter=0):
"""
Currently, only L2 regularization is implemented.
Args:
X (np.ndarray): Training data of shape[n_samples, n_features]
y (np.ndarray): Target values of shape[n_samples, 1]
gradient (bool): Optional use of gradient descent to
calculate weights.
if False, uses closed form solution to calculate weights.
reg_parameter (float): float to determine strength of
regulatrization penalty if 0, then no linear regression
without regularization is performed.
Returns: an instance of self
"""
y = np.asarray(y)
X = np.asarray(X)
X = np.column_stack((np.ones(np.shape(X)[0]), X))
if gradient:
self.weights = gradientdescent(X, y, self.grad,
reg_param=reg_parameter)
else:
# Calculate weights (closed form solution)
XtX_lambaI = np.dot(np.transpose(X), X) + reg_parameter * \
np.identity(len(np.dot(np.transpose(X), X)))
self.weights = np.dot(np.linalg.pinv(XtX_lambaI),
np.dot(np.transpose(X), y))
self.learned = True
return self
class LogisticRegression(BaseRegression):
"""Logistic Regression classifier with gradient descent implementation"""
@staticmethod
def logistic_function(logistic_input):
"""
Args:
logistic_input (np.ndarray): array of shape[n_samples, 1]
Returns:
np.ndarray: shape[n_samples, 1], logistic transformation of data
"""
return 1 / (1 + np.exp(-logistic_input))
def grad(self, X, y, weights):
"""
Args:
X (np.ndarray): Training data of shape[n_samples, n_features]
y (np.ndarray): Target values of shape[n_samples, 1]
weights (np.ndarray): Optional use of gradient descent to
calculate weights.
if False, uses closed form solution to calculate weights.
Returns:
np.ndarray: the gradient of the linear regression cost function
"""
hypothesis = self.logistic_function(np.dot(X, weights)) - y
gradient = np.dot(np.transpose(X), hypothesis) / np.size(y)
return gradient
def predict(self, X, probability=False):
"""
Args:
X (np.ndarray): Training data of shape[n_samples, n_features]
probability (bool): If True, return probabilities
If False, return class predictions.
Returns:
np.ndarray: shape[n_samples, 1], the predicted values
Raises:
ValueError if model has not been fit
"""
if not self.learned:
raise NameError('Fit model first')
# Add column of 1s to X for bias
X = np.asarray(X)
X = np.column_stack((np.ones(np.shape(X)[0]), X))
prediction = self.logistic_function(np.dot(X,
np.transpose(self.weights)))
if probability:
return prediction
return np.round(prediction)
def fit(self, X, y, reg_parameter=0):
"""
Currently, only L2 regularization is implemented.
Args:
X (np.ndarray): Training data of shape[n_samples, n_features]
y (np.ndarray): Target values of shape[n_samples, 1]
reg_parameter (float): float to determine strength of
regulatrization penalty.
if 0, then no linear regression without regularization
is performed
Returns: an instance of self
Raises:
ValueError if y contains values other than 0 and 1
"""
y = np.asarray(y)
if False in np.in1d(y, [0, 1]):
raise NameError('y required to contain only 0 and 1')
X = np.asarray(X)
X = np.column_stack((np.ones(np.shape(X)[0]), X))
self.weights = gradientdescent(X, y, self.grad,
reg_param=reg_parameter)
self.learned = True
return self
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,706 |
Calliandra cruegeri är en ärtväxtart som beskrevs av August Heinrich Rudolf Grisebach. Calliandra cruegeri ingår i släktet Calliandra och familjen ärtväxter. Inga underarter finns listade i Catalogue of Life.
Källor
Externa länkar
Ärtväxter
cruegeri | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,688 |
Aneto és una població situada a la part nord de la vall de Barravés, costat Aragó, comarca de la Ribagorça. Amb una altitud d'uns 1.350 metres sobre el nivell mitjà del mar és el poble més alt a la vall de Barravés. Pertany al municipi de Montanui, a l'Alta Ribagorça. Està regat pel Barranc d'Aneto, que desemboca a l'est del poble a la Noguera Ribagorçana
Resideixen al poble de forma permanent 31 persones (2006). La parla habitual és la catalana. Per qüestions purament cartogràfiques es va donar el 1817 el nom del poble al Pic d'Aneto, el més alt dels Pirineus, ja que un equip de topògrafs, conduït pel físic Reboul el va cartografiar en sortir d'aquest poble.
Economia
L'activitat principal és la ramaderia de muntanya i el turisme. Compta amb extenses praderies de pastura i també prats d'herba per dallar. La infraestructura túristica compren un bar restaurant, cases de pagès que ofereixen allotjament i una casa de colònies d'estiu, L'Estel, per a nens i joves. És el punt inicial d'una sèrie de rutes de senderisme.
Llocs d'interès
Centre d'interpretació del Parc Natural Posets-Maladeta, al qual pertany part del seu terme.
El sender de muntanya que duu fins a l'estany de Llauset, a 2100 metres d'altitud. Aquesta carretera és practicable, generalment, de juny a octubre. Es va construir als anys 1970, per bastir una gran presa i una sèrie de túnels i d'instal·lacions per a la central reversible anomenada de Llauset-Baserca.
Ermita de Sant Climent, edifici romànic dels segles XI-XII, modificat als segles XVI-XVII, i restaurat el 1979.
Pic d'Aneto (3404 m), culminant dels Pirineus al massís de la Maladeta.
Referències
Entitats de població de Montanui | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,655 |
Danijel Zagorac – calciatore croato
Rade Zagorac – cestista serbo
Saša Zagorac – cestista sloveno
Željko Zagorac – cestista sloveno | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,521 |
Tag: Why do some people say Jehovah and others say Yahweh?
Ancient Hebrew was written without the vowels. This special name for God was written in Hebrew with the consonants YHWH. German translations used the vowels JHVH. After not speaking this name for over 900 years, God's people weren't sure what vowels to add in. Since they often used Adonai as a replacement name for this sacred, unspoken name, they simply put the vowels of Adonai into the German translation to make Jehovah. Most scholars believe it should actually be translated as Yahweh. Continue reading Yahweh or Jehovah? | {
"redpajama_set_name": "RedPajamaC4"
} | 1,731 |
Q: Given four lat/long points, divide shape into grid of n square miles? I'm trying to 1) define a square-ish boundary on a map and 2) divide that shape into a grid consisting of 1-square-mile chunks. I'm doing this because I have a dataset of people's lat/long coordinates and another dataset of business lat/long coords and am looking to simplify the calculation of distances to certain businesses for each individual (so, grouping individuals into 1-square-mile grids as opposed to treating each one individually).
Regarding 1), I've defined the four points creating my "square" below: nw_point, sw_point, ne_point, and se_point.
Regarding 2), I start at nw_point and have been trying to increment latitude and longitude appropriately to make each grid piece. I'm using a formula from this answer to build a square bounding box around each lat/long point, but am running into issues around certain latitudes. See the results corresponding to box_id 45 at the bottom – the calculated longitudinal values seem much higher than the points/boxes preceding, and this is confirmed visually, as I've been plotting the points using this website. So I'm not sure if I'm just mis-using the website, misunderstanding the type of projection being used, or whether I'm going about this grid calculation in a technically wrong way.
import numpy as np
def add_latitude(lat, mi = 1):
modifier = mi / 69
return lat - modifier, lat + modifier
def add_longitude(lat, long, mi = 1):
modifier = mi / 69 / np.cos(lat)
return long - modifier, long + modifier
def bounding_coords(lat, long, mi = 1):
southernmost_lat, northernmost_lat = add_latitude(lat, mi = mi)
westernmost_long, easternmost_long = add_longitude(lat, long, mi = mi)
sw_point = (southernmost_lat, westernmost_long)
nw_point = (northernmost_lat, westernmost_long)
ne_point = (northernmost_lat, easternmost_long)
se_point = (southernmost_lat, easternmost_long)
return sw_point, nw_point, ne_point, se_point
def format_points_for_website(points, color = 'red', label = ''):
return '\n'.join(f'{p[0]},{p[1]},{color},marker,"{label}"' for p in points)
# Start with handling the contiguous United States,
# by picking maximal lat/longs that completely bound the lower 48
# https://en.wikipedia.org/wiki/List_of_extreme_points_of_the_United_States
# Northwest Angle Inlet, MN
continental_northernmost_lat = 49.38293539482664
# Ballast Key, FL
continental_southernmost_lat = 24.52108687199902
# Bodelteh Islands, WA
continental_westernmost_long = -124.76410018717496
# Sail Rock, Lubec, ME
continental_easternmost_long = -66.94700844863216
nw_point = (continental_northernmost_lat, continental_westernmost_long)
sw_point = (continental_southernmost_lat, continental_westernmost_long)
ne_point = (continental_northernmost_lat, continental_easternmost_long)
se_point = (continental_southernmost_lat, continental_easternmost_long)
# Starting at northwesternmost point above, begin building out "chunks" of land.
# You could technically start at any of the four points, but we'll start with this one.
# Start by traversing land until we've passed the southernmost point, then increment to the east
# and start all over again until we've traversed to the easternmost point.
curr_long = nw_point[1]
begin_lat, begin_long = nw_point
boxes = {}
box_id = 0
colors = ['red', 'green', 'blue', 'purple', 'orange']
points = []
# Until we've passed the easternmost continental longitude
while curr_long < continental_easternmost_long:
# And until we've passed the southernmost latitude
curr_lat = begin_lat
while curr_lat > continental_southernmost_lat:
if box_id == 46:raise
# First or 0th element represents a numerically lower latitude, which we need to
# use, since latitude increases the further north you go, and we're building from northwest to southeast
curr_lat = add_latitude(curr_lat)[0]
# Get lower latitude boundary for use in centroid of "next" bounding box
lower_lat = add_latitude(curr_lat)[0]
print(f'Center point: ({lower_lat}, {curr_long})')
sw_point, nw_point, ne_point, se_point = bounding_coords(lower_lat, curr_long)
print(format_points_for_website([sw_point, nw_point, ne_point, se_point], color = colors[box_id % len(colors)], label = box_id))
# Could use a more informative box ID to perhaps represent common lat/long
# boundaries across different boxes, but this suffices for now...
box_id += 1
# Use second element (numerically greater)
curr_long = add_longitude(curr_lat, curr_long)[1]
Relevant output provided below:
...
Center point: (48.7307614817832, -124.76410018717496)
48.71626872816001,-125.16592296075729,purple,marker,"43"
48.745254235406385,-125.16592296075729,purple,marker,"43"
48.745254235406385,-124.36227741359264,purple,marker,"43"
48.71626872816001,-124.36227741359264,purple,marker,"43"
Center point: (48.71626872816001, -124.76410018717496)
48.70177597453682,-125.43565414695419,orange,marker,"44"
48.7307614817832,-125.43565414695419,orange,marker,"44"
48.7307614817832,-124.09254622739573,orange,marker,"44"
48.70177597453682,-124.09254622739573,orange,marker,"44"
Center point: (48.70177597453682, -124.76410018717496)
48.687283220913635,-126.80827425555613,red,marker,"45" ***
48.71626872816001,-126.80827425555613,red,marker,"45" ***
48.71626872816001,-122.7199261187938,red,marker,"45" ***
48.687283220913635,-122.7199261187938,red,marker,"45" ***
A: I am going to put this as an answer because I'll post some code.
@blacksite (in the comments): It may be easier to work in a metric crs. Consider this, where I convert your point to UTM zone 10N (EPSG:32610), to get a metric projection, then create a circular buffer and take its bounding box:
import geopandas as gpd
from shapely.geometry import Point, box
p = Point((-124.76410018717496, 48.7307614817832)) # lon, lat
pp = gpd.GeoSeries(p).set_crs(4326).to_crs(32610)[0] # Convert to UTM for plot)
gs = gpd.GeoSeries(p).set_crs(4326).to_crs(32610).buffer(1609,34) # 1 mile circular buffer
gs_plot = gpd.GeoSeries([pp,box(*gs.bounds.values[0])]).set_crs(32610) # For plotting
# Plot
ax = gs_plot[1:].plot()
gs_plot[:1].plot(ax=ax, color="red")
ax = gs_plot.to_crs(4326)[1:].plot()
gs_plot[:1].to_crs(4326).plot(ax=ax, color="red")
I think, this is much easier. The only "difficult" part now would be to check for each of your points, in which UTM zone they lie in, but I'm pretty sure that there's a very nice way to find out by the lat/lon coordinates.
I hope this helps. I am not entirely sure whether this is what you are looking for.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,509 |
Q: Nothing comes to Sink defined in alsoTo alsoTo doesn't seem to be working for me. Items don't come to sink defined in it. Here is what I have.
val merged: Source[ArticleWithKeywords, _] = ...
val (ks, fut) = merged
.alsoTo(Flow[ArticleWithKeywords].map { a => a.id -> a.ids.toList }.to(queueManager.getIdsForAnsSink))
.map(_.id)
.groupedWithin(100, 5 seconds)
.mapAsync(4) { ids => runReferenceFetching(ids) }
.viaMat(KillSwitches.single)(Keep.right)
.toMat(Sink.ignore)(Keep.both)
.run()
But I see items reaching runReferenceFetching. What am I missing ?
A: Turned out problem has nothing to do with alsoTo. Problem was with sink which was created using Source.fromPublisher. I erroneously thought I can create multiple sinks using same Publisher[T]. Since there was already another sink second one didn't work.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,224 |
Are you considered one of many eight million Individuals who might possibly be getting a better deal? A Goldman Sachs report estimated that $211 billion in scholar loans are ripe for refinancing – about 70% of private student loans and 25% of loans from the Federal Family Education Mortgage Program. Not precisely. When contemplating a refinance mortgage it's essential to understand that the upper your credit standing the higher charge of curiosity you're going to get. So if you don't have wonderful credit you can still qualify for a refinance mortgage however you might wish to make sure that you're reducing the interest rate on your mortgage ample to make a refinance price it.
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SBA loans: The U.S Small Business Administration (SBA) affords specific lending packages for small businesses that don't qualify for standard financing. While the SBA would not current the loans directly to the business proprietor, it supplies loan ensures to lenders. This assure gives lenders the pliability to take on extra risky businesses. You'll have heard of the SBA 7(a), Group Profit and Develop loans. These loans have various mortgage purposes, including debt refinance.
A refinance includes the reevaluation of an entities credit score rating terms and credit rating standing. Shopper loans usually thought of for refinancing embody mortgage loans, automobile loans and scholar loans. Business traders might also search to refinance mortgage loans on business properties. Many business merchants will even evaluate their firm stability sheets for business loans issued by collectors that could profit from lower market rates or an improved credit score score profile. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,840 |
Q: "watchdog: BUG: soft lockup CPU stuck" error and black screen on login I've been having trouble using Ubuntu on my Dell XPS 15 9560.
I started by installing 17.10 a few months ago but the process didn't seem to work correctly. I was eventually able to log in and use the machine, but got errors of the form "watchdog: BUG: soft lockup CPU stuck" when trying to shut down the machine, and at other times as well. Typically these errors would be accompanied by the entire machine freezing or becoming largely unusable.
To try to fix this problem I recently downloaded and installed Ubuntu 18.04. I reinstalled from scratch. Once the installer was complete, I went to reboot the machine and the installer froze. I did a hard reboot and was able to boot into Ubuntu from disk. However, when I entered my password and logged in the screen remains a dark purple with just the cursor and nothing loads. Using ctrl alt f4 to switch to a command line prompt works, though I frequently see this same error above (soft lockup of CPUs). I've seen other people have this login problem on 18.04 so I've tried following the instructions in the question linked below
Cannot login with upgraded ubuntu 18.04
but updating the software doesn't seem to help.
Does anyone know what might be going on?
A: I was able to follow the instructions here to log in
Lubuntu 16.04 gets stuck at shutdown (nmi watchdog bug soft lockup - cpu#1 stuck for 22s)
and then installed the NVidia graphics drivers. That seems to have fixed the problem.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,273 |
Cot Meurak Baroh is een bestuurslaag in het regentschap Bireuen van de provincie Atjeh, Indonesië. Cot Meurak Baroh telt 473 inwoners (volkstelling 2010).
Plaats in Atjeh | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,944 |
\section{Introduction}
\label{sec:intro}
Networks are an essential tool for modeling complex systems. The nodes
of a network represent the components of the system and the links
between nodes represent interactions between those
components. Networks have been applied fruitfully to a wide variety of
social \cite{guimer_self-similar_2003, newman_social_2003},
technological \cite{broder_graph_2000}, and biological
\cite{jeong_large-scale_2000} systems. Many network properties have
been studied to discover how different functional or generative
constraints on the network influence the network's structure. In this
paper we examine five properties of particular importance: the degree
sequence \cite{newman_random_2001}, which counts the number of nodes
in the network with $k$ links; the clustering coefficient
\cite{newman_properties_2003}, which measures the tendency of
connected triples of nodes to form triangles; the number of
$q$-cliques, i.e. complete subgraphs with $q$ nodes; the assortativity
\cite{newman_assortative_2002}, which measures the tendency of nodes
to connect to other nodes of similar degree; and the modularity
\cite{newman_finding_2004}, which measures the tendency of nodes in
the network to form tightly interconnected communities. Their formal
definitions are recalled in Sec.~2.
Models of network {\it ensembles} are of interest because they
formalize and guide our expectations about real-world networks and their properties
\cite{foster_link_2007}. The most famous are the Erd\"os-R\'enyi model
of random networks \cite{erdos_random_1959}, and the scale-free
Barab\'asi-Albert model \cite{barabasi-albert_1999}. Comparison with an
{\it a priori} realistic ``null" model can also indicate which features of a
real network are expected based on the null model features, and which are surprising and thus of
interest, as in motif search \cite{milo_network_2002}. In the latter
context, the most popular ensemble is the {\it configuration model}
\cite{molloy-reed_1995} and related variants
\cite{maslov_specificity_2002}, in which all networks with a given
number of nodes and a given degree sequence have the same weight. One
problem of the configuration model is that it shows far too little clustering; this problem is especially important when the model is applied to motif search in,
e.g., protein interaction networks \cite{baskerville_2007}.
A model where clustering can be enhanced by means of a fugacity term
in a network Hamiltonian was introduced by D. Strauss
\cite{strauss_general_1986} and studied in detail in
\cite{park_solution_2005}. In the Strauss model, the density of edges
is also controlled by a second fugacity. Thus it is a generalization
of the Erd\"os-R\'enyi model with fixed edge {\it probability}, not
with fixed edge number. In the Strauss model there is a strong first
order phase transition \cite{park_solution_2005} from a phase with
weak clustering to a phase where nearly all edges condensate in a
single densely connected cluster consisting of high degree nodes. This
phase transition is often seen as a flaw, as it does not allow the
intermediate clustering observed in most real networks \footnote{This
transition can also be seen as first order {\it percolation}
transition, since a giant percolating cluster is formed when $\beta$
is increased through the critical point. It is, however, very
different from ``explosive percolation" in Achlioptas processes
\cite{achlioptas_2009}, which is also a first order percolation
transition. While the Strauss model is a genuine thermodynamic model
with Hamiltonian structure, and the phase transition happens as a
true control parameter is increased, explosive percolation is a
strictly nonequilibrium process where the control is done via a {\it
density} (of established bonds). We could also try to control the
bond density in the Strauss model, but then we would get a
continuous transition with phase coexistence, as in any system which undergoes a
thermodynamic first order transition.}.
In the present paper, we introduce and analyze the {\it Biased
Rewiring Model} (BRM). As in the configuration model, we fix the
exact degree sequence--accounting for quenched heterogeneity in node properties. But as in the Strauss model, we control the
average number of closed triangles by a Hamiltonian
\cite{park_statistical_2004} containing a conjugate fugacity $\beta$.
By fixing the degree sequence we prevent the extreme condensation of
edges typical of the Strauss model, and we might {\it a priori} hope
to achieve a smooth control of the clustering. Indeed, a very similar
model, but with a slightly different Hamiltonian, had been proposed in
\cite{milo_network_2002}.
To our surprise we found that this is not the case, and the clustering
cannot be smoothly controlled. To search for phase transitions, we
plotted several characteristics (number of triangles, number of
$q$-cliques with $q=4$ and 5, assortativity, and modularity) against
$\beta$. In all these plots and for all non-regular graphs
(i.e. graphs with a non-trivial degree distribution) we found {\it
several} jumps which look like first order phase transitions (or
large Barkhausen jumps in ferromagnets
\cite{Sears-Zemanski,Perkovic_1995,Zapperi_1997}. Associated with these
jumps are important hysteresis effects. Further, we found that high degree
nodes play a crucial role in generating these phase transitions. It is
thus not surprising that a somewhat simpler scenario holds for regular
graphs (same degree $k$ for all nodes), where we found a single phase
transition for all $k>2$. The only case where we found no transition
at all is that of regular graphs with $k=2$. Unfortunately it is only
in the last, somewhat trivial, case that we can do exact analytic
calculations. In all other cases our results are based on simulations.
In \cite{milo_network_2002}, the Hamiltonian was chosen to bias not
towards a {\it larger} number of triangles, but towards a {\it
specific} number. In order to achieve this reliably, one needs a
fugacity which is larger than that in the BRM. In the limit of large
fugacities this is
similar to a model with a hard constraint. In general, statistical
models with hard constraints show slower relaxation and worse ergodic
behavior than models with soft constraints \cite{barkema_MC}. We
expect thus that hysteresis effects might be even more pronounced in
the model of \cite{milo_network_2002} and might render it less useful
as a null model, even if the problem of phase transitions is
hidden. For simplicity we shall in the following call the model of
\cite{milo_network_2002} ``triangle conserving", although the name is
not strictly correct. We find that for triangle conserving rewiring,
important structures remain largely unchanged on extremely long time
scales, requiring particular care when using the method. In general, phase transitions, strong hysteresis, and persistent structures of highly connected nodes together present substantial pitfalls for null-models of clustered networks.
In the next section we shall collect some basic background
information, including the precise definitions of the model with
unbiased rewiring and the Strauss model. The definition of the BRM
and our numerical procedure is given in Sec.~II.F. Our main results are
found in Secs.~III.A to III.C, while some results for the model with hard
constraints of Milo {\it et al.} \cite{milo_network_2002} are
presented in Sec.~III.D Finally, Sec.~IV contains our conclusions.
\section{Background}
\label{sec:bg}
\subsection{Degree sequences}
\label{sec:deg}
The degree of a node is the number of links in which the node
participates. The network's degree sequence $\{n_k |\; k=0,1\ldots
k_{\rm max}\}$ counts the number of nodes in the network which degree
$k$. The networks studied in this paper are regular ($n_k =
\delta_{k,k_0}$), Erd\"os-R\'enyi (poissonian $n_k$), and several real
world networks with fat tails. Network properties often depend
strongly on the degree sequence \cite{newman_random_2001}. Thus real
networks are often compared with null models which preserve the degree
sequence.
\subsection{Clustering coefficient and $q$-cliques}
\label{sec:c}
Three nodes are {\it connected}, if at least two of the three possible
links between them exits. If all three links exist, they form a {\it
triangle}. The clustering coefficient \cite{watts_collective_1998}
measures the ``transitivity" of relationships in the network, i.e. the
probability that three connected nodes are also a triangle. Denoting
the number of triangles by $n_\Delta$ and the degree of node $i$ by
$k_i$, one has
\begin{equation}
C = {3n_\Delta\over {1\over 2}\sum_{i=1}^N (k_i-1)k_i}. \label{clust}
\end{equation}
If every relationship in the network is transitive, $C = 1$; if no
relationships are transitive, $C = 0$. Note that the denominator of
equation \ref{clust} depends only on the degree sequence, and thus $C
\propto n_\Delta$ in any ensemble with fixed degrees.
In addition to $C$, we can also define similar higher order clustering
coefficients based on $q$-cliques, i.e. on complete subgraphs with $q$
nodes, as
\begin{equation}
C_q = {q\;n_{q-\rm clique} \over \sum_{i=1}^N {k_i \choose q-1}},
\end{equation}
where $n_{q-\rm clique}$ is the number of $q-$cliques in the
network. Notice that $C=C_3$. As we shall see, we can use any $C_q$
as an order parameter in the phase transitions discussed below.
\subsection{Assortativity}
\label{sec:r}
The assortativity $r$ measures the tendency for nodes in the network
to be linked to other nodes of a similar degree. It is defined as the
Pearson correlation coefficient between the degrees of nodes which are
joined by a link \cite{newman_assortative_2002}.
\begin{equation}
r = \frac{L\sum_{i=1}^L j_i k_i - [\sum_{i=1}^L j_i]^2}
{L\sum_{i=1}^L j_i^2 - [\sum_{i=1}^L j_i]^2}
\label{assort}
\end{equation}
Here $L$ is the number of links in the network and $j_i$ and $k_i$ are
the degrees of nodes at each end of link $i$. Thus, if high degree
nodes are linked exclusively to other high degree nodes, $r \approx
1$. If high degree nodes are exclusively linked to low degree nodes,
$r \approx -1$.
\subsection{Modularity}
\label{sec:m}
There are many methods for identifying community structure in complex
networks \cite{porter_communities}, each with its own strengths and
drawbacks. We shall use a measure proposed by Newman and Girvan
\cite{newman_finding_2004} called {\it modularity}. Assume one has a
given partition of the network into $k$ non-overlapping
communities. Define $e_{ij}$ as the fraction of all edges which
connect a node in community $i$ to a node in community $j$. Thus $a_i
= \sum_j e_{ij}$ is the fraction of all links which connect to
community $i$. The modularity of the partition is then defined as:
\begin{equation}
Q = \sum_i (e_{ii} - a_i^2),
\label{mod}
\end{equation}
and the modularity of the network is the maximum of $Q$ over all
partitions. $Q$ measures the fraction of `internal' links, versus the
fraction expected for a random network with the same degree
sequence. It is large when communities are largely isolated with few
cross links.
The main problem in computing $Q$ for a network is the optimization
over all partitions, which is usually done with some heuristics. The
heuristics used in the present paper is a greedy algorithm introduced
by Newman \cite{newman_fast_2004}. We start with each node in its own
community (i.e., all communities are of size 1). Joining two
communities $i$ and $j$ would produce a change $\delta Q_{ij}$. All
pairs $(i,j)$ are checked, and the pair with the largest $\delta
Q_{ij}$ is joined. This is repeated until all $\delta Q_{ij}$ are
negative, i.e. until $Q$ is locally maximal. We follow the efficient
implementation of this method described by Clauset et al
\cite{clauset_finding_2004}.
\subsection{Exponential Network Ensembles and Network Hamiltonians}
Let us assume that ${\cal G}$ is a set of graphs (e.g. the set of all
graphs with fixed number $N$ of nodes, or with fixed $N$ and fixed
number $L$ of links, or with fixed $N$ and fixed degree sequence,
...), and $G\in {\cal G}$. Following \cite{park_statistical_2004}, a
network {\it Hamiltonian} $H(G)$ is any function defined on ${\cal
G}$, used to define an exponential ensemble (analogous to a
canonical ensemble in statistical mechanics) by assigning a weight
\begin{equation}
P(G) \propto e^{-H(G)}
\end{equation}
to any graph, similar to the Boltzmann-Gibbs weight.
Examples of exponential ensembles are the Erd\"os-R\'enyi model
$G(N,p)$ where $H = -L\ln [p/(1-p)]$ and the Strauss model with
\begin{equation}
H_{\rm Strauss} = \theta L - \beta n_\Delta.
\end{equation}
Here, $p$ (which is not to be confused with $P(G)$) is the probability
that a link exists between any two nodes, while $\theta$ and $\beta$
are ``fugacities" conjugate to $L$ and $n_\Delta$, respectively.
In the configuration model, ${\cal G}$ is the set of all graphs with a
fixed degree sequence and $H=0$. Thus all graphs have the same
weight. In contrast, in the ``triangle conserving" biased model of
Milo {\it et al.} \cite{milo_network_2002} ${\cal G}$ is again the
set of graphs with fixed degree sequence, but
\begin{equation}
H_{\rm Milo} = \beta |n_\Delta - n_{\Delta,0}|.
\end{equation}
where $n_{\Delta,0}$ is some target number of triangles, usually the
number found in an empirical network. Finally, in the BRM, ${\cal G}$
is again the same but
\begin{equation}
H_{\rm BRM} = - \beta n_\Delta.
\end{equation}
Thus, while large weights are given in the BRM (with $\beta >0$) to
graphs with many triangles (high clustering), in the model of
\cite{milo_network_2002} the largest weights are given to graphs with
$n_\Delta = n_{\Delta,0}$.
\subsection{Simulations: Rewiring}
\label{sec:rewire}
Simulations of these ensembles are most easily done by the Markov
chain Metropolis-Hastings method \cite{barkema_MC}. This is
particularly easy for models without fixed degree sequences,
e.g. the Strauss model. There, new configurations are simply
generated by randomly adding or removing links. This is not possible
for the ensembles with fixed degree sequences, where the most natural
method is {\it rewiring} \cite{maslov_specificity_2002}. We will
first discuss the unbiased case (the configuration model), and
then discuss the two biased cases $H_{\rm Milo}$ and $H_{\rm BRM}$.
\subsubsection{Unbiased Rewiring}
Starting from a current graph configuration $G$, a new graph $G'$ is
proposed as follows: Two links which have no node in common are chosen
at random, e.g. $X$---$Y$ and $W$---$Z$. Links are then swapped
randomly either to $X$---$W$ and $Y$---$Z$, or to $X$---$Z$ and
$Y$---$W$. If this leads to a double link (i.e. one or both of the
proposed new links is already present), the new graph $G'$ is
discarded and $G$ is kept. Otherwise, $G'$ is accepted. It is easily
seen that this conserves the degree sequence, satisfies detailed
balance, and is ergodic \cite{maslov_specificity_2002}. Thus it leads
to equidistribution among all graphs with the degree sequence of the
initial graph.
Although there seem to exist no exact results on the speed of
equilibration, previous experience
\cite{maslov_specificity_2002,baskerville_2007} suggests that
the above unbiased rewiring is very fast indeed, and can be used
efficiently even for large networks.
\subsubsection{Biased Rewiring}
For biased rewiring with a Hamiltonian $H(G)$, the proposal stage is
the same, and only the acceptance step has to be modified, according
to the standard Metropolis-Hastings procedure
\cite{hastings_monte_1970, barkema_MC}: If $H(G') \leq H(G)$, then
$G'$ is accepted (unless it has a double link, of course). Otherwise
the swap is accepted only with a probability
\begin{equation}
p = e^{H(G) - H(G')} \label{prob}
\end{equation}
which is less than 1.
The detailed protocols for simulating the two biased models studied in
this paper are different. For the BRM we start with the actual network
$G_0$ whose degree sequence we want to use, and propose first $M_0$
{\it unbiased} swaps, with $M_0$ sufficiently large so that we end up
in the typical region of the unbiased ensemble. After that we increase
$\beta$ in small steps (typically $\delta\beta = 0.002$), starting
with $\beta=0$. After each step in $\beta$ we propose $M_1$ swaps to
equilibrate approximately, and then take take at fixed $\beta$ an
ensemble average (with further equilibration) by making $m$
measurements, each separated by $M_2$ additional proposed swaps. Thus
the total number of proposed swaps at each fixed $\beta$ is $M_1 +
(m-1)M_2$. Typically, $M_0 \approx 10^6, M_1 > 10^5, M_2 \approx 10^3
- 10^5$, and $m\approx 500 - 10,000$.
Following the $m$ measurements we increase $\beta$ and repeat
this procedure, until a preset maximal value $\beta_{\rm max}$ is
reached. After that, we reverse the sign of $\delta\beta$ and continue
with the same parameters $M_1, M_2,$ and $m$ until we reach again
$\beta=0$, thereby forming a hysteresis loop. Fugacity values during
the ascending part of the loop will in the following be denoted by
$\beta^+$, those in the descending part as $\beta^-$. In cases where
we start from a real world network with $n_{\Delta,0}$ triangles, we
choose $\beta_{\rm max}$ sufficiently large so that
$n_{\Delta}(\beta^+) > n_{\Delta,0}$, i.e. the clustering covered by
the hysteresis loop includes the clustering coefficient of the
original network.
For the biased model of Milo {\it et al.} \cite{milo_network_2002} we
skip the first stage (i.e., we set $M_0=0$), and we jump immediately
to a value of $\beta$ (estimated through preliminary runs) which must
be larger than the smallest $\beta^+$ which gave rise to
$n_{\Delta,0}$ triangles in the ascending part of the loop discussed
above. We first make $M_1$ swaps to equilibrate, and then make $m$
measurements, each separated by $M_2$ further swaps (an alternative
protocol using multiple annealing periods will be discussed in
Sec.~\ref{sec:null}). Averages are taken only over configurations with
exactly $n_{\Delta,0}$ triangles. If $\beta$ is too small, the bias
will not be sufficient to keep $n_\Delta$ near $n_{\Delta,0}$, and
$n_\Delta$ will drift to smaller values. Even if this is not the case
and if $\beta$ is sufficiently large in principle, the algorithm will
slow down if $\beta$ is near its lower limit, since then $n_\Delta$
will seldom hit its target value. On the other hand, if $\beta$ is too
large then the algorithm resembles an algorithm with rigid constraint,
which usually leads to increased relaxation times. Thus choosing an
optimal $\beta$ is somewhat delicate in this model.
\section{Results}
\label{sec:results}
We explored the behavior of the BRM for three different classes of
degree sequences: Fixed $k$ networks, in which every node of the
network is degree $k$; Poisson degree distributions as in
Erd\"os-R\'enyi networks; and typical fat-tailed distributions as in
most empirical networks. Although we studied many more cases
(Erd\"os-R\'enyi networks with different connectivities and sizes and
several different protein-protein interaction networks), we present
here only results for fixed $k$ with different $k$, for one
Erd\"os-R\'enyi network, and for two empirical networks with
fat-tailed degree distributions: A high energy physics collaboration
network \cite{newman_structure_2001} and a protein-protein interaction
network for yeast ({\it S. cerevisiae})
\cite{gavin_functional_2002}). In all but fixed $k$ networks we found
multiple discontinuous phase transitions, while we found a single
phase transition in all fixed $k$ networks with $k>2$.
\subsection{Fixed $k$ networks, analytic and simulation results}
\label{sec:fixedk}
\begin{figure}
\includegraphics[scale=.32]{Figure1.pdf}
\caption{\label{Figure1} (color online)
Average number of triangles for networks with fixed $k=3$, plotted
against $\beta$. All curves are obtained by full hysteresis cycles,
with $M_1 = 200000$ initial swaps after increase/decrease of
$\beta$, and $M_2=5000$ additional swaps after each of $m = 40000$
measurements at the same value of $\beta$. Hysteresis loops are
seen for $N\geq 200$, but not for $\leq 100$. The straight line
corresponds to the approximation Eq.~(\ref{n_approx}).}
\end{figure}
\subsubsection{Fixed $k$ simulations}
For each $k$, the configuration with maximal $n_\Delta$ is a disjoint
set of $(k+1)-$cliques, i.e. the graph decomposes into disjoint
completely connected components of $k+1$ nodes. When $N$ is divisible
by $k+1$, this gives
\begin{equation}
n_\Delta^{(k,\rm max)} = {N\over k+1}{k+1\choose 3}. \label{n_max}
\end{equation}
For $k=2$, this $n_\Delta^{(k,\rm max)}$ is reached in a smooth
way. For each $k\geq 3$, in contrast, and for sufficiently large $N$,
$n_\Delta$ first increases proportional to $\exp(\beta)$, but then the
increase accelerates and finally it jumps in a discrete step to a value
very close to $n_\Delta^{(k,\rm max)}$. This is illustrated for $k=3$
in Fig.~\ref{Figure1}, where we plot hysteresis curves for $n_\Delta$
against $\beta$. From this and from similar plots for different $k$
we observe the following features:
\begin{itemize}
\item For small $\beta$, all curves are roughly described by
\begin{equation}
n_\Delta \approx {(k-1)^3 \over 6} e^\beta \label{n_approx}
\end{equation}
(see the straight line in Fig.~\ref{Figure1}), and this approximation
seems to become exact as $N\to\infty$. Notice that this implies that
$n_\Delta$ is independent of $N$, and the clustering coefficient is
proportional to $1/N$.
\item While the curves are smooth and do not show hysteresis for small
$N$, they show both jumps and hysteresis above a $k-$dependent value
of $N$. This is our best indication that the phenomenon is basically
a first order phase transition, similar to the one in the Strauss
model. Above the jump, the curves saturate (within the resolution of
the plot) the bound given in Eq.(\ref{n_max}).
\item The critical values of $\beta$ increase logarithmically with
$N$, although a precise determination is difficult due to the
hysteresis. Notice that size dependent critical points are not very
common, but there are some well known examples. Maybe the most
important ones are models with long range or mean field type
interactions, where the number of interaction terms increases faster
than $N$. In the present case the reason for the logarithmic
increase of $\beta_c$ is that networks with fixed $k$ become more
and more sparse as $N$ increases. Thus also the {\it density} of
triangles (the clustering coefficient) decreases, and in a Markov
chain MC method, there are increasingly more proposed moves which
destroy triangles than moves which create them. To compensate for
this and make the number of accepted moves equal, $\exp(\beta_c)$
has to increase $\propto N$.
\end{itemize}
\begin{figure}
\includegraphics[scale=.22]{Figure2.pdf}
\caption{\label{Figure2} Average number of triangles of fixed-$k$
degree sequence networks, with $k = 2,3,5,10,$ and $16$, versus the
fugacity (bias) $\beta$. Network size is $N=400$ for all curves. In
these simulations $\beta$ was slowly increased, until a jump in
$n_\Delta$ was seen (for $k\geq 3$). The straight line shows the
theoretical prediction for $k = 2$: $n_\Delta = \frac{1}{6}
e^{\beta}$. The inset shows $n_\Delta/e^{\beta}$ for $k=2$.}
\end{figure}
In Fig. \ref{Figure2} we show the average number of triangles as a
function of $\beta$ for fixed $k$ networks, $k = 2, 3, 5, 10,$ and
$16$, with $N = 400$ nodes. For each curve we used $M_1=4000000$
initial swaps after each increase in $\beta$, and $M_2=200000$ additional
swaps after each of $m\geq 5000$ measurements at the same value of
$\beta$. For clarity we show only values for increasing $\beta$,
although there is strong hysteresis for all $k\geq 3$ and for $N=400$.
For $k=2$ there is not only no hysteresis, but there is indeed no
indication of any phase transition. As seen from the inset, the data
for $k=2$ are for all values of $\beta$ very well described by
Eq.~(\ref{n_approx}), up to the point where it reaches the bound
Eq.(\ref{n_max}). Close to that point there is a tiny bump in the
curve shown in the inset, that will be explained in the next
sub-sub-section.
\subsubsection{$k = 2$ analytic results}
We now give an analytical derivation of Eq.~(\ref{n_approx}) for
$k=2$, and we also show that this should become exact in the
limit $N\to\infty$.
In a fixed $k = 2$ network, there are $N$ nodes and $N$ links all
arranged in a set of disjoint simple loops. Triangles are the smallest
possible loops, since self-links and double links are not allowed. For
large $N$ and small $\beta$ nearly all loops are large, thus the
number of loops of length $<7$ is of order $1/N$ and can be neglected
for $N\to\infty$ and finite $\beta$, except that we have to allow for
a small fraction of loops to have length 3, in order to achieve
equilibration of the rewiring procedure.
Consider now a network of size $N$ with $n_\Delta$ triangles and a
triangle bias $\beta$. The rewiring process will reach an
equilibrium, when the probability of destroying a triangle is equal to
the probability of creating a new one.
First we calculate the probabilities of randomly generating a swap
which destroys a triangle. The total number of ways to choose a pair
of links and perform a swap is $\cal{N}$ $= \frac{N(N - 1)}{2} \times
2$, where $\frac{N(N - 1)}{2}$ gives the number of distinct pairs of
links and the extra factor of 2 accounts for the two possible ways of
swapping the links. To destroy a triangle, one of the links must be
chosen from it, and the other from a larger loop (the chance that both
links are chosen from triangles, which would lead to the destruction
of both, can be neglected). There are $3n_\Delta$ possible links in
triangles to choose from, and $(N- 3n_\Delta)$ links in larger
loops. Thus the probability of choosing a swap which would destroy a
triangle is
\begin{equation}
p_{\Delta-} = \frac{3n_\Delta(N-3n_\Delta)\times 2}{\cal{N}} =
\frac{6n_\Delta}{N} \times [1+O(N^{-1})],
\end{equation}
where the factor of $2$ in the numerator corresponds to the fact that
both possible swaps destroy a triangle and the correction term takes
also into account the neglected loops of lengths 4,5, and 6.
To add a triangle to the network, two links must be chosen from the
same long loop. They must be separated by exactly two links. There are
$\ell$ such pairs in a loop of length $\ell$, and thus the total
number of such pairs in the network is $N$, neglecting terms of $O(1)$,
corresponding to the triangles and loops shorter than $7$. This leaves
us with the probability of adding a triangle
\begin{equation}
p_{\Delta+} = \frac{N}{\cal{N}} = N^{-1} \times [1+O(N^{-1})].
\end{equation}
where there is no factor of $2$ in the numerator because only one of
the two possible swaps will lead to triangle creation. Balance will be
achieved when
\begin{equation}
p_{\Delta+} = e^{-\beta}p_{\Delta-},
\end{equation}
giving
\begin{equation}
n_\Delta = \frac{e^\beta}{6} \label{balance2}
\end{equation}
up to correction terms of order $1/N$, which is just
Eq.~(\ref{n_approx}) for $k=2$.
The simple exponential behavior of $n_\Delta$ with $\beta$ occurs
because swaps create/destroy triangles (except in the rare case of
breaking up a loop of length 6) independently and one at a time. For
networks with nodes of degree greater than $2$ this is still basically
true when $\beta$ is small. But as $\beta$ increases, nodes cluster
together more densely, allowing each link to participate in many
triangles. For large values of $\beta$ these links, once formed,
become difficult to remove from the network. This cooperativity -- in which the presence of triangles helps other triangles to form and makes it harder for them to be removed -- explains intuitively the existence of first order phase transitions for $k\geq3$ but not for $k=2$, where the cooperative effect is not possible.
Indeed, for $n_\Delta$ very close to $n_\Delta^{(2,\rm max)}$ there is
{\it some} cooperativity even for $k=2$. The configuration with
$n_\Delta=n_\Delta^{(2,\rm max)}$ can be changed only by breaking up
{\it two} triangles and joining their links in a loop of length
6. When $n_\Delta$ is close to $n_\Delta^{(2,\rm max)}$, link swaps
which involve two triangles become increasingly prevalent. The
tendency to form and destroy triangles two at a time introduces a very
weak cooperativity, which is only strong enough to be effective when
$n_\Delta^{(2,\rm max)}-n_\Delta=O(1)$. It is thus not enough to give rise to a phase
transition, but it explains the small bump seen in the inset of
Fig.~\ref{Figure2}.
\subsection{Networks with non-trivial degree sequences}
\label{sec:ER}
\begin{table}
\begin{tabular}{ c c c c c c l }
\multicolumn{6}{c}{Network properties} \\
\hline \hline
Network & $N$ & $\langle k\rangle $ & $C$ & $r$ & $Q$ & Comment and Ref.\\
\hline
ER & $800$ & $5.0$ & $.002$ & $-.0004$ & $0.196$ & Erd\"os-R\'enyi \\
HEP & $7610$ & $4.1$ & $.33$ & $.29$ & $0.397$ & scientific
collab. \cite{newman_structure_2001}\\
Yeast & $1373$ & $10.0$ & $.58$ & $.58$ & $0.380$ & protein binding
\cite{gavin_functional_2002}\\
\end{tabular}
\caption{\label{table1} The number of nodes $N$, the number of links
$L$, the average degree $\langle k\rangle$, the clustering
coefficient $C$, and the assortativity $r$ for each of the networks
discussed in Sec.~\ref{sec:ER}.}
\end{table}
\begin{figure}
\includegraphics[scale=.22]{Figure3.pdf}
\caption{\label{Figure3} Average number of triangles in BRM
networks with an ER degree sequence with 800 nodes and $\langle
k\rangle = 5$, plotted against the bias $\beta$. The lower curve
corresponds to slowly increasing $\beta$, the upper to decreasing
$\beta$.}
\end{figure}
\begin{figure}
\includegraphics[scale=.22]{Figure4.pdf}
\caption{\label{Figure4} Similar to Fig.~\ref{Figure3}, but for the
HEP network (see Table~\ref{table1}). The dotted line indicates the number
of triangles in the real network.}
\end{figure}
\begin{figure}
\includegraphics[scale=.22]{Figure5.pdf}
\caption{\label{Figure5} Similar to Fig.~\ref{Figure3}, but for the
Yeast network (see Table~\ref{table1}).}
\end{figure}
We explored the behavior of our biased rewiring model for various
degree sequences. These included Erd\"os-R\'enyi graphs
with different sizes and different connectivities and several
real-world networks. The latter typically show more or less fat
tails. In order to find any dependence on the fatness, we also changed
some of the sequences manually in order to reduce or enhance the
tails. We found no significant systematic effects beyond those visible
already from the following three typical networks, and restrict our
discussion in the following to these: an Erd\"os-R\'enyi graph
\cite{erdos_random_1959} (henceforth ER), a high energy physics
collaboration network (HEP)
\cite{newman_structure_2001}, and a yeast protein binding network
(\cite{gavin_functional_2002} (Yeast). Some of their properties
are collected in Table~\ref{table1}.
\begin{figure}
\includegraphics[scale=.22]{Figure6.pdf}
\caption{\label{Figure6} (color online) Four network characteristics
(modularity ($Q$), clustering coefficient ($C_3$), 4-clique
clustering coefficient ($C_4$), and assortativity ($r$)) for BRM
networks with the Yeast degree sequence of Table~\ref{table1} versus
$\beta$. These data are drawn from the same simulation as in
Fig.~\ref{Figure5}, but for clarity only the results for
increasing values of $\beta$ are shown.}
\end{figure}
Figs.~\ref{Figure3}, \ref{Figure4}, and \ref{Figure5} show $n_\Delta$
for these three networks. In each case $M_0 = 10^6, M_1 = 1.5\times
10^5, M_2 = 50000$, and $m = 500$. In each of them a full hysteresis
cycle is shown, with the lower curves (labeled $\beta^+$)
corresponding to increasing and the upper curves ($\beta^-$)
corresponding to decreasing $\beta$. In Figs.~\ref{Figure4} and
\ref{Figure5} the dotted line shows the number of triangles in the
empirical networks.
For small values of $\beta^+$ all three figures exhibit a similar
exponential increase in the number of triangles as that observed in
fixed $k$ networks. At different values of $\beta$, however, there is
a sudden, dramatic increase in $n_\Delta$, which does {\it not},
however, lead to saturation as it did for fixed $k$. This first phase
transition is followed by a series of further transitions through
which the network becomes more and more clustered. Many of them are
comparable in absolute magnitude to the first jump. Although the rough
positions of the jumps depend only on the degree sequences, their
precise positions and heights change slightly with the random
number sequences used and with the speed with which $\beta$ is
increased. Thus the precise sequence of jumps has presumably no deeper
significance, but their existence and general appearance seems to be a
universal feature found in {\it all} cases.
Associated with the jumps in $n_\Delta$ are jumps in all other network
characteristics we looked at, see Fig.~\ref{Figure6}. Although the
locations of the jumps in $n_\Delta$ depend slightly on the details of
the simulation, the jumps in the other characteristics occur always at
{\it exactly} the same positions as those in $n_\Delta$. Obviously, at
each jump a significant re-structuring of the network occurs,
which affects all measurable quantities. Speculations how these
reorganizations can be best described and what is their most
``natural" driving mechanism will be given in the next subsection.
\begin{figure}
\includegraphics[scale=.32]{Figure7.pdf}
\caption{\label{Figure7} (color online) Values of the rescaled
characteristics $n_\Delta/n_{\Delta,\rm max}$ and $(r-r_{\rm
min})/(r_{\rm max}-r_{\rm min})$, measured at the same values of
$\beta^\pm$, and plotted against each other. The points represent
the values for the real HEP and Yeast networks.}
\end{figure}
In the downward branch of the hysteresis loop, as $\beta^-$ decreases
toward zero, the number of triangles remains high for a long time,
forming a significant hysteresis loop. This loop suggests that all
jumps should be seen as discontinuous (first order) phase
transitions. Since all studied systems are finite, these hysteresis
loops would of course disappear for infinitely slow increase/decrease
of the bias. But the sampling shown involved $>25$ million attempted
swaps at each value of $\beta$, and no systematic change in the
hysteresis was seen when compared to twice as fast sweeps.
In Fig.~\ref{Figure7}, we plotted $n_\Delta$ against the assortativity
for the {\it same} values of $\beta^\pm$, normalizing both quantities
to the unit interval. The hope was that in this way we would get
universal curves which are the same for $\beta^+$ and $\beta^-$, and
maybe even across different networks. Indeed we see a quite remarkable
data collapse. It is certainly not perfect, but definitely better than
pure chance. It suggests that biasing with the BRM leads to networks
where the two characteristics $n_\Delta/n_{\Delta,\rm max}$ and
$(r-r_{\rm min})/(r_{\rm max}-r_{\rm min})$ are strongly -- but
non-linearly -- correlated. This indicates a potential scaling relationship between these network parameters in our model. For the two empirical networks, we show
also the real values of these characteristics. They fall far from the
common curve, indicating that these networks are not typical for the
BRM with any value of $\beta$.
\begin{figure*}[htp]
\includegraphics[scale=.5]{Figure8.pdf}
\caption{\label{Figure8} (color online) Relevant parts of 3-clique
adjacency plots for the Yeast degree sequence. The color of each point indicates the number of $3$cliques (or triangles) in which the link participates, as given by the scale on the right hand side. Each pair of plots shows (from top to bottom) the 3CAP for a typical member of the
ensemble shortly before the first jump seen in Fig.~\ref{Figure5},
shortly after it, shortly after the second jump, and shortly after
the third jump. The plots on the left hand side show the 3CAP with
the nodes ranked in order of their degree. In the ``diagonalized"
plots we rearranged the ranking so that nodes which participate in
the three clusters formed by each jump are ranked together, at the
head of the list. The rest of the nodes are ranked by degree.}
\end{figure*}
Among the three networks studied here, the ER network is closest to a
fixed $k$ network, and it should thus show behavior closest to that
studied in the last subsection. This is not very evident from
Figs.~\ref{Figure3} to \ref{Figure5}. On the other hand, we see
clearly from these figures that the position of the first transition
-- in particular in $\beta^+$ -- decreases with the average
degree. Also, hysteresis seems to be more closely tied to individual
jumps for ER, while it is more global (and thus also more important
overall) for HEP and Yeast.
For the HEP and Yeast networks, we can compare the clustering of the
BRM ensemble to that in the real empirical networks. The latter
numbers are shown as a dashed lines in Figs.~\ref{Figure4} and
\ref{Figure5}. In both cases, the line intersects the hysteresis loop
where it is very broad. This means that a large value of $\beta^+$ is
required to reach the real network's level of clustering when the bias
is increased, whereas a much lower value $\beta^-$ must be reached
before these triangles can be rewired out of the network again. This
gap between $\beta^+$ and $\beta^-$ at fixed $n_\Delta$ has important
implications for the triangle ``conserving" null model of
Ref.~\cite{milo_network_2002}, as we will discuss later.
\subsection{Clique adjacency plots and clustering cores}
Up to now we have not given any intuitive arguments why clustering
seems to increase in several jumps, and not in one single jump or in a
continuous way. {\it A priori} one might suggest that each jump is related
to the break-up of a connected component into disconnected subgraphs,
just as the phase transition in regular graphs was associated to such
a break-up. By counting the numbers of disconnected components we
found that this is not the case, except in special cases \footnote{If
the degree sequence has, e.g., 20 hubs each of degree 19 and
otherwise only nodes with degrees $<4$, then we would expect that
the first jump leads to a clique with all 20 hubs which would then
be disconnected from the rest. But this is a very atypical
situation}.
Instead, we will now argue that each jump is associated with the
sudden formation of a highly connected cluster of high degree
nodes. The first jump in a scan with increasing $\beta$ occurs when
some of the strongest hubs link among themselves, forming a highly
connected cluster. Subsequent jumps indicate the formations of other
clusters with high intra- but low inter-connections. What
distinguishes this picture from the standard modularity observed in
many real-world networks is that it automatically leads to large
assortativity: Since it is high degree nodes which form the first
cluster(s), there is a strong tendency that clusters contain nodes
with similar degrees (for previous discussions on how clustering of
nodes depends on their degree, see
e.g. \cite{ravasz_hierarchical_2003, soffer_network_2005}). Even
though the modules formed are somewhat atypical, the BRM does
demonstrate the ability of a bias for triangle formation to give rise
to community structure {\it de novo}, whereas in other models,
community structure must be put in by hand \cite{newman_social_2003}.
In the following, the clusters of tightly connected nodes created by
the BRM are called {\it clustering cores}. To visualize them, we use
what we call $q${\it-clique adjacency plots} (qCAPs) in the
following. A $q$-clique adjacency plot is based on an integer-valued
$N\times N$ matrix $T^q_{ij}$ called the $q$-clique adjacency
matrix. It is defined as $T^q_{ij}=0$ when there is no link between
$i$ and $j$, and otherwise as the number of $q$-cliques which this
link is part of. In other words, if $q = 3$, $T^{q=3}_{ij}$ is
non-zero only when $i$ and $j$ are connected, and in the $3$CAP case
it counts the number of common neighbors. $T^q_{ij}$ can be
considered a proximity measure for nodes: linked nodes with many
common neighbors are likely to belong to the same community. Similar
proximity measures between nodes which depend on the similarity of
their neighborhoods have been used in
\cite{Ravasz_2002,leicht_2006,Ahn_2009}. To visualize $T_{ij}$, we
first rank the nodes and then plot for each pair of ranks a pixel with
corresponding color or gray scale. Possible ranking schemes are by
degree, by the number of triangles attached to the node, or by
achieving the most simple looking, block diagonalized, $q$-clique
adjacency.
Examples for the Yeast degree sequence are given in
Fig.~\ref{Figure8}. The four rows, descending from the top, show the
3CAP for typical members of the BRM ensemble before the first jump and
after the first, second, and third jumps. The plots in the left column
show the ranking done by the degrees of the nodes. The plots on the
right show the same matrices after ``diagonalization", with the nodes
forming the first cluster placed in the top ranks, followed by the
nodes forming the second cluster, and the nodes forming the third
cluster. Only the relevant parts of the 3CAPs are shown: nodes with
lower ranks do not play any substantial role except for very large
values of $\beta$. We notice several features:
\begin{itemize}
\item Not all highest degree nodes participate in the first clustering
cores. Obviously, the selection of participating nodes is to some
degree random, and when sufficiently many links are established they
are frozen and cannot be changed easily later. This agrees with our
previous observation that the positions of the jumps change
unsystematically with details like the random number sequence or the
speed with which $\beta$ is increased.
\item Clustering cores that have been formed once are not modified
when $\beta$ is further increased. Again this indicates that
existing cores are essentially frozen.
\item Clustering cores corresponding to different steps do not
overlap.
\end{itemize}
All three points are in perfect agreement with our previous finding
that hysteresis effects are strong and that structures which have been
formed once are preserved when $\beta$ is increased further.
From other examples (and from later jumps for the same Yeast sequence)
we know that the last two items in the list are not strictly correct
in general, although changes of cores and overlap with previous cores
do not occur often. Thus the results in Fig.~\ref{Figure8} are too
extreme to be typical. When a clustering core is formed, most of the
links connected to these nodes will be saturated, and the few links
left over will not have a big effect on the further evolution of the
core.
We find that as $\beta^-$ decreases, the clustering cores persist well
below the value of $\beta^+$ at which they were created (not shown
here). This shows again that once a link participates in a large
number of triangles, it is very stable and unlikely to be removed
again.
$3$-clique adjacency plots are also useful for analyzing empirical
networks, independent of any rewiring null model, to help visualize
community structure. While nodes in different communities often are
linked, these links between communities usually take part in fewer
triangles than links within communities. Thus simply replacing the
standard adjacency matrix by the $3$clique adjacency matrix should help discover and
highlight community structure \cite{Ravasz_2002,leicht_2006,Ahn_2009}.
In the top left panel of Figs \ref{Figure9} and \ref{Figure10} we show
parts of the 3CAPs for the yeast protein-protein
interaction and HEP networks respectively. In both cases,
nodes are ranked by degree. We see that the triangles are mostly
formed between strong hubs, as we should have expected. But clustering
in the real networks does not strictly follow the degree pattern, in
the sense that some of the strongest hubs are not members of prominent
clusters. This shows again that real networks often have features
which are not encoded in their degree sequence, and that a null model
entirely based on the latter will probably fail to reproduce these
features. We see also that links typically participate in {\it many}
triangles, if they participate in at least one. This is in contrast to
a recently proposed clustering model, which assumes that each link can
only participate in a single triangle \cite{newman_random_2009}.
\begin{figure}
\includegraphics[scale=.25]{Figure9.pdf}
\caption{\label{Figure9} (color online) Parts of 3CAPs for the real
yeast protein-protein interaction network of
\cite{gavin_functional_2002}, for a typical network of the
``triangle conserving" ensemble with no annealing, for a network
obtained after an ``annealing" period with $\beta=0$ and a
subsequent quench with $\beta\neq 0$ using `triangle conserving"
rewirings \cite{milo_network_2002}, and for an ensemble obtained by
500 of such annealing/quenching alternations.}
\end{figure}
\begin{figure}
\includegraphics[scale=.25]{Figure10.pdf}
\caption{\label{Figure10} (color online) Analogous to
Fig.~\ref{Figure9}, but for the real high energy physics
collaboration network and for the HEP degree sequence,
respectively.}
\end{figure}
\subsection{Triangle conserving null models}
\label{sec:null}
In the previous subsection we considered the case where the bias is
``unidirectional". In contrast to this, Milo {\it et al.}
\cite{milo_network_2002} considered the case where the bias tends
to increase the number of triangles when it is below a number
$n_{\Delta,0}$, but pushes it {\it down} when it is above. In this way
one neither encounters any of the jumps discussed above nor any
hysteresis. But that does not mean that the method is not plagued by
the same basic problem, i.e. extreme sluggish dynamics and effectively
broken ergodicity.
In the most straightforward
implementation of triangle conserving rewiring with the Hamiltonian
$H_{\rm Milo}$ \cite{milo_network_2002} one first estimates during
preliminary runs a value of $\beta$ which is sufficiently large so
that $n_\Delta$ fluctuates around $n_{\Delta,0}$. Then one starts with
the original true network and rewires it using this $\beta$, {\it
without first `annealing' it} to $\beta=0$. The effect of this is
seen in the top right panels of Figs. \ref{Figure9} and \ref{Figure10}.
In both cases, the $3$CAPs shown were obtained after $>10^9$ attempted
swaps. At $\beta=0$, this number would have been much more
than enough to equilibrize the ensemble. But for the large values of
$\beta$ needed for these plots ($\beta=1.5$ for Yeast, and $\beta=
2.4$ for HEP), few changes from the initial configurations are
seen. This is particularly true for the strongest clusters existing in
the real networks. Triangles not taking part in these clusters change
more rapidly, but are also less important.
Thus we see a pitfall inherent in triangle conserving rewiring: when
the bias is strong enough to push the number of triangles in the
network up to the desired target number, the bias will also be large
enough that links between high degree nodes are hardly ever
randomized.
\begin{figure}
\includegraphics[scale=.25]{Figure11.pdf}
\caption{\label{Figure11} (color online) Values of the assortativity
$r$ and of the number of 4-cliques in the real HEP network and in
400 members of the triangle-conserving biased ensemble. These 400
realizations were obtained approximately by 200 anneal/quench cycles
with $\beta = 2.3$ and 200 cycles with $\beta = 2.5$, as described
in the text. Notice that the results for biased simulations should
become more exact as $\beta$ decreases towards $\beta_c \leq 2$.}
\end{figure}
As a way out of this dilemma, we can alternate epochs where we use
triangle conserving swaps with ``annealing periods" where we use
$\beta=0$. In this way we would guarantee that memory is wiped out
during each annealing period (see the lower left panels in
Figs. \ref{Figure9} and \ref{Figure10}), and each ``quenching epoch"
would thus contribute essentially one independent configuration to the
ensemble. After many such cycles we would obtain an ensemble which
looks much more evenly sampled (lower right panels in
Figs. \ref{Figure9} and \ref{Figure10}), although even then we can not
be sure that it really represents the equilibrium ensemble for the
Hamiltonian $H_{\rm Milo}$. Apart from the last caveat, the method
would presumably be too slow for practical applications where high
accuracy and precise variances of ensemble observables are needed,
since one needs one entire cycle per data point.
But it can be useful in cases where it is
sufficient to estimate fluctuations roughly, and where high precision
is not an issue. To illustrate this, we present in Fig.~\ref{Figure11}
results for the HEP network where we made 200 anneal/quench cycles for
two different values of $\beta$ ($\beta = 2.3$ and $\beta = 2.5$). In
each cycle the quenching was stopped when the number of triangles
reached the value of the real network, and the values of $r$ and of
the number of 4-cliques was recorded. We see from Fig.~\ref{Figure11}
that these values scatter considerably, but are in all cases far from
the values for the real network. Thus the ensemble is a poor model for
the real HEP network. We also see from Fig.~\ref{Figure11} that $r$
and $n_{\rm 4-clique}$ depend slightly on $\beta$ (as was expected),
but not so much as to invalidate the above conclusion.
\section{Conclusion}
\label{sec:conc}
In highly clustered networks -- and that means for most real world
networks -- most of the clustering is concentrated amongst the
highest degree nodes. The Strauss model correctly pointed to an
important feature: clustering tends to be cooperative. Once many
triangles are formed in a certain part of the network, they help in
forming even more. Thus, clustering cannot be smoothly and evenly
introduced into a network; it is often driven by densely
interconnected, high-degree regions of the network. In triangle biased
methods these high-degree regions can emerge quite suddenly and
thereafter prove quite resistant to subsequent randomization.
The biased rewiring model studied in the present paper is of
exponential type, similar to the Strauss model, with the density of
triangles controlled by a `fugacity' or inverse `temperature'
$\beta$. However, we prevent the catastrophic increase of connectivity
at the phase transition of the Strauss model by imposing a fixed
degree sequence. Yet there is still a first order transition for
homogeneous networks, i.e. those with fixed degree. In the phase with
strong clustering (large fugacity / low temperature), the configuration
is basically a collection of disjoint $k-$cliques.
If the degree sequence is not trivial, the formation of {\it
clustering cores} can no longer happen at the same $\beta$ for
different parts of the network. Thus the single phase transition is
replaced by a sequence of discrete and discontinuous jumps, which
resemble both first order transitions and Barkhausen jumps. As in the
real Barkhausen phenomenon, frozen randomness is crucial for the
multiplicity of jumps. There, each
jump corresponds to a {\it flip} of a spin cluster {\it already defined}
by the randomness -- at least at zero temperature
\cite{Perkovic_1995,Zapperi_1997}. In the present case, however,
each jump corresponds
to the {\it creation} of a cluster whose detailed properties are not
fixed by the quenched randomness (the degree
sequence), but depend also on the `thermal' (non-quenched) noise.
As in any first order phase transition, our model shows strong
hysteresis. Clustering cores, once formed, are extremely stable and
cannot be broken up easily later. This limits its usefulness
as a null model, even if it is treated numerically such that the
phase transition jumps do not appear
explicitly, as in the version of \cite{milo_network_2002}. Because of
the very slow time scales involved, Monte Carlo methods cannot
sample evenly from these ensembles. Care should be
taken to demonstrate that results found using them are
broadly consistent across various sampling procedures.
The spontaneous emergence of clustering cores in the BRM does suggest
that triangle bias can give rise to community structure in networks,
without the need to define communities {\it a priori}, thanks to the
cooperativity of triangle formation.
Together with jumps in the number of triangles (i.e. in the clustering
coefficient), there are also jumps in all other network properties at
the same control parameter positions. In particular, we found jumps
in the number of $k-$cliques with $k>3$, in the modularity, and in the
assortativity. This immediately raises the question whether the model
can be generalized so that a different fugacity is associated to each
of these quantities. For assortativity, this was proposed some time
ago by Newman \cite{newman_assortative_2002}. With the present
notation, biased rewiring models with and without target triangle
number $n_{\Delta,0}$ and target assortativity $r_0$ are given by the
Hamiltonians
\begin{equation}
H_{\rm Milo}(G;\beta,\gamma) = \beta |n_\Delta(G) - n_{\Delta,0} |
+ \gamma |r(G) - r_0 |
\label{CandRHam1}
\end{equation}
and
\begin{equation}
H_{\rm BRM}(G;\beta,\gamma) = - \beta n_\Delta(G) -\gamma r(G),
\label{CandRHam2}
\end{equation}
respectively, where $\gamma$ is the fugacity associated to the
assortativity. It is an interesting open question whether such a
model might lead to less extreme clustering and thus might be more
realistic. First simulations \footnote{D. V. Foster {\it et al.}, in
preparation} indicate that driving assortativity leads to smooth
increases of all other quantities without jumps. The reason for that
seems to be that the basic mechanism leading to increased
assortativity -- the replacement of existing links by links between
similar nodes -- is not cooperative, but further studies are needed.
As Newman remarked in \cite{newman_random_2009}, clustering in
networks ``has proved difficult to model mathematically." In that
paper he introduced a model where each link can participate in one
triangle at most. In this way, the phase transitions seen in the
Strauss model and in the present model are avoided. However, in the
real-world networks studied here we found that the number of triangles
in which a link participates is broadly distributed, suggesting that
the Newman model \cite{newman_random_2009} may not be realistic for
networks with significant clustering. Indeed, specifying for each link
the number of triangles in which it participates adds valuable
information to the adjacency matrix (which just specifies whether the
link exists or not). The resulting `$3$ clique adjacency plots'
revealed structures which would not have been easy to visualize
otherwise and are useful also in other contexts. Thus, in contrast to
what is claimed in \cite{newman_random_2009}, the quest for realistic
models for network clustering is not yet finished.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,013 |
Gold price surges as 'Trump trade' unravels
"Maybe investors should forget the Trump trade and start prepping for the Trump correction," says Robert Burgess on Bloomberg, reporting that Wall Street equity gauges yesterday endured their worst single-day performance since October, with the Dow Jones and S&P 500 both falling well in excess of one per cent.
Pound plunges after Bank of England's dovish rates signal
At the same time, he adds, the dollar is in an "epic slump" and, after five days of decline, is the worst it has been since the election of Donald Trump in November.
"If markets truly believed that Trump's policies would juice the economy and spark faster inflation, then the dollar would be a prime beneficiary," he adds.
On the other hand, "safe haven" investments – assets seen to be a safe store of value in times of stress – are rising, with government debt bonds and gold both "back in vogue".
Gold benefits from a compound effect of the current sentiment shift: in addition to being a noted safe haven, it is inversely correlated to the dollar, against which it is held as a hedge.
As a result, prices rose one per cent to $1,247 an ounce overnight before paring back slightly to $1,245 this morning.
Just a week ago, gold was below $1,200 an ounce as the market priced in expectations, later vindicated, that the US Federal Reserve would increase interest rates.
Gold is also negatively correlated to rates, which increase the opportunity cost of holding non-yielding assets.
The market tremors, after four months of consistent rises and new all-time highs for equities, come amid mounting unrest about Trump's policy agenda.
In addition to having his controversial travel ban rejected by a federal court for a second time, his drive to repeal the so-called Obamacare health legislation is running into a quagmire of Republican division, the Financial Times says.
This is raising doubts among those who had piled into risk stocks in anticipation of promised tax cuts and reforms.
Alan Gayle, director of asset allocation at RidgeWorth Investments, said: "All the time they are spending on healthcare reform, they are not spending on tax reform."
Why did the gold price rally after the Fed raised interest rates?
Trading usually falls when rates go up, but the metal spiked overnight and is still ahead this morning
The gold price was expected to react badly yesterday after Federal Reserve officials voted to increase interest rates for the first time this year but the second time in three months.
In doing so, says The Times, rate-setters "signalled the end of an era of ultra-low borrowing costs" in the world's largest economy.
As gold does not offer an income and so losing out to yield-bearing assets, it tends to fall during periods of rising interest rates. Increasing rates also usually boost the US dollar, against which the metal is typically held as a hedge.
But in the event, the gold price, which had retreated in the past couple of weeks ahead of the policy announcement, rebounded strongly overnight, spiking from around $1,200 an ounce to close to $1,230 at one point.
By this morning, it was up more than two per cent to $1,224 an ounce.
This may seem counter intuitive, but in a note to clients, Ole Hansen, head of commodity strategy at Saxo Bank, said this was exactly the trend seen before and after the last two rates hikes.
As traders discount the price in the expectation of what is to happen - and with market bets on a rise yesterday running at 80 per cent this week - investors had effectively "priced in" the Fed's 0.25 per cent move.
On the day, then, they looked for evidence of the trend to come and the Fed's message in this respect was dovish, says Mining.com.
In their policy statement setting out the rise, rate-setters said the pace of increases would only be "gradual", reports Reuters, while the "dot plot" predicts only two more rate rises this year - the same as previously outlined.
This may not be enough to keep pace with rising inflation, which will keep "real" interest rates negative, and that is good for gold.
Another development overnight that may have influenced the metal was the election result in the Netherlands, where Geert Wilders' far-right PVV populist party lost ground.
It could be a significant development that signals destabilising populist movements across Europe have peaked. As such, the need for investors to seek noted "safe havens" such as gold is diminished.
Gold price holds above $1,200 as political risks ramp up
The gold price is holding its ground today. The yellow metal is back above the psychologically key level of $1,200 an ounce as investors seek protection from political risks.
Gold slipped below the threshold on Thursday and fell again on Friday afternoon in London as evidence continued to mount that the Federal Reserve would increase US interest rates again this week.
But gold ended the final session of last week slightly higher. After a positive Asian session overnight it was 0.3 per cent higher at $1,204 an ounce this afternoon in London.
The gold price tends to fall when rates are set to rise as the metal does not offer a yield and so loses out to income-bearing assets.
Yuichi Ikemizu, head of commodity trading at Standard Bank in Tokyo, told Reuters that "people are now quite sure that interest rates will go up" and that this is "discounted into the gold price".
Last week market bets on a rates rise at the Fed's March meeting rose to more than 80 per cent.
The focus is on the "safe haven" value of gold as potentially destabilising political events loom that could rock the global economy and so weaken demand for risk assets like equities.
The UK government has made it clear it intends to trigger Article 50 and formally begin the Brexit process as soon as tomorrow.
To do so would probably result in the House of Commons rejecting amendments to the legislation that was passed in the House of Lords last week, including the guarantee of a parliamentary vote on any EU deal.
Meanwhile the Dutch are going to the polls on Wednesday in the first of three major general elections in Europe this year, which will test the support for far-right populists.
Geert Wilders's Party for Freedom has led the polls for much of the campaign. As most of the main parties say they're not prepared to work with Wilders this could pose a problem when forming a stable coalition government.
"Gold should find some safe-haven bids at these levels this week as the Dutch election became more fraught over the weekend," said Jeffrey Halley, a senior market analyst with OANDA.
Gold price below $1,200 on rates expectations
Gold has fallen below $1,200 an ounce, continuing a recent bearish run as bets grow on the US increasing interest rates next week.
Trading overnight dipped below the threshold for the first time since the end of January, hitting a low of $1,196 an ounce. It pared losses this morning before turning negative again this afternoon.
This reflects the broader pessimistic view on gold that has taken hold of late, relating to economic data suggesting the Federal Reserve will increase interest rates in the near future.
The keenly watched non-farms payroll report, a monthly update on the number of jobs being created in the US economy, shows employers are estimated to have added 235,000 new jobs in February, well in excess of the 200,000 expected by analysts, reports the Financial Times.
Unemployment ticked down from 4.8 to 4.7 per cent – holding below the five per cent considered by many economists to indicate "full employment" – while wage growth accelerated slightly from 2.6 to 2.8 per cent.
All in all, it is hard not to see the figures as corresponding to the economic data remaining "strong", which Fed chairwoman Janet Yellen said last week would make an interest rates in the near future "appropriate".
Rate-setters meet again next week and bets on a rise have gone from 30 per cent at the beginning of this month to more than 80 per cent.
Rates rises tend to be negative for gold, which does not offer an income and so loses ground to yield-bearing assets.
Gold price hits four-week low on expected US rates hike
Investors are betting strongly on another increase in US interest rates next week and gold is falling in response.
Yesterday, the metal fell to $1,213 an ounce, its lowest level since 3 February. Despite having trimmed its losses overnight, it was sliding again this morning and stood at a dollar below yesterday's four-week low.
Helping trigger this downward trend have been comments from Federal Reserve officials pointing to a rate rise at their next policy meeting next week.
In particular, on Friday, Fed chairwoman Janet Yellen said explicitly that "a further adjustment of the federal funds rate would likely be appropriate" if the economic data remains strong.
Investing.com says "at the current level of market odds, a March hike is now locked in".
Reuters adds that "early last week, financial markets saw just a 30 per cent chance of the Fed raising interest rates in March; but by Friday… traders saw an 80 per cent chance".
Gold tends to respond badly to rates increases, as this boosts the value of income-bearing assets at the expense of non-yielding alternatives such as commodities.
Rising rates also typically coincide with a rising dollar, against which gold is often held as a hedge. In addition, they indicate rising confidence in the economy, which boosts risk assets and undermines gold's appeal as a "safe haven".
However, while gold is down on recent levels, trading remains well above its position late last year and ahead of where analysts expected it to be.
Societe Generale, for example, predicted an average gold price of $1,175 an ounce this year, while the World Bank believes it will average around $1,150.
Investing.com says: "Investors should not forget that real interest rates are what really matters for gold prices – a small rate hike may not be enough to combat inflation and raise real interest rates.
"The Fed being behind the curve is a positive factor in the gold market." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,660 |
Noahic Flood
Book Review: "The Grand Canyon: Monument to an Ancient Earth- Can Noah's Flood Explain the Grand Canyon?" Edited by Carol Hill, Gregg Davidson, Tim Helble, and Wayne Ranney
Posted by J.W. Wartick ⋅ May 16, 2016 ⋅ 3 Comments
The Grand Canyon: Monument to an Ancient Earth is one of the best analyses of young earth creationism on the market. In this beautifully illustrated text, the Grand Canyon is used as a test site to analyze Flood Geology, the notion that Noah's Flood radically shaped the face of the Earth and can account for much of the sedimentary layers we observe. The Grand Canyon is an especially appropriate test case because there are young earth creationist (hereafter YEC) books published on the Canyon, and many YEC works reference the Grand Canyon in explanations of their theories.
Part 1 outlines two views of the Grand Canyon: that of flood geology, in which the vast majority of the Canyon's sediment was laid down during Noah's Flood; and that of conventional geology, in which long time periods and observable, repeated processes can account for the Canyon. This part includes chapters contrasting the time frames of flood geology and conventional geology, showing the massive difference between the two views conclusions about how the Canyon formed. Part 2 is entitled "How Geology Works" and covers things like sedimentary rocks, plate tectonics, and time measurements. Part 3 looks at fossils and what they tell us about the age of the Grand Canyon. Part 4 surveys how the Grand Canyon was carved. Part 4 gives a verdict on flood geology from the evidence provided.
The authors provide an introduction to geology generally speaking, and then focus what is covered onto the Grand Canyon. Throughout the whole book, the Grand Canyon serves as the testing ground for what modern geology teaches about the Earth. Then, it is contrasted with what YECs claim about the age of the earth and the processes that formed it. Time and again, this shows that YEC claims are found wanting. The chapters on fossils are particularly telling in this regard.
For example, Joel Duff demonstrates, in "Tiny Plants – Big Impact: Pollen, Spores, and Plant Fossils" that there are entire, massive chunks of sediment without any pollen or plant spores contained therein. And these layers aren't just randomly distributed; they're in the oldest layers of the rock, such that it demonstrates what conventional scientists have claimed, that there simply were no pollinating plants long ago. But if flood geology is to be believed, these sediments were laid down during Noah's Flood, which would have entailed all kinds of mixing of dead plants and animals as the surface of the Earth was radically changed. How then, are there thousands of feet of sediment without any pollen? How did microscopic plant matter manage to get sifted out in such a clear distinction from other layers? This is the kind of in-depth look at the specifics of flood geology that abound everywhere in the book. YEC arguments are subjected time and again to direct refutation like this, making the book invaluable.
The book is also valuable simply as an introduction to geology as well as some biology and other sciences. I learned an extraordinary amount from the book, and I feel fairly confident that I had a working knowledge of geology. In other words, the book is not simply a refutation of flood geology in the Grand Canyon, it can also serve as a valuable introduction to several related topics.
I would be remiss if I did not call out the beauty of the book. There are breathtaking full-color photographs of the Grand Canyon throughout the book, accompanied by numerous graphs and charts. But these illustrations do more than just look pretty, they are almost always explicitly tied into the text in meaningful ways. I found myself thoroughly poring over each and every one, whether I was looking for the division between layers of rock in a photograph or flipping back to a chart repeatedly as I came to understand it better. These illustrations are perhaps made more impressive by the modest price of the book ($26.99 regular price on Amazon). Simply put, you can't get books with this much information and as beautifully put together as this for that price, yet here it is.
There are only two minor points I'd like to mention as negatives, but they are closer to nitpicking than anything else. First, although the introductory chapters (and a few other places) note that the young earth creationist arguments about the Grand Canyon are scientific and expressly stated as being testable, I suspect many YECs will respond to the book by appealing to some presuppositional theological perspective. Though this would be a mistaken response, it would have helped the book to perhaps include one chapter showing how the YEC claims about the Canyon are inherently scientific and can be tested without a specific theological narrative. Again, this point is made, I just think it could have been elaborated a bit more. Second, there was the briefest mention of one of the most popular arguments for Intelligent Design, that of the Cambrian explosion. The mention was so short that it is difficult to see what the authors were intending.
I have read dozens, perhaps hundreds of books on the debate over science and religion. That said, The Grand Canyon: Monument to an Ancient Earth is a remarkable achievement. It provides some of the most thorough, in-depth analysis of young earth creationist reasoning that is available to date. It is beautifully illustrated with photos and charts that are directly related to the text, and it is reasonably priced. If you're looking for analysis of flood geology from a scientific perspective, this book gives you the perfect test scenario. I cannot recommend it enough.
+Huge amount of information from geology to biology
+On-point analysis of flood geology
+Helpful charts and graphs
+Stunning photographs throughout linked to the text
+Features women's voices
+Direct engagement with prominent YEC writings
+Reasonable price
-Perhaps too light on the theological side
-Only the briefest engagement with ID
Disclaimer: I was provided with a review copy of the book by the publisher. I was not required to provide any specific kind of feedback whatsoever.
The Grand Canyon: Monument to an Ancient Earth (Kregel, 2016).
Book Reviews– There are plenty more book reviews to read! Read like crazy! (Scroll down for more, and click at bottom for even more!)
Eclectic Theist– Check out my other blog for my writings on science fiction, history, fantasy movies, and more!
"Oceans of Kansas," Unexpected Fossils, and Young Earth Creationism
Posted by J.W. Wartick ⋅ February 19, 2014 ⋅ 11 Comments
Recently, I reviewed the debate between Bill Nye and Ken Ham. In that debate, Bill Nye challenged Ken Ham to come up with just one fossil that was in the wrong place in the fossil sequence. In that review, I mentioned polystrate fossils as one possibility for the YEC rejoinder. Strictly speaking, these fossils are not "out of sequence" in a formal sense and so do not qualify as such evidence. Are there other possibilities? Michael J. Everhart's fascinating look at the natural history of the Western Interior Sea brings up another possibility which may draw some looking for out-of-sequence fossils. After an introductory narrative about how a mosasaur (pictured on the cover of the book getting chomped by a shark) fossil could end up broken up in the middle of the sea, he wrote:
"Bloating and Floating" is certainly the case in many instances and is the only reasonable explanation for how the remains of large dinosaurs, such as Niobrarasaurus coleii…could have found their way into the middle of the Western Interior Sea… (48)
There have been, he noted, discoveries of dinosaurs in the middle of what should have been fossils of only aquatic creatures in the chalk and limestone that covers much of the central states–what was in ancient times the Western Interior Sea. His proposed explanation is that a dinosaur might die on the shore and get swept out to sea, bloated and floating until coming to rest at the bottom and becoming fossilized. Though not necessarily the "only reasonable" explanation, Everhart's scenario provides an interesting test case for rival hypotheses.
Young Earth Creationists (YECs) tend to view evidences like these as proof of the Flood. That is, given a catastrophic global flood, one would expect that different life forms, all killed together by the flooding of the whole Earth, would be mixed together. Thus, a dinosaur in the middle of what should be sea creatures is alleged to provide evidence for the YEC Flood hypothesis.However, Everhart's scenario does seem to be more plausible than a young earth account for several reasons.
First, Everhart's proposed scenario is much simpler an explanation than the hypothesis that a global flood swept the dinosaur(s) into the position they are found among so many aquatic remains. This point is not to be understated; on a purely historical level, without any a priori assumptions of what should be the case given a specific reading of Genesis, it seems more reasonable to suppose that a dinosaur died and had its carcass swept out to sea before it was scavenged and sank to the bottom of the sea to be deposited than to suppose that a global catastrophe led to the dinosaur being found in its present location.
A picture I took at "Castle Rock" in central Kansas. This beautiful formation has huge amounts of deposited limestone and shells layered atop each other. One can walk to the walls and literally pull slabs of fossils out of the sides. If the YEC account of the flood were correct, one would expect to find multiple varieties of creatures found throughout these layers.
Second, and perhaps more problematic for the YEC position, is the fact that such finds as these are extremely rare, when, given a global flood, the expectation should be to constantly find such mixing of types of fossils. Simply finding one dinosaur fossil (or even several) among countless numbers of mosasaurs, icthyosaurs, fish, and of course limestone deposits from sea life (alongside shells of all sorts of varieties, etc.) does not actually provide sufficient evidence for the YEC account of the flood. We should instead find primates, dinosaurs, mosasaurs, trilobites, mammoths, and archaeopteryx fossils jumbled together. What we do find is a stunning uniformity of fossils such that the find of a dinosaur is means for speculation regarding how it got there rather than a commonality which demonstrates a planetwide flood.
Third, the dinosaur in question was contemporaneous with the aquatic life. That is, it lived at the same time as the creatures in the chalk in which it was deposited. Again, on a YEC scenario, one would expect instead to find all sorts of mixing of fossils from different time periods. The fact that these dinosaurs lived on land in the same time in which we find them at the bottom of the sea does not suggest a massive global flood which mixed all life (which all lived at the same time) together in one death pool; instead, it counts as direct evidence for the gradual diversification and extinction of life. The finds are consistent with what one would expect with longer periods of time instead of a global flood. Thus, it does not seem that fossils found in unexpected places may serve as evidence for Young Earth Creationism. Indeed, given the second point in particular (and in conjunction with the third), it seems that they serve as yet another evidence against the notion of a young earth and global flood. There are better options for Christians than Young Earth Creationism.
What options are there in the origins debate? – A Taxonomy of Christian Origins Positions– I clarify the breadth of options available for Christians who want to interact on various levels with models of origins. I think this post is extremely important because it gives readers a chance to see the various positions explained briefly.
Shells and the Biomass of Earth: A serious problem for young earth creationists– I argue that the sheer amount of living organisms we can discover weighs against a young earth position.
Michael Everhart has written more on the specific find related to the dinosaur in the Smoky Hill Chalk at the Oceans of Kansas site.
My thanks to fellow blogger "The Natural Historian" for some comments on the topic of this post prior to publication.
Michael J. Everhart, Oceans of Kansas: A Natural History of the Western Interior Sea (Indiana University Press, 2005).
"The Rocks Don't Lie" by David Montgomery: Chapter 4
Here, I continue my look at The Rocks Don't Lie by David Montgomery. I have not finished the book, but am rather writing these reviews as I read the chapters, so each one is fresh. Check out the end of the post for links to the other chapters as well as other related posts.
Chapter 4: World in Ruins
Montgomery begins by outlining the state of beliefs before early geological investigations. These were formed from theological understandings and thus derived themselves either from creation or the Flood.
The early theories of how the Flood shaped the rocks lent themselves as hypotheses for investigating the natural world. Although many of these theories would be dismissed immediately now, for their time they were serious ideas about how the world may have been shaped. Yet even in the early days of geological investigation, many theologians and geologists realized some of the major difficulties attributing the whole geologic story to the Flood would raise. Isaac Vossius, for example, "argued for a local flood on the grounds that there simply was not enough water on earth to submerge the highest mountains" (55). The amount of water needed for a global flood remains a great difficulty into today.
Other early geologic difficulties were centered around fossils. Were they really vestiges of once-living creatures, or merely tricks of the stones (59)? Steno entered this debate and, apart from noting that fossils were similar to those bones of living creatures, he also developed principles of geology which are used to this day. These were the notion that the bottom of a pile of sediment is oldest and that sedimentary layers are deposited horizontally (60).
As geologic investigations continued, more radical theories were put forth to hold a global flood. These included the notion that, prior to the Flood, the earth was smooth, and so it would have been easy to cover the globe with the water we observe now (66). Yet theories like this, which hypothesize the Flood wreaking havoc upon the earth, yield great difficulties of their own. For example, how could Noah's descendants have populated the ends of the earth so quickly? Thomas Burnet, who had proposed this theory, argued that Native Americans had also survived the Flood (68).
John Woodward became another champion for advocates of a global flood. He asserted that the Flood dissolved the Earth's crust and then laid down the sediment observable now (70). His theory was in keeping with others who held that a "mighty flood burst forth from a subterranean abyss" (71). However, John Arbuthnot, a physician, published an essay which not only showed that Woodward had plagiarized Steno, but also blew holes through the Flood theory Woodward had proposed. These included the fact that fossils did not rearrange according to specific gravity and that the layering of sediment could not have occurred within such a mix (71, 73).
Edmund Halley (of Halley's Comet fame) came up with a theory which involved a comet coming near the earth and disturbing it on its axis, which "heaved the seafloor up… carving the topography we know today." He also came up with the idea of a "vapor canopy" over the Earth which yielded the great amount of water needed to flood the entire planet (74).
Montgomery notes that it is "ironic" that many of the arguments used by young earth creationists for their positions on geology have been derived from the seventeenth-century geologists, who themselves "did not blindly trust particular literal interpretations of scripture. They had faith reason would lead to enlightened interpretation of God's creation, as read from the pages of the book of nature…" (76).
Montgomery has done a commendable job documenting the long history of the interplay between geology and theology related to the Flood. Moreover, he has shown how many of the ideas found in modern creationism reflect the debates of this period–some of which were acknowledged as refuted back then.
The importance of this historical background should not be understated. When one investigates the way that theories of the Flood developed alongside geology, it provides a fascinating case study for the interplay between science and faith. More importantly, studying the arguments of the past shows how easy it is to resurrect the same ideas in new contexts. Modern young earth creationism owes a great debt to people like Halley and Woodward. Unfortunately, many of these ideas remain just as refuted as they were shortly after they were first proposed.
It is also important to observe cases like Burnet, who started out trying to fit geology into his interpretation of Genesis, but ended up being forced to hypothesize all kinds of things which are not actually found in the Genesis account in order to maintain his theory. Modern creationists should be wary of doing the same: in attempting to stay true to the meaning of the text, people too often introduce concepts which are entirely foreign to the passages themselves. Ironically, this is often done in the name of being "literal." I hope that works like Montgomery's (and Young's, see below) will help inform the Church regarding this debate.
Again, Montgomery's book shows its great similarities with The Biblical Flood by Davis Young, which itself focuses almost entirely upon the interplay between geology and theology. Both of these books come recommended from me. Montgomery's work is a faster read with a bit more focus upon the arguments of modern young earth views, while Young's work provides more of the much-needed background for the debate. [I skipped ahead a bit and saw that Montgomery acknowledges Young's own contributions to this discussion. I am of the opinion that each of their works bring unique contributions and are worth having.]
The Rocks Don't Lie has so far proven to be a fantastic work in which the author acknowledges the complexities of the issues as well as the debt geology owes to Christianity. Soon, we will look into chapter 5.
Like this page on Facebook: J.W. Wartick – "Always Have a Reason"
Check out my review of a similar work by a Christian: The Biblical Flood. I think this book is vastly important and should be in every Christian's library.
Be sure to browse my extensive writings on the "Origins Debate" over creationism, theistic evolutionism, and intelligent design (among other views) in Christianity.
Source: David Montgomery, The Rocks Don't Lie (New York: W.W. Norton & Company, 2012).
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"The Rocks Don't Lie" by David Montgomery: Chapters 2 and 3
Chapter 2: A Grand Canyon
Those who are familiar with Young Earth Creationism know that a major contention is that the Grand Canyon can serve as evidence for a global flood. For example, both Answers in Genesis and the Institute for Creation Research have several articles dedicated to the topic. (Just do a search on the sites–I have linked two examples. In the latter, the ICR author notes that the Grand Canyon is "Exhibit A for the flood model of geology.")
David Montgomery notes this interest from young earth groups and so he dedicates a chapter to the topic. He uses his own exploration of the Canyon to lead into a discussion of the geological evidence. Some of the rock formations found there "require[d] both extreme heat and high pressure" to form (17). He turns to a brief explanation of radiometric dating: "…the age of a rock can be read like a geologic clock because radioactive isotopes decay at a fixed rate… If you know the half-life of an isotope–how long it takes for the remaining amount to decay–then the ratio of the parent-to-daughter isotope now in a rock tells you how long ago the rock crystallized" (17-18).
Next, Montgomery gives a fairly basic introduction to geology. He provides a brief overview of how one can note unconformities in the rock and how different formations cut across each other. These evidences, found in the Grand Canyon, show that it was formed by a series of events rather than one single event (20ff). Moreover, physical evidence of fossilized burrows from "wormlike animals" in the sandstone provides evidence against flood geology. "How could fragile worms have been crawling around on and burrowing into the seafloor during a flood powerful enough to remodel the planet? The biblical flood would have had to have dumped more than ten feet of sediment every day for a whole year in order to have deposited the thousands of feet of sediment exposed in the canyon walls" (22).
More evidence against flood geology is found in the way the sediments themselves were formed. First, the differing mass of types of silt, clay, sand etc. make it difficult to believe that they could have been mixed together in a flood and then been deposited with uniformity of layers. Second, layers like that of white sandstone are composed of "fine-scale features" which "would have been obliterated if they had formed underwater… These dunes were made by wind" (25).
Finally, the fossils found within the Canyon present another difficulty. "If all the creatures buried… had been put there by the biblical flood, then why aren't modern animals entombed among them? That the vast majority of fossils are extinct species presents a fundamental problem for anyone trying to argue that fossils were deposited by a flood from which Noah saved [at least] a pair of every living thing" (27).
Montgomery has presented a number of extremely difficult problems for young earth interpretations of the Grand Canyon. In particular, the difficulty with the species of animals found buried seems intractable. My reason for noting this in particular is because flood geologists must assert that all the animal life is either descended from or prior to the animals in existence at the flood. Of course, if the Grand Canyon was formed by the flood, we should observe some of these extinct animals now–or at least recently. Yet for many, we do not. Why is that? A young earth perspective cannot simply assert that they died in the flood, for these would have been preserved in the flood.
The other problems Montgomery noted may sometimes be dismissed by advocates of young earth theories. In particular, Montgomery does little to defend radiometric dating, which is itself a major target of young earth views. For those interested, Davis Young's The Bible, Rocks and Time gives an extended defense of radiometric dating, and Young writes from a Christian perspective on this topic. Overall, this chapter presents a number of problems young earth advocates must deal with.
Chapter 3: Bones in the Mountains
Montgomery surveys briefly and selectively a history of Christian interpretation of the Genesis account and argues that some found room for less literal interpretations. Moreover, he points out that those who insist upon a literal reading of the text for Genesis must present reasons for not taking other references to the sky as a dome, etc. as non-literal (44-46, 50). Yet he also notes that the perspective from which the Bible is written (on earth) alleviates these difficulties–but these difficulties can only be alleviated by "allowing for figurative or allegorical interpretations" in which we "acknowledge… the fact that we live on a planet" (50).
Another difficulty with young earth views is presented, because the discovery of the New World revealed a massive amount of new species which the Ark would have had to carry. How does one fit all of these species onto the Ark? More importantly, how did these species get to the Ark and back to their homes in North America without leaving their ancestors' bones behind in places other than their native lands? (42-43)
I have to say this chapter really surprised me, because Montgomery showed an appreciation for and interaction with Christian theology that I was not expecting. For just one example, he refused to set up the oft-rehearsed science-vs-religion rants that often accompanied discussions of Galileo. Instead, he explored the historical context, and noted that the ideas the church held were not necessitated by the text but were rather incorporated from Ptolemic ideas (49).
The Rocks Don't Lie continues to impress me. Montgomery is careful to avoid overstating his case. More importantly, he seems to genuinely respect the beliefs of those whose writings he surveys and he shows a true concern for accuracy regarding some of the controversies. Thus far, he has presented a number of significant scientific challenges to a young earth paradigm, as well as noting the change and variety of perspectives within theology. Be sure to follow the blog for the next chapter(s)!
"The Rocks Don't Lie" by David Montgomery: Preface and Chapter 1
Posted by J.W. Wartick ⋅ June 24, 2013 ⋅ 10 Comments
I recently finished reading the Christian geologist Davis Young's The Biblical Flood (see my review) and found it to be a vitally important work. More recently, David Montgomery, a secular geologist, released The Rocks Don't Lie , a book guided by a very similar notion: applying geology to Noah's Flood while looking into the history of thought on the topic.
It didn't take long before I had decided that I would go through this one on an extended basis (sometimes lumping more than one chapter together) similar to how I reviewed Rob Bell's work Love Wins. The reason is because I think the work has much to inform both Christian and atheist alike, while it also has some problems I would like to discuss as I go along.
I have not finished the book, but am rather writing these reviews as I read the chapters, so each one is fresh. Check out the end of the post for links to the other chapters as well as other related posts.
David Montgomery states that his purpose in writing the book was initially "to present a straightforward refutation of creationism, the belief that the world is a few thousand years old and that all the world's topography… was formed by the biblical Flood." However, he came to "a different story about the nature of faith" once he began researching the topic: "…I thought I'd find the standard conflict between reason and faith. Instead, I found a much richer story of people struggling to explain the world–and our place in it" (xii).
Essentially, he discovered that there was a complex interrelationship between science and theology which has played out in vastly different ways over time.
Montgomery begins the book by telling a story of how he discovered evidence for a local flood in Tibet. He observed various geological features and came to believe that a lake had once covered the land. He suspected that such a feature in memorable history would yield an oral tradition and was rewarded with a story of a flood in the area (2-7). He asserts that "People around the world tell stories to explain distinctive landforms and geological phenomena" (7).
These stories are often dismissed as "relic[s] of another time," but he believes that they may have an element of truth: "For most of our history as a species, oral traditions were the only way to preserve knowledge. So why wouldn't the world's flood stories record actual ancient disasters" (8-9). He notes that the story of Noah's Flood may perhaps be among these stories, and hints that there could be truth to the biblical tale (9).
When science has come to interact with evidence which may hint at explanations for Noah's Flood, certain forms of Christianity (here he uses "creationist" as he defined it in the preface) are "outraged" due to the preconceived notion that the Flood must have been global and account for all geologic history.
Yet the Flood has had a positive influence on geology by providing an early hypothesis to be tested once geology had progressed as a science (11-12). Theology and geology played off each other in a complex way which has spawned various factions of belief over the use of that evidence in theology (12-14).
David Montgomery presents his case in a very winsome manner. I cannot help but be pleased by the way he has begun his interaction with science and faith issues. Rather than ranting over the alleged war between science and faith (something he admits he was expecting), he discovered a different story of a complex relationship which has often been mutually beneficial. Would that all atheists–and yes, it is worth saying, theists–interacted with other views in such a generous manner.
Montgomery has provided a number of interesting insights already, particularly in regards to the fact that the relationship between science and faith is multifaceted and not as one-dimensional as many often portray it.
It is unfortunate, I think, that his own faith was seemingly built upon very poor theology. He writes, "In Sunday school I learned that Bible stories were parables to be read more for their moral message than their literal words. The story of Noah's Flood taught mankind to be stewards of the environment… Growing up, I was satisfied that Jesus taught how to live a good life and that science revealed how the world worked" (9-10). Here we see how an anemic theology cannot be sustained. Christianity is picture that is much fuller than a mere "moral message" or "how to live a good life." If only someone had taught that in Sunday school instead!
If the book continues in this fashion, I will have no qualms about recommending it. Tune in next week to continue the series!
The Rocks Cry Out: A visual journey on a lake and its implications for the age of the earth
I recently visited Mirror Lake in Wisconsin and had the opportunity to canoe along the lake. Looking up from rowing the canoe, one is able to see exposed rock formations on either side as one goes from one major part of the lake to the other. How did this lake get here? How did the rocks erode as they show?
Two Primary Paradigms
There are two primary paradigms for interpreting the formation of the Earth. These are naturalistic or supernaturalistic. A naturalistic paradigm excludes God from the outset. A supernaturalistic paradigm may have any number of gods or spiritual forces. The reason I make the split here is because it is important to note that, regarding the ultimate origins of the universe and the Earth Christians are in agreement. God is the ultimate cause of reality.
Although we occupy the same paradigm with regards to the origin of all things, Christians are divided along a spectrum of possibilities (other paradigms) about the origin and diversity of life and species. Moreover, Christians are divided on the age of the Earth itself. Is the Earth a few thousand years old or a few billion years old? It is around this question that I shall focus here. Which subdivision of the supernaturalist paradigm better accounts for the evidence? Is the Earth "young" or "old"?
The Rocks, the Flood, and the Questions
Take a look at the photo above. The stone you see there is largely sandstone, layered upon itself. One can go up to the wall and crumble some of the rock between one's fingers. The layers are extensive, going several dozen feet above the water level before diving below the surface. Where did all this sand come from? Why is it now here, above the ground and exposed?
Global Flood and a Young Earth
There are a number of ways to answer this question, but there is a stark difference between how the answers are given. Young Earth Creationists (hereafter YEC will refer to Young Earth Creationists, Young Earth Creationism, etc.) largely hold to the position that this sand was deposited during the Noahic Flood found in the Bible. That is, these layers of sand were deposited all at once during the great deluge which covered the surface of the earth. Other YECs hold that after the flood, some additional depositions were made by other catastrophic events, including the Ice Age.
What of the notion that nearly all this sediment was placed there by the Noahic Flood? There are immediate problems with this explanation. How is it that the layers are clearly distinct types of rock? For example, I canoed up to the rock shown in the picture and observed the fact that the rock was almost uniformly sandstone. But if the explanation for this is that the sediment was mired together in the Flood, how is it that the types of stone were so neatly parsed out? Should we not instead observe all types of different sediments congealed together? Now, a YEC might counter by pointing out that perhaps the granules were deposited according to their specific gravity, but this would be to appeal to a notion which has been proven wrong via direct observation since John Arbuthnot wrote An Examination of Dr. Woodward's Account of the Deluge in 1697 (Montgomery, 72-73, cited below).
But there are even more problems with this explanation. If the sediments were all stirred up during a violent Flood, then how did marine animals survive? How did fossilization occur when such violent activity was taking place? What of unconformities in the rock? The issues multiply the more one considers the explanation proffered.
The alternative YEC interpretation–that some of the sediment was placed only later, during the Ice Age, runs into its own share of major difficulties.
Geologic Time
Other explanations come forth via inference from principles of geology. It should be noted that the foundations of geology were largely laid down by Christians like Hugh Miller and Steno who had themselves reflected upon the Flood and its implications for geology, while also looking at the natural world.
The geology of the Mirror Lake area in Wisconsin, according to this position, was shaped over the course of very long periods of time. The sandstone was cut across during a period of glaciation about 10-20 thousand years ago, and it rests on top of millions of years of geologic processes which created other rock formations, which each have their own explanations of how they came to rest under the sandstone. The lakes themselves were formed by Dell Creek, which takes a right angle. The reason for this angle is explained by "glacial outwash" which blocked the flow of the Creek and forced it to proceed at an angle. The Creek then proceeded to flow into the area it now occupies, shaping the landscape as it moved. It is amazing to consider the time which one can observe as one travels through this area, which was carved by a Creek! For a detailed summary of the formation of the geology of this area, check out the Wisconsin Geological Survey's report on this region.
Another Challenge for the Flood Explanation
As I canoed through the two major portions of Mirror Lake with several friends, it was interesting to consider how all the winding we experienced as we traversed could have been formed. If this area were formed by the Noahic Flood, then how could it have occurred? After all, the sediment through which it cuts is supposed to have been formed during this flood. But how did the rock get hard enough to be carved through even as it was settling? Why would not the Flood waters have simply caused a mixing of materials?
Plus, one must consider the angle that the occurs in the Mirror Lake area. Why, given fresh layers of sediment deposited by the Flood, did the waters carve out an angle? There seems to be no physical explanation for this phenomenon, granting a YEC paradigm. If the Flood accounts for Earth's geologic past, then how does it actually explain the physical world?
YECs have sometimes contended that the great amount of pressure put on the sediments by the Flood waters would have allowed for these rocks to form quickly enough to then be carved by the Flood. But if this were the case, how did any marine life survive this extreme pressure? How did delicate fossils get preserved when so much pressure and turbulent water came crashing upon them? Again, we see the difficulties continue to multiply.
Catastrophism or Uniformitarianism?
Very often, YECs will make a distinction between their own view as catastrophism and other views as uniformitarianism. I have discussed this distinction elsewhere, but it is highly relevant for the observations I was able to make around Mirror Lake.
Generally speaking, catastrophism is the notion that catastrophes (such as a flood, earthquake, etc.) form Earth's geologic past. WIthin the parlance of YEC, this is generally tightened to mean something more akin to the notion that catastrophes can account for the vast majority of the geologic record. Uniformitarianism is the notion that the processes we observe today were the processes which formed Earth's geologic past.
It absolutely must be noted that this notion of either catastrophism or uniformitarianism is a false dichotomy. Note that standard geology describes the formation of the Mirror Lake region as both a series of lengthy events taking place over fairly uniform time periods (the formation of the rocks and layers of sediment themselves) and a series of catastrophic events (wherein the Wisconsin Glaciation both scoured the surface and left new deposits and later flooding from the glaciers melting helped carve a path through the area to help form much of the region). That is, there is no either/or question. It is a matter of both/and within standard geology. Catastrophes are part of Earth's past, but they do not destroy completely the record of the uniformities which have shaped the planet.
A Linchpin?
We have already noted briefly many problems for a YEC paradigm. Perhaps there is an even greater difficulty to be found. YECs wish to offer an explanation for the geologic past and they hold that their reading of the Bible is the most literal. But after looking into YEC explanations of how specific geological formations are formed, is it really the case that YECs are reading the Bible literally? Where does it, in the text, suggest extremely high pressures from the water, the destruction of Earth's crust or at least its extensive modification, the formation of lakes and rivers due to the activity of the Flood, the deposition of sediments, the formation of fossils, or any number of other specific things that YECs tend to argue are results of the Flood?
It should become clear that these suggestions made by YECs are merely attempts to match their interpretation of the text with the geologic record. It is a guiding presupposition which determines all interpretation of the Bible and natural history. And, as I have argued extensively, it is a presupposition which is misguided.
My journey along the Mirror Lake watershed was enlightening. It was as though I could observe geologic time simply by looking at the rock formations around me. Moreover, it presented me with ample opportunity for reflecting upon the varied explanations given for how all these things were formed and shaped. It seems clear to me that the YEC paradigm suffers from impossible difficulties.
Like this page on Facebook: J.W. Wartick – "Always Have a Reason." I often ask questions for readers and give links related to interests on this site.
Gregg Davidson vs. Andrew Snelling on the Age of the Earth– This debate was between two Christians about the age of the Earth. I found it highly informative. Check out this post, which surveys the arguments.
Answering Common Young Earth Creationist Arguments– I survey a number of theological, Biblical, and scientific arguments put forth for YEC and find them wanting.
Young Earth Creationism and Presuppositionalism– I argue that YEC is tied directly to a specific use of presuppositionalism, but that it provides an epistemological quandary by doing so.
Check out my other posts on the Origins Debate.
David Montgomery, The Rocks Don't Lie (New York: W.W. Norton & Company, 2012).
The Wisconsin Geologic Society.
Wisconsin DNR: Mirror Lake Geology.
Book Review: "The Biblical Flood" by Davis Young
Posted by J.W. Wartick ⋅ May 13, 2013 ⋅ 21 Comments
Davis Young seeks in his work, The Biblical Flood , to inform readers about the broad scope of church thought on the Biblical story of Noah's Flood. The book's subtitle is apt and sums up the content of the work: "A Case Study of the Church's Response to Extrabiblical Evidence."
Young, a Christian geologist, provides a detailed overview of the Church's theological and scientific musings on the Flood. He develops this overview chronologically, beginning with early Jewish thought. The focus within the entirety of his book is directly centered upon how extrabiblical evidence was used to shape theology and vice versa. The relation should not be understood as binary. Throughout history, there was a spectrum of approaches to the extrabiblical evidence which included resistance (not infrequently forged by ignorance) as well as integration. Here, I will survey only the broadest outline of Young's discussion.
Early Flood Views
Early Christians were aware of Pagan stories of floods but made little or no appeal to them as evidence for a universal flood, and in fact some argued that these other stories were clearly differentiated from the Biblical account because they were local as opposed to global. There was much speculation over the location of the Ark as well as the notion that fossils were the result of this universal deluge.
Middle Ages and Renaissance
Medieval thought regarding the Flood was steeped in the "ahistorical view of creation" found at the time. That is, the science of the time thought of creation as deductible from the character and nature of God. However, the discovery of the New World brought up many challenges to a universal deluge theory, which challenges began to get recognition. These included the vast number of species which would have had to fit onto the Ark and the discovery of people across the world. During this period, the discovery of flood stories in various cultures began to be viewed as evidence for a universal deluge (37).
The New World continued to present challenges to the universal deluge theory. One of the foremost among these was animal migration. Entirely new and distinct species were discovered in the New World which did not exist in Europe. How did these animals get to these distant lands? More importantly, how did they get there without leaving any traces of themselves behind if they all only came from one location: the Ark? These challenges continue to vex those who hold to a universal deluge (60ff).
Geology's Origins
The notion of a universal flood has contributed much to the development of geology as a science. The Christian worldview finally presented a picture of the universe which humans could explore in order to learn truths about reality. The Flood itself presented a theory about how to account for the geological features of the earth (65ff). Various features of the natural world were attributed to the flood, including the discovery of marine fossils on mountains and geological features like valleys. These early geologists were committed to an following the evidence where it led.
Diluvialism and Catastrophism
Various theories were put forward to explain the features of the earth. These included varied catastrophic notions, wherein the geological features were explained by a global, catastrophic flood. Such theories are repeated into today.
Geological Evidence Mounts into the Twentieth Century
Young establishes that the evidence against catastrophic diluvialism became weighty fairly early into the investigations of geologists (109ff). New discoveries related to mammoths and the way they died (over a period of time by a variety of causes rather than all at once) were greatly important, as the issue of these mammoths was found throughout the speculation about the flood. New dating methods were developed which were more accurate. Archaeological finds showed floods in areas of the Mesopotamia, but they were dated at different times. The discovery that humanity was widely spread over the earth and that there was no major extinction event throughout this spread raises a significant challenge for Flood Geologists (233). Other major challenges to Flood Geology include (but are by no means limited to): the dating of igneous formations, the cooling of the earth, metamorphism, and continental drift.
Theological Reflections
Throughout this period of discovery, theologians were not inert. Indeed, many theologians were at the front lines, actually participating in the discoveries themselves. Near Eastern Studies have revealed parallels with the Flood account which some have suggested show derivation. Others, however, argue these other flood stories merely show the perpetuity of such events and how ingrained they became on the human consciousness (236ff).
More recently, Flood Geologists have come into being once more. Their arguments parallel almost exactly those found spread in the early days of geology. Yet these arguments have been refuted by the evidence from the earth itself. Some continue to make false statements about the mammoths' deaths, the formation of sedimentation, dating methods, and more. Young argues that this is largely due to the specialization of studies found within various fields like theology and geology. Theologians are rarely acquainted with the geological evidence, while geologists are rarely versed in theological language.
Theologians who were versed in geology began to see how interpretations of the text, rather than the text itself, had shaped the Christian response to geological evidence. People like Hugh Miller appealed to extrabiblical data in support of their intepretations of the Flood narrative (147ff).
Miller professed puzzlement that learned, respectable theologians would accept "any amount of unrecorded miracle" rather than admit a partial deluge. Could they not see that the controversy was not between Moses and the naturalists but between the readings of different theologians? (151)
More recently, many and varied theories of the flood as local have been developed and defended. The reaction from Flood Geologists has been vigorous, but theories of a global flood include a multitude of quotes from various scientists which would support competing theories of rock formation, sedimentation, and more. That is, Catastrophic Flood views present mutually exclusive theories for how the geological (and other) evidence came to be.
Appendix: Arkeology
The book is capped off with a discussion of "arkeology": the search for Noah's Ark. Young notes the array of locations which have been given as well as the mutually contradictory accounts of those who claim to have seen the Ark or evidence of the Ark. He warns Christians to remain cautious of any such claims.
I believe that a good way to summarize the content of the book would be to view it as a challenge Young is issuing to those who allege that catastrophic theories are the only possible way to interpret the text and geological evidence. He himself writes, "If conservative and orthodox theology is to remain vital and relevant to a world in need of the Christian gospel… theologians will have to abandon their flirtation with flood geology and other forms of pseudo-science, reacquaint themselves with genuine scientific knowledge, and incorporate that knowledge into their thinking, secure in the realization that genuine insight into God's creation… is still a gift of God to be treasured" (215).
Young's book can be viewed through this lens. He shows how scientific knowledge challenged traditional readings of the text, but also how many theologians and Christian geologists alike interacted with this in order to gain "genuine insight" into God's word and creation.
The Biblical Flood is a vitally important work. Young demonstrates that throughout history, Christianity has been largely willing to have a kind of interplay between extrabiblical evidence and theology. Unfortunately, in our time, many are ignorant of this long history and development of thought and science surrounding geology and the Flood. Theories have been developed which stand in the face of evidence from multiple, independent sources and angles.
I do not claim to have touched upon even all the major points found in Young's work. The book is full of voluminous amounts of historical details which reveal interesting scientific and theological notions. The theory of a global flood was the one of the first major proposals for how the earth's geological history was formed. As geological discoveries mounted, this theory was falsified. Moreover, theologians who interacted with the extrabiblical evidence had a wide array of responses, from downright rejection of the evidence or reinterpretation of it to attempt to fit a global flood to concordist views in which the extrabiblical evidence informed interpretation of the text. Which direction should we go? Young has presented a major challenge to those wishing to maintain a notion of the global flood. He presents mountains of evidence to challenge catastrophism, while also showing how, historically, thought on the Noahic Flood has comfortably incorporated the extrabiblical evidence without any necessary compromise of the text or faith. I commend the book to the reader without reservation.
Be sure to check out my posts on the "origins debate" which feature a wide range of posts on issues related to varying Christian views on evolution, creation, and more.
Davis Young, The Biblical Flood (Grand Rapids, MI: Eerdmans, 1995).
Resource Review: "In the Days of Noah: A Deeper Look at the Genesis Flood"
Posted by J.W. Wartick ⋅ January 10, 2013 ⋅ 10 Comments
Reasons to Believe is a science faith think-tank dedicated to showing that Christianity is true. Recently, I had the opportunity to view their resource, "In the Days of Noah." The video features a lecture by Hugh Ross regarding the extent, location, and timing of the Noahic (Biblical) Flood.
One of the central points of Ross' argument is that people must take an integrative approach to the question of the Genesis Flood. It is not enough to look at just one verse or one chapter or even one book of the Bible and declare the question closed. Instead, Ross argues, one must take the entirety of the Scriptural data and see what it tells readers about the Flood. Not only that, but the relevant scientific findings must be taken into account as well.
For many Christians, the extent of the Flood is taken as a test for orthodoxy. Ross argues convincingly, however, that the Biblical account does not necessitate that the Flood covered the entire surface of the planet. He goes over a wide range of texts that discuss events that are said to be "world wide" or to "cover the whole earth" or that are supposed to bring "every nation" to a certain place and shows how the usage of the term was relative to the author. Ross cites a number of texts to back up this claim and shows how in many places–the Joseph narrative, writings about Solomon, etc.–the words taken as universals generally ("whole earth," "all nations," etc.) are used specifically to mean the whole immediate/relevant world.
There are a number of texts describing creation that go into greater detail about specific aspects of the Genesis account. Ross outlines his argument via these texts by specifically noting a number which discuss the limits set for the waters. For example, Proverbs 8:29 states quite explicitly that God gave the sea its boundary. Ross continues through the Bible and cites numerous examples wherein it talks about God setting boundaries for the waters. From there, he makes the argument that these verses give us a principle: God has set the oceans in their boundaries from Creation. He then utilizes this as an argument for a local flood as opposed to a global flood.
I think that this may be the weakest part of Ross' argument, because it is possible to counter this reasoning by saying that just because there are a number of texts talking about the boundaries set for the water, it does not mean that the water can never cross these boundaries. In fact, one might counter by noting that Ross' view entails a kind of uncertainty over what exactly is meant when the Bible discusses the boundaries or limits for the oceans. After all, even on Ross' view, some body of water covered a vast expanse of land–indeed, the whole inhabited world at the time. In fact, one may argue that due to what we know about plate tectonics, the oceans have not, in fact, had clear boundaries from the beginning but have instead been shifting as the continental plates drift.
Of course, Ross could counter by noting that those continental plates themselves act as boundaries for the oceans. Even though these plates shift, they remain 'fixed' in the sense of constant. Regardless, it seems that the rebuttal given above must be given at least some weight in considering Ross' overall argument. However, even if one denies the force of his argument for the Scriptural notion of fixed boundaries as being a limit for a global flood, one must still contend with his argument to open up the possibility of a local flood by noting the difference between general and specific uses of the notion of a "worldwide" event.
That said, Ross turns to the scientific evidence and notes a number of evidences against a global flood. First, there are such things as unambiguous signs of a flood. He points out the possibility of checking ice cores and sediment cores for the continuous record of the last several hundred thousand years, so if there was a global flood there should be a signal in the ice layers evidence for a global flood. These layers are annual and we know this by looking for volcanic eruptions lined up in the layers at the correct times. These can therefore be calibrated by lining them up with volcanic eruptions that we know of historically. Moreover, the ice layers line up with the ellipticity of the earth, so there are multiple independent ways to test these ice layers. However, in these layers there are none of the telltale signs for a global flood.
So where was the flood? Ross notes a number of verses in the Bible to narrow in on the location of Eden, and then extrapolates from that where civilization would flourish. Due to some geological evidence for there having been a blockage on the end of the Persian Gulf which would have, combined with the melting of ice and the extreme amount of rain noted in the Biblical account, flooded a huge portion of the Mesopotamian Plain. The region is surrounded by mountains which would have blocked in the water for the flood. Such a flood would have wiped out the extent of known humanity at the time, argues Ross.
There are a number of arguments that young earth creationists, who often rely upon "Flood Geology" to explain a number of features of the geological past to maintain their view of the history of the earth, would raise to Ross' presentation. For example, the image on the right was created by Answers in Genesis to parody the notion that a flood can be local when the Bible says that even the mountain-tops were covered (Genesis 7:18-20) [all credit for the image to Answers in Genesis, I make no claim to having produced it in any way]. Ross answers this argument by noting that the word can also mean hills and that with the extent of the flood he proposed, there would be no visible hills or mountains from the Ark. Thus, Ross' argument is much along the lines of his integrative approach: that we must take into account all the relevant Biblical texts as well as noting the scientific evidence.
It would be remiss to have a review of a video without looking into the visuals. The video is a lecture divided into chapters, so a decent portion of it is spent watching Hugh Ross talk. However, there are also a number of very useful images and slides presented which will provide viewers in groups with opportunity for discussion and individual viewers with valuable resources to discuss the Biblical Flood.
"In the Days of Noah" is a great resource for those interested in the Noahic Flood. Hugh Ross is a lucid thinker and clearly lays out his perspective on the flood in terms that listeners will easily comprehend. Ross' case is based off a holistic approach to natural and special revelation. Although Ross does not answer every counter-argument which those opposed to his view may present, the video can act as a valuable way to open discussions and perhaps come to a better understanding of God's truth.
"In the Days of Noah: A Deeper Look at the Genesis Flood" (Reasons to Believe), 2010.
Image Credit for the second image goes to Answers in Genesis.
Gregg Davidson vs. Andrew Snelling on the Age of the Earth
Posted by J.W. Wartick ⋅ January 7, 2013 ⋅ 44 Comments
I was recently at the Evangelical Philosophical Society conference (see my thoughts on every talk I attended) and one of the sessions was a debate between Gregg Davidson of Solid Rock Lectures and Andrew Snelling of Answers in Genesis on "Scripture, Geology & the Age of the Earth." A number of readers requested more information on this talk, and I found it very interesting myself. Here, I'll touch on the highlights of this dialogue as well as my own thoughts.
Davidson- A Biblical Worldview and an Ancient Earth
Gregg Davidson, a geologist who authored When Faith and Science Collide , and is a lecturer for Solid Rock Lectures, began the dialogue by noting several themes in the young earth/old earth dialogue. First, he noted a tendency to present young earth creationism (YEC) as the only Biblical worldview, while also presenting evidence for a young earth as exceptionally strong in contrast to weak evidence for an old earth. Unfortunately, Davidson pointed out that many people get to schools where they learn geology, astronomy, and more in the sciences and discover that the evidence for the young earth is actually fairly weak, while that for an old earth is quite strong. And, because YECs often link young earth creationism to being the only possible Biblical worldview, they begin to view the Biblical worldview as a whole as extremely weak. If the evidence for YEC was so weak as to falter, then because it is inherently tied to the Biblical worldview, that wolrdview must itself be extremely weak.
Another problem is that YECs fail to recognize that their position itself is an interpretation of Scripture. Their view is not Scripture itself. There is a tendency in debates about theology to view one's own position as what the Bible teaches, but that fails to take into account the possibility of fallible human interpretation.
Davidson argued for an approach to Scripture that takes note of the fact that God often deigns to make use of "the knowledge of the day to communicate truths about the nature of God." As an example, he referenced Jesus saying that the mustard seed is the smallest seed of all the plants on earth, despite the fact that it is not (Mark 4:30-32). The point was not the size of the seed, but rather the power of faith. Thus,we must be careful not to make Scripture teaching something it does not claim for itself. He pressed that to read into the Genesis text specific dates and time periods is to make the text teach something that it is not claiming.
Turning to the science, Davidson noted that there are any number of evidences for an ancient earth, but that he chose to focus upon just one area from a number of evidences in order to show how interdisciplinary and cross-confirmed the age of the earth is. He focused upon the Hawaiian Islands and their formation and age. There are multiple, independent ways to investigate the age of these islands. The islands were formed by a hot spot–a place where magma shoots up from underneath the crust and bubbles to the surface. This eventually would form islands when enough of the lava cooled and hardened. The islands are on a moving continental plate and so as they move away from the hot spot, the expectation is the islands get progressively older. Thus, in a series of 3 islands arranged thusly: 3-2-1-0 (0 being the hot spot), 3 would be the oldest island.
Davidson first noted the ages that were found by testing the age of the volcanic rock with radiometric dating. These ages yielded millions of years. Now of course most young earth creationists hold that radiometric dating methods are deeply flawed, but Davidson noted that this procedure can be tested for accuracy with independent methods. Before turning to that, he showed a picture of what the estimate for the movement per year of the plate over the hot spot would be based solely upon the radiometric dating. Basically, this works by just taking the distance of 3-2-1 and measuring how far each is from the hot spot, then dividing the radiometric date by that distance to see how far the islands move per year. The estimate yielded movement of 2.6-3.6 inches per year.
Recent technology has allowed us to utilize Global Positioning Systems (GPS) to actually measure the rate that the islands are moving. These measurements yield approximately 3.1 inches per year, which is exactly in the middle of the estimate given by the radiometric dating. Given the measured rate, scientists can extrapolate how many millions of years old the islands are based upon their distance from the hot spot. It's kind of an inverse way to get the date. They simply divide the measured distance of the islands from the hot spot by the measured rate of movement per year. Of course, this way of measuring is not dependent in any way upon radiometric dating. Thus, there are two independent sources showing the date in millions of years for the Hawaiian Islands.
The coral growth around the Islands was a third confirmation of the ancient age of these formations. This argument was more complex than the first two. Basically, it seemed the argument was that because different corals form closer to the surface, we can look at the coral reefs formed around the islands as they are farther out and see how much the coral has moved up the island as it subducted (moved under the water with the continental plate). Thus, as the islands move farther away, and therefore sink into the water, the coral that can only survive at certain depths is submerged too far for it to get adequate sunlight, and it dies. One can then measure radiometrically the age of rings of corals. When one measures the coral on the islands, they can correlate that with the ages of the corals and the islands themselves. This measurement also lined up with the previous two.
Davidson concluded that the problem with the YEC paradigm is that they will often focus upon rebutting multiple, independent claims. While this may work for each claim individually, the problem is that all of these types of evidence add up to form one cohesive picture. When they are cross-referenced and they all hit on the same age or date range, they all show the same predictions of distance, and the like, it becomes extremely implausible to say that every single way to find the age of the earth is faulty. They form a full picture. Furthermore, Davidson critiqued YECs for often presenting a selective picture of the evidence–only showing the evidence which favors their position.
Snelling- A Biblical and Geological Defense of a Young Earth and the Global Flood
Andrew Snelling is a well-known proponent of YEC, the author of Earth's Catastrophic Past , and his presentation was perhaps the best defense of his position I have ever seen.
Snelling began by offering the common argument that Jesus taught the global flood and young earth creationism. He argued that the Hebrew word used in Genesis 7:17 is only used for this event, which hints at the incredible devastation.
Furthermore, the language in Genesis states that the mountains were covered. Snelling's slideshow had the image shown here on the right, which is becoming pervasive in discussions about the extent of the Flood. The argument is that if the Flood were local, it makes a mockery of the Biblical text. (See a different perspective on this issue with Hugh Ross' "In the Days of Noah.")
Snelling outlined several things we should look for if there was a global flood. Among these expectations are:
1) Marine fossils in strata for terrestrial creatures- Snelling named a number of places these could be found. This is an expectation because the Flood covered the whole earth, so the creatures should all be mixed together.
2) Rapid burial of creatures and plants- Snelling noted a number of places where fossils show rapid burial. This is expected because the Flood would have suddenly come upon these creatures.
3) Fossil graveyards- The Flood would have killed huge numbers of animals, so we should expect to find huge fossil graveyards, which we do.
4) Evidence that the ocean flooded the continents- if the Flood were global, we would expect to find its sedimentation upon the continents, and we do.
He argued that these are all evidenced in Earth's catastrophic past, and he pointed to the Grand Canyon as evidence for a number of these evidences.
Snelling also looked at various geological features he said were evidences for a global flood and a young earth. Among these were several layers of sedimentary rock which are bent. He argued that this can only occur when the rock is liquefied like cement–otherwise it cracks–so this sedimentation had to happen during the Flood.
Discussion- Q+A
Next, there was a dialogue between Snelling and Davidson in the form of them asking each other questions. The highlights were a few specific questions:
Davidson asked Snelling about the Grand Canyon: specifically, he noted that the terrestrial fossils were found in similar strata, but never in the same layers, which instead suggests an ebbing and flowing of the water; not a global flood. Furthermore, he pointed out the lack of any pollinating plants in an entire mile of sediment. He asked how Snelling's account lines up with this data. Snelling responded by arguing that the fossils are indeed mixed together and that we even find footprints in the wrong layers. He argued that due to "devastating tsunamis" which would have swept the earth, some of this could be undone and/or specific types of creatures/plants might have been swept out of the layers.
Snelling gave a brief outline of problems with radiometric dating giving divergent ages and asked Davidson to comment on the difficulties he pointed out with radiometric dating. He argued that often, old earth proponents and "secularists" simply assume an age for the rock and interpret the tests to get that age. Davidson responded noting that he worked with radiometric labs for quite some time and that there is mixing in the chemicals which can be accounted for. He showed a picture showing how some of this can work and how labs have to account for certain elements contaminating the rocks. However, he pointed out there is a margin of error to account for some of these difficulties.
Davidson then brought up a slide with images of bent rocks. One was a "bench" at a graveyard in which the middle had sagged despite being made of stone. He argued that with enough pressure/time rock can sag under its own weight or (as the picture showed) even no weight at all. Given this evidence, he asked why bent rocks should count in favor of YEC. Snelling responded by saying that hard rock can be bent by pressure but that if the pressure is sufficient the rock will crack. He continued to emphasize that in the Grand Canyon one can observe rocks bending without fracture.
I have to say I was struck by how much this interaction turned on the scientific aspects of the debate. I had thought that Snelling would focus more upon an attack of Davidson's interpretation of Scripture, and while he did some of that, the majority of his responses were related to scientific arguments. Davidson followed suit and kept hammering examples that showed how the YEC interpretations Snelling gave of various natural phenomena failed.
Davidson's scientific presentation in his paper was extremely strong. It would be very hard to explain away the fact that three completely independent methods for dating the islands lined up so clearly to point towards an ancient earth. If I had been on the border between young earth or old earth going in, I would have come out as convinced of an old earth. I actually did go in as one who holds to an old earth, having been convinced by the evidence a few years ago, and I came away utterly convinced that YEC is false.
Snelling's talk was a great defense of the YEC position, but it demonstrated the flaws that Davidson was quick to capitalize on. I was really impressed by the fact that Davidson had a number of slides ready to respond to both Snelling's presentation and his questions. Davidson's critique of the "bent rocks" was particularly devastating.
Davidson's critique of YEC: that they focus upon independently repudiating various dating methods, came to fruition in this discussion. He really showed how the YEC paradigm is utterly dependent upon a selective presentation of data at the exclusion of pieces that do not fit.
One thing I would have liked to see was more debate over the Flood and the Bible passages in general. I was surprised by how much the talk focused on the science–though that was extremely interesting.
Let me know your thoughts on the topic. Have you any insights on any of these issues?
I have written on other talks that I attended at the ETS/EPS Conference in 2012. Specifically, check out my post on Caring for Creation: A discussion among evangelicals. I have also written briefly on every talk I attended. See my post on the ETS/EPS Conference 2012.
There are a great many posts on creation issues on my site. You can access them by checking out my page on the Origins Debate.
Naturalis Historia is a site that focuses primarily on the scientific evidence for an old earth. I highly recommend it.
For the theological aspects of the debate (and also more of the scientific discussion), check out The GeoChristian as well as Geocreationism, two fantastic sites.
Finally, for a comprehensive Biblical and scientific old earth view, see Reasons to Believe. | {
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Q: jQuery SlideUp...But dont disappear off screen Is it possible to use .slideUp, but the object only slideUp by (For instance) by 20px instead of disappearing off screen?
HTML:
<div class="toolbar">
<p>Hide</p>
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JQUERY:
$(".toolbar p").click(function() {
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A: Use animate instead.
$('#myDiv').animate(
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Slides your div up 20 pixels in 300 ms.
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Q: How to convert image buffer to file object in NodeJS? Purpose
How do I make a file in the same path in NodeJS in the same form as client request form?
// test.js
const readFile = fs.readFileSync(filepath, (err, data) => {
if (err) {
console.log(err)
} else {
return data
} })
// result : <Buffer 89 50 4e 47 0d 0a 1a 0a ..... >
mysdk(readFile)
// error : it need to file name, size(bytes) , type ...
I want File object like this.
File locate
A: I guess you are looking for something like this
const process = require('process');
const fs = require('fs-extra');
const express = require('express');
const cwd = process.cwd();
const app = express();
const PORT = 9091;
app.get('/read-file', async(req, res) => {
const rawFileData = 'data:image/png;base64,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';
var fileData = rawFileData.replace(/^data:image\/\w+;base64,/, "");
var buffer = Buffer.from(fileData, 'base64');
const newFileName = 'nodejs.png';
// now buffer contains the contents of the file we just read
await fs.writeFile(`./${newFileName}`, buffer, 'utf-8').then( () => {
res.status(200).sendFile(`${cwd}/${newFileName}`);
});
});
app.listen(PORT, () => {
console.log(`server listening on port: ${PORT}`)
});
output
A: I solved...
const fs = require('fs')
const path = require('path')
const filepath = path.join(__dirname, './success.png')
const image = fs.createReadStream(filepath)
// now image converted like file object...
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,576 |
same vs valid padding
### parameters sharing
We would like our CNNs to also possess this ability known as translation invariance.
Recognize objects regardless of their location in the image.
If we want a cat that's in the top left patch to be classified in the same way as a cat in the bottom right patch,
we need the weights and biases corresponding to those patches to be the same, so that they are classified the same way.
### Output Shape
```
H = height, W = width, D = depth
We have an input of shape 32x32x3 (HxWxD)
20 filters of shape 8x8x3 (HxWxD)
A stride of 2 for both the height and width (S)
Valid padding of size 1 (P)
```
```
new_height = (input_height - filter_height + 2 * P)/S + 1
new_width = (input_width - filter_width + 2 * P)/S + 1
```
The new height is 14, new width is 14, and new depth is 20.
```python
input = tf.placeholder(tf.float32, (None, 32, 32, 3))
filter_weights = tf.Variable(tf.truncated_normal((8, 8, 3, 20))) # (height, width, input_depth, output_depth)
filter_bias = tf.Variable(tf.zeros(20))
strides = [1, 2, 2, 1] # (batch, height, width, depth)
padding = 'VALID'
conv = tf.nn.conv2d(input, filter_weights, strides, padding) + filter_bias
```
The output shape of conv will be [1, 13, 13, 20].
It's 4D to account for batch size, but more importantly, it's not [1, 14, 14, 20].
This is because the padding algorithm TensorFlow uses is not exactly the same as the one above.
https://www.tensorflow.org/api_guides/python/nn#Convolution
### parameters number
**without parameters sharing**
```
Setup
H = height, W = width, D = depth
We have an input of shape 32x32x3 (HxWxD)
20 filters of shape 8x8x3 (HxWxD)
A stride of 2 for both the height and width (S)
Zero padding of size 1 (P)
Output Layer
14x14x20 (HxWxD)
```
Without parameter sharing, each neuron in the output layer must connect to each neuron in the filter.
In addition, each neuron in the output layer must also connect to a single bias neuron.
```
(8 * 8 * 3 + 1) * (14 * 14 * 20) = 756560
```
**with parameters sharing**
With parameter sharing, each neuron in an output channel shares its weights with every other neuron in that channel.
So the number of parameters is equal to the number of neurons in the filter, plus a bias neuron,
all multiplied by the number of channels in the output layer.
```
(8 * 8 * 3 + 1) * 20 = 3840 + 20 = 3860
```
### visualizing cnn
* https://www.youtube.com/watch?v=ghEmQSxT6tw
* http://www.matthewzeiler.com/pubs/arxive2013/eccv2014.pdf
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,351 |
Q: How to add or modify launchers to the compiz unity dock?
Possible Duplicate:
How can I edit/create new launcher items in Unity?
I'm using the natty unity compiz plugin and and I can't find a way to add, rearrange or remove launchers on the dock.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,954 |
Like most women in the world, Nita Ambani, too, always dreamt of becoming a mother. As a young girl, she would write essays in school on the things she would do after having kids. But, life didn't turn out as planned.
"A few years after I got married, I was told by the doctors that I would never have children. Even when I was in school, I would write long, copious essays titled, 'When I'll be a mother...' Here I was at the age of 23 being told that I would never conceive. I was shattered. However, with the help of Dr Firuza Parikh, who is one of my closest friends, I first conceived my twins," Nita Ambani said.
In February 2019, a month after her marriage to Anand Piramal, Nita and Mukesh Ambani's daughter Isha Ambani told Vogue in an interview that she and her twin brother Akash were born via In Vitro Fertilization (IVF).
By this time, she had gained almost twice the weight, from being 47 kgs to going up to 90 kgs. "Everything was double magnified. I was so overjoyed at being a mum that I had let myself go," she said. With diet and one-and-a-half hours of daily exercise, Nita managed to shed 58 kilos. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,604 |
Q: How to delete individual records in Laravel 4.2 using resourceful routing? I'm building a "cookbook" app in Laravel 4.2 with resourceful routing set up for recipes and categories. On the categories/{$id}/edit page (edit.blade.php), I have a model-bound form to edit the category, and underneath that, I have an additional form posting to the CategoryController@destroy method to delete, but every time I try, it throws a MethodNotAllowedHttpException (which is a protected method). I have tried both "delete" and "destroy" on my destroy($id) function, but each throws the same error. Do I need to put something on the model or routes.php to allow deletions?
Method being called:
public function destroy($id)
{
$category = Category::find($id);
$category->destroy();
return Redirect::to('/categories');
}
And form which is calling it:
{{ Form::open(array('action' => array('CategoryController@destroy', $category->id))) }}
{{ Form::submit('Delete Category', ['class' => 'red_button']) }}
{{ Form::close() }}
Category model (which has no reference to deletions, but I'm adding it just in case):
class Category extends \Eloquent {
/*Whitelist what user can enter into form and submit*/
protected $fillable = [
'name', 'description', 'thumbnail'
];
/*Set up One To Many relationship for users to recipes*/
public function recipes()
{
return $this -> hasMany('Recipe');
}
}
Thanks for any help!
A: By default when you open a form whith Form::open the method used is "POST", you need to set this method to DELETE instead.
Since you use resourceful routing the destroy action is attached to the HTTP DELETE method. To clarify this, execute this command:
php artisan routes
This command show you a detailed list of your routes asociations and HTTP methods.
To solve the problem try this:
{{ Form::open(array(
'action' => array('CategoryController@destroy', $category->id),
'method' => 'delete')) }}
I Hope works for you.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,467 |
OPD: Two men arrested in connection with burglary
The 191 News
191 News, 191 News
Conrad Cortez, 42, was charged with burglary of a habitation, a second-degree felony, according to a release from Odessa Police Department.
Odessa Police Department Show MoreShow Less
Ernesto Ortiz Jr., 32, was charged with burglary of a habitation, a second-degree felony, according to a release from Odessa Police Department. Ortiz also was charged with evading arrest or detention, a class A misdemeanor; resisting arrest, a class A misdemeanor; and manufacture or delivery of a controlled substance, a state jail felony.
Two men have been charged in a residential burglary that occurred on Monday.
Conrad Cortez, 42, and Ernesto Ortiz Jr., 32, were charged with burglary of a habitation, a second-degree felony, according to a release from Odessa Police Department. Ortiz also was charged with evading arrest or detention, a class A misdemeanor; resisting arrest, a class A misdemeanor; and manufacture or delivery of a controlled substance, a state jail felony.
Police responded to the 1200 block of North Lincoln Avenue at about 10 p.m. Monday in reference to a check building call. Dispatch advised that the lights were on in the residence and no one was supposed to be at home. Officers observed two men rummaging through the kitchen and placing items into a bin. Both men began to flee as soon as they saw the officers.
Both men -- later identified as Cortez and Ortiz – were caught. Ortiz resisted arrest but eventually was placed into custody by multiple officers, according to the release. Ortiz was found to be in possession of 45 hydrocodone pills that were individually packaged into groups of five and 10 pills, according to the release.
Staff Reporter for the 191 News publication. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,035 |
Published 04/21/2019 08:48:25 pm at 04/21/2019 08:48:25 pm in 5 Star Mini Storage Paradise Ca.
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"redpajama_set_name": "RedPajamaC4"
} | 47 |
\section{\label{intro} Introduction}
Dislocation patterns emerging and evolving under plastic deformation are often characterized by scaling relations which in the literature are commonly addressed as "law of similitude" \cite{Kuhlmann1962} or "similitude principle" and can be observed in a wide variety of materials and under various deformation conditions \cite{Raj1986,Sauzay11}. This principle states that the characteristic wavelength $d$ of dislocation patterns (cell size, spacing of dislocation walls) that form during deformation at a stress $\tau_{\rm f}$ is inversely proportional to the stress: $d = CGb/\tau_{\rm f}$, where $b$ is the length of the dislocation Burgers vector, $G$ is the shear modulus of the material, and the proportionality constant $C$ is approximately independent of material and deformation conditions.
In conjunction with the even more general Taylor relationship $\tau_{\rm f} = \alpha G b \sqrt{\rho}$ which relates the flow stress $\tau_{\rm f}$ to the dislocation density $\rho$ through a non-dimensional constant $\alpha \approx 0.3$ \cite{Sauzay11}, the similitude principle can be re-phrased as $d = D \rho^{-1/2}$: The dislocation pattern wavelength is proportional to the average dislocation spacing, with a proportionality constant $D = C/\alpha$ which is typically of the order of 10 \cite{Raj1986}. In this form, the similitude principle has been demonstrated to hold over 4 decades in cell size and 8 orders of magnitude in dislocation density \cite{Rudolph05}.
In view of the ubiquity of "similitude"-type behavior, it is natural to ask where lies the origin of this type of scaling behavior and what are its implications for dislocation simulations. While simulating the evolution of dislocation patterns at large strains is still beyond the capacity of present-day discrete dislocation dynamics models, such models are now quite capable of simulating the incipient formation of dislocation patterns at moderate strains and dislocation densities where the "similitude principle" generally holds \cite{Gomez06}. It is therefore important to ask which fundamental properties of dislocation systems are responsible for the formation of patterns with the observed scaling properties and what are the implications of these properties for simulations. We will approach this question from a somewhat unusual perspective: Rather than investigating what specific dislocation mechanisms are responsible for patterning, we will discuss generic invariance properties of the dynamic equations solved in both two- and three-dimensional dislocation simulations, and we will demonstrate that these invariance properties imply the similitude principle. We will then investigate how mechanisms such as dislocation cross slip and dislocation annihilation may lead to deviations from similitude, and we will determine the range of parameters where similitude scaling is expected to hold. We will apply our discussion of invariance properties to demonstrate how dislocation simulations performed at different density, stress, and strain rate can be related to each other, and to elucidate the minimal features of dislocation interactions which are needed in models or simulations in order to obtain dislocation patterns consistent with the similitude principle. We note that the scaling relations demonstrated in the following have been previously discussed by one of the present authors for the special case of two-dimensional dislocation systems evolving in single slip under a linear stress-velocity law \cite{Zaiser01,Zaiser02}. A comprehensive discussion of the mathematical background of "similitude scaling" has however, to our knowledge, never been published despite the simplicity of the underlying mathematical relations which appear to us almost self evident.
\section{\label{Basic invariance theorem} The fundamental invariance theorem}
\subsection{Formulation for 2D dislocation systems}
We consider a generic 2D dislocation simulation where $N$ edge dislocations of different slip systems are represented by points in the $xy$ plane. The dislocations are either contained within an infinite crystal (the boundaries are remote such that image stresses can be neglected), or the system is replicated periodically. The Burgers vector of the $i$-th dislocation is $\vec{b}^{\,i} = s^{\,i} b \vec{e}^{\;i}$ where $s^{\,i}$ is the sign of the dislocation, $b$ is the Burgers vector modulus, and $\vec{e}^{\;i}$ is the unit vector in the slip direction which coincides with the dislocation glide direction. The slip plane normal of this dislocation is $\vec{n}^{\,i} = \vec{e}^{\;i} \times \vec{e}_z$. The driving force for the motion of the $i$th dislocation is given by the glide component of the Peach-Koehler force which is proportional to the resolved shear stress at the dislocation position:
\begin{equation}
\label{eq:tau}
\tau^{i} (\vec{r}^{\;i}) = \tau^{{\rm ext}, i} + \tau^{{\rm int},i}(\vec{r}^{\;i}) \;,
\end{equation}
where the "external" resolved shear stress is $\tau^{{\rm ext},i} = M^{i}_{kl} {\sigma}^{\rm ext}_{kl}$ and we apply the Einstein summation convention for lower indices. (Upper indices, instead, are understood as dislocation labels). $\sigma^{\rm ext}_{kl}$ is the externally applied stress field caused by displacements and/or tractions applied to the remote boundaries of the system, and the projection tensor $M^{i}_{kl}$ is defined as $M^{i}_{kl} = (n^{i}_k e^{i}_l + e^{i}_k n^{i}_l)/2$ where $e^i_k$ and $n^i_k$ are the respective components of $\vec{e}^{\;i}$ and $\vec{n}^{\,i}$. Dislocation interactions are described by the internal stress field
\begin{equation}
\label{eq:taui}
\tau^{{\rm int},i}(\vec{r}^{\;i}) = M^{i}_{kl} \sum_{j \neq i} \sigma_{kl}(\vec{b}^{\,j}, \vec{r}^{\;i}-\vec{r}^{\;j})\;,
\end{equation}
where $\sigma_{kl}(\vec{b}^{j}, \vec{r}^{\;i}-\vec{r}^{\;j})$ is the stress caused at $\vec{r}^{\;i}$ by a dislocation of Burgers vector $\vec{b}^{\;j}$ located at $\vec{r}^{\;j}$. We approximate the dislocation stress field by the stress field of a dislocation in an infinite body, in case of periodic boundary conditions complemented by that of its periodic images.
The dislocation velocity is assumed to be a power of the driving force. Hence, the equations of motion of the dislocations are given by
\begin{equation}
\label{eq:motion}
\frac{\partial \vec{r}^{\;i}}{\partial t} = \vec{v}^{\;i}(\vec{r}^{\;i})\quad,\quad
\vec{v}^{\;i} (\vec{r}^{\;i}) = v_0 \vec{e}^{\;i} {\rm sign}(\tau^i) \left|\frac{\tau^i(\vec{r}^{\;i})}{G}\right|^n\;,
\end{equation}
where $v_0$ is a characteristic velocity and $n$ is the stress exponent. Two moving dislocations may react upon contact, forming either mobile dislocations of a third slip system or immobile barriers. No specific reaction radius is assigned to these reactions which, owing to the singularity of the stress fields, occur in finite time (this may pose practical problems from a numerical point of view but these are irrelevant as far as the mathematical structure of the equations is concerned).
{\bf Theorem:} The system of equations \eqref{eq:tau} and \eqref{eq:taui} is invariant under the transformation
\begin{equation}
\label{eq:trans}
\vec{r}_i \to \lambda \vec{r}_i\quad,\quad
\sigma^{\rm ext}_{kl} \to \lambda^{-1} \sigma^{\rm ext}_{kl}\quad,\quad
t \to \lambda^{n+1}t\quad.
\end{equation}
{\bf Proof:} Proof is obtained by substituting \eqref{eq:trans} into \eqref{eq:taui} and observing that the interaction stresses scale like $1/|\vec{r}^{\;i}-\vec{r}^{\;j}|$. Therefore, the dislocation stresses, \eqref{eq:taui}, decrease similarly to the external stress in proportion with $\lambda^{-1}$. As a consequence, in \eqref{eq:motion} upon insertion of \eqref{eq:trans} all factors $\lambda$ cancel.
{\bf Corollary 1:} Suppose we have a solution $\{\vec{r}^{\;i}(t)\}$ of the system (1,2) at some stress $\sigma_{kl}^{\rm ext}$. Let $\epsilon_{kl}^p(t)$ be the plastic strain which has accumulated due to dislocation motion during the evolution of this system from its initial state. Then there exists a solution $\{\vec{\tilde{r}}^{\;i}(\tilde{t})\}$ at the stress $\tilde{\sigma}_{kl}^{\rm ext} = \sigma_{kl}^{\rm ext}/\lambda$ where $\vec{\tilde{r}}^{\;i}(\tilde{t}) = \lambda \vec{r}^{\;i}$ and $\tilde{t} = \lambda^{n+1}t$. The plastic strain associated with this solution is $\epsilon_{kl}^p(\tilde{t}) = \epsilon_{kl}^p(t)/\lambda$.
{\bf Corollary 2:} For any stationary solution $\{\vec{r}^{\;i}\}$ of the system of equations (1,2), which is in static equilibrium at the stress $\sigma_{kl}^{\rm ext}$, there exists a one-parameter family of solutions $\{\lambda \vec{r}^{\;i}\}$ which are in static equilibrium at the respective stresses $\lambda^{-1}\sigma_{kl}^{\rm ext}$. If we associate, through some averaging procedure, a dislocation density $\rho$ to the solution $\{\vec{r}^{\;i}\}$, then these solutions are associated with the respective dislocation densities $\lambda^{-2}\rho$.
{\bf Corollary 3a:} If, in a dislocation simulation carried out at the stress $\sigma_{kl}^{\rm ext}$, a quasi-stationary pattern of wavelength $d$ and dislocation density $\rho$ emerges, then there exists a one-parameter family of stretched quasi-stationary patterns of wavelength $\lambda d$ and density $\rho/\lambda^2$ which emerge in simulations carried out at the stresses $\sigma_{kl}^{\rm ext}/\lambda$. These one-parameter families of solutions obey both the Taylor relationship and the "law of similitude".
{\bf Corollary 3b:} If in a dislocation simulation a dislocation pattern of wavelength $d$ and dislocation density $\rho$ emerges which is metastable after unloading, then it belongs to a one-parameter family of patterns of wavelength $\lambda d$ and density $\rho/\lambda^2$ which are also metastable in the unloaded state.
{\bf Remark 1:}
The above stated principle can be extended to nonlinear velocity laws describing thermally activated dislocation motion where the velocity law has the form
\begin{equation}
\vec{v}^{\;i} (\vec{r}^{\;i}) = v_0 {\rm sign}(\tau^i) f \left(T,\frac{\tau^i}{S}\right)
\label{eq:thermalact}
\end{equation}
{\em if} the strain-rate sensitivity $S$ in this law is proportional to the dislocation spacing (in physical terms, if we are dealing with thermally assisted overcoming of obstacles such as forest dislocations. This is generally expected to be the velocity-controlling mechanism in pure fcc metals where the Cottrell-Stokes relation \cite{Cottrell55} holds. In Eq. (\ref{eq:thermalact}), the function $f(T,\tau)$ may be strongly non-linear, e.g. $f = \exp(- [(G_0 - \tau V_{\rm a})/(k_{\rm B}T)]$ where $k_{\rm B}$ is Boltzmann's constant and the activation volume $V_{\rm a}$ relates to the strain-rate sensitivity $S$ via $S = k_{\rm B}T/V_{\rm a}$. The system of equations (\ref{eq:motion}) with the velocity law (\ref{eq:thermalact}) is invariant under the transformation
\begin{equation}
\label{eq:trans1}
\vec{r}_i \to \lambda \vec{r}_i\quad,\quad
\sigma^{\rm ext}_{kl} \to \lambda^{-1} \sigma^{\rm ext}_{kl}\quad,\quad
t \to t\quad.
\end{equation}
and the above corollaries apply accordingly.
{\bf Remark 2:}
Irrespective of the velocity law, the invariance property \eqref{eq:trans} holds for static dislocation arrangements where all dislocations are stress free and which therefore correspond to metastable minima of the elastic energy. This observation must, however, not lead to the conclusion that quasi-static metastable dislocation patterns -- which include all patterns which can be observed ex situ -- universally obey similitude. Such a conclusion would be warranted only if the sequence of metastable minima reached, under an given loading path, by a dislocation system could be considered unique, i.e., independent of the dynamics of evolution in between these configurations. Such uniqueness is found in the motion of elastic manifolds or charge-density waves in random media where it is implicit in Middleton's 'no passing' theorem \cite{Middleton92} and the dynamics of particular dislocation configurations such as pile ups \cite{Moretti04} exhibits analogous properties. For general dislocation systems in two and three dimensions, however, a proof along the lines of Middleton is not possible because of the strongly anisotropoic nature of dislocation interactions which change their sign depending on the relative orientation of two dislocations (dislocation segments). As a consequence, the stated invariance principles can in general {\em not} be expected to hold in situations where the dislocation velocity is controlled by obstacles other than dislocations, such as Peierls barriers, radiation debris, solute atoms, precipitates etc.
\subsection{Formulation for 3D dislocation systems}
The generalization of the considerations of the previous section towards 3D systems of dislocations requires some additional definitions and notations. We consider a situation where $N$ dislocation lines (numbered $i=1\ldots N$) with Burgers vectors $\vec b^{\,i}$ of modulus $b$ are positioned in slip planes ${\rm SP}_i$ with normal vectors $\vec n^{\;i}$. The dislocations initially form closed loops $C^i$ contained each within a single slip plane. These loops are labeled by $i = 1 \to N$ and parameterized by $\vec{r}(s^i)$ with local tangent vector $\vec{t}(s^i) = {\rm d}\vec{r}/{\rm d} s^i$. In analogy to the previous section, we again assume that the dislocation loops are either contained within a quasi-infinite crystal where the boundaries are remote such that image stresses can be neglected, or the system is replicated periodically.
Using the result that the displacement field of a closed planar dislocation loop can be derived using a Green's function together with the equilibrium conditions of elasticity theory \cite{deWit60}, the internal stress at a general position $\vec r$ can be written as a sum of line integrals over the loops:
\begin{eqnarray}
\sigma_{kl}^{\rm int}(\vec{r}) = -\frac{\mu}{8\pi} \sum_i \oint_{C^i} && \left\{ \frac{2}{1-\nu}\left( \frac{\partial^3 R}{\partial r_n \partial r_k \partial r_l} - \delta_{kl} \frac{\partial}{\partial r_n}\nabla^2R \right) b_o\epsilon_{nom}t_m \right. \nonumber\\
&+& \left.\left(\frac{\partial}{\partial r_n} \nabla^2 R\right) b_o \left[\epsilon_{nok}\, t_l + \epsilon_{nol}\, t_k \right] \right\}{\rm d}s^i,
\label{eq:3Dloopstress}
\end{eqnarray}
where $\epsilon$ is the permutation symbol, $r_k$ are the components of $\vec r$, furthermore $R^i:=|\vec r(s^i) - \vec r|$.
As the loops move, intersecting loops may react to form a dislocation network. In that case, the stress can still be evaluated according to \eqref{eq:3Dloopstress}, as the segment $\Sigma_i$ that results from a reaction can, from the point of view of stress calculations, be envisaged as a superposition of segments of the two intersecting loops. (This includes the case where dislocation annihilate through a collinear reaction \cite{Madec03} where $\Sigma$ is the superposition of two screw dislocations where the tangent vectors $\vec{t}$ have opposite sign such that the stress contributions cancel.) Alternatively to \eqref{eq:3Dloopstress}, we can then express the internal stress as a sum over all segments $\Sigma_j$ that either form closed loops or terminate at nodes where the sum of Burgers vectors is zero:
\begin{eqnarray}
\sigma_{kl}^{\rm int}(\vec{r}) = -\frac{\mu}{8\pi} \sum_i \int_{\Sigma_j} && \left\{ \frac{2}{1-\nu}\left( \frac{\partial^3 R}{\partial r_n \partial r_k \partial r_l} - \delta_{kl} \frac{\partial}{\partial r_n}\nabla^2R \right) b_o\epsilon_{nom}t_m \right. \nonumber\\
&+& \left.\left(\frac{\partial}{\partial r_n} \nabla^2 R\right) b_o \left[\epsilon_{nok}\, t_l + \epsilon_{nol}\, t_k \right] \right\}{\rm d}s^i,
\label{eq:3Dstress}
\end{eqnarray}
The resolved shear stress is obtained from the stress tensor as in the 2D case,
\begin{equation}
\tau(s^i) = M_{kl}\left( {\sigma}^{\rm ext}_{kl} + \sigma^{\rm int}_{kl}(\vec{r}(s^i))\right).
\end{equation}
The integral over $C^i$ in Eq. (\ref{eq:3Dstress}) has in this case to be understood as the principal value.
The dislocation glide velocity is, in analogy to the 2D case, assumed to be given by
\begin{equation} \label{eq:3D:v}
\frac{\partial \vec{r}(s^i)}{\partial t} = \vec{v}(s^i) =
v_0(\vec{t}) \vec{e}(s^i) {\rm sign}(\tau(s^i)) \left|\frac{\tau(s^i)}{G}\right|^n\;,
\end{equation}
where the local glide direction $\vec{e}(s^i)$ is given by $\vec{e}(s^i) = \vec{t}(s^i) \times \vec{n}^{\;i}$ and the characteristic velocity $v_0$ depends in general on the local orientation of the dislocation line.
{\bf Theorem 1A:} The system of equations (\ref{eq:3Dstress})-(\ref{eq:3D:v}) is invariant under the transformation (\ref{eq:trans}). Corollaries 1-3a/b and Remarks 1,2 hold accordingly also for the 3D case.
{\bf Proof:} Proof is obtained by substituting \eqref{eq:trans} into \eqref{eq:3Dstress} and noting that the differential dislocation line length rescales like ${\rm d}s^i \to \lambda {\rm d}s^i$. One then sees that the internal stresses decrease again in proportion with $\lambda^{-1}$. As a consequence, in \eqref{eq:3D:v} again all factors $\lambda$ cancel.
Thus, we observe that exactly the same invariance principle applies to 2D and to 3D dislocation simulations. Of course, there is one important difference between the described simulation settings, since the described 2D simulation setting does not consider multiplication, whereas the 3D setting naturally incorporates changes in dislocation line length, e.g. line length increases because of loop expansion. This leads to an important conclusion regarding models which introduce dislocation multiplication into 2D simulations by way of phenomenological rules: If such models aim at being consistent with 3D dislocation dynamics, the multiplication rules must be constructed in such a manner that the resulting dynamics still fulfills Theorem 1 stated above. This happens naturally when multiplication rates are directly matched to 3D simulations \cite{Gomez06}, whereas other rules need to be adapted carefully. For instance, the introduction of dipoles with "nucleation width" $L_{\rm nuc}$ (see e.g. \cite{VdG95}) is consistent with Theorem 1 only if the nucleation width is, in the course of a simulation, adapted to evolve in proportion with the mean dislocation spacing as new sources are being added.
\subsection{Line tension approximation}
An approximate method for treating the self-interaction of curved dislocation lines is to use a line tension approximation. In this case one replaces the internal stress field by a local term that is proportional to the line curvature, i.e., one writes
\begin{equation}
\tau(s) = M_{kl} {\sigma}^{\rm ext}_{kl} + T(\theta)/R(s) \;,
\end{equation}
where $T(\theta)$ is a dislocation line tension (energy per unit line length) where $\theta$ characterizes the dislocation line character, and $R = |\partial^2 \vec{r}/\partial s^2|$ is the local curvature radius of the dislocation line. If we assume $T(\alpha) \propto Gb^2$ to be independent of the dislocation arrangement, it is immediately evident that, upon the transformation \eqref{eq:trans} the curvature radii multiply with $\lambda$ and thus the self-interaction stresses again decrease like $\lambda^{-1}$. Hence, treating dislocation interactions in this approximation maintains the basic transformation invariance of 3D dislocation systems. Patterns forming in models which use a line tension approximation (see e.g. \cite{Gomez06}) are therefore bound to fulfill the similitude principle.
However, the dislocation line energy is not strictly independent on dislocation density: For a screened dislocation arrangement it exhibits a logarithmic density dependence, $T \propto G b^2 \log(b\sqrt{\rho})$. Including this dependence implies corrections to similitude, such as a logarithmic dislocation density dependence of the pre-factor $\alpha$ in the Taylor relationship as observed in experiment \cite{Basinski79} and commonly explained in terms of the line tension model \cite{Basinski79,Madec02}. This issue will be addressed in Section \ref{Limits} in more detail.
\section{\label{stresstraincontrol} Stress and strain rate controlled simulations}
Until now our considerations have been based upon the assumption of a constant stress. We now ask how these need to be modified if (i) stress is ramped up at a constant rate, or (ii) if stress is related to an imposed strain rate through a "machine equation". In these cases \eqref{eq:tau} and \eqref{eq:taui} need to be supplemented by an equation for the stress evolution. In case of stress controlled testing with constant stress rate this can be written as
\begin{equation}
\frac{\partial {\bm \sigma}_{\rm ext}}{\partial t} = \dot{\Theta} {\bm \Sigma}
\end{equation}
where $\dot{\Theta}$ is the characteristic stress rate and ${\bm \Sigma} = {\bm \sigma}_{\rm ext}/{\sigma_{\rm eq}}$ is a non-dimensional tensor which may be written as the ratio of the stress tensor and the corresponding equivalent stress $\sigma_{\rm eq} = \sqrt{(3/2){\bm \sigma}_{\rm ext}':{\bm \sigma}_{\rm ext}'}$. This equation is invariant upon the rescaling \eqref{eq:trans1} if we simultaneously re-scale the initial stress according to \eqref{eq:trans1} and the stress rate according to
\begin{equation}
\dot{\Theta} \to \lambda^{-n-2} \dot{\Theta} \;.
\end{equation}
In case of strain controlled testing, the external stress is imposed through displacements acting on the remote boundaries of the system which create a homogeneous stress state over the simulated volume. This can be expressed as
\begin{equation}
\frac{\partial {\bm \sigma}_{\rm ext}}{\partial t} = {\bm C \normalfont}\left[\dot{\bm \varepsilon}_{\rm ext} - \frac{1}{V} \int_V \dot{\bm \varepsilon}_{\rm pl}(\vec{r}) d^D r\right]
\label{eq:straincontrol}
\end{equation}
where $\bm C$ is the tensor of elastic constants, $\dot{\bm \varepsilon}_{\rm ext}$ is the remotely imposed strain rate, $V$ is the system volume, and $D=2,3$ for 2D and 3D dislocation systems, respectively. The local strain rate tensor $\dot{\bm \varepsilon}_{\rm pl}(\vec{r})$ is for 2D dislocation systems given by
\begin{equation}
\dot{\bm \varepsilon}_{\rm pl}(\vec{r})= \sum_i {\bm M}^i b\, \vec{e}^{\,i} \vec{v}^{\;i} \delta(\vec{r}-\vec{r}^{\;i}),
\label{eq:ep2D}
\end{equation}
and for 3D systems, it is given by
\begin{equation}
\dot{\bm \varepsilon}_{\rm pl}(\vec{r}) = \sum_i {\bm M}^i \int_{C^i} b\, \vec{e}(s^i) \vec{v}(s^i) \delta(\vec{r} - \vec{r}(s^i)) {\rm d} s^i,
\label{eq:ep3D}
\end{equation}
Under the rescaling \eqref{eq:trans1}, the domain $V$ of integration in \eqref{eq:straincontrol} transforms according to $V \to \lambda^D V$ while the dislocation velocities transform according to $\vec{v}_i \to \lambda^{-n} \vec{v}_i$, the Dirac function scales like $\lambda^{-D}$ and the line length in \eqref{eq:ep2D} increases like $s^i \to \lambda s^i$. Thus, both equations \eqref{eq:ep2D} and \eqref{eq:ep3D} are invariant under the transformation \eqref{eq:trans} if we simultaneously re-scale the imposed strain rate according to
\begin{equation}
\dot{\bm \varepsilon}_{\rm ext} \to \lambda^{-n-2} \dot{\bm \varepsilon}_{\rm ext}.
\end{equation}
In conclusion, under conditions of stress or strain rate control, simulation of a system of dislocation density $\rho$ and size $L$ at an imposed stress rate $\dot{\Theta}$ (strain rate $\dot{\bm \varepsilon}_{\rm ext}$) is equivalent to simulation of a system of dislocation density $\rho/\lambda^2$ and size $\lambda L$ at a stress rate $\lambda^{-n-2} \dot{\Theta}$ (strain rate $\lambda^{-n-2} \dot{\bm \varepsilon}_{\rm ext}$). This observation holds for both 2D and 3D dislocation systems.
\section{\label{Limits} Limits of similitude}
\subsection{Short-range self-interaction of curved dislocation lines}
An important technical problem in 3D dislocation dynamics simulations arises from the fact that the expression \eqref{eq:3Dloopstress} for the internal stress field becomes singular on the dislocation lines themselves. Whereas for a straight infinite dislocation the self force resulting from the singular stress terms is zero, the same is not true for general curved dislocations where the self force diverges. To regularize this divergence, various methods have been proposed in the literature \cite{Brown64,Gavazza76,Zbib98, Cai06}. All these methods have in common that they introduce an additional intrinsic length $\xi$ which physically relates to the extension of the dislocation core. As it would be unphysical to re-scale this length according to the stretching transformation $(\ref{eq:trans})$, this means that the self-interaction of a dislocation loop (dislocation segment) does not strictly obey similitude. (The interaction between different loops/segments, on the other hand, strictly obeys the stated invariance principles). The consequences are best illustrated by considering the self interaction in a line tension approximation. Cai et. al. \cite{Cai06} evaluate the line energy of a circular loop of radius $R$ (up to terms of the order of $(\xi/R)^2$) as
\begin{equation}
E(R)=2\pi R \frac{G b^2}{8\pi}\left(\frac{2-\nu}{1-\nu}\left[\ln\frac{8R}{\xi}-2\right]+\frac{1}{2}\right)\quad,
\end{equation}
with the average line tension
\begin{equation}\label{eq:T}
T = \frac{1}{2\pi} \frac{\partial E}{\partial R} = \frac{G^2}{8\pi}\left(\frac{2-\nu}{1-\nu}\left[\ln\frac{8R}{\xi}-1\right]+\frac{1}{2}\right)\quad.
\end{equation}
Thus, the line tension has a contribution which depends logarithmically on the ratio $R/\xi$ which leads to deviations from similitude scaling. To assess the order of magnitude of these deviations, let us consider the typical values $\nu = 1/3$, $\xi = 0.25$ nm, and compare two loops of radii $R$ and $R' = \lambda R$. The corresponding line tension values differ by a constant amount $\Delta T = \frac{G^2}{8\pi}\frac{2-\nu}{1-\nu}\ln \lambda$. Assuming that the flow stress is exclusively controlled by line tension effects, $\sigma_{\rm f} \propto T/R \propto T\sqrt{\rho}$, we find that the ensuing relative correction to the flow stress is $\Delta \sigma/\sigma = \Delta T/T$. This is shown in Fig. 1 as a function of the dislocation density $\rho$ and the parameter $\lambda$, taking $R \approx \rho^{-1/2}$ and using the parameters $\nu = 0.3,\; \xi =0.25$\,nm. For illustration: With $\rho=10^{13}/{\rm m}^2$, an increase in dislocation density by a factor $\lambda^2=64$ implies an increase in flow stress by a factor $\lambda=8$. The actual increase that follows from \eqref{eq:T} is about 25\% less (circle in Fig. 1). In typical dislocation simulations which cover the initial stages of deformation, the ensuing corrections to similitude scaling are small but not negligible. The corresponding corrections to the Taylor relationship are well known, see the review of Basinski and Basinski \cite{Basinski79}.
\begin{figure}
\begin{center}
\includegraphics[width=0.7\textwidth]{graph.png}
\end{center}
\vspace*{-0.2cm}
\caption{Flow stress corrections due to changes in line tension as a function of the scaling factor $\lambda$ for different reference dislocation densities $\rho$ (reference curvature radius $R \propto \rho^{-1/2}$)}
\label{fig:linetension}
\end{figure}
\subsection{Direct annihilation of non-screw dislocations}
Even in the absence of cross slip, dislocations of the same slip system may annihilate if the spacing of the respective slip planes falls below a critical value $y_{\rm e}$ \cite{Essmann79}. For dislocations of general orientation the atomic rearrangements occurring during this process lead to the formation of point defect agglomerates: We are dealing with a process related to the discreteness of the atomic lattice structure near the dislocation core. Again, $y_{\rm e}$ provides an additional length which does not rescale under the stretching transformation $(\ref{eq:trans})$ and therefore introduces corrections to similitude scaling. The conditions when this becomes relevant are straightforward to estimate: For dislocations of density $\rho$ on a given slip system, annihilation occurs after a mean free path $l_{\rm e} = 1/(\rho y_{\rm e})$. This corresponds to a critical shear strain $\gamma_{\rm e} = \rho b l_{\rm e} = b/y_{\rm e}$ which is independent of dislocation density. With $y_{\rm e} \approx 1.6$nm as suggested by Essmann for Cu \cite{Essmann79}, this strain is of the order of 20\%. As most current dislocation dynamics simulations extend only to much smaller strains, one does not expect to see much annihilation in these simulations. An exception are some published simulations where initial dislocation densities were extremely high, see e.g. \cite{Miguel02} where initial dislocation densities as high as $0.04 y_{\rm e}^{-2}$ were used. Such densities exceed, however, the values typically found in heavily deformed metals by one to two orders of magnitude. We also note that the removed dislocation configurations are extremely narrow dipoles which do not carry long-range stress fields and do not contribute to plastic flow. Hence, the impact of direct annihilation processes on the collective dynamics of dislocations is expected to be generally small.
\subsection{Jog formation}
Cutting of forest dislocations creates jogs on dislocations. Jogged dislocation loops represent non-planar dislocation configurations which can in general not be decomposed into systems of planar loops. Thus, equations \eqref{eq:3Dloopstress} and \eqref{eq:3Dstress} are no longer strictly valid for such configurations. However, estimates based on typical dislocation glide paths of some tens of dislocation spacings and typical dislocation spacings of the order of 1000b show that the atomic density of jogs on dislocations arising from cutting processes and the ensuing corrections to the stress fields are small. This may be different in situations where climb processes have an appreciable influence on dislocation motion.
\subsection{Cross slip and annihilation of screw dislocations}
Whether or not our considerations apply to materials where screw dislocation cross slip is prominent, depends on the factors which control the cross slip process. If cross slip is envisaged as an essentially athermal, stress controlled process as proposed by Brown \cite{Brown02} and recently explored by Paus and co-workers \cite{Paus13}, then our considerations of similitude scaling apply also to such processes. Cross slip of the screw part of a dislocation loop on a new slip plane creates a new, non-planar dislocation configuration. However, this process can be envisaged as the nucleation of a new loop on the cross slip plane (one segment of this loop cancels the originally cross slipped segment), and therefore \eqref{eq:3Dloopstress} and \eqref{eq:3Dstress} can still be used for evaluating the stress field of the resulting non-planar configuration. The same is true if the cross slip process leads to annihilation of two screw segments moving on different slip planes. Accordingly, all these processes must fulfill similitude scaling as discussed in previous sections.
However, separate considerations apply if cross slip requires the overcoming of a stress-dependent energy barrier (formation of a constriction in a split dislocation) with the aid of thermal activation. This is the classical viewpoint on cross slip (see e.g. \cite{Thornton62}) which also underlies most implementations of cross slip in 3D DDD codes (see e.g. \cite{Kubin92,Rhee98}). Irrespective whether the parameters governing the cross slip process are taken from experiment (e.g. \cite{Bonneville88}) or atomistic simulation \cite{Bulatov98}, if controlled by thermal activation the rate of thermally activated cross slip will depend on stress and temperature in a strongly nonlinear (exponential) manner and therefore this process is expected to lead to characteristic deviations from similitude scaling. The same is true for other thermally activated processes which may influence the motion of dislocations, such as thermally assisted overcoming of Peierls barriers, solute atoms, or precipitates. Conversely, for processes where similitude scaling is strictly observed, we may expect that the above mentioned thermally activated processes are of secondary importance.
\section{Discussion and Conclusions}
Our discussion of scaling relations in the dynamics of dislocation systems can be summarized into two simple statements: (i) If dislocation dynamics is mainly controlled by the elastic interactions between dislocations, then all characteristic lengths in evolving dislocation arrangements scale in proportion with the mean dislocation spacing (inverse square root of dislocation density). (ii) Under the same conditions, all characteristic stresses, in particular the flow stress, scale in proportion with the square root of dislocation density. These statements are supposed to hold whenever the dynamics of dislocations is mainly controlled by their elastic interactions, and processes on the scale of the dislocation cores (formation of constrictions in cross slip, overcoming of Peierls barriers, annihilation of parallel edge dislocations, presence of jogs), as well as interactions of dislocations and other defects (solute atoms, precipitates, radiation debris or grain boundaries) play a secondary role. As a paradigm, we may consider deformation of pure face-centered cubic metals at low to intermediate stresses/dislocation densities.
Empirically, both findings have been known for decades ("law of similitude", "Taylor relationship") and most researchers working on dislocation simulation will be aware of them. However, the far-reaching consequences of these relations are not always realized:
\begin{enumerate}
\item Implications for discrete simulations:
\begin{itemize}
\item The scale of a discrete dislocation simulation is not determined by the linear dimension $L$ of the simulated volume, but by the size in units of dislocation spacings. Thus in 2D, size is governed by $N = L^2 \rho$ (the number of dislocations), and in 3D, by the non-dimensional number $L^3 \rho^{3/2}$.
\item The scale of strain in bulk dislocation simulations is given by $b \sqrt{\rho}$, and the scale of stress by $G b \sqrt{\rho}$. The time scale, as stated above, scales in proportion with the scale of stress to the power $-(n+1)$, or the scale of dislocation density to the power $-(n+1)/2$. These relations need to be kept in mind when comparing dislocation simulations with different parameters. To take an example: A 3D DDD simulation of a cube of edge length 1$\mu$m with an initial dislocation density of $10^{14}$ m$^{-2}$, a strain rate of $5000$ s$^{-1}$, and an end strain of 10\%, using a linear stress-velocity law, may be almost equivalent to simulation of a cube of edge length 10$\mu$m with an initial dislocation density of $10^{12}$ m$^{-2}$, a strain rate of $500$ s$^{-1}$, and an end strain of 1\%.
\item If 3D processes such as dislocation multiplication or junction formation are incorporated into 2D dislocation dynamics models, care must be taken to make sure that the rules introduced are consistent with the scaling properties of bulk dislocation dynamics. For instance, a dislocation multiplication rule for 2D DDD simulations may be specified by requiring that a source of length $l_{\rm nucl}$ produces a dipole of the same width if, over a nucleation time $t_{\rm nucl}$, the resolved shear stress at the site of the source remains above a level $\tau_{\rm nucl} \propto Gb/l_{\rm nucl}$ \cite{VanderGiessen95,Benzerga04}. This rule is invariant under the transformation (\ref{eq:trans}) if the source length $l_{\rm nucl}$ is taken to be proportional to the dislocation spacing in the vicinity of the source and if the nucleation time scales in inverse proportion with the square of the externally applied shear stress $\tau_{\rm ext}$, or in proportion with $(\tau_{\rm ext}\tau_{\rm nucl})^{-1}$ as proposed in \cite{Benzerga04}. Thus, the scaling relations we have stated provide guidance whether 2D rules introduced to mimic 3D dislocation processes such as multiplication or junction formation are consistent with the properties of dislocation systems or not. If they are, then the resulting 2D dynamics will by construction obey the principle of similitude as indeed observed in corresponding simulations \cite{Gomez06}.
\end{itemize}
\item Implications for density-based and statistical models
\begin{itemize}
\item Attempts to model dislocation microstructure evolution in terms of the evolution of dislocation densities, irrespective of whether they consider deterministic \cite{Holt70,Ananthakrishna81,Walgraef85,Groma97,Groma03} or stochastic \cite{H"ahner96,H"ahner99}, space-dependent \cite{Holt70,Walgraef85,Groma97,Groma03} or space independent \cite{Ananthakrishna81,H"ahner96} evolution equations, should make sure that the formulated evolution equations are, at least in those cases where the underlying discrete dynamics is expected to obey similitude scaling, invariant under the transformations (\ref{eq:trans}) or (\ref{eq:trans1}). Equations which are not, cannot represent dislocations. This is a problem with many early models of nonlinear phenomena in dislocation systems (e.g. \cite{Ananthakrishna81,Walgraef85}) where parameters are not sufficiently well specified to decide whether or not they fulfill this basic requirement.
\item
We can use the scaling relations (\ref{eq:trans}) or (\ref{eq:trans1}) as heuristic tools to identify the structure of admissible terms in evolution equations. For instance if, in the spirit of Aifantis \cite{Aifantis84} we want to introduce a second gradient of strain in the flow stress expression, then from the stated scaling principles (strain scales in proportion with $\rho^{1/2}$, stress scales in proportion with $G b \rho^{1/2}$), it follows that the concomitant internal length scale must scale in proportion with the dislocation spacing for the resulting term to be consistent with (\ref{eq:trans}) - as is indeed found when such terms are derived by averaging the underlying discrete dynamics of dislocations \cite{Groma03}.
\end{itemize}
The analysis of density-based models for consistency with similitude scaling is exemplified in the Appendix where we consider four models - the dislocation patterning model formulated by Holt in 1970 \cite{Holt70}, a model of dynamic dislocation patterning during plastic flow, a stochastic model of fractal dislocation cell structure formation that was formulated by H\"ahner and Zaiser in the 1990s \cite{H"ahner99}, and the recently proposed 3D continuum dislocation dynamics model of Hochrainer and co-workers \cite{Hochrainer2014_JMPS}.
\item Implications for dislocation patterning, statistical properties of plastic flow, and size effects.
\begin{itemize}
\item In the regime of similitude scaling all characteristic lengths of bulk dislocation arrangements are bound to scale in proportion with the dislocation spacing. This is in particular true for the characteristic lengths of dislocation patterns - if such patterns form - and for the characteristic mean free path which governs dislocation storage and, hence, strain hardening. As a consequence of scaling invariance, meaningful statistical information about dislocation mean free paths and hardening can be extracted from discrete dislocation simulations, even if such simulations are "too small" (or confined to too low strains) to replicate the full phenomenology of dislocation patterning \cite{Devincre08}.
\item
As a consequence, any model (whether discrete or density based) which can reproduce dislocation patterning and which is consistent with dislocation properties must, in the regime where dislocation dynamics is controlled by elastic dislocation interactions, produce patterns with wavelengths that are proportional to the dislocation spacing, and inversely proportional to the stress at which they have formed. Conversely, patterns that do not have these properties \cite{Zhou12} may be artefacts of initial conditions, boundary conditions or numerical errors.
\item
Any statistical signatures of plastic flow and dislocation dynamics that can be deduced from simulations or statistical models of elastically interacting dislocations must be consistent with the stated principles. Hence, if dislocation systems at some critical stress undergo a jamming or depinning transition, then it is from their scaling properties self-evident they must do so at any dislocation density -- with a critical stress that scales in proportion with the square root of that density \cite{Tsekenis11}. Even scale free power law distributions as observed for instance for strain bursts and slip avalanches \cite{Zaiser06} must comply with these scaling principles: Since strain is proportional to the total area swept by dislocations per unit volume, it is clear that the upper and/or lower limits of power law regimes in strain burst size distributions must scale in proportion with the square root of dislocation density. Similarly, if the spatial structure of slip avalanches can be associated with a characteristic correlation length, this length must be proportional to the dislocation spacing. If we consider scale free distributions of internal lengths (cell sizes), as in the model of fractal dislocation structures proposed by H\"ahner and Zaiser \cite{H"ahner99,Zaiser99}, then the upper and lower ends of the fractal scaling regime must scale in proportion with the mean dislocation spacing, and in inverse proportion with the flow stress \cite{Zaiser99}.
\item
An interesting application of the stated principles concerns size effects. As long as no other length scales are relevant (e.g. the size of surface heterogeneities that control dislocation nucleation at the surface) a system of size $L$ and dislocation density $\rho$ at stress $\tau$ behaves similarly to a system of size $\lambda L$ and dislocation density $\rho/\lambda^2$ at stress $\tau/\lambda$. Let us assume that $\tau$ is a size dependent flow stress of the form $\tau = \tau_{\infty} [1 + \Delta(L,\rho)]$ where $\tau_{\infty}$ is the flow stress of the bulk system ($L \to \infty)$. It follows for the size dependent contribution $\Delta$ that for any $(\rho,\lambda)$ the relation $\Delta(L,\rho) = \Delta(\lambda L,\rho/\lambda^2)$ must be fulfilled. In other words, the size dependent fraction of the flow stress can depend only the product $(L \sqrt{\rho})$ but not on $L$ and $\rho$ separately. This has indeed been observed in simulations \cite{Tang07}: larger systems with lower initial dislocation density behave similarly to smaller systems with higher dislocation density. It follows that comparisons of size dependent flow stresses without data for the corresponding dislocation microstructures, as commonly presented in the literature \cite{Greer11,Uchic09}, may be of limited usefulness.
\end{itemize}
\end{enumerate}
In conclusion, we have stated invariance principles which are in a sense trivial. Nevertheless, they can serve as extremely useful tools to gauge the plausibility of simulation results, to compare simulations carried out on apparently different length and time scales, and to assess the validity of microstructure evolution models. In practice, in any given situation there can be many reasons why the stated principles may not or only partially apply - for instance, in dispersion- or precipitation hardened materials due to the length scales associated with the phase microstructure, in polycrystals due to the influence of grain boundaries, in low-temperature deformation of bcc metals due to the paramount influence of Peierls stresses, and in general in all situations where atomic-scale processes (dislocation nucleation/annihilation, cross slip etc.) are of importance. Nevertheless, these principles are at the core of the behavior of "pure" dislocation systems and provide a useful guideline for assessing the viability and performance of a broad class of models that purport to describe dislocation microstructure evolution.
\section*{Acknowledgment}
We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft
(DFG) through Research Unit FOR1650 'Dislocation-based Plasticity (DFG grant No
SA2292/1-1) and the European m-era.net project 'FASS' (grant No SA2292/2).
\section*{Appendix: Scaling analysis of some density-based dislocation models}
\section*{Appendix A: The patterning model of Holt}
\setcounter{equation}{0}
\renewcommand{\theequation}{A\arabic{equation}}
Holt \cite{Holt70} proposed in 1970 a model of dislocation patterning at zero applied stress, constructed in analogy with contemporary models of spinodal decomposition. He assumes the interaction energy functional for a system of screw dislocations of density $\rho$ in the form
\begin{equation}
E(\rho) = \int 2 \pi r f(r,\rho) \frac{Gb^2}{2 \pi} \ln \frac{R_0}{r} {\rm d}r \;,
\end{equation}
where $f$ is a radially dependent pair correlation function describing the excess of screw dislocations of opposite sign surrounding a given dislocation. This function is normalized, $\int 2 \pi r f(r,\rho) {\rm d}r = 1$, and assumed by Holt in a phenomenological manner (we note that, for a system of edge dislocations, the corresponding function has much later been explicitly computed by Groma and co-workers \cite{Groma06}). The energy change associated with spatially dependent fluctuations $\delta \rho({\boldsymbol{\mathnormal r}})$ around a homogeneous state $\rho_0$ follows in a long-wavelength approximation as
\begin{equation}
\delta E(\rho) \approx - F_1 \delta \rho({\boldsymbol{\mathnormal r}}) - F_2 \Delta (\delta \rho({\boldsymbol{\mathnormal r}}))\;,
\end{equation}
where $\Delta$ is the Laplace operator and $F_1$ and $F_2$ are given by
\begin{eqnarray}
F_1 &=& \frac{1}{\rho_0} \int 2 \pi r f(r,\rho) \frac{Gb^2}{2 \pi} \ln \frac{R_0}{r} {\rm d}r\;,\nonumber\\
F_2 &=& \frac{1}{\rho_0} \int \frac{\pi r^3}{2} f(r,\rho) \frac{Gb^2}{2 \pi} \ln \frac{R_0}{r} {\rm d}r\;.
\end{eqnarray}
In the spirit of linear irreversible thermodynamics, the flux ${\bm j} = \rho B {\bm \nabla} (\delta E(\rho))$ of dislocations is assumed to be proportional to the gradient of the energy fluctuation, i.e., to the net force. Assuming that the dislocation density $\rho$ is a conserved quantity, it follows that
\begin{equation}
\frac{\partial \delta \rho}{\delta t} = - \rho_0 B \Delta[F_1 \delta \rho + F_2 \Delta (\delta \rho)]
\label{eq:deltarhoholt}
\end{equation}
or, in Fourier space
\begin{equation}
\frac{\partial \delta \rho(k)}{\delta t} = \rho_0 B k^2 [F_1 - F_2 k^2] \delta \rho(k)\;.
\end{equation}
If both $F_1$ and $F_2$ are positive, then long-wavelength fluctuations are undamped with a dominant wavelength emerging at $\lambda = 2 \pi (2 F_2/F_1)^{1/2}$. To study the behavior of Holt's model under the scaling transformation (\ref{eq:trans}), we observe that the proportionality of the dislocation flux and the energy gradient (the force) implies that, for this model, the rate exponent has the value $n = 1$. Upon inserting the transformation (\ref{eq:trans}) into (\ref{eq:deltarhoholt}) we see that the model is invariant only if the parameters $F_1$ and $F_2$ transform according to $F_1 \to \lambda^2 F_1$, $F_2 \to \lambda^4 F_2$. Since the same transformation must also preserve the normalization of the pair correlation function $f$, this requires the pair correlation function $f$ to possess the structure $f(\rho,r) = \rho \phi(u)$ with
$u = r \sqrt{\rho}$ and $\int 2 \pi u \phi(u) {\rm d} u = 1$. It then follows immediately that the dominant wavelength of the emergent dislocation pattern is proportional to $1/\sqrt{\rho}$, i.e., to the dislocation spacing. We thus observe that, if the pair correlation function in Holt's model is chosen in a manner that is consistent with the scaling properties of dislocation systems, then the resulting dominant wavelength turns out to be consistent with similitude. Holt arrives in his 1970 paper \cite{Holt70} at the same result by way of several unnecessary ad-hoc assumptions -- e.g., he claims without proof that the correlation function should be proportional to $1/r$ and then introduces a finite-scale cut-off at a distance that is proportional to the dislocation spacing. None of these assumptions are necessary to arrive at the main result, which in fact derives from any normalized function of the structure $f(\rho,r) = \rho \phi(r \sqrt{\rho})$.
\section*{Appendix B: A model of dynamic dislocation patterning}
\setcounter{equation}{0}
\renewcommand{\theequation}{B\arabic{equation}}
Holt's model has been justly criticized for physical reasons. Dislocation patterns do not form close to thermal equilibrium, in absence of external stresses driving dislocation motion. Also, if one takes Holt's model at face value, then it is easy to see that for a system of parallel screw dislocations containing equal numbers of dislocations of both signs, the most efficient way to reduce the internal energy is to annihilate all the dislocations - a process formally excluded by Holt when he writes down the equation for the dislocation density as a conserved field.
In the following we demonstrate that, by using a pair correlation function of the correct structure to describe dislocation interactions, it is easy to formulate physically more plausible models which produce spontaneous symmetry breaking and dislocation patterning consistent with the similitude principle. As an example, we consider a system of equal numbers of straight parallel edge dislocations of both signs on a single slip system, moving by glide under a constant external resolved shear stress $\tau_{\rm ext}$. The slip direction is taken to be the $x$ direction of a Cartesian coordinate system. Since dislocation motion is constrained to a set of parallel glide planes, no annihilation is considered (see Section 4.2 for a discussion of this point). The equations of motion for the densities $\rho^+$ and $\rho^-$ of positive and negative edge dislocations are then given by
\begin{equation}
\frac{\partial \rho^+}{\partial t} = \partial_x(\rho^+ v) \quad,\quad \frac{\partial \rho^-}{\partial t} = - \partial_x(\rho^- v) \quad,
\end{equation}
or equivalently for the total dislocation density $\rho = \rho^+ + \rho^-$ and excess density $\kappa = \rho^+ - \rho^-$:
\begin{equation}
\frac{\partial \rho}{\partial t} = \partial_x(\kappa v) \quad,\quad \frac{\partial \kappa}{\partial t} = \partial_x(\rho v) \quad.
\end{equation}
The dislocation velocity $v$ is assumed in the form
\begin{equation}
v = \left\{\begin{array}{ll}
B (\tau_{\rm ext} + \tau_{\rm int}({\boldsymbol{\mathnormal r}}) - \tau_{\rm f}({\boldsymbol{\mathnormal r}}))\;,& \tau_{\rm ext} + \tau_{\rm int}({\boldsymbol{\mathnormal r}}) > \tau_{\rm f}({\boldsymbol{\mathnormal r}})\;,\\
0\;,& \tau_{\rm ext} + \tau_{\rm int}({\boldsymbol{\mathnormal r}}) \le \tau_{\rm f}({\boldsymbol{\mathnormal r}})\;.
\end{array}\right.
\end{equation}
Here the long-range internal stress $\tau_{\rm int}$ derives from the excess dislocation density $\kappa$ by
\begin{equation}
\tau_{\rm int}({\boldsymbol{\mathnormal r}}) = \int \kappa({\boldsymbol{\mathnormal r}}') \sigma_{xy}({\boldsymbol{\mathnormal r}} - {\boldsymbol{\mathnormal r}}') {\rm d}^2 r' \;,\;
\end{equation}
where $\sigma_{xy} = G b g(\theta)/r$ is the $xy$ component of the edge dislocation stress field. The flow stress $\tau_{\rm f}({\boldsymbol{\mathnormal r}})$ is assumed to relate to the total dislocation density in a non-local manner:
\begin{eqnarray}
\tau_{\rm f}({\boldsymbol{\mathnormal r}}) &=& \int \rho({\boldsymbol{\mathnormal r}}') \phi\left(\frac{{\boldsymbol{\mathnormal r}} - {\boldsymbol{\mathnormal r}}'}{\xi}\right) \sigma_{xy}({\boldsymbol{\mathnormal r}} - {\boldsymbol{\mathnormal r}}') {\rm d}^2 r' \nonumber\\
&\approx&
\alpha G b \xi \rho({\boldsymbol{\mathnormal r}}) + \beta_x G b \xi^3 \partial_x^2 \rho({\boldsymbol{\mathnormal r}}) + \beta_y G b \xi^3 \partial_y^2 \rho({\boldsymbol{\mathnormal r}})\;,
\label{eq:flowstress2}
\end{eqnarray}
where $\phi$ is a correlation function of range $\xi$. In physical terms, $\xi$ characterizes the characteristic extension of the "jammed" dislocation configurations (dipoles, multipoles, junctions) which control the flow stress. The non-dimensional coefficients $\alpha,\beta_x$ and $\beta_y$ of the long-wavelength expansion of the flow stress in Eq. (\ref{eq:flowstress2}) are given by
\begin{eqnarray}
\alpha &=& \int \phi(u,\theta) g(\theta) {\rm d} u {\rm d} \theta \;,\nonumber\\
\beta_x &=& \int u^2 \phi(u,\theta) g(\theta)\cos^2 \theta {\rm d} u {\rm d} \theta\;,\nonumber\\
\beta_y &=& \int u^2 \phi(u,\theta) g(\theta)\sin^2 \theta {\rm d} u {\rm d} \theta\;,
\end{eqnarray}
where $u = r/\xi$.
We envisage a space- and time-independent reference state $\rho({\boldsymbol{\mathnormal r}}) = \rho_0, \kappa({\boldsymbol{\mathnormal r}}) = 0, \tau_{\rm ext} = \tau_0 + \tau_1$ where $\tau_1 = \alpha G b \xi \rho$ is the rate-independent part of the flow stress and the rate-dependent stress contribution $\tau_0$ corresponds to homogeneous plastic flow at rate $\dot{\gamma}_0 = \rho_0 b v_0 = \rho_0 b B \tau_0$. We analyze the evolution of space-dependent fluctuations $\delta \rho(x)$ and $\delta \kappa(x)$. For simplicity, we consider only fluctuations which are homogeneous in the $y$ direction, since such fluctuations do not give rise to long-range internal stresses. The temporal evolution of $\delta \rho(x)$ and $\delta \kappa(x)$ is in linear approximation given by
\begin{eqnarray}
\label{eq:fluct}
\partial_t \delta \rho &=& B \tau_0 \partial_x \delta \kappa \;,\nonumber\\
\partial_t \delta \kappa &=& B \tau_0 \left[(1 - (\tau_1/\tau_0)(1+\eta)) \partial_x \delta \rho + (\beta_x/\alpha)(\tau_1/\tau_0) \xi^2 \partial_x^3 \delta \rho \right]\;.
\end{eqnarray}
where $\eta = (\rho_0/\xi) (\partial \xi/\partial \rho|_{\rho_0})$. These evolution equations are invariant under the scaling transformation (\ref{eq:trans}) if the characteristic length $\xi$ either scales in proportion with $1/\sqrt{\rho}$ or in proportion with $Gb/\tau_{\rm ext}$, or a mixture of both. In the former case, $\eta = 1/2$, and in the latter case, $\eta = 0$.
To investigate stability of the reference state, we make the Ansatz $\delta \rho(x,t) = \delta \rho(k) \exp(ikx) \exp(\lambda t)$ and $\delta \kappa(x,t) = \delta \kappa(k) \exp(ikx) \exp(\lambda t)$ which leads to the matrix equation
\begin{equation}
\displaystyle{
\Lambda \left[\begin{array}{l} \delta \rho \\ \delta \kappa \end{array} \right] = B \tau_0
\left[\begin{array}{ll}
0 & i k \\
i k [1 - (1+\eta)(\tau_1/\tau_0) - (\beta_x/\alpha)(\tau_1/\tau_0) \xi^2 k^2]
& 0 \end{array} \right]
\left[\begin{array}{l} \delta \rho \\ \delta \kappa \end{array} \right]}\;,
\end{equation}
with the eigenvalues
\begin{equation}
\Lambda = \pm (k B) \sqrt {\tau_1(1+\eta)- \tau_0 - (\beta_x/\alpha)\tau_1 \xi^2 k^2}\;.
\end{equation}
Positive real-valued eigenvalues exist if $\tau_1(1+\eta) > \tau_0$. In that case, a dominant wavelength (maximum of $\Lambda$) emerges at
$\lambda = 2 \pi \xi [(\alpha/2 \beta_x)(1 + \eta - \tau_0/\tau_1)]^{-1/2}$. In either of the two cases discussed above, $\xi = 1/\sqrt{\rho}$ or $\xi = Gb/\tau_{\rm ext}$, this wavelength is consistent with the similitude principle. A plot of the positive eigenvalue $\Lambda$ (the "amplification factor") as a function of wavelength and for different values of the steady-state strain rate is shown in Figure \ref{fig:amplification}. At low strain rate (quasi-static deformation), the dominant wavelength approaches a constant value of about 10$\xi$ (10 dislocation spacings).
\begin{figure}
\begin{center}
\includegraphics[width=0.7\textwidth]{Graph2.png}
\end{center}
\vspace*{-0.2cm}
\caption{Positive eigenvalue (amplification factor) as a function of pattern wavelength $\lambda$ for different values of the steady-state strain rate $\dot{\gamma}$; lowermost curve: $\dot{\gamma} = 0.9 \dot{\gamma}_{\rm c}$, uppermost curve: $\dot{\gamma} = 0.01 \dot{\gamma}_{\rm c}$; curves calculated for $\beta_x/\alpha = 2$.}
\label{fig:amplification}
\end{figure}
It is interesting to have a closer look at the condition for symmetry breaking in this model, $\tau_1(1+\eta) > \tau_0$. This condition is tantamount to the requirement that the strain rate must not exceed the critical value $\dot{\gamma}_{\rm c} = B \tau_1(1+\eta) b \rho_0$ where the rate-dependent part of the flow stress, $\tau_0$, exceeds the rate-independent part $\tau_1$ by a factor $(1 + \eta)$.
In other words, the requirement for patterning is that the motion of dislocations must be mainly controlled by their interactions, rather than by the externally imposed driving stress. Patterning arises in this model from the fact that dislocation interactions impede the motion of dislocations -- hence, the dislocation velocity is reduced in regions of increased dislocation density which, in conjunction with the conserved nature of the transport dynamics, leads to further accumulation of dislocations in these regions. In the absence of plastic flow, no patterning is possible in this model since the dislocation arrangement remains frozen in the initial state.
\section*{Appendix C: The stochastic model by H\"ahner and Zaiser}
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\renewcommand{\theequation}{C\arabic{equation}}
The model proposed by H\"ahner and Zaiser to describe the evolution of fractal dislocation microstructures is defined by two coupled stochastic evolution equations for densities of mobile and immobile dislocations,
\begin{eqnarray}
\label{stoch1}
\partial_t \rho_{\rm m} = A \tau_{\rm ext} \langle \dot{\gamma} \rangle - B \sqrt{\rho} \dot{\gamma}\;,\\
\partial_t \rho_{\rm i} = (B-C) \sqrt{\rho} \dot{\gamma}\;.
\label{stoch2}
\end{eqnarray}
Here, the plastic strain rate is considered a randomly varying quantity with the statistical properties
\begin{eqnarray}
\langle \dot{\gamma} \rangle = \rho_{\rm m} b v\\
\langle \delta\dot{\gamma}(t)\delta\dot{\gamma}(t') \rangle = 2 \langle \dot{\gamma} \rangle^2 t_{\rm corr} \frac{\tau_{\rm int}}{S} \delta(t - t').
\end{eqnarray}
The correlation time $t_{\rm corr}$ is supposed to follow the relation $t_{\rm corr} \langle \dot{\gamma}\rangle = \rho_{\rm m} b L$ where $L$ is the dislocation mean glide path. The internal stress $\tau_{\rm int}$ is assumed to be approximately equal to the external stress.
To analyze the scaling behavior of these equations under the transformations (\ref{eq:trans}) or (\ref{eq:trans1}) we first investigate how the strain rate transforms. Since $\rho_{\rm m,i} \to \lambda^{-2} \rho_{\rm m,i}$ and $v \to \lambda^{-n} v$ we find that $\langle \dot{\gamma} \rangle \to \lambda^{-2-n} \langle \dot{\gamma} \rangle$ (note that the transformation (\ref{eq:trans1}) can formally be considered by setting $n = -1$). The fluctuations transform in the same manner if the ratio $\tau_{\rm int}/S$ is a constant and the dislocation glide path transforms like $L \to \lambda L$. As discussed above, the former condition is fulfilled if the strain-rate sensitivity $S$ is controlled by overcoming of dislocation obstacles, and the latter if dislocation storage is controlled by dislocation interactions ($L \propto \rho^{-1/2}$).
The left-hand sides of Eqs. (\ref{stoch1},\ref{stoch2}) transform under (\ref{eq:trans}) like $\partial_t \rho_{\rm m,i} \to \lambda^{-n-3} \partial_t \rho_{\rm m,i}$ and the model as a whole is invariant if all terms on the right-hand side transform in the same manner. For the dislocation multiplication term this is the case if $A$ depends neither on stress nor on dislocation density, or if it depends on both variables only through a function of the invariant ratio $\tau_{\rm ext} \rho^{-1/2}$. The same is true for the constants $B$ and $C$ characterizing the dislocation storage terms in Eqs. (\ref{stoch1},\ref{stoch2}). If these conditions are fulfilled, the stochastic model can, even for time dependent stress $\tau_{\rm ext}$, be transformed to a non-dimensional form by setting
\begin{equation}
\rho_{\rm m,i} = (A \tau_{\rm ext}^2/C)^2 \tilde{\rho}_{\rm m,i},\quad t = A \tau_{\rm ext}^2/(C^2 \langle \dot{\gamma} \rangle) \tilde{t},
\label{stochscale}
\end{equation}
which automatically satisfies the scaling invariance requirements.
With $\tilde{\rho} = \tilde{\rho}_{\rm m} + \tilde{\rho}_{\rm i}$, the resulting non-dimensional model is given by \cite{H"ahner99}
\begin{eqnarray}
\partial_{\tilde {t}} \tilde{\rho}_{\rm m} = 1- \tilde{\theta}\tilde{\rho}_{\rm m} - \frac{B}{C} \sqrt{\tilde{\rho}}(1 + \sigma \dot{w}) \;,\\
\label{stoch1a}
\partial_t \rho = 1 - \tilde{\theta}\tilde{\rho} - \sqrt{\tilde{\rho}}(1 + \sigma \dot{w})\;.
\label{stoch2a}
\end{eqnarray}
where $\dot{w}$ is a standard correlated stochastic process, $\sigma$ the corresponding noise amplitude, and $\tilde{\theta} = (2A/C^2) \partial \tau_{\rm ext}/\partial \langle \gamma \rangle$ is a non-dimensional hardening coefficient which, in the regime of similitude scaling, is time independent (hardening stage II). Solutions of the Fokker-Planck equation corresponding to this stochastic model converge towards stationary solutions $p(\tilde{\rho})$; the corresponding solutions for the dimensional dislocation density describe a dislocation system whose stochastic signatures evolve with time only parametrically, through the scaling rules (\ref{stochscale}), and which thus in the course of hardening remains consistent with the similitude principle. Of course, deviations from this principle might be relevant -- e.g. if one includes an dynamic recovery term that is proportional to $\rho$ and which thus violates similitude scaling, the behavior at high stresses/dislocation densities will exhibit characteristic deviations from similitude as discussed in the main paper in the context of dislocation annihilation.
\section*{Appendix D: The Continuum Dislocation Dynamics (CDD) model by Hochrainer and co-workers}
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\renewcommand{\theequation}{D\arabic{equation}}
The model proposed by Hochrainer and co-workers \cite{Hochrainer2014_JMPS,Sandfeld2011_JMR,Hochrainer2013_MRS} describes the evolution of curved dislocations in a statistically averaged continuum model. We discuss this model here in order to illustrate how the scaling invariance principles we have formulated are reflected in a model which goes beyond standard dislocation density measures.
In the model by Hochrainer and co-workers, the evolution of systems of dislocations is described by a set of evolution equations for the total density $\rhot$, the vector of 'geometrically necessary dislocation' (GND) density $\Bkappa=[\kappa_1,\kappa_2]$, and a 'curvature density' $\qt$:
\begin{eqnarray}
\label{eq:drhotdt}
\partial_t\rhot &=-\div(v\Bkappa^\perp)+v\qt\;,\\
\label{eq:dkappadt}
\partial_t\Bkappa &= -\curl(v\rhot{\boldsymbol{\mathnormal n}})\;,\\
\label{eq:dqtdt}
\partial_t\qt&=-\div\left( -v{\boldsymbol{\mathnormal Q}}^{(1)} + {\boldsymbol{\mathnormal A}}^{(2)}\cdot \nabla v \right)\;,
\end{eqnarray}
where ${\boldsymbol{\mathnormal n}}$ denotes the slip plane normal and $\Bkappa^\perp=[\kappa_2,-\kappa_1]$. The evolution of these quantities depends on higher-order tensorial dislocation density measures, here the tensors ${\boldsymbol{\mathnormal A}}^{(2)}$ and ${\boldsymbol{\mathnormal Q}}^{(1)}$ in \eqref{eq:dqtdt}. These measures need to be related to the fields $\rhot,\Bkappa$ and $\qt$ through closure assumptions \cite{Monavari2013}, e.g. one may assume
\begin{equation}\label{eq:closea1}
{{\boldsymbol{\mathnormal A}}}^{(2)} = \frac{1}{2}\left[ (\rhot +\kappa) {{\boldsymbol{\mathnormal l}}}_{\kappa} \otimes {{\boldsymbol{\mathnormal l}}}_{\kappa} + (\rhot -\kappa) {{\boldsymbol{\mathnormal l}}}_{\kappa}^{\perp} \otimes {{\boldsymbol{\mathnormal l}}}_{\kappa}^{\perp}\right]
\quad \textrm{and}\quad
{\boldsymbol{\mathnormal Q}}^{(1)} = -\Bkappa^\perp \frac{\qt}{\rhot}.
\end{equation}
Therein, ${{\boldsymbol{\mathnormal l}}}_{\kappa}^{\perp}$ is the unit vector perpendicular to ${{\boldsymbol{\mathnormal l}}}_{\kappa} = \Bkappa/\kappa$ which is a unit vector in the direction of the GNDs and $\kappa = |\Bkappa|$ is the scalar GND density.
Furthermore, the evolution of the plastic slip $\gamma$ is given by Orowan's law as
\begin{eqnarray} \label{eq:dgammadt}
\partial_t\gamma=\rhot b v.
\end{eqnarray}
To analyze the scaling behavior of these equations under the transformations (\ref{eq:trans}) or (\ref{eq:trans1}) we note that the dislocation velocity according to (\ref{eq:trans}) or (\ref{eq:trans1}) transforms like $v \to \lambda^{-n}v$ where (\ref{eq:trans1}) formally corresponds to the case $n = -1$. Thus, the strain rate transforms as $\partial_t\gamma\rightarrow\lambda^{-2-n}\partial_t\gamma$. The left-hand sides of Eqs. (\ref{eq:drhotdt}, \ref{eq:dkappadt}) transform under \eqref{eq:trans} as $\partial_t\rhot\rightarrow\lambda^{-n-3}\partial_t\rhot$ and $\partial_t\Bkappa\rightarrow\lambda^{-n-3}\partial_t\Bkappa$. For the right-hand sides to transform in the same manner, it is then necessary that the 'curvature density' must transform as $\qt \to \lambda^{-3} \qt$. This is consistent with the understanding of $\qt$ as a product
of dislocation density and mean curvature, $\qt=\rhot k$ where $k$ has the dimension of a reciprocal curvature radius and thus transforms as $k \to \lambda^{-1}k$. The left-hand side of \eqref{eq:dqtdt} then obeys the transformation $\partial_t\qt\rightarrow\lambda^{-n-2}\partial_t\qt$. For the right-hand side to transform similarly, it is necessary that ${\boldsymbol{\mathnormal Q}}^{(1)}$ transforms like $\qt$, and ${\boldsymbol{\mathnormal A}}^{(2)}$ like $\kappa$ or $\rhot$. One easily ascertains that the closure equation (\ref{eq:closea1}) is consistent with this requirement.
In order to scale the CDD model equations to a non-dimensional form we need to specify how the velocity $v$ depends on the dislocation fields. In principle, every dependence is admissible which leads to the correct scaling. For instance, we may write the dislocation velocity as a function of different interaction stresses, as e.g. a backstress $\taub$, a line tension contribution $\tault$ and a Taylor-type yield stress $\tauy$:
\begin{equation}
\tau^{\rm b} = -{D\mu b}\frac{\nabla \cdot \Bkappa^\perp}{\rhot}\,,
\qquad
\tau^{\rm lt} = \frac{T}{b} \frac{q^{\rm t}}{\rho^{\rm t}}\,,
\qquad
\tau^{\rm y} = \alpha G b \sqrt{\rho^{\rm t}}
\label{eq:stresses}
\end{equation}
where $T\approx\mu b^2$ and the two non-dimensional parameters $D=0.6\ldots 1$ and $\alpha=0.2\ldots 0.4$. We can easily ascertain that all stresses in (\ref{eq:stresses}) have the correct scaling behavior. Assuming a linear relationship between stress and dislocation velocity ($n=1$) one gets
\begin{equation} \label{eq:v}
v = \left\{
\begin{array}{cc}
B(\tauext+\taub+\tault-\tauy) & \quad\textrm{if}\quad |\tauext+\taub+\tault|\geq|\tauy| \\
0 & \quad\textrm{else}
\end{array}
\right.
,
\end{equation}
We may then define the following scaling relations between stresses $\tau$, densities $\rho$ and lengths $x$ and their dimensionless counterparts (indicated by the tilde)
\begin{eqnarray}\label{eq:scaling}
\tau =\alpha Gb\rho_0^{1/2} \,\tilde\tau, \qquad
\rho =\rho_0 \,\tilde\rho , \qquad
x =D\rho_0^{-0.5} \,\tilde x,
\end{eqnarray}
where $\rho_0$ is the average initial dislocation density. By insertion into \eqref{eq:v} we can also derive scaling relations for the velocity $v$, the time $t$ and curvature density $\qt$
\begin{eqnarray}
v = \frac{b^2}{B}\alpha G\sqrt{\rho_0} \,\tilde v,\qquad
t = \frac{DB}{\alpha b^2G\rho_0}\,\tilde t,\qquad
\qt = \frac{\rho_0^{3/2}}{D} \,\tilde\qt.
\end{eqnarray}
Replacing all dimensional variables in \eqref{eq:v} by their scaled counterparts we obtain the non-dimensional velocity
\begin{eqnarray}
\tilde v &=& \tilde\tauext
- \alpha^{-1} \frac{\tilde\nabla\cdot\tilde{\Bkappa}^\perp}{\tilde\rho}
+ (\alpha D)^{-1} \frac{\tilde q}{\tilde \rho}
- \sqrt{\tilde\rho},
\end{eqnarray}
where $\tilde\nabla(\bullet)$
is the gradient operator w.r.t. the scaled coordinates. This equation only depends on two factors, $\alpha$ and $D$ which relate to dislocation pair correlation functions and thus characterize the mutual arrangement of dislocations; no material parameters occur which a posteriori justifies our choice in \eqref{eq:scaling}. Again, these equations automatically satisfy the scaling invariance requirements of similitude. The corresponding non-dimensional CDD evolution equations are then obtained from
\begin{eqnarray}
\partial_t\tilde\rhot = Q \, \partial_t\rhot, \qquad
\partial_t\tilde{\Bkappa} = Q \, \partial_t\Bkappa, \qquad
\partial_t\tilde\qt = (Q\sqrt{\rho_0}/D) \; \partial_t\qt, \nonumber\\
\partial_t\tilde{\gamma} = (QD/\sqrt{\rho_0}) \; \partial_t\gamma \qquad
\textrm{where}\quad Q = \frac{\alpha b^2 G\rho_0^2}{BD}.
\end{eqnarray}
Analyzing the stability of these equations reveals patterning phenomena which are very similar to those discussed in Appendix B. A detailed discussion of these patterning phenomena will be presented elsewhere. Here, we only note that, again, the invariance of the fundamental equations under the scale transformations (\ref{eq:trans}) or (\ref{eq:trans1}) ensures that any dislocation patterns arising from these equations are consistent with the similitude principle.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,851 |
Q: React Animations - change only one logo at a time from a list of 6 initial logos displayed? I am working on a feature where I need to change only one logo at a time out of a list of 6 logos displayed initally.
The example is shown here:: https://www.loom.com/share/6a282423368a46418248a789ce4fc139
And its there in this website also in the bottom:: https://www.wonderlandams.com/about?fbclid=IwAR0wfFrqYVwor1UJfZGcWK2MaU0kBWNiaacg8kGb_IC--VaziorY6BDt7lA.
import React, { useState, useEffect } from 'react'
import tw from 'twin.macro'
import Image from './image'
const LogoGrid = ({ logos, style }) => {
const groupDisplay = logos.slice(0, 6);
const [group, setGroup] = useState(groupDisplay);
const [groupLength, setGroupLength] = useState(0);
let shuffledLogos, i;
const shuffle = (array) => array.sort(() => Math.random() - 0.5);
useEffect(() => {
console.log("UEFFECT RUNNING");
const timer = setInterval(() => {
i = Math.floor(Math.random() * 6);
shuffledLogos = shuffle(logos);
let gl = groupLength + 1 ;
if(groupDisplay[i] == logos[i]) {
let k = i + 1;
groupDisplay[i] = shuffledLogos[k];
}
else {
groupDisplay[i] = shuffledLogos[i];
}
setGroupLength(gl)
setGroup(groupDisplay)
}, 2000)
return () => clearInterval(timer)
}, [group, groupLength])
return (
<div css={[tw`relative`, style]}>
<div
css={[
tw`opacity-0 grid-cols-3 grid-rows-2 gap-12
lg:(gap-x-16 gap-y-12 mt-26) xl:gap-x-32`,
tw`grid transition transition-opacity duration-300 ease-in-out opacity-100`,
]}
>
{(group || []).map((logo, index) => (
<div key={index} css={tw`h-12`}>
<Image image={logo} />
</div>
))}
</div>
</div>
)
}
export default LogoGrid
I have made one component using tailwind css but it does not work as expected. Can anyone kindly point me in the right direction or any changes in the logic that can give me similar effects ?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 315 |
Q: Selenium - Visual Studios- C# - All (chrome, firefox, and internet explorer) webdrivers unable to start driver service I'm trying to set up Selenium for testing and none of my webdrivers seem to work. I have tried moving them around in the project folder and the only way I can get Visual Studios to locate them is with a @"path" statement.
The real problem is... Once Visual Studio locates the webdriver, the operation times out and I get the following exception:
An unhandled exception of type 'OpenQA.Selenium.WebDriverException' occurred in WebDriver.dll
Additional information: Cannot start the driver service on http://localhost:(random port number that changes every time)
I have tried restarting my computer and having the system administrator check the firewall and malware blocker logs, but neither seems to have helped (or they don't know the correct thing to look for).
I figure this is something super simple and I'm just missing it... Any help would be greatly appreciated.
Here is a copy of my code:
using OpenQA.Selenium;
using OpenQA.Selenium.Firefox;
using OpenQA.Selenium.Support.UI;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using OpenQA.Selenium.Chrome;
using OpenQA.Selenium.IE;
namespace SeleniumWork
{
class Program
{
static void Main(string[] args)
{
IWebDriver driver = new InternetExplorerDriver(@"C:\blahblahpathstring");
driver.Navigate().GoToUrl("http://www.google.com/");
IWebElement query = driver.FindElement(By.Name("q"));
query.SendKeys("Cheese");
query.Submit();
var wait = new WebDriverWait(driver, TimeSpan.FromSeconds(10));
wait.Until(d => d.Title.StartsWith("cheese", StringComparison.OrdinalIgnoreCase));
Console.WriteLine("Page title is: " + driver.Title);
}
}
}
Here is a copy of the debug output I receive:
A first chance exception of type 'System.Net.WebException' occurred in System.dll
A first chance exception of type 'System.Net.WebException' occurred in System.dll
A first chance exception of type 'System.Net.WebException' occurred in System.dll
A first chance exception of type 'System.Net.WebException' occurred in System.dll
A first chance exception of type 'OpenQA.Selenium.WebDriverException' occurred in WebDriver.dll
A: I have had the same problem on my work machine, but not on my personal machine. The only difference I could attribute between the two was that I was using VS 2015 at home and VS 2017 at work.
What fixed it was I used the NuGet Package Manager for the project and downloaded the Selenium.Firefox.WebDriver by jbaranda, which uses the new marionette based web driver rather than gecko driver.
With this installed I was able to get a firefox browser up and running without any extra configuration or options:
IWebDriver driver = new FirefoxDriver();
driver.Url = "www.google.com";
Whereas before it would throw the 'Cannot start the driver service...' exception you mentioned. There are NuGet packages for other browsers which I suggest for the particular one you're using, but the only one I didn't have that issue with was IE. Hope that helps
A: I had the same issue, and had had no idea how to fix it. In the end I found out that the Firewall blocked the traffic to loopback. The firewall installed on the machine is McAffe.
All I did was stopping the service which manages traffic scan.
Hope it will help you.
A: I've been hitting this consistently on IEDriverServer and rarely on FireFox.
Fixed it twice when it happened on FireFox - first time I updated the gecko driver, second time I restarted my PC. Something in the environment's going on, maybe the driver does not fully quit sometimes, so new instantiations are being blocked?
A: I think mostly beginners face this problem when they are running Selenium with C# for the first time.
As i also faced this situation. As highlighted in one of the answer and let me show with images
You have installed Selenium.webDriver but you have not installed Selenium.Firefox.WebDriver
Step 1 :- Go to Nugget Manager
Step 2 :- Select Selenium.Firefox.WebDriver and install it
Now run the program once again and that problem will go away.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,529 |
Following is a list of all Article III United States federal judges appointed by President John Adams. In total, John Adams appointed 23 Article III United States federal judges during his tenure (1797–1801) as President of the United States. Of these, 3 were appointments to the Supreme Court of the United States, 16 were to the United States circuit courts, and 4 to the United States district courts. Fourteen of the sixteen circuit court judges appointed by Adams were to positions created at the end of his tenure in office, in the Judiciary Act of 1801, 2 Stat. 89, which became known as the Midnight Judges Act. All of these offices were abolished by the repeal of this Act on July 1, 1802, by 2 Stat. 132. The remaining two were to judgeships for the District of Columbia, authorized under a different Act of Congress, not the Judiciary Act.
Nonetheless, Adams made an indelible impact on the federal judiciary with the appointment of John Marshall as Chief Justice to succeed Oliver Ellsworth, who had retired due to ill health. Adams himself called this appointment "the proudest act of my life."
United States Supreme Court justices
Also appointed, but declined: John Jay (Chief Justice).
Circuit courts
Also appointed, but declined: Thomas Bee (5th circuit), Joseph Clay Jr. (5th circuit), Jared Ingersoll (3rd circuit), Thomas Johnson (D.C. circuit), Charles Lee (4th circuit), and John Sitgreaves (5th circuit).
District courts
See also
Marbury v. Madison (1803)
Stuart v. Laird (1803)
United States v. More (1805)
Notes
References
Sources
Federal Judicial Center
Judicial appointments
Adams, John | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,418 |
crypto
======
Simple PHP library letting you check if a field has been altered after form submit
===
### How-to-use
In a form:
```php
<?php
$value = 24;
$salt_key = 2; // can be everything in your array of salt keys
?>
<input type="hidden" name="clear_value" value="<?php echo $value ?>" />
<input type="hidden" name="encrypted_value" value="<?php echo Crypto::encrypt($value, $salt_key); ?>" />
```
In your controller (for example):
```php
<?php
if(Crypto::checkIntegrity($_POST['clear_value'], $_POST['encrypted_value'], 2)) {
// everything's ok
} else {
// someone cheated the DOM
}
?>
```
| {
"redpajama_set_name": "RedPajamaGithub"
} | 248 |
Q: How do I create a table in R? I want to create a table for the output of an sqlite command that I run repetitively in a for loop.
are the pictures of my code and the intended output.
I use PrettyTable when I code in Python. Is there a similar option in R?
A: Why not preallocate a dataframe and [over]write values with each iteration of the for loop?
before the loop:
output <- data.frame('region' = regions)
output$good_traffic <- 0
output$bad_traffic <- 0
within the loop:
output[output$region == region, 'good_traffic'] <- good_percent
output[output$region == region, 'bad_traffic'] <- bad_percent
after the loop:
print(output)
A: If I understand what you means, you should try with kable() from knitr package
library(knitr)
t <- table(mtcars$cyl,
mtcars$am)
kable(t)
summary(lm(hp ~ cyl, data = mtcars))
coef.lmfit <- coef(summary(lm(hp ~ cyl, data = mtcars)))
kable(coef.lmfit)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,384 |
Q: Recommendation needed: Rails, Postgres and fuzzy full text search I have Rails app with a Postgres backend.
I need to add full text search which would allow fuzzy searches based on Levenshtein distance or other similar metrics. Add the fact that the lexer/stemmer has to work with non-English words (it would be ok to just switch language-dependent features off when lexing, to not mess with the target language which may have meaningful words considered by English engine as irrelevant).
I guess Postgres' tsearch won't apply here as it doesn't have fuzzy search -- please correct me if I'm wrong.
What are possible combinations of backends & plugins? It'd like to prefer solutions which add less to the infrastructure (eg. if Postgres can have fuzzy fts, why use external Lucene); OTOH, the quality of Rails plugins involved is important as well.
What would you recommend?
update: seems like I'd need rather n-gram based metrics than Levenshtein.
A: Rails + Postgres + Solr + Sunspot
Solr is based on Lucene so you can take advantage of all Lucene features. Sunspot is an excellent Ruby wrapper for Solr API.
Both Sunspot and Solr work great with Rails and PostgreSQL, I used it for a project no more than one month ago.
A: PostgreSQL comes with an extension called pg_trgm (in the contrib/ directory). In my experience, it is too slow (more like a proof-of-concept implementation), but for your application it might work.
A: texticle offers beta fuzzy search for Postgres.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,297 |
{"url":"http:\/\/dommelen.net\/quantum2\/style_a\/nt_hfederiv.html","text":"### D.52 Sim\u00adpli\u00adfi\u00adca\u00adtion of the Hartree-Fock en\u00adergy\n\nThis note de\u00adrives the ex\u00adpec\u00adta\u00adtion en\u00adergy for a wave func\u00adtion given by a sin\u00adgle Slater de\u00adter\u00admi\u00adnant.\n\nFirst note that if you mul\u00adti\u00adply out a Slater de\u00adter\u00admi\u00adnant\n\nyou are go\u00ading to get terms, or Hartree prod\u00aducts if you want, of the form\n\nwhere the num\u00adbers of the sin\u00adgle-elec\u00adtron states can have val\u00adues from 1 to , but they must be all dif\u00adfer\u00adent. So there are such terms: there are pos\u00adsi\u00adbil\u00adi\u00adties among for the num\u00adber of the sin\u00adgle-elec\u00adtron state for elec\u00adtron 1, which leaves re\u00admain\u00ading pos\u00adsi\u00adbil\u00adi\u00adties for the num\u00adber of the sin\u00adgle-elec\u00adtron state for elec\u00adtron 2, re\u00admain\u00ading pos\u00adsi\u00adbil\u00adi\u00adties for , etcetera. That means a to\u00adtal of terms. As far as the sign of the term is con\u00adcerned, just don't worry about it. The only thing to re\u00admem\u00adber is that when\u00adever you ex\u00adchange two val\u00adues, it changes the sign of the term. It has to be, be\u00adcause ex\u00adchang\u00ading val\u00adues is equiv\u00ada\u00adlent to ex\u00adchang\u00ading elec\u00adtrons, and the com\u00adplete wave func\u00adtion must change sign un\u00adder that.\n\nTo make the above more con\u00adcrete, con\u00adsider the ex\u00adam\u00adple of a Slater de\u00adter\u00admi\u00adnant of three sin\u00adgle-elec\u00adtron func\u00adtions. It writes out to, tak\u00ading to the other side for con\u00adve\u00adnience,\n\nThe first two rows in the ex\u00adpan\u00adsion cover the pos\u00adsi\u00adbil\u00adity that 1, with the first one the pos\u00adsi\u00adbil\u00adity that 2 and the sec\u00adond one the pos\u00adsi\u00adbil\u00adity that 3; note that then there are no choices left for . Sim\u00adi\u00adlarly the sec\u00adond two rows cover the two pos\u00adsi\u00adbil\u00adi\u00adties that 2, and the third that 3. You see that there are 3! = 6 Hartree prod\u00aduct terms to\u00adtal.\n\nNext, re\u00adcall that the Hamil\u00adton\u00adian con\u00adsists of sin\u00adgle-\u200belec\u00adtron Hamil\u00adto\u00adni\u00adans and elec\u00adtron-pair re\u00adpul\u00adsion po\u00adten\u00adtials . The ex\u00adpec\u00adta\u00adtion value of a sin\u00adgle elec\u00adtron Hamil\u00adton\u00adian will be done first. In form\u00ading the in\u00adner prod\u00aduct , and tak\u00ading apart into its Hartree prod\u00aduct terms as above, you are go\u00ading to end up with a large num\u00adber of in\u00addi\u00advid\u00adual terms that all look like\n\nNote that over\u00adlines will be used to dis\u00adtin\u00adguish the wave func\u00adtion in the right hand side of the in\u00adner prod\u00aduct from the one in the left hand side. Also note that to take this in\u00adner prod\u00aduct, you have to in\u00adte\u00adgrate over scalar po\u00adsi\u00adtion co\u00ador\u00addi\u00adnates, and sum over spin val\u00adues.\n\nBut mul\u00adti\u00adple in\u00adte\u00adgrals, and sums, can be fac\u00adtored into sin\u00adgle in\u00adte\u00adgrals, and sums, as long as the in\u00adte\u00adgrands and lim\u00adits only in\u00advolve sin\u00adgle vari\u00adables. So you can fac\u00adtor out the in\u00adner prod\u00aduct as\n\nNow you can start the weed\u00ading-out process, be\u00adcause the sin\u00adgle-elec\u00adtron func\u00adtions are or\u00adtho\u00adnor\u00admal. So fac\u00adtors in this prod\u00aduct are zero un\u00adless all of the fol\u00adlow\u00ading re\u00adquire\u00adments are met:\n\nNote that does not re\u00adquire for a nonzero value, since the sin\u00adgle-elec\u00adtron func\u00adtions are most def\u00adi\u00adnitely not eigen\u00adfunc\u00adtions of the sin\u00adgle-elec\u00adtron Hamil\u00adto\u00adni\u00adans, (you would wish things were that easy!) But now re\u00admem\u00adber that the num\u00adbers in an in\u00addi\u00advid\u00adual term are all dif\u00adfer\u00adent. So the num\u00adbers in\u00adclude all the num\u00adbers that are not equal to . Then so do , , ..., , ,..., be\u00adcause they are the same. And since must be dif\u00adfer\u00adent from all of those, it can only be equal to any\u00adway.\n\nSo what is left? Well, with all the val\u00adues equal to the cor\u00adre\u00adspond\u00ading val\u00adues, all the plain in\u00adner prod\u00aducts are one on ac\u00adcount of or\u00adtho\u00adnor\u00admal\u00adity, and the only thing left is:\n\nAlso, the two signs are equal, be\u00adcause with all the val\u00adues equal to the cor\u00adre\u00adspond\u00ading val\u00adues, the wave func\u00adtion term in the right side of the in\u00adner prod\u00aduct is the ex\u00adact same one as in the left side. So the signs mul\u00adti\u00adply to 1, and you can fur\u00adther fac\u00adtor out the spin in\u00adner prod\u00aduct, which is one since the spin states are nor\u00admal\u00adized:\n\nwhere for brevity the re\u00admain\u00ading in\u00adner prod\u00aduct was called . Nor\u00admally you would call it , but an in\u00adner prod\u00aduct in\u00adte\u00adgral does not care what the in\u00adte\u00adgra\u00adtion vari\u00adable is called, so the thing has the same value re\u00adgard\u00adless what the elec\u00adtron is. Only the value of the sin\u00adgle-elec\u00adtron func\u00adtion num\u00adber makes a dif\u00adfer\u00adence.\n\nNext, how many such terms are there for a given elec\u00adtron and sin\u00adgle-elec\u00adtron func\u00adtion num\u00adber ? Well, for a given value for elec\u00adtron , there are pos\u00adsi\u00adble val\u00adues left among for the value of the first of the other elec\u00adtrons, then left for the sec\u00adond of the other elec\u00adtrons, etcetera. So there are a to\u00adtal of such terms. Since 1\/, if you sum them all to\u00adgether you get a to\u00adtal con\u00adtri\u00adbu\u00adtion from terms in which elec\u00adtron is in state equal to . Sum\u00adming over the elec\u00adtrons kills off the fac\u00adtor 1 and so you fi\u00adnally get the to\u00adtal en\u00adergy due to the sin\u00adgle-elec\u00adtron Hamil\u00adto\u00adni\u00adans as\n\nYou might have guessed that an\u00adswer from the start. Since the in\u00adner prod\u00aduct in\u00adte\u00adgral is the same for all elec\u00adtrons, the sub\u00adscripts have been omit\u00adted.\n\nThe good news is that the rea\u00adson\u00ading to get the Coulomb and ex\u00adchange con\u00adtri\u00adbu\u00adtions is pretty much the same. A sin\u00adgle elec\u00adtron to elec\u00adtron re\u00adpul\u00adsion term be\u00adtween an elec\u00adtron num\u00adbered and an\u00adother num\u00adbered makes a con\u00adtri\u00adbu\u00adtion to the ex\u00adpec\u00adta\u00adtion en\u00adergy equal to , and if you mul\u00adti\u00adply out , you get terms of the gen\u00aderal form:\n\nYou can again split into a prod\u00aduct of in\u00addi\u00advid\u00adual in\u00adner prod\u00aducts, ex\u00adcept that you can\u00adnot split be\u00adtween elec\u00adtrons and since in\u00advolves both elec\u00adtrons in a non\u00adtriv\u00adial way. Still, you get again that all the other val\u00adues must be the same as the cor\u00adre\u00adspond\u00ading val\u00adues, elim\u00adi\u00adnat\u00ading those in\u00adner prod\u00aducts from the ex\u00adpres\u00adsion:\n\nFor given val\u00adues of and , there are equiv\u00ada\u00adlent terms, since that is the num\u00adber of pos\u00adsi\u00adbil\u00adi\u00adties left for the -val\u00adues of the other elec\u00adtrons.\n\nNext, and must to\u00adgether be the same pair of num\u00adbers as and , since they must be the two num\u00adbers left by the set of num\u00adbers not equal to and . But that still leaves two pos\u00adsi\u00adbil\u00adi\u00adties, they can be in the same or\u00adder or in re\u00adversed or\u00adder:\n\nThe first pos\u00adsi\u00adbil\u00adity gives rise to the Coulomb terms, the sec\u00adond to the ex\u00adchange ones. Note that the for\u00admer case rep\u00adre\u00adsents an in\u00adner prod\u00aduct in\u00advolv\u00ading a Hartree prod\u00aduct with it\u00adself, and the lat\u00adter case an in\u00adner prod\u00aduct of a Hartree prod\u00aduct with the Hartree prod\u00aduct that is the same save for the fact that it has and re\u00adversed, or equiv\u00ada\u00adlently, elec\u00adtrons and ex\u00adchanged.\n\nCon\u00adsider the Coulomb terms first. For those the two Hartree prod\u00aducts in the in\u00adner prod\u00aduct are the same, so their signs mul\u00adti\u00adply to one. Also, their spin states will be the same, so that in\u00adner prod\u00aduct will be one too. And as noted there are equiv\u00ada\u00adlent terms for given and , so for each pair of elec\u00adtrons and , and each pair of states and , you get one term\n\nwith\n\nAgain, the are the same re\u00adgard\u00adless of what and are; they de\u00adpend only on what and are. So the sub\u00adscripts and were left out, af\u00adter set\u00adting and .\n\nYou now need to sum over all pairs of elec\u00adtrons with and pairs of sin\u00adgle-elec\u00adtron func\u00adtion num\u00adbers . Since there are a to\u00adtal of elec\u00adtron pairs, it takes out the fac\u00adtor 1\/, and you get a con\u00adtri\u00adbu\u00adtion to the en\u00adergy\n\nThe fac\u00adtor was added since for every elec\u00adtron pair, you are sum\u00adming both and , and that counts the same en\u00adergy twice.\n\nThe ex\u00adchange in\u00adte\u00adgrals go ex\u00adactly the same way; the only dif\u00adfer\u00adences are that the Hartree prod\u00aduct in the right hand side of the in\u00adner prod\u00aduct has the val\u00adues of and re\u00adversed, pro\u00adduc\u00ading a change of sign, and that the in\u00adner prod\u00aduct of the spins is not triv\u00adial. De\u00adfine\n\nand then the to\u00adtal con\u00adtri\u00adbu\u00adtion is\n\nFi\u00adnally, you can leave the con\u00adstraint on the sums away since , so they can\u00adcel each other.","date":"2021-06-18 14:22:33","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8292696475982666, \"perplexity\": 6583.559102686288}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487637721.34\/warc\/CC-MAIN-20210618134943-20210618164943-00425.warc.gz\"}"} | null | null |
Q: Matrix multiplication error with Open MPI Im trying to compute a NxN matrix multiplication using the OpenMPI and C. Everything runs as expected, except for the MPI_Bcast(). As far as I understand, the MASTER must broadcast matrix_2 to the rest of the WORKER processes. At the same time, when WORKERS reach the MPI_Bcast() they should wait there until the selected process (in this case the MASTER) does the broadcast.
The error I'm getting is a Segmentation fault and Address not mapped, so it surely has something to do with the dynamic allocation of the matrices. What I do is send parts of matrix_1 to each process, and each one of them then does partial multiplications and additions with the previously broadcast matrix_2.
I know that the error must be on the MPI_Bcast() because when I comment it the program finishes correctly (but obviously without computing the product). There must be something I'm not being aware of. I leave both the code and the error message I got. Thanks in advanced.
CODE
#include <mpi.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
/* MACROS */
#define MASTER_TO_SLAVE_TAG 1
#define SLAVE_TO_MASTER_TAG 4
#define MASTER 0
#define WORKER 1
int *matrix_1;
int *matrix_2;
int *result;
double start_time;
double end_time;
int procID;
int numProc;
int size, numRows, from, to;
int i,j,k;
MPI_Status status;
MPI_Request request;
void addressMatrixMemory(int);
int main(int argc, char *argv[]){
size = atoi(argv[1]);
MPI_Init (&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &procID);
MPI_Comm_size(MPI_COMM_WORLD, &numProc);
addressMatrixMemory(size);
/* MASTER starts. */
if(procID == MASTER){
start_time = MPI_Wtime();
for(i = 1; i < numProc; i++){
numRows = size/(numProc - 1);
from = (i - 1) * numRows;
if(((i + 1) == numProc) && ((size % (numProc - 1))) != 0){
to = size;
} else {
to = from + numRows;
}
MPI_Isend(&from, 1, MPI_INT, i, MASTER_TO_SLAVE_TAG, MPI_COMM_WORLD, &request);
MPI_Isend(&to, 1, MPI_INT, i, MASTER_TO_SLAVE_TAG + 1, MPI_COMM_WORLD, &request);
MPI_Isend(matrix_1, (to - from) * size, MPI_INT, i, MASTER_TO_SLAVE_TAG + 2, MPI_COMM_WORLD, &request);
}
}
MPI_Bcast(&matrix_2, size * size, MPI_INT, MASTER, MPI_COMM_WORLD);
/* WORKERS task */
if(procID >= WORKER){
int row, col;
int *matrix = malloc(sizeof(matrix_1[0])*size*size);
MPI_Recv(&from, 1, MPI_INT, MASTER, MASTER_TO_SLAVE_TAG, MPI_COMM_WORLD, &status);
MPI_Recv(&to, 1, MPI_INT, MASTER, MASTER_TO_SLAVE_TAG + 1, MPI_COMM_WORLD, &status);
MPI_Recv(matrix, (to - from) * size, MPI_INT, MASTER, MASTER_TO_SLAVE_TAG + 2, MPI_COMM_WORLD, &status);
for(row = from; row < to; row++){
for(col = 0; col < size; col++){
result[row * size + col] = 0;
for(k = 0; k < size; k++);
result[row * size + col] += matrix[row * size + k] * matrix_2[k * size + col];
}
}
MPI_Isend(&from, 1, MPI_INT, MASTER, SLAVE_TO_MASTER_TAG, MPI_COMM_WORLD, &request);
MPI_Isend(&to, 1, MPI_INT, MASTER, SLAVE_TO_MASTER_TAG + 1, MPI_COMM_WORLD, &request);
MPI_Isend(&result[from], (to - from) * size, MPI_INT, MASTER, SLAVE_TO_MASTER_TAG + 2, MPI_COMM_WORLD, &request);
}
/* MASTER gathers WORKERS job. */
if(procID == MASTER){
for(i = 1; i < numProc; i++){
MPI_Recv(&from, 1, MPI_INT, i, SLAVE_TO_MASTER_TAG, MPI_COMM_WORLD, &status);
MPI_Recv(&to, 1, MPI_INT, i, SLAVE_TO_MASTER_TAG + 1, MPI_COMM_WORLD, &status);
MPI_Recv(&result[from], (to - from) * size, MPI_INT, i, SLAVE_TO_MASTER_TAG + 2, MPI_COMM_WORLD, &status);
}
end_time = MPI_Wtime();
printf("\nRunning Time = %f\n\n", end_time - start_time);
}
MPI_Finalize();
free(matrix_1);
free(matrix_2);
free(result);
return EXIT_SUCCESS;
}
void addressMatrixMemory(int n){
matrix_1 = malloc(sizeof(matrix_1[0])*n*n);
matrix_2 = malloc(sizeof(matrix_2[0])*n*n);
result = malloc(sizeof(result[0])*n*n);
/* Matrix init with values between 1 y 100. */
srand(time(NULL));
int r = rand() % 100 + 1;
int i;
for(i = 0; i < n*n; i++){
matrix_1[i] = r;
r = rand() % 100 + 1;
matrix_2[i] = r;
r = rand() % 100 + 1;
}
}
ERROR MESSAGE
[tuliansPC:28270] *** Process received signal ***
[tuliansPC:28270] Signal: Segmentation fault (11)
[tuliansPC:28270] Signal code: Address not mapped (1)
[tuliansPC:28270] Failing at address: 0x603680
[tuliansPC:28270] [ 0] /lib/x86_64-linux-gnu/libpthread.so.0(+0x10340) [0x7f0a98ce0340]
[tuliansPC:28270] [ 1] /lib/x86_64-linux-gnu/libc.so.6(+0x97ffe) [0x7f0a9899fffe]
[tuliansPC:28270] [ 2] /usr/lib/libmpi.so.1(opal_convertor_pack+0x129) [0x7f0a98fef779]
[tuliansPC:28270] [ 3] /usr/lib/openmpi/lib/openmpi/mca_btl_sm.so(mca_btl_sm_prepare_src+0x1fd) [0x7f0a923c385d]
[tuliansPC:28270] [ 4] /usr/lib/openmpi/lib/openmpi/mca_pml_ob1.so(mca_pml_ob1_send_request_start_rndv+0x1dc) [0x7f0a93245c9c]
[tuliansPC:28270] [ 5] /usr/lib/openmpi/lib/openmpi/mca_pml_ob1.so(mca_pml_ob1_isend+0x8ec) [0x7f0a9323856c]
[tuliansPC:28270] [ 6] /usr/lib/openmpi/lib/openmpi/mca_coll_tuned.so(ompi_coll_tuned_bcast_intra_generic+0x3fc) [0x7f0a914f49fc]
[tuliansPC:28270] [ 7] /usr/lib/openmpi/lib/openmpi/mca_coll_tuned.so(ompi_coll_tuned_bcast_intra_pipeline+0xbc) [0x7f0a914f4d5c]
[tuliansPC:28270] [ 8] /usr/lib/openmpi/lib/openmpi/mca_coll_tuned.so(ompi_coll_tuned_bcast_intra_dec_fixed+0x134) [0x7f0a914ec7a4]
[tuliansPC:28270] [ 9] /usr/lib/openmpi/lib/openmpi/mca_coll_sync.so(mca_coll_sync_bcast+0x64) [0x7f0a917096a4]
[tuliansPC:28270] [10] /usr/lib/libmpi.so.1(MPI_Bcast+0x13d) [0x7f0a98f5678d]
[tuliansPC:28270] [11] ej5Exec() [0x400e8c]
[tuliansPC:28270] [12] /lib/x86_64-linux-gnu/libc.so.6(__libc_start_main+0xf5) [0x7f0a98929ec5]
[tuliansPC:28270] [13] ej5Exec() [0x400ac9]
[tuliansPC:28270] *** End of error message ***
--------------------------------------------------------------------------
mpirun noticed that process rank 0 with PID 28270 on node tuliansPC exited on signal 11 (Segmentation fault).
--------------------------------------------------------------------------
A: Let's start with the first problem that jumps out. You're using non-blocking communication incorrectly. MPI_Isend is a non-blocking send function which means that when you call MPI_Isend, all you are really doing is telling MPI about a message that you'd like to send at some point in the future. It may get sent right then, it may not. In order to guarantee that the data is actually sent, you need to complete the call with something like MPI_Wait.Usually when people use non-blocking calls (MPI_Isend), they don't mix them with blocking calls (MPI_Recv). If you use all non-blocking calls, then you can have all of them complete with a single function, MPI_Waitall.
Try fixing these issues first and see if that solves your problem. Just because you commented out the collective, doesn't mean that the other issues weren't there. MPI programs can be notoriously difficult to debug because of weird behavior like this.
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China has experienced large and sustained reductions in pesticide use as a result of adopting GMO cotton, according to the largest-ever scientific study on the impacts of Bt cotton use in that country.
Although Bt was only targeting the cotton bollworm, the subsequent reduction in pesticide applications allowed natural predators to further control other insect pests, such as aphids, suggesting benefits to farmers resulting from a more healthy ecosystem.
However, the reduction in broad-spectrum insecticide sprays allowed some insect pests, particularly mirid bugs, to proliferate and present a new problem for farmers. This meant that some insecticide use has continued.
Reducing pesticides in Chinese cotton farming is a top priority because China is the largest cotton producer in the world, using four times more pesticides (in tons of active ingredients) than the United States.
Historically, about a third of pesticides in China are used on cotton, and many of these are classed as extremely hazardous by the World Health Organization, contributing to 400-500 farmer deaths annually due to pesticide poisoning.
The study, lead-authored by Wei Zhang of the International Food Policy Research Institute, examines cotton pest severity and insecticide use at a county scale in China over a 25-year period, from 1991 to 2015.
Unlike Bt cotton in India and the US, which was originally developed by Monsanto, Chinese Bt cotton was produced in government research laboratories at the Chinese Academy of Agricultural Sciences.
It was first introduced to Chinese cotton farmers in 1997 and reached full adoption in all eight cotton-growing provinces by 2012.
As expected, both cotton bollworm infestations and the use of insecticide sprays to control the pest declined dramatically between 1997 and 2015. The use of pesticide sprays to control aphids also declined slightly over that time period.
But the decreased use of pesticides allowed mirid bugs to flourish after 2000, leading to a partial resurgence in the use of insecticides.
Since 2008, however, both spraying and pest infestations show a slightly decreasing trend, suggesting that cotton production in China is steadily becoming less environmentally destructive.
The authors note that their study is consistent with the findings of Lu et al., whose 2012 paper in Nature found a resurgence in beneficial insect and arthropod predators thanks to China's widespread adoption of Bt cotton and the resulting decline in insecticide use.
As many researchers note, this latest study, published in the prestigious peer-reviewed journal PNAS, shows that adopting genetically modified Bt crops is not a silver bullet when it comes to the need to reduce pesticides in agriculture.
However, the study does add to an overwhelming body of scientific data showing that GMO crops — despite constant attacks from environmentalist critics — can make farming more sustainable by helping to drive down the use of agrochemicals. | {
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Song Writing Workshops
2ND COURSE BOOKED OUT IN 5 HOURS!
NECOM's second song writing course has sold out in 5 hrs! The response to the first song writing course with Luke Byrne was incredible and sold out in less than 24 hours! Luke agreed to add a second course for those who missed out. Bookings opened on Thursday 3 September and sold out by 4pm.
Song Writing Course No 2 with Luke Byrne
Learn song writing from Australian composer and song writer Luke Byrne in this unique 6 week course at NECOM that covers the essential song writing foundations and techniques with the goal of recording your final composition.
Luke Byrne is a Sydney-based composer whose recent commissions include Earthrise, Capricorn and Desert Sea for Sydney Philharmonia, Storm Bird, Buruwan Elegy and Birinyi for Gondwana Indigenous Children's Choir with the Australian Chamber Orchestra and Where Sails Once Flew for Adelaide Chamber Singers. Luke also writes songs across a range of genres, including for children's television, theatre and even school songs. In 2018, Luke's musical Between the Sea and Sky was selected for the New York Musical Festival where it won awards including Best Musical and Outstanding Music. Luke is also a musical director in theatre whose credits include The Harp in the South, Muriel's Wedding and Chimerica for Sydney Theatre Company and The Events and Hamlet for Belvoir St.
6-week Course: 5 x 1 hour sessions on Wednesdays via Zoom + Recording workshop IN PERSON on a Sunday.
Wk 1-5: Wed 14, 21 & 28 Oct; 4, 11 & 18 Nov at 5:00–5:45pm including Open Q&A from 5:45-6:00pm
Wk 6: Sunday 22 November, 9:00 – 4:00pm at NECOM. Workshop to rehearse, perform and record.
Eligibility: Open to secondary school students with some music reading ability
Number: Strictly limited to 10 participants only so book early and don't miss your spot!
Fee: $120 * Eligible for Creative Kids Voucher www.service.nsw.gov.au/transaction/apply-creative-kids-voucher
To book: https://www.trybooking.com/BLILC
* Initial impressions and observations of songs of several styles, understanding the continuity of 'folk' music and 'popular' music, i.e. they have the same word stem and are music of 'the people'.
* Lyrics: how is writing lyric text different to writing prose text, poetry or spoken dialogue. Rhyme schemes, foot and syllable count, understanding the naturalistic setting of text in songs, and above all: simplicity and repetition.
* Setting lyric text to music: pitch contour, rhythm, stressed and unstressed syllables: how these things give rise to melody, and the fundamental binary of Verse and Chorus.
* Extending your melody and aligning it with harmony, i.e. chord progressions, expanding a basic triadic harmony with added notes like 7ths and 9ths or with suspensions. By now you will have (at least) the text of a verse and chorus, the vocal melody for these and chord progressions to accompany them.
* Instrumentation: the basics of piano, guitar, bass and drums
More course information? Email NECOM Program Manager Corinne Arter: corinne@necom.org.au or call 6788 2139
Creative Kids voucher and booking information? Email: admin@necom.org.au or call 6788 2135 | {
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{"url":"http:\/\/pballew.blogspot.com\/2016\/10\/on-this-day-in-math-october-17.html","text":"## Monday, 17 October 2016\n\n### On This Day in Math - October 17\n\nTo parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.\n\nThe 291st day of the year; 291 is the largest number that is not the sum of distinct non-trivial powers.\n\n$\\phi(291) = 192$\u00a0 The number of integers less than, and relatively prime to 291 is equal to it's reversal, 192.\n\nEVENTS\n\n1604 In Prague, Kepler first observes the supernova now known as supernova 1604 and Kepler's Star. The first recorded observation of this supernova was in northern Italy on October 9, 1604. It was named after Kepler because his observations tracked the object for an entire year and because of his book on the subject, entitled De Stella nova in pede Serpentarii (\"On the new star in Ophiuchus's foot\", Prague 1606). Here is an image of Kepler's De Stella Nova, open to the foldout star map placing the supernova of 1604, from the twitter feed of @Libroantiguo . It was the second supernova to be observed in a generation (after SN 1572 seen by Tycho Brahe in Cassiopeia). No further supernovae have since been observed with certainty in the Milky Way, though many others outside our galaxy have been seen since S Andromedae. *Wik\n\n1776 Euler read a paper to the St. Petersburg Academy of Science entitled \u201cDe quadratis magicis,\u201d in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. *Peter Ullrich, \u201cAn Eulerian square before Euler and an experimental design before R. A. Fisher: On the early history of Latin squares,\u201d Chance, vol. 12, no. 1, Winter 1999, pp. 22\u201326.\n\n1831 After discovering induced current on October 1st using two electrified coils,\u00a0 on the 17th of October Michael Faraday\u00a0 observers the same effect on the galvanometer when he inserts a permanent steel magnet into the electrified coil. *A history of physics in its elementary branches By Florian Cajori\n\n1843 Hamilton Writes to his friend, John Graves, with a description of Quaternions. By December, Graves will have extended the idea to an eight dimensional algebra which will become \"octonians\".\n\nObservatory, October 17, 1843\nMy dear Graves,|A very curious train of mathematical speculation occurred to me\nyesterday, which I cannot but hope will prove of interest to you. You know that I have long\nwished, and I believe that you have felt the same desire, to possess a Theory of Triplets,\nanalogous to my published Theory of Couplets, and also to Mr. Warren's geometrical representation\nof imaginary quantities. Now I think that I discovered1 yesterday a theory of\nquaternions which includes such a theory of triplets.\n\nThe complete letter is available at this site. *David R. Wilkins, *John Derbyshire, Unkown Quantity\nIn his preface to the \u2018Lectures on Quaternions\u2019 and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. *Wik\n\n1858 DeMorgan writes a letter about Euler\u2019s\u00a0 prodigious output. *W W Rouse Ball, from The genius of Euler: reflections on his life and work, By William Dunham, pg 89\n\n1933 Albert Einstein seeks asylum in the US, one of many Jewish\/left-wing intellectuals fleeing the Nazi govt in Germany and Europe. The Nazi government put a bounty now worth \u00a350,000 on his head while a German magazine included him in a list of the Nazis\u2019 enemies who were 'not yet hanged'.\n1952 D. H. Lehmer, University of California, announced that 2n \u2212 1 for n = 2203 and 2281 are Mersenne primes. He was aided by a SWAC computing machine, the \ufb01rst result taking 59 minutes. *VFR This may have been predated by Raphael Mitchel Robinson (November 2, 1911 \u2013 January 27, 1995) at Berkeley may have beaten him by a week or so on October 7th of the same year.\nD. H. Lehmer continued his fathers interest in combinatorial computing and in fact wrote the article \"Machine tools of Computation,\" which is chapter one in the book \"Applied Combinatorial Mathematics,\" by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series. In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. (see below)*Wik\n\n1952 The California Supreme Court declared the state loyalty oath unconstitutional and declared that the eighteen faculty members who had refused to sign the oath be reinstated.*VFR\n\n1978 James Burke's history of science series Connections first airs, on BBC Television in the United Kingdom (with accompanying book). *Wik\n\n1983 Gerard Debreu, who holds a joint appointment in Mathematics and Economics at Berkeley, won a Nobel Prize for his work in mathematical economics. For a non-technical description of his work see The Mathematical Intelligencer, 6(1984), no. 2, pp. 61\u201362. *VFR\n\n2012 Car size pieces of Halley's Comet lit up the skies over the Bay Area in California. Hundreds of residents from Oakland, San Francisco and Santa Cruz called ABC News station KGO-TV, reporting a loud boom, explosions and streaks of light around 7:45 p.m. local time. The Orionids are one of two annual meteor showers produced by icy pieces of Halley's Comet. The other shower, called the Eta Aquarids, peaks each year in early May, according to NASA. Video *ABC News\n\nBIRTHS\n\n1759 Jakob II Bernoulli (17 October 1759, Basel \u2013 3 July 1789, Saint Petersburg), younger brother of Johann III Bernoulli. Having finished his literary studies, he was, according to custom, sent to Neuch\u00e2tel to learn French. On his return he graduated in law. This study, however, did not check his hereditary taste for geometry. The early lessons which he had received from his father were continued by his uncle Daniel, and such was his progress that at the age of twenty-one he was called to undertake the duties of the chair of experimental physics, which his uncle\u2019s advanced years rendered him unable to discharge. He afterwards accepted the situation of secretary to count de Brenner, which afforded him an opportunity of seeing Germany and Italy. In Italy he formed a friendship with Lorgna, professor of mathematics at Verona, and one of the founders of the Societ\u00e0 Italiana for the encouragement of the sciences. He was also made corresponding member of the royal society of Turin; and, while residing at Venice, he was, through the friendly representation of Nicolaus von Fuss, admitted into the academy of St Petersburg. In 1788 he was named one of its mathematical professors. *Wik\nHe drowned while bathing in the Neva in July 1789, a few months after his marriage with a granddaughter of Leonhard Euler.\u00a0 (Can't tell your Bernoulli's without a scorecard?\u00a0 Check out \"A Confusion of Bernoulli's\" by the Renaissance Mathematicus.)\n\n1788 Paul Isaak Bernays (17 Oct 1888; 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS\n\n1927 Friedrich Ernst Peter Hirzebruch (17 October 1927 \u2013 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as \"the most important mathematician in the Germany of the postwar period.\nAmongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*Wik\n\nDEATHS\n\n1817 John West (10 April 1756 in Logie (near St Andrews), Scotland - 17 Oct 1817 in Morant Bay, Jamaica) The achievements of the little-known Scottish mathematician, John West (1756\u20131817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of \u201ccontinental\u201d analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.\nFirst an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described. *abstract for Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica, Alex D.D. Craik\n\n1877 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS\n\n1923 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.\nSince he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.\nThis 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU\n\n1937 Frank Morley (9 Sept 1860 in Woodbridge, Suffolk, England-17 Oct 1937 in Baltimore, Maryland, USA) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational literature.\u00a0 Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle. In 1899 he observed the relationship described above, but could find\u00a0 no\u00a0 proof. It spread from discussions with his friends to become an item\u00a0 of\u00a0 mathematical gossip. Finally in 1909 a trigonometric solution was\u00a0\u00a0 discovered by M. Satyanarayana. Later an elementary proof was developed.\u00a0\u00a0 Today the preferred proof is to begin with the result and work\u00a0\u00a0 backward. Start with an equilateral triangle and show that the vertices\u00a0\u00a0 are the intersection of the trisectors of a triangle with any given set\u00a0\u00a0 of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25. Find more about this unusual man here.\u00a0 *PB\n\n1941 John Stanley Plaskett (17 Nov 1865, 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years.*TIS\n\n1952 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.\u00a0 Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Acad\u00e9mie des Sciences in 1943. *SAU\n\n1963 Jacques-Salomon Hadamard (8 Dec 1865, 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n\/ln(n) is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vall\u00e9e Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalization of Green's functions (1932). *TIS\n\n1978 Gertrude Mary Cox (January 13, 1900 \u2013 October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik\n\n2008 Andrew Mattei Gleason (November 4, 1921 \u2013 October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood\u2013Gleason graph. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. (In graph theory, the Greenwood\u2013Gleason graph (Image at top of page) is also known as the Clebsch graph. It is an undirected graph with 16 vertices and 40 edges. It is named after Alfred Clebsch, a German mathematician who discovered it in 1868. It is also known as the Greenwood\u2013Gleason graph after the work of Robert M. Greenwood and Andrew M. Gleason (1955), who used it to evaluate the Ramsey number R(3,3,3) = 17 *Wik\n\nCredits :\n*CHM=Computer History Museum\n*FFF=Kane, Famous First Facts\n*NSEC= NASA Solar Eclipse Calendar\n*RMAT= The Renaissance Mathematicus, Thony Christie\n*SAU=St Andrews Univ. 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Rollicking ride down the Wall Street
Ali Syed
A fascinating insight into a world where multi-million-dollar bonuses and even larger egos abound
Ever wonder what happens when the worlds of high finance, politics and corruption collide? Well, wonder no more as David Enrich lays bare behind the scenes shenanigans in his fast-paced book: Dark Towers: Deutsche Bank, Donald Trump, and an Epic Trail of Destruction.
Enrich a veteran of the Wall Street Journal (WSJ), tracks the 150-year progress of Deutsche Bank and how it evolved from a sleepy German bank to a powerhouse in global finance.
The bank weathered crisis after crisis starting with the disastrous dealing with the American railroads in the 1880s to dalliances with the Nazis. Post World War II, with Germany in ruins, the Allies encouraged the resurgence of Deutsche Bank from the ashes of defeat. They needed German banks to help the German economy pay back billions of dollars of war reparations.
Led by Reagan and Thatcher, the loosening of the financial regulations opened the floodgates of modern finance. It was in these go-go '80s that the brash investment bankers, as we now know them, came to the fore.
At this time, the Deutsche executives decided the staid European banking model could not be sustained. Acquisitions of Morgan Grenfell, a venerable City of London institution, and, later, Bankers' Trust, the American derivatives house, soon followed. They transformed the culture of the bank and the senior management now had a distinctly international flavour.
The new breed of Deutsche bankers was talented but also loaded with ambitions and avarice. They were not afraid to fly too close to the edge and ended up doing business deals that were reckless and often with dubious counterparties. It was a global finance highly charged on testosterone. Dodgy real estate tycoons, Middle Eastern dictators and sanctioned countries were welcome to transact with the bank. The book provides fascinating details on some of the more dubious deals including the Banca Monte dei Paschi scandal in Italy.
With Swiss Josef Ackermann and Indian Anshu Jain at the helm, the bank's risk-taking reached a new height and by 2007, it was the largest bank in the world (in terms of its balance sheet). A lot of corners had been cut to reach that point and along the way, hundreds of millions of bonuses had been collected by the top bankers.
The most interesting and colourful portion of the book is reserved for the bank's dealing with Donald Trump. I will not provide any spoilers here, but the US president certainly seems to have run circles around the bank through a spate of troublesome deals.
By the time the regulators had wised up to these practices and slapped the bank with a record seven billion dollar fine, Jain had already left the bank. These regulatory intrusions finally led to the decline which saw the bank aggressively cut its investment banking business leading to tens of thousands of job losses around the world. The greed and recklessness of the few spelt catastrophe for the many.
Aside from documenting the headline-grabbing antics of the bank, the book also recounts the fascinating characters behind the scenes. A son searching for the truth after his father, a senior Deutsche banker, committed suicide due to the intense pressure. An American duo oversaw the transformation of the bank into a global powerhouse. A raft of aggressive bankers showed a penchant for risk-taking, with other people's money, might I add.
This is a well-researched book that will certainly find favour with those who appreciate this genre popularised by writers such as Michael Lewis (of Liar's Poker and The Big Short fame). It is a fascinating insight into a world where multi-million-dollar bonuses and even larger egos abound.
It should come as no surprise that this book does not shed a kind light on Deutsche Bank and its practices. That said, there is hardly a bank on Wall Street that can hold a torch for
ethical conduct. Nevertheless, the escapades of the bankers at the helm of Deutsche Bank make for an entertaining read.
Dark Towers: Deutsche Bank, Donald Trump, and an Epic Trail of Destruction (2020)
Author: David Enrich
Publisher: Custom House
The writer is a finance professional based in Dubai | {
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San José, Costa Rica Small group activities
Our most recommended San José, Costa Rica Small group activities
1. San Jose: Walking Nature Tour with Sloths, Birds, and Trees
Departing from the nearby meeting point, visit the University of Costa Rica campus, home to some of the largest patches of forest in San Jose. Guided by young biologists, discover the nature hiding in the middle of Costa Rica's largest city. Experience wildlife you wouldn't have imagined existed minutes away from downtown. On the first stop, you'll look for resident and migratory birds, lots of incredible insects and amazing flowers. Then, see the largest indigenous stone sphere in San Jose, thought to derive from the extinct Diquis culture. Lastly, visit the main campus to seek out the friendly sloths climbing freely. The goal of this tour is to change the way tourism is done in Costa Rica, while supporting young scientists, researchers, and local entrepreneurs.
2. From San Jose: Irazu Volcano Crater Hike and Cartago Trip
Depart from San Jose to discover the highest volcano in Costa Rica. Enjoy a trek through breathtaking scenery to reach the summit of Irazu Volcano and gaze into the emerald lagoon in its crater. Descend from the peak to explore the city of Cartago and enter the Basilica. Get picked up from your accommodations in San Jose and meet your friendly guide and group for the day. Leave the city behind as you travel to the Cartago Province. Arrive at Irazu Volcano and begin the easy hike up to the summit. Pass by all types of vegetation including coffee plantations and ferns as you ascend. Take a deep breath as you make it to the summit and be blown away by spectacular views of the massive crater. Wonder at the green lagoon beneath you and on a clear day enjoy views across the Atlantic and Pacific Ocean. Climb down the rocky trail to the historic city of Cartago, a former capital of Costa Rica. Enter the famous pilgrim site of the Basilica of Our Lady of the Angels and wander under the large vaulted ceilings before returning to San Jose.
3. From San Jose: Irazu Volcano & Hacienda Orosi Hot Springs
Visit a variety of Costa Rican highlights on a single tour leaving from San Jose. Travel to Irazu Volcano National Park, Orosi Basilica, Orosi Valley, and Hacienda Orosi Hot Springs. Make the most of a single day by visiting multiple stops and seeing several iconic Costa Rican sites. Embark from San Jose along the South Panamerican Highway, to start ascending the large Irazu Volcano. Zip along the winding road as it travels through fertile lands cultivated with all kinds of vegetables and observe lovely panoramic views of the farmland. Travel to the top of the volcano, where a number of its volcanic craters can be seen if the weather is clear, and see the Pacific Ocean and the Caribbean Sea. Descend the volcano and move on to the city of Cartago, and enjoy a stop at the Virgin of the Angels Basilica, a peregrination site for many believers. Move on to La Hacienda Orosi, surrounded by beautiful rainforest and lush vegetation, and visit the hot springs, where the land has been gifted with hypothermal mineral water, filtered between layers of the earth, and warmed to nearly 65 degrees Celsius, with properties to stimulate the senses and enrich the skin.
4. San José: Guided City Bus Tour With Lunch & Welcome Drink
Get to know Costa Rica's bustling capital San José on a bus tour with a local guide. Make stops at La Sabana Metropolitan Park, the Museum of Costa Rican Art, the National Theater, and more. Round off your fun-packed day with lunch at a local restaurant, then get taken back to your hotel. Begin your tour by getting picked up directly from your hotel. Hop on board the double decker bus to the sound of live folk music and enjoy a refreshing welcome cocktail. Sit back and let yourself be entertained by your charming guides, who will begin with a short history of the city. Make your first stop La Sabana Metropolitan Park, where you will be able to take a quick stroll as well as have a look inside the Museum of Costa Rican Art. Hop back on the bus and head to the outdoor Central Market. Take in the atmosphere and buy local goods and food (not included in the price). Next, visit the city's Central Park to witness the National Monument, a bronze statue of five women. Listen to your guide tell you about the meaning behind the statue and the history of Central American resistance to colonization. Continue on to the National Theater. Follow your guide around the lavish lobby in European design, which was constructed with money from taxes on coffee exports. After another short bus ride, stop at the Pre-Columbian Gold Museum, and marvel at the impressive gold collection. At the end of the tour, stop off at a nearby eatery for lunch, and chow down on some traditional Costa Rican dishes. Use the opportunity to ask your guide any questions you may have about the city's history and culture. Finally, allow the bus to drop you off at your hotel.
5. San José: Night Food and Culture Tour with Dinner
Follow an expert local guide and explore San José at night on a small-group, food-themed walking tour. See important cultural sites and feast on a traditional dinner with wine or beer pairings. Get up close and personal with the nightlife in San José, starting with Morazán Park where we will learn post-colonial Costa Rican history. From there, the appreciation for San José's historical architecture continues, with a walk by the Metallic Building, then on to Spain Park for a fantastic view of the Yellow House (now the Ministry of Foreign Affairs). Continue to the harming Barrio Escalante, one of the oldest residential areas neighborhoods in San José. Nowadays, Barrio Escalante has reinvented itself and is now home to many up-and-coming restaurants and at night is a favorite meeting spot for locals and visitors alike. The evening will end with a contemporary traditional meal with wine or beer tastings at a hip local restaurant that is very popular with locals and offers a sampler of traditional Costa Rican pub fare.
6. San José: Irazú and Turrialba Volcanoes with Guayabo Tour
After getting picked up at your hotel, head to the Irazú Volcano National Park where you can admire and even enter the crater of the highest volcano in the country. You will also be able to experience the unique miniature fauna and flora of Paramo, a tropical dwarf forest nestled in the highlands. Afterward, take the back road to Turrialba Volcano. Here, visit the "Central Town" located at the foot of the volcano. Enjoy time to explore and take some photos of the eerily abandoned town, still filled with farmhouses and buildings. Next, stop for dinner at a family-run grill house for a traditional Costa Rican lunch. Finally, before beginning the drive back to San José visit the Archaeological Site of Guayabo, declared a Civil Engineering World Heritage landmark and the most important milestone of pre-Hispanic culture in the country.
7. From San José: Punta Leona Hotel All-Access Day Pass
Spend an Exclusive Beach Day at the beautiful Hotel Punta Leona Resort, this White Sand Beach Resort is just 60 minutes from the capital city of San José; It has an exuberant tropical forest surrounding the entire resort, beautiful white sand beaches with the most amazing green-emerald waters of the Pacific Ocean. Along the way enjoy breathtaking views of the mountains and stop at the world famous Tarcoles River, where you will have the opportunity to view and take photos of crocodiles in their natural environment, some of them measuring up to 19ft long. Once at the resort you will have the opportunity to enjoy the beach with your own beach chairs and umbrella, immerse yourself in the Pacific Ocean and discover our own underwater museum with our snorkeling tour. Then enjoy a first-class buffet lunch and make sure you visit the butterfly garden and natural trails.
8. From San José: Carara National Park and Tárcoles River Tour
Begin your journey by being picked up from your hotel, and going on a scenic 1.5-hour drive along Route 27, making your way to your first stop at Carara National Park. Head straight out onto some flat walking trails suitable for all fitness levels and wheelchair users, and admire the biological reserve's abundant jungle life in person. Look up to the 40-meter high canopy, and keep an eye out for bright scarlet macaws, agouti rodents, stunning poison dart frogs, spider monkeys, dozens of birds, fantastic fungi, and huge wild cashew trees. Next, enjoy lunch like a local and eat at a traditional soda diner, where you have the option of eating fresh fish or seafood. Re-energized, lower your gears and enjoy a relaxing boat ride for some birdwatching on the Tárcoles River. Admire the river's mangroves, which are some of the most unique and scarce ecosystems of the world, and considered to be biodiversity hotspots. Keep a lookout for the 6-meter-long American crocodiles — the largest of the continent. Finally, dig your toes into the sand of a peaceful beach at your last stop, where you will relax with the sound of the waves before heading back to your accommodation.
9. San Jose: Central Market Tour with Food and Coffee Tasting
Explore the biggest and oldest market in San Jose City on a guided tour. Founded in 1880, stroll through a site that offers a glimpse into the true Costa Rican way of living, their customs, and traditions. Browse through the intricate aisles and taste unique snacks and sweets. Join your professional guide for a trip into the heart of Costa Rican culture. Dive into the busy Central Market for an authentic experience of the local lifestyle. Hear about the history of this ancient market and learn about each of the traditional products sold. Observe and shop for typical handcrafts as you walk around. Sample exotic fruits and dishes that may include empanadas, cheese tortillas, 'chicharrones' (pork rind), and tamales. Sip on artisanal coffee and taste the emblematic 'sorbetera' ice cream.
10. From San Jose: Tabacon Hot Springs & Arenal Volcano Day Trip
See the best of both worlds - the raw, untamed beauty of the imposing Arenal Volcano juxtaposed against the soothing thermal waters of Tabacon hot springs - on a day tour from San Jose. Enjoy the backdrop of lush vegetation and breathtaking views of the nearly perfectly conical volcano. After hotel pickup, head to your first stop, the famous town of Sarchi, known as Costa Rica's craftwork center. Appreciate many of the arts and crafts that Costa Rica has to offer, and perhaps pick up some brightly colored or wooden handicrafts to take back home with you as a souvenir. Next, head to La Fortuna, home to the magnificent natural wonder of the Arenal Volcano, where you will have a Costa Rican lunch. After eating, head to the impressive Arenal Volcano and take a short hike around the base to take photos. Marvel at the conical volcano and its plumes of white smoke. Then, relax at one of the best hot springs in the area, Tabacon hot springs, where you will revel in the cleansing and rejuvenating effects of the thermal waters. Enjoy the combination of the heat of the volcano, the flowing waters of the hot springs, and the pure air of the rainforest. Finally, be dropped back at your hotel in San Jose.
San Jose: Walking Nature Tour with Sloths, Birds, and Trees
From San Jose: Irazu Volcano Crater Hike and Cartago Trip
San José: Guided City Bus Tour With Lunch & Welcome Drink
San José: Night Food and Culture Tour with Dinner
From San José: Carara National Park and Tárcoles River Tour
San José: Irazú and Turrialba Volcanoes with Guayabo Tour
From San Jose: Irazu Volcano & Hacienda Orosi Hot Springs
From San Jose: Tabacon Hot Springs & Arenal Volcano Day Trip
San Jose: Central Market Tour with Food and Coffee Tasting
From San José: Punta Leona Hotel All-Access Day Pass
From San Jose: Braulio Carillo National Park Rainforest Tram
San Jose Mountains: walking and traditional masks
Zipline Tour in Braulio Carrillo National Park From San José
From San Jose: Coffee Plantation Day Trip with Coffee Sample
Frequently asked questions about San José, Costa Rica
What top attractions are a must-see in San José, Costa Rica?
The must-see attractions in San José, Costa Rica are:
Juan Santamaría International Airport, Costa Rica
San José Central Market
National Theatre of Costa Rica
La Sabana Park
National Theater
See all must-see sights in San José, Costa Rica
What are the best tours in San José, Costa Rica?
The best tours in San José, Costa Rica are:
San José: Arenal Volcano, Hot Springs, & Zip Lining w/ Meals
San Jose Bites and Sights Walking Tour
San Jose: Irazú Volcano, Cartago City & Orosi Valley Tour
Poás Volcano, Coffee Plantation & La Paz Waterfall Gardens
See all in San José, Costa Rica on GetYourGuide
What are the best day trips and excursions from San José, Costa Rica?
The best day trips and excursions from San José, Costa Rica are:
See all day trips and excursions from San José, Costa Rica on GetYourGuide
What are the best tours to do in San José, Costa Rica with kids?
The best tours to do in San José, Costa Rica with kids are:
Manuel Antonio National Park Combo Tour from San Jose
San José: Guided Volcano, Waterfall & Coffee Farm Day Trip
San Jose: Animal Rescue Center Entry with Guided Tour
See all family-friendly activities in San José, Costa Rica on GetYourGuide
What are the best outdoor activities to do in San José, Costa Rica?
The best outdoor activities to do in San José, Costa Rica are:
See all outdoor activities in San José, Costa Rica on GetYourGuide
Top Attractions in San José, Costa Rica
1 Juan Santamaría International Airport, Costa Rica
2 San José Central Market
3 National Theatre of Costa Rica
4 La Sabana Park
5 National Theater
6 Pre-Columbian Gold Museum
7 Plaza de La Cultura, San Jose
8 Metropolitan Cathedral of San José
9 Plaza de la Democracia y de la Abolición del Ejército
10 Supreme Court of Justice
11 Museum of Costa Rican Art
12 National Museum of Costa Rica
13 Central Park, San Jose
14 The National Monument of Costa Rica
15 Morazán Park
16 San José Central Park
17 Municipal Craft Market
18 Parque Nacional, San Jose
19 Costa Rica's National Stadium
20 Monumento Nacional
Things to Do in San José, Costa Rica
1 San José, Costa Rica Tours
2 San José, Costa Rica Activities
3 San José, Costa Rica Nature & adventure
4 San José, Costa Rica Outdoor activities
5 San José, Costa Rica Outdoor sports
6 San José, Costa Rica Day trips
7 San José, Costa Rica Natural Attractions & National Parks
8 San José, Costa Rica National parks
9 San José, Costa Rica Jungle tours
10 San José, Costa Rica Safaris & wildlife activities
11 San José, Costa Rica Birdwatching
12 San José, Costa Rica Volcano tours
13 San José, Costa Rica Family-friendly activities
14 San José, Costa Rica Hiking
15 San José, Costa Rica Photography tours
16 San José, Costa Rica Wheelchair accessible
17 San José, Costa Rica Culinary & nightlife
18 San José, Costa Rica Small group activities
19 San José, Costa Rica Food & drinks
20 San José, Costa Rica Private tours
Cities in Costa Rica
1 La Fortuna
4 Monteverde
6 Jaco
9 Aquiares, Costa Rica
11 Puerto Viejo de Sarapiqui, Costa Rica
14 Santa Teresa, Costa Rica
Other Sightseeing Options in San José, Costa Rica
Want to discover all there is to do in San José, Costa Rica? Click here for a full list.
What people are saying about San José, Costa Rica
Cello, our amazing guide From Oropopo Experience Tour Co. promptly picked us up at the hotel in a very comfy van. There were only three people on the tour which was great because it made us feel like we were on a private tour. Previously, we had tours from a different company where they jammed 16-18 people on a small bus. Cello was very patient, knowledgeable, and passionate about his job. During our tour of the Carara National Park, Cello pinpointed monkeys, toucans, and various species of insects. Next, he took us to Tarcoles River for a boat tour. In this relaxing cruise on the river, we encountered multiple crocodiles, a wide variety of bird species including hundreds of pelicans on tree tops. After the boat ride, Cello took us to a small family-owned restaurant by the beach for an excellent lunch. After lunch, he drove us to a secluded beach taking a short trail to the beach enjoying beautiful scenery, huge rock formations, and surrounding mountain greenery. Amazing day!
From San José: Carara National Park and Tárcoles River Tour Reviewed by Robert, 1/1/2023
Our guide was very friendly and very knowledgeable. Above all, he was passionate, which is plain to see. Amaral gave us a great and thorough tour of San Jose downtown and the marketplace. We learned SO much and tried SO many foods. If you are a foodie, this is a must for you. Great food, great prices and great tour guide. (Come hungry!) 10/10.
San Jose: Central Market Tour with Food and Coffee Tasting Reviewed by Antoinette, 1/2/2023
Very good combination of the activity in the day. Nice tour guide, small group, very convenient.
From San José: Carara National Park and Tárcoles River Tour Reviewed by , 12/30/2022
Rigo was an amazing tour guide! Learned so much from him and he takes the best pictures!
San Jose: Walking Nature Tour with Sloths, Birds, and Trees Reviewed by Kiara, 1/5/2023
Great guide, great excursion. I can only recommend
From San Jose: Irazu Volcano Crater Hike and Cartago Trip Reviewed by Daniel, 1/3/2023
San José Province
Small group activities | {
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return true;
}
}
return false;
} // end FUNCTION isTypedArray()
// EXPORTS //
module.exports = isTypedArray;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,662 |
from django.conf.urls import url, include
from bioshareX import views as bioshare_views, jsutils
from bioshareX.api import views as api_views
from bioshareX import file_views
from rest_framework import routers
# from bioshareX.api.views import GroupViewSet, MessageViewSet
router = routers.DefaultRouter()
router.register(r'groups', api_views.GroupViewSet,'Group')
router.register(r'messages', api_views.MessageViewSet,'Message')
router.register(r'shares', api_views.ShareViewset,'Share')
urlpatterns = [
url(r'^$', bioshare_views.index, name='index'),
url(r'^messages/?$', bioshare_views.view_messages, name='view_messages'),
url(r'^forbidden/?$', bioshare_views.forbidden, name='forbidden'),
url(r'^create/?$', bioshare_views.create_share, name='create_share'),
url(r'^create_subshare/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', bioshare_views.create_subshare, name='create_subshare'),
url(r'^edit/(?P<share>\w{15})/?$', bioshare_views.edit_share, name='edit_share'),
url(r'^cloud/?$', bioshare_views.tag_cloud, name='tag_cloud'),
# url(r'^list/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', bioshare_views.list_directory, name='list_directory_old'),
# url(r'^view/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', bioshare_views.list_directory, name='list_directory'),
# url(r'^wget/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?wget_index.html$', bioshare_views.wget_listing, name='wget_listing'),
url(r'^list/(?P<share>[-\w]+)/(?:(?P<subdir>.*/))?$', bioshare_views.list_directory, name='list_directory_old'),
url(r'^view/(?P<share>[-\w]+)/(?:(?P<subdir>.*/))?$', bioshare_views.list_directory, name='list_directory'),
url(r'^wget/(?P<share>[-\w]+)/(?:(?P<subdir>.*/))?wget_index.html$', bioshare_views.wget_listing, name='wget_listing'),
url(r'^shares/$', bioshare_views.list_shares, name='list_shares'),
# url(r'^groups/(?P<group_id>[\d]+)/shares/?$', bioshare_views.list_shares, name='list_group_shares'),
url(r'^groups/(?P<group_id>[\d]+)/shares/create/?$', bioshare_views.create_share, name='create_group_share'),
url(r'^permissions/(?P<share>[\da-zA-Z]{15})/?$', bioshare_views.share_permissions, name='share_permissions'),
# url(r'^goto/(?P<share>[\da-zA-Z]{15})/(?:(?P<subpath>.*/?))?$', bioshare_views.go_to_file_or_folder, name='go_to_file_or_folder'),
url(r'^goto/(?P<share>[-\w]+)/(?:(?P<subpath>.*/?))?$', bioshare_views.go_to_file_or_folder, name='go_to_file_or_folder'),
url(r'^ssh_keys/list/?$', bioshare_views.list_ssh_keys, name='list_ssh_keys'),
url(r'^ssh_keys/create/?$', bioshare_views.create_ssh_key, name='create_ssh_key'),
url(r'^groups/?$', bioshare_views.manage_groups, name='groups'),
url(r'^groups/(?P<group_id>[\d]+)/?$', bioshare_views.list_shares, name='group'),
url(r'^groups/(?P<group_id>[\d]+)/manage/?$', bioshare_views.manage_group, name='manage_group'),
url(r'^groups/(?P<group_id>[\d]+)/modify/?$', bioshare_views.create_modify_group, name='modify_group'),
url(r'^groups/create/?$', bioshare_views.create_modify_group, name='create_group'),
# url(r'^account/update_password/?$', 'update_password', name='update_password'),
url(r'^delete_share/(?P<share>[\da-zA-Z]{15})/?$', bioshare_views.delete_share, kwargs={'confirm':False},name='delete_share'),
url(r'^confirm_delete_share/(?P<share>[\da-zA-Z]{15})/?$', bioshare_views.delete_share, kwargs={'confirm':True},name='confirm_delete_share'),
url(r'^search/files/?$', bioshare_views.search_files, name='search_files'),
url(r'^jsurls.js$', jsutils.jsurls, {}, 'jsurls'),
]
# urlpatterns += [
# url(r'^account/update_password/$', auth_views.password_change, {'password_change_form': PasswordChangeForm,'post_change_redirect':'auth_password_change_done'},name='update_password'),
# ]
urlpatterns += [
url(r'^api/get_permissions/(?P<share>[\da-zA-Z]{15})/?$', api_views.get_permissions, name='api_get_permissions'),
url(r'^api/set_permissions/(?P<share>[\da-zA-Z]{15})/?$', api_views.set_permissions, name='api_set_permissions'),
url(r'^api/update/(?P<share>[\da-zA-Z]{15})/?$', api_views.update_share, name='api_update_share'),
url(r'^api/get_group/?$', api_views.get_group, name='api_get_group'),
url(r'^api/search/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', api_views.search_share, name='api_search_share'),
url(r'^api/share_autocomplete/$', api_views.share_autocomplete, name='api_share_autocomplete'),
url(r'^api/ssh_keys/delete/?$', api_views.delete_ssh_key, name='api_delete_ssh_key'),
url(r'^api/edit_metadata/(?P<share>[\da-zA-Z]{15})/(?P<subpath>.*)/?$', api_views.edit_metadata, name='api_edit_metadata'),
url(r'^api/get_addresses/?$', api_views.get_address_book, name='api_get_address_book'),
url(r'^api/get_user/?$', api_views.get_user, name='api_get_user'),
url(r'^api/get_tags/?$', api_views.get_tags, name='api_tags'),
url(r'^api/share/(?P<share>[\da-zA-Z]{15})/?$', api_views.share_with, name='api_share_with'),
url(r'^api/shares/create/?$', api_views.create_share, name='api_create_share'),
url(r'^api/email_participants/(?P<share>[\da-zA-Z]{15})/(?P<subdir>.*)/?$', api_views.email_participants, name='api_email_participants'),
url(r'^api/logs/$', api_views.ShareLogList.as_view()),
# url(r'^api/shares/$', api_views.ShareList.as_view()),
url(r'^api/', include(router.urls)),
]
urlpatterns += [
url(r'^upload/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.upload_file, name='upload_file'),
url(r'^create_folder/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.create_folder, name='create_folder'),
url(r'^rename/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.modify_name, name='modify_name'),
url(r'^delete/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.delete_paths, name='delete_paths'),
url(r'^move/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.move_paths, name='move_paths'),
url(r'^stream_archive/(?P<share>[\da-zA-Z]{15})/(?:(?P<subdir>.*/))?$', file_views.download_archive_stream, name='download_archive_stream'),
url(r'^download/(?P<share>[\da-zA-Z]{15})/(?P<subpath>.*)/?$', file_views.download_file, name='download_file'),
url(r'^preview/(?P<share>[\da-zA-Z]{15})/(?P<subpath>.*)/?$', file_views.preview_file, name='preview_file'),
url(r'^directories/(?P<share>[\da-zA-Z]{15})/?$', file_views.get_directories, name='get_directories'),
url(r'^wget/(?P<share>[\da-zA-Z]{15})/(?P<subpath>.*)/?$', file_views.download_file, name='wget_download_file'),
url(r'^md5sum/(?P<share>[\da-zA-Z]{15})/(?P<subpath>.*)/?$', file_views.get_md5sum, name='md5sum'),
]
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,554 |
for $99,900 with 2 bedrooms and 1 full bath. This 850 square foot home was built in 1935 on a lot size of 850 SqFt.
Call showing time for all appointments .A cute 2BR-1BA Bungalow in Southeast JC. Many updates, ready to move into.Perfect starter home, investment property or business office.Nice covered front porch, large living room with fireplace(capped off), 2 spacious bedrooms, hall way leading to the full bath, a formal dining room large enough for family gatherings, nice size kitchen with lots of cabinets-work space, stove, refrigerator, built-in shelves, a laundry room with washer & dryer.The home has original hardwood floors, solid wood doors, new tile in kitchen & laundry-2016, HVAC-2013, roof-2015, pex plumbing-2015, new electric box-wiring-2015, attic insulation-R37-2016, windows repaired & reglazed-2015, new toilet-2017, new faucet in kitchen sink-2016.Zoning B4.Large level lot-front & back entrance-street & side parking.A concrete pad in back yard for patio cookouts.(CURTAINS DO NOT CONVEY)Come see it Today! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,392 |
Era il secondo figlio di Goffredo III di Brabante e Margherita di Limburgo.
Biografia
Avviato fin da piccolo alla carriera ecclesiastica, divenne ben presto arcidiacono.
A causa della pressione esercitata dal fratello, il duca Enrico I di Brabante e dallo zio venne eletto l'8 settembre 1191 vescovo di Liegi mentre una minoranza degli elettori si era espressa a favore di Alberto di Rethel, cugino di Baldovino V, duca di Hennegau e zio dell'imperatrice.
Le parti si rivolsero all'imperatore per dirimere la contesa. Dopo aver sentito il parere di 14 prelati l'imperatore Enrico VI si appellò ad una clausola di diritto canonico sancita nel concordato di Worms e nominò vescovo Lotario di Hochstaden. Alberto si rifiutò di cedere lo scranno e si appellò al papa Celestino III che lo confermò nella sua posizione e nel maggio del 1192 lo nominò cardinale diacono. Il Papa incaricò l'arcivescovo di Colonia di rinnovare la nomina a vescovo, al suo rifiuto incaricò l'arcivescovo di Reims. Alberto venne nominato vescovo il 19 settembre 1192 a Reims.
Alberto venne assassinato a Reims il 24 novembre 1192 da alcuni cavalieri tedeschi.
L'assassinio destò scalpore, l'imperatore venne ritenuto responsabile e ciò contribuì alla formazione di una fazione di nobili che si oppose all'imperatore nel periodo 1193-1194.
Genealogia episcopale
La genealogia episcopale è:
Vescovo Maurice de Sully
Cardinale Guglielmo dalle Bianche Mani
Cardinale Alberto di Lovanio
Ascendenza
Altri progetti
Collegamenti esterni
Santi per nome
Santi del XII secolo
Morti assassinati
Vescovi di Liegi
Alberto di Lovanio | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,033 |
package com.wenyu.rtmp.controller.video;
import android.annotation.TargetApi;
import android.content.Intent;
import android.hardware.display.DisplayManager;
import android.hardware.display.VirtualDisplay;
import android.media.projection.MediaProjection;
import android.media.projection.MediaProjectionManager;
import android.os.Build;
import android.view.Surface;
import com.wenyu.rtmp.configuration.VideoConfiguration;
import com.wenyu.rtmp.constant.SopCastConstant;
import com.wenyu.rtmp.controller.video.IVideoController;
import com.wenyu.rtmp.mediacodec.VideoMediaCodec;
import com.wenyu.rtmp.screen.ScreenRecordEncoder;
import com.wenyu.rtmp.utils.SopCastLog;
import com.wenyu.rtmp.video.OnVideoEncodeListener;
import static android.os.Build.VERSION_CODES.LOLLIPOP;
@TargetApi(LOLLIPOP)
public class ScreenVideoController implements IVideoController {
private MediaProjectionManager mManager;
private int resultCode;
private Intent resultData;
private VirtualDisplay mVirtualDisplay;
private MediaProjection mMediaProjection;
private VideoConfiguration mVideoConfiguration = VideoConfiguration.createDefault();
private ScreenRecordEncoder mEncoder;
private OnVideoEncodeListener mListener;
public ScreenVideoController (MediaProjectionManager manager, int resultCode, Intent resultData) {
mManager = manager;
this.resultCode = resultCode;
this.resultData = resultData;
}
@Override
public void start() {
mEncoder = new ScreenRecordEncoder(mVideoConfiguration);
Surface surface = mEncoder.getSurface();
mEncoder.start();
mEncoder.setOnVideoEncodeListener(mListener);
mMediaProjection = mManager.getMediaProjection(resultCode, resultData);
int width = VideoMediaCodec.getVideoSize(mVideoConfiguration.width);
int height = VideoMediaCodec.getVideoSize(mVideoConfiguration.height);
mVirtualDisplay = mMediaProjection.createVirtualDisplay("ScreenRecoder",
width, height, 1, DisplayManager.VIRTUAL_DISPLAY_FLAG_AUTO_MIRROR, surface, null, null);
}
@Override
public void stop() {
if(mEncoder != null) {
mEncoder.setOnVideoEncodeListener(null);
mEncoder.stop();
mEncoder = null;
}
if (mMediaProjection != null) {
mMediaProjection.stop();
mMediaProjection = null;
}
if (mVirtualDisplay != null) {
mVirtualDisplay.release();
mVirtualDisplay = null;
}
}
@Override
public void pause() {
if(mEncoder != null) {
mEncoder.setPause(true);
}
}
@Override
public void resume() {
if(mEncoder != null) {
mEncoder.setPause(false);
}
}
@Override
public boolean setVideoBps(int bps) {
//重新设置硬编bps,在低于19的版本需要重启编码器
boolean result = false;
if (Build.VERSION.SDK_INT < Build.VERSION_CODES.KITKAT) {
//由于重启硬编编码器效果不好,此次不做处理
SopCastLog.d(SopCastConstant.TAG, "Bps need change, but MediaCodec do not support.");
}else {
if (mEncoder != null) {
SopCastLog.d(SopCastConstant.TAG, "Bps change, current bps: " + bps);
mEncoder.setRecorderBps(bps);
result = true;
}
}
return result;
}
@Override
public void setVideoEncoderListener(OnVideoEncodeListener listener) {
mListener = listener;
}
@Override
public void setVideoConfiguration(VideoConfiguration configuration) {
mVideoConfiguration = configuration;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,647 |
\section{Introduction}
The journal \textit{Monthly Notices of the Royal Astronomical Society} (MNRAS) encourages authors to prepare their papers using \LaTeX.
The style file \verb'mnras.cls' can be used to approximate the final appearance of the journal, and provides numerous features to simplify the preparation of papers.
This document, \verb'mnras_guide.tex', provides guidance on using that style file and the features it enables.
This is not a general guide on how to use \LaTeX, of which many excellent examples already exist.
We particularly recommend \textit{Wikibooks \LaTeX}\footnote{\url{https://en.wikibooks.org/wiki/LaTeX}}, a collaborative online textbook which is of use to both beginners and experts.
Alternatively there are several other online resources, and most academic libraries also hold suitable beginner's guides.
For guidance on the contents of papers, journal style, and how to submit a paper, see the MNRAS Instructions to Authors\footnote{\label{foot:itas}\url{http://www.oxfordjournals.org/our_journals/mnras/for_authors/}}.
Only technical issues with the \LaTeX\ class are considered here.
\section{Obtaining and installing the MNRAS package}
Some \LaTeX\ distributions come with the MNRAS package by default.
If yours does not, you can either install it using your distribution's package manager, or download it from the Comprehensive \TeX\ Archive Network\footnote{\url{http://www.ctan.org/tex-archive/macros/latex/contrib/mnras}} (CTAN).
The files can either be installed permanently by placing them in the appropriate directory (consult the documentation for your \LaTeX\ distribution), or used temporarily by placing them in the working directory for your paper.
To use the MNRAS package, simply specify \verb'mnras' as the document class at the start of a \verb'.tex' file:
\begin{verbatim}
\documentclass{mnras}
\end{verbatim}
Then compile \LaTeX\ (and if necessary \bibtex) in the usual way.
\section{Preparing and submitting a paper}
We recommend that you start with a copy of the \texttt{mnras\_template.tex} file.
Rename the file, update the information on the title page, and then work on the text of your paper.
Guidelines for content, style etc. are given in the instructions to authors on the journal's website$^{\ref{foot:itas}}$.
Note that this document does not follow all the aspects of MNRAS journal style (e.g. it has a table of contents).
If a paper is accepted, it is professionally typeset and copyedited by the publishers.
It is therefore likely that minor changes to presentation will occur.
For this reason, we ask authors to ignore minor details such as slightly long lines, extra blank spaces, or misplaced figures, because these details will be dealt with during the production process.
Papers must be submitted electronically via the online submission system; paper submissions are not permitted.
For full guidance on how to submit a paper, see the instructions to authors.
\section{Class options}
\label{sec:options}
There are several options which can be added to the document class line like this:
\begin{verbatim}
\documentclass[option1,option2]{mnras}
\end{verbatim}
The available options are:
\begin{itemize}
\item \verb'letters' -- used for papers in the journal's Letters section.
\item \verb'onecolumn' -- single column, instead of the default two columns. This should be used {\it only} if necessary for the display of numerous very long equations.
\item \verb'doublespacing' -- text has double line spacing. Please don't submit papers in this format.
\item \verb'referee' -- \textit{(deprecated)} single column, double spaced, larger text, bigger margins. Please don't submit papers in this format.
\item \verb'galley' -- \textit{(deprecated)} no running headers, no attempt to align the bottom of columns.
\item \verb'landscape' -- \textit{(deprecated)} sets the whole document on landscape paper.
\item \verb"usenatbib" -- \textit{(all papers should use this)} this uses Patrick Daly's \verb"natbib.sty" package for citations.
\item \verb"usegraphicx" -- \textit{(most papers will need this)} includes the \verb'graphicx' package, for inclusion of figures and images.
\item \verb'useAMS' -- adds support for upright Greek characters \verb'\upi', \verb'\umu' and \verb'\upartial' ($\upi$, $\umu$ and $\upartial$). Only these three are included, if you require other symbols you will need to include the \verb'amsmath' or \verb'amsymb' packages (see section~\ref{sec:packages}).
\item \verb"usedcolumn" -- includes the package \verb"dcolumn", which includes two new types of column alignment for use in tables.
\end{itemize}
Some of these options are deprecated and retained for backwards compatibility only.
Others are used in almost all papers, but again are retained as options to ensure that papers written decades ago will continue to compile without problems.
If you want to include any other packages, see section~\ref{sec:packages}.
\section{Title page}
If you are using \texttt{mnras\_template.tex} the necessary code for generating the title page, headers and footers is already present.
Simply edit the title, author list, institutions, abstract and keywords as described below.
\subsection{Title}
There are two forms of the title: the full version used on the first page, and a short version which is used in the header of other odd-numbered pages (the `running head').
Enter them with \verb'\title[]{}' like this:
\begin{verbatim}
\title[Running head]{Full title of the paper}
\end{verbatim}
The full title can be multiple lines (use \verb'\\' to start a new line) and may be as long as necessary, although we encourage authors to use concise titles. The running head must be $\le~45$ characters on a single line.
See appendix~\ref{sec:advanced} for more complicated examples.
\subsection{Authors and institutions}
Like the title, there are two forms of author list: the full version which appears on the title page, and a short form which appears in the header of the even-numbered pages. Enter them using the \verb'\author[]{}' command.
If the author list is more than one line long, start a new line using \verb'\newauthor'. Use \verb'\\' to start the institution list. Affiliations for each author should be indicated with a superscript number, and correspond to the list of institutions below the author list.
For example, if I were to write a paper with two coauthors at another institution, one of whom also works at a third location:
\begin{verbatim}
\author[K. T. Smith et al.]{
Keith T. Smith,$^{1}$
A. N. Other,$^{2}$
and Third Author$^{2,3}$
\\
$^{1}$Affiliation 1\\
$^{2}$Affiliation 2\\
$^{3}$Affiliation 3}
\end{verbatim}
Affiliations should be in the format `Department, Institution, Street Address, City and Postal Code, Country'.
Email addresses can be inserted with the \verb'\thanks{}' command which adds a title page footnote.
If you want to list more than one email, put them all in the same \verb'\thanks' and use \verb'\footnotemark[]' to refer to the same footnote multiple times.
Present addresses (if different to those where the work was performed) can also be added with a \verb'\thanks' command.
\subsection{Abstract and keywords}
The abstract is entered in an \verb'abstract' environment:
\begin{verbatim}
\begin{abstract}
The abstract of the paper.
\end{abstract}
\end{verbatim}
\noindent Note that there is a word limit on the length of abstracts.
For the current word limit, see the journal instructions to authors$^{\ref{foot:itas}}$.
Immediately following the abstract, a set of keywords is entered in a \verb'keywords' environment:
\begin{verbatim}
\begin{keywords}
keyword 1 -- keyword 2 -- keyword 3
\end{keywords}
\end{verbatim}
\noindent There is a list of permitted keywords, which is agreed between all the major astronomy journals and revised every few years.
Do \emph{not} make up new keywords!
For the current list of allowed keywords, see the journal's instructions to authors$^{\ref{foot:itas}}$.
\section{Sections and lists}
Sections and lists are generally the same as in the standard \LaTeX\ classes.
\subsection{Sections}
\label{sec:sections}
Sections are entered in the usual way, using \verb'\section{}' and its variants. It is possible to nest up to four section levels:
\begin{verbatim}
\section{Main section}
\subsection{Subsection}
\subsubsection{Subsubsection}
\paragraph{Lowest level section}
\end{verbatim}
\noindent The other \LaTeX\ sectioning commands \verb'\part', \verb'\chapter' and \verb'\subparagraph{}' are deprecated and should not be used.
Some sections are not numbered as part of journal style (e.g. the Acknowledgements).
To insert an unnumbered section use the `starred' version of the command: \verb'\section*{}'.
See appendix~\ref{sec:advanced} for more complicated examples.
\subsection{Lists}
Two forms of lists can be used in MNRAS -- numbered and unnumbered.
For a numbered list, use the \verb'enumerate' environment:
\begin{verbatim}
\begin{enumerate}
\item First item
\item Second item
\item etc.
\end{enumerate}
\end{verbatim}
\noindent which produces
\begin{enumerate}
\item First item
\item Second item
\item etc.
\end{enumerate}
Note that the list uses lowercase Roman numerals, rather than the \LaTeX\ default Arabic numerals.
For an unnumbered list, use the \verb'description' environment without the optional argument:
\begin{verbatim}
\begin{description}
\item First item
\item Second item
\item etc.
\end{description}
\end{verbatim}
\noindent which produces
\begin{description}
\item First item
\item Second item
\item etc.
\end{description}
Bulleted lists using the \verb'itemize' environment should not be used in MNRAS; it is retained for backwards compatibility only.
\section{Mathematics and symbols}
The MNRAS class mostly adopts standard \LaTeX\ handling of mathematics, which is briefly summarised here.
See also section~\ref{sec:packages} for packages that support more advanced mathematics.
Mathematics can be inserted into the running text using the syntax \verb'$1+1=2$', which produces $1+1=2$.
Use this only for short expressions or when referring to mathematical quantities; equations should be entered as described below.
\subsection{Equations}
Equations should be entered using the \verb'equation' environment, which automatically numbers them:
\begin{verbatim}
\begin{equation}
a^2=b^2+c^2
\end{equation}
\end{verbatim}
\noindent which produces
\begin{equation}
a^2=b^2+c^2
\end{equation}
By default, the equations are numbered sequentially throughout the whole paper. If a paper has a large number of equations, it may be better to number them by section (2.1, 2.2 etc.). To do this, add the command \verb'\numberwithin{equation}{section}' to the preamble.
It is also possible to produce un-numbered equations by using the \LaTeX\ built-in \verb'\['\textellipsis\verb'\]' and \verb'$$'\textellipsis\verb'$$' commands; however MNRAS requires that all equations are numbered, so these commands should be avoided.
\subsection{Special symbols}
\begin{table}
\caption{Additional commands for special symbols commonly used in astronomy. These can be used anywhere.}
\label{tab:anysymbols}
\begin{tabular}{lll}
\hline
Command & Output & Meaning\\
\hline
\verb'\sun' & \sun & Sun, solar\\[2pt]
\verb'\earth' & \earth & Earth, terrestrial\\[2pt]
\verb'\micron' & \micron & microns\\[2pt]
\verb'\degr' & \degr & degrees\\[2pt]
\verb'\arcmin' & \arcmin & arcminutes\\[2pt]
\verb'\arcsec' & \arcsec & arcseconds\\[2pt]
\verb'\fdg' & \fdg & fraction of a degree\\[2pt]
\verb'\farcm' & \farcm & fraction of an arcminute\\[2pt]
\verb'\farcs' & \farcs & fraction of an arcsecond\\[2pt]
\verb'\fd' & \fd & fraction of a day\\[2pt]
\verb'\fh' & \fh & fraction of an hour\\[2pt]
\verb'\fm' & \fm & fraction of a minute\\[2pt]
\verb'\fs' & \fs & fraction of a second\\[2pt]
\verb'\fp' & \fp & fraction of a period\\[2pt]
\verb'\diameter' & \diameter & diameter\\[2pt]
\verb'\sq' & \sq & square, Q.E.D.\\[2pt]
\hline
\end{tabular}
\end{table}
\begin{table}
\caption{Additional commands for mathematical symbols. These can only be used in maths mode.}
\label{tab:mathssymbols}
\begin{tabular}{lll}
\hline
Command & Output & Meaning\\
\hline
\verb'\upi' & $\upi$ & upright pi\\[2pt]
\verb'\umu' & $\umu$ & upright mu\\[2pt]
\verb'\upartial' & $\upartial$ & upright partial derivative\\[2pt]
\verb'\lid' & $\lid$ & less than or equal to\\[2pt]
\verb'\gid' & $\gid$ & greater than or equal to\\[2pt]
\verb'\la' & $\la$ & less than of order\\[2pt]
\verb'\ga' & $\ga$ & greater than of order\\[2pt]
\verb'\loa' & $\loa$ & less than approximately\\[2pt]
\verb'\goa' & $\goa$ & greater than approximately\\[2pt]
\verb'\cor' & $\cor$ & corresponds to\\[2pt]
\verb'\sol' & $\sol$ & similar to or less than\\[2pt]
\verb'\sog' & $\sog$ & similar to or greater than\\[2pt]
\verb'\lse' & $\lse$ & less than or homotopic to \\[2pt]
\verb'\gse' & $\gse$ & greater than or homotopic to\\[2pt]
\verb'\getsto' & $\getsto$ & from over to\\[2pt]
\verb'\grole' & $\grole$ & greater over less\\[2pt]
\verb'\leogr' & $\leogr$ & less over greater\\
\hline
\end{tabular}
\end{table}
Some additional symbols of common use in astronomy have been added in the MNRAS class. These are shown in tables~\ref{tab:anysymbols}--\ref{tab:mathssymbols}. The command names are -- as far as possible -- the same as those used in other major astronomy journals.
Many other mathematical symbols are also available, either built into \LaTeX\ or via additional packages. If you want to insert a specific symbol but don't know the \LaTeX\ command, we recommend using the Detexify website\footnote{\url{http://detexify.kirelabs.org}}.
Sometimes font or coding limitations mean a symbol may not get smaller when used in sub- or superscripts, and will therefore be displayed at the wrong size. There is no need to worry about this as it will be corrected by the typesetter during production.
To produce bold symbols in mathematics, use \verb'\bmath' for simple variables, and the \verb'bm' package for more complex symbols (see section~\ref{sec:packages}). Vectors are set in bold italic, using \verb'\mathbfit{}'.
For matrices, use \verb'\mathbfss{}' to produce a bold sans-serif font e.g. \mathbfss{H}; this works even outside maths mode, but not all symbols are available (e.g. Greek). For $\nabla$ (del, used in gradients, divergence etc.) use \verb'$\nabla$'.
\subsection{Ions}
A new \verb'\ion{}{}' command has been added to the class file, for the correct typesetting of ionisation states.
For example, to typeset singly ionised calcium use \verb'\ion{Ca}{ii}', which produces \ion{Ca}{ii}.
\section{Figures and tables}
\label{sec:fig_table}
Figures and tables (collectively called `floats') are mostly the same as built into \LaTeX.
\subsection{Basic examples}
\begin{figure}
\includegraphics[width=\columnwidth]{example}
\caption{An example figure.}
\label{fig:example}
\end{figure}
Figures are inserted in the usual way using a \verb'figure' environment and \verb'\includegraphics'. The example Figure~\ref{fig:example} was generated using the code:
\begin{verbatim}
\begin{figure}
\includegraphics[width=\columnwidth]{example}
\caption{An example figure.}
\label{fig:example}
\end{figure}
\end{verbatim}
\begin{table}
\caption{An example table.}
\label{tab:example}
\begin{tabular}{lcc}
\hline
Star & Mass & Luminosity\\
& $M_{\sun}$ & $L_{\sun}$\\
\hline
Sun & 1.00 & 1.00\\
$\alpha$~Cen~A & 1.10 & 1.52\\
$\epsilon$~Eri & 0.82 & 0.34\\
\hline
\end{tabular}
\end{table}
The example Table~\ref{tab:example} was generated using the code:
\begin{verbatim}
\begin{table}
\caption{An example table.}
\label{tab:example}
\begin{tabular}{lcc}
\hline
Star & Mass & Luminosity\\
& $M_{\sun}$ & $L_{\sun}$\\
\hline
Sun & 1.00 & 1.00\\
$\alpha$~Cen~A & 1.10 & 1.52\\
$\epsilon$~Eri & 0.82 & 0.34\\
\hline
\end{tabular}
\end{table}
\end{verbatim}
\subsection{Captions and placement}
Captions go \emph{above} tables but \emph{below} figures, as in the examples above.
The \LaTeX\ float placement commands \verb'[htbp]' are intentionally disabled.
Layout of figures and tables will be adjusted by the publisher during the production process, so authors should not concern themselves with placement to avoid disappointment and wasted effort.
Simply place the \LaTeX\ code close to where the figure or table is first mentioned in the text and leave exact placement to the publishers.
By default a figure or table will occupy one column of the page.
To produce a wider version which covers both columns, use the \verb'figure*' or \verb'table*' environment.
If a figure or table is too long to fit on a single page it can be split it into several parts.
Create an additional figure or table which uses \verb'\contcaption{}' instead of \verb'\caption{}'.
This will automatically correct the numbering and add `\emph{continued}' at the start of the caption.
\begin{table}
\contcaption{A table continued from the previous one.}
\label{tab:continued}
\begin{tabular}{lcc}
\hline
Star & Mass & Luminosity\\
& $M_{\sun}$ & $L_{\sun}$\\
\hline
$\tau$~Cet & 0.78 & 0.52\\
$\delta$~Pav & 0.99 & 1.22\\
$\sigma$~Dra & 0.87 & 0.43\\
\hline
\end{tabular}
\end{table}
Table~\ref{tab:continued} was generated using the code:
\begin{verbatim}
\begin{table}
\contcaption{A table continued from the previous one.}
\label{tab:continued}
\begin{tabular}{lcc}
\hline
Star & Mass & Luminosity\\
& $M_{\sun}$ & $L_{\sun}$\\
\hline
$\tau$~Cet & 0.78 & 0.52\\
$\delta$~Pav & 0.99 & 1.22\\
$\sigma$~Dra & 0.87 & 0.43\\
\hline
\end{tabular}
\end{table}
\end{verbatim}
To produce a landscape figure or table, use the \verb'pdflscape' package and the \verb'landscape' environment.
The landscape Table~\ref{tab:landscape} was produced using the code:
\begin{verbatim}
\begin{landscape}
\begin{table}
\caption{An example landscape table.}
\label{tab:landscape}
\begin{tabular}{cccccccccc}
\hline
Header & Header & ...\\
Unit & Unit & ...\\
\hline
Data & Data & ...\\
Data & Data & ...\\
...\\
\hline
\end{tabular}
\end{table}
\end{landscape}
\end{verbatim}
Unfortunately this method will force a page break before the table appears.
More complicated solutions are possible, but authors shouldn't worry about this.
\begin{landscape}
\begin{table}
\caption{An example landscape table.}
\label{tab:landscape}
\begin{tabular}{cccccccccc}
\hline
Header & Header & Header & Header & Header & Header & Header & Header & Header & Header\\
Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit \\
\hline
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
\hline
\end{tabular}
\end{table}
\end{landscape}
\section{References and citations}
\subsection{Cross-referencing}
The usual \LaTeX\ commands \verb'\label{}' and \verb'\ref{}' can be used for cross-referencing within the same paper.
We recommend that you use these whenever relevant, rather than writing out the section or figure numbers explicitly.
This ensures that cross-references are updated whenever the numbering changes (e.g. during revision) and provides clickable links (if available in your compiler).
It is best to give each section, figure and table a logical label.
For example, Table~\ref{tab:mathssymbols} has the label \verb'tab:mathssymbols', whilst section~\ref{sec:packages} has the label \verb'sec:packages'.
Add the label \emph{after} the section or caption command, as in the examples in sections~\ref{sec:sections} and \ref{sec:fig_table}.
Enter the cross-reference with a non-breaking space between the type of object and the number, like this: \verb'see Figure~\ref{fig:example}'.
The \verb'\autoref{}' command can be used to automatically fill out the type of object, saving on typing.
It also causes the link to cover the whole phrase rather than just the number, but for that reason is only suitable for single cross-references rather than ranges.
For example, \verb'\autoref{tab:journal_abbr}' produces \autoref{tab:journal_abbr}.
\subsection{Citations}
\label{sec:cite}
MNRAS uses the Harvard -- author (year) -- citation style, e.g. \citet{author2013}.
This is implemented in \LaTeX\ via the \verb'natbib' package, which in turn is included via the \verb'usenatbib' package option (see section~\ref{sec:options}), which should be used in all papers.
Each entry in the reference list has a `key' (see section~\ref{sec:ref_list}) which is used to generate citations.
There are two basic \verb'natbib' commands:
\begin{description}
\item \verb'\citet{key}' produces an in-text citation: \citet{author2013}
\item \verb'\citep{key}' produces a bracketed (parenthetical) citation: \citep{author2013}
\end{description}
Citations will include clickable links to the relevant entry in the reference list, if supported by your \LaTeX\ compiler.
\defcitealias{smith2014}{Paper~I}
\begin{table*}
\caption{Common citation commands, provided by the \texttt{natbib} package.}
\label{tab:natbib}
\begin{tabular}{lll}
\hline
Command & Ouput & Note\\
\hline
\verb'\citet{key}' & \citet{smith2014} & \\
\verb'\citep{key}' & \citep{smith2014} & \\
\verb'\citep{key,key2}' & \citep{smith2014,jones2015} & Multiple papers\\
\verb'\citet[table 4]{key}' & \citet[table 4]{smith2014} & \\
\verb'\citep[see][figure 7]{key}' & \citep[see][figure 7]{smith2014} & \\
\verb'\citealt{key}' & \citealt{smith2014} & For use with manual brackets\\
\verb'\citeauthor{key}' & \citeauthor{smith2014} & If already cited in close proximity\\
\verb'\defcitealias{key}{Paper~I}' & & Define an alias (doesn't work in floats)\\
\verb'\citetalias{key}' & \citetalias{smith2014} & \\
\verb'\citepalias{key}' & \citepalias{smith2014} & \\
\hline
\end{tabular}
\end{table*}
There are a number of other \verb'natbib' commands which can be used for more complicated citations.
The most commonly used ones are listed in Table~\ref{tab:natbib}.
For full guidance on their use, consult the \verb'natbib' documentation\footnote{\url{http://www.ctan.org/pkg/natbib}}.
If a reference has several authors, \verb'natbib' will automatically use `et al.' if there are more than two authors. However, if a paper has exactly three authors, MNRAS style is to list all three on the first citation and use `et al.' thereafter. If you are using \bibtex\ (see section~\ref{sec:ref_list}) then this is handled automatically. If not, the \verb'\citet*{}' and \verb'\citep*{}' commands can be used at the first citation to include all of the authors.
\subsection{The list of references}
\label{sec:ref_list}
It is possible to enter references manually using the usual \LaTeX\ commands, but we strongly encourage authors to use \bibtex\ instead.
\bibtex\ ensures that the reference list is updated automatically as references are added or removed from the paper, puts them in the correct format, saves on typing, and the same reference file can be used for many different papers -- saving time hunting down reference details.
An MNRAS \bibtex\ style file, \verb'mnras.bst', is distributed as part of this package.
The rest of this section will assume you are using \bibtex.
References are entered into a separate \verb'.bib' file in standard \bibtex\ formatting.
This can be done manually, or there are several software packages which make editing the \verb'.bib' file much easier.
We particularly recommend \textsc{JabRef}\footnote{\url{http://jabref.sourceforge.net/}}, which works on all major operating systems.
\bibtex\ entries can be obtained from the NASA Astrophysics Data System\footnote{\label{foot:ads}\url{http://adsabs.harvard.edu}} (ADS) by clicking on `Bibtex entry for this abstract' on any entry.
Simply copy this into your \verb'.bib' file or into the `BibTeX source' tab in \textsc{JabRef}.
Each entry in the \verb'.bib' file must specify a unique `key' to identify the paper, the format of which is up to the author.
Simply cite it in the usual way, as described in section~\ref{sec:cite}, using the specified key.
Compile the paper as usual, but add an extra step to run the \texttt{bibtex} command.
Consult the documentation for your compiler or latex distribution.
Correct formatting of the reference list will be handled by \bibtex\ in almost all cases, provided that the correct information was entered into the \verb'.bib' file.
Note that ADS entries are not always correct, particularly for older papers and conference proceedings, so may need to be edited.
If in doubt, or if you are producing the reference list manually, see the MNRAS instructions to authors$^{\ref{foot:itas}}$ for the current guidelines on how to format the list of references.
\section{Appendices and online material}
To start an appendix, simply place the \verb'
\section{Introduction}
Recently, the LIGO and Virgo collaborations have directly detected gravitational waves ({GWs}) from merging pairs of black holes and neutron stars thereby opening a new observational window to astrophysics and cosmology (Abott {\it et al.} 2016a, 2016b, 2017). This successful centenary prediction of general relativity is now pressing for world-wide observational efforts involving the next generation of space-based and ground-based detectors of {GWs}, planned to ``listen" unprobed frequency bands from a large variety of sources.
The recent detection of {GWs} is the result of a long process. Implicitly, it also suggests that the existence of numerous sources with different characteristic frequencies is quite probable. Currently, we are just starting the exciting work of studying and characterizing the basic properties of GWs and their potential sources regardless of its cosmic abundance or even whether they are nearby or very far from the solar system.
It is also usually believed that the main observable candidates to GW observations are ultracompact binary black hole and neutron star systems, rotating black holes and supernovas, that is, very massive and extremely compact systems because these violent systems or events can generate gravitational waves intense enough to be detected even at very great distances (Maggiore 2008). However, since these sources are rather exotic it seems interesting to investigate the potentialities of nearby and less extreme sources. In principle, the small distance from nearest sources may compensate their relatively low intensity thereby providing important targets for a continued observation.
In this concern, an increasing number of exoplanetary systems were observed in the last few years, some of them composed by super Jupiters with orbits very near to their parent stars. Such galactic system have recurrently been reported and are much closer to the solar system than known pulsars and binaries of black holes or neutron stars (the only identified sources up to now).
Beyond the expected emission from the orbital motion, usually treated in the quadrupole approximation, the gravitational wave intensity from exoplanets can also be amplified from gravitational interaction, as for instance, through the resonant excitation of oscillating modes from central stars (Kajima 1987; Berti \& Ferrari 2001).
On the other hand, the already observed population of exoplanets can be extrapolated to obtain the abundance of such objects in the Galaxy and even in all the Universe. Recent estimates are claiming the existence of at least one planet per star thereby leading to nearly two hundred billions of exoplanets in the Milky Way (Cassan et al. 2012). Some authors have also predicted the collective contribution of exoplanets appearing as a stochastic GW background (SGWB) from the Milky Way and also from the whole Universe, a result relevant to space-based instruments like LISA. In principle, such an approach may provide near future an interesting window to probe the cosmic abundance of such objects (Ain, Kastha \& Mitra 2015). Here, instead to analyze the collective emission forming the SGWB, a different strategy it will be adopted.
Basically, we are interested on a special class of exoplanetary systems already identified in the very recent literature. This happens because these Galactic GW sources are very near to us and orbiting their parent star with ultra short periods, say, of the order of one hour or less. Further, there is also a growing interest of the community with several large international consortia pointing to an increasing rate of known systems. Thus, it is reasonable to expect that a part of them must have ultra short periods.
The gravitational luminosity of such systems can be even greater than their electromagnetic counterpart, an aspect that may have a strong influence on the so-called habitable planetary zone. Thus, since they are not far away, we believe that such systems are excellent candidates for a new class of targets whose pattern of GWs are not only different from the ones presented by extreme events (like the ringdown of binary black holes) but also have the advantage that the emitted GWs can be continuously detected.
In this Letter we show that exoplanetary systems are also interesting sources of gravitational waves for the next generation of detectors. For a subset of extra solar planets orbiting their parent stars with extremely short periods, we calculate the local GW luminosity, the strain and the conditions for detecting the emitted pattern of gravitational waves. As we shall see, they are within the standard sensitivity curve of LISA and other planned instruments. Reciprocally, we also argue that the GW astronomy may provide a complementary window to identify extrasolar planets, a new procedure that may be even more efficient than the available methods (like the transit time) based on optical instruments and techniques.
\section{Basic Equations}\label{sec:Basic Equations}
The gravitational quadrupole emission from two orbiting celestial massive bodies like an extrasolar system formed by a star and a given planet can be precisely calculated (Peters \& Mathews 1963; Maggiore 2008). If the system have masses $m_1$ and $m_2$ moving in Keplerian orbits around the center of mass with an effective semi-major axis $a$ and eccentricity $e$, the total average gravitational emission over one period of the elliptical motion reads:
\begin{equation}\label{LGW}
L_{GW}=\frac{32}{5}\frac{G^4}{c^5}\frac{m_1^2m_2^2(m_1+m_2)}{a^5{(1-e^2)^{7/2}}}\left(1+\frac{73}{24}e^2+\frac{37}{96}e^4\right) ,
\end{equation}
which is the same equation used to calculate the gravitational luminosity emitted from ultracompact binary systems (Maggiore 2008; Postnov and Yungelson 2014). For a source of absolute luminosity $L_{GW}$, the flux or apparent luminosity ($\ell$) received on Earth is $\ell = L_{GW}/4 \pi d^2$.
It is also widely known that the emitted radiation in the eccentric case is no longer monochromatic. In general, the absolute GW luminosity in the $n^\mathrm{th}$ harmonic, at a frequency $f=n \omega / \pi$, is given by
\begin{equation}
L^{(n)}_{GW} \ = \ \frac{32}{5}\frac{G^4}{c^5}\frac{m_{1}^2 m_2^2(m_1+m_2)}{a^5}B(n,e) \, ,
\label{eq:Power}
\end{equation}
where,
\begin{equation}
\begin{split}
B(n,e) & = \frac{n^4}{32}\bigg(\big[ J_{n-2}(ne)-2eJ_{n-1}(ne) \ + \\
\frac{2}{n} J_n(ne) & + 2eJ_{n+1}(ne)-J_{n+2}(ne)\big]^2 \ + (1-e^2) \times \\
[J_{n-2}(ne) & - 2J_n(ne)+J_{n+2}(ne)]^2 +\frac{4}{3n^2}{[J_n(ne)]}^2\bigg) \, ,
\label{eq:harmonics}
\end{split}
\end{equation}
where $J_n$ denotes the Bessel function of first kind.
The above equations imply that the average radiated power is a rapidly rising function of the eccentricity (Peters \& Mathews 1963). It is also worth noticing that whether a binary system has a non-zero eccentricity and the emission of GWs is strong, its motion rapidly degenerate into a circular orbit. This happens because the average value $ <de/dt>$ is negative in virtue of the radiation reaction.
In what follows, we are interested only in exoplanetary systems with very short periods which potentially may produce reasonably intense GW emission. So, let us approximate (\ref{LGW}) by taking $e=0$ to calculate the GW emission. In practise, this means that we have a lower bound on the absolute GW luminosity. In this case, the frequency of the emitted GW, $f_{GW} = \frac{2}{P}= \frac{1}{\pi}\sqrt{\frac{G(m_1+m_2)}{a^3}}$, is twice the orbital frequency.
Another important quantity when studying gravitational waves is the strain, the perturbation in the space-time metric. To obtain it, let us consider two point masses $m_1$ and $m_2$, but due to our approximation we consider again only circular orbits. In the quadrupole approximation (Landau \& Lifshitz 1985), the GW amplitudes are fully determined by the so-called ``chirp mass'' of the binary system, $M_{\ast} \equiv\mu^{3/5}m^{2/5}$, where $\mu = m_1m_2/(m_1 + m_2)$ is the reduced mass and $m = m_1 + m_2$ is the total mass.
After averaging over the orbital characteristic periods, the standard expression for the GW amplitude is readily obtained (Roelofs {\it{et al.}} 2006; Postnov \& Yungelson 2014):
\begin{eqnarray}
h = \left(\frac{32}{5}\right)^{1/2}\frac{G^{5/3}}{c^4}\frac{M_{\ast}^{5/3}}{d}(\pi f_{GW})^{2/3} \sqrt{cos^{4}i + 6cos^{2}i + 1}
\label{eq02}
\end{eqnarray}
where $i$ is the inclination of the binary system, the angle between the line of sight to the binary orbit. Usually, the inclination effect is small but always increases the strain.
Other key quantity when studying GW from binary systems is the period deviation or, more specifically, the cumulative period variation. By considering $e=0$, such an expression is easily obtained:
\begin{eqnarray}
\frac{\dot P}{P}=-\frac{96}{5}\frac{G^{5/3}\mu m^{2/3}}{c^5} \left( \frac{P}{2\pi}\right)^{-8/3}\,, \label{eq03}
\end{eqnarray}
where the cumulative shift of periastron time expression is
\begin{eqnarray}
\Delta Periastron = \frac{\dot P}{2P} (\Delta t)^2\,,\label{eq04}
\end{eqnarray}
where $\Delta t$ is the time of periastron passage (Maggiori 2008).
Given these well known results, let us now consider a specific sample of short period exoplanetary systems which can be seen as promising targets for a direct GW detection.
\begin{table}
\centering
\caption{Orbital quantities of 14 confirmed short period exoplanetary systems. The data were taken from http://exoplanet.eu/catalog/. Due to their short period, the emitted gravitational power can be measured by the next generation of detectors (see next section).}\label{tab1}
\begin{tabular} {lccccc} \hline
\centering
Planet & $\frac{M_p}{M_J}$ & $\frac{M_s}{M_{\odot}}$ & $P$(day) & $a(10^5km)$ & $d(pc)$ \\ \hline
GP Com b & 26.2 & 0.435 & 0.032 & 2.28 & 75 \\
V396 Hya b & 18.3 & 0.345 & 0.045 & 2.64 & 77 \\
J1433 b & 57.1 & 0.8 & 0.054 & 3.97 & 226 \\
PSR J1807-2459b & 9.4 & 1.4 & 0.070 & 5.58 & 2790 \\
PSR 1719-14b & 1 & 1.4 & 0.090 & 6.58 & 1200 \\
PSR J2051-0827b & 28.3 & 1.4 & 0.099 & 7.05 & 1280 \\
PSR J2241-5236b & 12 & 1.35 & 0.145 & 8.96 & 500 \\
Kepler-70 b & 0.014 & 0.496 & 0.240 & 8.95 & 1180 \\
Kepler-70 c & 0.002 & 0.496 & 0.342 & 11.3 & 1180 \\
Kepler-78 b & 0.005 & 0.81 & 0.355 & 13.7 & 12.64 \\
PSR B1957+20b & 22 & 1.4 & 0.380 & 17.3 & 1530 \\
EPIC 201637175b & 1.4 & 0.6 & 0.381 & 13.0 & 225 \\
CVSO 30 b & 6.2 & 0.39 & 0.448 & 12.6 & 330 \\
Kepler-42 c & 0.006 & 0.13 & 0.453 & 8.75 & 38.7 \\ \hline
\end{tabular}
\end{table}
\section{Exoplanetary (Short Period) Data}
Surely, in comparison with black holes and neutron star binaries, one may expect that exoplanetary systems are relatively weak sources of gravitational waves. However, since they are very near to us, in principle, there may exist a special class of orbiting exoplanets that ripples the space-time beyond the expected stochastic background of GWs whose spectrum peaks at $10^{-5}$Hz (Ain, Kastha \& Mitra 2015) thereby providing favorable conditions for direct detection.
\begin{table}
\centering
\caption{Calculated gravitational wave parameters of 3 exoplanetary systems of extremely short periods which are within the standard LISA sensitivity curve (see next section). The luminosity, $L_{GW}$, is given in erg s$^-1$ and $\dot{P}/{P}$ in s$^{-1}$. In the last column we see the value of the inclination needed to obtain the strain $h$ according to equation (4). }\label{tab2}
\begin{tabular} {lcccc} \hline
Planet & $L_{GW}(10^{30})$ & $h (10^{-22})$ & $\frac{\dot{P}}{P} (10^{-17})$ & $i (rad)$ \\ \hline
GP Com b & $1.45$ & $1.98$& $-3.44$ & $0.97$ \\
V396 Hya b & $0.17$ & $0.98$ & $-0.83$ & $0.91$ \\
J1433 b & $2.69$& $0.89$ & $-2.78$ & $1.47$ \\\hline
\end{tabular}
\end{table}
\begin{figure*}
\centerline{\epsfig{figure=LumGW.eps,width=3.1truein,height=2.5truein}
++\epsfig{figure=PHT.eps,width=3.1truein,height=2.5truein}}
\begin{minipage}[t]{6in} \caption{a) Absolute GW luminosity as a function of the frequency $f_{GW}$. The black dot depict the PSR 1913+16 (H-T) pulsar while the 14 red dots are exoplanetary systems with known keplerian parameters (see Table 1). b) Precession of the periastron. By taking the errors on the orbital parameters we plot the theoretical prediction for the cumulative period shift of the 3 exoplanets listed in Table 2. For comparison we show the standard result for the H-T pulsar (solid black curve).}
\end{minipage}
\end{figure*}
Keeping this in mind, we see from (1) and (5) that systems with greatest masses and smallest semi-major axis - those with shorter periods ($P^2 = 4 \pi^2 a^ 3 / G m) $ - present the most favorable conditions to maximize the GWs emission.
In {Table 1} we list the chosen exoplanets and their basic parameters. As one can see there, the most important orbital data for our calculations are: the mass of the planet in terms of the mass of Jupiter ($M_p/M_J$); the mass of the parent star in terms of the mass of the Sun ($ M_s/M_{\odot}$); the orbital period ($P$); the distance of the planet to the star ($a$); and the distance from the system to Earth ($d$). It has been organized in descending order of the orbital period. It should also be noticed that the periods of all exoplanets are restricted on the interval $0.032 \leq P (days) \leq 0.453$. Note also that some planets have masses equivalents to Earth ($M_E\simeq 0.00315 M_J$), and other solar planets.
In {Table 2} we have selected a subset containing the most promising GW emitters formed by exoplanets and their parent stars based on the above criterion (shorter periods, see also {Table 1}).
The associated parameters in {Table 2} are: The calculated $L_{GW}$ and strain $h$ appearing in the first and second columns, respectively. In the third column we depicted the time variation of the orbital period, and, finally, in the fourth column, we show the orbital inclination angle of the selected subsystem ($i$). As we shall see, this last information is also interesting because it represents for exoplanets a severe restriction to some optical methods when compared with the detection by gravitational waves (see section 4).
As far as we know, such objects are endowed with the most favorable orbital parameters whose GW pattern is detectable at least by two distinct instruments: (i) indirectly through the SKA measurements of the cumulative orbital phase shift of the periastron time, and (ii) directly by the space-based LISA (see section 4).
Observations and/or discovery of exoplanets is a very active field of research, and thus the number of objects is expected to climb substantially over the next few years. In this way, even more extreme systems, those with much shorter periods, may be discovered.
It should also be noticed that at least for the J1433 b system the electromagnetic luminosity, $(3.1 \pm 0.1)\times 10^{-4}L_{\odot} \simeq 1.18\times 10^{30}$ erg s$^{-1}$ (Hern\'andez Santisteban {\it{et al.}} 2016; Showman 2016), is nearly two times smaller than the GW emission, $\simeq 2.69\times 10^{30}$ erg s$^{-1}$. Potentially, a GW emission at this level may alter significantly the planetary habitable zone for this sort of systems. As we shall see next, these ultra short period exoplanetary probes, mainly binary systems like the ones shown in Table 2, are also suitable targets for the next generation of GWs detectors. Another interesting possibility is the discovery of exoplanets of ultra short periods through gravitational waves (see next section).
\section{Discussion}
It is widely known that Hulse and Taylor indirectly measured GWs from the binary radio pulsar PSR 1913+16 and tested the predictions of general relativity based on its cumulative deviation of the periastron. We argue here that the same can also be done for a subset of exoplanets, starting by the three short period systems listed in {Table 2}.
In {Figure 1a} we display the calculated GW luminosity as a function of the frequency for the 14 binary systems (red-points) appearing in Table 1. For comparison we have also shown (see black dot) the Hulse-Taylor pulsar.
To see how the distance is crucial, we recall that the binary Hulse-Taylor (H-T) pulsar emits $\sim 7.5\times 10^{31} erg s^{-1}$, it is at $8.4$ kpc and has cumulative period shift of the periastron of $45$ seconds in 33 years (Weisberg, Nice \& Taylor 2010). The three proposed targets have emission $\sim 10^{30} erg s^{-1}$ and distances of the order $75 - 226$ pc while their cumulative period deviation fall between $5 - 20$ seconds (see Table 2 and Figure 1b). In general, the ratio between the apparent GW luminosities of exoplanet systems (Es) and other binary systems [e.g., pulsar systems (Ps)] arriving at the Earth surface reads:
\begin{equation}
\frac{\ell^{Es}}{\ell^{Ps}} = \frac{L^{Es}_{GW}}{L^{Ps}_{GW}}\left[\frac{d^{Ps}}{d^{Es}}\right]^{2}\,.
\end{equation}
where $d^{Es}$ and $d^{Ps}$ are the corresponding distances. This result follows directly from the standard $d^{-2}$ distance law (see section 2). In particular, for the exoplanets of Table 2 and the H-T pulsar, the corresponding ratios are, respectively: 242, 27 and 50. Thus, the GW flux on Earth surface from short period exoplanetary systems can be much greater than the one from H-T pulsar.
In {Figure 1b} we show the theoretical prediction for the cumulative deviation of the periastron by taking into account the orbital parameters (objects for lines blue, green and red are indicated in the insert). The black line stands for the well known H-T pulsar. By comparing with the three predicted curves for the exoplanets with the binary radio H-T pulsar one may see the interest to observe this subset of exoplanets with the same techniques. In principle, such objects can be investigated through a combination of radio and optical observations, as usually done for white dwarfs binaries and pulsars (Taylor \& Weisberg 1989; Antoniadis {\it{et al.}} 2013).
In {Figure 2} we display the calculated strain as predicted from orbital parameters of the exoplanets versus the GW frequency. The black line represents the LISA sensitivity curve (Larson \& Hiscock 2000; Prince, Tinto \& Larson 2002), while the red circles are the exoplanetary systems of Table 1. The LISA sensitivity curve was obtained using the typical data: signal to noise ratio $1.0$, arm length $5.0\times 10^{9}$ meters, laser power $1.0$W, etc. - more details in Larson's personal page http://www.srl.caltech.edu/$\sim$shane/sensitivity/ - in this connection see also also Petiteau et al. (2008). For comparison we also show the strain associated to the H-T Pulsar. Clearly, one may conclude that the objects of Table 2 can be detected by the space-based LISA instrument.
It thus follows that short period exoplanetary systems can be considered as a distinct subset of binaries sources forming suitable targets for prospecting gravitational waves. In principle, the possibility of detection must be enhanced for the next generation of space-based and ground-based instruments.
Now, let us finish this section drawing attention to some interesting physical effects of gravitational waves from exoplanetary systems of ultra short period to different areas:
\begin{itemize}
\item The planetary habitable zone is, primarily, the distance to the parent star where liquid water may exist. Thus, exoplanetary systems whose GW luminosity is of the same order or greater than the electromagnetic luminosity from the central star (see the specific example in Section 3) may change significantly the planetary habitable zones as long as there is a mechanism converting gravitational radiation into heat. Corrections of the order of $(L_{GW}/L_{EM})^{1/2}$ where $L_{EM}$ is the electromagnetic luminosity, are expected. This could be the first direct connection involving general relativistic effects, habitable zone and the possibility of formation and maintenance of life. The physical consequences of GW for circumstellar habitable zones deserves a closer scrutiny and it will be detailed investigated in a forthcoming communication.
\item To date many multiple exoplanetary systems were already discovered (see, for instance, Luger {\it et al.} 2017). The presence of any inner short period planet will change not only the local habitable zone but also creates new interesting possibilities. The remaining planets behave like gravitational antennas by absorbing and transforming in heat part of the incident GWs energy. This is interesting because the energy changes in planets are well modeled, especially Earth-like planets whose electromagnetic environmental interaction has been discussed for decades (Coughlin \& Harms 2014; Lopes \& Silk 2015; Mulargia 2017). Any observed anomalous thermal behavior may impose constraints on the cross section and also in the interaction between matter and the incident gravitational waves. In principle, this kind of observation could be used to test new aspects of general relativity and other gravity theories.
\item Detection of exoplanets by optical techniques is a time-consuming task. For transiting time, for instance, this happens because not all planet's orbit as seen from the Earth have the precise geometry to eclipse, and, as such, the probability to obtain the right narrow range of inclinations is very low (the transit probability to the Earth viewed outside from Solar System is less than 1\%). Actually, precise transit time measurements require nearly edge-on planetary orbits observable only by a special class of observers. Apart measurements with enough precision, time sampling and spectroscopic follow-up observations, the low probability also explains why a great number of stars must be searched before expecting to find a transiting planet. However, this is not the case for a direct detection through gravitational waves. For ultra short period systems like the ones appearing in Table 2, the detection of gravitational waves may provide an interesting tool for discovering new exoplanets, in principle, even more efficient than the available optical methods.
All these connections reinforce the idea that nearby short period exoplanetary systems provide a key class of GW emitters which may be relevant both from a methodological and a physical viewpoint. Potentially, as argued here, such systems are capable to open new avenues of investigation.
\end{itemize}
\begin{figure}
\centerline{\epsfig{figure=Strain.eps,width=3.4truein,height=2.8truein}}
\caption{Strain versus frequency for the exoplanets listed in Table 1. Black solid line is a characteristic LISA sensitivity curve for one year of integration and typical parameters as mentioned in the text (see Larson {\it et al.} 2000). Note that the 3 objects within the blue elipse also appearing in Table 2 may be detected by LISA.}
\end{figure}
\section{Conclusions}
Based on some already observed sources we have shown that a subset of ultra short period exoplanetary systems are suitable targets to direct detection of gravitational waves for the next generation (space-based) instruments (see {Table 2} and {Figure 2}). In principle, as shown in ({Figure 1b}), even indirect observations of gravitational waves through the cumulative time variation of the periastron for this sort of extrasolar planets should be considered an interesting possibility.
The examples discussed here suggest the existence of a subset of nearby exoplanetary systems composed by relatively massive bodies endowed with small orbital period thereby making the GW emission (and the associated strain) strong enough to be detected from Earth. Although less intense than extreme binary systems, the gravitational wave emission of ultra short period exoplanets are interesting targets for the next generation of planned instruments.
Some interesting observational consequences are: (i) the gravitational wave emission must change the electromagnetic habitable zone around multi-exoplanetary systems; (ii) limits on the absorption cross section of the gravitational wave interacting with matter can be constrained by the outer planets working like gravitational antennas absorbing and decreasing the original signal, and (iii) the emitted gravitational wave pattern may provide an efficient tool to discover new ultra short period exoplanets. Hopefully, studies in this field may bring valuable results to different areas including astrobiology, physics and astrophysics.
\section*{Acknowledgements}
The authors thank L. A. Almeida, J. D. Nascimento and C. E. Pellicer, for helpful discussions. JASL is grateful to CAPES (PROCAD project, 2013), FAPESP (LLAMA Project) and fellowship from CNPq. The basic ideas of this paper were discussed during the 3rd Workshop on Cosmology and Gravitation: Celebrating the 100 years of Cosmology (1917- 2017) in Natal-RN, Brazil.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,745 |
class Point(object):
def __init__(self, x, y):
self._x = x
self._y = y
# Сравнение
def __eq__(self, other):
if not isinstance(other, Point):
return NotImplemented
return self._x == other._x and self._y == other._y
def __ne__(self, other):
return not (self == other)
# hash
def __hash__(self):
return hash((self._x, self._y))
# Арифметика
# Точки можно складывать и вычитать.
def __add__(self, other):
if not isinstance(other, Point):
return NotImplemented
return Point(self._x + other._x, self._y + other._y)
def __sub__(self, other):
if not isinstance(other, Point):
return NotImplemented
return Point(self._x - other._x, self._y - other._y)
@property
def x(self):
return self._x
@property
def y(self):
return self._y
def __radd__(self, other):
if not isinstance(other, Point):
return NotImplemented
return other + self
def __rsub__(self, other):
if not isinstance(other, Point):
return NotImplemented
return other - self
#
print Point(1, 2) == Point(1, 2)
print Point(1, 2) == 1
print {Point(1, 2): 0}
print {Point(1, 2): 0}
Point(1, 2) + Point(2, 3)
print Point(3, 5)
Point(1, 2) - Point(2, 3)
print Point(-1, -1) | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,698 |
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"redpajama_set_name": "RedPajamaC4"
} | 6,686 |
Shaji
Music is not to be learnt but to be felt
Mehdi Hassan – The Music Eternal
We part now
We may meet again in dreams
Like the dried up flower
That blooms between pages of an old book...
-Mehdi Hassan Ghazal
It was an afternoon of this past June, when I was talking to a friend of mine in his factory. I had in my hands a good length of metal wire, chancing my strength, when I received an SMS from my music friend Babu from Bangalore. Frozen in shock by the message, I had strained my hands against the metal wire and blood dripped from the cut finger on my left hand. Tears welled up in my eyes. Suddenly the world was dead to me and I simply walked out of the place, wandering aimlessly under the hot sun. Mehdi Hassan, my ideal ghazal singer was no more! Where am I to go? In a weird hallucination his songs went floating one by one in my mind. When I started writing articles on music in Tamil six years ago, the one on Mehdi Hassan was among the very first. I had dedicated my book of articles on music, 'Isaiyin Thanimai' in Tamil, to Mehdi Hassan. For me Mehdi Hassan was not a musician's name, but the name of a deeply felt emotion.
Mehdi Hassan was the living example of the singing heights at which a singer can continue to sing decade after decade, of how a singer should render his songs in an impeccable pitch, completely naturally and totally true to music and yet be emotionally overwhelming. His utterly devoted fans addressed him respectfully as 'Khan Sahib'. He was the builder of the bridge, entirely with the sweetness of his music, between two nations that had lived in hatred for 65 years. That summer day, well and truly cooked by an angry sun, the great singer, a perennial source of my sensitivity to the truth of music, passed away. The voice that held us spell-bound, rendering thousands of ghazals with an out-of-this-world musical chastity, will never again waft live in the airwaves!
Thar Desert in the North Eastern part of Rajasthan holds many villages hostage to desiccating hot winds by day and biting cold by night. Luna is one such village which is wracked to this day by terrible shortage of water and lack of any kind of progress. Pokhran, where India 'tests' its nuclear devices, is not very far away from here. Indian border with Pakistan is not very far, either. It was in this village that Mehdi Hassan was born on 18th July of 1927. It was a big joint family, a family of musicians. His father and his uncles were all classical singers. Rajasthan means a province of kings. Mehdi Hassan was born in a traditional family of musicians who were court musicians for 12 generations in one court or the other of the kings of the many small vassal 'kingdoms' of the area. But the Indian Classical 'dhrupad' music which was their forte was not the musical form 'approved' for or by Muslims.
Dhrupad is a classical form of music created out of devotional songs that were sung in Hindu temples since many centuries. The Hindu kings were the patrons who sustained the evolution of this form of music. The singers who were Muslims largely followed the 'khayal' system of music that evolved from thirteenth century onwards from singing traditions brought from Persia, the modern day Iran, and patronized by Muslim rulers. There were pressures, direct and indirect, that Muslim singers adopt only 'Khayal' singing. However, Mehdi Hassan's forefathers did not change to 'khayal' singing. They continued to be 'dhrupad' singers in the courts of Hindu kings.
It was a custom to call Muslim musicians 'Ustad' and the Hindu musicians 'Pundit'. But musicians from Mehdi Hassan's family were called 'Pundits' because of their 'dhrupad' singing traditions. The founding doyens of Hindustani music like Mian Tansen and Abdul Karim Khan had all converted to Islam from Hinduism. Mian Tansen who was reputed to have lit a lamp by singing the Raag Deepak and brought rains by singing Raag Megha Malhar was born as Ramdhanu Mishra! Grand father of Ustad Abdul Karim Khan, the founder of Agra Gharana, was again a Hindu who converted to Islam.
Mehdi Hassan's grandfather, Imamuddin Khan was not only the court singer of the ruler of Rajaputana, but he also sang in the courts of Kings of Nepal, Indore and Baroda. The then King of Nepal was his disciple as well. Mehdi Hassan's father Azeem Khan and maternal uncle Ismail Khan were court singers at the courts of small kingdoms like Manakpur, Chattarpur and Bijawal. And they taught and opened the doors of musicdom to Mehdi Hassan. He was taught both 'dhrupad' and 'khayal' singing.
Mehdi Hassan began to perform as a mature vocalist at the age of eight, but did not have the benefit of a formal education. His very first concert was at the court of Maharaja of Baroda, where he rendered the alaap of Raag Basant for forty minutes. Patronage by kings enabled Mehdi Hassan to perform in many courts of kings of small provinces and live a fairly comfortable life and grow with his music. Along with riyaaz of music, he was training his body with regular exercise. He nurtured his body with a sumptuous diet of mutton, milk and nuts. He strongly believed that a well-built body and strong lungs were essential for a good singer.
And then came 1947. Mehdi Hassan was 20 years old. Indian subcontinent was heaving towards freedom. The small kingdoms and their courts faced the prospect of being swept away. Mehdi Hassan's entire family, making a living with music supported only by the courts of these small-time rulers, was pushed to face frighteningly uncertain times. Indian subcontinent was partitioned into India and Pakistan, as a condition precedent to Independence, and Muslim and Hindu minorities were frightened and forced to emigrate. Ominous slogans of 'Pakistan for Muslims' and 'Hindustan for Hindus' began to be raised and Mehdi Hassan's family, leaving all their possessions, found refuge in the town of Chichawatni in Pakistani Punjab.
Going was tough in the new environment and family was living in dire poverty. Mehdi Hassan worked as an assistant in a cycle repair shop to support his family. His father, a genius in music, started a fuel wood shop, finding no other way to make a living. Mehdi Hassan was so hurt by the stark reality facing them that he started a cycle repair shop of his own. The effort flopped and he found work as an assistant in a workshop repairing cars and tractors. Somehow, he earned his daily keep. But even in such dire times, he did not give up his music practice, not even for a day.
When a little money came to his hand, he left for Lahore, where the then Radio Pakistan had a station, looking for opportunities. There, many who heard him praised his singing style. He even got the opportunity of singing a song for the Radio. Everyone spoke of the difference in his singing style. But no follow-up opportunity came his way. Frustrated, he started working in the farm of a person known to him. He worked day and night for the next eight months on the arid desert-like two acres field and made it lush green.
He used the money earned from the enterprise to make another foray in search of opportunities, this time in Karachi, the centre of Urdu films in Pakistan. That was in 1956 when he was 29. This time he was able to immediately secure a few singing opportunities. The first song was the ghazal 'Nazar milte hi dil ki bat ka labon par charcha na ho jaye' in the film Shikar. The same year opportunities came to sing and record six more film songs.
Mehdi Hassan, with great self-confidence, stayed in Karachi. But, he secured a mere two songs in the five years that followed. He found it tough competing with great playback singers of those days like Munir Hussain, Saleem Raza and Inayat Hussain Bhatti. Truth to tell, nobody in the film industry of those days liked Mehdi Hassan's style of rendering which was more like singing to his own self without any exaggerated expression of emotions. On the other hand, the songs he sang in those days over the radio was broadcast all over Pakistan was widely noticed.
In those days, Noor Jehan who had emigrated from India during India-Pakistan partition was at the height of her popularity both as singer and actress. In one late night broadcast, she happened to hear Mehdi Hassan's ghazal ' Yeh Dhua Sa Kahaan Se Uththa Hai'. She was simply stunned and wanted to meet Mehdi Hassan immediately. After the ghazal Jis ne mere dil ko dard diya' in the Sasural in 1962 Mehdi Hassan became Pakistan's most important playback singer. In the twenty years that followed it was he who sang all the ghazal songs of the Pakistani films.
Though these songs were released first as film songs, Mehdi Hassan later elaborated them in different forms and popularized them as stage ghazals. Apart from these, he also created many special ghazals in his own music and it was through these ghazals that Mehdi Hassan became famous outside Pakistan. His ghazal music attracted much more fans in India, Nepal and Gulf countries than in Pakistan itself. He has sung many thousands of songs in Urdu, Punjabi, Hindi, Rajasthani, Marwari, Sindhi, Pashto, Bengali, Persian and Arabic. But his repertoire of over two thousand ghazals was truly the world of Mehdi Hassan's music.
I doubt if another singer like Mehdi Hassan had been born in the history of man. The musical silence that he infuses between the lines and words of his ghazals cannot be heard but can only be felt. When we lose ourselves in his ghazals we are overwhelmed by sorrow and pain like waves in the sea during the high tide. But we never once desire to come out of them. When he renders 'Dekhna Bhi To Unhe, Door Se Dekha Karna' our eyes moisten in memory of the love that had disappeared for ever from our life. It makes us feel the sorrows of all men who live bearing the pain of true love lost for ever. The voice and rendering style of Mehdi Hassan is the alter ego of the pain, sacrifice, dedication and resurrection of love. The clarion call of that voice is that death is preferable to a life without love. Many ghazals like 'Kya Toota Hai Andar Andar' of Mehdi Hassan have the ability to melt even the stoniest of human minds.
Mehdi Hassan was born to be a total ghazal singer and nothing else. His song is the soul that animates his lines and his music. His rendering style conveys the impression that he sings entirely for his own self. There is no place there for exaggerated emotions or artificial pretensions or the egotistic 'come and watch my musical prowess' challenges.
His rendering is totally innocent of pyrotechnics or forced emotions. Yet he sings in a fashion that all the emotions of his ghazals strike the chords in the depths of our heart. If this is not magic what is it? Mehdi Hassan's ghazals are woven with endless ecstasies of simple ragas and meanings expressed in exact words and tones. Mehdi Hassan raised ghazal singing, once looked down upon as the art of high class courtesans, to the level of khayal and dhrupad singing and even better, he won for it the popular respect and appreciation.
Even when Mehdi Hassan was a great classical singer with ability to render any difficult classical raga with all its emotions and nuances in detail, he chose the lighter version of the classical music, the ghazal, as his signature form of music. He effortlessly expressed the many dimensions of classical music through ghazal. He brought the many finer points of dhrupad and khayal singing besides scintillating expressions of Rajasthani folk music into his ghazal rendering. Naturally no other ghazal singer in this world could match the soft touch, nuances, the poetic touch, the bubbling emotions, the magical silences that Mehdi Hassan delineated in his rendering. The music form of ghazal which had over ten centuries of tradition was rejuvenated to popularity by Mehdi Hassan. In fact the popular opinion is that Mehdi Hassan has bequeathed to the world a new music form, The Mehdi Hassan ghazal.
Mehdi Hassan mostly rendered the ghazals penned by the great poets of Urdu and Persian literature. But when he renders Shola Tha Jal Bujha Hoon, Dil Ki Baat Labon Par Lakar, Zindagi Mein To Sabhi Pyaar Kiya Karte Hain, Ranjish Hi Sahi Dil Dukhaane Ke Liye Aa, Yoon Zindagi Ki Raah Mein, Bhooli Bisri Chand Umeedein.. etc, the lines of these poems become Mehdi Hassan's own lines, his very own music animated by the indescribable depth and sorrows of his voice.
Mehdi Hassan was decorated with every possible award that a musician can win in Pakistan. King of Nepal had accorded him the highest award of his land. He was accorded the Saigal Award in India. Mehdi Hassan, who counted hundreds of prominent people from the world of Music, Cinema and Politics like Dilip Kumar, Amitabh Bachhan, Lata Mangeshkar, Jagjit Singh, Atal Behari Vajpayee, Manmohan Singh, Hariharan and Shreya Ghosal as his fans, not to mention millions like me from all over the world as die-hard fans, was essentially simplicity, honesty and humaneness personified.
A few years after the two horrifying and debilitating wars were fought between India and Pakistan, Mehdi Hassan came to India in 1978 to stay a few days in his native village of Luna. He was most pained to see that his native place still did not have connecting roads or electricity or water supply. He announced that he was not going to participate in the dinner being hosted in his honour at the residence of Governor of Rajasthan.
The village of Luna was given electricity supply facilities within three days. When the Government told him that they did not have the financial allocation for roads and water supply, he offered to raise funds through a ghazal concert in the nearby town of Jhunjhuna. Nearly 15,000 fans thronged the concert organized with the help of the Government. He donated the entire fund collected for the development works in the village of Luna. Mehdi Hassan was moved to tears by the sight of poor students being taught under the trees, squatting on the ground, in the Government Primary School in his native village, due to paucity of rooms. He arranged to build two class rooms at his own expense!
Towards the end of 1990s, his hemiplegia and lung problems caused Mehdi Hassan to retire from music. In the year 2000, he came to Kottakkal Arya Vaidhyashala in Kerala, looking for a cure to his diseases. The event then organized in Kozhikkode was the last time Mehdi Hassan ascended the stage! There was some temporary relief, but no lasting cure resulted from the treatment. An event was organized in Mumbai in 2008 to honour him. But since some Pakistanis were behind the terrible terrorist attack that year, Mehdi Hassan could not come to India, being a Pakistani!
In this period, amidst all his debilitating health problems, Mehdi Hassan composed and sang a song with Lata Mangeshkar, fulfilling her long time wish! He sang and recorded his portion of the song in Pakistan and sent the tape to Lata Mangeshkar. The song Tera Milna Bahut Acha Lage Hai was released only in 2011 through the album 'Sarhadein'(Borders).
Mehdi Hassan spent his last years in terrible misery. He was struggling to breath because of his lung problems that was the result of constant singing without a break from the age of five. He also suffered from Parkinson's disease and was bed-ridden the last few years, unable to recognize people. Seeing the pathetic condition in which he was lying in a Karachi Nursing Home unable to pay for his treatment, media had made it a headline news everywhere!
Mehdi Hassan had 14 children through his two wives. Many of them live in places like America! But it was his lot to live in a dilapidated house with peeling paint and broken steps during his last days. He had not mastered the art of deal-making to encash his out-of-this-world music. Countless were the free events and causes that he sang for during his lifetime. He lived a great and humane life trusting only his music, truth and hard work.
He was called the Voice of God by many! He was by far the best ghazal singer ever born. But he did not have, in his old age, the money even for the medicines he needed! Today Mehdi Hassan is liberated from all his sorrows and lies in eternal state with his immortal music as his guard of honour.
Ilaahi Aansu Bhari Zindagi Kisi Ko Na De…..
Dear God!
Please don't bequeath to anyone
A Life filled with tears alone!
Push no one into the depths of total helplessness!
Posted by SHAJI at 12:10 PM
The art of listening music is a gift of nature like the art of creating music. Man does not learn music but he feels it.
shaajichennai@gmail.com
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">RMail | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,923 |
Q: Problema con Login de mysql php ajax html con apache cordova Estoy haciendo una aplicación basada en web con cordova, ya tengo el splash y el frontend de la aplicación, pero quiero hacer el login y que se conecte a la base de datos del servidor.
Para esto tengo un archivo llamado www/Login.html tengo dos input y jalo su valor por el id, al momento de dar clic, hago una función para que me los compare con un php que esta alojado en un servidor, los paso por POST y que inicie la función cuando le de clic al botón de login, pero no paso de la autenticación, se queda trabado.
No me dice errores solo eso "authenticating". Espero y me puedan ayudar. Lo estoy probando un un celular y no en un emulador.
<html>Email: <input id="email" type="email" placeholder="" /> <br />
Password: <input id="password" type="password" placeholder="" /> <br />
<button id="loginButton">Login</button>
<button id="registerButton">Register</button>
<br />
Message: <p id="status"></p></html>
Email: <input id="email" type="email" placeholder="" /> <br />
Password: <input id="password" type="password" placeholder="" /> <br />
<button id="loginButton">Login</button>
<button id="registerButton">Register</button>
<br />
Message: <p id="status"></p>
<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>
<script>
$(document).ready(function () {
var url = "https://get-data.php";
$("#loginButton").click(function () {
var email = $.trim($("#email").val());
var password = $.trim($("#password").val());
$("#status").text("Authenticating...");
var loginString = "email=" + email + "&password=" + password + "&login=";
$.ajax({
type: "POST", crossDomain: true, cache: false,
url: url,
data: loginString,
success: function (data) {
if (data == "success") {
$("#status").text("Login Success..!");
localStorage.loginstatus = "true";
window.location.href = "Portal.html";
}
else if (data == "error") {
$("#status").text("Login Failed..!");
}
}
});
});
});
</script>
<?php
$con = mysqli_connect("","","","") or die("connection error");
$email = $_POST['email'];
$password = $_POST['password'];
if(isset($_POST['register']))
{
$register = mysqli_num_rows(mysqli_query($con, "SELECT * FROM `users` WHERE `email`='$email'"));
if($register == 0)
{
$insert = mysqli_query($con,"INSERT INTO `users` (`email`,`password`) VALUES ('$email','$password')");
if($insert)
echo "success";
else
echo "error";
}
else if($register != 0)
echo "exist";
}
else if(isset($_POST['login']))
{
$login = mysqli_num_rows(mysqli_query($con, "SELECT * FROM `users` WHERE `email`='$email' AND `password`='$password'"));
if($login != 0)
echo "success";
else
echo "error";
}
mysqli_close($con);
?>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,977 |
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