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{"url":"https:\/\/discuss.d2l.ai\/t\/gradient-descent\/351","text":"Hi, I would like to ask a question on the formula (11.3.12). Why do we calculate the gradient of the vector x instead of the function f(x)? Should it be \u201cxx\u2212\u03b7diag(Hf)^(\u22121)\u2207f(x)\u201d here? Thank you!\n\nGreat catch @nxby! Would you like to post a PR and be a contributor?\n\nThank you @goldpiggy! I\u2019ve just made a pull request.\n\nHi, I wonder if there is a typo in the sentence just below the formula (11.3.11): \"Plugging in the update equations leads to the following bound e_{k+1} <= e^2_k f'''(\\xi_k)\/f'(x_k)\u2018\u2019, instead of \u201ce_{k+1} <= e^2_k f'''(\\xi_k)\/f'(x_k)\u201d, shouldn\u2019t it be \u201ce_{k+1} <= \\frac{1}{2} e^2_k f'''(\\xi_k)\/f''(x_k)\u201d? Thanks a lot for your attention.\n\nThanks. I revised this part recently and made it slightly different from the previous version. Just let me know if you spot any issue.\n\nThe Peano R_n of Taylor expansion got one extra power, which was wrong.","date":"2023-02-08 21:08:19","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\": 0.8403751254081726, \"perplexity\": 992.502353860982}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"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-2023-06\/segments\/1674764500904.44\/warc\/CC-MAIN-20230208191211-20230208221211-00433.warc.gz\"}"}
| null | null |
{"url":"http:\/\/mkweb.bcgsc.ca\/pnas\/","text":"Lips that taste of tears, they say, are the best for kissing.get crankymore quotes\n\n# making poetry out of spam is fun\n\nIn Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017\n\n# visualization + design\n\nCover image accompanying our article on mouse vasculature development. Biology turns astrophysical. PNAS 1 May 2012; 109 (18) (zoom, PNAS)\n\n# Creating the PNAS Cover\n\nOne of my goals in life, which I can now say has been accomplished, is to make biology look like astrophysics. Call it my love for the Torino Impact Hazard Scale.\n\nRecently, I was given an opportunity to attend to this (admittedly vague) goal when Linda Chang from Aly Karsan's group approached me with some microscopy photos of mouse veins. I was asked to do \"something\" with these images for a cover submission to accompany the manuscript.\n\nWhen people see my covers, sometimes they ask \"How did you do that?\" Ok, actually they never ask this. But being a scientist, I'm trained me to produce answers in anticipation of such questions. So, below, I show you how the image was constructed.\n\nThe image was published on the cover of PNAS (PNAS 1 May 2012; 109 (18))\n\n## Tools\n\nPhotoshop CS5, Nik Color Efex Pro 4, Alien Skin Bokeh 2 and a cup of coffee from a Rancilio Silvia.\n\n## source images\n\nBelow are a few of the images I had the option to work with. These are mouse embryonic blood vessels, with a carotid artery shown in the foreground with endothelial cells in green, vascular smooth muscle cells in red and the nuclei in blue.\n\nOf course, as soon as I saw the images, I realized that there was very little that I needed to do to trigger the viewer's imagination. These photos were great!\n\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\nMouse carotid arteries. (zoom)\n\n## memories of star trek\n\nImmediately I thought of two episodes of Star Trek (original series): Doomsday Machine and the Immunity Syndrome, as well as of images from the Hubble Telescope.\n\nEnterprise is about to be consumed by a horror tube: a planet killer! (The Doomsday Machine)\nEnterprise heads into a giant amoeba. Who eats whom? I'll let you guess. (The Immunity Syndrome)\nOrion nebula (M42) as seen by the Hubble telescope. (zoom)\n\nI though it would be pretty easy to make the artery images look all-outer-spacey. They already looked it.\n\n## centerpiece image\n\nAnd then I saw the image below.\n\nA particularly spectacular image of a mouse carotid artery. I'm thinking 10 on the Torino scale. (zoom)\n\n## constructing the cover\n\n### background\n\nThe background was created from the two images shown here. The second image was sampled three times, at different rotations.\n\nImages used for background. (zoom)\nImages used for background. (zoom)\nLayer composition for background elements. (zoom)\n\nThe channel mixer was used to remove the green channel and leave only red and blue.\n\nBackground elements for PNAS cover image. (zoom)\n\n### middle ground\n\nThe next layer was composed of what looked like ribbons of blue gas. This was created by sampling the oval shapes from the source images. Here the red channel was a great source for cloud shapes, and this was the only channel that was kept. The hue was shifted to blue and a curve adjustment was applied to increase the contrast.\n\nFirst set of middle ground elements, before adjustments. (zoom)\nFirst set of middle ground elements, after channel adjustments. (zoom)\nSecond set of middle ground elements. (zoom)\nLayer composition for middle ground elements. (zoom)\n\nWhen the foreground and middle ground elements were combined, the result was already 40 parsecs away.\n\nBackground and foreground elements for PNAS cover image. (zoom)\n\n### foreground\n\nThe foreground was created from the spectacular comet-like image of a mouse artery. Very little had to be done to make this element look good. It already looked good.\n\nI applied a little blur using Alien Skin's Bokeh 2 to narrow the apparent depth of field, masked out elements at the bottom of the image and removed some of the green channel. The entire blue channel was removed altogether (this gave the tail of the comet a mottled, flame-like appearance).\n\nForeground element, after channel adjustments. (zoom)\nLayer composition for foreground element. (zoom)\n\n### post processing\n\nInitial composition of background, middle ground and foreground elements. (zoom)\n40% localized application of Nik's Tonal Contrast (Color Efex 4 plugin) to increase structure in red channel. (zoom)\n50% blend with Nik's Pro Contrast (Color Efex 4 plugin). (zoom)\n\nAnd here we have the final image.\n\nFinal PNAS cover. Spacey! (zoom)\nVIEW ALL\n\n# Find and snap to colors in an image\n\nSat 29-12-2018\n\nOne of my color tools, the $colorsnap$ application snaps colors in an image to a set of reference colors and reports their proportion.\n\nBelow is Times Square rendered using the colors of the MTA subway lines.\n\nColors used by the New York MTA subway lines.\n\nTimes Square in New York City.\nTimes Square in New York City rendered using colors of the MTA subway lines.\nGranger rainbow snapped to subway lines colors from four cities. (zoom)\n\n# Take your medicine ... now\n\nWed 19-12-2018\n\nDrugs could be more effective if taken when the genetic proteins they target are most active.\n\nDesign tip: rediscover CMYK primaries.\n\nMore of my American Scientific Graphic Science designs\n\nRuben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.\n\n# Predicting with confidence and tolerance\n\nWed 07-11-2018\nI abhor averages. I like the individual case. \u2014J.D. Brandeis.\n\nWe focus on the important distinction between confidence intervals, typically used to express uncertainty of a sampling statistic such as the mean and, prediction and tolerance intervals, used to make statements about the next value to be drawn from the population.\n\nConfidence intervals provide coverage of a single point\u2014the population mean\u2014with the assurance that the probability of non-coverage is some acceptable value (e.g. 0.05). On the other hand, prediction and tolerance intervals both give information about typical values from the population and the percentage of the population expected to be in the interval. For example, a tolerance interval can be configured to tell us what fraction of sampled values (e.g. 95%) will fall into an interval some fraction of the time (e.g. 95%).\n\nNature Methods Points of Significance column: Predicting with confidence and tolerance. (read)\n\nAltman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843\u2013844.","date":"2019-01-24 07:28:35","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\": 0.3377087116241455, \"perplexity\": 6266.6015636014645}, \"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-2019-04\/segments\/1547584519382.88\/warc\/CC-MAIN-20190124055924-20190124081924-00463.warc.gz\"}"}
| null | null |
3.1 What is Palmers Skin Success Eventone Fade?
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\section{Introduction}
\begin{theorem} \label{gap}
Four mutually tangent spheres form two gaps. In each of these gaps, there is a unique way to inscribe four mutually tangent spheres in such a way that, for each one of these spheres, there is exactly one of the original spheres that is not tangent to this one (and the non-tangent sphere is different for each of the four inscribed spheres).
\end{theorem}
\begin{example} \label{octuref}
Consider the planes $z=1$ and $z=-1$ and the $2$ spheres of radius $1$ and centers $(-1,-1,0)$ and $(-1,1,0)$. These form a set of $4$ mutually tangent spheres, which define two gaps, in each of which we can inscribe $4$ spheres according to the procedure defined before.
\\
In one of the gaps, the two spheres of radius $1$ and centers $(1,1,0)$ and $(1,-1,0)$, and the two spheres of radius $\frac{1}{2}$ and centers $(0,0,\frac{1}{2})$ and $(0,0,-\frac{1}{2})$ can be inscribed.
\begin{center}
\includegraphics[scale=0.24]{3dpack.jpg}
\end{center}
\end{example}
\begin{proof}[Proof of Theorem \ref{gap}]
Using a M\"{o}bius transformation, a rotation, a translation and a scaling, one can transform any configuration of four mutually tangent spheres into the configuration seen in Example \ref{octuref}. In this case, the result can be proven using simple geometry.
\end{proof}
Thus, in either of the two gaps formed by four mutually tangent spheres, we can pack four more spheres, forming an octuple. In each octuple, the spheres come in four pairs: each sphere can be paired with the only sphere in the octuple which does not touch it. The spheres of a pair do not touch each other, but are tangent to all the six other spheres in the octuple.
\\
Now, pick four mutually tangent spheres amongst those in the octuple. They again form two gaps, in which, using Theorem \ref{gap}, we can pack four new spheres. Repeating the process results in what we will call a generalized Apollonian sphere packing.
\\
This construction is a generalization to the $3$-dimensional case of the work of Guettler and Mallows in \cite{Mallows}. Analogously to the classical Apollonian circle or sphere packings, and to the generalized Apollonian circle packings, this kind of constructions is the source of several questions. One of them, which will be tackled here, concerns the curvatures (the inverses of the radii) of the spheres appearing in the packing.
\\
The first section will be dedicated to generalities. It will be shown that the curvatures can be described using the orbit under the action of a certain group of integral matrices on a certain vector depending on the packing. This will allow us to study the case of integral sphere packings, in which the spheres all have integer curvatures.
\\
In the second section, we will use a method due to Sarnak \cite{Sarnak} to prove the local-global principle for generalized Apollonian sphere packings. This method was originally used in an attempt to prove the strong positive density conjecture for Apollonian circle packings. It happened to be insufficient, and the proof needed further work by Bourgain and Fuchs \cite{Bourgain} and then Bourgain and Kontorovich \cite{Konto}. In the case of sphere packings, and similarly to the work of Kontorovich on the classical Apollonian sphere packings \cite{Konto2}, Sarnak's method happens to be strong enough, as being in a $3$-dimensional case adds more variables to the problem which ultimately comes to studying the integers represented by a quadratic form.
\\
It should be noted that a similar, but independent, proof has been very recently submitted on arXiv by K. Nakamura \cite{Nakam}.
\subsection*{Acknowledgements}
I would like to thank my supervisor, Professor Andrew Granville, for discussions that greatly helped me with my work and Professor Alex Kontorovich who took time to answer my questions. I would also like to thank my friends Oleksiy Klurman, Crystel Bujold, Kevin Henriot, Mohammad Bardestani, Daniel Fiorilli and Marzieh Mehdizadeh for their helpful comments.
\section{Generalities}
We begin with some generalities about generalized Apollonian sphere packings. Most of this section is a direct generalization of \cite{Mallows}. Their notations and method will be used here.
\\
A sphere $\mathcal{S}$ of curvature (or bend) $b$ (the inverse of its radius) and center $(x,y,z)$ can be described by its ``augmented bend, bend*center'' ($abbc$) coordinates $\textbf{a}(\mathcal{S})=(\overline{b},b,bx,by,bz)$, where $\overline{b}$ is the curvature of the sphere that is the inverse of $\mathcal{S}$ in the unit sphere, that is
\begin{equation*}
\overline{b}=b(x^2 + y^2 + z^2) - \frac{1}{b} \, .
\end{equation*}
For planes, which are considered as spheres of infinite radius, this definition needs to be modified. If our plane has equation $p_1x + p_2y + p_3z = h$, with $(p_1,p_2,p_3)$ a unit vector, we define its $abbc$ coordinates to be $(2h,0,p_1,p_2,p_3)$.
\subsection{Octuples of spheres}\
In the following, an octuple configuration will denote a set of eight spheres obtained from the procedure of Theorem \ref{gap}. As explained in the introduction, an octuple can be seen as a set of four pairs of spheres, where a pair of spheres consists in a sphere in the octuple and the only sphere that is not tangent to it. The spheres in a pair will usually be denoted by $\mathcal{S}$ and $\mathcal{S}'$.
\begin{remark} \label{outer}
In the case where we have an outer sphere enclosing the seven other spheres, this sphere will be given a negative curvature. There can only be one sphere with a negative curvature in an octuple (and in a packing).
\end{remark}
Let
\begin{equation*}
\textbf{W} = \begin{pmatrix}
0 & -\frac{1}{2} & 0 & 0 & 0 \\
-\frac{1}{2} & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix} \, .
\end{equation*}
\begin{lemma} \label{lem1}
Let $\mathcal{S}_1$ and $\mathcal{S}_2$ be two spheres. Then,
\begin{align*}
\textbf{a}(\mathcal{S}_1) \textbf{W} \textbf{a}(\mathcal{S}_2)^t &= 1 \text { if } \mathcal{S}_1=\mathcal{S}_2 \\
&=-1 \text{ if } \mathcal{S}_1 \text{ and } \mathcal{S}_2 \text{ are externally tangent}.
\end{align*}
\end{lemma}
\begin{proof}
Easy computations.
\end{proof}
\begin{remark}
If, as in Remark \ref{outer}, we define the curvature of the outer sphere to be negative, we still have $\textbf{a}(\mathcal{S}_1) \textbf{W} \textbf{a}(\mathcal{S}_2)^t = -1$ if the spheres are internally tangent.
\end{remark}
\begin{lemma} \label{lem2}
Let $\mathcal{S}$ and $\mathcal{S}'$ be two non-tangent spheres in an octuple configuration. Then,
\begin{equation*}
\textbf{a}(\mathcal{S}) \textbf{W} \textbf{a}(\mathcal{S}')^t = -3 \, .
\end{equation*}
\end{lemma}
\begin{proof}
This can be easily proven for the octuple introduced in the previous example. Any octuple can be seen as the image by a M\"{o}bius transformation of this configuration, i.e., a composition of rotations, translations, scalings and inversions in the unit sphere. Thus, we just have to study the effect of rotations, translations, scalings and inversions in the unit sphere on the $abbc$ coordinates of a sphere.
\\
\\
Let $\textbf{a}(\mathcal{S})$ be the $abbc$ coordinates of a sphere $\mathcal{S}$. Then,
\begin{itemize}
\renewcommand{\labelitemi}{$\bullet$}
\item a scaling by $\lambda$ consists in replacing $\textbf{a}(\mathcal{S})$ by $\textbf{a}(\mathcal{S}) \textbf{m}$, where
\begin{equation*}
\textbf{m}=\begin{pmatrix}
\frac{1}{\lambda} & 0 & 0 & 0 & 0 \\
0 & \lambda & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix} \, ,
\end{equation*}
\item a rotation consists in replacing $\textbf{a}(\mathcal{S})$ by $\textbf{a}(\mathcal{S}) \textbf{m}$, where
\begin{equation*}
\textbf{m}=\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & \cos \theta & -\sin \theta \\
0 & 0 & 0 & \sin \theta & \cos \theta
\end{pmatrix} \text{ or }
\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & \cos \theta & 0 & \sin \theta \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & -\sin \theta & 0 & \cos \theta
\end{pmatrix} \text{ or }
\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & \cos \theta & -\sin \theta & 0 \\
0 & 0 & \sin \theta & \cos \theta &0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix} \, ,
\end{equation*}
\item a translation by a vector $(x,y,z)$ consists in replacing $\textbf{a}(\mathcal{S})$ by $\textbf{a}(\mathcal{S}) \textbf{m}$, where
\begin{equation*}
\textbf{m}=\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
x^2 + y^2 + z^2 & 1 & x & y & z \\
2x & 0 & 1 & 0 & 0 \\
2y & 0 & 0 & 1 &0 \\
2z & 0 & 0 & 0 & 1
\end{pmatrix} \, ,
\end{equation*}
\item the inversion in the unit sphere consists in replacing $\textbf{a}(\mathcal{S})$ by $\textbf{a}(\mathcal{S}) \textbf{m}$, where
\begin{equation*}
\textbf{m}=\begin{pmatrix}
0 & 1 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 &0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix} \, .
\end{equation*}
\end{itemize}
Now, it can easily be checked that $\textbf{m} \textbf{W} \textbf{m}^t=\textbf{W}$ for any of the previous matrices.
\end{proof}
\begin{lemma}
In an octuple containing the spheres $\mathcal{S}_1$ and $\mathcal{S}_1'$, $\mathcal{S}_2$ and $\mathcal{S}_2'$, $\mathcal{S}_3$ and $\mathcal{S}_3'$, $\mathcal{S}_4$ and $\mathcal{S}_4'$, we have
\begin{equation*}
\textbf{a}(\mathcal{S}_1) + \textbf{a}(\mathcal{S}_1') = \textbf{a}(\mathcal{S}_2) + \textbf{a}(\mathcal{S}_2') = \textbf{a}(\mathcal{S}_3) + \textbf{a}(\mathcal{S}_3') = \textbf{a}(\mathcal{S}_4) + \textbf{a}(\mathcal{S}_4') \, .
\end{equation*}
\end{lemma}
\begin{proof}
For $1 \leq j \leq 4$, let $\textbf{w}_j=\frac{\textbf{a}(\mathcal{S}_j)+\textbf{a}(\mathcal{S}_j')}{2}$.
\\
From Lemmas \ref{lem1} and \ref{lem2}, we have that $\textbf{w}_i \textbf{W} \textbf{w}_j^t = -1$ for every $1 \leq i,j \leq 4$. Therefore, if $\textbf{F}_j$ is the $5 \times 5$ matrix with rows $\textbf{a}(\mathcal{S}_1), \textbf{a}(\mathcal{S}_2), \textbf{a}(\mathcal{S}_3), \textbf{a}(\mathcal{S}_4)$ and $\textbf{w}_j$, we have
\begin{equation} \label{FKF}
\textbf{F}_i \textbf{W} \textbf{F}_j^t = \textbf{K} = \textbf{F}_j \textbf{W} \textbf{F}_j^t
\end{equation}
with
\begin{equation*}
\textbf{K}=\begin{pmatrix}
1 & -1 & -1 & -1 & -1 \\
-1 & 1 & -1 & -1 & -1 \\
-1 & -1 & 1 & -1 & -1 \\
-1 & -1 & -1 & 1 & -1 \\
-1 & -1 & -1 & -1 & -1
\end{pmatrix} \, .
\end{equation*}
This gives us that $\textbf{F}_i=\textbf{F}_j$ for every $1 \leq i,j \leq 4$. This implies that $\textbf{w}_i = \textbf{w}_j$ for every $1 \leq i,j \leq 4$.
\end{proof}
This result allows us to use the following convenient representation of any octuple.
\begin{definition} \label{defi}
Given an octuple containing the spheres $\mathcal{S}_1$ and $\mathcal{S}_1'$, $\mathcal{S}_2$ and $\mathcal{S}_2'$, $\mathcal{S}_3$ and $\mathcal{S}_3'$, $\mathcal{S}_4$ and $\mathcal{S}_4'$, we define a matrix $\textbf{F}$ associated to the octuple to be a matrix whose first four rows are the $abbc$ coordinates of four of the spheres (one from each pair) and the fifth row is the average of the $abbc$ coordinates of the two spheres of any pair.
\end{definition}
\begin{remark}
Since we can choose the pairs in different orders and since we have two choices of a representative for each pair, there are (at most) $384$ different $\textbf{F}$ matrices associated to the same octuple.
\end{remark}
\begin{theorem} \label{eq}
Let $\mathcal{S}_1$, $\mathcal{S}_2$, $\mathcal{S}_3$ and $\mathcal{S}_4$ be four mutually tangent spheres with respective curvatures $b_1,b_2,b_3,b_4$, enclosing two gaps. Then, the curvatures of the two sets of four spheres that can be inscribed in these gaps are given by $(2\omega - b_1,2\omega - b_2,2\omega - b_3,2\omega - b_4)$ and $(2\omega' - b_1,2\omega' - b_2,2\omega' - b_3,2\omega' - b_4)$, where $\omega$ and $\omega'$ are the roots of
\begin{equation} \label{equa}
2\omega^2 - 2 \omega (b_1+b_2+b_3+b_4) + b_1^2+b_2^2+b_3^2+b_4^2=0
\end{equation}
\end{theorem}
\begin{proof}
Using (\ref{FKF}), we have that $\textbf{F} \textbf{W} \textbf{F}^t = \textbf{K}$, thus $\textbf{F}^t \textbf{K}^{-1} \textbf{F} = \textbf{W}^{-1}$. Looking at the $(2,2)$ element of this equation gives us (\ref{equa}).
\end{proof}
\subsection{Generalized sphere packings}\
Given four mutually tangent spheres, enclosing two gaps, we have a unique way to inscribe four mutually tangent spheres in each of these gaps using the construction of Theorem \ref{gap}. The four original mutually tangent spheres belong to two different octuples. Equation (\ref{equa}) of Theorem \ref{eq} allows us to pass from one to another, since it implies that $\omega + \omega' = b_1 + b_2 + b_3 + b_4$.
\\
More precisely, if $\textbf{F}$ is the matrix associated to one of these octuples, with its first four rows containing the $abbc$ coordinates of the four original spheres, then the other octuple can be described by the matrix $\textbf{A}_5 \cdot \textbf{F}$, where
\begin{equation*}
\textbf{A}_5=
\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
1 & 1 & 1 & 1 & -1
\end{pmatrix} \, .
\end{equation*}
Any octuple of spheres is described by a matrix $\textbf{F}$, which explicitly gives the $abbc$ coordinates of four of the spheres in the octuples. Using the definition of the last row of $\textbf{F}$, the $abbc$ coordinates of the other spheres can be retrieved by looking at the products $\textbf{A}_i \cdot \textbf{F}$, $1 \leq i \leq 4$, where
\begin{align*}
\textbf{A}_1 = \begin{pmatrix}
-1 & 0 & 0 & 0 & 2 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix}, \quad \textbf{A}_2 = \begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 2 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix}, \\ \textbf{A}_3 = \begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 2 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix}, \quad \textbf{A}_4 = \begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & -1 & 2 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix} \, .
\end{align*}
Repeating the process of inscribing spheres in the gaps results in a generalized Apollonian sphere packings. Therefore, the set of $abbc$ coordinates of spheres in the packing is exactly the set of the first four coordinates of matrices in the orbit $\mathcal{A} \cdot \textbf{F}$, where $\mathcal{A}$ is the group
\begin{equation*}
\mathcal{A} = \langle \textbf{A}_1,\textbf{A}_2,\textbf{A}_3,\textbf{A}_4,\textbf{A}_5 \rangle \, .
\end{equation*}
\begin{remark}
The packing can be constructed from any octuple it contains.
\end{remark}
\begin{lemma} \label{inte}
If the curvatures of any octuple in a generalized Apollonian sphere packing are integers (or, equivalently, the second column of a matrix $\textbf{F}$ associated to this octuple has integer coordinates), then the same holds for all the spheres in the packing. Such a packing is called an integral generalized Apollonian sphere packing.
\\
If the curvatures of any octuple in an integral generalized Apollonian sphere packing are coprime (or, equivalently, the second column of a matrix $\textbf{F}$ associated to this octuple has coprime coordinates), then the same holds for any octuple in the packing. Such a packing is called a primitive integral generalized Apollonian sphere packing.
\end{lemma}
\begin{proof}
Let $(b_0,b_1,b_2,b_3,b_4,b'_0,b'_1,b'_2,b'_3,b'_4)$ be any integral octuple in the packing and $\omega$ the average of the curvatures in each pair. We have $2\omega \in \mathbb{Z}$. Now, from (\ref{eq}), we also have that $2 \omega^2 \in \mathbb{Z}$. Therefore, $\omega \in \mathbb{Z}$. Reciprocally, if $\omega \in \mathbb{Z}$ and $b_0,b_1,b_2,b_3,b_4$ are all integers, the same holds for all the spheres in the octuple.
\\
\\
Hence, the integrality of an octuple of curvatures is the same as the integrality of the second column of the matrix associated to this octuple.
\\
The group $\mathcal{A}$ is generated by matrices with integer coefficients. Therefore, if the second column of a matrix $\textbf{F}$ associated to some octuple in the packing has integer coordinates, the same will be true for the second column of the matrix associated to any octuple in the packing, since we just have to look at matrices in the orbit $\mathcal{A} \cdot \textbf{F}$.
\\
\\
Suppose that the octuple $(b_0,b_1,b_2,b_3,b_4,b'_0,b'_1,b'_2,b'_3,b'_4)$ is such that
\begin{equation*}
gcd(b_0,b_1,b_2,b_3,b_4,b'_0,b'_1,b'_2,b'_3,b'_4)=1 \, .
\end{equation*}
We have $gcd(b_1,b_2,b_3,b_4,b'_1,b'_2,b'_3,b'_4) =gcd(b_1,b_2,b_3,b_4,2\omega)=1$. Therefore, $gcd(b_1,b_2,b_3,b_4,\omega)=1$.
\\
\\
Reciprocally,
\begin{equation*}
gcd(b_1,b_2,b_3,b_4,\omega)=1 \Longrightarrow gcd(b_1,b_2,b_3,b_4,2\omega)=1 \text{ or } 2 \, .
\end{equation*}
But it cannot be $2$, since from (\ref{eq}) we would have $2| \omega$ and then $gcd(b_1,b_2,b_3,b_4,\omega)=2$. Hence, $gcd(b_0,b_1,b_2,b_3,b_4,b'_0,b'_1,b'_2,b'_3,b'_4)=gcd(b_1,b_2,b_3,b_4,2\omega)=1$.
\\
Now, one can easily see that the multiplication by any matrix of $\mathcal{A}$ does not change the $gcd$ of $(b_1,b_2,b_3,b_4,\omega)$.
\end{proof}
\begin{lemma} \label{parit}
Let $b_1,b_2,b_3,b_4$ be the curvatures of four mutually tangent spheres in a primitive octuple. Then, amongst $b_1,b_2,b_3,b_4$, there are two even numbers and two odd numbers. Furthermore, the two odd numbers are congruent modulo $4$.
\end{lemma}
\begin{proof}
First, we reduce equation (\ref{eq}) $\bmod{2}$. This yields
\begin{equation*}
b_1+b_2+b_3+b_4 = 0 \bmod{2} \, .
\end{equation*}
We have $3$ possibilities for the parities of the $b_1,b_2,b_3,b_4$
\begin{itemize}
\renewcommand{\labelitemi}{$\bullet$}
\item $b_1,b_2,b_3,b_4$ are all even,
\item $b_1,b_2,b_3,b_4$ are all odd,
\item there are $2$ even elements and $2$ odd elements amongst $b_1,b_2,b_3,b_4$.
\end{itemize}
$b_1,b_2,b_3,b_4$ cannot all be even by primitivity, since we would have $gcd(b_1,b_2,b_3,b_4,2\omega)=2$, which is impossible.
\\
\\
Suppose that $b_1,b_2,b_3,b_4$ are all odd. Looking at equation (\ref{eq}) $\bmod{4}$ gives $2\omega^2 = 0 \bmod{4}$, thus $\omega$ is even. Now, $\bmod{8}$, the same equation gives $b_1^2 + b_2^2 + b_3^2 +b_4^2 = 0 \bmod{8}$, but, since $b_1,b_2,b_3,b_4$ are all odd, $b_1^2 + b_2^2 + b_3^2 +b_4^2=4 \bmod{8}$.
\\
\\
Therefore, there are $2$ even elements and $2$ odd elements amongst $b_1,b_2,b_3,b_4$. Looking at the equation (\ref{eq}) $\bmod{4}$, we deduce that $\omega$ is odd. Suppose, without loss of generality, that $b_1,b_2$ are the two odd elements and that they are not congruent modulo $4$. Looking at equation (\ref{eq}) $\bmod{8}$ yields
\begin{equation*}
-2\omega(b_3+b_4)+(b_3+b_4)^2 \equiv 4 \bmod{8} \Rightarrow (b_3+b_4)(b_3+b_4-2\omega) \equiv 4 \bmod{8}
\end{equation*}
But, since $\omega$ is odd, $b_3+b_4-2\omega \equiv b_3+b_4 -2 \bmod{4}$, which makes it impossible for $(b_3+b_4)(b_3+b_4-2\omega)$ to be $4 \bmod{8} $.
\end{proof}
\begin{lemma} \label{odd}
In any primitive integral packing, all the odd curvatures are congruent modulo $4$.
\end{lemma}
\begin{proof}
From the previous lemma, the two odd curvatures of our starting octuple are congruent modulo $4$. Now, one can easily check that, since $\omega$ is odd, none of the matrices of $\mathcal{A}$ changes the residue modulo $4$ of an odd element.
\end{proof}
Similarly to the classical Apollonian circle or sphere packing case, or to the generalized Apollonian circle packing case, we can define the notion of root octuple, which is the \enquote{minimal} octuple in the packing, in the sense that it describes the biggest spheres in the packing (it is the octuple with the smallest $\omega$).
\begin{definition}
Let $v^t=(a,b,c,d,\omega)$ be an octuple in the packing $\mathcal{P}$. $v^t$ is said to be a root octuple if $a \leq 0 \leq b \leq c \leq d \leq \omega$ and $\omega \leq a+b+c+d$.
\end{definition}
\begin{remark}
Analogously to the classical Apollonian circle or sphere packing case, or to the generalized Apollonian circle packing case, the root octuple is unique. Like in these kinds of packings, there is a reduction algorithm that allows us, from any octuple in $\mathcal{P}$, to find the root octuple.
\end{remark}
\section{The local-global principle}
In this section, we will use a method of Sarnark \cite{Sarnak} to prove the local-global principle for integral generalized Apollonian sphere packings. We are only interested in the curvatures and no longer need to use the full matrix $\textbf{F}$ associated to an octuple. We will only focus on the second column of this matrix, in which the first four coordinates are the curvatures of four spheres (one in each pair) in the octuple and the fifth coordinate is the average of the curvatures in each pair.
\\
$\mathcal{P}$ will always denote a primitive integral generalized Apollonian sphere packing. Let $v_{\mathcal{P}}^t=(a_0,b_0,c_0,d_0,\omega_0)^t$ be the root octuple of the $\mathcal{P}$. Using Lemma \ref{parit}, two elements amongst $a_0,b_0,c_0,d_0$ are even and two are odd. Relabeling $a_0,b_0,c_0$ or $d_0$, we can assume that $a_0$ is even and $b_0$ is odd. If $a_0 = 0$, we can replace $a_0$ by $2\omega - a_0$ to make it non-zero. Notice that $a_0 + b_0$ will be odd and positive, since if $a_0 < 0$, we have $b_0 > \vert a_0 \vert$ (because in this case the sphere of curvature $b_0$ is inside the one of curvature $a_0$). We will again call this vector $v_{\mathcal{P}}^t$. Notice that such a $v_{\mathcal{P}}^t$ might no longer be a root quadruple.
\begin{theorem} \label{curva}
Let $v_{\mathcal{P}}^t=(a_0,b_0,c_0,d_0,\omega_0)^t$ as above. Then, the set of curvatures of spheres in $\mathcal{P}$ contains the set of integers of the form
\begin{equation*}
f_{a_0}(\alpha_1,\alpha_2,\beta_1,\beta_2) - a_0 \quad \text{with} \quad \text{gcd}_{\mathbb{Z}[i]}(\alpha_1 + i \alpha_2,\beta_1 + i\beta_2) = 1
\end{equation*}
where $f_{a_0}$ is the following positive definite integral quaternary quadratic form
\begin{equation*}
f_{a_0}(x,y,z,t)=A_0 x^2 + A_0 y^2 + 4D_0 z^2 + 4D_0 t^2 + 4xt B_0 - 4 yz B_0 + 4xz C_0 + 4yt C_0
\end{equation*}
\begin{align*}
A_0 = a_0 + b_0, \quad
B_0 = -\frac{a_0 + b_0 + c_0 + d_0 - 2\omega_0}{2}, \\
C_0 = -\frac{a_0 + b_0 + c_0 - d_0}{2}, \quad
D_0 = a_0 + c_0 \, .
\end{align*}
\end{theorem}
\begin{proof}
As seen before, the set of curvatures of spheres in the packing is exactly the set of the first four coordinates of vectors in the orbit $\mathcal{A} \cdot v_{\mathcal{P}}^t$.
\\
\\
We will focus on the smaller orbit $\mathcal{A}_1 \cdot v_{\mathcal{P}}^t$, where
\begin{equation*}
\mathcal{A}_1 = \langle \textbf{A}_2,\textbf{A}_3,\textbf{A}_4,\textbf{A}_5 \rangle \, .
\end{equation*}
This subgroup of $\mathcal{A}$ leaves the first coordinate of any vector invariant. Using Theorem \ref{eq}, we know that, for any vector $(a_0,b,c,d,\omega)$ in this orbit,
\begin{equation*}
2\omega^2 - 2 \omega (a_0+b+c+d) + a_0^2+b^2+c^2+d^2=0 \, .
\end{equation*}
The change of variables $(x_2,x_3,x_4,x_5) = (b + a_0, c + a_0, d + a_0,\omega + a_0)$ allows us to rewrite the equation as
\begin{equation} \label{eqmod}
Q(x_2,x_3,x_4,x_5)=2x_5^2 - 2 x_5(x_2 + x_3 + x_4) + x_2^2 + x_3^2 + x_4^2 = -2 a_0^2
\end{equation}
and, in the context of the orbit, is equivalent to conjugating the group $\mathcal{A}_1$ to $\mathcal{A}_1' = U^{-1} \mathcal{A}_1 U$ where
\begin{equation*}
U=\begin{pmatrix}
1 & 0 & 0 & 0 & 0 \\
-1 & 1 & 0 & 0 & 0 \\
-1 & 0 & 1 & 0 & 0 \\
-1 & 0 & 0 & 1 & 0 \\
-1 & 0 & 0 & 0 & 1 \\
\end{pmatrix} \, .
\end{equation*}
$\mathcal{A}_1'$ is isomorphic to $\Gamma = \langle \textbf{M}_2,\textbf{M}_3,\textbf{M}_4,\textbf{M}_5 \rangle$, where
\begin{align*}
\textbf{M}_2=\begin{pmatrix}
-1 & 0 & 0 & 2 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix} \, , \quad&
\textbf{M}_3=\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 2 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix} \, , \\
\textbf{M}_4=\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & -1 & 2 \\
0 & 0 & 0 & 1
\end{pmatrix} \, , \quad&
\textbf{M}_5=\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
1 & 1 & 1 & -1
\end{pmatrix} \, .
\end{align*}
The action of $\mathcal{A}_1$ on $v_0^t$ can be understood by studying the action of $\Gamma$ on $u_0^t=(x_2^0,x_3^0,x_4^0,x_5^0)^t = (b_0 + a_0,c_0 + a_0, d_0 + a_0,\omega_0 + a_0)^t$. We also have that $\Gamma \leq O_{Q}(\mathbb{Z})$.
\\
\\
We make another change of variables, $(x_2,x_3,x_4,x_5)=(A,D,A+2C+D,A+B+C+D)$. This allows us to rewrite the equation as
\begin{equation*}
\Delta(A,B,C,D)=B^2 + C^2 - AD = -a_0^2 \, .
\end{equation*}
In the context of the orbit, it is equivalent to conjugating the group $\Gamma$ to $G=V^{-1} \Gamma V$ where
\begin{equation*}
V=\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
1 & 0 & 2 & 1 \\
1 & 1 & 1 & 1
\end{pmatrix} \, .
\end{equation*}
Then, $G = \langle \textbf{g}_2,\textbf{g}_3,\textbf{g}_4,\textbf{g}_5 \rangle$ where
\begin{align*}
\textbf{g}_2 = \begin{pmatrix}
1 & 2 & 2 & 2 \\
0 & 0 & -1 & -1 \\
0 & -1 & 0 & -1 \\
0 & 0 & 0 & 1
\end{pmatrix} \, , \quad&
\textbf{g}_3 = \begin{pmatrix}
1 & 0 & 0 & 0 \\
-1 & 0 & -1 & 0 \\
-1 & -1 & 0 & 0 \\
2 & 2 & 2 & 1
\end{pmatrix} \, ,
\\
\textbf{g}_4 = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix} \, , \quad&
\textbf{g}_5 = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix} \, ,
\end{align*}
and $G \leq O_{\Delta}(\mathbb{Z})$. Let $G'= G \cap SO_{\Delta}(\mathbb{Z}) = \langle \textbf{g}_2\textbf{g}_3,\textbf{g}_2\textbf{g}_4,\textbf{g}_2\textbf{g}_5,\textbf{g}_3\textbf{g}_4,\textbf{g}_3\textbf{g}_5,\textbf{g}_4\textbf{g}_5 \rangle$.
\\
Proceeding as in Chapter 13.9 of \cite{Cassels} or as in \cite{Konto2}, we have the morphism
\begin{equation}
\begin{array}{ccc}\rho:\textrm{PSL}_2(\mathbb{C}) &\longrightarrow & \textrm{SO}_{\Delta}(\mathbb{R})\\
{\left(\begin{array}{ll}\alpha&\beta\\ \gamma&\delta\\ \end{array}\right)}&{\longmapsto}&{\begin{pmatrix}
|\alpha|^2 & 2 \Im(\beta \overline{\alpha}) & 2 \Re(\beta \overline{\alpha}) & |\beta|^2 \\
\Im(\alpha \overline{\gamma}) & \Re(\overline{\alpha} \delta - \overline{\beta} \gamma) & \Im(\alpha \overline{\delta} + \beta \overline{\gamma}) & \Im(\beta \overline{\delta}) \\
\Re(\alpha \overline{\gamma}) & \Im( \overline{\alpha} \delta - \overline{\beta} \gamma) & \Re(\alpha \overline{\delta} + \beta \overline{\gamma}) & \Re(\beta \overline{\delta}) \\
|\gamma|^2 & 2 \Im(\delta \overline{\gamma}) & 2 \Re(\delta \overline{\gamma}) & |\delta|^2
\end{pmatrix}
}\\
\end{array} \, .
\end{equation}
Let
\begin{align*}
\textbf{M}_1=\begin{pmatrix}
1 & 1+i \\
-1+i & -1
\end{pmatrix} \, , \quad&
\textbf{M}_2=\begin{pmatrix}
i & -1+i \\
0 & -i
\end{pmatrix} \, ,
\\
\textbf{M}_3=\begin{pmatrix}
(-1+i)\frac{\sqrt{2}}{2} & i\sqrt{2} \\
0 & (-1-i)\frac{\sqrt{2}}{2}
\end{pmatrix} \, , \quad&
\textbf{M}_4=\begin{pmatrix}
i & 0 \\
-1-i & -i
\end{pmatrix} \, ,
\\
\textbf{M}_5=\begin{pmatrix}
(-1+i)\frac{\sqrt{2}}{2} & 0 \\
-i\sqrt{2} & (-1-i)\frac{\sqrt{2}}{2}
\end{pmatrix} \, , \quad&
\textbf{M}_6=\begin{pmatrix}
(1+i)\frac{\sqrt{2}}{2} & 0 \\
0 & (1-i)\frac{\sqrt{2}}{2}
\end{pmatrix} \, .
\end{align*}
Then, we have
\begin{align*}
\rho(\textbf{M}_1)=\textbf{g}_2\textbf{g}_3 \, , \quad \rho(\textbf{M}_2)=\textbf{g}_2\textbf{g}_4 \, , \\
\rho(\textbf{M}_3)=\textbf{g}_2\textbf{g}_5 \, , \quad \rho(\textbf{M}_4)=\textbf{g}_3\textbf{g}_4 \, , \\
\rho(\textbf{M}_5)=\textbf{g}_3\textbf{g}_5 \, , \quad \rho(\textbf{M}_6)=\textbf{g}_4\textbf{g}_5 \, .
\end{align*}
Let $\mathcal{M}=\langle \textbf{M}_1, \textbf{M}_2, \textbf{M}_3, \textbf{M}_4, \textbf{M}_5, \textbf{M}_6 \rangle$. A brute force search gives
\begin{align*}
\textbf{M}_6 \textbf{M}_4 \textbf{M}_2 \textbf{M}_4 \textbf{M}_6^{-1} \textbf{M}_2^{-1} &=\begin{pmatrix}
1 & 2 \\
0 & 1
\end{pmatrix} \, , \quad
\textbf{M}_5^{-1} \textbf{M}_4^{-1} \textbf{M}_6^{-1} \textbf{M}_5^{-1} \textbf{M}_6^{-1} \textbf{M}_4 =\begin{pmatrix}
1 & 0 \\
2 & 1
\end{pmatrix} \, , \\
\textbf{M}_4^{-1} \textbf{M}_6^{-1} \textbf{M}_5 &=\begin{pmatrix}
1 & 0 \\
2i & 1
\end{pmatrix} \, , \quad
\textbf{M}_6^{-1} \textbf{M}_1 \textbf{M}_5 \textbf{M}_6 \textbf{M}_5^{-1} \textbf{M}_7 =\begin{pmatrix}
1 & 2i \\
0 & 1
\end{pmatrix} \, , \\
\textbf{M}_2 \textbf{M}_1 \textbf{M}_5 \textbf{M}_4^{-1} \textbf{M}_5 &=\begin{pmatrix}
i & 0 \\
0 & -i
\end{pmatrix} \, , \quad
\textbf{M}_3^{-1} \textbf{M}_2 \textbf{M}_6^{-1} \textbf{M}_4^{-1} \textbf{M}_3^{-1} \textbf{M}_5^{-1} \textbf{M}_4^{-1} \textbf{M}_6^{-1} \textbf{M}_5=\begin{pmatrix}
1+2i & 2 \\
2 & 1-2i
\end{pmatrix} \, , \\
\textbf{M}_4^{-1} \textbf{M}_5 \textbf{M}_6 &\textbf{M}_1^{-1} \textbf{M}_3^{-1} \textbf{M}_4^{-1} \textbf{M}_6^{-1} \textbf{M}_1^{-1} \textbf{M}_2^{-1} \textbf{M}_4=\begin{pmatrix}
1-2i & 2i \\
-2i & 1+2i
\end{pmatrix} \, , \\
\textbf{M}_6^{-1} \textbf{M}_2^{-1} &\textbf{M}_6^{-1} \textbf{M}_4^{-1} \textbf{M}_5^{-1} \textbf{M}_6^{-1} \textbf{M}_2^{-1}=\begin{pmatrix}
1+2i & 2i \\
-2i & 1-2i
\end{pmatrix} \, .
\end{align*}
This set of matrices generates the following subgroup of the Picard group $PSL_2(\mathbb{Z}[i])$
\begin{equation*}
\Xi = \Gamma(2) \cup \begin{pmatrix}
i & 0 \\
0 & -i
\end{pmatrix} \Gamma(2)
\end{equation*}
where $\Gamma(2)$ is the principal congruence subgroup of $PSL_2(\mathbb{Z}[i])$
\begin{equation*}
\Gamma(2) = \left\lbrace \begin{pmatrix}
\alpha & \beta \\
\gamma & \delta
\end{pmatrix} \in PSL_2(\mathbb{Z}[i]) \text{ such that } \begin{pmatrix}
\alpha & \beta \\
\gamma & \delta
\end{pmatrix} \equiv \begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix} \bmod{2} \right\rbrace \, .
\end{equation*}
More precisely, as proven in \cite{Fine}, $\Gamma(2)$ is the normal closure of $\langle \begin{pmatrix}
1 & 2 \\ 0 & 1
\end{pmatrix}, \begin{pmatrix}
1 & 2i \\ 0 & 1
\end{pmatrix} \rangle$ in $PSL_2(\mathbb{Z}[i])$. Since the generators of $PSL_2(\mathbb{Z}[i])$ are known, one can compute all the conjugates and show that the matrices above generate a normal subgroup of $PSL_2(\mathbb{Z}[i])$, which therefore contains $\Gamma(2)$, hence contains $\Xi$.
\\
\\
Therefore,
\begin{align*}
V \rho(\Xi) V^{-1} \subset \Gamma \Rightarrow V \rho(\Xi ) V^{-1} . u_0^t \subset \Gamma . u_0^t \, .
\end{align*}
Let
\begin{equation*}
\begin{pmatrix}
A_0 \\ B_0 \\ C_0 \\ D_0
\end{pmatrix} = V^{-1} . u_0^t = \begin{pmatrix}
a_0 + b_0 \\ -\frac{a_0 + b_0 + c_0 + d_0 - 2\omega_0}{2} \\ -\frac{a_0 + b_0 + c_0 - d_0}{2} \\ a_0 + c_0
\end{pmatrix} \, .
\end{equation*}
From Lemma \ref{parit}, we know that this vector has integer coordinates. Using the definition of $\rho$, we have that the set of vectors of the form
\begin{equation} \label{set}
V \begin{pmatrix}
|\alpha|^2 & 2 \Im(\beta \overline{\alpha}) & 2 \Re(\beta \overline{\alpha}) & |\beta|^2 \\
\Im(\alpha \overline{\gamma}) & \Re(\overline{\alpha} \delta - \overline{\beta} \gamma) & \Im(\alpha \overline{\delta} + \beta \overline{\gamma}) & \Im(\beta \overline{\delta}) \\
\Re(\alpha \overline{\gamma}) & \Im( \overline{\alpha} \delta - \overline{\beta} \gamma) & \Re(\alpha \overline{\delta} + \beta \overline{\gamma}) & \Re(\beta \overline{\delta}) \\
|\gamma|^2 & 2 \Im(\delta \overline{\gamma}) & 2 \Re(\delta \overline{\gamma}) & |\delta|^2
\end{pmatrix} \begin{pmatrix}
A_0 \\ B_0 \\ C_0 \\ D_0
\end{pmatrix}
\end{equation}
with
\begin{equation*}
\begin{pmatrix}
\alpha & \beta \\
\gamma & \delta
\end{pmatrix} \in \Xi
\end{equation*}
forms an explicit subset of the orbit $\Gamma . u_0^t$.
\\
\\
Considering the change of variables we used, the integers of the form $x_2 - a_0$, $x_3 - a_0$, $x_4 - a_0$ and $x_5 - a_0$, when $(x_2,x_3,x_4,x_5)^t$ runs through the orbit $\Gamma . u_0^t$, appear in the second, third, fourth and fifth coordinates of vectors in the orbit $\mathcal{A}_1 . v_0^t$.
\\
\\
In particular, from (\ref{set}), we have that the integers of the form
\begin{equation*}
|\alpha|^2 A_0 + 2\Im(\beta \overline{\alpha})B_0 + 2\Re(\beta \overline{\alpha})C_0 + |\beta|^2 D_0 - a_0
\end{equation*}
with
\begin{equation*}
\begin{pmatrix}
\alpha & \beta \\
\gamma & \delta
\end{pmatrix} \in \Xi
\end{equation*}
appear in the second coordinate of vectors in the orbit $\mathcal{A}_1 . v_0^t$. This means that the set of integers of the form
\begin{equation*}
A_0 \alpha_1^2 + A_0 \alpha_2^2 + D_0 \beta_1^2 + D_0 \beta_2^2 + 2\alpha_1 \beta_2 B_0 - 2\alpha_2 \beta_1 B_0 + 2\alpha_1 \beta_1 C_0 + 2 \alpha_2 \beta_2 C_0 - a_0
\end{equation*}
with $\begin{pmatrix}
\alpha & \beta \\
\gamma & \delta
\end{pmatrix} \in \Xi$ and $\alpha=\alpha_1 + i \alpha_2$ and $\beta=\beta_1 + i \beta_2$, is a subset of the set of integers appearing in the second coordinate of vectors in the orbit $\mathcal{A}_1 . v_0^t$. From the definition of $\Xi$, this means that the set of integers of the form
\begin{equation*}
f_{a_0}(x,y,z,t) - a_0
\end{equation*}
with $x+iy$ and $z+it$ coprime in $\mathbb{Z}[i]$, $x+iy \equiv 1 \text{ or } i \bmod{2}$ and
\begin{equation*}
f_{a_0}(x,y,z,t)=A_0 x^2 + A_0 y^2 + 4D_0 z^2 + 4D_0 t^2 + 4xt B_0 - 4 yz B_0 + 4xz C_0 + 4yt C_0
\end{equation*}
is a subset of the set of curvatures in the packing. Since, from our choice of $v_{\mathcal{P}}^t$, $A_0=a_0+b_0$ is odd, if $m$ is an odd integer which can be written $m=f_{a_0}(x,y,z,t)$ with $x+iy$ and $z+it$ coprime in $\mathbb{Z}[i]$, we automatically have that $x$ and $y$ are not of the same parity, i.e., that $x+iy \equiv 1 \text{ or } i \bmod{2}$.
\end{proof}
\begin{remark}
\begin{equation*}
\text{disc}(f_{a_0})=16\left( A_0 D_0 - 4(B_0^2 + C_0^2) \right)^2 = 16 a_0^4
\end{equation*}
and one can check that $f_{a_0}$ is positive definite (since $A_0$ is positive, all the leading principal minors are positive).
\end{remark}
\begin{remark} \label{remk}
Let $z=z_1 + iz_2 \in \mathbb{Z}[i]$. Then,
\begin{align*}
\vert z_1 + iz_2 \vert^2 f_{a_0}(x_1,x_2,x_3,x_4) &= f_{a_0}(z_1 x_1- z_2 x_2, z_2 x_1 + z_1 x_2,z_1 x_3- z_2 x_4, z_2 x_3 + z_1 x_4) \\
&=f_{a_0} \left( \Re (z(x_1 + ix_2)), \Im (z(x_1 + ix_2)), \Re (z(x_3 + ix_4)), \Im (z(x_3 + ix_4)) \right) \, .
\end{align*}
\end{remark}
\subsection{The integers $\mathbb{Z}[i]$-primitively represented by $f_{a_0}$}\
We will study the integers coprime to $disc(f_{a_0})$ which can be written as $m=f_{a_0}(x,y,z,t)=f_{a_0}(x+iy,z+it)$ with $x+iy$ and $z+it$ coprime in $\mathbb{Z}[i]$. Such a representation will be called $\mathbb{Z}[i]$-primitive. We will use known results about the representation of integers by positive quaternary quadratic forms to obtain results about $\mathbb{Z}[i]$-primitive representations.
\\
To handle the coprimality in $\mathbb{Z}[i]$, we need the M\"{o}bius function generalized to Gaussian integers. We recall that any ideal $I$ of $\mathbb{Z}[i]$ can be factored as
\begin{equation*}
I=\mathfrak{p}_1^{\alpha_1} \dots \mathfrak{p}_k^{\alpha_k}
\end{equation*}
where the $\mathfrak{p}_i$ are prime ideals of $\mathbb{Z}[i]$. This factorization is unique, up to permutations of the factors. Using this factorization, we define the function $\mu$ on the ideals of $\mathbb{Z}[i]$ as
\begin{equation*}
\mu(I)=
\begin{cases}
0 & \text{ if } \alpha_i \geq 2 \text{ for some } i, \\
(-1)^k & \text{ otherwise }.
\end{cases}
\end{equation*}
\\
Analogously to the case of the integers, $\mu$ is multiplicative, and we have
\begin{equation} \label{mob}
\sum_{\substack{J \text{ ideal of } \mathbb{Z}[i] \\ J \supset I}} \mu(J) =
\begin{cases}
1 & \text{ if } I= (1), \\
0 & \text{ otherwise}.
\end{cases}
\end{equation}
From now on, $m$ will be an integer coprime with $disc(f_{a_0})$. Let $\mathcal{N}(m)$ be the number of representations of $m$ by $f_{a_0}$ and $\mathcal{N}_P(m)$ those which are $\mathbb{Z}[i]$-primitive. Remark \ref{remk} allows us to associate representations of $f_{a_0}(x,y,z,t)=m$ with $gcd_{\mathbb{Z}[i]}(x+iy,z+it)=\pi \in \mathbb{Z}[i]$ with $\mathbb{Z}[i]$-primitive representations of $\frac{m}{\vert \pi \vert^2}$ by $f_{a_0}$, and yields
\begin{equation*}
\mathcal{N}(m)=\sum_{\substack{\pi \in \mathbb{Z}[i] \\ \vert \pi \vert^2 | m}} \mathcal{N}_P \left( \frac{m}{\vert \pi \vert^2} \right) = 4 \hspace{-0.3cm} \sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} \mathcal{N}_P \left( \frac{m}{\textit{N}(I)} \right) \, .
\end{equation*}
\\
Using (\ref{mob}), we can invert this relation
\begin{equation} \label{inv}
\mathcal{N}_P(m)= \frac{1}{4} \sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} \mu(I) \mathcal{N} \left( \frac{m}{\textit{N}(I)} \right) \, .
\end{equation}
The asymptotic formula for $\mathcal{N}(m)$ is known (see for example Corollary 1 of \cite{HB} or Theorem 20.9 of \cite{IK}).
\begin{theorem}
\begin{equation*}
\mathcal{N}(m)=\frac{\pi^2}{2a_0^2} m \mathfrak{S}(m) + O(m^{\frac{3}{4}+\varepsilon})
\end{equation*}
for every $\varepsilon>0$, where
\begin{equation*}
\mathfrak{S}(m)=\prod_{p} \delta_p(n)
\end{equation*}
with
\begin{equation*}
\delta_p(n)=\lim_{k \rightarrow \infty} p^{-3k} \vert x \in \left( \mathbb{Z}/p^k \mathbb{Z} \right)^4 \text{ such that } f_{a_0}(x) \equiv m \bmod{p^k} \vert \, .
\end{equation*}
The implied constant depends only on $\varepsilon$.
\end{theorem}
From this and (\ref{inv}), we obtain
\begin{equation} \label{equaref}
\mathcal{N}_P(m)=\frac{\pi^2}{8a_0^2} m \sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} \frac{\mu(I)}{\textit{N}(I)} \mathfrak{S} \left( \frac{m}{\textit{N}(I)} \right) + O \left( m^{\frac{3}{4}+\varepsilon} \sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} \frac{1}{\textit{N}(I)^{\frac{3}{4}+\varepsilon}} \right) \, .
\end{equation}
\subsubsection{The error term}\
\begin{lemma} \label{lemmaerror}
The error term in (\ref{equaref}) is $O(m^{\frac{3}{4}+\varepsilon})$ for any $\varepsilon > 0$ (and the implied constant depends only on $\varepsilon$).
\end{lemma}
\begin{proof}
Let $r_2(d)$ be the number of representations of $d$ as a sum of two squares. Since $r_2(d) \ll \tau(d)$,
\begin{align*}
\sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} \frac{1}{\textit{N}(I)^{\frac{3}{4}+\varepsilon}} &= \frac{1}{4} \sum_{d|m} \frac{r_2(d)}{d^{\frac{3}{4}+\varepsilon}} \\
& \ll \sum_{d|m} \frac{\tau(d)}{d^{\frac{3}{4}+\varepsilon}} \\
& \ll \tau(m) \sum_{d|m} \frac{1}{d^{\frac{3}{4}+\varepsilon}} \\
& \ll \tau(m)^2 \, .
\end{align*}
Therefore, the error term is $O(m^{\frac{3}{4}+\varepsilon})$ for any $\varepsilon > 0$.
\end{proof}
\subsubsection{The main term}\
To get a more explicit expression for the main term, we need a better understanding of the local densities $\delta_p (\frac{m}{\textit{N}(I)})$. This can be achieved using the following lemma (see, for example, \cite{sie}).
\begin{lemma} \label{sieg}
Let $p \not | disc(f_{a_0})$, then
\begin{equation*}
\delta_p(m)=\left( 1-\frac{1}{p^2} \right) \left( 1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}} \right)
\end{equation*}
where $v_p(m)$ is such that $p^{v_p(m)} || m$.
\end{lemma}
\begin{lemma} \label{lemprim}
Let $(p,m)=1$. Then, $\delta_p(\frac{m}{\textit{N}(I)})=\delta_p(m)$ for any ideal $I$ of $\mathbb{Z}[i]$ with $\textit{N}(I) | m$.
\end{lemma}
\begin{proof}
\begin{equation*}
\delta_p \left( \frac{m}{\textit{N}(I)} \right) = \lim_{k \rightarrow \infty} p^{-3k} A_{p^k} \left( \frac{m}{\textit{N}(I)} \right)
\end{equation*}
with
\begin{align*}
A_{p^k} \left( \frac{m}{\textit{N}(I)} \right) &=\vert x \in \left( \mathbb{Z}/p^k \mathbb{Z} \right)^4 \text{ such that } f_{a_0}(x) = \frac{m}{\textit{N}(I)} \bmod{p^k} \vert \\
&=\frac{1}{p^k} \sum_{x \in \left( \mathbb{Z}/p^k \mathbb{Z} \right)^4} \sum_{h \in \mathbb{Z}/p^k \mathbb{Z}} {\mathrm e} \left( \frac{(f_{a_0}(x) - \frac{m}{\textit{N}(I)})h}{p^k} \right) \, .
\end{align*}
Using the change of variables $h \longrightarrow \textit{N}(I)h$ (which is an isomorphism of $\mathbb{Z}/p^k \mathbb{Z}$ because $\textit{N}(I) | m$ and $(p,m)=1$)
\begin{equation*}
A_{p^k} \left( \frac{m}{\textit{N}(I)} \right) = \frac{1}{p^k} \sum_{x \in \left( \mathbb{Z}/p^k \mathbb{Z} \right)^4} \sum_{h \in \mathbb{Z}/p^k \mathbb{Z}} {\mathrm e} \left( \frac{(\textit{N}(I)f(x) - m)h}{p^k} \right) \, .
\end{equation*}
$I=(z_1 + i z_2)$ for some $z_1 + i z_2 \in \mathbb{Z}[i]$ (since $\mathbb{Z}[i]$ is a principal ideal domain), therefore, using Remark \ref{remk},
\begin{equation*}
\textit{N}(I)f_{a_0}(x)=f_{a_0}(xA)
\end{equation*}
with
\begin{equation*}
A=\begin{pmatrix}
z_1 & z_2 & 0 & 0 \\
-z_2 & z_1 & 0 & 0 \\
0 & 0 & z_1 & z_2 \\
0 & 0 & -z_2 & z_1
\end{pmatrix}
\end{equation*}
and the map $x \longrightarrow xA$ is an isomorphism of $\left( \mathbb{Z}/p^k \mathbb{Z} \right)^4$ (because $p \not \vert N(I) = det(A)$). Thus
\begin{align*}
A_{p^k} \left( \frac{m}{\textit{N}(I)} \right) &= \frac{1}{p^k} \sum_{x \in \left( \mathbb{Z}/p^k \mathbb{Z} \right)^4} \sum_{h \in \mathbb{Z}/p^k \mathbb{Z}} {\mathrm e} \left( \frac{(f_{a_0}(x) - m)h}{p^k} \right) \\
&= A_{p^k}(m) \, .
\end{align*}
\end{proof}
\begin{lemma} \label{lemmamain}
The main term in (\ref{equaref}) is
\begin{equation*}
\frac{\pi^2}{8a_0^2} m \mathfrak{S}(m) \prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \left( 1-\frac{1}{p} \right)^2 \left( 1- \frac{1}{p^{v_p(m)+1}} \right)^{-2} \prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \left( 1-\frac{1}{p^2} \right) \left( 1- \frac{1}{p^{v_p(m)+1}} \right)^{-1} \, .
\end{equation*}
\end{lemma}
\begin{proof}
Using Lemma \ref{sieg} and Lemma \ref{lemprim},
\begin{align*}
\mathfrak{S} \left( \frac{m}{\textit{N}(I)} \right) &= \prod_{(p,m)=1} \delta_p \left( \frac{m}{\textit{N}(I)} \right) \prod_{p|m} \delta_p \left( \frac{m}{\textit{N}(I)} \right) \\
&= \prod_{(p,m)=1} \delta_p(m) \prod_{p|m} \left( 1-\frac{1}{p^2} \right) \left( 1+\frac{1}{p} \dots + \frac{1}{p^{v_p(\frac{m}{\textit{N}(I)})}} \right) \\
&= \mathfrak{S}(m) \prod_{p| \textit{N}(I)} \left( \frac{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(\frac{m}{\textit{N}(I)})}}}{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}}} \right) \, .
\end{align*}
Therefore, the main term is given by
\begin{equation*}
\frac{\pi^2}{8a_0^2} m\mathfrak{S}(m) \hspace{-0.3cm} \sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} g(I)
\end{equation*}
with
\begin{equation*}
g(I)=\frac{\mu(I)}{\textit{N}(I)} \prod_{p| \textit{N}(I)} \left( \frac{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(\frac{m}{\textit{N}(I)})}}}{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}}} \right) \, .
\end{equation*}
In $\mathbb{Z}[i]$, there are only two possible types of norms for a prime ideal of norm $\ne 2$. Let $\mathfrak{p}$ be an ideal with $\textit{N}(\mathfrak{p}) \ne 2$, then
\begin{equation*}
\textit{N}(\mathfrak{p}) = p \text{ with } p \equiv 1 \bmod{4} \quad \text{ or } \quad \textit{N}(\mathfrak{p}) = p^2 \text{ with } p \equiv 3 \bmod{4} \, .
\end{equation*}
Reciprocally, for any $p \ne 2$, there exists exactly two ideals of norm $p$ if $p \equiv 1 \bmod{4}$ and a unique ideal of norm $p^2$ if $p \equiv 3 \bmod{4}$, and these ideals are prime.
\\
\\
Notice that $g$ is multiplicative, and that, if $\mathfrak{p}$ is a prime ideal of $\mathbb{Z}[i]$ with $\textit{N}(\mathfrak{p})|m$, we have
\begin{equation*}
g(\mathfrak{p})=\left( 1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)-1}} \right) \left( p(1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}}) \right)^{-1} \text{ if } \textit{N}(\mathfrak{p})=p \text{ with } p \equiv 1 \bmod{4} \, ,
\end{equation*}
\begin{equation*}
g(\mathfrak{p})=\left( 1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)-2}} \right) \left( p^2(1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}}) \right)^{-1} \text{ if } \textit{N}(\mathfrak{p})=p^2 \text{ with } p \equiv 3 \bmod{4} \, .
\end{equation*}
Therefore, the sum can be transformed into a product, and we get
\begin{align*}
\sum_{\substack{I \text{ ideal of } \mathbb{Z}[i] \\ \textit{N}(I) | m}} g(I) &= \prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \left( 1 - \frac{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)-1}}}{p(1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}})} \right)^2 \prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \left( 1 - \frac{1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)-2}}}{p^2(1+\frac{1}{p} \dots + \frac{1}{p^{v_p(m)}})} \right) \\
&= \prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \left( 1-\frac{1}{p} \right)^2 \left( 1- \frac{1}{p^{v_p(m)+1}} \right) ^{-2} \prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \left( 1-\frac{1}{p^2} \right) \left( 1- \frac{1}{p^{v_p(m)+1}} \right)^{-1} \, .
\end{align*}
\end{proof}
\begin{lemma} \label{pospos}
\begin{equation*}
\mathcal{N}_P(m)=\frac{\pi^2}{8a_0^2} m \mathfrak{S}(m) \hspace{-0.2cm} \prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \hspace{-0.1cm} \left( 1-\frac{1}{p} \right)^2 \left( 1- \frac{1}{p^{v_p(m)+1}} \right) ^{-2} \hspace{-0.3cm} \prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \hspace{-0.1cm} \left( 1-\frac{1}{p^2} \right) \left( 1- \frac{1}{p^{v_p(m)+1}} \right)^{-1} \hspace{-0.2cm} + O(m^{\frac{3}{4}+\varepsilon}) \, .
\end{equation*}
\end{lemma}
\begin{proof}
This is a direct consequence of Lemmas \ref{lemmaerror} and \ref{lemmamain}.
\end{proof}
\subsection{The local-global principle}\
\begin{theorem} \label{positi}
Let $m$ be an integer coprime with $disc(f_{a_0})$. Suppose that the equation $f_{a_0}(x) \equiv m \bmod{p}$ has solutions for every $p|disc(f_{a_0})$, $p \ne 2$, and that the equation $f_{a_0}(x) \equiv m \bmod{8}$ has solutions. Then, for such an $m$, with $m$ large enough, $m$ is $\mathbb{Z}[i]$-primitively represented by $f_{a_0}$.
\end{theorem}
\begin{proof}
We use Lemma \ref{pospos}.
\\
\\
Using Mertens' formula,
\begin{equation*}
\prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \left( 1-\frac{1}{p} \right) \geq \prod_{p \leq m} \left( 1-\frac{1}{p} \right) \sim \frac{{\mathrm e}^{-\gamma}}{\log m} \, .
\end{equation*}
Furthermore,
\begin{equation*}
\prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \left( 1-\frac{1}{p^2} \right) \geq \prod_{p} \left( 1-\frac{1}{p^2} \right) =\frac{1}{\zeta(2)}
\end{equation*}
and
\begin{equation*}
\prod_{\substack{p \equiv 1 \bmod{4} \\ p | m}} \left( 1- \frac{1}{p^{v_p(m)+1}} \right) ^{-1} \prod_{\substack{p \equiv 3 \bmod{4} \\ p^2 | m}} \left( 1- \frac{1}{p^{v_p(m)+1}} \right)^{-1} \geq 1 \, .
\end{equation*}
We now have to show that $\mathfrak{S}(m)$ is bounded away from zero. Using Lemma \ref{sieg},
\begin{equation*}
\prod_{p \not \vert disc(f_{a_0})} \delta_p(m) \gg 1 \, .
\end{equation*}
It remains to prove that $\delta_p(m)$ is bounded away from zero for the finite set of primes $p \vert disc(f_{a_0})$.
\\
\\
Using Lemma 13 of \cite{sie}, for $p \ne 2$, $\delta_p(m) = p^{-3}\vert x \in (\mathbb{Z}/p\mathbb{Z})^4 \text{ such that } f_{a_0}(x) \equiv m \bmod{p} \vert$.
\\
But, by assumption, there exist solutions to $f_{a_0}(x) \equiv m \bmod{p}$, therefore $\delta_p(m)>0$ for those $p$.
\\
\\
Finally, using Lemma 13 of \cite{sie} again, for $p=2$, $\delta_2(m) = \frac{1}{512}\vert x \in (\mathbb{Z}/8\mathbb{Z})^4 \text{ such that } f_{a_0}(x) \equiv m \bmod{8} \vert$. As before, this is positive.
\end{proof}
\begin{theorem}[The local-global principle]
Let
\begin{equation*}
\mathcal{S} = \left\lbrace n \in \mathbb{Z}, n > 0 \text{ such that } n \equiv b_0 \bmod{4} \right\rbrace \, .
\end{equation*}
Then, an integer $m$ large enough with $gcd(m,a_0)=1$ is the curvature of some sphere in the packing if and only if $m \in \mathcal{S}$.
\end{theorem}
\begin{proof}
We will look for the integers $m$ satisfying the following conditions:
\begin{itemize}
\item $m+a_0$ is odd,
\item $gcd(m+a_0,disc(f_{a_0}))=1$,
\item $m+a_0$ is represented by $f_{a_0}$ modulo $8$ and modulo any odd prime dividing the discriminant.
\end{itemize}
From our choice of $v_{\mathcal{P}}^t$, $a_0+b_0$ is odd. As seen before, this implies that $f_{a_0}$ will only $\mathbb{Z}[i]$-primitively represent odd values. That is why we need $m+a_0$ to be odd.
\\
\\
We also want $gcd(m+a_0,disc(f_{a_0}))=gcd(m+a_0,16a_0^4)=1$ to apply Theorem \ref{positi}. But since $m+a_0$ is odd, it simply means $gcd(m,a_0)=1$.
\\
\\
We want $m+a_0$ to be represented by $f_{a_0}$ modulo $8$. But, since $A_0$ is odd, it is easy to check that $f_{a_0}$ represents exactly the two odd classes modulo $8$, $A_0$ and $5A_0 \bmod{8}$. We can therefore just look modulo $4$, and $m+a_0$ needs to be in the class $A_0 \bmod{4}$, i.e., $m \equiv b_0 \bmod{4}$. Notice that this condition contains the condition $m+a_0$ odd.
\\
\\
We want $m+a_0$ to be represented by $f_{a_0}$ modulo any odd prime dividing the discriminant. Notice that, since $A_0$ is odd,
\begin{align*}
gcd(A_0,B_0,C_0,D_0) &= gcd(a_0+b_0,a_0+b_0+c_0+d_0-2\omega_0,a_0+b_0+c_0-d_0,a_0+c_0) \\
&=gcd(a_0+b_0,a_0+c_0,a_0+d_0,a_0+\omega_0) \, .
\end{align*}
But, from equation (\ref{eqmod}),
\begin{align*}
p\ne 2 \text{ and } p \vert gcd(a_0+b_0,a_0+c_0,a_0+d_0,a_0+\omega_0) &\Rightarrow p|a_0 \\
&\Rightarrow p \vert gcd(a_0,b_0,c_0,d_0,\omega_0)
\end{align*}
which is a contradiction to the primitivity. Now, one can easily check that this means that $f_{a_0}$ can take all the possible values modulo $p$. Hence, this imposes no restriction on $m+a_0$, except the one already seen before $gcd(m,a_0)=1$.
\\
\\
From Theorem \ref{curva}, we know that the set of integers of the form
\begin{equation*}
f_{a_0}(x,y,z,t)-a_0 \quad gcd_{\mathbb{Z}[i]}(x+iy,z+it)=1
\end{equation*}
is a subset of the set of curvatures in $\mathcal{P}$. From Theorem \ref{positi} and the previous observations, we deduce that all the integers $m$ large enough with $gcd(m,a_0)=1$ and $m \equiv b_0 \bmod{4}$ are $\mathbb{Z}[i]$-primitively represented by $f_{a_0}(x,y,z,t)-a_0$, and therefore are curvatures of some sphere in the packing.
\\
\\
Reciprocally, from Lemma $\ref{odd}$, any curvature $m$ in the packing with $gcd(m,a_0)=1$ will verify $m \equiv b_0 \bmod{4}$.
\end{proof}
\begin{remark}
This result gives us that the set of curvatures in an integral generalized Apollonian sphere packing has positive density. More precisely, the density is at least
\begin{equation*}
\frac{1}{4} \prod_{\substack{p \vert n \\ p \ne 2}} \left( 1-\frac{1}{p} \right) \, .
\end{equation*}
\end{remark}
\bigskip
\nocite{*}
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lmctfy (pronounced *l-m-c-t-fi*, IPA: /ɛlɛmsitifаɪ/) is the open source version of [Google](http://google.com)'s container stack, which provides Linux application containers. These containers allow for the isolation of resources used by multiple applications running on a single machine. This gives the applications the impression of running exclusively on a machine. The applications may be container-aware and thus be able to create and manage their own subcontainers.
The project aims to provide the container abstraction through a high-level API built around user intent. The containers created are themselves container-aware within the hierarchy and can be delegated to be managed by other user agents.
lmctfy was designed and implemented with specific use-cases and configurations in mind and may not work out of the box for all use-cases and configurations. We do aim to support more use-cases and configurations so please feel free to [contribute](#contributing) patches or send e-mail to the [mailing list](#mailing-list) so that we may incorporate these into the [roadmap](#roadmap).
lmctfy is released as both a C++ library and a CLI.
## Current Status
lmctfy is beta software under heavy development and may change as it evolves. The latest release version is `0.5.0`. It currently provides isolation for CPU, memory, and devices. It also allows for the creation of Virtual Hosts which are more heavily isolated containers giving the impression of running as an independent host.Take a look at our [roadmap](#roadmap) for areas of development and possible [contributions](#contributing).
## Getting Started
This section describes building the CLI, running all unit tests, and initializing the machine. The [CLI Commands](#cli-commands) section provides some examples of CLI operations and [C++ Library](#c-library) describes the use of the underlying library.
### Dependencies
lmctfy depends on the following libraries and expects them to be available on the system:
* [Protocol Buffers](https://code.google.com/p/protobuf/)
* [gflags](https://code.google.com/p/gflags/) (version >= 2.1.1)
* [RE2](https://code.google.com/p/re2/)
* [AppArmor](http://packages.ubuntu.com/precise/libapparmor-dev)
* glibc (version >= 2.14)
Addtionally to build lmctfy you also need:
* make
* go compiler
* g++ or clang version with C++11 support (tested with g++-4.7 and clang-3.2)
We've tested the setup on **Ubuntu 12.04+**. We are happy to accept patches that add support for other setups.
### Building the CLI
To build the `lmctfy` CLI:
```bash
make -j <number of threads> lmctfy
```
The CLI should now be available at: `bin/lmctfy/cli/lmctfy`
### Building the C++ Library
To build the lmctfy library:
```bash
make -j <number of threads> liblmctfy.a
```
The library should now be available at: `bin/liblmctfy.a`.
### Running Unit Tests
To build and run all unit tests:
```bash
make -j <number of threads> check
```
### Initialization
lmctfy has been tested on **Ubuntu 12.04+** and on the **Ubuntu 3.3** and **3.8** kernels. lmctfy runs best when it owns all containers in a machine so it is not recommended to run lmctfy alongside [LXC](http://lxc.sourceforge.net/) or another container system (although given some configuration, it can be made to work).
In order to run lmctfy we must first initialize the machine. This only needs to happen once and is typically done when the machine first boots. If the cgroup hierarchies are already mounted, then an empty config is enough and lmctfy will auto-detect the existing mounts:
```bash
lmctfy init ""
```
If the cgroup hierarchies are not mounted, those must be specified so that lmctfy can mount them. The current version of lmctfy needs the following cgroup hierarchies: `cpu`, `cpuset`, `cpuacct`, `memory`, and `freezer`. `cpu` and `cpuacct` are the only hierarchies that can be co-mounted, all other must be mounted individually. For details on configuration specifications take a look at `InitSpec` in [lmctfy.proto](/include/lmctfy.proto). An example configuration mounting all of the hierarchies in `/sys/fs/cgroup`:
```bash
lmctfy init "
cgroup_mount:{
mount_path:'/sys/fs/cgroup/cpu'
hierarchy:CGROUP_CPU hierarchy:CGROUP_CPUACCT
}
cgroup_mount:{
mount_path:'/sys/fs/cgroup/cpuset' hierarchy:CGROUP_CPUSET
}
cgroup_mount:{
mount_path:'/sys/fs/cgroup/freezer' hierarchy:CGROUP_FREEZER
}
cgroup_mount:{
mount_path:'/sys/fs/cgroup/memory' hierarchy:CGROUP_MEMORY
}"
```
The machine should now be ready to use `lmctfy` for container operations.
## Container Names
Container names mimic filesystem paths closely since they express a hierarchy of containers (i.e.: containers can be inside other containers, these are called **subcontainers** or **child containers**).
Allowable characters for container names are:
* Alpha numeric (`[a-zA-Z0-9]+`)
* Underscores (`_`)
* Dashes (`-`)
* Periods (`.`)
An absolute path is one that is defined from the root (`/`) container (i.e.: `/sys/subcont`). Container names can also be relative (i.e.: `subcont`). In general and unless otherwise specified, regular filesystem path rules apply.
### Examples:
```
/ : Root container
/sys : the "sys" top level container
/sys/sub : the "sub" container inside the "sys" top level container
. : the current container
./ : the current container
.. : the parent of the current container
sub : the "sub" subcontainer (child container) of the current container
./sub : the "sub" subcontainer (child container) of the current container
/sub : the "sub" top level container
../sibling : the "sibling" child container of the parent container
```
## CLI Commands
### Create
To create a container run:
```bash
lmctfy create <name> <specification>
```
Please see [lmctfy.proto](/include/lmctfy.proto) for the full `ContainerSpec`.
Example (create a memory-only container with `100MB` limit):
```bash
lmctfy create memory_only "memory:{limit:100000000}"
```
### Destroy
To destroy a container run:
```bash
lmctfy destroy <name>
```
### List
To list all containers in a machine, ask to recursively list from root:
```bash
lmctfy list containers -r /
```
You can also list only the current subcontainers:
```bash
lmctfy list containers
```
### Run
To run a command inside a container run:
```bash
lmctfy run <name> <command>
```
Examples:
```bash
lmctfy run test "echo hello world"
lmctfy run /test/sub bash
lmctfy run -n /test "echo hello from a daemon"
```
### Other
Use `lmctfy help` to see the full command listing and documentation.
## C++ Library
The library is comprised of the `::containers::lmctfy::ContainerApi` factory which creates, gets, destroys, and detects `::containers::lmctfy::Container` objects that can be used to interact with individual containers. Full documentation for the lmctfy C++ library can be found in [lmctfy.h](/include/lmctfy.h).
## Roadmap
The lmctfy project proposes a containers stack with two major layers we'll call CL1 and CL2. CL1 encompases the driver and enforcement of the containers policy set by CL2. CL1 will create and maintain the container abstraction for higher layers. It should be the only layer that directly interacts with the kernel to manage containers. CL2 is what develops and sets container policy, it uses CL1 to enforce the policy and manage containers. For example: CL2 (a daemon) implements a policy that the amount of CPU and memory used by all of a machine's containers must not exceed the amount of available CPU and memory (as opposed to overcommitting memory in the machine). To enforce that policy it uses CL1 (library/CLI) to create containers with memory limits that add up to the machine's available memory. Alternate policies may involve overcommitting a machine's resources by X% or creating levels of resources with different guarantees for quality of service.
The lmctfy project currently provides the CL1 component. The CL2 is not yet implemented.
### CL1
Currently only provides robust CPU and memory isolation. In our roadmap we have support for the following:
* *Disk IO Isolation:* The specification is mostly complete, we're missing the controller and resource handler.
* *Network Isolation:* The specification and cgroup implementation is up in the air.
* *Support for Root File Systems:* Specifying and building root file systems.
* *Disk Images:* Being able to import/export a container's root file system image.
* *Checkpoint Restore:* Being able to checkpoint and restore containers on different machines.
### CL2
The most basic CL2 would use a container policy that ensures the fair sharing of a machine's resources without allowing overcommitment. We aim to eventually implement a CL2 that provides different levels of guaranteed quality of service. In this scheme some levels are given stronger quality of service than others. The following CL2 features are supported in our roadmap:
* Monitoring and statistics support.
* Admission control and feasibility checks.
* Quality of Service guarantees and enforcement.
We have started work on CL2 under the [cAdvisor](https://github.com/google/cadvisor/) project
## Kernel Support
lmctfy was originally designed and implemented around a custom kernel with a set of patches on top of a vanilla Linux kernel. As such, some features work best in conjunction with those kernel patches. However, lmctfy should work without them. It should detect available kernel support and adapt accordingly. We've tested lmctfy in vanilla **Ubuntu 3.3*** and **3.8** kernels. Please report any issues you find with other kernel versions.
Some of the relevant kernel patches:
* *CPU latency:* This adds the `cpu.lat` cgroup file to the cpu hierarchy. It bounds the CPU wakeup latency a cgroup can expect.
* *CPU histogram accounting:* This adds the `cpuacct.histogram` cgroup file to the cpuacct hierarchy. It provides various histograms of CPU scheduling behavior.
* *OOM management:* Series of patches to enforce priorities during out of memory conditions.
## Contributing
Interested in contributing to the project? Feel free to send a patch or take a look at our [roadmap](#roadmap) for ideas on areas of contribution. Follow [Getting Started](#getting-started) above and it should get you up and running. If not, let us know so we can help and improve the instructions. There is some documentation on the structure of lmctfy in the [primer](/PRIMER.md).
## Mailing List
The project mailing list is <lmctfy@googlegroups.com>. The list will be used for announcements, discussions, and general support. You can [subscribe via groups.google.com](https://groups.google.com/forum/#!forum/lmctfy).
|
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Q: pullback of pushforward In the case where $k$ is a field and $L$ a finite Galois extension of $k$ we can consider the projection map $\pi: X\otimes_k L\rightarrow X$, where $X$ is a smooth projective variety over $k$. If we take a coherent sheaf $\mathcal{F}$ (or locally free sheaf $\mathcal{E}$. I guess it is true that $\pi^*\pi_*\mathcal{E}\simeq \mathcal{E}\otimes_k L[G]\simeq \mathcal{E}^{\oplus r}$, where $G$ is the Galois group and $r=ord(G)$.
My question:
What happens for infinite Galois groups or in the absolute case i.e. $k\subset \bar{k}$ and $G$ the absolute Galois group. What is $\pi^*\pi_*\mathcal{E}$ for $\pi:X\otimes_k\bar{k}\rightarrow X$ ?
A: That's not true. Consider a coherent sheaf $\mathcal E$ on $X \otimes_k L$ which is not Galois-invariant, like a line bundle on an elliptic curve correspoinding to a point of the Jacobian which is not defined over $k$, Then $\pi^* \pi_* \mathcal E$ is conjugation-invariant, but $\mathcal E^{\oplus r}$ usually isn't.
In the finite case, this will be the sum over all the Galois conjugates of $\mathcal E$. In the infinite case, $\pi^* \pi _ * \mathcal E$ is the subsheaf of the infinite product sheaf $\Pi_{\sigma \in G} \mathcal E^\sigma$ consisting of functions that are locally constant in the profinite topology on $G$.
The map $\mathcal E \otimes_k L \to \Pi_{\sigma \in G} \mathcal E^\sigma$ just comes from evaluating the product of a function in $\mathcal E$ with an element in $L$ by twisting with the automorphism. The key fact being that the action of $L$ on $\mathcal E \otimes_k L$ in this construction comes from the right $L$, not the left $\mathcal E$, which is why it is $\mathcal E_\sigma$. The functions we get are locally constant because any element in the tensor product depends on only finitely many elements of $L$. The map to locally constant functions is an isomrophism because we can check it's an isomorphism for each finite-degree subfield of $L$ / submodule of functions constant on an open index subgroup of the Galois group.
(What you said is true for $\pi_* \pi^*$, though. )
|
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| 360
|
{"url":"http:\/\/www.ni.com\/documentation\/en\/labview\/1.0\/m-ref\/win-tukey\/","text":"# win_tukey\n\nVersion:\n\nGenerates a cosine tapered window of a specified number of points.\n\n## Syntax\n\nc = win_tukey(a)\nc = win_tukey(a, b)\nLegacy name: tukeywin\n\n## a\n\nSize of the cosine tapered window. a is a positive integer.\n\n## b\n\nRatio of the length of the tapered section to the length of the entire signal.\n\nDefault: 0.5\n\n## c\n\nCosine tapered window of size a. c is a real column vector.\n\nc = win_tukey(8, 0.3)\n\nWhere This Node Can Run:\n\nDesktop OS: Windows\n\nFPGA: This product does not support FPGA devices","date":"2017-12-15 20:10:37","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\": 1, \"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\": 0.4210256040096283, \"perplexity\": 10614.443185516933}, \"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-2017-51\/segments\/1512948579564.61\/warc\/CC-MAIN-20171215192327-20171215214327-00495.warc.gz\"}"}
| null | null |
Christoph Lieder (* um 1959) ist ein deutscher Dirigent, Musiker und Offizier.
Leben
Lieder trat im Juli 1977 in die Bundeswehr ein. Er absolvierte ein Studium zum Kapellmeister an der Robert Schumann Hochschule Düsseldorf und war anschließend stellvertretender Leiter des Stabsmusikkorps der Bundeswehr in Siegburg, Chef des Musikkorps der 1. Gebirgsdivision in Garmisch-Partenkirchen (1987–1992) und über 14 Jahre des Heeresmusikkorps 7 in Düsseldorf.
Zum Jahr 2008 übernahm er die Big Band der Bundeswehr als Bandleader. Mit diesem Klangkörper trat er mehrfach bei TV total und im ZDF-Fernsehgarten auf.
Im Oktober 2012 wechselte er als stellvertretender Leiter zum Zentrum Militärmusik der Bundeswehr, dessen Leitung ihm schließlich am 17. Februar 2016 übertragen wurde. Dabei wurde er auch Leiter der Militärmusikdienstes. Am 22. Februar 2022 übergab Lieder die Leitung des Militärmusikdienstes und des Zentrums Militärmusik an Thomas Klinkhammer. Zum 1. April 2022 wurde er in den Ruhestand versetzt. Er hatte zuletzt den Rang eines Oberst.
Einzelnachweise
Militärmusiker
Musiker (Deutschland)
Militärperson (Bundeswehr)
Dirigent
Deutscher
Geboren im 20. Jahrhundert
Mann
|
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| 1,660
|
{"url":"https:\/\/zbmath.org\/?q=an:1075.11049","text":"# zbMATH \u2014 the first resource for mathematics\n\nQuadratic forms of signature $$(2,2)$$ and eigenvalue spacings on rectangular 2-tori. (English) Zbl\u00a01075.11049\nA quantitative version of the Oppenheim conjecture proved by Margulis states that for a nondegenerate indefinite quadratic form $$Q$$ in $$n$$ variables there exists a constant $$\\lambda_{Q,\\Omega}$$ such that for any interval $$(a b)$$ as $$T\\to\\infty$$ $$\\text{Vol}\\{x\\in\\mathbb{R}^n: x\\in T\\Omega$$ and $$a\\leq Q(s)\\leq b\\}\\sim\\lambda_{Q,\\Omega(b- a)T^{n-2}}$$, where $$\\Omega= \\{v\\in\\mathbb{R}^n\\mid\\| v\\|<\\rho(v\/\\| v\\|)\\}$$ and $$\\rho$$ is a continuous positive function on the sphere $$\\{v\\in\\mathbb{R}^n\\mid\\| v\\|=1\\}$$. Eskin, Margulis and Mozes have shown that $$N_{Q,\\Omega}(a,b,T)\\sim \\lambda_{Q,\\Omega}(b- a)T^{n-2}$$ where $$Q$$ is an indefinite quadratic form (not proportional to a rational form) of signature $$(p, q)$$ with $$p\\geq 3$$, $$q\\geq 1$$, $$n= p+ q$$ and $$N_{Q,\\Omega}(a, b, T)$$ denotes the cardinality of the set $$\\{x\\in\\mathbb{Z}^n:x\\in T\\Omega$$ and $$a< Q(x)< b\\}$$. If the signature of $$Q$$ is $$(2,1)$$ or $$(2,2)$$ then the above result fails. Whenever a form of signature $$(2,2)$$ has a rational isotropic subspace $$L$$ then $$L\\cap T\\Omega$$ contains on the order of $$T^2$$ integral points $$x$$ for which $$Q(x)= 0$$, hence $$N_{Q,\\Omega}(-\\varepsilon, \\varepsilon, T)\\geq cT^2$$, independently of the choice of $$\\varepsilon$$.\nThus to obtain an asymptotic formula in the signature $$(2,2)$$ case, we must exclude the contribution of the rational isotropic subspaces. The main result of this paper is as follows: Let $$Q$$ be an indefinite quadratic form of signature $$(2,2)$$ which is not extremely well approximable by split forms then for any interval $$(a, b)$$ as $$T\\to\\infty$$, $$\\widetilde N_{Q,\\Omega}(a, b, T)\\sim\\lambda_{Q,\\Omega}(b- a)T^2$$ where $$\\widetilde N_{Q,\\Omega}$$ counts the points not contained in isotropic subspaces. It turns out that points belonging to a wider class of subspaces have to be treated separately. In order to estimate $$N_{Q,\\Omega}$$ a transition to considering certain integrals on the space of unimodular lattices in $$\\mathbb{R}^n$$ is made. This transition is based on the transitivity of the action of the orthogonal group $$\\text{SO}(Q)$$ on the level sets of the quadratic form $$Q$$. One also needs to have an estimate of the contribution of elements of lattices lying at the cusps of $$\\text{SL}(n,\\mathbb{R})\/\\text{SL}(n,\\mathbb{Z})$$.\n\n##### MSC:\n 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 22E40 Discrete subgroups of Lie groups\n##### Keywords:\nquadratic form; isotropic; orthogonal group; unimodular\nFull Text:","date":"2021-06-14 05:25:11","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\": 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\": 0.8711184859275818, \"perplexity\": 136.11346327929448}, \"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-2021-25\/segments\/1623487611445.13\/warc\/CC-MAIN-20210614043833-20210614073833-00127.warc.gz\"}"}
| null | null |
Een pluim (panicula) is een bloeiwijze met een spil, een lange hoofdas, met vertakte zijassen, die dichter bij de top van de bloeiwijze meestal korter en minder vertakt zijn en ieder een verdere bloemtros met bloemen dragen. Een voorbeeld is de bloeiwijze van de sering. In ruimere zin elke samengestelde vertakte bloeiwijze, zoals de synflorescenties bij grassen en cypergrassen.
Vele grassen hebben als bloeiwijze de pluim. Soms zijn de aartjes zeer kort gesteeld en vormen dan samen een dichte, smalle aarpluim, zoals bij de grote vossenstaart. Soms zijn ze ook iets langer gesteeld, zoals bij het kamgras.
Bloeiwijze
|
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| 7,752
|
layout: page
title: Fire Media Executive Retreat
date: 2016-05-24
author: Jerry Cross
tags: weekly links, java
status: published
summary: Pellentesque gravida malesuada eros, ac porta ante.
banner: images/banner/meeting-01.jpg
booking:
startDate: 05/19/2019
endDate: 05/22/2019
ctyhocn: CRPPTHX
groupCode: FMER
published: true
---
Fusce augue arcu, sagittis vitae lacinia vel, ullamcorper dapibus risus. Ut sodales placerat magna, et elementum tellus rhoncus eleifend. Maecenas id accumsan tellus, ac molestie ligula. Praesent finibus quam ut felis imperdiet dignissim. Mauris ut arcu dolor. Nulla a suscipit odio. Nulla pulvinar, diam a feugiat convallis, velit eros accumsan tellus, eget ultricies justo turpis vitae nunc.
1 Phasellus scelerisque massa sit amet eleifend faucibus
1 Nulla luctus turpis sed accumsan aliquam.
Integer faucibus venenatis finibus. Nam euismod lacus ut nisi lobortis, et venenatis nunc sollicitudin. Morbi consequat cursus leo, id faucibus diam aliquam vel. In placerat malesuada mi, id interdum ex laoreet ut. Integer ornare convallis erat. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Aenean ut tristique magna. Curabitur blandit tortor lorem, sagittis maximus dui sollicitudin eu. Nullam nisl elit, faucibus eu odio in, euismod ornare mi. Proin lorem dui, cursus ut turpis ac, consectetur ultrices diam.
|
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| 3,689
|
Copyright
Copyright © 2005 by Michael Levine
All rights reserved.
Warner Business Books
Warner Books
Hachette Book Group
237 Park Avenue
New York, NY 10017
Visit our website at www.HachetteBookGroup.com
The Warner Business Books logo is a trademark of Warner Books.
First eBook Edition: April 2010
ISBN: 978-0-446-53558-8
To the champions, the heroic men and women who understand that business is more than the toil for money—it is a demand for excellence. Their rare passion in the cause of commerce inspires all of those inside and out of their enterprise, and to them this book is enthusiastically dedicated.
# _Acknowledgments_
It's been said before, better and more forcefully than I can, that writing a book is not a solitary undertaking. It's encouraged, refined, assisted, and expanded by any number of smart, passionate, inspiring people, who sometimes do the most when they don't realize they're doing anything at all. Such is the process of writing a book, at least for me.
To each of these benevolent witnesses, my gratitude, real and lasting:
Rick Wolff, my determined, diligent editor at Warner Books, whose contributions to the birth of this work were indispensable.
Craig Nelson, my longtime and valued agent and friend, who has watched over my publishing life with the care of a dedicated and experienced surgeon.
Jeffrey Cohen, a smart and valued friend, who continues to encourage my writing.
My LCO-Levine Communications Office staff and associates, headed by Chief Operating Officer Dawn Miller. Staff: Mike Abrams, Clarissa Clarke, Liam Collopy, Shannon Hartigan, and Brian McWilliams. Associates: Rick Citron, Cindy Carrasco, Phil Kass, Steve Shapiro, and David Weiss.
My closest personal friends, every single one of whom has brightened darkness when life has inevitably cast shadows, but just as often celebrated my victories as if they were their own: Peter Bart, Adam Christing, Craig Hollander, Richard Imprescia, Karen Karsian, Nancy Mager, John McKillop, Mark Miller, Evadne Morakis, Cable Neuhaus, Alyse Reynolds, Tara Kennan, Dr. Robert Kotler, and Lisa Yukelson.
Publishing associates far and wide, who continue to use their formidable skills to prod me to get my ideas into print: Craig Black, Bill Hartley, and Michael Viner.
Contents
Copyright
_Acknowledgments_
_Introduction_
Chapter One: Broken Windows in Business
Chapter Two: Can McDonald's Be Saved?
Chapter Three: Obsession and Compulsion
Chapter Four: How the Mighty Have Fallen
Chapter Five: Expectation vs. Reality
Chapter Six: Branding and Broken Windows
Chapter Seven: The Employee as Broken Window
Chapter Eight: Why Krispy Kreme Is Better Than Dunkin' Donuts (and Vice Versa)
Chapter Nine: Fly the _What_ Skies?
Chapter Ten: Doing It Right
Chapter Eleven: Do You Google?
Chapter Twelve: Broken Wires: Broken Windows on the Net
Chapter Thirteen: The Public, Watchdog
Chapter Fourteen: The Ultimate Broken Window
Chapter Fifteen: What a Difference a Pianist Makes
Chapter Sixteen: Broken Windows, No Building
Chapter Seventeen: What's in It for... You?
_The Broken Windows for Business Pledge_
# _Introduction_
When is a dirty bathroom a broken window?
No, that's not a riddle. It's a question that could today be at the core of a business's success or failure. Answer that question correctly and use that answer as a beacon, and your business could dominate its competition indefinitely. Ignore the solution to the puzzle, and you will be condemning your business to failure in a very short period of time.
The "broken windows" theory, first put forth by criminologists James Q. Wilson and George L. Kelling in a piece called "Broken Windows" in the _Atlantic Monthly_ magazine in March 1982, explains what a broken window is in criminal justice terms. But the brilliance of that theory goes much further than one interpretation. It can and should be applied to business, too, and it can make a critical difference—if American businesses will simply take the time and have the courage to notice.
When Wilson and Kelling first unveiled the theory, the idea of concentrating on seemingly petty criminal acts like graffiti or purse snatching seemed absurd: How would a crackdown on jaywalking lead to a decrease in murders?
The broken windows theory states that something as small and innocuous as a broken window does in fact send a signal to those who pass by every day. If it is left broken, the owner of the building isn't paying attention or doesn't care. That means more serious infractions—theft, defacement, violent crime—might be condoned in this area as well. At best, it signals that no one is watching.
This is the heart of the broken windows theory: Wilson and Kelling write that "social psychologists and police officers tend to agree that if a window in a building is broken and is left unrepaired, all the rest of the windows will soon be broken." Why? Because the message being sent out by a broken window—the _perception_ it invites—is that the owner of this building and the people of the community around it don't care if this window is broken: They have given up, and anarchy reigns here. Do as you will, because nobody cares.
Wilson and Kelling suggested that a "broken window"—any small indication that something is amiss and not being repaired—can lead to much larger problems. It sends signals, they said, that the bad guys are in charge here; no one cares about maintaining some kind of order, and anyone who wishes to take advantage of that situation would be unopposed. It leads to lawlessness, a kind of anarchy by neglect.
"Just as physicians now recognize the importance of fostering health rather than simply treating illness, so the police—and the rest of us—ought to recognize the importance of maintaining, intact, communities without broken windows," wrote Wilson and Kelling.
Years later, Wilson told me that the idea behind the broken windows theory "had to do with the responsibility of the police to take seriously small signs of disorder because people were afraid of disorder, and there was a chance disorder could lead to more serious crime." Still, critics of the theory greeted it with skepticism, believing that attention to small infractions would necessarily decrease the amount of attention that could be devoted to much more serious crimes.
The same objection, in slightly less genteel verbiage, was raised when Rudolph Giuliani, the newly elected mayor of New York City in 1994, announced his intention to eliminate graffiti on subway cars and move the hookers and pimps out of Times Square, to make Manhattan more "family-friendly." Critics practically laughed in Giuliani's face, intimating that the "law and order" mayor—who had been elected based largely on his experience as U.S. attorney for the New York area—was dealing with the small crimes because he knew he couldn't contain the larger ones.
They were proved wrong. Giuliani and his new police commissioner, William Bratton, believed that if they sent out clear signals to criminals, and to New York's citizenry generally, that a "zero tolerance" policy would be applied to _all_ crime in the city, the result would be a safer, cleaner city. And the statistics bore them out: Over the following few years, the numbers of murders, assaults, robberies, and other violent crimes all went down dramatically. And it had all started with graffiti on subway cars.
I can hear you asking, "What does that have to do with my business? It's all about crime and criminals."
That same theory is applicable to the world of business. If the restroom at the local Burger King is out of toilet paper, it signals that management isn't paying attention to the needs of its clientele. That could lead the consumer to conclude that the food at this restaurant might not be prepared adequately, that there might be health risks in coming here, or that the entire chain of fast food outlets simply doesn't care about its customers.
Given that scenario, it is not a stretch of the imagination but in fact a point of logic to conclude that the broken windows theory should be applied to business, as it was to the problems of crime in urban areas. Certainly, the perception of the average consumer is a vital part of every business, and if a retailer, service provider, or corporation is sending out signals that its approach is lackadaisical, its methods halfhearted, and its execution indifferent, the business in question could suffer severe—and in some cases, irreparable—losses.
This book is about broken windows in business: how they happen, why they happen, why they are ignored, and the fatal consequences that can result from their being allowed to go unchecked. It is meant as a cautionary tale, a primer, a road map, a manifesto, and a salute to those companies that fix their broken windows promptly. It will explore not only specific examples of broken windows, how they occurred, and what their long-term results were but also the culture that creates an environment in which windows are broken and left unfixed.
I believe that small things make a huge difference in business. The messy condiment area at a fast food restaurant might lead customers to believe the company as a whole doesn't care about cleanliness, and therefore the food itself might be in question. Indifferent help at the counter in an upscale clothing store—even if just one clerk—can signal to the consumer that perhaps standards here aren't as high as they might be (or used to be). An employee at the gas station who wears a T-shirt with an offensive slogan can certainly cause some customers to switch brands of gasoline and lose an enormous company those customers for life.
But that's only the tip of the iceberg. I think we as a society have fostered and encouraged broken windows in our businesses by standing by and letting them happen. If the waiter at a local chain restaurant is impolite, or even merely complacent, about our order, we chalk it up to a bad day, one employee in one outlet of a large chain, and we don't send a letter to management or the corporate level. Even if we do change brands of gasoline after seeing an attendant in an offensive T-shirt, we do not write or e-mail the president of the oil company to alert him to the problem. We are enablers to window breakers in every aspect of every business. We don't even necessarily patronize those companies that fix their broken windows, if the less attentive one is in a more convenient location or has a slightly lower price.
That's not to say we are all to blame when a company has broken windows and doesn't fix them, but it does mean we all bear some responsibility to stand up for what we actually want and have every right to expect out of a company to which we're giving our hard-earned money. In a capitalist society, we can assume that a company that wants to succeed will do its best to fulfill the desires of its consuming public. If the company sees sales slipping but doesn't have data from consumers as to what made them decrease their spending on a retail level, the company will not necessarily know what to fix.
Still, corporations and even small businesses that don't notice and repair their broken windows should not simply be forgiven because their consumers didn't make enough of a fuss. It is the responsibility of the business to tend to its own house. The owner of a Starbucks franchise who decides that revenues are at a healthy level, such that he or she can put off painting the store for another year, is asking for trouble: Yes, things are fine now, but when the paint is faded and peeling and consumers are no longer getting the experience they've come to expect, it will be too late to fix things with, literally, a fresh coat of paint. The time to repair broken windows is the minute they occur.
It's better, however, to prevent such smashed panes of glass to begin with. This book will examine the origins of broken windows with two purposes in mind. First, we will see how the small things that can snowball into large problems develop, so we can best illustrate how to repair the damage once it's been done. But it is equally important to see how these things happen so that a smart business owner can make sure to prevent them at—or before—the very first sign of trouble. If you have a policy to paint the store every year, you'll never have to worry about whether this was the year you waited too long.
In order to best understand how the broken windows theory relates to business, it's important to examine the original theory—as it related to criminal activity—in some detail. Because of the brilliant thinking of Wilson and Kelling, "Broken Windows" illustrated a serious societal problem that was going unnoticed, and helped turn around some of the country's largest cities (including the largest of all) by paying attention to detail.
It began with a program in New Jersey in the mid-1970s. The Safe and Clean Neighborhoods Program was meant to improve the quality of life in twenty-eight Garden State cities, and it was to do so, in part, by increasing the number of police officers on foot patrol, rather than in patrol cars. Police chiefs, Wilson says today, felt that such a move was not likely to lower crime levels, "and the police chiefs were right: They didn't have an effect on crime rates. But they _did_ have an effect—and in my view, a powerful effect—on how people felt about their community and their willingness to use it, suggesting that fear of disorder was as important as fear of crime."
Indeed, as Wilson and Kelling wrote in the _Atlantic_ , "residents of the foot-patrolled neighborhoods seemed to feel more secure than persons in other areas, tended to believe that crime had been reduced, and seemed to take fewer steps to protect themselves from crime (staying at home with the doors locked, for example). Moreover, citizens in the foot-patrol areas had a more favorable opinion of the police than did those living elsewhere."
What does this all mean to business? It's not likely that having police officers walk the aisles of a Wal-Mart store will increase sales. But it was the _perception_ that something was being done to increase order that made the difference for the people living in these New Jersey cities.
In a business (as we'll discuss in detail throughout this book), the broken windows can be literal or metaphorical. Sometimes a broken window really is a broken window, and a new pane of glass needs to be installed as quickly as possible. Most of the time, however, broken windows are the little details, the tiny flaws, the overlooked minutiae, that signal much larger problems either already in place or about to become reality.
We'll examine companies—huge ones, household names—that have failed to notice and repair their broken windows and have suffered greatly for it. We'll also look at those that have made it a priority to attend to every _potentially_ broken window and ordered plenty of replacement panes to make quick, seamless repairs. The lessons learned will be many, and varied, and they will have happy and, well, not-so-happy endings. Sometimes companies that deserve to be rebuked for their laziness will go unpunished, but other times there will be retribution at the hands of the public, which shows exactly what happens when you give the people what they _don't_ want.
What the public wants more than anything else is to feel that the businesses—retail or service-oriented, consumer or business-to-business—that work for them _care_ about what they want. Consumers are looking for businesses that anticipate and fulfill their needs and do so in a way that makes it clear the business understands the consumers' needs or wants and is doing its best to see them satisfied.
Broken windows indicate to the consumer that the business doesn't care—either that it is so poorly run it can't possibly keep up with its obligations or that it has become so oversized and arrogant that it no longer cares about its core consumer. Either of these impressions can be deadly to a business, and we'll see examples of both as we proceed.
If you run a business, and you truly believe that little things don't make a difference, you really should read this book—it may save your business. If you don't run a business but would like to, this can be the road map to your success. If you're merely interested in business and wonder why one succeeds where a very similar one fails, perhaps the examples contained here might help answer that question for you.
But it can't be overemphasized that tiny details—the smaller, the more important—can indeed make a tremendous difference in a business's success or failure. Sometimes, yes, a company can make a huge mistake (the whole New Coke thing was less a broken window than a neutron bomb placed dead center at corporate headquarters), but often, even those are foreshadowed by the little things that go, alas, unnoticed.
A broken window can be a sloppy counter, a poorly located sale item, a randomly organized menu, or an employee with a bad attitude. It can be physical, like a faded, flaking paint job, or symbolic, like a policy that requires consumers to pay for customer service. When the waiter at a Chinese restaurant is named Billy Bob, that's a broken window. When a call for help in assembling a bicycle results in a twenty-minute hold on the phone (playing the same music over and over), that's a broken window. When a consumer asks why she can't return her blouse at the counter and is told, "Because that's the rule," that is a broken window.
They're everywhere. Except at the really sharp businesses. Read on.
# _Chapter One_
# Broken Windows in Business
The broken windows theory was such a revolutionary, seminal concept in criminal justice that when it was published in 1982, it was considered a complete and total reversal of everything that had come before it. The notion that perception was as important in controlling crime as statistics, that letting "small" crimes slide by was sending a signal not only that the criminals were in charge but that the police were either unwilling or unable to stop them, was laughed at, ridiculed, considered absurd or "radical."
It wasn't until the theory was put into practice in the 1990s on the world's largest stage, in the city of New York, that its seeming simplicity was shown to be genius. Between Mayor Rudolph Giuliani and Police Commissioner William Bratton, the commitment to fixing New York's broken windows—graffiti, fare jumping, squeegee wielding, and the like—might have sounded like an assault on an insignificant annoyance, but it was actually a call to arms, a declaration of war on crime, that proved to be the salvation of a city in crisis. In showing the world that New York City would not tolerate _any_ infraction, Giuliani and Bratton were making the larger point that serious lawbreakers would be facing much harsher penalties. The good guys _would_ be in charge here.
It is a distinction between "law" and "order," one that is important, because it defines what the broken windows theory means and how it will apply to the business world. To adhere to the _law,_ one simply manages to live without violating the set code. Simple enough. But to maintain _order_ in a city, country, or company, the goal must be to have _everyone_ follow the same rules and to make sure that each rule carries the same weight.
To have a rule that says "Thou shalt not murder" and one that says "Don't cross the street against the light" seems like something approaching a contradiction—it sounds like the two infractions shouldn't even be mentioned in the same sentence. But both are rules, both are laws as set up by society. If it is generally accepted that we can violate one, isn't it logical that we could violate the other without any additional fear of punishment?
Rules don't have to be universal, either; they can vary from neighborhood to neighborhood, as the authors of "Broken Windows" discovered when the Newark, New Jersey, police made sure more officers on foot patrol were dispatched as an experiment in the 1970s. In one neighborhood, the foot-patrol officer, whom Wilson and Kelling called Kelly, was careful to enforce the informal, unwritten rules that were set up in that section of the city:
"Drunks and addicts could sit on the stoops, but could not lie down. People could drink on side streets, but not at the main intersection. Bottles had to be in paper bags. Talking to, bothering, or begging from people waiting at the bus stop was strictly forbidden. If a dispute erupted between a businessman and a customer, the businessman was assumed to be right, especially if the customer was a stranger. If a stranger loitered, Kelly would ask him if he had any means of support and what his business was; if he gave unsatisfactory answers, he was sent on his way. Persons who broke the informal rules, especially those who bothered people waiting at bus stops, were arrested for vagrancy. Noisy teenagers were told to keep quiet."
Wilson and Kelling noted that "these rules were defined and enforced in collaboration with the 'regulars' on the street. Another neighborhood might have different rules, but these, everybody understood, were the rules for _this_ neighborhood."
The rules in and of themselves were not exactly revolutionary, nor were they especially strict. There was not a "no tolerance" policy for addicts or alcoholics—they were simply asked to stay in certain areas and to not do certain things in public places. But the rules, as stated, were expected to be enforced, every one.
The same is true in the larger and more dramatic experiment that took place in New York City. When Giuliani and Bratton chose to crack down on graffiti artists, squeegee men, and fare jumpers (those who leap over turnstiles to gain free access to the subway system), they were making the statement that some things that were tolerated before would no longer be acceptable.
It was a calculated expression of control that was meant to make a statement not only to those who would spray-paint subway cars or jump over turnstiles—it was also meant (and, it could be argued, _mostly_ meant) to be seen by the public.
As Wilson explained to me recently, the police chiefs to whom he and Kelling spoke were actually correct in their expectations that increased foot patrols would not make a difference in the overall crime rate. Where they did have an effect, however—and it was a major one—was on public perception: "on how people felt about their community and their willingness to use it, suggesting that fear of disorder was as important as fear of crime."
Giuliani, speaking to the Conference of Mayors in May 2000, added to that sentiment: "New York City during the 1960s, '70s, '80s and into the early '90s served as a symbol of decline. I keep a national magazine cover describing New York City in 1990 as 'the Rotting Apple,' a city in decline. And at that time, people in the City of New York _accepted it._ They accepted the idea that this was our lot in life: that we were an old city that had seen our greatest days... the perception was that things were never going to be as good as they used to be."
Notice that the "perception" of the city's population is what is being mentioned here. The more people saw their city as a place with a glorious past and a mediocre present, the more it became the truth. It wasn't until the little details, the minor infractions, were dealt with that the quality of day-to-day life for citizens of the city showed noticeable improvement, and at that point, real change could be achieved.
Now, how does this apply to business?
The broken windows theory is all about the unmistakable power of perception, about what people see and the conclusions they draw from it. It doesn't claim that cracking down on graffiti will lead to fewer murders; in fact, crime rates overall are not necessarily affected by the theory being put into practice, as Wilson himself acknowledged. What is important is that as the quality of life in these areas improved, even on a scale that might seem insignificant, the population began feeling better about its surroundings, and _that_ led to significant change: People spent more time out of their homes, participating in events and patronizing local businesses.
In business, perception is even more critical. The way a customer (or potential customer) _perceives_ your business is a crucial element in your success or failure. Make one mistake, have one rude employee, let that customer walk away with a negative experience _one time,_ and you are inviting disaster.
I work in the public relations business in Hollywood. I have represented Barbra Streisand, Charlton Heston, Linda Evans, Fleetwood Mac, Vanna White, Demi Moore, Michael J. Fox, Robert Evans, and Michael Jackson, among many others. I understand the power of perception, and believe me, it can be devastatingly powerful—for good or for bad.
Perception is also something that happens in the blink of an eye. There is nothing more fleeting than a first impression; it is made in a heartbeat. But a perception can be made at any time, even after you have been acquainted with a person or company for years. And opinions turn on such perceptions.
For example, let's say you have bought your coffee at the same store every day for the past five years on your way to work in the morning. You've gone there unfailingly, sometimes added a bagel or muffin, and occasionally stopped in at lunchtime. The counter staff knows your name, knows your usual order, and can anticipate your preferences.
But one day, even without thinking about it, you happen to notice as you stand in line waiting to order that the walls haven't been painted in years. There are slight cracks and chips in the paint just behind the counter help. It's never occurred to you before, but that small perception makes a difference.
Maybe you start to wonder if those paint chips aren't falling into the coffee or onto a surface where rolls and bagels are cut and prepared for sale. Perhaps the fact that you noticed the paint job makes you realize just how long you've been waiting on line every morning. It's just possible that you consider which other aspects of the store's physical plant—including its cleanliness—might be in disrepair. You might end up by wondering exactly why you've been frequenting this particular business all along.
That one little perception can pack an extraordinary wallop, can't it?
Now, nothing assumed in this scenario is necessarily true: There's no reason to think the coffee outlet's cleanliness, commitment to service, sanitary conditions, or food preparation are at all in question. But you perceived one flaw, and from that allowed your mind to wander into territories it might not have ventured without some direction.
It's not a place the owner would want his customers to go. And if he takes care of broken windows like the paint job, he can avoid such mental journeys. It's better to create a _positive_ perception, of course, but avoiding the negative ones is far and away the most critical thing one can do to attract and keep customers. There is no alternative for an unbroken window _,_ other than one that is under repair.
Let this book be your manifesto, your obsession, your bible of perception. From this moment on, consider how everything _seems_ to your customers, your employees, the public in general. Yes, you have to care about what really _is_ , but you also have to concern yourself with the way things _appear_ to be.
It doesn't matter if you tell a suspicious customer about your scrupulous cleaning techniques, your patented methods for keeping the food away from anything that might fall on it, or your plan to speed up counter lines. Mostly, it doesn't matter because the customer _isn't ever going to tell you about her concerns;_ she's just not coming back to your store again. Generally speaking, consumers will not voice their complaints. (I know, you've heard plenty of bitching and will argue with me, but the truth is that the vast majority of those who find something wrong will not communicate that perception to you—they'll just stop being a customer.)
The thing about a broken window is that it's not always obvious. The owner of the coffee outlet in this scenario isn't necessarily someone who doesn't care about his business or is given to outrageously lax upkeep. This is someone who either didn't notice that his paint job was starting to erode or felt that by waiting another year to paint he could save some operating capital, and besides, sales were consistent and the customers hadn't complained. There are other, squeakier wheels to grease.
Unfortunately, that is the attitude that can sound a death knell for a business, but on a frequency the human ear can't detect. Let things slip, let the clientele notice things you haven't, and you might as well throw a Molotov cocktail into your store and start from scratch: Your business is on its way out. Constant vigilance, an absolute obsession with detail, is essential to running a business today, particularly one that deals directly with the public (although we will be considering business-to-business broken windows as well).
If you're not obsessed with the details of your business, you can believe me, there will be someone who _is_ obsessed with his, and he will see to it that he overruns your customer rolls and decimates the loyalty you've built up with your regular clientele. Show the slightest chink in the armor you've built up, and an exposed weakness will become the most obvious flaw you can imagine. Your business, to put it simply, will not survive too many broken windows. And "too many" is "one."
Consider the case of Martha Stewart. Was Ms. Stewart convicted of insider trading? Fraud? Tampering with a public trust? No. She was convicted of wrongdoings involved with _covering up_ whatever alleged improprieties had gone on. Why was she trying to cover up? Because she was concerned about the _perception_ that her business was unscrupulous and that she, personally, was not trustworthy. Obsession with detail? Perhaps, but far too late. You can't fix a broken window by throwing rocks through all the others.
Many a politician has been brought down not by accusers who had solid evidence that the official had done something illegal or unscrupulous, but by the effort to suppress the _perception_ that might have come from the allegation itself. History is littered with the carcasses of officials who were discarded after trying to cover up something that might not have been as serious a scandal had it been dealt with quickly and efficiently—and publicly.
A broken window, make no mistake, is best repaired _before_ it breaks. The most desirable scenario is to fix the problem before it is visible, and never to have to consider perception, because there will be nothing to perceive. But if a flaw arises, the only course of action—the _only_ course—is to deal with it immediately, to do so without trying to put a cosmetic sheen on it, and to make sure it is, without question, repaired. A piece of masking tape on a cracked window might prevent it from breaking, but it will be visible for all to see and will have the same perceived effect as a broken window itself. Repairs must be complete and immediate.
But what constitutes a broken window in business? It's easy to spot the physical ones, like the peeling paint on a wall, but what about the less obvious problems? What about employees who don't follow the company's stated policies and present a flawed, incorrect picture to the consuming public? How can you deal with a broken window when you're in corporate headquarters and there are thirty thousand outlets to oversee?
Well, consider the case of the world's largest restaurant chain. Its broken windows have come very close to bringing down the house. The last chapter in this story has yet to be written, but the fact that it was ever in question is a testament to the power of broken windows and how far the mighty can fall. Indeed, consider the case of McDonald's, which once was considered (and considered itself) invincible, and see what broken windows can do, even to a giant.
## PERCEPTION VS. REALITY
* It is your customer's _perception_ of your business that will dictate his or her level of loyalty to your business. Make one mistake, and you can damage that perception.
* Little things mean a lot. If you notice that the carpet on the floor at your dentist's office is a little worn, you might find yourself wondering whether the dental instruments have been replaced recently.
* Broken windows are best repaired before they break.
* It's the cover-up that gets you—don't make excuses for broken windows or deny that they're broken. Take your hit, own up to the problem, and fix it.
* Obsession to detail is essential. There is no substitute.
# _Chapter Two_
# Can McDonald's Be Saved?
For those born during or after the 1950s, a world without McDonald's is just short of unthinkable. The golden arches making up the hamburger behemoth's logo create a symbol so ubiquitous, so huge, so utterly pervasive, that the thought of it vanishing from the street, let alone the world, is practically laughable.
But it could happen someday. And why? Because the huge company has neglected its broken windows, and the public has taken notice.
Despite its presence in virtually every country, on every continent, in almost every town in the United States, McDonald's is not the paragon of customer satisfaction or brand integrity it once was. In fact, consumers are fed up with Mickey D's indifference toward them, its abandonment of its core principles, and its obvious contempt for those who patronize its tens of thousands of stores.
Consider this: The American Customer Satisfaction Index (ACSI) is compiled each year from quarterly surveys made by the University of Michigan's National Quality Research Center, in conjunction with the American Society for Quality, a Milwaukee institute, and CFI Group, a consulting firm based in Ann Arbor, Michigan. In February 2003, it was reported that for the tenth year in a row, McDonald's had scored below average—and significantly so—for the fast food industry.
On the 100-point scale used by the ACSI, McDonald's score was 61, down over 1.5 points from a similar survey done a year earlier. And the company's average score was 5 to 10 points below the industry average since 1994, according to the ACSI.
Among the questions the sixteen thousand consumers surveyed answered were evaluations of the outlet's food, its service, and whether the order was handled correctly.
The same time period's survey results saw Taco Bell's scores go up 1.5 points, Domino's Pizza up 2.7 percent, Wendy's up 2.8 percent, and chief rival Burger King's scores up 4.6 percent, a good 7 points higher than McDonald's.
Bad enough? Wait: A _Fortune_ magazine article of April 2002 showed a sixth consecutive quarter of "disappointing profits" for McDonald's. The stock price took a good number of hits, and there were wholesale changes in the executive suites at the company's Oak Brook, Illinois, headquarters. In 2004, the purveyor of the Big Mac with Cheese was announcing it would eliminate the "supersize" option from its stores, calling the process "menu simplification."
All right, so McDonald's, one of the world's largest corporations, is going through a rough time. Well, what does that have to do with _your_ business? If you sell hamburgers, french fries, or sodas, you might _welcome_ the collapse of a behemoth competitor like McDonald's.
Well, if something of this magnitude can happen to McDonald's because it is failing to fix its broken windows, can't the same thing happen to you, no matter what business you might be in, if you don't see to the small things that make all the difference?
What is especially puzzling about McDonald's is that the company's core philosophy would seem to stand for exactly the kind of attention to detail and basic service that seems to be lacking in its practice. The corporation's headquarters boasts a posted list of promises made to consumers that _must_ be kept, under any circumstances. Among them are fast service and clean facilities, two areas that were cited by consumers as lacking in McDonald's restaurants during the ACSI survey.
By contrast, Papa John's, the pizza chain with far fewer outlets than McDonald's, is at the top of the fast food industry (which likes to call itself "rapid service") in consumer satisfaction and has been consistently so for a few years. With a score of 78 in the 2002 survey, Papa John's not only came in first among fast food restaurants but was also the only such chain to beat the retail sector average and do so for a number of years in a row.
McDonald's, it was noted by the ACSI, ranked last in its category and among _all retail outlets_ for the eighth consecutive year.
In fact, the American Society for Quality quoted its past president, Jack West, as saying that "the greatest weakness for McDonald's is service quality. People go to McDonald's for a combination of fast service, consistent products, low price and convenience. Obviously, McDonald's is not consistently meeting those expectations."
# Roots of the Problem
Granted, some of McDonald's troubles were not directly the fault of the company itself. An epidemic of mad cow disease in 2001 and 2002 caused some panic, particularly in Europe, regarding eating beef, and that certainly didn't help the sales in hamburger outlets. Globally and in the United States, economic lethargy meant jobs being cut, fewer people eating in restaurants, and slower sales. Concerns about cholesterol and heart disease led to a decrease in the consumption of beef overall. These things were outside McDonald's control, although the corporation was capable of responding to some of them, a subject we'll touch upon a bit later.
The point is, those outside concerns were not the main reasons for McDonald's decline in customer satisfaction, which led directly to decreased sales. (The corporation announced closings of its outlets in a number of countries, something that would have been unthinkable just a few years ago.) The University of Michigan study of consumer satisfaction found in 2001 that 11 percent of McDonald's customers were dissatisfied with their visit on any given day. Close to 70 percent of those dissatisfied customers were even more disgruntled following some contact with the company, because the complaints were not handled to the customer's satisfaction. And here's the part that really tells the story: _More than half of all dissatisfied customers cut back on their visits to McDonald's and told as many as ten other people about their experience._
McDonald's brand contract, stated in its headquarters and at all its outlets in writing, states that the brand vision is "to be the world's best quick service restaurant experience," which is to include outstanding service, quality, value, cleanliness, and "having every customer in every restaurant smile." If eleven out of every one hundred people who walk in aren't smiling on the way out, are angry about the way their complaints are received, and might become less frequent visitors, there is something wrong.
According to the University of Michigan study, the top five complaints by McDonald's customers were rude employees, not having Happy Meal toys, slow service, missing items or receiving the wrong order, and unclean restaurants. All of these points of contention fly directly in the face of McDonald's stated goals, their most basic promises made to consumers.
These are all broken windows, and they are not being repaired. In fact, as is the case with most broken windows, more glass is being shattered while the first cracks still await attention.
It starts, clearly, with something as seemingly insignificant as an inadequate supply of toys to go with Happy Meals, the prepackaged products aimed at young children. Because McDonald's does a great deal of advertising and promotion to children, and emphasizes the Happy Meal toy in all of it, children will often ask to be taken to the restaurant specifically to get that particular toy. When the franchise owner or manager has not ordered an adequate number of toys, or the company itself has failed to produce enough and supply its restaurants, the child is disappointed, the parent frustrated, and the cycle of dissatisfaction set in motion.
But the broken windows at McDonald's are much more plentiful than the absence of expected toys. For adults, they are often so obvious and numerous that a discussion of them seems superfluous, but they are worth examining.
# Come Back, Ray!
It is my contention that if Ray Kroc, who bought the McDonald's name and system and built the corporation almost single-handedly into one of the largest companies in the world, were to rise from the grave and walk into a present-day McDonald's franchise, he would die a second, more painful death.
From embarrassment.
In many locations, the cleanliness and efficiency Kroc so diligently guarded are nonexistent. The condiment areas are not cleaned regularly. The counter help is, at best, indifferent. The bathrooms... well, let's stay out of the bathrooms.
Key points are the ones that Ray Kroc emphasized a half century ago: dependable quality; fast, accommodating service (it doesn't have to be "friendly," but it sure as hell should be "polite"); a clean, comfortable place to eat; and value for the working people who make up the overwhelming majority of McDonald's customers.
On the surface, that doesn't seem like such a tall order: The company should just go back to Kroc's principles and then enforce them strictly. But it's not that simple. The world isn't the same today as when Kroc walked into a San Bernardino hamburger stand in 1954.
The broken windows at McDonald's are not all that different from those in other large businesses that have seen their star power decline in recent years. But when the business is based on speed and consumer satisfaction, and both of those begin to erode at the same time, the prognosis is not good. McDonald's needs to get in touch with its inner Ray Kroc, and fast.
And if it can happen to them, it can happen to you. Think about it.
## DESERVE A BREAK?
* Customer loyalty is a wonderful thing to have, but customer _stupidity_ should not be expected. Customers won't stick with you if you stick it to them.
* Core values—the things that a business promises its customers—are never to be taken for granted. If you make a promise to consumers and don't keep it, you are asking for bankruptcy.
* The little things that plague McDonald's aren't the quality of the food or the promises the company makes. They are the promises _not_ kept—the dirty bathrooms, the absent Happy Meal toys. Customers are disgruntled because they've been told to expect something and then are given less.
* Broken windows can be repaired, but they have to be seen and fixed as quickly as possible.
# _Chapter Three_
# Obsession and Compulsion
Some people suffer from a condition known as OCD, obsessive-compulsive disorder. Its symptoms may include an incredibly focused interest in one topic or the inability to function without certain rituals, like frequently washing hands or locking doors over and over. These people often seek treatment and can sometimes lead what is considered a normal life through therapy, medication, or other avenues.
While in personal life OCD is a challenge, in business, obsession and compulsion are _good_ things. In fact, they are necessary. Without an obsessive attention to detail and a compulsive drive to fix broken windows in a business, disaster is being courted. In today's business climate, everyone should have OCD concerning broken windows.
And no window is too small to break; nor is any break too small to repair. Everything counts, significantly more than you might think.
The concepts of obsession and compulsion are central to the idea of broken windows. I can't stress strongly enough how important it is to have a driving, obsessive fixation on your business, and a compulsion to see everything done in the right way every single time. Repairing what mistakes are made along the way can't be an optional thing; it has to be an absolute, unquestioned necessity that would literally cause you to lose sleep were it not taken care of immediately and completely.
# Obsession
Obsession is the fixation on one idea, subject, or concept. It allows virtually no other thoughts and becomes an all-consuming, all-important idea in the mind. It would not be an exaggeration to say that in order to prevent and repair all broken windows, you must be—not _should_ be, not _may_ be, but _must_ be—obsessed with your business.
You have to feel personally affronted if something goes wrong with your business. And that "something" can be _anything._ The idea that a trash can hasn't been emptied, that a counter hasn't been cleaned, needs to be a personal insult, an abomination. You have to feel physically ill if you find a problem in your business, no matter how small and (here's a word I use with great caution) insignificant it might seem.
_Nothing is small, and absolutely nothing is insignificant._
It's not enough to be concerned about your business; it's not enough to be interested in its success. You have to be obsessed, or you are inviting disaster. If you're not lying in bed at night trying to think of ways to improve business, to serve your customers better, and to fix the broken windows you have or will have soon, you are not doing your job properly. And that fervor must be communicated to every single employee you have. It's not enough for _you_ to be obsessed— _everyone_ who works for the company must be equally single-minded.
There are few companies as well entrenched in the American landscape these days as Starbucks. The company that convinced the world that a four-dollar cup of coffee is not ridiculous has a presence on what seems like every corner, has become part of the language, and now sells coffee in supermarkets, convenience stores, and bodegas in addition to its own stores. Its service is still considered exemplary, and its product is being accepted by people the world over. It's hard to imagine that things could get much better for Starbucks.
Indeed, even the company's chairman, Howard Schultz, believes Starbucks is doing as well as it can do. He has warned his investors that the current sales performance can't be sustained indefinitely. But he knows where the windows that might be broken are, and he has a plan to keep them crack-free.
Schultz increased the paid training time for the company's "most motivated employees" by as much as a third, to thirty-two hours, in early 2004. His plan was to make the employees better educated about coffee generally and, by extension, better at selling more brewed coffee and bags of whole beans. He wanted to make sure that customers entering a Starbucks would be met by employees who knew their product inside and out, and could discuss it, recommend choices, and answer questions as well as anyone in the industry.
That's impressive, and it is also a sign of obsession. Schultz understands that Starbucks has expanded rapidly and that such growth often presages a fall. Companies like Boston Market, Crazy Eddie, and Kmart have all suffered from too much too soon. Schultz wants to ensure that no such thing would happen to the upscale coffee chain in his charge.
His choice—to improve the Starbucks brand by improving its employees' knowledge of the product—is a bold move. It shows obsession on his part, and it demands obsession on the part of those who work for the chain. By knowing as much as they can possibly know about their product, Starbucks employees must cross over from interested to obsessed with coffee, and they must demonstrate this obsession to their customers by exhibiting the level of education and training they have received. It's a fine line to walk, as the employees must know how to be helpful and knowledgeable without being irritating know-it-alls.
Obsession is a dangerous tool. It's essential, but it has to be handled properly to be effective. Yes, the customer base should be made aware of your total commitment to service, but you can't demonstrate it in such an overbearing fashion that it becomes obnoxious.
How obsessed must you be? Keep in mind that Ray Kroc used to grab a mop and clean up when he visited a McDonald's he felt wasn't up to snuff. Rudolph Giuliani didn't rest until every New York City subway car was free of graffiti. CEOs hire mystery shoppers to report on the state of their retail outlets, then go into the stores themselves and double-check what the mystery shoppers have reported. It's not enough to demand that something be done—you have to make sure that it is done by checking _yourself_.
The saying that a chain is as strong as its weakest link has great resonance in the world of the broken windows for business theory. An employee—especially one who has direct contact with customers—is the most visible type of broken window imaginable. Nothing will drive customers away faster than an employee who isn't with the program.
Service is the absolute center of broken windows for business. Your product might very well be the best in the world, but if it's being sold and represented by employees who with every word and action betray their complete indifference toward the customer and the customer's needs, you will fail, without question. Indeed, if the first employee to come into contact with the customer (counter help in a retail setting, the receptionist in a doctor's office, etc.) is not the best possible face for your business, you have a broken window that could very easily shatter your business very quickly.
Become obsessed with your hiring practices, since it is much more difficult, expensive, and damaging to hire a bad employee and then be forced into a firing situation. Know ahead of time what kind of person you need, and then take steps to hire one with the proper knowledge for the job and the proper _attitude_ to exhibit that knowledge. Hire the obsessed, but hire the obsessed who can relate to customers if the employee is going to have any contact with your clientele at all.
Obsession is not just a line of perfume—it's a tool, and a valuable one. Without it, you will be operating at a disadvantage, and in business today, you need every single advantage you can get. Eat, drink, and sleep your business. Worry about it. Load up on antacids. It's not going to be an easy ride, but you can make it a successful one if you're obsessed enough.
# Compulsion
There is a very clear line between obsession and compulsion. Where obsession demands merely an intense, focused interest on all aspects of your business, compulsion requires more practice. It is just as powerful and just as essential a concept as obsession, but it relies more on instinct and conditioned responses than thought and planning. Compulsion is to obsession what lust is to love.
It's one thing to like your living room to be neat; it's quite another to be incapable of leaving the room if everything is not in exactly the proper place. Compulsive behavior means that you are paralyzed if things aren't precisely the way you have decided they should be. Watch the television series _Monk_ and you'll get the idea: The character might be investigating a horrible murder, but he can't really concentrate on the clues if the shades on the windows aren't all lowered to the same level. That's compulsion: the involuntary need to have things be a certain way.
In business, compulsion is as useful a tool as exists on the planet. It is perfect to help fix broken windows, as it will not allow you to even consider going on with your day until that window has been repaired. Compulsion implies a stubbornness, a devotion to detail and order, that goes far beyond what most businesspeople believe to be sufficient, even excessive.
Compulsion means not ever letting a customer see a bathroom that isn't spotless. It means never letting someone stay on hold with a voice mail system for more than one minute before contact with a real human being. It means not one employee who isn't going to say "please" and "thank you" to every customer, no matter what the circumstances. Compulsion is all about consistency, since it tolerates nothing outside the established order, and it requires all repairs to be made immediately.
George Steinbrenner III is not the most popular employer on the planet. In fact, he is legendary for being demanding and uncompromising with his employees, from the parking lot attendant to the $25-million-a-year Yankee third baseman. Nothing is ever good enough, and nothing escapes Steinbrenner's notice. If something is going on at Yankee Stadium, the man everyone calls the Boss knows about it. If that something is not what the Boss wants, it is changed— _now_.
Steinbrenner's insistence on having enough bathrooms in the stadium, a building that existed for fifty years before he owned the team that plays there, has been well documented. He knows about the ushers showing people to their seats, he knows about the concession stand employees, he understands the grounds crew and what it must do, and he certainly oversees the players and on-field management.
"Buying the Yankees is like buying the _Mona Lisa,_ " Steinbrenner has said. "You don't put the _Mona Lisa_ into a cheap frame and hide it in the closet."
Some of the rules imposed on all Yankee employees—no beards; suits and ties whenever traveling in public—are cosmetic, but they are imposed from on high, from the Boss himself (who, it must be pointed out, often wears turtlenecks). Steinbrenner knows that image is important to perception and that the perception of his product, which happens to be a baseball team made up of men, is essential to ticket sales and other revenue streams. He makes sure that every detail is attended to, and when one is not, he fixes that broken window immediately.
When, on occasion, one of his players has defied the "no beards" policy during the baseball season, or let his hair grow to lengths the Boss felt was not in keeping with the Yankees' image, that player—no matter how beloved, well paid, or integral to the team's success—was disciplined. Image was maintained, and perception was consistent.
Is this a sign of a compulsive nature? In business, it should be. A broken window allowed to stay broken—even if there is every intention of fixing it eventually—is the wrong sign to the outside world. It tells passersby that no one is in charge here and no one cares what happens. That is the death knell of any business, and it simply can't be tolerated. If that means you have to be compulsive, then be compulsive.
When it doesn't come naturally, compulsion is a practiced art. Train yourself to notice the broken windows and then act on them immediately. Refuse to move on to the next item on the agenda until that window is repaired, or until the mechanism to repair it is in place and operating properly. If the broken window is an employee, or a policy of the company, deal with it as quickly and efficiently as possible and make sure that every company employee is aware of the move. People can't be expected to comply with a rule they have not been informed about.
Swift, decisive action is essential in fixing broken windows. Every day that goes by without visible action is a signal that the engineer is asleep at the switch and anarchy rules. It is important, even if the window can't be fixed at this moment, to erect a sign that reads "Broken window being repaired." That can be a literal, physical sign when the broken window is a physical flaw, and it can be a metaphorical, implied signal when the broken window is a policy that needs revamping or a change in the company's direction.
Still, compulsion is as useful a tool as obsession, if not an even more useful one, because it does demand swift action. If you are not able to move on until you are satisfied that a problem is being solved, you will be sure to solve that problem quickly. The key is in planning; the idea is to train yourself to notice the broken windows when, or before, they occur and to deal with them as fast as you can. Many large companies have found themselves in extremely difficult circumstances when they did not act compulsively.
## OBSESSIVE/COMPULSIVE ORDER
* In the world of business, it is a positive thing to be obsessive and compulsive. It's the only way to successfully avoid and repair broken windows that can lead to disaster.
* _Nothing_ is insignificant. There is no such thing in business. If it's wrong, and it can be right, it _must_ be made right. If you tell yourself that no one will notice, someone _will_ notice—and you'll never see that customer again.
* It's not enough to be obsessed yourself: You must hire the obsessed as well. You can't be everywhere at all times, but you can hire people who are, and they have to be just as irrationally dedicated to perfection as you are.
* Compulsive behavior feeds the image of no-defects performance you're trying to cultivate. It is never enough to be dedicated to doing well; it has to become a reflex action.
* In most aspects of life, obsession and compulsion can be debilitating or at least inconvenient. In business, they are useful tools. Cultivate them.
# _Chapter Four_
# How the Mighty Have Fallen
In the 1980s and '90s, few symbols were as recognizable in this country as the Kmart logo. When the chain reached its all-time high of 2, 323 stores in 1994, there appeared to be a Kmart on every highway, in every shopping mall, virtually around every bend in the road. So when Kmart announced in 2002, its fortieth-anniversary year, that it was seeking bankruptcy protection and that it would close stores in forty-four states and Puerto Rico as part of its reorganization plan, the news came as a shock.
It shouldn't have.
"Kmart's dismal bottom line is directly related to its lack of customer service and its out-of-control operating costs," says John Tschohl, an international management consultant and speaker. "If the company had taken just 10 percent of its advertising or renovation budgets and used that money to train its employees in the art of customer service, Kmart might have realized profits similar to those of Wal-Mart."
Poor customer service is the ultimate broken window. It is the thing that all consumers will notice immediately, that will make an enormous negative impact and that will not only hurt the company offering the service but give consumers strong incentive to patronize its competition. And demonstrable customer service problems will not only convince consumers that the company doesn't care about its own business—the message of broken windows throughout the business world—they will make an even more damaging point: that the company doesn't care about its _customers,_ either. That will kill a business faster and more completely than any other oversight.
Kmart grew from the S. S. Kresge chain and opened its first store in 1962, the same year Sam Walton opened the first Wal-Mart. Today, while Kmart does its best to emerge from bankruptcy by merging with Sears, Wal-Mart is the world's largest retailer. Where did the paths separate, and why so dramatically?
In January 2002, George Chamberlin wrote in the San Diego-area _North County Times:_ "Five years ago, the betting money might have favored Kmart. They had just signed up an exclusive distribution contract with Martha Stewart, a sure magnet for baby boomers. And supermodels like Kathy Ireland and Jaclyn Smith were hawking merchandise every Sunday in the Kmart newspaper supplements. At the same time, Wal-Mart was pursuing a different strategy: position the company as the place to shop if you want to save money. Advertising was designed to build a corporate image, not sell specific products. At the same time, Wal-Mart started aggressively selling food products and today is the largest grocery store chain in the United States."
Chamberlin also noted that while Wal-Mart made sure to place its stores in high-traffic, shopper-friendly locations, Kmart was more interested in saving money on rent. Kmart is a classic example of what I call _Broken Windows Hubris_ , the unfortunate—and destructive—tendency in some huge corporations (and some less enormous) to believe that they are so successful, so large, so invincible, so much a part of modern society, that they are not subject to the same scrutiny by the public that makes any other company answerable to the broken windows theory. These companies—and among them are McDonald's, Sears, and Disney—suffer from attacks of ego, yes, but that's too simple an explanation. The type of miscalculation we're discussing here is much more pervasive, from the CEO to the janitor; it is the overwhelming perception from within the company that _nothing can ever bring us down because we're just too good._
Kmart's Broken Windows Hubris was evident in its blasé customer service; in prices that weren't the lowest in town; in policies that seemed to make sense, but really demonstrated how little the company cared about its customer base.
The truth is, Kmart's problems began long before Target and Wal-Mart began to overtake it in sales and in the public's perception. And keep in mind that the public's perception of a company might be more important than the truth, since the truth, if it is not what the public believes, can't really set you free.
Consider how many people truly believed that Procter & Gamble had some kind of ties with satanic cults, due to a symbol on some of the company's products, which was rumored to be linked to such groups. While the rumors bore no truth whatsoever, it was a public relations nightmare to reverse that perception in the public's mind. The company, with some extremely aggressive and well-planned public relations tactics, did manage to get out the message that the rumors were utterly groundless, but it cost P&G a good deal of money, and it still requires some public relations maintenance to this day.
In Kmart's case, the problems were considerably more pervasive and the windows broken at a much more basic level. The covenant made with the public—that Kmart would be the place for low prices and quality merchandise—was not maintained. The trademark Blue Light Specials, which could be activated at any time in a Kmart store and represented unusually deep price cuts on a particular item for a limited time, underlined this point for the consumer. In other words, there was always the possibility that a product— _any_ product—could be had for a very low price in a Kmart store. Low prices were the point. By making sure that the price cuts were seemingly random and that the base of products sold in Kmart stores was very broad, Kmart made sure the public was getting the message: "We have what you want, and we are selling it at the lowest possible price." It also pushed the point that it was _exciting_ to shop at Kmart, because you never knew when a terrific bargain might be offered.
How, then, did Kmart reach a point where it closed six hundred stores and cut 67, 000 jobs between January 2002 and May 2003, when it emerged from Chapter 11 protection? How did it manage to lose $3.22 _billion_ in 2002, even as it became leaner and meaner, cutting its size by almost 33 percent?
Kmart lost sight of its covenant with the consumer. It stopped offering Blue Light Specials because the company saw itself as something other than a discount retailer. Because of Broken Windows Hubris, the boardroom became tired of "Blue Light Special" being a late-night comedian's punch line and of having the company seen as something akin to the tiny chains around the country that sold all items for a dollar. Kmart, in short, wanted respect, and in seeking it, lost the consumer's trust. It was the wrong trade to make, and it cost the company dearly.
Clearly, this was a company that wasn't listening to its customers. If customer service had been a priority with Kmart at that point, it might have saved its business and its market share. Then again, if customer service had been a priority with Kmart from the beginning, it might not have found itself in this predicament to begin with.
What Kmart hadn't learned was that consumers make or break a retail business. The ultimate broken window—customer service difficulties—will overwhelm any marketing plan, even deep discounts. People simply want their retail businesses to serve the customer, not the business, and without that component, no retailer of any product is going to survive for long.
American Airlines, once the country's largest and seemingly most invincible airline, came within inches of bankruptcy in 2003, surviving only because its unions agreed to last-minute concessions that kept the company out of Chapter 11 protection. An upstart that emphasizes customer service above all other things, jetBlue was thriving at the same time. Consumers want to be treated better, and businesses only sporadically notice or act on that desire. It's the reason Nordstrom has a pianist on staff full-time and offers impeccable customer service. It's the reason no L. L. Bean customer will ever end an encounter with that company unsatisfied if the company has a say in the matter (and it does).
Apple Computer holds a small fraction of the market share for its industry, perhaps 4 or 5 percent. Microsoft dominates its industry, eating up market share and dictating to the rest of the world what programs will and will not be run on the vast majority of the world's personal computers. But Apple users are never disgruntled; they are almost exclusively described in the press as "enthusiasts," while the computing world in general detests the policies of Microsoft and particularly its customer service. Does this constitute a dichotomy? Does it disprove the idea that the company with superior customer service will prevail? Does it mean that broken windows in business don't really mean that much?
Not at all. While Microsoft's policies do alienate some consumers, its products deliver precisely what the company promises they will deliver. Microsoft does not make the mistake of Kmart, trying to be something it is not in order to attract a minority of consumers. But Apple, which does appeal to a smaller percentage of the public, _knows_ it is a niche market. Surely, the company's board of directors would be thrilled if the vast majority of consumers decided to pay higher prices for a more elegant system and friendly customer service. But Mac enthusiasts are just that—enthusiasts—and they are among the most loyal consumers on this planet.
The lessons of Kmart are many, but the key is in this area: Poor customer service, the ultimate broken window, coupled with an unrealistic view of the company from within (Broken Windows Hubris), will sink a company, no matter how large and ubiquitous it may once have been. Kmart tried to fix its broken windows by covering them over with clear plastic, but the shattered glass beneath could still be seen by the consuming public, and as of this writing, it is still visible.
## WHAT WENT WRONG
* A company that believes itself to be too big and powerful to worry about customer service suffers from Broken Windows Hubris, and unless it changes its ways, it will come to no good end.
* Not paying more attention to customer service than to anything else is business suicide.
* When sales start to slip or business is not what it once was, blaming the consumer is not only counterproductive, it's ridiculous. There is no point to saying that the wrong people are buying your product or service—the effort should go into providing the best possible experience for the person who is doing the buying, and catering your whole business to that consumer.
* Trying to find a new consumer instead of servicing the loyal customers you have is Broken Windows Hubris at its most destructive.
* Never assume you are smarter or more sophisticated than your customer. If you think you need to _explain_ your business to the customer, perhaps you need the customer to explain your business to you.
* You can't fix a broken window by hiding it. A cracked pane of glass covered in clear plastic will still show the damage. Real repairs must be made, and made quickly, when a broken window is discovered.
# _Chapter Five_
# Expectation vs. Reality
When you walk into a movie theater, would you expect to walk out with a free book?
Some East Coast moviegoers who went to Loews theaters in April 2004 were given a promotional copy of "teaser" chapters from two books by best-selling author Harlan Coben in a professionally bound paperback edition with a slick cover. Yes, it was a promotional item and could be seen as advertising, but it was hardly a throwaway flyer or coupon. It felt like a real book. People took it home and read it.
Will some of them spend twenty-five dollars for a hardcover edition of one of the books? Perhaps. But all of them will remember that they went to the movies and came home with a little something extra.
That's an example of the difference between expectation (seeing a movie) and reality (being given a book). Other examples—even easier to implement and which the consumer is probably not expecting—include saying "hello," "thank you," "please," and "you're welcome." Two of the biggest words to say in order to avoid broken windows—and, perhaps, give a customer a new idea of what reality can and should be: "I'm sorry."
Every time a customer or client calls or enters your business, that customer has an expectation. Depending on the nature of your business, that expectation might be a quality product, excellent service, help with a problem, or simply the presence of a product the consumer has always relied upon. If that expectation is met, the customer will be satisfied, although probably not overwhelmed. If the expectation is not met, or if the personnel fulfilling it are not helpful or courteous, the customer will walk away with a negative impression of your business, and you may have lost a customer—for life.
But consider another possibility: You might _exceed_ your customer's expectation. Maybe you'll deliver more than he or she anticipated, be just a little bit more courteous, more helpful, friendlier. Maybe you'll put in extra effort and make it show; or simply put in the extra effort so that the negative things that _could_ show don't ever materialize. Train employees to always say "please" and "thank you" and to take responsibility when they do something wrong, to apologize for mistakes or inconveniences. Do more than the competition.
Now, suppose you did all that by design.
It seems like the most basic, simplest rule a business could have: _exceed expectations_. But the vast majority of businesses today would be hard-pressed simply to _meet_ expectations, let alone surpass them. If the broken windows for business theory teaches anything, it should be that _the customer may not always be right, but customerscertainly always think they are, and if you agree with them, you are all on your way to exceeding their expectations._
"Our expectation is to meet and exceed the customer's anticipation," says Steve Shapiro, vice president of entertainment services for City National Bank in Los Angeles. "When little things go wrong, it drives me nuts, because they didn't have to go wrong."
Think about your experiences as a consumer. When you're dealing with a small retail or service business today, you are rarely greeted with a smile. You are, in fact, rarely greeted at all. At best, you are met with a tolerant gaze and asked (if you're lucky), "Can I help you?" The honest answer is usually, "I've been wondering that myself."
Dealing with a large corporation can be even worse. Call one sometime and have a stopwatch handy. See how long it takes for you to speak to a living, breathing human being after you're done with all the automated phone system prompts. Press 1, press 2, press 3, and still, you're listening to endless minutes of Kenny G interrupted only by a computer voice telling you how important your call is to the company that's kept you on hold now for ten minutes without even knowing what your problem is.
During the 2000 presidential campaign, Ralph Nader was fond of saying that if he was working late at the office and wanted to listen to classical music, he'd call United Airlines. They were certain to be playing "Rhapsody in Blue," and he'd get to hear a very long segment of the piece before anyone picked up.
Once you get that person on the line, you are subject to the downside of outsourcing; in other words, you're lucky if the person trying to help you can speak English. If he or she can (count your blessings), the corporate system will start to show through. This means the person will be trained in responding to your concern—whatever it may be—with a series of scripted lines that are meant to placate you but are more likely to raise your blood pressure, since they are often delivered in a monotone that makes you question not only the company's commitment to customer service but also the service personnel's ability to read.
All of this would be unfortunate, but not necessarily harmful to the business, if the person assigned to help consumers were actually trained to do so. Too often the problem is beyond the abilities of the person on the phone line, and too often the personnel could not care less. There's not so much as an "I'm sorry"; there is only the disheartening information that you'll have to solve your problem yourself, and we don't especially care how it comes out. Don't call us, and we won't call you.
But that's not the way things have to be. It's a simple formula of promises made vs. promises kept.
If you promise A, B, and C, but deliver only A and B, your customer base will be disappointed. But if you promise only A, and deliver A and B, your customer base will be delighted at how you exceeded their expectations.
In some ways, it's easy to fix a broken window once you've discovered it. You can see it, you can diagnose it, and you can devise a plan to repair it. It might not be easy to make the repair, but that doesn't mean it can't be done. At that point, it's a question of motivation and effort.
The _real_ trick is to _prevent_ broken windows. It's harder to do, but more rewarding when done properly. Obviously, doing so means the problem that could have arisen will not, and thus the consuming public has an image of your company that is free of faults, or at least the faults that could have been.
Pairing expectation with reality, and then exceeding the expectation, is a wonderful way to avoid broken windows. Analyze your business, determine what the average customer would expect from it, and then give that customer more. There will be very few cases in which this will be seen as negative.
# Above and Beyond
In the military, personnel are awarded citations and decorations (and sometimes promotions) for actions "above and beyond the call of duty." This same principle can be applied to your business. Let your employees know that they will be rewarded for effort that goes beyond what most would consider to be the norm. Encourage them to suggest ideas that can improve service or operations. Make sure the right person gets the credit, and promote from within those who do so on a consistent basis.
Remember that a broken window can happen only when someone isn't paying attention—but it doesn't have to be someone who isn't paying attention to his or her job. If the person who works behind the counter at the Dairy Queen is doing a splendid job of serving customers and making sundaes, but also notices that the paint on the ceiling is peeling or that the store is overordering on vanilla and doesn't have enough chocolate, that's "above and beyond."
It's not a question of rewarding someone for being a tattletale—you're not asking your employees to inform on each other. If the counter help mentions the ordering on one flavor or another, this is not an opportunity to chastise the person who is in charge of ordering. It's an opportunity to praise the person who noticed something that can help the company in general.
Having a policy of being considerate and polite to customers is essential, but it's not enough. Those employees who go out of their way to help customers with a problem, who notice the "regulars" and remember their preferences, but are just as accommodating and helpful to newcomers, are the ones who are going above and beyond. But it should be made clear that you expect _all_ your employees to go above and beyond, that this is a _company_ policy, not an individual initiative. Set standards and then ask the employees for suggestions on how to exceed them.
Ask yourself these questions about expectations and reality:
1. What does my customer have a right to expect when he or she contacts my business?
2. Am I currently providing what my customer should logically expect?
3. Is it being provided by every employee, even the ones who don't come into contact with the public?
4. Are there ways I can _exceed_ my customers' expectations for my business?
5. How can I implement these "above and beyond" provisions and remain profitable?
6. Are my employees motivated to find ways to exceed our customers' expectations? Am I encouraging them to do so?
7. What should I do to go beyond the norm and make my business stand out in the customer service area?
Once you have asked those questions, the answers should tell you a good deal about your dedication, commitment, and procedure. Consider these answers:
### **What does my customer have a right to expect when he or she contacts my business?**
Obviously, this varies from business to business, but there are some constants in all aspects of a customer-oriented business plan. Everyone who contacts any business deserves to be treated with respect and courtesy, to be spoken to as an intelligent human being, to be served as promptly as is physically possible, and to be sure that the person serving his or her needs is dedicated to the same goal as the customer. If the customer has a problem, the employee serving that customer must consider it _his_ problem until it is successfully solved.
### **Am I currently providing what my customer should logically expect?**
This can be answered best with the implementation of a mystery shopper. A person who walks into the business unrecognized, presents himself or herself as a customer, goes through every aspect of customer service, and then reports in detail on the experience can be invaluable to the successful business. It's no good if the employees know that someone will be judging them and reporting back—they will only engage in atypical behavior that will not give you an accurate picture of your operation. Once you know what your business is providing, you can fix broken windows and work on what you _should be_ providing.
### **Is it being provided by every employee, even the ones who don't come into contact with the public?**
Often the worst broken windows are people. Employees who do not get the idea of what you're trying to accomplish, who won't "get with the program," who can't push themselves beyond the abysmal standard we have set for ourselves in this society, have no place in a progressive, aggressive business. They need, quite frankly, to shape up or ship out. Get them out before they sink the business.
### **Are there ways I can** _**exceed**_ **my customers' expectations for my business?**
There had better be. If you're not doing everything you possibly can to make the customer's experience as satisfying and rewarding as it can be, you're not doing all you should do. And there are very few businesses indeed that are doing all they can do. It's a whisker shy of impossible. So think outside the box and consider what you can do that your competitors and others in related industries are not doing, and if it has a benefit to the customers you serve, try it. In most cases, you'll find that customers will react favorably.
### **How can I implement these "above and beyond" provisions and remain profitable?**
In most cases, there is very little or no cost in doing things the right way and getting noticed for it. How much does it cost for each employee to smile? How much does it cost for an employee to take a sense of responsibility for each problem he or she is presented? If an employee can't smile, even for minimum wage, you have the wrong employee, period.
### **Are my employees motivated to find ways to exceed our customers' expectations?**
The mystery shopper can tell you if your employees are doing what you hope they will do—going above and beyond the call. Motivation is another story. Do the employees see a reward in doing things the right way? Are they being recognized for their extra effort (and I don't just mean an Employee of the Month plaque on the wall)?
### **Am I encouraging them to do so?**
Make yourself visible to the employees. Make sure they know that this is a company plan, something that comes from the top and stops at every level down to the person who empties the wastebaskets. It's imperative that your employees understand the benefits of exceeding expectations, and why you expect it to work.
### **What should I do to go beyond the norm and make my business stand out in the customer service area?**
You, as the employer, set the example. If you own a small business, you probably have some contact with the customers yourself. _You_ must go above and beyond in order for your employees to understand the importance of the concept. If you are an executive in a larger company, you might not have the kind of contact you once did with the end user. You have to use mystery shoppers and occasionally go to the sales floor or the customer service area yourself. See what's going on and formulate strategies.
Ask your employees for suggestions, but don't rely on them to the exclusion of your own ideas. Be innovative, creative, and open to ideas. Only then can you exceed the expectations that anyone walking into your business might logically have.
## WHAT IS REALITY?
* When a customer enters a business, he or she has an _expectation_. How that expectation measures up against the _reality_ of the experience will determine how satisfied the customer feels when he or she leaves, and could determine whether the customer will patronize this business again.
* If a business wants to avoid broken windows, its goal must not be to meet expectations for its customers, but to exceed them.
* The customer might not always be right, but he certainly always _believes_ he is, and arguing with him will not alter this perception. The two most important words in the broken windows lexicon have to be "I'm sorry." They will be followed closely by "How can I help?"
* If you offer consumers A, B, and C, but deliver only A and B, the consumer will be frustrated and disappointed and will probably not recommend your business. If, however, you offer only A, and then deliver A and B, the customer's expectation is exceeded, and his/her perception of your company will be a much more positive one.
* Employees who go above and beyond the call of duty are the ones who will spot and repair broken windows. Motivating employees to do so is one of the most important jobs a manager has.
# _Chapter Six_
# Branding and Broken Windows
Branding no longer refers only to a process that identifies cattle as property of one rancher or another. Today the word also has a much deeper and more vital definition: Branding is the process, the craft, and the art of defining a business in the minds and hearts of the consuming public.
To create a personality for a business, and to have that personality permeate every aspect of the business, to have it _become_ the business in the minds of customers, is the goal of branding. It's one thing to have a product, like a plastic coat hanger or a roll of paper towels. It's quite something else to be a _brand_ , like Coca-Cola or Sony.
In order to become a brand, to inspire the kind of trust and identification that makes a brand in the consumer's mind, a number of factors must be addressed. Of course, the product or service that makes up the brand must deliver what it promises. It must establish a personality the public finds agreeable and dependable. It must distinguish itself from its competition in some way—by being unique, by aiming at a particular market segment, or by being more attractive to the public than the competition's products or services.
But all these things are tied to a larger concept: the idea of trust. For consumers to accept a brand, to have an opinion—preferably a favorable one—about the brand, and to embrace it to the point that the mention of the brand name is enough to evoke a positive image in the mind, it must _never disappoint_.
In other words, there must be no broken windows.
There is nothing worse for business than to disappoint the customer. In the preceding chapter, I discussed the concept of exceeding expectations. Disappointment, by definition, is the act of falling short of expectations, and that is as bad as it gets for a business. If you don't exceed expectations, you run the risk that the customer will abandon your company for the competition. But if you disappoint the customer, you guarantee that will happen.
When one of the world's most established brands (if not _the_ most established), Coca-Cola, decided in the 1980s to abandon its core product and replace it with a drink it called New Coke, the company grossly underestimated the response it would get from its core consumers. Not only did the public not warm up to the new product, it resented the company's elimination of the old favorite, and the fallout from soda drinkers worldwide was devastating. Coca-Cola was forced to reverse gears in a hurry, bring back its old standby as "Coke Classic," and try to convince the public, millions at a time, that it was just kidding.
Try finding a can of New Coke on the shelves today.
This plan was a broken window of epic proportions. It wasn't a tiny thing gone wrong—it was an enormous, elephantine thing gone hideously wrong, a disaster that made the _Titanic_ look like a rowboat with a leaky hull. It was a miscalculation that seemed impossible—how could a company not know its consumers well enough to predict that they'd be upset when the product they'd come to know and love for decades was suddenly removed and replaced with something that was closer to—dare I say it?—Pepsi, the drink detested by hard-core Coke fans?
There are, of course, conspiracy theorists who believe the move was a calculated gamble on Coke's part, to create a public relations uproar, a demand for its product so strong it would prove how popular and beloved Coca-Cola was, and to generate goodwill when the original product was resurrected. But it seems extremely unlikely that a company so large, so pervasive, so all-encompassing, would willingly jeopardize its multibillion-dollar prize formula on a hunch. Maybe it always was the plan to bring back "classic" Coke, but I'm willing to bet that the company had much higher hopes for New Coke that never came true. Believe me, they didn't make money on this deal.
The broken window that was New Coke represented more than a wrong guess on the part of some executives. It was a branding catastrophe. When a company goes out of its way to demean its own standing in the marketplace, to take its own core product and say, in essence, that it wasn't good enough and should therefore be eliminated, millions of consumers are going to take that _personally_. They had invested years of loyalty to a product, had in fact been encouraged by the company's advertising to identify themselves as "Coke people" rather than the "Pepsi Generation." The term "cola wars" came to its highest point during the New Coke debacle, given the fact that there were so many consumers who were so angry all at once. It was a golden opportunity for the competition, and one that had been handed to them on a silver platter by a business that was supposed to be one of the smartest in the world. This was a broken plate-glass window the size of the Grand Canyon.
Branding is a process that encourages consumers to identify with a product and to have a positive emotional response to the product. That is exactly what branding theory is about. If you feel good about buying Michelin tires because the animated man made out of rubber is a friendly character who is looking out for your safety, you have willingly given in to the brand's marketing. If you believe that Chrysler cars are made for a different driver than those marketed by Toyota, and you can say clearly which consumer would drive which car, and why, you have been affected by branding.
A broken window that affects the reputation of the entire brand can ruin a business more quickly than a broken window in one franchise, one outlet, or one product. A quick (and entirely hypothetical) example: You walk into a Dairy Queen and see that the counter has not been washed. Your immediate thought is that the crew _at this Dairy Queen_ is not performing as well as it should. (Granted, if this is your first visit to a Dairy Queen, you might condemn the whole company for the one store, and if you had seen it consistently in outlet after outlet, you would be right to assume there was a problem with the parent company's policies and switch to another ice cream store, like Baskin-Robbins or Carvel.) If, however, you hear on the news that 130 people across the country have been stricken ill and that the only common trait they have is that they all had Dairy Queen ice cream before getting sick, your perception of the entire chain is now damaged, perhaps irreparably. It will be quite some time, and take a huge effort by the company, before you will set foot in a Dairy Queen again.
This illustrates the danger of a branding broken window. Annoy a consumer in an isolated incident, and you have deteriorated his trust. Break a window on a brand level, and you have made an enemy for life.
What is a brand broken window?
Anything that deteriorates the consumer's impression of the company as a whole, anything that makes the customer or the potential customer think less of the company, is a brand broken window. It's the difference between a mistake that will reflect on one part of the company—a worn rug in one office, for example—and one that will reflect on the company as a whole, for instance, a revelation that the company has been employing sweatshop employees to create its products.
But the implications of a brand broken window go much further than simply a black mark on the company name. It is an emotional response when the public takes a brand to its bosom, and an emotional bond is formed. People can be absolutely passionate about their choice of vehicle, soft drink, basketball team, or coffee. Yes, they "vote" by spending their money on those products, but they also open themselves up just a tiny bit emotionally. They commit to that brand, and not others, because there is something about the product _and the way it identifies itself_ that strikes a chord in their sensibilities.
Try to get a Coca-Cola drinker to switch to Pepsi. Talk to a New York Yankee fan about rooting for the Boston Red Sox. Ask the user of an Apple Macintosh what he thinks about Microsoft Windows.
Then you'd better stand back. Fast.
People believe that American Airlines provides a different travel experience than Continental Airlines. Is there that much difference on the flight? Not really; you still get from New York to Los Angeles in five and a half hours or so. You still get a bag of pretzels and a soft drink for free. You still have to stuff your feet and a carry-on bag under the seat in front of you if you're in coach.
But there are differences, and they are the little things that cause a person to choose one airline over another. Let's say one offers a frequent-flier program that allows for a free flight sooner. One brings the drink cart through twice, not once, during a transcontinental flight. One gives you the headphones for the movie for free, and the other charges four dollars. If the fare is roughly the same, which airline are you going to choose?
The devil may be in the details, but the road to success is paved through them as well. Do the small things right—in other words, avoid broken windows—and you can attract a whole new group of consumers who might not have tried your business before.
Now, once you have established yourself in an area, consider how the consumer will react. Your business has worked hard and long, and spent a good deal of money, establishing a brand personality. For an airline, it can be a guarantee of on-time service for business travelers, or an emphasis on comfort. It can have something to do with accommodating families traveling for pleasure. It can be centered on being the lowest-cost airline that still caters to its customers.
Whatever that personality might be, it has to be consistent. After American Airlines came within an eyelash of bankruptcy in 2003, the new CEO, Gerard Arpey, announced that the company would reverse its advertised policy of having more legroom in coach and that it would add more seats so the flights would be more profitable. This may have pleased Wall Street, but consumers (even business travelers) who were choosing American's flights based on the extra comfort were surely not as enthralled. American chose to explain by saying that adding the seats made the flights less expensive.
It doesn't seem like a big thing, a few extra inches of space. I'm six foot two, and I'd rather drink hemlock than fly in a coach seat. But anyone who has ever traveled across the country with cramped legs will tell you just how much those few inches can mean. And the brand reversal—the redefinition of American from the airline that gives you more room to the airline that is taking the room back so your flight can be cheaper—represented an emotional betrayal for some American customers.
When a brand tries to reposition itself, it runs the risk of alienating the core consumers who chose it for what it was to begin with. The slogan "It's not your father's Oldsmobile" was a blatant declaration that the General Motors brand no longer wanted to be associated with the aging clientele it had established, and instead wanted to be seen as young and hip. The strategy didn't work (for one thing, it still _was_ your father's Oldsmobile), and the loyal Olds customers were offended by being identified as old and obsolete. Eventually, Oldsmobile was phased out.
Can little things turn a consumer against an entire brand? Certainly, they can. A customer who sees a cockroach at the donut store, for example, might very well stop patronizing every outlet in that chain. The "weakest link" theory is at work here, and it is very strong.
I recently sat with a group of fourteen- to sixteen-year-old girls at a fast food chain called In-and-Out Burger, which operates on the West Coast. Here the core audience for a fast food chain told me they preferred the smaller, lesser-known In-and-Out to a larger chain like McDonald's or Burger King, and it was because In-and-Out paid attention to details.
The bathrooms at In-and-Out weren't as swank as those in a Manhattan hotel, but they were clean, the girls said. The ones at other chains "I try to avoid," one told me. The help at In-and-Out was accommodating and friendly, where others were slow and surly, the girls thought.
Aside from families with young children, teenagers make up the most significant demographic for the "rapid service" industry. And here was a group of teens saying that the little things that weren't done—the broken windows—would turn them away from one chain and toward another.
When a broken window leads to an acceptance or rejection of the brand as a whole, it has transcended its initial role and become a brand broken window. When that happens, it can lead to more than a customer having a complaint for the manager; it becomes something that can alienate the customer from the entire brand, no matter where it is found, forever. And that can't be acceptable to any business, anywhere, ever.
So what can you do? You insist on employees knowing that details are important to the company as a whole, and you enforce the rules. You make sure the rules—whatever your business might be—are enforced throughout the business, in every outlet, by every employee, all the time. In short, you have a burning, maniacal, raging obsession about the details that will set you apart from your competition. And you employ mystery shoppers (best made up of previously disgruntled customers who have registered complaints) to constantly check that the details are being attended to and the broken windows are being avoided or repaired immediately.
You can't allow a broken window to reflect on your brand, or the integrity of your brand and its image will be seriously jeopardized. If you think this is not an important issue, consider two words:
New Coke.
## BRAND, NOT BLAND
* To transcend the idea of a product identity and move into the upper reaches of business, it is necessary to establish a brand. And the only way to become a brand in the eyes of the consuming public is to establish trust. There is no other way. None.
* When a company betrays the trust of its customers (think New Coke), it runs the risk of outright revolt and the possibility that its most loyal consumers could very soon be using their wallets to vote for the other side.
* Consumers identify with the brand identity established by the company. It's an emotional attachment, and when it is broken, it is extremely difficult to repair.
* When a consumer has a bad experience with a brand in any outlet, it reflects on every single outlet in the chain. One broken window in one store will become a broken window in every store for the consumer.
# _Chapter Seven_
# The Employee as Broken Window
Often the worst broken windows are people.
Yes, I know I've said this before, but it bears repeating. When an employee—any employee—becomes a detriment to the company, for any reason, that employee has become a broken window, and the ripple effect from his or her failure, however slight, can be devastating to your business.
Your employees are human beings, and as such, they are given to human frailty. They will make mistakes, and those are not broken windows. Employees who learn from their mistakes, who become better at their jobs because of those errors, are the best possible workers you can employ. I'm not saying you should fire every employee of your company who has ever made a mistake, because you would have to begin with yourself.
However, there is a significant tendency in business today to forgive more than is rational. We understand why someone is not producing as well as that employee should, we see the problem, and we explain it to that employee. The employee nods and promises to do better. The problem? That employee _doesn't_ improve—he or she continues to make the _same_ mistakes, have the _same_ bad attitude, display the _same_ ineptitude or indifference toward the consumers who use the business. And no matter how devastating emotionally it might be for the manager who oversees that employee, there is only one way to make sure that problem won't recur—the employee must go.
The Los Angeles city government employs 37, 000 people. In a fifteen-month period in 2003 and 2004, it fired only six workers for doing a poor job. Instead, the system institutes what some people call the Dance of the Lemons, moving incompetent workers from one job to another, losing none of them. This Lemon Dance perpetuates the problem—in fact, compounds the problem—because it guarantees that the worst workers will work in multiple departments. Because laws, civil service regulations, and city ordinances protect incompetent workers, the city doesn't get the service it needs from its employees, who can't be fired. This is about as ridiculous a situation as you could imagine, but it's far from an isolated case.
I'm not advocating cruelty, and I'm not suggesting that you don't treat your employees like people. But continued, persistent bad performance can't be tolerated if you're going to have the intense, obsessive dedication necessary from every employee in order to have success in any business.
The context is irrelevant: What's important is that employees are not so much as admonished for their behavior, which certainly alienates at least one longtime customer and probably irritates considerably more than one. It is an example of the lax, laissez-faire attitude that has infected American businesses in the area of customer service. And the vast majority of such offenses can be traced to employees who have not been given a reason to care.
The concept of training for employees is far from revolutionary. This has been going on since there has been business, starting with the apprentice system and moving on from there (Donald Trump notwithstanding). But the concept of training employees to actually serve customers in a fashion that has all but gone out of style—with courtesy, a helpful attitude, and a smile—has sadly become revolutionary in today's business climate.
A lot of large businesses will tell you (through their publicists) that they work hard and long on employee training. They'll point to concepts worked out by experts in motivation and customer service and how each of these concepts is posted on the wall of every outlet the company owns. McDonald's loves to tell you about its dedication to cleanliness and speed. How clean and fast is the McDonald's you frequent?
The whole concept of employee training in almost every business needs to be overhauled, and here are the concepts that need to be stressed:
1. Customer service
2. Customer service
3. Customer service
4. Employee motivation
5. Advancement for excellent performance
6. Punishment for poor performance
7. See 1, 2, and 3.
**Customer service** is more important than anything else your business does. It separates loyal customers from ex-customers, and it guarantees a steady stream of revenue for the life of the business. Sales are extremely important, but if customers who buy the product because it's what they want find that the system behind it doesn't for one moment regard them as important, they will look elsewhere. Customer service has to go beyond what is considered good, and enter the "unbelievably accommodating" area. No customer must be allowed to leave a customer service encounter unsatisfied, and that doesn't mean not solving the problem and then asking, "Is there anything else I can do for you today?"
Customer service, in other words, has to far exceed the customer's expectations. It has to be a pleasant experience, not merely an acceptable one, for the consumer. It has to be handled with utmost delicacy, especially with those customers who are, let's say, a little more demanding than others.
How does customer service recover from the abysmal condition it finds itself in today? **Employee motivation.** Employees, even those on minimum wage, can no longer be allowed to sleepwalk through a day's work when dealing with the clientele. They can't be "putting in their time" at work and failing to uphold the integrity of the company with each and every encounter they have. They can no longer be allowed to consider their jobs a distraction from their "real lives." When you're at work, this _is_ your real life.
**Advancement** should be stressed. Employees should know—not just from the corporate statements but through examples they can see in their own outlets—that excellent performance will be rewarded with advancement in responsibility and salary. They should know that those who put in extra effort (and extra effort can no longer be considered smiling and greeting the customer, because those should be the _minimum_ standards for encountering a customer) will be noticed and rewarded. They should also know that **punishment** will be the result of poor performance (which in this case will be defined as anything except excellent performance) and that, after the proper number of warnings, they will be terminated.
Businesses these days are far too slow to fire people. Yes, you read that right. More employees should be getting fired. Often they should be fired immediately. Why? Because they are not adequately performing the jobs for which they were hired in the first place. They are coasting, doing their time, merely existing in the company, and not showing the enthusiasm and dedication necessary for making a business run successfully. And I mean every employee, from the newest hire on the counter to the CEO him/herself. Everyone must be accountable, and the person to whom they are all accountable is the customer. There is no higher authority.
Look what happened in corporate America when the customer and the stockholder were considered to be far less important than the people running the company: We got Enron, Adelphia, and WorldCom. Greed overtook good sense, and there was no one at the switch. Even in the largest corporations in the country, when the goal is forgotten, the consequences are as dire as they can be.
In other words, more people should have been fired. _Someone_ should have been watching, evaluating the activities of those in charge. On a less criminal (but no less serious) scale, broken windows like poor customer service or slowly declining physical plant—chipped paint, worn carpets—must be someone's responsibility, and that someone needs to be accountable. Fix it or face the consequences.
Jack Welch, the amazing executive who ran General Electric, said that managers who felt they were doing an employee a favor by being lenient were actually doing the exact opposite. They were creating an atmosphere where the employee could do a poor job and feel he was doing an excellent one, and then, when the ax inevitably fell, the employee would not only be unemployed but amazed that such a thing could happen to him. Excuses like problems at home are legitimate, but they can't be allowed to become chronic excuses for poor performance.
The first time a salesperson fails to make his or her sales quota for the month, there must be a warning and an explanation. The second time it happens, if the explanation remains the same and it is not attributable to general conditions in the marketplace that are unquestionably out of the employee's control, that employee must be told in no uncertain terms that the next poor performance will be grounds for termination. Three strikes, and you're out.
But it can get worse. If the worst broken windows are people, consider this: An employee who is a broken window often becomes a virus.
Remember the original premise of the broken windows theory: that seemingly insignificant crimes left unanswered (fare jumping, graffiti, panhandling) will lead to the impression that no one cares here and that therefore any infraction will be tolerated. Take that idea and apply it to an ineffective, indifferent, or downright bad employee. Left unchecked, that worker will demonstrate to the rest of your staff that poor behavior and an inability (or unwillingness) to perform one's job to the best of one's abilities will be tolerated, even accepted. Silence is agreement. And that will lead the others to emulate the bad employee, and not the example that other, more dedicated workers—including the upper management—might be offering.
A virus spreads through contact with an infected person (in many cases; some are airborne). A broken windows virus starts as an employee who doesn't "get with the program" and is not sufficiently disciplined immediately. Every day that goes by with that employee running visibly counter to the stated policy of the company allows the virus to spread farther and wider throughout your company—what incentive does a worker have to produce when those who do nothing are being rewarded in exactly the same way as those who put in maximum effort?
If the paint department at the home improvement store shows a lack of concern about the customers' needs, it could spread to the flooring department, the cashiers, or the electrical supply—or all three, and more. People tend to emulate what they see, particularly when they are new to a situation, so freshly hired employees will take a look at the existing situation when they begin, and rise or sink to the level of the employees they see in place.
Can you see where this is going? The fact is, there is no excuse whatsoever for letting a poorly performing employee stay on the job. None. If you hire someone with good intentions, and that employee is trying his or her best but can't harness the skills necessary for the job, you have two choices: find another job for this person that better suits his/her skill level or fire that employee. There is no third choice.
If the employee is simply not trying hard enough, or doesn't care enough, to do the job properly, you have to let him or her go. There is, in this case, no second choice.
Jack Welch, arguably the greatest CEO of this generation, addressed the concept of "false kindness," something that I believe too many companies practice regularly. Welch said that companies see their employees as individuals, which is admirable. It's when those individuals start taking on more importance than the company itself that they become broken windows.
If a store manager feels kindly toward a cashier despite that employee's inability or unwillingness to perform her job properly—perhaps because of health problems or trouble at home—the manager might be inclined to let the poor performance slide for a time. That's fine, if a warning is issued in no uncertain terms: "I understand your problem, and I'll do whatever I can to help, but your performance must improve or you will be let go."
And here's the tricky part: _That manager must mean every word he or she says_.
There can't be any hollow promises made here. If that employee does not improve her work, she must be let go _no matter what her personal problem might be_. The company employs many people, and its performance in the marketplace will affect all their lives. Letting one person dictate the fate of the company is not acceptable, and if that sounds like hyperbole, think about it: The other employees don't necessarily know about their colleague's personal problem. They see only the performance, which may be lackluster or downright negligent. And if they see nothing done to undo this problem, _they will assume it's all right with management to behave that way_.
That employee has become a broken windows virus. And it will spread.
#### **Symptoms of a Broken Windows Virus**
* The patient (your business) begins to feel sluggish and tired (revenues decline almost imperceptibly at first).
* The patient complains of localized pain (certain departments seem to experience inexplicable slowdowns, due to employee indifference as a learned behavior).
* Family members (other employees) exhibit symptoms (one employee sees another slacking off and emulates that behavior).
* Nonfamily members ask about the patient's health (customers notice the poor customer service and complain).
* Diagnosis is difficult to pinpoint (management doesn't notice the problem and the window is not fixed—the employee is not reprimanded or let go because of poor performance).
* Patient's condition declines more rapidly (as reputation of poor service grows, sales decline and customers find alternative sources for product or services offered by the company).
* Extraordinary measures are implemented (no longer able to deny a problem, management closes retail outlets, lays off a percentage of the workforce, and asks creditors for more time to repay debts).
* Patient is put on life support (company files for Chapter 11 protection).
* Patient dies (company goes out of business).
In customer service, the stakes are even higher. One dissatisfied customer is a cancer on the business—they talk to people, they make noise, and they are likely to sway opinions of those who otherwise wouldn't have thought negatively about the company. _Two_ disgruntled customers are a full-fledged emergency; they will poison the market. _Three_ , and you have a disaster on your hands. Now the entire community thinks of your company as inept, indifferent, or incompetent.
You can't afford that kind of scenario. Your employees must always smile, must always be gracious, must always solve the customer's problem. There is no excuse for anything else. And there's more: Not only must the problem be solved, but the customer has to feel that the problem was the _employee's_ problem for the time that the employee was seeing to it. There must be a sense of a common goal, and the goal is always a satisfied customer.
At a coffee bar I once patronized (I feel obligated to note that it was not a Starbucks), a woman working behind the counter told me in no uncertain terms that "smiling is not in my job description." Wow! Imagine that. Nothing can be more basic, more elemental, to customer service than a smile, and this employee felt it was above and beyond the call of duty for her—in fact, was unreasonable to expect of her. A _smile_!
The manager of that store should have immediately apologized, given me a free cup of coffee, and told the employee that the next customer she faced with anything but a friendly smile would be her last. Instead, like most consumers, I shrugged my shoulders, paid for my coffee, and left.
But I didn't go back to that coffee outlet. Not ever. I'm sure that employee isn't working there anymore, but that's not the point. It's my ultimate power as a consumer, to vote with my wallet.
It's inevitable that the attitude being exhibited was noticed by more than just one consumer. It was undoubtedly seen by many more, and at least some of them would have the same reaction I had—to walk out and never return, because there's always competition, and a customer always has the option of going elsewhere.
As a consumer, you should do exactly that. You should patronize only those businesses you think exhibit the attitude and priorities you feel are important. As a business owner, if you're not paying attention to that kind of broken window, the kind that walks in and punches the time clock every morning, you are inviting disaster. Nothing less. And if you are still in business a year after you've read this book, I can only assume you will have taken this chapter to heart. You're not doing your employees a favor by allowing them to ruin your business. Soon, not only will they no longer have a job, but neither will anyone else who works for you. Because your business will have gone bankrupt and shut its doors.
That is not an overstatement. Let bad employees go, or you are putting your business at risk.
## BROKEN PEOPLE
* The worst broken windows are sometimes people. That means an employee who is not on board with the needs and expectations of the company's consumers can do immeasurable damage and is a broken window of the most urgent variety.
* Bad service is inexcusable. Bad service, no matter how good the rest of the factors may be, will always sink your business.
* An employee who can't do the job properly should be fired. Not warned, not shifted to another position, not admonished. Fired. Fast. Before another customer can be spoiled.
# _Chapter Eight_
# Why Krispy Kreme Is Better Than Dunkin' Donuts (and Vice Versa)
Be honest: If you were blindfolded and given two donuts to taste, one from Krispy Kreme and one from Dunkin' Donuts, could you really tell which was which?
I don't think so.
Here we have two extremely strong brand names, each selling a product that is not much different from the other's. They are marketed in similar, albeit not identical, fashion, their distribution is similar, and they aim to attract roughly the same type of consumer with the same need. Each would seem, on the surface, to be merely a reflection of the other. The same product with two different names.
But the brand loyalty these two companies command is staggering. Approaching the level of the Coke vs. Pepsi debate, disagreement among consumers about which is better, Krispy Kreme or Dunkin' Donuts, is intense. They are the Boston Red Sox and New York Yankees of pastry.
How is this possible? It happens because the brand identity engendered by each company is so strong that the consumer feels an emotional connection to the product, one that demands a loyalty not usually seen with so common and affordable a product. It happens because the marketers at each company managed to establish in the consuming public's mind the idea that _their_ donut, and not the other one, was the friendly, lovable donut. People care about their donut choice in ways that they don't care about their choice of fax machines, bananas, or paper towels.
I can hear you asking: What does this have to do with broken windows? Hang on. I'll show you.
The emotional connection formed between a product or a company and a consumer is the strongest, best possible bond a business can hope to achieve. It establishes a dedicated, loyal customer for a very long time, and if a company can create enough such consumers, it can ensure itself a long, successful run in its business assuming everything is done correctly. That kind of loyalty is the gold standard for business and is exactly what every business in the world should be striving to achieve.
But it is established early on, when the consumer and the business have their first contact, via advertising, reputation (word of mouth), or direct contact, which would be a retail experience or a service provided by the company to the consumer. In other words, the _first impression_ made by the business on the consumer is vital in establishing this strong, important link.
Clichés become clichés because they are, for the most part, true: You have only one chance to make a first impression.
If there's a broken window in the way of that first meeting, you are missing out on an enormous opportunity, and doing yourself irreparable damage. The importance can't be overstated.
Joe DiMaggio was quoted as saying that he always played to the best of his ability on any given day, because there was surely someone in the stands who had never seen him play before, and he owed it to that person to "give them my best." Every day. Every time. DiMaggio, it should be noted, is most famous for having a streak of fifty-six games in a row in which he got at least one hit. That record is mentioned often as being one of the least likely to be broken, and it speaks of consistency and dedication. It would not have been possible if DiMaggio hadn't been thinking of that newcomer in the stands who hadn't seen him before. Joe DiMaggio had no broken windows because he had the obsessive, maniacal rage to do his best every single time.
The first time a person encounters your business, you will make an impression, either positive or negative. And quite often the person your customer will first encounter, the one who will _be_ your company for the customer on first glance, will be a cashier, a counter employee, or a retail representative. For online or service-based businesses, that person might be the one who answers the phone. The point is, these employees are usually not the first-hired, best paid, or most personally involved members of the company.
But they had better be the most representative.
Of course, some degree of the responsibility in a first impression is going to fall on the quality of the product or service you offer. You can have the friendliest, most hospitable, most helpful staff in the world, but if your widget doesn't do the job, it's going to sour the experience for the customer, no matter what. Broken windows that start with a bad product or a useless, inefficient service have to be repaired from the ground up and can't be tackled after the fact.
Remember the comparison between Krispy Kreme and Dunkin' Donuts. If either one made a product that tasted bad, a donut that simply wasn't what the customer wanted, it wouldn't matter how well the counter help managed to move the customer through quickly and efficiently. The consumer would simply remember that he or she had gone to a donut store and gotten an inferior product, and there would be no return visit.
But our premise—that the products involved here are not all that different from each other—assumes that there must be some other factor involved in the intense loyalty consumers show toward one or the other. If it's not the product, then what could it be?
There are a number of possibilities, but the two most probable are the physical plant the customer sees and the employees with whom the customer interacts. Remember that a dirty bathroom can be a broken window, and a powerful one. If the customer sees peeling paint, worn carpets, and unwiped counters (especially in an establishment that sells food), a warning light will go off in the customer's head. It is not an overstatement to say that if a traveler pulls down the tray table on a flight and sees the ring of a coffee cup left by the previous passenger, he or she is likely to assume that the engine maintenance done by this airline is not efficient. If that doesn't color a person's view of the airline, nothing will.
If you think that tiny signs of wear or dirt in your facility don't constitute a major problem, you haven't been paying attention to this book. Small signs of negligence from the management of any business are signals that the large things aren't being looked after properly, either, and they alert customers that something is very, very wrong.
When asked about the problems they saw at restaurants (including fast food establishments) they called unsatisfactory, consumers more often than not cite dirty bathrooms, messy counters or tables, condiment areas that have not been cleaned, and other cleanliness problems. Yes, people are upset with lackadaisical or surly service, but they are just as worried about the idea that their food is being prepared and served in an unsanitary facility.
The next most likely factor to make a bad first impression is the employee as a broken window. When a customer encounters a bored, disengaged, listless employee who does not even attempt to solve the customer's problem, the customer will consider this type of treatment to be the company's policy and wonder why the company is so indifferent to serving the people who pay its bills. The customer may indeed reconsider his or her choice of this store or service provider.
But at least there's a chance that a repeat customer has had a positive experience with the company at one time or another, too. In fact, it's likely that's the case, since the customer has chosen to patronize the company more than once, and there must be some reason he's made that decision. There must have been something good at some time that this consumer saw in the company's operations or product to bring him back. It's possible you will lose him based on one negative experience, but not necessarily.
When the bad impression is made on the _first_ experience with the company, however, it's extremely unlikely the consumer will become a regular customer. In fact, it's better than even money that you'll never see this particular customer again. Ever.
"People want to go places where they feel welcome," says Jason Binn, publisher of such publications as _L.A. Confidential, Gotham,_ and _The Hamptons_. "The second that message is broken up, it leaves a bad impression on any level."
Broken windows aren't simply bad experiences in customer service, however. They can be anything that diminishes the experience the consumer rightfully expects on entering the establishment.
So let's get back to our original question: How do Krispy Kreme and Dunkin' Donuts manage to attract such a loyal base of consumers when the products they sell are not easily distinguishable from each other?
Because one is clearly superior, that's how. Which one? The one with which you had a positive experience _first_.
Let's say you're a Dunkin' Donuts fan. You probably tried that brand before you tried Krispy Kreme. And you had a pleasant experience: The donut you bought was what you expected it to be, or better; it was served quickly and in what appeared to be a clean environment; and the staff serving you was, at the very _worst,_ efficient.
In that case, all factors being equal, the product probably made the difference for you. You tried it (maybe you loved the coffee you got as well), you liked it, and you stored that information away in your memory under "Places I Enjoy Visiting."
Perhaps you established a habit at Dunkin'. You went every morning, or every week, or whenever you closed a big deal, as a reward. You tried different varieties of the product, and you liked most of them. You watched their ads on TV and found them amusing. Maybe you bought a Dunkin' Donuts coffee mug to further identify yourself as a fan of the chain.
Now you're invested emotionally as a Dunkin' Donuts consumer. Maybe you told friends about the great coffee they have, or maybe you simply bought a dozen donuts for the last office wedding shower and were given a promotional dozen free. Whatever the situation, you now think of yourself as a Dunkin' Donuts consumer.
When Krispy Kreme came to town, you didn't think of it as a threat—that would be carrying the emotional commitment way too far. Perhaps you were curious about this new brand, and you had heard things about it from others. Maybe you decided that one day on the way to work, instead of the usual stop at Dunkin', you'd give Krispy Kreme a shot.
That's what you gave it—a shot. A chance. An attempt to lure you away from your established brand. And you tried the product, and it was just fine. Maybe the store was about the same: clean, fast, not at all a negative experience.
But the experience wasn't especially superior, either. It was just about the same as what you were used to. If you'd never been to a Dunkin' Donuts in your life, maybe you would now be establishing a new habit, a new emotional commitment to a company or a product.
But you _have_ been to Dunkin' Donuts, and you have already established that commitment. There's no reason to change, because nothing here is demonstrably better.
There are two speeds in today's business climate: fast and dead. The consumer who went to Dunkin' Donuts is lost to Krispy Kreme unless it can be demonstrated that the latter brand is in some way better. If it's the same, the consumer will in all likelihood continue with the buying pattern he or she has already established.
You see how important a first impression can be? And how important it is to make one _fast,_ before the competition gets there?
(By the way, the above example could easily be just as true with the product names reversed. If you were a Krispy Kreme fan first and then tried Dunkin' Donuts, there's no reason to think you'd change brands midstream now, either.)
The consumer believes that his brand (and by that, I mean the one he has chosen, not one that he owns personally) is better. Why? Because it validates his choice of that brand to begin with—he identifies himself, even to a tiny degree, as a "Pepsi person" or a "Coke person." He will argue to the death the merits of his brand over the other. And he'll be right, because the human experience is a subjective one, and if he decides his brand is better, it _is_ better—for him.
When a broken window like a slow server or a dirty counter establishes a bad impression in the consumer's mind, it is too late. The emotional connection has been short-circuited, and it can't be repaired on the first impression. The only thing that can help is the immediate and total acknowledgment that anything negative was the responsibility of the business and the fault of the manager (or whichever employee is visibly in charge) and the offer of a reward: Here's a free donut, a coupon for a coffee, and the promise that this will never ever happen again.
That might work. But it might not. It's probably best not to get to the point where you have to find out.
## HOLE IN DONUT: BROKEN WINDOW?
* Customer loyalty is paramount to establishing and maintaining a strong business. It's great to have lots of customers, but if they come in once and never return, you won't be in business very long.
* First impressions can determine the future of the business. The person who first encounters your customers will be the one they'll remember most. You had better be very careful about who that employee is. The wrong one makes a bad first impression, and there will thus be no opportunity for a second impression.
* The first things your customer will encounter are your employees and your physical plant. The ambiance might be planned, but has it been maintained?
* If your new customer is a loyal consumer of the competition and is here merely to sample the experience, keep in mind that an equal experience (something not better than what he or she has become used to) will not break the customer's loyalty to your competitor. The experience you offer must be _better_.
# _Chapter Nine_
# Fly the _What_ Skies?
David Neeleman founded jetBlue in 2000, based on the idea that a low-cost airline need not be the no-frills, strap-hanging experience that many people remembered from the People Express experiment in the 1970s and '80s. The new airline would offer no distinction in terms of class—in other words, all seats were the same, and all service was the same; there would be no first class or coach. It did not skimp in terms of the entertainment it provided, offering DirecTV satellite service on most flights. Food was limited to snacks, but not the traditional tiny bag of pretzels thrown at travelers on "the majors."
Above all, the broken window of service would be repaired and never allowed to break again. Charting a course between the saccharine smiles and "buh-byes" of the old days and the surly, irritated flight personnel of most major airlines today, jetBlue decided to insist on service that was professional and efficient without being apathetic.
Neeleman was quoted by the _Los Angeles Times Magazine_ as saying that his priorities were to find the middle ground and keep costs down while not sacrificing customer service. In other words, he would pay attention to the details.
"We've tried to say, look, we'll get rid of the food because you don't care about it anyway," the paper quoted him as saying. "We'll have some cool snacks instead and we'll be liberal with those. We'll do tray service so you can get up when the seat belt sign is off and not have a flight attendant tell you to sit down because you're blocking the beverage cart. And we'll do it all with a smile, as opposed to with a whip."
That smile was key. Business and leisure travelers were tired of having to deal with flight attendants, ticket agents, and other airline personnel who seemed so unhappy in their jobs that they couldn't bear to move a facial muscle when dealing with the air travel industry's lifeblood, the traveler. Stand-up comics were doing routines on airline food decades before the airlines cut back massively on serving meals on airplanes, but the food was never the main problem: It was a broken window. The _attitude_ that allowed unpalatable food to appear on planes and not be corrected was the problem, and here was jetBlue, dealing with it and solving it in a way that made sense to most travelers. The smile was the signal that things on this airline weren't just going to be different—they were going to be _better_.
The experiment worked well enough for jetBlue to expand its service to airports on the East Coast by 2003 and for other airlines to take notice and try to emulate the success. Delta began a division it called Song, and United opened a division it called (for no discernible reason) Ted; both offer lower-priced flights with some cuts in service but a different image. It is too early to know if these divisions will flourish and become the wave of the future.
Part of what makes jetBlue work is that it operates much more inexpensively than major airlines. Its flight attendants are not unionized, so wages and benefits for employees are considerably lower than at United or American or Continental. Work schedules and rules are relaxed, and that means lower operating costs. Also contributing to lower costs are the lack of meal service on flights and the entertainment deal with DirecTV (which means no fees to Hollywood for in-flight movies). The seats are no more comfortable than on other airlines, but that's easier to take when you're spending a fraction of the cost of a ticket.
Alas, jetBlue is not the rule; it is the exception.
There used to be a slogan that United Airlines had the unmitigated nerve to use: "Fly the Friendly Skies of United." This was, one assumes, in response to customer research that indicated frequent customers felt the service they received on the planes flown by United wasn't accommodating or "friendly" enough. United, it has to be said, missed the point.
It's not enough to _tell_ people you're friendly. You have to _be_ friendly, too. Otherwise, they will notice the lie, and the consequences can be dire.
United Airlines was hit just as hard as the rest of the travel industry by the September 11 attacks on New York and Washington. Its friendliness, or lack thereof, wasn't a factor in that aspect of its decline. But United _has_ declined, and badly. In 2004, its application for relief from the government was rejected. No one in the airline business thinks this is a good thing.
But United's woes are far from an isolated case. American Airlines found itself an eyelash from filing for Chapter 11 protection in 2003, and even without the terrorist attacks of 2001, tourists and business travelers were already disgruntled with the handling they received on the country's airlines (and, for the most part, on other countries' airlines as well).
Why? Well, consider the experience of traveling from one place to another—let's say from New York to Los Angeles, a common business and leisure route. The seats are generally uncomfortable for the six-hour trip, the food is hardly worth considering, the restrooms are tiny, cramped, and often dirty. The entertainment is sometimes acceptable, sometimes not. The service is at best neutral, and often surly. Rules that make no sense are quoted and adhered to without question ( _why_ can't you listen to a Discman while the plane is taxiing down the runway?), and the airlines make their regard for our intelligence clear to us when, no matter where we're going or for how long we'll be in the air, they insist on instructing us on the proper operation of a seat belt.
And that's in first class. Coach is a form of torture that shouldn't be inflicted on prisoners of war.
There are so many broken windows in the airline industry that it's a wonder any plane is ever in the air, let alone the tremendous number of flights constantly crisscrossing the globe.
The fact is that airlines have had it too easy for too long when it comes to customer service. They know they have us over a barrel—there's no other way to travel across the country in six hours—and so they inflict whatever cruel and unusual punishment they deem necessary upon us, and we take it. We don't have a choice, other than to go to another airline, which isn't going to treat us a heck of a lot better.
Is it a wonder that people looked at the despicable act of terrorism and, even after the fear had subsided, gave a second thought to traveling by plane? _Without_ the attacks, air travel was an ordeal, not a pleasure. It was a necessity, not an enjoyable experience. It was, and is, something we do because we have to, not because we want to. If Captain Kirk's molecular transporter were introduced to the market tomorrow, and the cost was three times that of an airline ticket to the same destination, there would be a grand total of perhaps seventeen people flying the ol' friendly skies the day after tomorrow. And most of them would be pilots.
This wasn't always the case. At one time, flying was considered adventurous, even glamorous, by most travelers. The _Los Angeles Times Magazine,_ in December 2003, lamented the loss of glamour in flying, noting that "the airlines lost more than $10 billion in 2002 and have cut more than 100, 0000 jobs and parked hundreds of planes in the Mojave for lack of passengers. Planes are flying at near capacity partly because there are fewer of them flying. Some analysts estimate... that further bankruptcies and liquidations are inevitable."
Indeed, as airlines like United and American flirted with (and sometimes took advantage of) bankruptcy protection, it became obvious that people, even before the terrorist attacks, weren't as enthusiastic about flying as they had been since the 1960s. Flying was expensive, it was inconvenient (compared to car or train travel), and it was becoming, seemingly more so every day, unpleasant and impersonal.
Why? Because the airlines knew they had travelers over a barrel, and they didn't care how much they showed it. Food service, long a bane of many travelers' existence, got worse instead of better. Airlines spent less per passenger on food, and in the post-9/11 climate, they _charged_ customers for the food the passengers didn't like in the first place. Seats actually got smaller. As noted earlier, American Airlines increased the amount of legroom in coach, advertised it to the public, did not see an increase in revenues, and cut the amount of legroom again.
The airlines were clearly indifferent to the public's sensibilities, but worse than that, they were slapping their key customers—business travelers—in the face. Fares climbed as corporations became more cost-conscious. Service in business class resembled coach more than first class, as the seats were not larger, were not leather, and were not fewer. Attitude among airline staff, from the impersonal Web site booking button that replaced the travel agent to the unsmiling distributor of drinks who replaced the overzealous flight attendant of decades past, was not helpful.
Large air carriers are slaves to customer service surveys, so they had to know something was wrong, but they did very little to stop it. After the September 11 tragedy, there was such a wide swing of emphasis toward security that customer service seemed almost frivolous.
But it has been a few years now since security became the most pressing issue in air travel, and airlines still have not gotten the picture. At least the major airlines have not.
# How to Fix the Airlines
When jetBlue's star really started to rise, and the airline began expanding to cities like Boston and two airports in New York City, larger airlines took notice, and they fought back.
American and Delta offered special deals to their customers in those cities: They let customers fly from any New York-area airport (including Newark, New Jersey) to select cities twice during the winter of 2004—and then gave them a ticket free to anywhere in the world the airline flew. That was a huge incentive, although there were stringent restrictions on the use of the free ticket that many customers probably didn't realize at the time. This was a broken window waiting to happen, since travelers would be ecstatic at the time of the offer and then resent the company when they tried to capitalize on the deal.
Delta also competed with fierce intensity when jetBlue announced it would offer a few flights between Atlanta and Long Beach, California. Despite the fact that Delta didn't even fly that route, it matched the jetBlue fare of $99 each way (an introductory loss-leader fare) to Los Angeles, Ontario, and Orange County airports in California and sweetened the pot with triple frequent-flyer miles to Delta SkyMiles members, which practically guaranteed that the members flying from Atlanta to California and back would qualify for a free flight through the program. As a result, jetBlue blinked, and left the Atlanta market.
At the same time, Delta was launching Song and United was unveiling Ted, both of which served limited areas with low cost and the same kind of hipper attitude that jetBlue had pioneered.
Is this the way to fix the airline industry?
Well, yes and no. The broken windows in the airline business are perhaps easier to spot than in most other industries. An airplane, after all, is an enclosed environment and one that most people know very well. A flight is, for the passenger, a simple experience and in most cases a relatively dull and uninspiring one. It's a good sign that some airlines are moving (after considerable prodding from jetBlue) toward lower fares and a better overall experience for their customers.
But so far, that attitude and that philosophy have not bled onto the major airlines; they have been limited to smaller companies-within-companies, and never extended to an entire service area or even the operations in one whole airport, for anyone but jetBlue. United and Delta seem to be giving their customers a choice: Sign up for lower fares in limited runs and get more efficient, friendlier service, or pay full price and get the same miserable experience they'd come to expect.
This hardly seems like a strategy destined for great success. Until the airlines—all of them—are willing to step back, take a look at their windows, and see which are broken, there will be no full-fledged recovery for the air travel industry. The cavalier, callous attitude large airlines have taken with their core customers for decades is now coming home to roost. People fly when they _have_ to, not when they _want_ to, and they generally shop price, both for family vacations and for business travel.
The lesson taught by jetBlue has been learned by other airlines, but only to a limited extent. In time-honored fashion, they rush to imitate what works without analyzing why it works. Broken windows like airline food, surly service, back-breaking seats, and abominable customer service on the phone are all going unrepaired. Instead, what the public gets is a subindustry of small airlines that want to be jetBlue, but that would prefer to drive jetBlue out of business so they can go back to being Great Big Airlines again and stop with all this customer service nonsense.
The broken windows in the airline industry are not fixed. They are merely taped into place awaiting the next brick to be thrown through them.
The captain has requested you return to your seats and fasten your seat belts. We are experiencing some turbulence.
## CARRY-ON LUGGAGE
* All airlines will get you from one airport to another—it's the quality of the experience and the price that will determine a traveler's preference.
* Details like food, entertainment, and comfortable seats make a difference, but indifference and lack of attention are driving the core customer away.
* It is possible to repair broken windows that other companies have missed. By concentrating on details and eliminating what customers didn't like to begin with, jetBlue reinvented the air travel business.
* Imitating success isn't fixing broken windows.
* Only by understanding why the windows were broken can you truly repair them and improve your business. Pretending to fix broken windows by saying you are doing so, and then taking no action, is worse than leaving a broken window unrepaired.
# _Chapter Ten_
# Doing It Right
The shining example of the broken windows theory was the spectacular turnaround accomplished in New York City by Mayor Rudolph Giuliani and Police Commissioner William Bratton. While the two, along with others, focused on such broken windows as what Bratton calls "squeegee pests" (men who wash car windshields as a method of begging) and fare jumpers (who leap over turnstiles in subway stations to beat the fare), the murder rate in the city fell from more than 2, 200 to fewer than 1, 000 per year, and even jaded New Yorkers began to believe their city was more livable than it had been.
Broken windows _can_ be repaired, and when they are, the turnaround in public perception is palpable and rapid. But even Bratton himself told me recently that he was "not a believer" in the broken windows theory when it was being developed in the 1970s. It wasn't until later, as a staff lieutenant in Boston, that he saw what he calls "the disconnect."
"I'd go into high-crime neighborhoods and most people did not want to talk about the serious crime," he says. "People were often not aware of the murders, rapes, and robberies because the press was not reporting them. What they were complaining about were the broken windows: What about that abandoned car, what about that prostitute who's on my doorstep every night, what about those kids keeping me up all night? It became apparent to me that we, the police, were focusing too much on too narrow a set of problems, the major crimes. What was causing fear in the neighborhoods was what they were facing every day. In the so-called victimless crimes, the victim was the neighborhood."
What Giuliani, Bratton, and others in New York managed was to shift the focus away from the intangible crimes, the ones that the vast majority of New Yorkers never saw, toward the ones that made their lives less livable—graffiti, panhandling, fare beating. When New Yorkers saw that those seemingly lesser crimes were being handled with an iron fist, their confidence in the police to deal with more serious matters of murder, rape, and assault rose. It was the perception, as well as the reality, in New York City that the broken windows had been repaired.
"In some respects, broken windows was based on what is more common in the business community," Bratton, now the police chief of Los Angeles, says. "Customer service is seen as a broken window. In the police environment, a broken window refers to anything that creates fear or a sense of disorder. It's lack of attention to detail."
When it's done right, repairing broken windows can have a tremendous impact. New York is no longer seen, even after Giuliani's administration is gone, as a haven for crime or a dangerous place. The threat of terrorism, a much more national concern and certainly anything but a broken window, is considerably more palpable in the city today than the fear of crime. Police officers on the street are seen as public servants and heroes, not corrupt individuals unwilling to deal with the problems of average citizens.
What Bratton and Giuliani did in New York was remarkable, but it came down to the fixing of some broken windows. Businesses, as well as governments, can and must do the same.
In some cases, the results of broken window repairs have been staggering.
I referred in the preceding chapter to the success of jetBlue, the airline that lowered fares while increasing customer service. It has to be noted that by avoiding broken windows, jetBlue managed to create an image of itself as the people's airline, the one looking out for the traveler, and not merely its own bottom line. It even ran an ad in which everyone at the airport got along famously—right down to the dogs and cats. "Is it always like this around here?" someone asks. "Only when the jetBlue flights arrive," another answers.
That's the kind of good feeling the airline aims to create for its customers. And based on the ticket sales and revenues, it has to be concluded that jetBlue is succeeding.
It's easy to point a finger when windows are broken, especially when those broken windows are left unrepaired for long periods of time. It's easy to assume the company doesn't care—and in some cases, that assumption would be correct. Broken Windows Hubris isn't an isolated disease; it affects many large corporations whose executives think they are more important than the satisfaction of the company's customers. It happens quite a bit in business, and in each case, it is deplorable and inexcusable. But it is easy to find and point out.
Much more unusual is the company whose broken windows are noticed, identified, and repaired promptly, so as to best serve the customer base and keep the company's mission alive and well. There are some, and they deserve a good deal of attention.
# Target Stores
Where Kmart stumbled and Wal-Mart ran into problems, Target quietly became perhaps the most respected and trusted name in the mass merchandise market—no small feat for any company, let alone one that was hardly well known as little as ten years ago.
The concept with Target was always clear, and its windows remained gloriously unbroken. Yes, there would be plenty of merchandise on the shelves, and yes, the prices would be competitive, if not guaranteed to be the lowest. But Target concentrated on establishing its identity as the mass merchant whose stores were designed with the _customer_ in mind, and that made the difference.
Speed was the key: Even consumers whose priority was to find the lowest price on every single article on their shopping list wanted to be in and out of the store quickly. Target made sure that could happen: There would be no long waits on checkout lines. If too many people were on line in one location, another register would immediately be opened, and the wait was decreased. Even during the madness of the holiday season, Target kept its customers moving through the store (and especially the process of paying for merchandise) as quickly as it possibly could.
Was this a simple business practice, designed merely to increase traffic by speeding customers through the store in order to make room for others? Certainly, it was. But it was also an acknowledgment to consumers that the owners of Target had been to large chain stores before, knew what the problems (broken windows) were, and were making an extraordinary effort to avoid them _in order to make the shopping experience easier and more pleasant for the customer_.
Even when Target's stores inevitably fall victim to the same broken windows inherent to the mass merchandising industry—less-than-sparkling facilities, underpaid, indifferent help—its mission, to remain competitive with and faster than the rest of the industry, is intact and noticeable. The broken windows it suffers are repaired more quickly than most, and the communication with consumers (some of whose complaints are studied carefully by executives) is better than the rest of the industry. Better than that, Target has stayed off the front page of the news section, with no class-action suits filed against it and no Chapter 11 protection requested. Those broken windows are harder than most others to repair, as they are the result of many other, less noticeable broken windows that must be repaired at the same time.
Target has managed to retain its original concept even while expanding into many new markets, which is usually the critical juncture for a chain of businesses. The larger a chain becomes, the more difficult it is to maintain the obsessive, raging devotion I've described as essential to the discovery and repair of broken windows. So it is especially interesting to watch a business as it goes from one store to two, from two stores to six, from a small chain in one state to a regional chain in three, and then to a nationwide business. At each step along the way, as more control is ceded, it is often easier to see the broken windows accumulate.
Not in Target's case. Here, as the chain moved into every state in the Union and expanded its presence further, the original concept of the stores and the devotion to preventing and fixing broken windows remained evident. This was a case of a business that kept sight of its vision and made sure its windows stayed uncracked.
# The Walt Disney Company
Let's forget for a moment that Disney seems to own half the planet. Let's overlook the subsidiary businesses of television networks, retail stores, and clothing manufacturers. Let's examine the core business of the Walt Disney Company: family entertainment and theme parks.
Consider, especially, the experience one has when attending a Disney theme park in Florida, California, or anywhere else around the globe. If ever there was an atmosphere in which no windows are broken, this is it. Cleanliness is famously obsessive; there is never— _never_ —a candy wrapper left on the street. Problems are solved immediately by a staff that is (get ready, it'll be a shock) _cheerful_ about doing their jobs, and enthusiastic about making sure the customer's (guest's) priorities are the most important thing. If you have a problem and a Disney "cast member" can't solve it for you, it must be quite a problem, because your enjoyment of the stay in the park is what has been drummed into the head of every employee in that park, and you'd be hard-pressed to find one who doesn't adhere to that philosophy.
Nothing is perfect: No one can regulate the weather, and Disney parks tend to be in areas where the sun shines bright but hot. Lines are unavoidable in a place that has tens of thousands of visitors each day, all of whom want to attend the same attractions and might even have similar schedules in mind. But consider the lengths to which the Disney parks go to accommodate those conditions and make the guest's stay easier and more enjoyable.
A few years ago, a system was installed called Fastpass, which allows guests to reserve a place in line. Guest tickets are swiped in a machine, and a time to return is reserved on a ticket. The guest can then go to any other attraction in the park, come back at the appointed time, and see the attraction without waiting in line. This addressed the most serious broken window in the parks—families having to spend long, hot hours on line for an attraction that would last four minutes.
The solution was simple, yet demonstrated the park's obsession with making the day enjoyable for its customers.
By the same token, Disney's entertainment arms (its film divisions, particularly Walt Disney Pictures, over which the company maintains total control) offer what has to be described as a branded experience. Go to a Disney movie for the family, and you know what you're going to get. Not to worry about the kids dealing with issues or images they may find confusing or frightening; in this case, the experience will be what was intended by the company's founder. Yes, other divisions of the same company will offer more challenging fare, but it will be labeled as such and come out under a different banner.
Disney has its problems, like any other enormous corporation. But its core businesses retain their vision and make sure their windows remain unbroken.
# Apple Computer
Scoff if you want to; tell me that Apple controls only 3 or 4 percent of the personal computer market. But then talk to any Apple owner and see if the glint in his eye is maybe a little bit more intense than someone who just bought a Windows system. Ask him if he'd like to change his allegiance in computers. Then stand back, because the response will not be a calm one.
Apple's crowning achievement is in creating obsessed, crazed _consumers_. Its products, innovative as they have been for two decades, are more expensive than IBM-based systems. They don't have access to nearly as much software as those running Microsoft systems. Apple users are, from any rational standpoint, at a considerable disadvantage in today's marketplace.
And yet they are the most devoted consumers on the planet. They will not change their purchasing alliance in computers under threat of death. They will spend hours explaining to you why 95 percent of the world's computer buyers are wrong and they are right. And they will happily pay those higher prices for that hardware that can't run as many programs as the less expensive ones and will be happy and proud each time they do so.
Now, _that's_ loyalty.
How has Apple engendered such devotion? I contend it is through their policy of noticing and repairing broken windows, sometimes before they are broken.
Each of Apple's innovations, from its initial operating system through the introduction of the Macintosh, and then the iMac, computer, has been designed with one thought in mind: making computing easier or more enjoyable for the consumer. Microsoft's Windows system is largely based on the original Macintosh operating system and still lags behind in speed and ease of use. Apple continues to think like a computer user, not like a computer company.
Then there is the issue of customer service. Call Microsoft with a problem sometime and try to get help. I dare you. You'll get endless voice mail prompts, demands for money, and eventually an outsourced computer tech in Pakistan who may or may not solve your problem after charging you for the call.
Call Apple with the same problem. Your warranty will last longer on an Apple computer, so you might not have to pay a dime for help. But you'll get a human being sooner, and unless there's something seriously wrong with your computer, your problem will be solved—and solved by someone whose problem is yours until it is solved—before you get off that phone.
Apple users are considered fanatics. Most businesses would be hard pressed to find such customers; for Apple, they are the rule, not the exception. I think it has something to do with the company's windows.
## GETTING IT RIGHT
* Fixing broken windows is like quitting smoking—the sooner you do it, the more completely your problem will heal and reverse itself.
* Broken windows _can_ be fixed, and they _can_ be detected before causing trouble. The crime situation in New York City is an example in government, while Apple Computer, Disney, and Target are examples in business.
* Simply saying you've fixed the window isn't enough. You have to demonstrate your devotion to customer satisfaction and make sure your customers know it's more than talk.
# _Chapter Eleven_
# Do You Google?
There are many successful businesses in the world. Very few of them have become a verb.
Can you "Coca-Cola"? Do you "Sony"? Have you ever "BMW-ed" or "McDonald's-ed"?
But I'll bet that you've Googled. You may have done it today, as a matter of fact. You might have found this book via Googling.
Google, which started out as the Little Search Engine That Could and became a multibillion-dollar public stock offering, does not any longer need to explain its function to any member of the general public. If you tell someone that you Googled them as a way of finding out about their business, they will probably nod in recognition. Before this meeting, they probably Googled you.
Naturally, a semantic change doesn't mean you have a successful business. But the fact that your business name has become recognizable enough that people are using it independently and everyone knows what it means is an indication that you have defined your business well. Few things are as important in business.
But that kind of name recognition, when it's not negative (Enron, anyone?), is also an indication of something else: It means that you have done a good job in fixing your broken windows.
The Internet is an incomparable information-gathering tool, but its windows can be absolutely shattered when things don't go right. A key example of such broken windows had been the very core of the Internet itself: the Web search engine. After all, if you aren't able to find the information available, what good is it to have the information available in the first place? From a business's point of view, the search engine can be much more valuable; having a killer company Web site is of very little use if the public isn't being made aware of its existence. Search engines have come and gone and until recently, were interchangeable, easily confused machines that couldn't really be counted on to perform the task they were designed to undertake.
That changed when Google became synonymous with "search engine." In what seemed like a flash, www.google.com was _the_ place to go for data searches, and it provided the same basic service as the rest, only better.
How can something this generic (you ask for information, and you get it) be characterized as better? How can one be a better search engine than another? Is Google really of higher quality than Excite, Yahoo!, AltaVista, Magellan, or Ask Jeeves? Why does a Web site that charges nothing for information (and none of these search engines charge) have to be better?
Google managed to turn itself into the most visible and well-known search engine through its handling of potential, and existent, broken windows. It saw problems with the way some other search engines handled their service, and it avoided them. Even when Google itself had a breakdown of some sort, the focus was kept on service of the user (you can't call someone a customer if the service is free), and the broken window was repaired quickly and efficiently. In many cases, users didn't even notice.
Search engines proliferated wildly in the 1990s. As home and business Internet use increased dramatically through the decade, the need for a "road map through the information superhighway" became clearer. But once people (mostly home users) got over the novelty of the concept—the ability to find almost any piece of information in an instant—the cracks in the windowpanes began to show.
In some cases, search engines that were asked for information wouldn't understand the request. Unless certain words were put in quotation marks, they would be misinterpreted. Capitalization mattered in some cases, but not in others. Keywords were helpful, but they sometimes led to the wrong conclusion. There wasn't anyone to ask for help.
The companies that owned the search engines were also trying to establish their Web sites as "destination sites" for users, so as to increase the probability that larger companies would advertise on the sites, which is the way search engines make money for their owners. It was hard to establish a brand personality, since the product being sold—information—was the same for each search engine, but different for each user attempting to find it.
In short, the only difference among search engines was the broken windows—the number and type of them. The sites with more broken windows (slow service, programs that didn't understand the questions) fell by the wayside, and the familiar names we know now remained.
But Google became a verb.
Somewhat late to the starting gate, Google learned from the experience of those who had preceded it into the search engine parade. Its founders, Sergey Brin and Larry Page, knew that users didn't want to be held up in their search for whatever tidbit of information was the emergency of the moment, so speed—the currency of the Internet—was essential. Google would be fast.
Google also had to be accurate. Here its founders decided to err on the side of excess: If you asked Google for a piece of information, it would bring back every Web site it could find (and it is currently scanning more than 4 billion sites) that had the keywords you requested. Sometimes the list of "hits" would be compressed, but when it was, Google would let you know it had done so for efficiency's sake, and offer to give you the entire list of eligible sites, no matter how ridiculously long it might be.
Still, was that enough to make an impact on the millions of users who thought that one search engine was roughly the same as the next? It took time, but Google began to separate itself from the pack largely through word of mouth, but also through effective marketing. Google became the search engine of choice for other sites offering news and information. "Powered by Google" became the logo most often seen when a related Web site would offer a search engine. The implied message was that if another site thinks enough of Google to use it instead of creating a search engine of its own, Google must be good.
And the fact was, from a user's standpoint, Google _was_ good. It was better than other search engines in small ways that made a difference. In short, it had fewer broken windows, and they weren't broken as badly as others.
#### **Google's Road to Success**
1. **Google was fast.** Most search engines were, and are, but Google's speed was designed to be especially noticeable—and if you didn't notice it yourself, the elapsed time of the search (0.35 seconds seemed pretty fast) was listed on the first page of your search results.
2. **Google was accurate.** If you searched for a keyword, Google would highlight that word in each result it gave you, to show that you had gotten what you asked for. If you got something else, the highlighted keyword would indicate that maybe the problem was yours. But it could be fixed.
3. **Google was easy to understand.** If you did get inappropriate results, Google had a help button that would clearly explain the procedure and demonstrate how to repair the problem (the broken window on your part?) and get the results you wanted.
4. **Google was thorough.** Other search engines would take your request and give you the top ten results (those most likely to be the site you were seeking) and give you more only if those weren't good enough. Google gave you as many results as it could find, and let you sort through them. Yes, it ranked the results by the same criteria as the other engines, but it let you decide what was enough.
5. **Google was free.** Okay, so was every other search engine (except for specialized supersites like Lexis-Nexis), but when you're offering improvements on what's available elsewhere, and you're still not charging any more than the competition (or in this case, not charging anything), you're in line to succeed.
Google's success—it came from nowhere and got itself into a position to make its founders multibillionaires—can be attributed mostly to its ability to deal with broken windows. This is key, as Google offers no tangible, physical product. It offers a service and, as such, must serve its consumer base better than its competition to stand out and keep its reputation. The fact that the site is listed as one of the five most often visited every week is an indication that the strategy is working.
This is another example of a company whose founders and chief executives got it right. They knew that windows could not be broken and stay broken in a business that relies on satisfied consumers to be profitable. They knew that little things—an extra second or two of waiting, a few highly placed search results that didn't really match the request—would make a large impression on the people the company could least afford to offend. And they determined that such things would not happen and that the tiniest infraction (broken window) would be alleviated as quickly as was possible.
Google doesn't rely on face-to-face contact with the consumer; that is, the average user is rarely in contact, either in person, by phone, or even online, with another human being who is concerned with his or her situation. Google, as a search engine, is run (from the consumer's viewpoint) by computers. No person could possibly search through 4 billion Web sites in 0.35 seconds.
So customer service for Google is different than for most consumer-based companies. It means the delivery of the promise the company makes without, in almost all cases, direct human contact. It means the product must almost literally speak for itself, and it had better be good, all the time, because users are going to come back to it again and again if it is, and give up after one try if it's not.
Google's staff deals much more intimately with the advertisers who pay their bills, but as long as the product delivers the "eyeballs" the industry tracks in large numbers, those advertisers will be happy to be seen on a site that has a prestigious name. They know that consumers make multiple trips to Google and that they are almost always satisfied in what they have set out to do.
Ask anyone you know if they have Googled, and even if they don't answer affirmatively, they'll know what you mean. But more important than that, they will not have a negative story to tell about the Google experience, and in a service-oriented business, that is not only remarkable, it is absolutely key to success.
The experience of using Google isn't, to be fair, all that different from the experience of using most other major search engines. The variations I discussed above—speed, accuracy, and volume—aren't enormously pronounced, although they are noticeable. Consumers will detect a difference, but it's not like other search engines are awful and Google is impeccable; it's a question of degree.
Still, the difference in _perception_ is quite large. People don't talk about "AltaVista-ing" something to find it on the Internet or "Yahoo!-ing" their own name to discover what information about themselves is available to the general public. Google has gone beyond most brand names—and in the minds of consumers, it has gone beyond most services—in reliability and consumer friendliness. Google just has a better place in the public's mind than its competitors.
It has done this essentially without advertising and without making a huge consumer campaign that would define its persona and create an impression in the public's mind. Google has managed this feat chiefly through performance, which is rare in consumer culture and rarer still on the Internet, where almost nothing is what it claims to be.
This should speak to all businesses, not just Web-based ones, on the power of performance and fixing broken windows (or avoiding them altogether). It should be a wake-up call to every business that believes it can create an image with advertising, public relations, and public pronouncements, but not deliver on its core promises. If a business believes it can make charitable contributions and publicize them, but not see to the small details of its own operations, it should look to Google not for inspiration, but for an object lesson in everything Google isn't doing wrong.
Practicality dictates that a business do what it promises to do, and Google does that. But broken windows are often hiding below the surface (in the basement, if you want to carry the metaphor that far), where they aren't easily visible. The fact that a business that almost never comes into direct contact with consumers can establish itself as a worldwide presence and a household name by getting the little things right should speak volumes to anyone who is trying to start or maintain a business in today's climate.
Don't just Google something; think about Google when you do it. There are myriad lessons to be learned here, and most of them are tiny, not easy to see. They require a dedication to observe, but their importance can't possibly be overestimated—they can be the difference between your business's success and its failure.
Does that remind you of anything?
## GOOGLE ME THIS, BATMAN!
* Even for a business whose relations with the public are not face-to-face, performance counts. Tiny imperfections in the product or service offered become amplified when there is no human contact with the company.
* When a business is not enormously distinguishable from its competition, the details become even more pronounced and important. Broken windows make the difference when the competition is close to your level. Go a little bit further, and you will be noticeable. Don't, and you're a member of the pack.
* A broken window doesn't have to be a "problem"; it can be merely a service you could offer and don't. If you can do something more for your customers, do it, and you will make a lasting positive impression.
# _Chapter Twelve_
# Broken Wires: Broken Windows on the Net
It's one thing to interact with your consuming public in your retail stores, or on the phone when a customer service call is made. It's something else again to interact with the people spending their money on your product or service via your company's Web site or by e-mail.
The Internet is the most perfect, pervasive, and all-encompassing source of information in the world—you can find virtually (pardon the pun) anything you could possibly want to know in a matter of seconds. And as a business, you are able to convey the message you especially want to communicate quickly, without filtering, and inexpensively. It seems a perfect tool.
But the Net is also a minefield of broken windows. When something goes wrong with your Web site, especially if it is not well organized or designed, the public will find it immediately and become increasingly annoyed with your company—and the worst part is, you might not even know there's a problem until it's much too late.
Imagine: A customer buys your product in a traditional, brick-and-mortar retail outlet. He brings it home, opens the packaging, begins to assemble it, and discovers that there is a small piece of hardware—a bolt, let's say—missing.
Let's say that instead of calling customer service personnel on the phone, this consumer decides to go online and visit your Web site to alleviate his problem. There are any number of ways this transaction can become a broken window, and because there are very few scenarios in which the consumer interacts with an actual human being online, it's quite possible you won't be aware of the problem until the customer is already more than irritated and might be a customer of yours no longer.
First, the consumer has to find your Web site. Most companies are savvy enough these days to list their Web address (URL) on all promotional materials and even packaging, so the customer in question here would be able to look on the box or the instruction booklet to find the proper address. It had better be there, or that is a major broken window.
Assuming that the address is found, either on your materials or via a search engine like Google (see the preceding chapter), the consumer will now search your home page for the customer service link. This brings up two distinct, and eminently possible, broken windows: You must have a customer service link on your home page, and it must be easily findable.
A consumer who needs assistance with your product or service is not in a forgiving mood to begin with—he has spent money on something that doesn't seem to be working properly, and he is heading toward frustration. So if the road to the customer's solution runs through the Internet site for your company, it had better lead there directly and quickly. Finding a home page with a badly placed assistance link (or worse, none at all) is just going to add to the customer's sense of irritation. That's not a help; it's a broken window. A _big_ broken window.
Let's assume, though, that you've managed to vault those hurdles: Your URL is easily attainable, your home page has a link to customer assistance, and it's easy to find. Now, how does the customer assistance page on your Web site work?
In many cases, customer service on company Web sites is relegated to a section labeled "contact us," and it is merely a link to a general e-mail address the company uses to field customer complaints and comments. But this doesn't give the customer a sense that his problem is being considered or solved quickly; it serves only to make him more anxious and annoyed than he was before. It could be days—weeks!—before his seemingly simple problem is even considered, let alone solved. This is the information superhighway? It feels more like an unpaved road leading to a dead end.
A customer service page should offer exactly that—customer service. A consumer bringing his or her problem to your Web site is in need of answers, solutions, and he or she needs them _now_. When you use a communications system that can send millions of messages in a fraction of a second and your use actually adds time to the problem, that's a broken window.
Yes, there should be a way for a consumer to contact the company on your Web site, and yes, it can certainly be a direct link to an e-mail generator. But it should also include the company's "snail mail" address and phone number, in case the consumer wants to get in touch the old-fashioned way. And that contact link should not be considered the customer service section of the Web site.
Instead, there should be a separate section for those who have issues that need to be addressed, and it should be comprised of three elements. There should be a "frequently asked questions" (FAQ) link, where the most common, and easily solved, complaints are listed and explained in clear language. There should also be a detailed section for each product the company sells, detailing its operation and answering its FAQs, plus offering order forms for extra parts or accessories.
But most of all, there should be, whenever financially possible, a real-time, live-person customer service feature. This is available from many larger companies' Web sites and ensures that customer service professionals, usually the same ones who answer phones for the company's consumer help lines, are available online to answer questions in an instant message (IM) format, speaking directly to and with the consumer as questions are asked.
Yes, it's expensive, and smaller companies might not be able to afford the luxury. But if you have a staff of people answering customer service calls on the phone, there is no reason not to expand that service to the Internet, since you are already paying the employees, and the overwhelming odds are that all of them have a computer terminal at their workstations.
Here's why it's important: A consumer who is contacting customer service begins with a problem. In almost every case, this is someone who doesn't have a _question_ about your product or service, it's someone who has gone ahead and purchased that commodity and is now having trouble using it. It's entirely possible that the problem is of the consumer's making—perhaps he or she doesn't understand (or hasn't read) the instructions or is trying to customize the product in some way for which it wasn't intended. That doesn't matter. The consumer has a problem and needs it to be solved.
When someone chooses to contact customer service (where, you'll recall, we have already established that the bulk of broken windows are broken), he has made a conscious decision not only to seek an answer to the problem at hand but to try to obtain that answer quickly. He could, after all, have returned to the place where he bought the product or service, or written a letter to the company requesting assistance. No. He has opted, instead, to call or go online to get an answer _now_.
The choice of online help, rather than telephone assistance, is a significant one. Remember, the whole idea of personal Internet use is that the information is supposed to be delivered conveniently and quickly. That's the reputation that the Web has, and as Marshall McLuhan noted, the medium is the message. The customer is sending you a message by choosing to contact you through his computer, the fastest communications device yet invented by man.
"You have so many choices, and we have so little to go on to make choices," says Malcolm Gladwell, author of _The Tipping Point_ and _Blink,_ a man who knows a great deal about why consumers make specific choices. In a recent interview, Gladwell told me that "our decisions come down to relatively subtle things. Our unconscious acts as a filter and then our conscious mind takes over from there. We can reject things on an unconscious level without even realizing we're rejecting them. We gather every available piece of information very quickly and then do a kind of first cut."
Gladwell, whose book _The Tipping Point_ was a massive best seller and a brilliant examination of what makes businesses work well or not at all, knows about decisionmaking, and he knows that the "unconscious filter" extends to the decisions we as consumers make in interacting with companies. Maybe the awful telephone experiences that many consumers have with customer service (the multiple broken windows of phone message systems, long waits on hold, and surly customer service representatives outsourced in countries where the accents make it difficult to communicate) lead us to opt for online assistance. If so, companies should note that the online customer service experience had better be demonstrably more efficient and pleasant an experience, because the consumer is coming in with a negative expectation, even if it is an unconscious one.
Given that, we have to examine the way in which the average company Web site deals with the public in general, even when they are not coming to the URL with a problem. Because remember, the little things you do, good or bad, send psychic signals to the people with whom you most hope to communicate: your customers.
When someone stumbles across, or seeks out, your home page, what does that person find? If the information there is delivered in a cluttered, disorganized, confusing fashion, what does that tell the visitor about your company? If the most logical, predictable questions about the company—address, phone number, type of business—aren't answered easily, what message does that convey? If the personality projected by the site isn't one that is friendly, helpful, and useful, what message do you expect the visitor to take away from this experience?
It's important that your message and your image be consistent every time you come into contact with the public—and that certainly includes your Web site. As the face of your company on the Internet, this section, which is designed and executed by people who work for your company, must be an absolute paragon of unbroken windows. Here, where you have the most control over your message, every detail must be exactly right. And that means special attention to every possible facet _before_ anything is posted and open to exposure to the general public.
But don't make the mistake of promising more than you can deliver. We all know the difference between the TV commercials aired by McDonald's (in which gleaming, smiling young people offer wholesome food in sparkling settings) and the reality of going to a McDonald's outlet (well documented in chapter 2). Making claims on your Web site—even subliminal ones like "cleaning up" images that you can't hope to duplicate in real life—that won't match the customer's experience in a nonvirtual setting is a broken window, and a dangerous one.
"The distance between the beautiful image on the television [commercial] and the reality in the [McDonald's] store is now so great that you've made the [negative] encounter in the store more salient," says Gladwell. "This is not the McDonald's you expected."
By the same token, if a company's Web site offers an image that is unrealistic and inflated, it will poison the experience the customer can logically expect to have with the company in "real life." So make sure your Web site offers a positive view of your business, but one that is true, or you will be asking for unfavorable comparisons, a seriously broken window.
Make sure everything on the site is easy to understand. People are more sophisticated technologically than they were even a few years ago, but the general public should not be expected to understand even the basics of HTML code. Make it easy for them to point and click their way to the information they need, in as few moves as you can manage. Ease and simplicity of use are enormously important factors in a commercial Web site.
There are a number of reasons a person will seek out your Web site: information about your product or service; information about getting a job with your company; information about contacting your company; information about the history of your company; customer service. In any one of these cases, the information should be simple to find and written in language that is easy to understand. This is not because you're assuming the consumer is an idiot; it's because people want a pleasant, stress-free experience from your Web site, and while you don't have to write everything on a second-grade level, there's no reason to make it any more confusing than it needs to be.
In addition, design is important. Make the site easy to look at, as it will be seen by any number of people, including those who might stumble across it by accident. Don't you want their business?
Broken windows on the Internet can include things you don't have on your site. For example, if a person comes to the home page with the intent of e-mailing a specific person in your company (one who deals with the public, as every employee does not need to be listed), that person's e-mail address, or at least a common address through which that person can be reached, should be listed. If there's no way to find that information on your site, you're increasing the visitor's frustration level, and that is never good for business.
The key is to remember what you yourself find helpful and irritating about your visits to corporate or company Web sites. Use what you think is a positive factor and make sure that the negative ones (the broken windows) are avoided. And test everything before you post it to your site.
When the site is up and running, it's a good idea to mystery shop your Web site as you would your business. Visit every once in a while. Make sure all the links still work. Make sure you can e-mail with a question or complaint and that no new product (or old one) is unrepresented.
If you get only one chance at a first impression, keep in mind that the first time many people encounter your business is online. Do you want to begin with a bad experience?
## WEB GEMS
* A company's Web site is a place where impressions are made and customer service is rendered. It is as important as any aspect of a business in which consumers are directly encountered.
* Simplicity is important, in both design and operation. Make sure the Web site for your company is easy (and hopefully enjoyable) to use.
* Customer service on the Web is important and tricky. If you can't offer twenty-four-hour live help, by all means include e-mail addresses and toll-free phone lines where the answers to consumer questions can be gotten as quickly as possible.
* Don't make Web promises you can't keep. If you include pictures of facilities that are more impressive than your actual ones, you are creating an image for the customer that your business can't live up to.
* Make sure you present the information in clear, concise, easy-to-read formats and offer as much information as you think consumers might need, and then some.
# _Chapter Thirteen_
# The Public, Watchdog
My friend Jeffrey Cohen is a New Jersey-based author and freelance writer, but he's also a serious movie buff. Between Jeff and his son, pretty much every studio release is open to discussion. So they go to the movies a _lot_.
One thing that some theater chains have done in the past few years to increase revenues (and keep in mind that studios, not theaters, make most of the money from your ticket purchase on a new film) is to show television-style—and in some cases, actual made-for-television—commercials for products other than upcoming movies. The pre-show, as theater owners call it, the time after the lights go down and before the movie begins, used to be for coming attractions featurettes, or trailers, as they're known in the trade. Now ads for sodas, cars, and clothing, among other products, are being added to the pre-show.
This steams my friend in New Jersey more than I can tell you. "If I want to see TV commercials, I don't have to spend nine dollars to do that," he'll say. "I can stay at home and watch them for free."
So when Jeff discovered there was a chain in his area that didn't include commercials in the pre-show, but retained only the coming attractions trailers, he made sure he and his son patronized that chain whenever possible, which is almost all the time.
But that's not the whole story. Jeff has been telling his friends in the area (and out of the area, like me) about the chain that keeps commercials out of the theater. He's making sure they know, and encouraging them to pay their money—to vote with their wallets—to the theater chain that doesn't show commercials.
Now, by our definition, showing commercials before a movie isn't necessarily a broken window. It doesn't automatically convey to the consumer that the chain isn't paying attention to details or doesn't care about serving the needs of its patrons. But it could be construed as a sign that the business is more interested in improving its bottom line in any way possible than it is in the sensibility of its customers. The movie will be the same in any theater showing it, give or take a decibel or two. Why not patronize the one that keeps an annoying trend out?
Will Jeff and his friends make a huge impact on the theater chains they shun? Probably not so much that the owners would even notice. But if enough people feel the way he does, and notice that there is a place that doesn't show commercials before the movie, that could start a trend. Think Malcolm Gladwell's _The Tipping Point_.
The public is the final arbiter in almost every business. They buy your products, use your services, and pay your bills. In Hollywood, movie stars' careers rise and fall based on the number of people who attend their films. In politics, the numbers are even clearer (most of the time): The candidate with the highest number of votes is the one who gets to have, or keep, the job.
Thinking that you can get by because "they won't notice" is tantamount to putting a noose over your head and jumping off a stepladder. You can't count on the public not noticing the things you miss, or the things you've decided aren't important. They'll notice, and they'll decide every time whether or not they're still going to be your customers tomorrow. Quite often, that answer will be no.
Jason Binn, the publisher of such dynamic publications as _L.A. Confidential, Gotham,_ and _The Hamptons,_ knows that every detail, no matter how minuscule it may seem, will be spotted by a consumer. "Everything you do is part of a domino effect," Binn says. "When you walk out of your room and you don't put the suit you wore the night before away, or you don't hang up the tie, it won't make any difference—unless someone walks into your room. Then it sends a message that you didn't take pride in your personal hygiene or your living environment."
By the same token, a sloppy corporate appearance can signal to consumers that your business doesn't care about its product, service, or physical plant. That can lead to questions about your commitment to quality, to service, and to serious business practices.
Because I am in the public relations business, I know about image. I know that a business that wants to project a certain image must take every step possible toward making it consistent. There can't be so much as one single detail that doesn't conform to the image the company is trying to project, or it will be found, it will be publicized, and it will be exploited. There is no covering up; there is merely damage control. It's infinitely better, believe me, to have no damage in the first place.
The public doesn't even always know what it wants, but it always knows what it _doesn't_ want, and it will not be shy in making that known. The television landscape, for example, is littered with shows that the networks thought couldn't miss, the critics adored, the Emmys honored—and nobody watched. Broken windows? There must have been—if the programming was _that_ good and no one watched it, the only explanation lies in broken windows. Perhaps the scheduling was bad, the publicity was ineffective, or the advertising not thought through properly. But something had to go wrong, or _Sports Night_ would still be on the air.
The classic example is one of the most famous: the 1980s battle between videotape formats—VHS vs. Sony's Betamax (remember _that_?). Sony had a technology that virtually everyone in the consumer electronics business admitted was better, more efficient, longer lasting, and destined for history. It even had the good sense to make it to the market first, usually a crucial factor in a contest between two closely competing products.
But Beta didn't happen. A difference that many in the industry thought would be a boon for Sony's format—the fact that Beta cassettes were smaller—turned out to be a broken window. VHS, which was developed by JVC and Panasonic's parent company, Matsushita, had wider, larger cassettes, which meant that more tape could fit inside them. Therefore, a VHS cassette, taping at the standard speed, could store up to two hours of programming, whereas a Beta cassette could store only ninety minutes. Industry experts hadn't expected the difference to be important to consumers, but it was a huge broken window that left the format in the dust.
Consumers bought VHS units because they could tape a two-hour movie on one cassette, and Beta—which most believed delivered a better, clearer picture—was finished in a few years. Try to find someone with a Betamax tape deck today. Try to find someone who doesn't still own a VHS machine and a library of tapes. Even with recordable DVD on the market, VHS remains the format of record.
The public saw the broken window and determined that Sony was interested in making a fine product, but not one that did what consumers wanted it to do. When a company loses sight of its customers' needs and wants, and instead concentrates on what it thinks its customers _should_ need or want, the company is a giant broken window waiting to happen. Get out of the way before some glass falls on you.
In 1989, the Fox Network was a fledgling group of television stations that didn't broadcast most nights of the week, didn't cover the whole country, and wasn't considered much of a threat to the Big Three—CBS, ABC, and NBC. It was, in fact, considered something of a joke in Hollywood. The Fox Network? A network that didn't even have initials? Please.
That year, programmers at Fox decided to take a very large risk and order a series that was never expected to do very well. An animated sitcom for adults, the show wouldn't offer the kind of heartwarming reassurance that something like _The Cosby Show,_ which was the powerhouse of television, did, and it wasn't about to offer real-life situations with flesh-and-blood characters. Besides, cartoons were, um, for kids, weren't they?
There was very little attention paid when the show debuted in 1989, and even as it began to gain momentum, there was confusion in Hollywood. If this was going to be a hit, the conventional wisdom went, how could anything in show business ever make sense again?
Yet _The Simpsons_ became more than a hit; it became a genuine, undisputed cultural phenomenon and is considered by a pretty large group to be among the best comedies ever offered on television. And, oh yeah, it became something of a billion-dollar franchise for Fox, launched the network into the stratosphere, and is now in its sixteenth season, the longest for any television comedy in history.
The following year, a powerhouse producer of television drama decided he could take the genre and do something completely unexpected with it. Steven Bochco had produced such fare as _Hill Street Blues_ and had almost single-handedly reinvented the police show, and in 1990, everything he did was considered magic.
Then came _Cop Rock_ , a show in which the police officers would take time out to illustrate their emotions in song. Big-name songwriters like Randy Newman were commissioned to create original tunes for the show. This was going to be an innovation like nothing before.
It didn't last a whole season.
The public was willing to watch unconventional shows and was that very year embracing _The Simpsons_ and turning its characters into cultural icons. The singing cops on _Cop Rock_ are considered a blip on the TV radar.
Was _Cop Rock_ a broken window? From a business standpoint, not really. The network that took a chance on the show knew it had something extremely unconventional on its hands and didn't hide that fact. The executives who gave the show a green light were counting on the innovative producer who had come through so brilliantly before. It just didn't work.
The broken window came in the process. Somewhere in the midst of the development of the program, through reading the scripts, seeing the pilot episode, discussing the story lines, and (I'm confident) screening what was on film for focus groups of television watchers, didn't it ever occur to anyone that this was _too_ innovative, _too_ different? Apparently not, or at least no one was willing to say out loud that in this case, the emperor wasn't wearing any clothes. Or that the emperor couldn't carry a tune.
You can't tell the public what it wants. You can only find out, _from_ the public, what it _doesn't_ want.
The key is to keep an eye, and an ear, open to the consumer at all times. That doesn't just mean you should have customer service representatives available to answer questions and assist with problems at all times. It means you have to constantly seek out consumers, ask your own questions, and _listen to the answers,_ whether they're the ones you want or not. Ego is a broken plate-glass window; it's huge, and it overshadows all else. If you want to hear only nice things about yourself, don't ask anyone except your mother.
Don't wait to hear about broken windows from employees or consumers. If you're hearing from a consumer, you can assume that a thousand more noticed the problem and didn't mention it, and you've lost a hefty percentage of those as your customers for life, or at least quite a long time (consumers don't forgive easily, but they do sometimes forgive). If you're finding out about the problem from an employee, you risk losing some respect, since the employees know you should have spotted it first. Do your own dirty work and walk the floor of your retail outlets. Call the office and see how many rings it takes for someone to pick up the phone. Ask for customer service and present the representative with a problem. Pretend it's not your business, but another one with which you have a genuine problem, and see it through less biased eyes. Are things running as smoothly as they should be?
I didn't think so.
## GIVE THE PEOPLE WHAT THEY WANT
* Never assume that your consumers "won't notice" broken windows. You might as well close the business today.
* Assume that one disgruntled consumer has friends. And they will hear about how your business's broken windows affected that consumer's experience. The ripple effect could be disastrous.
* Image is important, and a broken image is a broken window. Always have your business's image in mind, even when you're not dealing directly with the public.
* Having a superior product doesn't guarantee success. Having superior customer service and fixing broken windows almost always do.
# _Chapter Fourteen_
# The Ultimate Broken Window
If a customer in your bookstore notices that the wallpaper is a little faded, that's a broken window. But it's a broken window that is easily repaired: you can replace the wallpaper with a minimum of difficulty and an affordable expense (in most cases).
What's more important is that the customer in a bookstore probably won't stop coming to the store because the wallpaper is faded. Yes, her image of the company might be a bit diminished, and she might indeed wonder if the books are dusted often enough, but if the titles that customer wants are in stock and the prices are acceptable to her, she will likely overlook the wallpaper unless and until another broken window makes itself known to her.
That will not be true if the broken window occurs in customer service.
I know, you've read it here before, but this point can't possibly be stressed vehemently enough: _Bad customer service is the ultimate broken window_. There is nothing more damaging to your business than the consumer's belief that you don't care about what is bothering him or her.
Think about it: You offer a product or service to the public or a segment of the public. Every member of that group has a right to expect that you will deliver that service or product to their satisfaction. It's not an option; it's a necessity, in order to have anything even resembling a successful business.
In the case of customer service, we have the person who is meant to provide that service or product interacting directly with the public. This is the person who is the face of your business to the consumer. And if that encounter goes badly, especially because the person entrusted with delivering service doesn't do so, it goes beyond worn carpets and loose neckties. It enters into the realm of deal breaker.
It doesn't take a huge amount of imagination to understand that a person who enters a business expecting something—anything—and not getting it will be disappointed. Take that idea a little further, and you'll see that one bad customer service experience—one—can take a customer and turn him or her into a former customer in a heartbeat. No second chances.
Think about this disturbing scenario: You go to a restaurant and order spaghetti; when your order comes, you find an insect crawling on your pasta. Here's my question: Are you going to throw out the bug and eat the spaghetti, or are you going to insist that the entire plate be removed? Or will you leave the restaurant? And even when that is done, how likely are you to go to that restaurant again?
Exactly.
Customer service isn't just the department where complaints are addressed. It's any encounter between an employee of your company (or, if we extend this idea as far as it goes, any representative of your company, including your product) and the people who might ever be interested in buying your product or service. Any encounter. Sales personnel are involved, clearly, in customer service—they serve the customer directly. But those who deliver the product, service it, and install it are also involved in customer service. The receptionist who answers the phone is a customer service employee. The people who drive your trucks, write your press releases, design your packaging, and pay your bills are all customer service employees. _You_ are a customer service employee.
This means you can't afford to have any employee of your organization have a negative encounter with a consumer (and we should make it clear that every business has consumers, not just the ones that sell a product directly to the public). Each person in your employ is an ambassador representing your company in its relations with other nations, and every human being on this planet is another nation, by our definition.
A good ambassador keeps in mind that the art of diplomacy is his first and best tool. Are some customers going to be unreasonable? Of course, some will. Does that mean an employee is justified in treating that person in a curt or irritated manner? Absolutely not.
Every business deals with disgruntled customers, even those that work business-to-business. And in many cases, those customers will not understand the workings of your business and will therefore demand something that you really and truly can't deliver. Many of these will be belligerent or unreasonable and will not approach your employee in a friendly, jovial, accepting manner.
These are the very people to whom your employees must be most accommodating. An ambassador knows that the loudest, nastiest, least reasonable representative of another country is the one who can cause him the most trouble. That belligerent diplomat will go back to his capital, report that although he was making a most understandable demand, it was met with total ambivalence or, worse, outright contempt, and he will recommend that diplomatic relations with the other country be discontinued immediately.
By the same token, a loud and unreasonable customer does not see herself that way. She sincerely believes that her complaint is justified and natural, that her needs, indeed, demand action, and fast action at that. She thinks that your employee, in denying her request, is the one being rigid and unhelpful.
Furthermore, trying to dissuade a customer from complaining is counterproductive. The customer should be made to believe that the company agrees that her complaint is justified and is doing everything it can to correct the problem. Thanking the complainer for pointing out the broken window (real or imagined, in your estimation) is not a bad tactic. Think of the times that you have brought a problem to the attention of a company you have dealt with, as a colleague or a consumer. Which would you have preferred: being told you were wrong in your complaint or being appreciated for your observation and told specifically what would be done to rectify the problem?
Every relationship has a seller and a buyer. Yes, every relationship. And this means that in every situation, someone wants something from the other, and someone is deciding whether or not to grant that request. In business, the lines are usually very well drawn, and we know very clearly who is selling and who is buying. But when problems arise and one of the parties decides a complaint must be made, everything changes.
Keep in mind that a customer who is voicing a complaint is already in a state of mind you'd rather avoid. This person is likely to be irritated and could very well be agitated to the point of behavior that is not characteristic of the relationship as it has been established to this point. Voices might be raised. Unfamiliar words (or at least those that have not been used in the relationship up to this point) might be uttered.
The key is not to respond in kind. _Two_ angry people are going to get a lot less done than one angry person and one who is keeping a cool head. You can make points with all your customers by making sure you remain calm and collected in all dealings, especially when they don't do the same. It demonstrates control and reiterates the point that you are taking the situation seriously and trying everything you can to help resolve it to their satisfaction.
All of your employees need to have this idea drummed into their heads on a regular basis. It doesn't matter how agitated and verbally abusive a customer might get, there is no excuse for returning that attitude in kind, and any employee who does so will be fired on the spot, no matter how justified the abrasive behavior may seem at the time. No exceptions, no second chances, no excuses. Fired. On the spot.
Poor customer service is the ultimate broken window because customer service is the one thing that every business must deliver to its consumers. A breach of that trust, an employee whose actions indicate that he or she is not interested in the customer's concerns, is as blatant and damaging a broken window as you can imagine. And a muddled chain of command is as bad as an obnoxious employee.
I hope you've never had to spend any time in a hospital, but if you have, you probably understand the idea of poor customer service. Members of the support staff (that is, anyone except doctors) in a hospital know their jobs extremely well, I'm sure. They understand the routine, speak the language of medicine, and know the reasons that things work the way they do for patients.
The problem is, the patient is not included in this particular information stream. Patients are generally worried about their health and might not be reacting to situations the way they normally react to stress when living their normal lives. They are, understandably, on edge. But patients also don't understand the routine of hospital work: the time at which certain things are done, the jargon that surrounds virtually any aspect of health care, the reasons that doctors appear when they appear and leave the orders that they leave. Patients don't live in the hospital for a good chunk of their lives, and so they don't "get" the rules the way staff members, who have had years of experience, do.
So when patients are told that things are the way they are and that they, the patients, must adhere to rules they don't understand and have never encountered before, they are likely to be a little less calm and pleasant than they might in another situation.
The problem is, I've yet to find a hospital where the staff understands this. Indeed, they seem to think that patients _should_ know what they, the trained staff, know and that patients are simply being obtuse—or worse, stupid—when they ask questions or challenge a rule that to the staff is perfectly justified. There is less explaining and more complaining in hospitals than anywhere else on the planet, in my experience.
Dr. Robert Kotler, a prominent Beverly Hills plastic surgeon, says his practice is run with the idea that the patient should be included in every aspect of care, and he makes it a top priority to hire support staff (nurses, receptionist, office manager and so on) who will empathize and understand a patient's needs.
"Before they get to see the doctor, patients deal with the office staff on the phone, in the office, and in the examining room," he says. "If they have an experience that is unpleasant with one of those people, they'll have a bad taste in their mouth before I walk into the room, and I might not be able to change that. It won't matter how well I do my job if the people who run the office can't validate the valet parking ticket. The patient will already have a bad impression of my practice."
Customer service relates to every aspect of business, and once it becomes a broken window, it is remarkably hard to repair. Remember the insect in the spaghetti? No matter how apologetic the restaurant owner might be, and how diligently he might ensure that the situation can never recur, how likely do you think it is that the customer will return for another chance?
Now, it's possible that you might gain more customers after the changes are implemented to increase customer satisfaction, but how many have you lost for life before that happens? Find out what your customers' concerns are by mystery shopping yourself and asking the most disgruntled of your customers to mystery shop your business for you (turn an enemy into an ally) and give them some discount or free incentive to do so. Yes, you can do it yourself, and you should, but only in addition to the people who are going to be most critical and who don't have the emotional attachment you have to your business and the people in it.
Poor customer service is the ultimate broken window. Excellent customer service is the ultimate pristine, clear, clean window. Which would you rather have?
## CAN I HELP YOU?
* A product failure or glitch in delivery creates bad will. Bad customer service loses you a customer for life.
* _All_ employees are customer service employees. Everyone in the company does something that affects the consumer's experience with the company. Doing so without respect for the consumer is fatal.
* Each employee is an ambassador for the company, in all dealings with other people. If the employee talks to a friend about the company, the employee is representing the company. Employees must know they are important "faces of the company" and must act accordingly.
* Support staff matters. If you think an employee who doesn't provide the core service of the company isn't representing the company in all dealings with the public, you are asking for trouble.
# _Chapter Fifteen_
# What a Difference a Pianist Makes
What is the opposite of a broken window?
Throughout this book, I've been discussing the idea of avoiding and repairing the little things that can go wrong and make a business seem uncaring, incompetent, or simply bad. And we've also looked at the idea of going "above and beyond the call" of customer service, to do more than is expected and to exceed a reasonable expectation on the part of the customer. We've examined businesses that have done well and repaired their broken windows quickly and efficiently.
But what about something that goes beyond? What about a business that goes out of its way to improve the level of customer service in its industry? What about businesses that do things that aren't just unexpected but unprecedented? If you break new ground and raise the level of discussion into something that's never been considered, let alone accomplished, before, is that fixing a broken window, or is it something... more?
On the surface, Nordstrom is a department store much like other department stores. Its locations, in shopping malls or stand-alones around the country, offer roughly the same merchandise as, say, Macy's, Bloomingdale's, or Lord & Taylor. Its salespeople are instructed to be helpful, and they do offer more services than most, but they are not so efficient as to be considered a new standard for service in the industry. Its prices are usually competitive with its closest rivals, and occasionally better, when on sale, but sometimes higher than others, too. It's not the discount pricing that's bringing shoppers into Nordstrom, trust me.
So, what, then? If you can buy the same article of clothing at another department store, and one store is not a lot farther from your home than the other, and the pricing is competitive but not demonstrably better, what brings a shopper into Nordstrom and not another store that would be just as easy to patronize?
Am I crazy, or is it the pianist?
In the common area of many Nordstrom locations, where virtually every shopper in the area can see and hear, the company has taken some prime floor space where more upscale merchandise might be displayed, and instead installed a grand piano, and a pianist is most often sitting at it, playing beautifully. The music can be heard throughout the area but is not loud or intrusive. It is undeniably live.
It's not easy to measure, or even to describe, the effect that this live music has on the shopping experience. Customers actually smile as they walk through the area. Some stop to listen for a while. They applaud at the end of a song, and the well-dressed musician acknowledges the appreciation, then moves on to the next piece.
There is no tip jar on the piano. That's important. Very important. This is not the store asking for more of your money, and it's not a way for the pianist to bring in extra bucks.
So you see that the absence of a tip jar on the piano at Nordstrom is especially significant. It represents the store's attempt to provide something extra—and to expect nothing more for the effort.
In fact, it could be argued by efficiency experts that the inclusion of the piano in a department store is a negative thing. It takes up a good deal of floor space that, as I noted, might be used to sell more merchandise. It requires not only an expensive musical instrument that must be purchased and maintained but also an experienced and talented musician to play it. It requires in fact a number of talented musicians, since one couldn't possibly be there to play every hour the store is open every day of the week.
And, as I also noted above, it does not bring a single dime into the store, even for the musician's benefit.
Now, that's the very definition of an added benefit. Here's a corporation thinking about its customers in a way that most don't. It asks nothing and provides a signature touch that will enhance the consumer's experience in the store without diminishing at all from the core business—selling clothing and other merchandise.
If that's not the polar opposite of a broken window, I have no idea what is.
This is not the only example of such a thing in business, by a long shot. But the Nordstrom piano might indeed be the most obvious, the most successful, and the most perfect _unbroken_ window in business. It's noticeable—and indeed, became a defining feature of the store; if you say "Nordstrom piano," many people know what you mean—and it speaks volumes about the dedication and thought that goes into Nordstrom's business practices. Does that mean Nordstrom is the best department store chain in the country? Not necessarily. You might feel better about shopping at Macy's or Bloomingdale's (or for that matter, at Target or Wal-Mart), but you can't say you didn't know that Nordstrom has a pianist playing during shopping hours. And you can't say that it doesn't conjure up an image that other department store chains simply don't attempt.
In adding a touch of luxury to an experience that's usually fraught with stressful rushing, tedium, and expense, Nordstrom shows itself to be a company that doesn't just fix its broken windows or do its best to avoid breaking new ones; it makes the statement that Nordstrom is trying to find ways to make the experience of shopping more relaxing and enjoyable, not just more acceptable or less unpleasant. That's more than fixing broken windows; it's a declaration of concern for the people who shop in the store, not those who work there or own the chain, and many customers find that sentiment refreshing.
Consider another company, albeit one not as upscale, that tries to anticipate its consumers' needs and to add touches that will make the experience easier and less stressful. Ikea sells furniture that in most cases the consumer will take home in a box and assemble. It is not in the same neighborhood, in terms of its price structure, as upscale furniture boutiques, where designer items are sold with designer price tags attached.
But Ikea understands its consumer base. Most of the people who come to the chain to buy furniture are just starting out and need affordable but sturdy and useful furniture. The clientele tends to be younger and less affluent than in the fancier stores that sell high-end furniture. Many of the consumers at Ikea are families, especially younger families, trying to find the right furniture for a first home or to furnish children's rooms.
Hence the Ball Room.
In a play area for children, loaded with plastic balls in primary colors, parents can drop off their children while at the Ikea location. The children can play in the ball area (it's like a sandbox without the mess, and the kids can dive in and immerse themselves) or watch a video under supervision by adults. The parents, who sign their children in when entering the store, can look for the items they need without any worry about their children—and without the children expressing boredom with the shopping experience.
This not only makes Ikea a much more family-friendly furniture store, it also makes the experience much more pleasant for those of us who don't want to listen to bored children complaining. It is also a brilliant stroke on the part of Ikea, making the experience more pleasant for everyone (including the kids, who have a wonderful time) and making sure that parents can spend more time shopping for more items—and spending more money—with no impatient children asking "Can we go home now?"
Talk about a win-win situation! The store makes out like a bandit, getting more parents (who are famous for sharing information about kid-friendly stores with other parents) to shop for more items, having children anything but upset about having to go shopping, making a better experience for those who come without children, and costing only a relatively small area of the store, on a floor where there really isn't any merchandise on display, and some employees to supervise the children. When the store is really crowded, the Ball Room might set a time limit, and then parents are paged and asked to pick up their children at a certain time. This ensures that everyone who wants to use the Ball Room during their visit to Ikea will be able to do so and have some uninterrupted shopping time. Oh, and by the way, the Ball Room service is completely free of charge. Try finding a babysitter who charges $0 an hour.
Now, given its merchandise type and price structure, Ikea could probably have gotten away without including the Ball Room in its stores. It would probably have established just as strong a reputation, but it would not be the _same_ reputation. It would have been thought of among its target audience—young adults and young families—as that place where you can find inexpensive furniture that has interesting Swedish names.
Instead, what Ikea managed to build was a reputation as a place that _understands families and is trying to help_. It didn't have to say that's what it was doing. Ikea created that statement without having to tell anyone about it—it simply demonstrated the concern by anticipating a need and filling it. And it let its consumers tell its story among the uninitiated. The strategy worked perfectly, mostly because it was based on reality. Ikea really did provide a service that hadn't been asked for, and because of that, it communicated a message that words couldn't have done as effectively.
That's good branding, but it's also the definition of a nonbroken window. This wasn't a bad situation that was corrected; it was a _good_ situation that was created before anyone realized it was needed. By the time Ikea had established itself in this country and included a Ball Room in each location, it was too late for competing retail chains to catch up without looking like "me-too" followers.
Companies that anticipate, rather than react to, a need will always be a step ahead of the competition; that goes without saying. But when that anticipation is based not only on sales projections and market research but also on a concern for the core consumer of the merchandise or service, the resulting action will be seen as a real service. Consumers will believe, without being told by advertising, that the company cares about their concerns and is doing something to help. That perception is invaluable, but it can't be faked.
It helps if you are a consumer of the type of product or service you sell, or if you have been a consumer of it in the past. If so, you will know what the needs, the concerns, the problems, of your consumer might be, and you might be able to anticipate a need that you can fill before the customer even knows he or she has it.
If you manage to do that, you will have done more than simply fixing a broken window. You will have created a new, clean, sparkling window that no one could see through before, and a glimpse at the lovely view on the other side.
## PIANIST ENVY
* Providing more than the customer expects is good. Providing something the customer wants before she knows she wants it is great.
* Prove to your customer that you know her concerns, care about her welfare, and have a plan to help her with something, and you will create a friend (and a customer) for life. That's more than fixing broken windows; it's creating an impression in the consumer's mind that you know her and care about her.
* Gestures don't have to be profit-driven. Assume that if the consumer believes you have her best interests in mind, she will visit your business more often and spend more money there.
# _Chapter Sixteen_
# Broken Windows, No Building
It's not always easy to spot the broken windows in any business. Carpet starts wearing the minute after people start walking on it; at what point does it become a broken window? Fifteen of your on-floor sales staff are right on top of their jobs and doing everything possible to help their clients; one is falling down on the job, not adhering to the dress code, coming in looking disheveled, and you know he has short-term problems at home that might be contributing to his decline. When does he become a broken window?
Now imagine that there is no store, no visual cue to notice. You're operating out of an office, in a business that doesn't sell a product or service to the public in retail stores. You're working from home or through the Internet or as a catalog mail-order business. All the usual broken windows are still important, except the ones that pertain to issues of physical plant. No, you don't have to worry about the wallpaper on your walls or the shirt you're wearing. But if you think you don't have to concern yourself with broken windows as much as those who operate out of brick-and-mortar facilities, you are mistaken.
You have to worry about broken windows even more.
Consider this: Businesses working out of physical retail stores have many more sensory inputs to distract their customers from minor broken windows. If the carpet is a little worn, well, perhaps the bright lights, wall displays, and music piped in through the stereo system will make that less noticeable. If there's a spill in aisle 12, it's entirely possible the customer will overlook that in favor of the sign announcing a sale on an item in aisle 8.
But if the customer's entire experience with your company is conducted on the phone, by mail, or on the Internet, or if your service requires that someone from your company visit the customer at his or her home or business, there will be no distractions from impressive signage or a song being pumped into the ear of your client. There will be, simply, the service the customer receives from your staff, and we've already seen that customer service can be a broken window when even the slightest thing goes wrong.
Think about the experiences you've had with businesses you can't physically visit yourself. When you call Lands' End, for example, you are almost guaranteed to have a more satisfying experience than you will if you call Wal-Mart and ask for customer service in their clothing department.
Why? Because Lands' End, until very recently, never sold one item of clothing inside a retail outlet. (The company, a wholly owned subsidiary of Sears, has recently begun selling its merchandise in Sears stores, but it has never opened a retail store in its own name.) It doesn't have rack after rack of merchandise for you to browse, to feel, to try on before you make a purchase. All it has is a catalog, a Web site, and an army of customer service representatives who will be the only people ever to deal with the company's customers one-on-one. They'd better be good at what they're doing, and in this case, they almost always are. Lands' End representatives on the phone are trained to be polite, accommodating, and helpful, and they do so in such a natural and unforced manner that you'd never know they were carefully trained.
You see, it's not enough to _pretend_ to be pleasant. Even in a face-to-face encounter with a sales or service staff member, a customer can tell the difference between a real smile and a trained, forced, phony one. The staff (excuse me, cast members) at Disney World are hired for their ability to perform their jobs without showing the seams. The smiles really aren't saccharine there; they are genuine and believable because the hiring practices from the top down make sure the right people are in the right jobs.
On the phone, you can't see the smile, but you can certainly hear the attitude. And when the customer service personnel is, as is too often the case these days, outsourced to a country where English is not the first language spoken, there can be problems with American customers.
#### _**10 Ways to Avoid Face-to-Phone (or -Screen) Broken Windows**_
1. If nothing else, remember this: **Hire only those people whom you can trust to be accommodating, pleasant, and helpful to deal directly with your customers.** They aren't just your first line of defense; they're the _only_ representatives you have with the people who pay your bills. Nothing is more important.
2. **Train your customer service employees diligently.** Do not rely on their peers to "show them the ropes," and don't post your priorities in a lovely framed parchment declaration. Talk to employees. Explain why this is the top priority of the company and why they are the frontline representatives who must do better than expected to do as well as they should.
3. **Don't compromise on customer relations.** If a voice is the only thing your customers are hearing, make sure that voice speaks the language most of your customers speak, fluently and understandably. If you have a multilingual clientele, have representatives who speak the languages you need, fluently. And then add a message system prompt that will get the right customers to the right representatives. Heavy accents are not acceptable on the phone.
4. **Arm your troops well.** Make sure they have the information they need at their disposal quickly and easily. Don't make them ask a supervisor every time a customer has a question. Keep them up-to-date on company policies and product changes. Make sure they have the answers to the questions.
5. **Allow for creative solutions.** Let your customer service representatives help your customers in ways that might not seem standard. Let them find solutions for each problem and keep each customer happy, and reward them for that. Don't tell your employees that they can't think outside the box, or your customers will believe your business to be rigid and unreasonable when problems arise—which is the last thing you want.
6. **Cut down on hold time.** When your business is based on the phone, it is deadly to make customers wait interminably for contact with an actual human. If it's possible for the customer to solve his or her problem via prompts, that's fine, but if he or she needs a human being to discuss the situation, make sure that person is available in only a few minutes, tops. If that means hiring more representatives, it means your business is growing, so do it.
7. **If your business is on the Internet, make sure the links work and that the customer will not get all the way through the purchasing process only to run into a glitch on the last screen** —nothing is more frustrating. Have online personnel available to help on demand.
8. **Ordering by phone or by mail must be simple and easy.** Complicated forms are not over the head of the customer's intelligence, but they might very well be beyond his or her level of patience. Remember that customers are doing you a favor, not the other way around, by purchasing your product. If you make it hard for them, they might decide against it. A complex form is a broken window.
9. **Mystery shop your people.** Call, log on, send in a form, whatever it is the customer would do—you do it. See what the problems are, how long it takes to complete the process, and how high your level of frustration rises. Those things that aren't working, fix. Those that are demonstrably better than the competition's, reward.
10. **Make sure your employees know that customer service is the most important priority in the business.** Show them by getting your hands dirty and doing some of it yourself every week or every month. Deal with the customers, come up with innovative solutions, find out how difficult it is to retain your equilibrium while someone is screaming through a headpiece that a new toy won't work. Then come up with ways to help the customers and pass them along to the employees.
It's helpful sometimes to consider the origins of a broken window, tracing it back to the source in order to correct it. In most cases, particularly when a business can't rely on in-store personnel, problems begin with unreasonable rules for customer service or with people hired to do that job who aren't qualified by temperament to perform it. In such cases, you have to consider the origin of the rule or the hiring practices that allowed the wrong person on the bus to begin with.
When a rule is made to deal with a customer problem (we don't offer refunds after ninety days, for example) and that rule conflicts with a customer who seems to have a legitimate problem (the product has malfunctioned on the ninety-first day), you have to reconsider the rule. If a set warranty period is not adhered to, the company will be responsible for the product for a lifetime, and some things are not meant to last forever (you'll notice that most things with a "lifetime warranty" are products like a hammer, which would have to go through a serious calamity to malfunction). However, if that rule is strictly followed with no exceptions, there will invariably be customers who will be left frustrated, with a negative view of the company. Is it worth gaining the cost of a replacement product or a repair to lose the customer for life?
Perhaps an accommodation or a compromise can be reached. All right, so the customer whose product stopped working the day after the warranty period ended might not be entitled to a new product. But perhaps he or she can buy another one at a very large discount, or perhaps the company will pay for the shipping if the customer wants to have it repaired. Giving customer service reps leeway to make their own solutions, so long as they don't abuse the privilege and start giving away the company's inventory, is good for the employees and good for your customers, which makes it good for your business.
In the case of a customer service employee who is not suited to such work, the solution is to remove that person from that job and perhaps give him or her a position that doesn't require one-on-one contact with customers. But the root of the problem is your hiring practices. If you're not hiring people with the proper mind-set for a customer service job, is it the employee's fault when he or she can't do that job properly?
Don't just look at a résumé; look at the _person_. If he has the right personality to help customers, he's right for the job, and it doesn't matter if he graduated high school or went to Yale. If he _doesn't_ have the right personality to help customers, he's wrong for the job, and it doesn't matter if he graduated high school or went to Yale.
Consider the _root_ of the problem, and you can kill the weed. Consider the _solution_ to the problem, and you'll be doing a lot of weeding.
## OUTSIDE THE BOX
* Businesses that don't have retail locations have to rely on customer service more than others. That means the broken windows are more subtle and much more damaging.
* Let employees think outside the box; let them come up with solutions that satisfy the customer while keeping the company's interest in mind. Applaud efforts to come up with creative solutions; don't insist on such a strict interpretation of the rules that the customer never comes back.
* Broken windows begin at the root. Hire the right people and set the right rules, and there won't be as many broken windows to fix. If you deal only with the immediate situations, today's problem might be solved, but tomorrow's is waiting to blossom.
* Be an example for your employees. Don't expect them to come up with creative solutions and strive to placate customers if you don't do so yourself. They're going to watch you for an example, even when you're not trying to set one. So always try to set one.
* Mystery shop, mystery shop, mystery shop. You can't know what your online, phone-based, or mail-in problems are if you haven't gone through the experience yourself.
# _Chapter Seventeen_
# What's in It for... You?
When Kelling and Wilson unveiled the broken windows theory in 1982, they knew it would stir up discussion, argument, and controversy in the world of law enforcement, and I expect this book will have a similar effect among people who own businesses or are interested in business generally. It is not "business as usual," and it is not "the way things have always been done." It is meant to unsettle some people, to shake up the status quo, and to motivate business owners and employees into a new way of thinking about the way they go about their work and their lives.
After all, as you've read, the broken windows theory for business is based on the premise that something is wrong—very wrong—with the way most businesses are run in this and other countries. It presumes that most small mistakes, most oversights and neglected details, are not being noticed or, worse, corrected, and that in turn presumes that most business owners are not as invested, intellectually and emotionally, in the businesses they run.
Throwing money at a business and expecting it to perform well is not enough. If the owner and the people who work for him or her are not committed, to the point of exhaustion and obsession, to the work they do, the business will not be as successful as it could be. In most cases, in fact, it will not be successful at all.
It's estimated (and this is apocryphal) that over 70 percent of the restaurants that open in Manhattan will fail within two years. Is it because the owners didn't have a good idea? Because they served bad food? Because people in New York City aren't hungry? It happens because the details—the broken windows—are not being anticipated or repaired and, in many cases, because the restaurant owners don't know what they should be looking for. People simply don't believe that details amount to much. I think in the course of this book, we've seen that they do.
I've told you about the tiny things that have made huge differences, both good and bad. I've mentioned names of companies—some of which probably wish I hadn't—and pointed to examples you'd probably heard about before but hadn't considered in just this way. Now you know that the details make an enormous difference, and you know just how all-encompassing a pursuit it is to run a business successfully, keeping an eye on all the windows for the first signs of cracks.
Throughout this book, you have read about companies that ignored their broken windows or never saw them in the first place. You've also read about companies that not only repaired their broken windows but anticipated them and went above and beyond the call of duty to stay ahead of the curve and give customers more than what they might logically have been expecting.
But what do all those stories mean to _you_? If you're not the owner of a huge fast food chain, a major clothing retailer, or a movie star, what could it possibly matter to you if a company sinks or swims based on its dedication to detail? Why should you care if the coffee is too hot, the carpet is worn, or the counter staff doesn't smile enough (or at all)? Perhaps you own one small dry cleaning outlet or a company that provides information technology services to other businesses. Does it matter to you whether the people serving hamburgers know how to speak English?
It should.
Maybe the examples you've read about in these pages aren't directly related on a physical level to your own. Maybe you don't have counter staff or sell a physical product. But the lessons learned have implications that go far beyond those concrete examples. They are meant to open your mind to the concept of broken windows for business and to build your own bridges to the issues that will make or break the business you've chosen to be in.
The parable about Kmart, for example, was to illustrate the concept of Broken Windows Hubris, one of the deadliest forms of broken windows, in which companies get the idea that they are larger and more powerful than the people who, by way of patronizing them, keep the company in business. Even a small company suffers from this disorder when it decides that it has become popular, that its customers are loyal and therefore complacent, and that the business can run on automatic pilot for a while. That's when the broken windows are guaranteed to shatter, loudly.
It's important to find the concept behind the story and to extrapolate it to your own situation. That's why the summaries at the end of each chapter have been included: to help you recap what you've read and perhaps to decide on your own how you might apply the concept to your own business.
You know your business much better than I can. You know the particulars of the trade you're in and how they relate to the people you consider your clientele. I can't hope to make that claim for every industry in which a person who reads this book might be employed. But I _can_ tell you about the broken windows theory for business, and you can make the leap from there. See if these concepts don't strike a chord with you, as some of them are universal and can be applied to every business:
• **Obsession and compulsion are vital to a manager's mastery of broken windows.** There is no excuse for letting something go when you know it could be improved, and there is no excuse for not caring enough.
• **Employees are vital to every business, whether they have direct contact with the general public or not.** But when employees are given contradictory signals from management (when, for example, a directive to punch in on time every day is posted over the time clock, and then the department manager comes and goes as he or she pleases), the employees will understandably be confused and irritated, and will become broken windows.
• **The worst broken windows may be people.** Employees who have the wrong attitude, who don't care about the company (and, by extension, the customer), will become a virus that will spread throughout the ranks. Eventually, if these employees are not dealt with noticeably and either corrected or removed, the majority of the company's employees will become infected with the virus and could pass it on to the rest. Swift action is absolutely imperative.
• **Appearance** _**does**_ **matter.** The physical look of your business, from the walls to the carpet to the windows (broken, dirty, or otherwise) to the employees, is going to make an impact on the image your customers see. This is just as true when your clientele doesn't come to the premises if you present the image of the company through advertising, in company vehicles, or through the representatives you send into the field. Uniforms are an option, since they present a, well, _uniform_ image, but in any event, proper appearance is very important. Maintenance on company vehicles and especially on the company premises is extremely noticeable. Especially when it isn't done.
• **When a customer deals with your business, he or she expects something.** Your business has three options at that point: It can meet the expectation, it can exceed the expectation, or it can fail to meet the expectation. Guess which one is best and which is not acceptable. It can be beneficial sometimes to promise _less_ than you know you will deliver, in order to best exceed expectations and make a positive reputation for your business.
• It sounds New Agey and silly to discuss a customer's "experience" when dealing with, say, a plumbing company or a business-to-business service company, but when all is said and done, **what the customer experiences in dealing with your business will determine** **whether you will see that customer again.** Yes, some of that experience will depend on the quality of the product and the price the customer has to pay, but the variables—the broken or unbroken windows—will make the majority of the difference in most cases. Make the customer's experience a pleasant, even rewarding, one, and you have a much better chance of making a friend for life.
• It can't be stressed enough: **The only way to know what a customer experiences in dealing with your business is to act like a customer yourself.** Walk the floor of the business, call the office and see what that's like, register a complaint (even if you don't have one) and see how your staff handles the situation. Only when you have lived as a customer can you best anticipate the needs of the customer, and that is half the battle in fixing the broken windows. If you're too recognizable to the staff, get someone you know and trust implicitly to do so. Find the customers who register the most complaints and give them an incentive to mystery shop the business and report back to you.
• **In cyberspace, everyone can hear you scream.** Internet broken windows travel faster and spread farther than any other kind. Sometimes they're not controllable, but most of the time they are. Keep a sharp eye on your Web site and make sure six times over that your online customer support representatives and the mechanisms they operate are always working properly.
• **Give the customer** _**more**_ **than you should, and you will make an impression.** Fix windows that aren't broken by using your experience to think like your customer, and determine what would impress you. Then provide that.
These are just a few of the ways you can apply the broken windows theory for business to your own industry. There are literally millions of ways to do it, but you don't need a list. What you need is what I hope this book has provided for you: a new outlook on business that includes, and in fact stresses, a devotion to detail.
Broken windows can come from any aspect of business, and they can be dealt with if you know what to look for. What's important to take away from the experience of reading this book is the desire to find those cracks: the obsessive, compulsive, almost violent need to find the flaws before they become damage, and to eradicate them as swiftly and completely as possible. It's a never-ending job, and one that requires a ruthless dedication and an insatiable hunger for excellence. No: _Perfection_.
As I noted before, every relationship, in every aspect of life, has a seller and a buyer. In business, the roles are usually very clear. As a seller, you must consider what the buyer wants, what he or she expects, and what will please and displease him or her. You need to provide the service along with the product that will make an impression, and a favorable one, to attach to your business as a whole. Keeping your windows in one piece is a very strong step in that direction. It's all stagecraft, and it's about not letting them see you sweat. It's about covering up the cracks and making them disappear, and about being on a constant, unending search for potential cracks so you can make them disappear before they appear.
We started with the question: When is a dirty bathroom a broken window? I hope that question has been answered in these pages, more than once. And I hope it has launched ten thousand other questions you've already begun to ask yourself about your own business, about what you can do to improve it, to make it _seem_ better, and to make it really and truly better. Because once you've embraced the concept of broken windows, you can't ever go back. It's a curse and a blessing. You'll be left with the power to see the breaks and the determination to fix every last one of them.
It's an awesome concept, and one that you should now just be starting to use on your own. If you do, I promise you, your business will be a more efficient, more impressive, more effective one in a relatively short time. But this is not the kind of idea you can implement a little bit. Fixing and maintaining your broken windows will be an all-encompassing activity, or it will be none at all. You'll find yourself thinking about it when you're lying in bed at night and when you wake up in the morning. Your mind will wander to possible breaks in your business's windows when you're in the shower or having dinner. You'll notice things others will miss, and even when you point them out, I warn you, they will deny such things exist or insist they are unimportant and that you are being ridiculous, obsessive, and paying too much attention to trivial details.
But you and I both know that there is no such thing as too much attention to detail.
At the end of this chapter, you'll find the Broken Windows for Business Pledge. It's a serious statement outlining the tenets of the broken windows for business theory. It's actually a restatement of everything you've learned in this book, and it should be taken very seriously. I hope you'll read it, and sign it when you're finished.
If you live up to the promises in the pledge and make them second nature, you will discover your business—and maybe your life—running more smoothly and efficiently than ever before.
Good luck with your new knowledge and your new power. I believe that if you use it, you will have positive results. But no matter what, I can definitely guarantee one thing: You will never look at a broken window—or an unbroken one—the same way again.
# The Broken Windows for Business Pledge
I, ______________________, having read the concepts of the broken windows for business theory, do hereby pledge to do the following:
* I will pay attention to every detail of my business, especially those that seem insignificant.
* I will correct any broken windows I find in my business, and I will do so immediately, with no hesitation.
* I will screen, hire, train, and supervise my employees to notice and correct broken windows in the least amount of time possible.
* I will treat each customer like the only customer my business has.
* I will be on constant vigil for signs of Broken Windows Hubris and will be sure never to assume my business is invulnerable.
* I will mystery shop my own business to discover broken windows I hadn't noticed before.
* I will make sure every customer who encounters my business is met with courtesy, efficiency, and a smile.
* I will exceed my customers' expectations.
* I will be sure always to make a positive first impression and will assume that every impression is a first impression.
* I will make sure that my online and telephone customer service representatives do everything possible to solve a customer's problem perfectly the first time.
* I will be obsessive and compulsive when it comes to my business.
Signed the __________ day of ____________, in the year ________, by ______________________.
Mr. Levine is a frequent speaker at corporations and universities.
He can be contacted at mlevine@LCOonline.com.
1. James Q. Wilson and George L. Kelling, "Broken Windows: The Police and Neighborhood Safety," _Atlantic Monthly,_ March 1982.
2. Rudolph W. Giuliani, "Remarks to the Conference of Mayors on Restoring Accountability in City Government," May 9, 2000, as delivered. Italics mine.
1. <http://teamapproach.com/kmart.asp>.
2. www.nctimes.com/news/2002/20020123/85214.html.
1. Michael Walker, "The Thrill Is Gone," _Los Angeles Times Magazine,_ December 14, 2003.
2. _Ibid._
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"redpajama_set_name": "RedPajamaBook"
}
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Sullivan High School is a public four-year high school located in the Rogers Park neighborhood on the north side of Chicago, Illinois, United States. Sullivan is a part of the Chicago Public Schools district. Opened in 1926, the school is named for businessman and Illinois politician Roger Charles Sullivan.
History
Sullivan opened in 1926 as a junior high school under the Chicago Board of Education's plan creation of junior high schools in Chicago. The school begin serving as a traditional high school when junior high schools in the city were phased out in 1933.
In the 2010s, Sullivan High School has served a large number of refugee students. As of 2017, 45% of students were foreign-born and came from 38 different countries. That same year, the school was designated a "newcomer center" by Chicago Public Schools for its programming for refugee and immigrant students.
Athletics
Sullivan competes in the Chicago Public League (CPL) and is a member of the Illinois High School Association (IHSA). The schools sport teams are nicknamed the Tigers. Sullivan boys' soccer team were regional champions and sectional finalists in 2016 and 2017. Sullivan girls' basketball team were regional champions in 2008–09. The boys' track and field became public league champions in 1938–39. In 1977–78, the school's football team won the Public League championship.
Notable alumni
Ira Berkow – New York Times sportswriter and author<tref name="Sun Times SotW"></ref>
Elizabeth Ann Blaesing – illegitimate daughter of President Warren G. Harding
Sidney Blumenthal – journalist and aide to Bill Clinton
Hal Bruno – Newsweek correspondent and political director of ABC News; served as moderator for 1992's vice-presidential debate
Shecky Greene – comedian and actor
Robert Spencer Long – president of Shimer College
Dick Marx – jazz pianist, arranger, and composer, best known for writing commercial jingles for Kellogg's Raisin Bran and Ken-L Ration dog food; scored the film A League of Their Own; his son is musician Richard Marx
Clayton Moore – actor, best known for his portrayal of The Lone Ranger
Danny Newman – publicist and author who worked for Jimmy Durante, Milton Berle, the New York Philharmonic, and the Lyric Opera of Chicago; pioneered the idea of subscription sales
Art Paul – former Playboy Art Director and designer of its rabbit-head logo
Charles Percy – U.S. Senator
Dewey Robinson – Major League Baseball pitcher (1979–81), playing his entire career for the Chicago White Sox; currently a minor league coach
Jan Schakowsky – United States Representative for Illinois's 9th congressional district (1999–present)
Gordon Segal – CEO and co-founder of Crate & Barrel
Haskell Wexler – two–time Oscar-winning cinematographer (Who's Afraid of Virginia Woolf?, Bound for Glory)
Bobby Dixon - Euroleague basketball player
Richard Alan Greenberg - Oscar-nominated special effects designer
ruth weiss - American poet and filmmaker
References
External links
Sullivan High School website
Educational institutions established in 1923
Public high schools in Chicago
1923 establishments in Illinois
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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My Years With Elvis
Charles Stone
Charles Stone, a veteran concert tour manager and producer started his career in the mid '60s working with all the major entertainers of the time. Charles joined forces with Elvis and the Colonel int he '70s and toured around America with Elvis and the Colonel, Taking Care of Business until Elvis' death in 1977.
"Charles has worked with many amazing talents throughout his career, and has years of memories and personal stories to share, nothing compares to his time spent on tour and in Vegas with Elvis, the Colonel, and all the enthusiastic, supportive fans. There is nothing he enjoys more than having the opportunity to relive his Elvis years as he shares his memories and experiences during frequent speaking engagements around the world." -A Texas Tribute to Elvis
Charles has written several books detailing sharing his memories with Elvis fans worldwide. His books take fans on a behind the scenes journey into the Elvis world. Charles Stone opens his original tour books, giving fans access to reprinted documents, commentary and photos. Visit the store for books and collector's items.
MOVING ON BOOK
LIFE IN THE ELVIS WORLD
SIGNED PHOTOS
MY YEARS WITH ELVIS AND THE COLONEL
Copyright © 2023 My Years With Elvis All rights reserved. Theme: Flash by ThemeGrill. Powered by WordPress
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: How can I ignore bodies while recording in wiremock I would like to record requests in such a way that the mappings end up with no bodyPatterns tag. In other words I want recorded mappings to be matched only based on path and regardless of body. Is it possible?
A: Although not exactly the removal of the tag, the contents of it can be influenced by setting the extractBodyCriteria to 1 byte. In the documentation on Record and Playback there is also a java example:
"extractBodyCriteria" : {
"textSizeThreshold" : "1",
"binarySizeThreshold" : "1"
},
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,168
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Q: Popup menu does not appear on Android using "react-native-popup-menu" I am making a mobile app using react-native-popup-menu. (React Native)
The popup unit works fine on iOS. But it will not shop up on Android when I test it on Android simulator.
I've seen a post that suggests a fix that involves MenuContext> element. but it looks like that element has been deprecated by the plug-in developers since.
Popup menu does not overlay other components in Android
I'm looking for a up-to-date solution that works for React Native Android environment.
My app looks like this right now:
Import all the tools.
import { MenuProvider } from 'react-native-popup-menu';
import { Menu, MenuOptions, MenuOption, MenuTrigger } from 'react-native-popup-menu';
The main app looks like this. Everything is wrapped within MenuProvider.
export class App1 extends Component {
render() {
return (
<MenuProvider>
<View style={styles.container}>
<MoreStuff navigation={this.props.navigation} />
<TopMenu1 navigation={this.props.navigation} />
<View1Map />
</View>
</MenuProvider>
);
}
}
This is where I built the pop-up menu. I am following example from the official tutorial.
https://github.com/instea/react-native-popup-menu
In the order of appearance, I have View> element, followed by Menu>, MenuTrigger>, MenuOptions> and MenuOption>.
export class MoreStuff extends Component {
render(){
return (
<View>
<Menu>
<MenuTrigger>
<Image
source={require('./assets/Burger.png')}
>
</Image>
</MenuTrigger>
<MenuOptions>
<MenuOption
onSelect={() => {
//DEFINT ACTION HERE
}} text='Item 1' />
<MenuOption onSelect={() => {
//DEFINE ACTION HERE
}} text='Item 2' />
<MenuOption text='Close'
onSelect={() => this.close}/>
</MenuOptions>
</Menu>
</View>
);
}
}
Expected: When you click on the MenuTrigger element, the popup menu will come up.
Actual result: When you click on the MenuTrigger element, nothing happens.
A: You can resole the issue by making sure that MenuProvider is the first component that is rendered in the tree.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,564
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\section{Introduction}
A century after the discovery of the Blazhko effect in RR~Lyrae stars \citep{blazhko}, it can still not be explained theoretically in a satisfactory way \citep{rrlyr}.
The Blazhko effect manifests itself in the frequency spectrum of the light variations
as one or more side frequencies close to the main pulsation frequency.
The beat period resulting from the interaction between the main frequency and the side frequency is called the Blazhko period.
The question focuses on how many side frequencies there are.
Resonance models involving non-radial pulsations with degree $\ell=1$ lead to an equidistant triplet structure that is most commonly observed:
two additional frequencies, one on each side of the main frequency and at the same distance.
In some cases only doublets are observed, presumably because the amplitude of the third frequency is too low to be detected.
Oblique magnetic models with $\ell=2$ lead to an equidistant quintuplet structure.
Recently a frequency quintuplet was found for the first time in RV~UMa \citep{rvuma}.
Although admittedly very rare, some RR~Lyrae stars show two Blazhko periods.
These stars pose a particular challenge for the theories.
LS~Her is one of the stars known to have two Blazhko periods.
It was discovered to be variable by \citet{hoffmeister} and first classified as a W~UMa type
eclipsing binary. Observations on six consecutive nights by \citet{binnendijk} revealed its nature
as an RR~Lyrae star pulsating in the first overtone mode (an RRc type object).
With a period of 0.2316 days \citep{binnendijk} it has one of the shortest periods among the RRc stars.
Binnendijk also noted variations in the light curve from night to night,
but did not find a beat period because of the short timespan of his observations.
From the public survey data of the Northern Sky Variability Survey \citep[NSVS; ][]{nsvs},
\citet{rrnsvs} found LS~Her to be a Blazhko star with a Blazhko period of 13 days.
\citet{rrasas} found two pairs of Blazhko triplets resulting in periods of 11.5
and 12.8 days from data of the All Sky Automated Survey \citep[ASAS-3; ][]{asas}.
Other Galactic examples with multiple Blazhko periods are XZ~Cyg with periods of 57.5 and 41.6 days \citep{xzcyg},
UZ~UMa with periods of 26.7 and 143 days \citep{uzuma}
and SU~Col with periods of 65.8 and 89.3 days \citep{rrasas}.
Unlike LS~Her, all these stars are fundamental mode pulsators (RRab stars).
Until recently, only a few Galactic field Blazhko RRc stars were known \citep{smith, kolenberg}.
Because of its short period it is possible to observe a full pulsation cycle of LS~Her during a night.
Combined with its double short Blazhko cycles, this made LS~Her a very interesting object for detailed study.
The spectral type of LS~Her has been given as A2 \citep{goetz}, A5 \citep{gcvs}
and F0 \citep{pmcco}.
\section{Observations}
LS~Her was observed on 63 nights during six months in 2007 from two private observatories.
On three nights the star was observed at both observatories.
More than 240 hours of CCD photometry were secured in $V$ and $I_C$, and 65 hours on 22 nights in $R_C$.
The complete observation log, together with information on the instruments used, is given in Table~\ref{log}.
\begin{table*}
\begin{center}
\caption{Observation log.}
\label{log}
\begin{tabular}{cllcccrccc}
\hline
Observer & Telescope & CCD camera & Timespan & Nbr of & Nbr of & \multicolumn{3}{c}{Number of data points} \\
initials & & & {\small (JD-2450000)} & nights & hours & $V$ & $R_C$ & $I_C$ \\
\hline
SK & 30-cm LX200 & SBIG ST-7XMEI & 4199-4362 & 44 & 181.1 & 3613 & - & 3619 \\
EB & 20-cm C8 & SBIG ST-7XMEI & 4206-4366 & 22 & 65.5 & 899 & 901 & 892 \\
Total & & & 4199-4366 & 63 & 243.2 & 4512 & 901 & 4511 \\
\hline
\end{tabular}
\end{center}
\end{table*}
\begin{figure*}
\centering
\includegraphics[width=17cm]{LSHerfig1.eps}
\caption{$V$ (top curve), $R_C$ (middle) and $I_C$ (bottom curve) data of LS~Her on a number of nights.
The zero points of the $R_C$ and $I_C$ magnitude scales have been arbitrarily chosen.
Labels on the horizontal axis are $HJD-2450000$.
The model plots from Table~\ref{freq} are shown as well.}
\label{plot}
\end{figure*}
Differential photometry was performed using GSC~1507-598 or GSC~1507-660 as comparison star
and GSC~1507-776 or GSC~1507-327 as check star.
Nightly standard deviations on the difference between the check star and comparison star were usually around 0.01 magnitude or better.
All magnitudes were reduced to a common scale assuming the difference in magnitude between GSC~1507-660 and GSC~1507-598
to be $\Delta V = -0.446$, $\Delta R_C = -0.254$ and $\Delta I_C = -0.060$ (determined from our data on 13 nights).
GSC~1507-598 was then further assumed to have $V = 12.16$ from ASAS-3.
No instrumental corrections were applied to the data.
Some nightly plots are shown in Fig.~\ref{plot}, together with the model fit derived in the next section.
\section{Frequency analysis}
Period04 \citep{period04} was used for the frequency analysis.
Table~\ref{freqsurveys} gives the frequencies found in the NSVS and ASAS-3 survey data.
It lists the value of the frequency, its semi-amplitude in mmag and the signal to noise ratio ($S/N$).
Uncertainties on the given values are the standard deviations from the results obtained from Monte Carlo simulations.
\begin{table*}
\begin{center}
\caption{Frequencies for LS~Her found in NSVS and ASAS-3 data.}
\label{freqsurveys}
\begin{tabular}{clrrlrr}
\hline
& \multicolumn{3}{c}{NSVS} & \multicolumn{3}{c}{ASAS-3} \\
Ident. & Frequency & \multicolumn{1}{c}{$A_{NSVS}$} & $$S/N$$ & Frequency & \multicolumn{1}{c}{$A_V$} & $$S/N$$ \\
& \multicolumn{1}{c}{(c/d)} & \multicolumn{1}{c}{(mmag)} & & \multicolumn{1}{c}{(c/d)} & \multicolumn{1}{c}{(mmag)} \\
\hline
$f_0$ & 4.33262(4) & 150(4) & 31.5 & 4.33258(1) & 181(5) & 33.5 \\
$f_0 + f_1$ & 4.41097(20) & 45(4) & 9.3 & 4.41088(8) & 58(5) & 10.8 \\
$f_0 - f_1$ & 4.25426(20) & 27(4) & 5.6 & 4.25429(8) & 45(5) & 8.4 \\
$f_0 + f_2$ & 4.42009(20) & 20(4) & 4.3 & 4.42090(30) & 22(7) & 4.2 \\
$f_0 - f_2$ & 4.24514(20) & 33(4) & 6.8 & \multicolumn{1}{c}{-} & \multicolumn{1}{c}{-} & \\
\hline
\end{tabular}
\end{center}
\end{table*}
The five frequencies listed in Table~\ref{freqsurveys} constitute in fact two triplets around the main frequency which is common to both triplets.
The two triplets were also found in our own data sets.
The Blazhko (or beat) period resulting from the first triplet is $12.75\pm0.02$ days and $11.42\pm0.04$ days from the second triplet.
Surprisingly however our data also revealed a third triplet, again with the side frequencies close to those of the first triplet
but on the other side of those of the second triplet and at about the same distance.
This third triplet corresponds to a Blazhko period of $14.45\pm0.07$ days.
A schematic presentation of these frequencies is given in Fig.~\ref{freqs}.
A logarithmic scale is used for the $V$ amplitudes.
\begin{figure}
\centering
\includegraphics[width=8.5cm]{LSHerfig2.eps}
\caption{Schematic diagram of the observed frequencies around the main pulsation frequency.}
\label{freqs}
\end{figure}
Due to the proximity of all the side frequencies and the limitations of the procedure to find the next significant frequency in the data,
it was impossible to find a good frequency fit while imposing equidistance conditions from the start
(see \citet{equidistance} for a discussion on the equidistance of the triplets).
Instead, a satisfactory solution could only be found by leaving all frequencies independent of each other.
In the end, when seven independent frequencies were found, it was clear that
the distances to the main pulsation frequency of the frequencies on both sides of the main frequency in each triplet
were equal within the uncertainties.
For example the distance to the main frequency for the most significant side peak to the right of the main frequency was found to be
$f_{1+}=0.07840\pm0.00009$ cycles per day (c/d), while for the peak on the left it was found to be $f_{1-}=0.07847\pm0.00006$ c/d.
Similarly the distance between the side frequencies of the first and second triplet was found to be $f_{c+}=0.0092\pm0.0007$ c/d,
and the distance for those of the first and third triplet was $f_{c-}=0.0093\pm0.0010$ c/d.
The final frequency solution was then obtained using the equidistance criterion and is listed in Table~\ref{freq}.
Only frequencies with $S/N > 4$ were retained \citep{breger}.
In addition to amplitudes and signal to noise ratio in $V$, $R_C$ and $I_C$,
the phase difference of the frequencies between $V$ and $I_C$ are given.
The latter may aid in mode identification \citep[see e.g. ][ and references therein]{dasz}.
The small positive phase difference for the radial mode $f_0$ is consistent with that found for other RR~Lyrae variables \citep[e.g. RV~UMa, ][]{rvuma}.
Only one of the six side frequencies has a phase difference different from zero at the 1-$\sigma$ level,
but it is not significant at the 2-$\sigma$ level.
\begin{table*}
\begin{center}
\caption{Frequencies for LS~Her detected in our data sets. }
\label{freq}
\begin{tabular}{cr@{}lr@{}lrr@{}lrr@{}lrr}
\hline
\multicolumn{3}{c}{Frequency} & \multicolumn{2}{c}{$A_V$} & \multicolumn{1}{c}{$S/N$}
& \multicolumn{2}{c}{$A_R$} & \multicolumn{1}{c}{$S/N$}
& \multicolumn{2}{c}{$A_I$} & \multicolumn{1}{c}{$S/N$}
& \multicolumn{1}{r}{$\Phi_V - \Phi_I$} \\
Identification & \multicolumn{2}{c}{(c/d)}
& \multicolumn{2}{c}{(mmag)} & \multicolumn{1}{c}{$V$}
& \multicolumn{2}{c}{(mmag)} & \multicolumn{1}{c}{$R_C$}
& \multicolumn{2}{c}{(mmag)} & \multicolumn{1}{c}{$I_C$}
& \multicolumn{1}{r}{(degrees)} \\
\hline
$f_0$ & 4.33261 & (2) & 176.3 & (4) & 147.0 & 144.7 & (10) & 73.2 & 108.2 & (4) & 90.1 & $2.6\pm0.3$ \\
$f_0+f_1$ & 4.41101 & (15) & 55.4 & (7) & 46.6 & 48.0 & (16) & 24.6 & 35.3 & (4) & 29.3 & $-0.6\pm1.1$ \\
$f_0-f_1$ & 4.25421 & & 44.4 & (5) & 36.4 & 26.3 & (18) & 13.1 & 28.3 & (4) & 23.2 & $0.9\pm1.1$ \\
$f_0+f_1+f_c$ & 4.42021 & (34) & 32.5 & (5) & 27.4 & 22.5 & (17) & 11.5 & 20.5 & (4) & 17.0 & $0.4\pm1.6$ \\
$f_0-f_1-f_c$ & 4.24501 & & 26.6 & (5) & 21.8 & 23.0 & (17) & 11.5 & 16.6 & (4) & 13.6 & $1.0\pm2.1$ \\
$f_0+f_1-f_c$ & 4.40181 & & 10.9 & (6) & 9.1 & & & & 7.5 & (4) & 6.2 & $2.1\pm5.0$ \\
$f_0-f_1+f_c$ & 4.26341 & & 16.8 & (10) & 13.8 & 17.2 & (14) & 8.6 & 10.4 & (4) & 8.6 & $7.5\pm3.8$ \\
$2f_0$ & 8.66522 & & 16.5 & (4) & 18.0 & 15.9 & (11) & 11.9 & 11.8 & (5) & 14.1 & $4.6\pm2.5$ \\
$2f_0+f_1$ & 8.74362 & & 13.5 & (4) & 14.6 & 11.4 & (11) & 8.6 & 9.6 & (4) & 11.5 & $-11.4\pm3.3$ \\
$2f_0-f_1$ & 8.58681 & & 10.0 & (4) & 10.8 & 8.9 & (11) & 6.7 & 6.8 & (4) & 8.1 & $4.4\pm3.7$ \\
$2f_0+f_1+f_c$ & 8.75282 & & 8.4 & (5) & 9.1 & & & & 4.7 & (4) & 5.6 & $5.4\pm5.5$ \\
$2f_0-f_1-f_c$ & 8.57762 & & 6.0 & (4) & 6.5 & & & & & & & \\
$2f_0+2f_1$ & 8.82202 & & 5.0 & (4) & 5.4 & & & & 3.3 & (4) & 4.0 & $-7.1\pm8.4$ \\
$3f_0$ & 12.99783 & & 6.9 & (6) & 7.7 & 6.0 & (9) & 4.8 & 4.5 & (4) & 6.3 & $2.8\pm6.4$ \\
$3f_0-f_1$ & 12.91942 & & 4.7 & (4) & 5.3 & & & & & & & \\
$4f_0$ & 17.33043 & & 4.6 & (5) & 6.1 & & & & 2.9 & (4) & 4.8 & $0.3\pm9.5$ \\
\hline
\end{tabular}
\end{center}
\end{table*}
Fig.~\ref{fourier} shows several frequency spectra created from the $V$ data.
Besides the spectral window it shows the frequency spectrum after removal of the first, second and third triplet side frequencies.
It can be seen that after removing all frequencies given in Table~\ref{freq},
there seems to be some power left at frequencies near integer fractions of a day.
The amplitude is however small, less than 6 mmag.
This remaining power is possibly caused by small zero point shifts in the data from night to night,
likely introduced by the corrections needed to account for the use of different comparison stars.
Phase diagrams after consecutive cleaning of our $V$ data with the three frequency triplets are given in Fig.~\ref{phase}.
\begin{figure}
\centering
\includegraphics[width=8cm]{LSHerfig3.eps}
\caption{Frequency spectrum of our $V$ data for LS~Her. The top panel shows the spectral window.
Panels a, b and c show the spectrum after consecutively prewhitening for the first, second and third triplet respectively.}
\label{fourier}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=7.5cm]{LSHerfig4.eps}
\caption{Phase diagrams of our $V$ data for LS~Her plotted with the main pulsation period of 0.230808 days.
From top to bottom the data are plotted without prewhitening and then with consecutively prewhitening for the first, second and third triplet.
In order not to overload the diagrams, only one out of three data points have been plotted.}
\label{phase}
\end{figure}
The second and third triplets may be viewed as changing the (primary) Blazhko modulation itself.
With a period of $109\pm4$ days the amount of variation in amplitude and phase will change.
In the frequency spectrum this manifests itself by the side frequencies of the first Blazhko triplet being equidistant triplets themselves.
In Table~\ref{freq} we have therefore dubbed $f_c = f_2 - f_1$ as the frequency of this superposed modulation.
To illustrate the modulation of the Blazhko period, an analysis was done of small subsets of the $V$ data set.
Each subset was taken to be 25 days in length (about two Blazhko cycles),
and the best fitting amplitudes and phases were determined for the pulsation frequency $f_0$,
the main Blazhko frequencies $f_0+f_1$ and $f_0-f_1$, and their linear combinations.
Precise determination of the frequencies themselves is rather sensitive to the distribution of the data in such a small set.
Therefore the frequencies were kept fixed at the values determined from the total dataset.
A change in their value would then be manifested as a change in their phase.
The results of this analysis are shown in Fig.~\ref{change}.
The top panel shows the change in amplitude of $f_0$, $f_0+f_1$ and $f_0-f_1$, as a function of the phase in the 109-day cycle.
The lower panel of Fig.~\ref{change} shows the change in phase.
As there is no change in phase of the main pulsation period, it remains effectively constant during the long cycle.
However, the Blazhko period appears to vary cyclically in that interval, as can be seen from the phase changes of the Blazhko frequencies.
The variation in the Blazhko modulation may perhaps be compared to the four year cycle in the Blazhko period of RR~Lyr \citep{detre}.
However, possible splitting of the side frequencies similar to what is observed in LS~Her, has not yet been detected in RR~Lyr, perhaps because of this long period and the very long data sets needed.
A phase shift of the Blazhko maximum as seen at the end of a 4-year cycle in RR~Lyr was not observed in LS~Her.
As can be seen in Table~\ref{freq}, the second order triplet frequencies (around the first harmonic of the main pulsation frequency)
are found for the first ($f_1$) and second ($f_1+f_c$) triplet, but not for the third ($f_1-f_c$), presumably because their amplitude is too low.
There is no indication of the quintuplet frequencies $f_0\pm2f_1$,
However, the frequency $2f_0+2f_1$ has a significant amplitude in the data.
\begin{figure}
\centering
\includegraphics[width=8cm]{LSHerfig5.eps}
\caption{Changes of the amplitude (top panel) and phase (bottom panel) during the long cycle of 109 days of the main pulsation frequency $f_0$ (crosses) and the Blazhko frequencies
$f_0+f_1$ (filled circles) and $f_0-f_1$ (open circles).}
\label{change}
\end{figure}
\section{Conclusion}
LS~Her was found to be an RRc Blazhko star with three close Blazhko triplets around the main pulsation frequency.
The side frequencies of each of the three triplets are at the same distance from the main first overtone pulsation frequency.
In addition, the side frequencies of the second and third triplets are at the same distance from the side frequencies of the first triplet, within uncertainties.
Consequently the maximum amplitude and maximum phase shift of the Blazhko effect changes.
The Blazhko effect was found to have a primary period of 12.75 days, while its influence on amplitude and phase shifts, due to the additional triplets, changes in a cycle of 109 days.
The frequency spectrum of LS~Her has been found to be unique so far, but it is not excluded that other stars
which are known to have two Blazhko periods also show this complex frequency structure.
As their Blazhko periods are much longer, the missing triplet would also be much harder to detect.
Adequate coverage of a number of consecutive Blazhko cycles would be required to reveal additional frequencies in the spectrum of a Blazhko star.
The complex frequency spectrum of LS~Her cannot easily be inferred from the current theories of the Blazhko effect.
LS~Her is therefore an important star against which to verify any theory of the Blazhko effect.
\section*{Acknowledgements}
The authors gratefully acknowledge Katrien Kolenberg for helpful suggestions,
Brian Skiff for providing the spectral type references, and the referee for his valuable comments.
EB acknowledges the AAVSO and the Curry Foundation for providing the CCD camera and filters on loan.
This study used data from the Northern Sky Variability Survey
created jointly by the Los Alamos National Laboratory and the University of Michigan,
and funded by the US Department of Energy,
the National Aeronautics and Space Administration (NASA) and the National Science Foundation (NSF).
This study also used NASA's Astrophysics Data System, and the SIMBAD and VizieR
databases operated at the Centre de Donn\'ees Astronomiques (Strasbourg) in France.
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{
"redpajama_set_name": "RedPajamaArXiv"
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Social networking web sites seem to be the big rage in Internet-land with News Corp, Microsoft and Google all owing a piece of the action in this hot segment.
Now media laggard HT Media, parent company of the Hindustan Times newspaper, has belatedly developed the social networking itch.
The slow-moving HT Media says its subsidiary Firefly e-Ventures in the process of acquiring a social networking web site to establish a footing in this rapidly-growing space and complement its other proposed web initiatives.
Firefly also intends to roll out online vertical classifieds around jobs, matrimonials and real estate.
HT did not provide details but claimed that the relaunched Hindustantimes.com web site was seeing higher page views.
Long term, we are skeptical that the HT group's forays in the Internet domain will amount to much.
The HT folks are too slow-moving compared to other Indian media players like Times of India. Come on, it took HT decades to launch a business newspaper. And Mint, HT's busines daily is still published only in Delhi and Bombay. The Bangalore edition of Mint is expected to show up sometime in the third quarter.
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Der Stechpalmenkönig und der Eichenkönig sind die Personifikationen von Winter und Sommer in verschiedenen Mythologien und im Volksglauben. Populär gemacht wurde die Geschichte durch das Alexandrische Wicca. Die beiden Könige befinden sich in einem ewigen Kampf, welcher den Kreislauf des Jahres darstellt. Doch nicht nur der Wechsel zwischen der hellen und dunklen Hälfte des Jahres wird durch ihr Duell symbolisiert, sondern auch der Wechsel zwischen der Zeit der Ernte und der Brache. Während der warmen und hellen Tage um Litha ist der Eichenkönig am stärksten; der Stechpalmenkönig gewinnt zu Mabon die Oberhand, bis er sich dann zu Jul geschlagen geben muss. Der Eichenkönig wird zu diesem Zeitpunkt neu geboren, erlangt seine Stärke zurück und übernimmt zu Ostara wieder die Regentschaft.
Interpretationen
Robert Graves berichtet in seiner wissenschaftlichen Abhandlung Die Weisse Göttin: Sprache des Mythos unter anderem von anderen Wesenheiten aus Legenden und Folklore, die mit dem Stechpalmenkönig und dem Eichenkönig starke Ähnlichkeit haben oder sogar gleichgesetzt werden können. Diese sind:
Lleu Llaw Gyffes und Gronw Pebr
Gwyn und Gwynthyr
Lugh und Balor
Balan und Balin
Gawain und der grüne Ritter
Jesus Christus und Johannes der Täufer
Auf diese Ähnlichkeit hat auch bereits der schottische Ethnologe Sir James George Frazer hingewiesen. Frazer zog Parallelen zu dem Maifeiertag und zu Traditionen aus Skandinavien, Bayern und den Ureinwohnern Amerikas. Trotz der Forschung von Frazer wurden die Werke von Graves deutlich bekannter und so setzte sich auch seine Auffassung vom Mythos des Stechpalmenkönigs und des Eichenkönigs durch.
Stewart und Janet Farrar charakterisieren den Eichenkönig als Herrscher über die helle Hälfte des Jahres und den Stechpalmenkönig als Herrscher über die dunkle Hälfte des Jahres. Dies ist heute die geläufigste Vorstellung, vor allem da sie im Wicca und anderen neopaganen Religionen bereits eine Art Kultstatus besitzt und oft zum Jahreskreisfest Jul die Geschichte über den Kampf zwischen den beiden Königen nach den Werken der Farrars erzählt wird.
Nach aktuellem Stand der Forschung wird davon ausgegangen, dass der Stechpalmenkönig im Verlauf der Christianisierung zum Weihnachtsmann wurde oder die Vorstellung des Weihnachtsmanns zumindest stark prägte.
Kultur und Moderne
Der Kampf zwischen Licht und Dunkelheit wird zu Maibeginn und zur Wintersonnenwende vor allem in Großbritannien in Form von Mummenschanz dargestellt. Vor allem in Wales und unter dem Namen Jack in the Green auch in anderen Teilen Großbritanniens werden diese Maskenspiele jedes Jahr aufs Neue praktiziert und meist durch eine Art rituelles Gefecht dargestellt.
Im Wicca werden der Stechpalmenkönig und der Eichenkönig auch in manchen Traditionen als zwei Aspekte des gehörnten Gottes gesehen, die um die Gunst der großen Göttin duellieren.
Siehe auch
Wicca-Jahreskreis
Julfest
Krampus
Einzelnachweise
Allegorie
Wicca
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{"url":"http:\/\/tex.stackexchange.com\/questions\/128819\/table-cell-height-too-small-when-wrapping-text","text":"# Table cell height too small when wrapping text\n\nI have the following problem with my table:\n\nThe height of the 2nd row is slightly too small and the text overlaps with the line at the bottom and the top of the cell. My code is below:\n\n\\begin{longtabu} to \\linewidth {| m{0.41\\textwidth} | m{0.53\\textwidth} |}\n\\hline\n\\multicolumn{1}{|c}{Static (stuff)} & \\multicolumn{1}{|c|}{Dynamic (stuff)} \\\\ \\hline\n\\hline\n\\endfoot\n\\endlastfoot\ntextetxtetxtexttext & textetxtetxtexttext$-$Buffer: X\\textbackslash Y\\textbackslash y\\textbackslash G\\textbackslash X\\textbackslash H\\textbackslash J\\textbackslash x00$-$\\\\ \\hline\ntextetxtetxtexttext & textetxtetxtexttext$-$Information: XYZ\\textbackslash x00 ???\\\\ \\hline\n\\caption{calls}\n\\label{tab:alls}%\n\\end{longtabu}\n\nAny help is appreciated. Using packages tabu, booktabs and longtable. Thanks\n\n-\n\nYou can add struts to the beginning and end of your columns as follows:\n\n\\documentclass{article}\n\\usepackage{tabu}\n\\usepackage{longtable}\n\\pagestyle{empty}\n\\newcommand{\\aefrontstrut}{\\rule{0pt}{0.8\\baselineskip}}\n\\newcommand{\\aebackstrut}{\\rule[-0.6\\baselineskip]{0pt}{0.8\\baselineskip}}\n\\begin{document}\n\n\\begin{longtabu} to \\linewidth {| m{0.41\\textwidth} | >{\\aefrontstrut}m{0.53\\textwidth}<{\\aebackstrut} |}\n\\hline\n\\multicolumn{1}{|c}{Static (stuff)} & \\multicolumn{1}{|c|}{Dynamic (stuff)} \\\\ \\hline\n\\hline\n\\endfoot\n\\endlastfoot\ntextetxtetxtexttext & textetxtetxtexttext$-$Buffer: X\\textbackslash Y\\textbackslash y\\textbackslash G\\textbackslash X\\textbackslash H\\textbackslash J\\textbackslash x00$-$\\\\ \\hline\ntextetxtetxtexttext & textetxtetxtexttext$-$Information: XYZ\\textbackslash x00 ???\\\\ \\hline\n\\caption{calls}\n\\label{tab:alls}%\n\\end{longtabu}\n\\end{document}\n\nYou can use LaTeX's own \\strut command, or you can make your own customized struts as I've done above. By using two different style struts and the > and < modifiers for columns, you can control the spacing above the first line and after the last line in that column.\n\nBy changing the height of the first strut and the depth of the second strut, you can finely control the spacing.\n\n\\rule[<raise>]{<width>}{<height>}\n\nTechnically, the optional argument to \\rule is not the depth; it's a dimension by which the rule is raised or lowered. By using a negative value you are essentially setting the depth of the strut. Since the strut should not be visible, make sure the <width> is set to Opt.\n\nUPDATE\n\nAs noted in the comments below, the alignment can be off if the last column contains some short text. To get around this, use the > < directives for both columns:\n\n\\begin{longtabu} to \\linewidth {| >{\\aefrontstrut}m{0.41\\textwidth}<{\\aebackstrut} | >{\\aefrontstrut}m{0.53\\textwidth}<{\\aebackstrut} |}\n-\nThanks, This almost works, but now if there is only one line in the 2nd column it is top aligned vertically not centered? \u2013\u00a0 Jerome Aug 18 '13 at 16:06\nAdd the directives to all the columns. I'll update my answer to reflect this. \u2013\u00a0 A.Ellett Aug 18 '13 at 16:12\nThe parameter \\baselineskip sometimes gets messed with by authors who need to change the line spacing of their documents. (I know, they really shouldn't be affecting the line space by modifying \\baselineskip, but enough people seem to do it anyway to make this a problem to be reckoned with.) To increase the generality\/robustness of your answer, you may want to express the heights and depths of the struts as multiples of a font-related parameter such as ex rather than as multiples of \\baselineskip. \u2013\u00a0 Mico Aug 18 '13 at 16:23\n@Mico Excellent point. \u2013\u00a0 A.Ellett Aug 18 '13 at 16:52\nFor another recent posting involving the use of struts to provide padding in cells of a tabular environment, see tex.stackexchange.com\/a\/126542\/5001 (shameless self-citation alert!). \u2013\u00a0 Mico Aug 18 '13 at 17:11","date":"2014-11-26 18:41:31","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\": 0.9612436294555664, \"perplexity\": 4059.5928337506352}, \"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-2014-49\/segments\/1416931007324.75\/warc\/CC-MAIN-20141125155647-00247-ip-10-235-23-156.ec2.internal.warc.gz\"}"}
| null | null |
Sergei Vladimirovich Lemeshko (; 8 July 1972 – 9 December 2016) was a Russian professional footballer and manager.
Club career
He made his professional debut in the Soviet Second League in 1990 for FC Shakhtyor Leninsk-Kuznetsky. He played one game in the UEFA Cup Winners' Cup 1995–96 for FC Dynamo Moscow.
Personal life
He died in Kaliningrad in 2016 at the age of 44.
References
1972 births
People from Kemerovo Oblast
2016 deaths
Soviet footballers
Russian footballers
Russia under-21 international footballers
FC Dynamo Moscow players
FC Rostov players
FC Tekstilshchik Kamyshin players
FC Tyumen players
FC Tom Tomsk players
FC Baltika Kaliningrad players
FC Arsenal Tula players
Russian Premier League players
Association football midfielders
FC Novokuznetsk players
FC Chita players
FC Spartak Nizhny Novgorod players
Sportspeople from Kemerovo Oblast
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"redpajama_set_name": "RedPajamaWikipedia"
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Q: ErrorItemNotFound for Sent Items message notification We have created a subscription for all mailbox folders as
users/email@email.email/messages?$filter=isDraft eq false
When creating a subscription the Prefer header is specified: IdType = "ImmutableId".
The problem is that for all folders via the webhook we successfully receive a notification with an immutable ID and get by this ID email using Graph messages API, but in the case of emails sent from Outlook, the webhook first receives the ID, which triggers an error on Message get:
Status Code: NotFound Microsoft.Graph.ServiceException: Code: ErrorItemNotFound Message: The specified object was not found in the store., Item not found.
After this, the second webhook associated with the Sent Items folder arrives. I don't know what the first webhook is related to, possibly the Outbox folder. How can this be overcome?
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{
"redpajama_set_name": "RedPajamaStackExchange"
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| 8,960
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if you happened to be browsing around buzzfeed last night, you may have seen a familiar face. check out this article on the dopest kids at the white house easter egg roll. theo is in #18 AND #30!
that's right, at only 13-months-old, my child is way cooler than i can ever hope to be. needless to say, i'm a pretty proud momma.
we spent the morning yesterday at the white house, rolling eggs, listing to the president read 'where the wild things are,' and pinching ourselves.
to say we had a great time would be an understatement.
here are some photos from our trip to the white house.
theo, you just heard the president speak!
what do you think about that, kiddo?
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"redpajama_set_name": "RedPajamaC4"
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BRUCE WOOD
Artistic Team
"Dance should give you an experience
that is human and humane."
Founder I Artistic Director I Choreographer I Mentor
PHOTO ABOVE BY BRIAN GUILLIAUX
PHOTO BY SHAREN BRADFORD
Bruce Wood® was a nationally acclaimed choreographer of 80 works from 1994 until his untimely death in 2014. He was a passionate artist driven by a maverick spirit. He poured his heart and soul into his dances, and loved being in the dance studio working with his dancers.
Bruce Wood's professional dance career spanned 35 years. He began his training at the Gayle Corkery School in Fort Worth. At age 16, he received a scholarship to a summer intensive in New York at the School of American Ballet under the direction of George Balanchine. Among the companies he went on to perform with are New York City Ballet, San Francisco Ballet, Les Ballets Jazz de Montréal, Twyla Tharp Dance Company, and Lar Lubovitch Dance Company. He toured the world 10 times with Les Ballets Jazz de Montréal. As a guest artist, he performed internationally with DV8 Physical Dance in London, Contemporary Dance Canada, and in Canada with Margie Gillis.
Wood returned to Texas, creating his first work in Austin in 1994. He then moved home to Fort Worth and founded the Bruce Wood Dance Company, where he was artistic director and sole choreographer from 1996 to 2007. Bruce Wood Dance Company presented annual seasons at Bass Hall in Fort Worth; was on the Texas Commission on the Arts Touring Roster; and went on three national tours. Wood created works to a vast range of music—from Bach, Beethoven, Ravel, and Gershwin, to Philip Glass, Lyle Lovett, and Grace Slick. Proud of his Texas heritage, he created Lovett!; Dust, Texas; and Cowboy Songs. The latter was a full–evening work set to live music by country/western singer Michael Martin Murphey. In 2004, Wood was commissioned to create a work in honor of the United States Army infantry. Follow Me premiered at the RiverCenter in Columbus, Georgia. Among Wood's many commissions are Orlando Ballet; Dallas Black Dance Theatre; Texas Ballet Theater; SMU Meadows School of the Arts; and TITAS Command Performance.
In 2010, Wood and a group of Dallas investors formed the Bruce Wood Dance Project. Over five years, Wood created a body of new, acclaimed work, mentored professional dancers, and produced shows at the Dallas City Performance Hall. Wood's favorite saying was, "It's about the work." He had an aesthetic that set his work apart. He drew his subject matter from human nature, distilling the ups and downs, and the loves and the losses of daily life into pieces that range from dramatic to comic, compassionate to hilarious, psychological to pedestrian. All the elements—dancers, movements, lights, music, costumes—work together seamlessly. Wood's productions are transformative; they resonate with audiences and leave lasting memories. He was particular about the transition from studio to stage, and for Bruce Wood Dance Project, Wood renewed his collaborations with renowned lighting designer Tony Tucci, costume designer John Ahrens, and production director Deborah Barr.
Wood received numerous awards, including the 2010 Mary McLarry Bywaters Award for Lifetime Contribution to Dance from Dance Council North Texas. The Mary Award honored his extraordinary impact on the cultural life and growth of dance audiences in the greater North Texas region. Wood was honored by his high school alma mater, Richland High School, with induction into its inaugural Hall of Fame in April 2013.
Wood was honored posthumously by the Senate of The State of Texas Proclamation No. 962 in June 2014.
Bruce Wood Dance has received outstanding commendations and also was selected to be among the Top Dance Lists of 2012: #2 on The Dallas Morning News list and TheaterJones.com list; #1 on DFW.com; D Magazine's Best of awards for 2013, 2014, 2017, and 2019.
Bruce Wood Dance Logo
WE ARE GRATEFUL FOR THE SUPPORT OF OUR SPONSORS
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Five–Time
Bruce Wood Dance Gallery
101–103 Howell Street
214–298–9212 I info@brucewooddance.org
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©2022 Bruce Wood Dance. All rights reserved. Bruce Wood Dance Company is a 501(c)3 nonprofit arts organization. Contributions are tax–deductible. Bruce Wood is a registered trademark.
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\section{Introduction}
\label{intro}
An understanding of charged species transport is critical to the development of electrochemical and electrokinetic systems relevant to a wide range of disciplines (engineering, chemistry, physics) and applications (sensing, energy, water purification). Systems that employ non-linear electrokinetics, in which the electric field is varied spatially (and also temporally in some cases), are especially difficult to model. For example, charged species can be electrokinetically focused along a steep electric field gradient formed near an ion-selective membrane or a bipolar electrode (BPE)~\cite{li2016recent,mavre2010bipolar}. In both cases, the electric field gradient results from the local depletion of charge carriers at one end of the membrane (by selective charge transport) or BPE (by faradaic reactions)~\cite{bondarenko2020current}. The formation of an ion depletion zone (IDZ) and ion enrichment zone (IEZ) at opposite sides of the membrane or BPE is called ion concentration polarization (ICP). A few prominent applications include water purification and desalting~\cite{kim2010direct,berzina2018electrokinetic}, biomedical engineering~\cite{berzina2018electrokinetic}, and enrichment and detection of trace analytes~\cite{anand2011bipolar,kim2020concentration}. In all of these applications, the stability of the IDZ drastically limits the volumetric throughput of these devices. Therefore, the ability to simulate species transport in these systems is critical to their advancement.
Species transport in electrochemical systems, such as ICP, is a complex multi-physics problem driven by diffusion, electromigration, and convection \cite{probstein2005physicochemical}. Experimental approaches employed to characterize this multi-physics problem are generally limited to the measurement of electrical current or to the visualization of fluorescent tracer molecules. As a result, it is difficult to fully understand the mechanism of ICP using these methods alone. Therefore, there have been several numerical studies of transport in such systems to compliment experimental results. For example, Zangle et al.~\cite{mani2009propagation,zangle2009propagation} derived 1-dimensional (1D) governing equations for ICP in a system comprising a micro-nano-micro junction and calculated shock wave-like IDZ and IEZ propagation along the microchannel segments, originating at the nanochannel. Using this approach, they found that Dukhin number (surface conductivity over bulk fluid conductivity) and the electrophoretic mobility of charged species are the parameters that dictate the rate and extent of the propagation. Numerical results obtained by Mani and collaborators showed that chaotic fluid motion originates from the locally high electric field~\cite{druzgalski2013direct} or alternating current (AC)~\cite{kim2019characterization} even in the low Reynolds number regime. ICP is made further complex when, in addition to convection, diffusion, and migration, chemical reactions are involved. To address such a case, Kler et al. included reaction terms to simulate electrophoresis accompanied by acid and base reactions \cite{kler2011modeling}. Similarly, Tallarek and coworkers included acid/base and faradaic reaction terms in the simulation of ICP at BPEs \cite{hlushkou2016numerical}.
Although these studies exemplify successful simulation of charged species transport in non-linear electrokinetics, it is still challenging to obtain reliable results with a reasonable computational cost. The primary reason for this difficulty is the multi-scale nature of the problem~\cite{boy2008simulation}. The smallest scale feature that impacts the physics in electrochemical and electrokinetic systems is the electrical double layer ($\sim$\(10 nm\)) or EDL, which comprises electrical potential and ion concentration gradients in the boundary layer present at a liquid-solid interface. In contrast, species transport relevant to most applications of such systems extend over length scales of $\sim$\(10 \mu m\) to $\sim$\(1000 \mu m\). Importantly, unresolved boundary layers can result in unfavorable oscillations extending outside of the boundary layers into the bulk domain. Refining the mesh near the boundary is a reasonable approach to address challenges from multi-scale characteristics \cite{druzgalski2013direct,patankar1998numerical} and provides reliable results in the entire domain. However, the computational cost incurred by the increased mesh density in the boundary layer can be prohibitive for very small Debye lengths. Considering that most applications are interested in what happens in the 'bulk' of the fluid domain (and its impact on current flux), not in the vicinity of the boundary, resolving the mesh near this layer is not computationally economical. Jia et al. ~\cite{jia2014multiphysics1,jia2014multiphysics2}, using a commercial code, simplified complex boundary physics with electroosmotic slip velocity, which minimizes computational costs. However, there is ambiguity in the selection of the location where the slip boundary condition imposed away from an ion selective membrane transitions to a no-slip boundary condition, imposed on or adjacent to the membrane. Moreover, replacing the boundary layer with the slip boundary condition ignores concentration gradient driven flow \cite{alizadeh2017multiscale,cho2014overlimiting}. Therefore, there remains a need to reduce the computational cost of representing the boundary layer without oversimplifying the underlying physics.
In this work, we address this need by utilizing an approach used in fluid mechanics -- the Dirichlet-to-Neumann transformation -- this is used to efficiently model the no-slip condition (Dirichlet boundary condition)\cite{bazilevs2007weak}. The Dirichlet-to-Neumann transformation, also known as Nitsche's method or symmetric interior penalty Galerkin method (SIPG), provides a consistent and robust way of enforcing Dirichlet conditions by variational weakening of the no-slip condition into a Neumann type condition, especially in the context of Finite Element (FE) analysis. \cite{juntunen2009nitsche, brenner2008weakly} Such a strategy releases the point-wise no-slip condition imposed at the boundary of the fluid domain, thus minimizing the mesh resolution required to track the steep gradients close to the boundaries. This effect reliably imitates the presence (and effect) of the thin boundary layer~\cite{bazilevs2009computational,hsu2012wind}. Enforcing Dirichlet boundary conditions weakly allows for an accurate overall flow solution even if the mesh size in the wall-normal direction is relatively large. This approach has substantially benefited efficient simulations of turbulent flow scenarios~\cite{bazilevs2007turbulent,bazilevs2007variational} as well as other multi-physics flow scenarios~\cite{hansbo2003nitsche,xu2019residual}.
The present study develops a FEM framework for the fully coupled Navier-Stokes and Poisson-Nernst-Planck (NS-PNP) equations to simulate electrochemical and electrokinetic systems. To overcome difficulties from thin boundary layers, Dirichlet boundary conditions are weakly enforced \cite{nitsche1971variationsprinzip, bazilevs2007weak} in the PNP equations. While usage of the developed framework is not limited to specific application to electrochemical and electrokinetic systems, we demonstrate its efficacy in resolving calculations of electroosmotic flow (EOF) and ion concentration polarization (ICP). EOF and ICP were selected as test cases for two reasons - first, there has been growing interest in these phenomena due to their potential impact in chemical, biomedical, and environmental fields, and second, because these examples include the three fundamental transport mechanisms - convection, diffusion, and migration. Our findings are significant because, despite a much coarser mesh, the results obtained with weak BC showed good agreement to those obtained with strong BC, and furthermore, boundary flux calculations converged much faster to the solution using the weak BC. Collectively, these results demonstrate a significant reduction in computational load while retaining accuracy. Therefore, we expect that this weak BC approach will provide greater stability and accuracy in the simulation of a wide range of electrochemical and electrokinetic systems.
The outline of the rest of the paper is as follows: We begin by revisiting the governing equations for charged species transport followed by the non-dimensional forms of these governing equations in Section 2. Then, the FEM problems are defined with weakly imposed Dirichlet boundary conditions in Section \ref{Problem formulation}. The solving strategy for the numerical method was discuss in Section \ref{section:NumericalMethod}. In Section \ref{sec:results}, the developed framework is validated with a manufactured solution and by simulation of EOF, for which an analytical solution exists. Next, 1D and 2D IDZs are simulated with weakly imposed Dirichlet boundary conditions. For 3D applications, the developed platform was tested for electrolyte separation (desalting) in a microchannel.
For each example, the calculated boundary flux is compared with that obtained with strongly imposed Dirichlet boundary conditions.
We also test the weakly imposed boundary conditions for the simulation of the electrokinetic instabilities near a perm-selective membrane.
We conclude in Section \ref{sec:conclusion}.
\section{Charged species transport}\label{chargedspeciestransport}
\subsection{Governing equations} \label{GoverningEquations}
\noindent\textbf{Poisson-Nernst-Planck (PNP)}: Without loss of generality, we consider a canonical problem of solvent flow and species transport in a (micro)channel configuration. This problem encompasses both the electroosmotic and pressure driven regimes. We consider $N > 1$ number of charged species with subscript \(i\) indicating the species index. The species flux $\bm{j}_i^*$\footnote{The asterisk (*) is used for dimensional quantities, so that the notation is simplified when we consider non-dimensional terms.}, which is driven by diffusion, migration, and convection, is written as:
\begin{equation}
\label{eq:NPFlx}
\vec{j_{i}}^* = -D_i\nabla^* c_{i}^* - D_i\frac{z_{i}F}{RT}c_{i}^*\nabla^* \phi^* + \vec{u}^* c_{i}^*.
\end{equation}
Eq.~(\ref{eq:NPFlx}) is the Nernst-Planck equation~\cite{probstein2005physicochemical} for the $i^{th}$ species. \(D_i\) is the diffusivity, \(c_i^*\) is concentration of the species, \(z_i\) is the valence of species, \(F\) is the Faraday constant,
\(R\) is the gas constant,
\(T\) is the temperature, \(\phi^*\) is the electric potential, and \(\vec{u}^*\)\footnote{We follow the convention that bold symbols represent vectors with dimension, $d$. } is the fluid velocity. We get the rate of change of the species concentration by considering flux balance,
\begin{equation}
\label{eq:NPDimensional}
\frac{\partial c_i^*}{\partial t^*}+ \vec{u}^* \cdot \nabla^* c_{i}^*
= \nabla^* \cdot (D_i\nabla^* c_{i}^* + D_i\frac{z_{i}F}{RT}c_{i}^*\nabla^* \phi^*).
\end{equation}
Potential \(\phi^*\) is obtained from the Poisson equation, which describes Gauss's law,
\begin{equation}\label{eq:PoissonDimensional}
-\varepsilon\nabla^{*2}\phi^* = \rho_e^*,
\end{equation}
where \(\varepsilon\) is the electric permittivity of solvent, and \(\rho_e^*\) is the charge density given by
\begin{equation}\label{eq:chargeDensity}
\rho_e^*=F\sum_{i=1}^N z_i^*c_i^*.
\end{equation}
\noindent \textbf{Boundary conditions (PNP)}: We focus on the boundary conditions of a permselective membrane. Typical boundary conditions for the counter-ion concentration $c_i^*$ at the permselective membrane are Dirichlet \begin{equation}\label{eq:charge_DBC}
c_i^* = c_{i,M}^*
\end{equation}
and (zero) Neumann for co-ion species
\begin{equation}\label{eq:charge_NBC}
\vec{j_{i}}^*\cdot\vec{n} = 0
\end{equation}
where, $\vec{n}$ is the outward pointing normal.
The boundary conditions for the potential at the permselective membrane are also typically Dirichlet
\begin{equation}\label{eq:phi_DBC}
\phi^* = \phi_M^*
\end{equation}
\begin{remark}
The zero Neumann condition Eq.~\ref{eq:charge_NBC} represents zero flux across the boundary. To maintain a zero current flux, diffusion and electric migration (in Eq.~\ref{eq:NPFlx}) cancel each other at the boundary. As a result, there can be non-zero gradients of the concentration and the potential with a zero current flux boundary condition. This condition is in contrast to heat transfer or diffusion-convection problems involving a single variable.
\end{remark}
\noindent \textbf{Navier-Stokes (NS)}: In conjunction with the Poisson-Nernst-Planck equations, the solvent momentum transport is described by the Navier-Stokes equation
\begin{equation}\label{eq:NSDim}
\rho^*\frac{\partial \vec{u}^*}{\partial t^*}+\nabla^* \cdot (\rho^* \vec{u}^*\otimes \vec{u}^*)=-\nabla^* p^* + \eta^*\nabla^{*2}\vec{u}^*+\vec{f_b}^*.
\end{equation}
\(\rho^*\) is the density of solution, \(p\) is pressure, \(\eta^*\) is the dynamic viscosity. The last term of equation (\ref{eq:NSDim}) is the body force due to an electric field acting on charged species, which couples the Navier-Stokes equation with equations (\ref{eq:NPDimensional}) and (\ref{eq:PoissonDimensional})
\begin{equation}\label{eq:bodyForce}
\vec{f_b}^*=-F\sum_{i=1}^N c_i^* z_i^*\nabla^* \phi^*.
\end{equation}
The carrier fluid is assumed to be incompressible
\begin{equation}\label{eq:NDContinuity}
\nabla^* \cdot \vec{u}^* = 0.
\end{equation}
\noindent \textbf{Boundary conditions}: At the electrodes, the no-slip condition for velocity is enforced, $\vec{u^*} = 0$
\subsection{Non-dimensional forms of governing equations} \label{NDequations}
The variables and operators in the governing equations are scaled by characteristic quantities to obtain non-dimensional forms of the governing equations,
\begin{equation} \label{eq:scalingV}
x=\frac{x^*}{L_c}, \quad
\vec{u}=\frac{\vec{u}^*}{U_{c}},
\quad p=\frac{p^*}{p_{c}}, \quad c_i=\frac{c_i^*}{c_{c}}, \quad \phi=\frac{\phi^*}{\phi_{c}}, \quad \phi=\frac{\rho^*}{\rho_{c}}, \quad \phi=\frac{\eta^*}{\eta_{c}},
\end{equation}
\noindent where subscript \(c\) denotes characteristic quantities. The reference length \(L_{c}\)\footnote{From now on we drop the subscript \(c\) for concise notation.} is chosen to be the channel width, \(L\). The characteristic concentration, potential, fluid velocity, pressure, and time scale (which is derived from velocity and length references) respectively are as follows,
\begin{equation} \label{eq:refQ}
\begin{split}
c_{c}=I_b=\frac{1}{2}\sum_{i=1}^N z_i^2 c_{i}^{initial},
\quad \phi_{c} = V_T=\frac{RT}{F} \\
U_{c}=\frac{D}{L}, \quad p_{c}=\frac{\eta D}{L^2}, \quad \tau=\frac{L^2}{D}.
\end{split}
\end{equation}
Where \(I_b\) is the ionic strength of the bulk electrolyte and \(V_T\) is thermal voltage, $D$ is the average diffusion coefficient of the species. Substituting dimensional quantities and operators with normalized variables and operators provides the non-dimensional equations as follows,
\begin{align}
\textit{Species flux:} & \quad \vec{j}_{i} = -\nabla c_{i} - z_{i}c_{i}\nabla \phi + \vec{u} c_{i}, \label{eq:NonDimFlx}\\
\textit{Nernst-Planck:} & \quad \frac{\partial c_i}{\partial t} + \vec{u} \cdot \nabla c_{i}
= \nabla \cdot (\nabla c_{i} + z_{i} c_{i}\nabla \phi), \label{eq:NDNP}\\
\textit{Poisson:} & \quad -2 \Lambda^2 \nabla^2\phi = \rho_e, \label{eq:NDP}\\
\textit{Navier-Stokes:}
&\quad\frac{1}{Sc}\left(\frac{\partial \vec{u}}{\partial t} + \vec{u}\cdot\nabla\vec{u}\right) =-\nabla p + \nabla^{2}\vec{u}
+\vec{f_b}\label{eq:NDNS}\\
\textit{Continuity: }&\quad \nabla \cdot \vec{u} = 0, \label{eq:NDCont}\\
\textit{Normalized charge density:} & \quad \rho_e=\sum_{i=1}^N z_i c_i,\label{eq:chargeDensityND} \\
\textit{Body force:} & \quad \vec{f_b}=- \frac{\kappa}{2\Lambda^2}\sum_{i=1}^N c_i z_i\nabla \phi, \label{eq:chargeDensityND}
\end{align}
\noindent where \(\Lambda\) is the normalized Debye length \footnote{The Debye length, or Debye screening length, \(\lambda\) characterizes the electrokinetics near a charged wall. The surface charge at the wall repels co-ions and attracts counter-ions. This electrokinetic repulsion and attraction is countered by thermal energy, thereby forming a diffuse layer adjacent of the wall. \(\lambda\) is the length from the wall into the fluid at which the electric static potential balances the thermal energy \cite{probstein2005physicochemical}. } \(\Lambda = \lambda/L\),
\begin{equation}\label{eq:Debye}
\lambda = \sqrt{\frac{1}{2}\frac{\varepsilon RT}{F^2I_b}}.
\end{equation}
\noindent \(Sc = \frac{\eta}{\rho D}\) is the Schmidt number which is the ratio of viscous effects to diffusion, and \(\kappa\) is electrohydrodynamic coupling constant~\cite{druzgalski2013direct} given by,
\begin{equation}\label{eq:electrohydrodynamicconst3}
\kappa = \frac{\varepsilon}{\eta D} \left (\frac{RT}{F}\right)^2.
\end{equation}
and the non-dimensionalized boundary conditions corresponding to those detailed in the previous sub-section.
\\
\begin{remark}
For a typical microchannel (channel hydraulic diameter ranging from 1\(\mu m\) to 1\(mm\)), \(\Lambda\) is small (ranging from \(\Lambda = \) $\num{1e-2}$ to $\num{1e-5}$), forming a thin boundary layer for species concentration and potential. However, the flow is in the laminar regime. Thus, we focus on applying the Dirichlet-to-Neumann transformation only on the PNP equations, and strongly enforce the no-slip conditions for velocity.
\end{remark}
\begin{remark}
There are several alternate choices for the characteristic length scale, which in turn affect the characteristic timescale. One alternative is to use the Debye length, $\lambda$ as the characteristic length. This results in a very small characteristic timescale~\cite{morrow2006time}. Another alternative defines the characteristic length scale as the harmonic mean of the channel hydraulic diameter and the Debye length, $L_c = \sqrt{L\lambda}$. These alternative timescales are particularly useful to resolve scenarios with small \(\Lambda\). See details in \ref{app:lambdaT}. In this study, $L_c = \sqrt{L\lambda}$ (and thus, \(\tau = L\lambda/D\)) was used for small \(\Lambda\) (\(\Lambda<\SI{1e-2}{}\)), while $L_c = L$ (and thus, \(\tau = L^2/D\)) was used for moderate to large \(\Lambda\) (\(\Lambda\geq\SI{1e-2}{}\)).
\end{remark}
\section{Variational form and the Dirichlet-to-Neumann transformation} \label{Problem formulation}
\subsection{Weak form of the equations}
\label{section:Variational problem and finite element approximation}
Consider the spatial domain as $\Omega_D$, with $\partial\Omega_D$ as its boundary, and by $\Gamma_D$ the boundary where the weak boundary conditions are enforced. We can define the variational problem as follows.
\begin{definition}
Let $(\cdot,\cdot)$ be the standard $L^2$ inner product over the subscript (i.e. either $\Omega_D$ or $\partial\Omega_D/\Gamma_D$). We state the variational problem as follows: find $\vec{u}(\vec{x}) \in \vec{H}_0^1(\Omega)$, $c_1(\vec{x}),...,c_N(\vec{x}), \phi(\vec{x}), p(\vec{x})$ $\in {H}^1(\Omega)$ such that\footnote{Here the subscript 0 for the Sobolev space $\vec{H}_{0}^1(\Omega)$ represents zero velocities on the boundary in the trace sense.}
\begin{align}
%
\text{Nernst Planck Eqns:} & \quad \mathcal{B}_{NP,i}\Big(q;c_i,\phi,\vec{u}\Big)
+ \mathcal{L}_{NP,i}\Big(q;c_i,\phi\Big) = 0, ~\texttt{for}~i = 1,...,N,
\label{varNP}\\
%
\text{Poisson Eqn:} & \quad \mathcal{B}_{P}\Big(q;\phi\Big)
+ \mathcal{L}_{P}\Big(q;\phi\Big) = 0, \label{varPoisson} \\
%
\text{Navier-Stokes:} & \quad
\mathcal{B}_{NS}\Big(\vec{w},q;\vec{u},p\Big) + \mathcal{L}_{NS}\Big(\vec{w};\vec{u}\Big) = 0, \label{varNS}
\end{align}
$\forall \vec{w} \in \vec{H}^1_0(\Omega)$, $\forall q \in H^1(\Omega)$.
\label{def:variational_form}
\end{definition}
\noindent where $\mathcal{B}$ and $\mathcal{L}$ represent the bilinear and linear forms respectively for each equation given by,
\begin{align}
\begin{split}
\textit{Nernst-Plank Eqns:}
&\quad
\mathcal{B}_{NP,i}\Big(q;c_i,\phi,\vec{u}\Big) = \Big(q,\frac{\partial c_i}{\partial t}\Big)_{\Omega_D}
+\Big(q,\vec{u}\cdot \nabla c_i\Big)_{\Omega_D}
+(\nabla q,\nabla c_i)_{\Omega_D}\\
&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+(\nabla q,z_i c_i \nabla \phi)_{\Omega_D},
\end{split}\label{eq:varNPBilinear}\\
\begin{split}
&\quad \mathcal{L}_{NP,i}\Big(q;c_i,\phi\Big) =
-(q,\nabla c_i \cdot \vec{n}+z_{i}c_{i} \nabla \phi \cdot \vec{n})_{\partial \Omega_D/\Gamma_D},
\end{split}\label{eq:varNPFlux}\\
\begin{split}
%
\textit{Poisson Eqns:}
&\quad
\mathcal{B}_{P}\Big(q;\phi\Big) =
2\Lambda^2(\nabla q; \nabla \phi)_{\Omega_D},
\end{split}\label{eq:varPBilinear}\\
&\quad \mathcal{L}_{P}\Big(r;\phi\Big) =
-2\Lambda^2(r,\nabla \phi \cdot \vec{n})_{\partial \Omega_D/\Gamma_D}
-(r,\rho_e)_{\Omega_D},\label{eq:varPFlux}\\
\begin{split}
\textit{Navier-Stokes Eqns:}
&\quad
\mathcal{B}_{NS}\Big(\vec{w},q;\vec{u},p\Big) =
\frac{1}{Sc}\Big(\vec{w},\frac{\partial\vec{u}}{\partial{t}}\Big)_{\Omega_D}
+\frac{1}{Sc}\Big(\vec{w},\vec{u}\cdot\nabla\vec{u}\Big)_{\Omega_D}
+(q,\nabla\cdot\vec{u})_{\Omega_D}\\
&\quad\quad\quad\quad\quad\quad\quad\quad\quad
-(\nabla\cdot \vec{w},p)_{\Omega_D}
+(\nabla{\vec{w}},\nabla{\vec{u}})_{\Omega_D},
\end{split}\label{eq:varNSBilinear}\\
&\quad \mathcal{L}_{NS}\Big(\vec{w};\vec{u},p\Big) =
-(\vec{w},\nabla\vec{u}\cdot\vec{n})_{\partial \Omega_D}
+(\vec{w}\cdot\vec{n},p)_{\partial \Omega_D}
-(\vec{w},\vec{f_b})_{\Omega_D}.\label{eq:varNSFlx}
\end{align}
\subsection{Semi-discrete time-scheme}\label{section:timescheme}
We utilize a fully-implicit first order backward Euler scheme. Let $k$ be a time-step; let $t^n := nk$; We can then define the time-discrete variational problem as follows.
\begin{definition}[time-scheme]
Let $(\cdot,\cdot)$ be the standard $L^2$ inner product over the subscript (i.e. either $\Omega_D$ or $\partial\Omega_D/\Gamma_D$). We state the variational problem as follows: find $\vec{u}^{n+1}(\vec{x}) \in \vec{H}_0^1(\Omega)$, $c_1^{n+1}(\vec{x}),...,c_N^{n+1}(\vec{x})$, $\phi^{n+1}(\vec{x})$, $p^{n+1}(\vec{x})$ $\in {H}^1(\Omega)$ such that
\begin{align}
%
\text{Nernst Planck Eqns:} & \quad \mathcal{B}_{NP,i}\Big(q;c_i^{n+1},c_i^{n},\phi^{n+1},\vec{u}^{n+1}\Big)
+ \mathcal{L}_{NP,i}\Big(q;c_i^{n+1},\phi^{n+1}\Big) = 0, ~\text{for}~i = 1,...,N,
\label{varNPtd}\\
%
\text{Poisson Eqn:} & \quad \mathcal{B}_{P}\Big(q;\phi^{n+1}\Big)
+ \mathcal{L}_{P}\Big(q;\phi^{n+1}\Big) = 0, \label{varPoissontd} \\
%
\text{Navier-Stokes:} & \quad
\mathcal{B}_{NS}\Big(\vec{w},q;\vec{u}^{n+1},\vec{u}^{n}, p^{n+1}\Big) + \mathcal{L}_{NS}\Big(\vec{w};\vec{u}^{n+1},p^{n+1}\Big) = 0, \label{varNStd}
\end{align}
$\forall \vec{w} \in \vec{H}^1_0(\Omega)$, $\forall q \in H^1(\Omega)$, given $\vec{u}^{n} \in \vec{H}_0^1(\Omega)$, and $c_1^{n}(\vec{x}),...,c_N^{n}(\vec{x}), \in H^1(\Omega)$.
\label{def:variational_form_sem_disctd}
\end{definition}
\noindent with the bilinear and linear forms for each equation given by,
\begin{align}
\begin{split}
%
\textit{Nernst-Plank Eqns:}
&\quad
\mathcal{B}_{NP,i}\Big(q;c_i^{n+1},c_i^{n},\phi^{n+1},\vec{u}^{n+1}\Big) = \Big(q,\frac{c_i^{n+1} - c_i^{n}}{k}\Big)_{\Omega_D}
+\Big(q,\vec{u}^{n+1}\cdot \nabla c_i^{n+1}\Big)_{\Omega_D}\\
&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+\left(\nabla q,\nabla c_i^{n+1}\right)_{\Omega_D}
+\left(\nabla q,z_i c_i^{n+1} \nabla \phi^{n+1}\right)_{\Omega_D},
\end{split}\label{eq:varNPBilinear_td}\\
%
\begin{split}
&\quad \mathcal{L}_{NP,i}\Big(q;c_i^{n+1},\phi^{n+1}\Big) =
-\left(q,\nabla c_i^{n+1} \cdot \vec{n} + z_{i} c_i^{n+1} \nabla \phi^{n+1} \cdot \vec{n}\right)_{\partial \Omega_D/\Gamma_D},
\end{split}\label{eq:varNPFlux_td}\\
%
\begin{split}
%
\textit{Poisson Eqns:}
&\quad
\mathcal{B}_{P}\Big(q;\phi^{n+1}\Big) =
2\Lambda^2\left(\nabla q; \nabla \phi^{n+1}\right)_{\Omega_D},
\end{split}\label{eq:varPBilinear_td}\\
%
&\quad \mathcal{L}_{P}\Big(r;\phi^{n+1}\Big) =
-2\Lambda^2\left(r,\nabla \phi^{n+1} \cdot \vec{n}\right)_{\partial \Omega_D/\Gamma_D}
-\left(r,\rho_e^{n+1}\right)_{\Omega_D},\label{eq:varPFlux_td}\\
%
\begin{split}
\textit{Navier-Stokes Eqns:}
&\quad
\mathcal{B}_{NS}\Big(\vec{w},q;\vec{u}^{n+1},\vec{u}^{n}, p^{n+1}\Big) =
\frac{1}{Sc}\Big(\vec{w},\frac{\vec{u}^{n+1}-\vec{u}^{n}}{k}\Big)_{\Omega_D}
+\frac{1}{Sc}\Big(\vec{w},\vec{u}^{n+1}\cdot\nabla\vec{u}^{n+1}\Big)_{\Omega_D}\\
&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
-\left(\nabla\cdot \vec{w},p^{n+1}\right)_{\Omega_D}
+\left(\nabla{\vec{w}},\nabla{\vec{u}^{n+1}}\right)_{\Omega_D}\\
&\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+\left(q,\nabla\cdot\vec{u}^{n+1}\right)_{\Omega_D}\,\,\, ,
\end{split}\label{eq:varNSBilinear_td}\\
%
&\quad \mathcal{L}_{NS}\Big(\vec{w};\vec{u}^{n+1},p^{n+1}\Big) =
-\left(\vec{w},\nabla\vec{u}^{n+1}\cdot\vec{n}\right)_{\partial \Omega_D}
+\left(\vec{w}\cdot\vec{n},p^{n+1}\right)_{\partial \Omega_D}
-\left(\vec{w},\vec{f_b}^{n+1}\right)_{\Omega_D}.\label{eq:varNSFlx_td}
\end{align}
Note that the continuity equation is combined with the Navier-Stokes equation here. This is done because this is a fully-implicit pressure coupled time discretisation.
\subsection{Spatial discretization with stabilization}\label{section:SUPG}
For notational simplicity we consider the time derivatives as continuous while we describe the spatial discretization. As we seek a continuous Galerkin discretization with equal order interpolation for velocity and pressure, we utilize a popular stabilization-based approach --- streamwise/upwind Petrov--Galerkin (SUPG) in conjunction with pressure stabilized Petrov-Galerkin (PSPG)~\citep{article:BrooksHughes1982, article:TezMitRayShi92}. The SUPG stabilization also allows us to stabilize advective terms in Navier-Stokes and Nernst-Planck equations.
To achieve the spatial discretization, we substitute the infinite-dimensional spaces in \textbf{\cref{def:variational_form}} by their discrete counterparts (denoted here by a superscript $h$) using conforming Galerkin finite elements augmented along with SUPG stabilization. Considering a tessellation of the domain $\Omega = \bigcup_{i=1}^{N_{el}} \Omega_i $ into $N_{el}$ non-overlapping elements, the space-discrete form of the Navier-Stokes---Possion-Nernst-Plank (NS-PNP) variational problem is given by:
\begin{definition}
find $\vec{u}(\vec{x}) \in \vec{H}_0^{1,h}(\Omega)$, $c_1(\vec{x}),...,c_N(\vec{x}), \phi(\vec{x}), p(\vec{x})$ $\in {H}^{1,h}(\Omega)$ such that
\begin{align}
%
\begin{split}
\text{Nernst Planck Eqns:} & \quad \mathcal{B}_{NP,i}^{h}\Big(q_i^{h};c_i^{h},\phi^{h},\vec{u}^{h}\Big)
+ \mathcal{L}_{NP,i}^{h}\Big(q_i^{h};c_i^{h},\phi^{h}\Big) \\
\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
&+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{SUPG}(\nabla\phi^{h} + \vec{u}^{h}) \cdot\nabla q_i^{h},
\frac{\partial c_i^h}{\partial t} + \vec{u}^h \cdot \nabla c_{i}^h\Big)} = 0, ~\text{for}~i = 1,...,N,
\end{split}\label{eq:FEMNP}\\
%
\text{Poisson Eqn:}& \quad
\mathcal{B}_{P}^{h}\Big(q^{h};\phi^{h}\Big)
+ \mathcal{L}_{P}^{h}\Big(q^{h};\phi^{h}\Big) = 0,\label{FEMPoisson}\\
\begin{split}
\text{Navier-Stokes Eqns:}& \quad
\mathcal{B}_{NS}^{h}\Big(\vec{w}^{h},q^{h};\vec{u}^{h},p^{h}\Big)
+ \mathcal{L}_{NS}^{h}\Big(\vec{w}^{h},\vec{u}^{h}\Big)\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{SUPG}\vec{u}^{h}\cdot\nabla \vec{w}^{h},
\frac{\partial \vec{u}^{h}}{\partial t} + \vec{u}^{h}\cdot \nabla \vec{u}^{h} - \vec{f_b}^{h}\Big)}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{PSPG}\nabla{q}^{h},
\frac{\partial \vec{u}^{h}}{\partial t} + \vec{u}^{h}\cdot \nabla \vec{u}^{h} - \vec{f_b}^{h} \Big)}= 0,
\end{split}\label{eq:FEMNS}
\end{align}
$\forall \vec{w} \in \vec{H}^{1,h}_0(\Omega)$, $\forall q \in H^{1,h}(\Omega)$.
\end{definition}
The last term (in blue) in Eq.~\ref{eq:FEMNP}, and the second last term (in blue) in Eq.~\ref{eq:FEMNS} are the SUPG stabilization terms, while the last term in Eq.~\ref{eq:FEMNS} is the pressure stabilized petro-galerkin (PSPG) stabilizer. Where, $\tau_{SUPG}$ and $\tau_{PSPG}$ are element based standard coefficients for the SUPG and PSPG terms~\citep{article:TezMitRayShi92}.
\begin{remark}
As our discretization is restricts the basis functions to discrete counterparts of~$\vec{H}_0^1$~and ~${H}^1$ spaces. Terms in the SUPG and PSPG residual which require higher regularity than $\vec{H}_0^1$ and ${H}^1$ are therefore neglected. For example, the drift terms in the Nernst-Planck equations given by,
\begin{equation}
\sum_{K=1}^{N_{el}}\Big(\tau_{SUPG}(\nabla\phi^{h} + \vec{u}^{h}) \cdot\nabla q_i^{h},
\nabla \cdot (\nabla c^{h}_{i} + z_{i} c^{h}_{i}\nabla \phi^h)\Big) \,\, ,
\end{equation}
would require representation of second order derivatives on $c^{h}_i$ and $\phi^{h}$ which do not reside in~${H}^1$ space.
\end{remark}
\subsection{Dirichlet-to-Neumann transformation for the Poisson-Nernst-Plank equation}\label{section:weakBC}
Now, we present the formulation for weakly imposing Dirichlet boundary conditions.
Without loss of generality, we consider the Dirichlet-to-Neumann transformation on the boundary, $\Gamma_D$. On this boundary, Dirichlet conditions are imposed on the species concentration, $c_i = g_{ci}$, and potential $\phi = g_{\phi}$. The Dirichlet-to-Neumann transformation replaces the strong imposition of these boundary conditions by a set of three boundary integral terms~\citep{bazilevs2007weak} --- representing the standard weakening (for consistency), its adjoint, and a penalty term. The penalty term ensures that as the mesh is refined, the strong imposition (i.e. Dirichlet condition) of boundary condition is recovered.
The variational form of the NS--PNP equations including these three additional terms (in red) for the Poisson, and the Nernst-Plank equation is given as:
\begin{definition}
find $\vec{u}(\vec{x}) \in \vec{H}_0^{1,h}(\Omega)$, $c_1(\vec{x}),...,c_N(\vec{x}), \phi(\vec{x}), p(\vec{x})$ $\in {H}^{1,h}(\Omega)$ such that
\begin{align}
%
\begin{split}
\text{Nernst Planck Eqns:} & \quad
\mathcal{B}_{NP,i}^{h}\Big(q_i^{h};c_i^{h},\phi^{h},\vec{u}^{h}\Big)
+ \mathcal{L}_{NP,i}^{h}\Big(q_i^{h};c_i^{h},\phi^{h}\Big) \\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{SUPG}(\nabla\phi^{h} + \vec{u}^{h}) \cdot\nabla q_i^{h},
\frac{\partial c_i^h}{\partial t} + \vec{u}^h \cdot \nabla c_{i}^h\Big)} \\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
- \textcolor{red}{\left(q_i^{h},\nabla c_i^{h} \cdot \vec{n} + z_{i}c_i^{h} \nabla \phi^{h} \cdot \vec{n}\right)_{\Gamma_D}}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
- \textcolor{red}{\left(\nabla q_i^{h}\cdot\vec{n},c_i^{h} - g_{ci}\right)_{\Gamma_D}}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+\textcolor{red}{\left(\frac{C_{NP}}{h_{el}}q_i^h,c_i^{h} - g_{ci}\right)_{\Gamma_D}} = 0, ~\text{for}~i = 1,...,N,
\end{split}\label{eq:FEMNP_wBC}\\
%
\begin{split}
\text{Poisson Eqn:}& \quad
\mathcal{B}_{P}^{h}\Big(q^{h};\phi^{h}\Big)
+ \mathcal{L}_{P}^{h}\Big(q^{h};\phi^{h}\Big)
- \textcolor{red}{2\Lambda^2\left(q^h,\nabla \phi^h \cdot \vec{n}\right)_{\Gamma_D}}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
- \textcolor{red}{2\Lambda^2\left(\nabla q^h\cdot \vec{n},\phi^h-g_{\phi}\right) _{\Gamma_D}}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{red}{\left(\frac{C_P}{h_{el}}q_i^h,c_i^{h} - g_{\phi}\right)_{\Gamma_D}} = 0,
\end{split}\label{eq:FEMPoisson_wBC}\\
\begin{split}
\text{Navier-Stokes Eqns:}& \quad
\mathcal{B}_{NS}^{h}\Big(\vec{w}^{h},q^{h};\vec{u}^{h},p^{h}\Big)
+ \mathcal{L}_{NS}^{h}\Big(\vec{w}^{h},\vec{u}^{h}\Big)\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{SUPG}\vec{u}^{h}\cdot\nabla \vec{w}^{h},
\frac{\partial \vec{u}^{h}}{\partial t} + \vec{u}^{h}\cdot \nabla \vec{u}^{h} - \vec{f_b}^{h}\Big)}\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad
+ \textcolor{blue}{\sum_{K=1}^{N_{el}}\Big(\tau_{PSPG}\nabla{q}^{h},
\frac{\partial \vec{u}^{h}}{\partial t} + \vec{u}^{h}\cdot \nabla \vec{u}^{h} - \vec{f_b}^{h} \Big)}= 0,
\end{split}\label{eq:FEMNS_wBC}
\end{align}
$\forall \vec{w} \in \vec{H}^{1,h}_0(\Omega)$, $\forall q \in H^{1,h}(\Omega)$.
\end{definition}
The last term in Eq.~\ref{eq:FEMNP_wBC} and Eq.~\ref{eq:FEMPoisson_wBC} are the penalty-like terms \cite{bazilevs2007weak}. \(C_{NP}\) and \(C_{P}\) are the penalty coefficients that are specified based on inverse element estimates~\citep{article:TezMitRayShi92,Harari1992}. We set them equal to 4 for the simulation results shown in this work. The first two terms in red in Eq.~\ref{eq:FEMNP_wBC} and Eq.~\ref{eq:FEMPoisson_wBC} represent, respectively, the consistency term (arising from weakening the highest derivative terms in these equations), and the adjoint consistency term. The adjoint consistency term ensures better conditioning of the ensuing stiffness matrix.
\begin{remark}
The weak imposition of Dirichlet boundary conditions on NS is not considered, as the main focus of the current study is the charged species transport in microfluidic applications. Low \(Re\) in microfluidic applications ensures reasonably large fluid boundary layers \footnote{We do not consider electroconvection~\cite{mani2020electroconvection}, where steep gradients in both concentration and velocity are expected. It is straightforward to incorporate weak boundary conditions for velocity~\cite{bazilevs2007weak}. We defer this exercise to later work.}; thus, the necessity of weakly imposed boundary condition for the Navier-Stokes equation diminishes.
\end{remark}
\begin{remark}
We use a block iterative approach for solving the Poisson-Nernst-Planck, and Navier-Stokes equations per time step. This ensures decoupled treatment of the \(c_i\) and \(\phi\) terms in the boundary terms. Block iteration between the Poisson and Nernst-Planck equations allows separate weak BC implementation for \(c_i\) and \(\phi\), as \(\phi\) can be treated like a constant during the iteration for NP. In addition, block iteration removes the non-linearity in the NP equation, see Section \ref{section:NumericalMethod} for more details on numerical methods.
\end{remark}
\section{Strategy for implementation} \label{section:NumericalMethod}
As specified before, we use a block iterative strategy to solve the set of equations. This approach provides several advantages, including (a) reducing the number of degrees of freedom per solve, (b) mitigating the numerical stiffness that exists between the equations (especially the large body force in the momentum equation), (c) enabling (simplified) weak imposition of Dirichlet boundary conditions by allowing separate treatment for \(c_i\) and \(\phi\) (see the boundary condition terms in Eq.~\ref{eq:FEMNP_wBC} and Eq.~\ref{eq:FEMPoisson_wBC}), and (d) converting the non-linear PNP equation into a set of two linear equations -- Poisson and Nernst-Planck.
A flow chart of the approach is illustrated in Figure ~\ref{fig:Flowchart}. We utilize a Backward Euler time step for all equations. We implement a parallel version of this method within our in-house parallel finite element framework. The domain decomposition is achieved via ParMETIS~\cite{karypis1997parmetis}.
We make use of the {\textsc{Petsc}} library, which provides efficient parallel implementations of linear and non-linear solvers along with an extensive suite of preconditioners~\citep{petsc-efficient, petsc-web-page, petsc-user-ref}. Specifically, we utilize the SNES construct (line search quasi-Newton) for the Navier-Stokes solver, and the KSP construct for the linear system.
\begin{figure}[!hbtp]
\begin{tikzpicture}
\matrix (m)[matrix of nodes, column sep=1cm,row sep=8mm, align=center, nodes={rectangle,draw, anchor=center} ]{
& |[block]| {{\small Load Initial Conditions} \(\phi_{k=0}^{n=0}, c_{i,k=0}^{n=0}, \vec{u}_{k=0}^{n=0}\)} & \\
& |[block]| {{\small Increment time step}, $n=n+1$} & \\
& |[block]| {{\small Increase block iteration counter}, $k=k+1$} & \\
& |[block]| {{\small Solve Poisson to obtain}, \(\phi_{k}^{n}\)} & \\
|[block]| {{\small Initialize block iteration counter}, $k=0$} & |[block]| {{\small Solve Nernst-Planck to obtain}, \(c_{i,k}^{n}\)} & \\
& |[block]| {{\small Solve non-linear Navier-Stokes to obtain}, \(\vec{u}_{k}^{n}\)} & \\
& |[decision]| {
$\norm{\vec{U}_{k}^{n}-\vec{U}_{k-1}^{n}}_{L^2}$ $<\SI{e-3}{}\norm{\vec{U}_{k}^{n}}_{L^2}$} & \\
& |[decision]| {\(n \geq N\)} & \\
& |[block]| {{\small Stop}} & \\
};
\path [>=latex,->] (m-1-2) edge (m-2-2);
\path [>=latex,->] (m-2-2) edge (m-3-2);
\path [>=latex,->] (m-3-2) edge (m-4-2);
\path [>=latex,->] (m-4-2) edge (m-5-2);
\path [>=latex,->] (m-5-2) edge (m-6-2);
\path [>=latex,->] (m-6-2) edge (m-7-2);
\draw [rectangle connector=5cm] (m-7-2) to node[descr] {{\small No}} (m-3-2);
\draw [straight connector] (m-7-2) to node[descr] {Yes} (m-8-2);
\draw [straight connector] (m-8-2) to node[descr] {Yes} (m-9-2);
\draw [>=latex,->] (m-8-2) -| node[descr, pos=0.25] {{\small No}} (m-5-1);
\draw [>=latex,->] (m-5-1) |- (m-2-2);
\end{tikzpicture}
\caption{Flow chart of NS-PNP solver} \label{fig:Flowchart}
\end{figure}
\section{Numerical experiments}\label{sec:results}
\subsection{Convergence against manufactured solution}
We use the method of manufactured solutions to assess the convergence of our implementation. We select an input ``solution'', and substitute it in the full set of governing equations. We then use the residual as a body force on the right-hand side of Eqs~\ref{eq:FEMNP},\ref{FEMPoisson},\ref{eq:FEMNS}.
We choose the following ``solution'' with appropriate body forcing terms:
\begin{equation}\label{eq:mms}
\begin{cases}
u = cos(2\pi t)sin(2\pi x)cos(2\pi y), \\
v = -cos(2\pi t)cos(2\pi x)sin(2\pi y), \\
p = cos(2\pi t)sin(2\pi x)cos(2\pi y),\\
c_+ = cos(2\pi t)cos(2\pi x)sin(2\pi y),\\
c_- = cos(2\pi t)sin(2\pi x)cos(2\pi y),\\
\phi = -cos(2\pi t)cos(2\pi x)sin(2\pi y).
\end{cases}
\end{equation}
Note that the manufactured solution for the fluid velocity is divergence free. Our numerical experiments use the following non-dimensional parameters: $\Lambda = 10^{-2}$, $Sc = 1$, $\kappa = 1.0$. We fix the time step at $k = 10^{-4}$ to minimize contribution of error from temporal discretization. We vary the spatial mesh resolution by increasing the number of elements. Figure \(\ref{fig:mms}\) shows the spatial convergence of $L^2$ errors (numerical solution compared with the manufactured solution) at $t = 1$. We observe second order convergence for velocity, species concentration and potential as expected for linear conforming Galerkin basis functions.
\input{5.RESULTS/FIGURES/convergence.tex}
\subsection{Electroosmotic flow (EOF) simulation and comparison with analytical results}
Electroosmotic flow is a canonical microfluidic flow where the flow is driven by a potential drop \(\Delta \phi\) maintained across a channel with charged walls~\cite{kirby2010micro}. In the bulk solution away from the charged wall, charge neutrality is maintained (\(\rho_e = 0\)). Hence, the bulk fluid does not respond to the applied potential drop. However, the charged wall attracts counter-ions and expels co-ions breaking the charge neutrality (\(\rho_e\neq 0\)) in the fluid domain that is wall adjacent. This results in a non-zero body force term in the Navier-Stokes equation near the walls. Subsequently, the rest of bulk fluid is driven to a steady state profile by the shear stress from the near wall flow. This flow profile has a characteristic plug shape, which is distinct from pressure driven Poiseuille flow in microchannels. The plug velocity can be analytically computed and is given by~\cite{kirby2010micro}
\begin{equation}\label{eq:EOFAnal}
U_{max} = -\frac{\varepsilon \phi_0}{\eta}E.
\end{equation}
where \(\phi_0\) is potential difference between the channel wall and bulk fluid.
We demonstrate the ability of the NS-PNP framework to accurately predict this EOF profile. The boundary conditions and problem geometry are shown in Figure \(\ref{fig:EOF}\). The dimensional values of all quantities are provided in Table \ref{Tab:EOF}, while all simulations are performed in dimensionless terms. The applied potential difference per unit length across the channel was $\Delta \Phi = 0.039$, the wall potential was $\Phi_0= -2.32$, and the inlet and outlet cation \(c_+\) and anion \(c_-\) concentrations are set to 1. The charge valences of the species, \(z_i\), are 1 and -1, respectively. The dimensionless Debye layer thickness, \(\Lambda\) was 0.097, Schmidt number, \(Sc\) was 686.68, and electrohydrodynamic coupling constant was 0.4037. The analytic solution for $U_{max}$ from Eq.~\ref{eq:EOFAnal} gives a non-dimensional value of 0.0429 (and dimensional value of $\SI{5.5711e-04}{m/s}$).
\input{5.RESULTS/FIGURES/EOF}
\input{5.RESULTS/table.tex}
We discretize the domain into $200 \times 40$ linear elements and use a time step of $k = 10^{-4}$. Figure \ref{fig:EOFProfile} shows the time evolution of the velocity profile. At early times, the body force results in non-zero fluid velocity only in the wall adjacent regions. This near wall flow subsequently drives the bulk. After about 100 time steps, the flow profile nearly reaches steady state, exhibiting the classic plug shape. As seen from Figure \ref{fig:EOFProfile}, the computed value of $U_{max}$ is $0.0413$.
\input{5.RESULTS/FIGURES/eofPlot.tex}
\subsection{Electrokinetics near a permselective membrane: 1D simulations and flux comparisons} \label{1D_IDZ}
We next illustrate the framework for practical application involving electrokinetics near permselective membranes, which is an area of research that is seeing increasing interest. In particular, we showcase how the weak enforcement of boundary conditions allows accurate capture of current fluxes at boundaries without very fine mesh resolution. A permselective membrane selectively transports species forming a depletion zone and an enrichment zone at the opposite sides of the membrane \cite{li2016recent}. For example, Nafion is a cation selective membrane that is widely used in electrokinetic applications. Under an applied electric current, Nafion selectively transfers cations across the membrane, while blocking anions. This behavior is critical for a wide variety of applications including separation of biological entities \cite{berzina2018electrokinetic} and sea water desalination \cite{kim2010direct}.
Our model accurately predicts the formation of a depletion zone near the permselective membrane. A simple binary electrolyte ($N = 2$, \(z_1\) = 1 and \(z_2\)= -1) was considered for the simulation. The cation selective membrane was located at \(x=0\), and the bulk electrolyte is at \(x=1\). \(\phi(x=0) =\) 0 at the membrane, and \(\phi(x=1) =\) 50 at the bulk. Both \(c_+\) and \(c_-\) were set to 1 at \(x=1\). The non-dimensional Debye length, \(\Lambda\), was 0.01. \(c_+\) was set to 2 at the membrane.
The results of the PNP calculation with strongly imposed boundary conditions are shown in Figure \ref{fig:depStr} as the baseline. As explained above, both cations and anions were depleted near the cation selective membrane. The magnitude of the electric field (absolute value of the potential gradient) was high in the depletion zone and drops as it extends into the bulk. Adjacent to the membrane, a thin boundary layer of cations forms.
\input{5.RESULTS/FIGURES/depStr.tex}
The thickness of the thin boundary layer is proportional to the non-dimensional Debye length, \(\Lambda\). Thus, a very thin concentration boundary layer is expected. Traditionally, without significant mesh resolution, inaccurate evaluation of the stiff gradients at the boundary result in significant error in the current flux calculation. Accurate evaluation of charge flux is especially critical, because in most electrokinetic or electrochemical experiments, flux is the single most important measurement used to understand the system \cite{bard2000electrochemical}.
The weak imposition of Dirichlet boundary conditions allows relaxation of the mesh resolution requirements, while retaining accuracy of boundary flux computations. The boundary flux at the membrane was calculated considering global conservation \cite{bazilevs2007weak}, and setting the test basis function to 1, resulting in:
\begin{equation}\label{eq:flxCal}
\textit{Species i flux,}~~\vec{j}_i \cdot \vec{n} = - \left(1,\nabla c_i^{h} \cdot \vec{n} + z_{i} c_i^{h} \nabla \phi^{h} \cdot \vec{n}\right)_{\Gamma_D} +\left(\frac{C_{NP}}{h_{el}}1,c_i^{h} - g_{ci}\right)_{\Gamma_D}
\end{equation}
\input{5.RESULTS/FIGURES/1Dflux.tex}
We compare the boundary flux calculation at different mesh resolutions between a strong imposition versus two types of weak imposition of the Dirichlet boundary conditions: \textit{Type 1:} weak BC for both Poisson and Nernst-Planck equations; \textit{Type 2:} weak BC only for Nernst-Planck equation. Note that only the first term in equation (\ref{eq:flxCal}) is used to compute the strong flux (which is equivalent to surface integral of equation (\ref{eq:NonDimFlx})), while both terms in equation (\ref{eq:flxCal}) are used to compute boundary fluxes under weak imposition.
As the membrane only transports cations, and the applied potential is high at the bulk (\(x=1\)) and low at the membrane (\(x=0\)), the direction of cation flux is from the bulk to the membrane. Under steady state conditions, the influx of the cations from the bulk must be equal to the outflux at the membrane. Thus, the influx from the bulk provides a baseline to compare the outflux computed at the membrane using the three different approaches. As seen from Figure ~\ref{fig:depStr}, the gradients of the species concentrations and potential at the bulk ($x = 1$) are significantly smaller, hence we expect the flux computed from imposition of strong boundary conditions to provide accurate values here.
The flux calculation results with various mesh sizes are shown in Figure~\ref{fig:1Dflx}. Notice that in panel (a) of Figure~\ref{fig:1Dflx} the outflux at the membrane (x=0) from strong imposition has still not converged to the influx from the bulk (even at fine mesh resolutions), the flux from weak imposition (panel (b) of Figure~\ref{fig:1Dflx}) has converged to the influx current even for dramatically coarse mesh sizes. For a range of mesh resolutions, we can see only a minute difference between the influx and the outflux calculated using weak BC. The enlarged plot in panel (b) of Figure~\ref{fig:1Dflx} shows that the difference between the fluxes when weak boundary conditions are imposed for both $\phi$ and $c_i$ vs only for $c_i$ is negligible.
We next investigate electrokinetics near the membrane with various \(\Lambda\) (Figure~\ref{fig:depStrLCtrl} and Table~\ref{Tab:EOF_bFlx}) spanning two orders of magnitude. For all \(\Lambda\), the size of the mesh was set to \(h=\SI{1e-3}{}\). The boundary conditions were the same as the ones shown in Figure~\ref{fig:depStr}. Weak boundary conditions are applied at $x = 0$, while strong boundary conditions are applied at $x = 1$. Representative cation and anion distributions after steady state is reached are plotted in Figure~\ref{fig:depStrLCtrl}. As expected, with smaller \(\Lambda\), the thickness of the boundary layer decreases. We also see that the size of the depletion zone is correlated with \(\Lambda\). We compare the flux at $x = 0$ with the flux at $x = 1$ in Table \ref{Tab:EOF_bFlx}. As stated before, these fluxes should match at steady state and serve as an excellent validation test of the weakly imposed boundary condition. Across two orders in magnitude variation in \(\Lambda\), the fluxes reliably match, with a maximum deviation of less than $3\%$, even for the case when a single element is larger than the boundary layer (for $\Lambda = 5\times 10^{-4}$). We note that the calculated boundary flux decreased with decreasing \(\Lambda\), which agrees with other literature \cite{chu2005electrochemical}.
\input{5.RESULTS/FIGURES/LCtrl.tex}
\input{5.RESULTS/table_bFlx}
\subsection{Electrokinetics near cation selective membrane: 2D simulations}
In this section, we illustrate the use of this approach to generate a 2D model of electrokinetic enrichment of a charged species near an IDZ generated by ICP in a microfluidic device. The device consists of two straight microchannels interconnected by a cation selective membrane (see Figure~\ref{fig:2DConcept}). A voltage bias is applied across the device through electrodes immersed in the fluid filled reservoirs of the two channels. The current resulting from the applied voltage is carried by cations and anions along the channels. The membrane transports only cations, while blocking anions, which creates an IDZ in the anodic channel and an IEZ in the cathodic channel~\cite{li2016recent}.
To simulate the formation of an IDZ, the Poisson-Nernst-Planck equations were solved for the left half of the anodic channel. The boundary condition for the cation concentration is strongly enforced at the inlet (\(c_+=1\)) and weakly at the membrane (\(c_+=2\)). The concentration of the anion is set to \(c_-=1\) at the inlet. The boundary condition defining potential is strongly enforced at the inlet (\(\phi=50\)) and weakly at the membrane (\(\phi=0\)). At the walls and the line of symmetry, a no flux boundary condition (\(\boldsymbol{j}_i\cdot\boldsymbol{n} = 0\)) was applied. We use an unstructured triangular mesh that exhibits moderate mesh refinement at the membrane and a coarse mesh close to the inlet. A contour plot of cation concentration is shown in Figure \ref{fig:2DWeakComp}. Notice that, at the membrane boundary, a thin cation boundary layer is formed; along with the formation of the IDZ.
\begin{figure}[!hbtp]
\centering
\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/2D_IDZ.png}
\subcaption{}
\end{subfigure}
\begin{subfigure}{.45\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/2Dmsh_crop_grey.png}
\subcaption{}
\end{subfigure}
\caption{Formation of IDZ and IEZ near the cation selective membrane (a), and the domain and meshes for the simulation (b). The left half of the IDZ channel was considered for the simulation.}
\label{fig:2DConcept}
\end{figure}
The boundary flux of cation \(c_+\) at the membrane was calculated from Eq. (\ref{eq:flxCal}) and compared with the calculation from strong BC, for progressively refined meshes (that are refined close to the membrane). Like the results from 1D, the boundary flux calculation obtained by using weak BC show remarkable convergence even for coarse mesh resolutions. This effect is clearly seen in Figure~\ref{fig:2Dflx}, which shows that the weakly imposed boundary is able to accurately capture the flux even for fairly coarse meshes.
\begin{figure}[!hbtp]
\centering
\includegraphics[width = 0.8\linewidth,trim=3cm 7.5cm 3cm 7.5cm,clip]{figures/2D_weak.png}
\caption{\(c_+\) concentration near the cation selective membrane.}
\label{fig:2DWeakComp}
\end{figure}
\input{5.RESULTS/FIGURES/2Dflux.tex}
\subsection{Electrokinetic analyte separation: 3D simulation}
In this section, we test our platform on a canonical electrochemical system --- electrolyte separation (desalting) in a 3D microchannel equipped with a permselective membrane.
The device configuration is shown in Figure \ref{fig:3DSeparation}, with the channel branching into two channels. The cation selective membrane is located along the outer wall of the straight channel, just downstream of the branch point.
A constant flow of electrolyte is maintained by a pressure difference, Figure \ref{fig:3DSeparation} (a). A potential difference across the microchannel is applied, with anodic conditions applied at the inlet, and ground conditions applied at the membrane surface. The fully coupled Navier-Stokes Poisson-Nernst-Planck equations were solved for the microchannel geometry. An unstructured tetrahedral mesh was created using the mesh generating software, Gmsh (V2.10.1). The non-dimensional parameters defining this system are as follows: \(Sc=686.81\), \(\kappa=0.39\), and \(\Lambda=0.097\).
The boundary conditions for the variables at various boundaries are as follows:
(a) Membrane surface: weak imposition of Dirichlet conditions for potential ($\phi = 0$), and cation concentration ($c_+ = 2$), and zero anion current flux boundary condition (\(\vec{j_{-}}\cdot \vec{n}=0\)); (b) Inlet: Strong imposition of Dirichlet condition for potential ($\phi = 150$), anion concentration ($c_+=1$), cation concentration ($c_{-}=1$), and inlet velocity ($u=100$); (c) Walls: no flux boundary conditions for both species, no slip for velocity; (d) Outlet: pressure set to zero.
The steady state results are shown in Figure \ref{fig:3DSeparation}.
Once the electric field is applied, an IDZ forms near the membrane surface, as can be seen in Figure \ref{fig:3DSeparation} (b). This dramatic reduction in the concentration of the conductive species upstream of the perm-selective membrane creates a high electric field at the junction of the splitting channels as can be seen in Figure \ref{fig:3DSeparation} (c). This electric field, in conjunction with the pressure driven flow results in separation of the electrolyte. Specifically, as charged species are transported to the channel by bulk flow, anions entering the lower channel are screened by the high electric field and are redirected to the upper channel, Figure \ref{fig:3DSeparation} (d). Conversely, cations are attracted by the electric field and removed out of the device through the cation selective membrane. This results in near complete removal of charged species from the channel that is intersected by the junction. This result illustrates the mechanism used in water purification and fluid management related to hemodialysis~\cite{kim2010direct, knust2013electrochemically}.
\begin{figure}[!hbtp]
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U100/VelVec.png}
\subcaption{}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U100/IonicStrength.png}
\subcaption{}
\end{subfigure}
\newline
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U100/EField.png}
\subcaption{}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U100/FlxAn.png}
\subcaption{}
\end{subfigure}
\caption{Analyte separation in a diverging microfluidic channel. (a) Magnitude of flow velocity. (b) ionic strength, $I=1/2\sum_{i=1}^{N} c_i z_i^{2}$, which is an average concentration of species for binary electrolyte. (c) Iso-surfaces of electric field near the membrane. The membrane is shown in gray at the bottom surface after the junction. (d) Anion flux is screened out from the membrane channel by high electric field.}
\label{fig:3DSeparation}
\end{figure}
To showcase the impact of weak imposition of boundary conditions, we check how well total flux is conserved. That is, we compute the sum of cation fluxes across the inlet, outlet and membrane, which following conservation of charge should sum to zero. Since we expect sharp gradients of concentrations near the membrane, we vary the discretization near the membrane while keeping the mesh size in the rest of the domain fixed at \(\SI{3e-2}{}\). Table \ref{Tab:flux_3D} compares this total flux in the case of strong imposition of boundary conditions at the membrane versus weak imposition of boundary conditions at the membrane. We can clearly see that the weak imposition of boundary conditions results in significantly more accurate fluxes, even for relatively coarse meshes.
As before, we note that the flux calculation at the membrane remains challenging due to the large gradients of variables. This result is important, as it shows that even complex 3D electrochemical systems can be efficiently simulated using weakly imposed boundary conditions.
\input{5.RESULTS/table_bFlx_3d_U100}
\begin{figure}[!hbtp]
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U200/ionic_Strength.png}
\subcaption{}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U200/EField.png}
\subcaption{}
\end{subfigure}
\newline
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U200/AnFlx.png}
\subcaption{}
\end{subfigure}
\begin{subfigure}{.5\textwidth}
\centering
\includegraphics[width = \linewidth]{figures/3D/U200/CaFlx.png}
\subcaption{}
\end{subfigure}
\caption{ \textit{Failure to achieve separation during high influx:} Analyte separation in the diverging channel with excessive influx. When the convection is dominant over the electric field, the separation at the junction is not maintained. (a) ionic strength, $I=1/2\sum_{i=1}^{N} c_i z_i^{2}$, which is an average concentration of species for binary electrolyte; (b) Iso-surfaces of electric field near the membrane. The membrane is shown in gray at the bottom surface after the junction. (c) Anion flux passes through the membrane channel due to high convection; (d) Cation flux either passes through the membrane region or leaves through the membrane.}
\label{fig:3DSeparationU200}
\end{figure}
The previous numerical example showed electrochemical separation as a consequence of a balance between the electric migration away from the IDZ and the convective flux due to imposed flow rate. We conclude this section by simulating a case where the imposed flow rate is sufficiently large to overwhelm the electromigration, thus disrupting the separation process. Figure \ref{fig:3DSeparationU200} shows the result obtained when the flow rate is doubled relative to the previous case, while the potential and inlet concentration remains unchanged. Figure \ref{fig:3DSeparationU200}(a) show high ionic strength at both outlets, which implies high cation and anion concentration at both outlets indicating a failure to achieve separation. The structure and magnitude of electric field around the membrane is similar to that observed in the earlier simulation, see iso-surfaces in Figure \ref{fig:3DSeparationU200} (b). However, due to high convection, the charged species penetrate the electric field barrier at the channel junction, see Figure \ref{fig:3DSeparationU200} (c) and (d). As a result, a significant amount of cation and anion concentration is found at the membrane outlet as well.
We again evaluate the conservation of total cation flux in the simulation. Table \ref{Tab:flux_3D_U200} shows the net flux across the permselective membrane calculated for a range of mesh sizes. The net flux resulting from the weak BC approach is significantly closer to zero, indicating a clear advantage in comparison to a strong imposition of boundary conditions.
\input{5.RESULTS/table_bFlx_3D_U200.tex}
\subsection{Electrokinetic instability near a perm selective membrane}
In this sub-section we illustrate the ability of the framework to capture electroconvective instability. This instability occurs due to the interplay between the hydrodynamics with electrostatic forces~\citep{druzgalski2013direct} causing chaotic fingers of charge density to emanate from an ion selective membrane (beyond a critical applied electric field). This is an interesting, yet challenging phenomena to capture, requiring very fine resolution close to the membrane boundary. Here, we show that qualitatively identical results can be simulated using relatively coarse meshes having no more than 2 elements across the Debye layer.
We consider a long rectangular channel with an aspect ratio $8\times1$. The cation selective membrane boundary conditions are enforced at the bottom, with reservoir boundary conditions enforced at the top. A potential difference of $120$ is maintained across the domain. This corresponds to (a) cation boundary conditions of $C_{+} = 2$ at the bottom and $C_{+}=1$ at the top, (b) anion boundary conditions of zero flux at the bottom, and $C_{-}=1$ at the top, (c) potential boundary conditions of 120 at the top and 0 at the bottom, (d) no slip boundary conditions for velocity at the top and bottom. Symmetric boundary conditions are applied to the side walls.
This domain is discretized using a rectangular mesh with 1280 $\times$ 180 quad elements created using the Gmsh (V2.10.1) software. A geometric progression ($\texttt{ratio} = 1.021$) based stretching was applied along the height to get a clustered mesh. This produced a mesh refined at the bottom, with the smallest element exhibiting a height of $\sim \SI{5e-4}{}$.
The non-dimensional Debye layer, $\Lambda$ is $\SI{1e-3}{}$ thick.
This corresponds to a little less than two elements representing the Debye layer in the mesh.
Note that this scenario is a realistic case corresponding to $\sim \SI{10}{\micro\metre}$ channel heights seen in several electrolyte applications~\citep{kim2010direct, berzina2020tutorial,kim2010nanofluidic}.
The Schmidt number, $Sc$, is $\SI{1e-3}{}$ and the electrohydrodynamic coupling constant,$\kappa$, is 0.5. The Dirichlet-Neumann transition for the cation is applied at the bottom by weakly enforcing the concentration.
A time step of $\Delta t = \SI{1e-6}{}$ is used to solve this problem.
Figure \ref{fig:instability} shows the development of the instability in the system, matching the results from benchmark simulations~\cite{druzgalski2013direct}. The results at initial times are analogous to the 1D results seen in section \ref{1D_IDZ}. The electrolyte concentration is stratified with the formation of a depletion zone near the membrane. Note the charge separation in the depletion zone. This non-zero charge density together with the local electric field drives the fluid flow, which results in the electrokinetic instabilities at later times. These appear as fingers of differential charge density emanating from the ion selective membrane. This qualitatively matches the numerical and analytical studies reported in \cite{druzgalski2013direct, zaltzman2007electro} and experimental studies in \cite{kwak2013microscale, yossifon2008selection}. We defer a more qualitative comparison of these simulations (including a parametric sweep across various potential differences) to a subsequent study.
\input{5.RESULTS/FIGURES/instability}
\section{Conclusion}\label{sec:conclusion}
In this study, we simulate electrokinetic systems represented by the Navier-Stokes-Poisson-Nernst-Planck equations, with a key quantity of interest being the current flux at the system boundaries. Accurately computing the current flux is challenging due to the thin boundary layers (small Debye lengths) that require fine mesh to resolve. We address this challenge by using the Dirichlet-to-Neumann transformation to weakly impose the Dirichlet conditions. The framework was validated against manufactured solutions and the analytical solution for electroosmotic flow. We next simulated the dynamics near a permselective membrane in 1D and 2D. Then, the simulation was tested in a 3D application for electrolyte separation (desalting) in a branching microchannel. Lastly, the electrokinetic instability near a perm-selective membrane was simulated by the coupled Navier-Stokes-Poisson-Nernst-Planck equations.
We showed that weak imposition of boundary conditions can produce accurate boundary flux values, even with a coarse mesh and independent of flow conditions. This approach substantially reduces the computational cost of modeling complex electrochemical systems.
\section{Acknowledgments}
We thank Kumar Saurabh from the Ganapathysubramanian group for technical discussions and implementation support, as well as for proof-reading the manuscript.
\section{Different types of time scaling}
\label{app:lambdaT}
The smallest timescales in electrochemical system are electric double layer charging time and chemical reaction time. In the current work frame, chemical reaction is not considered; thus, the double layer charging time is the smallest time scale of the system. The double layer charging time is directly correlated with the double layer thickness in steady state \cite{morrow2006time}. Therefore, it is reasonable to consider the double layer thickness as a term in defining the characteristic timescale,
\begin{equation}
\tau=\frac{L\lambda}{D}.
\end{equation}{}
The corresponding non-dimensional Nernst-Planck equation becomes
\begin{equation}\label{eq:NDNP}
\frac{dc_{i}}{dt} + \Lambda \boldsymbol{u} \cdot \nabla c_{i}
= \Lambda \nabla \cdot (\nabla c_{i} + z_{i} c_{i}\nabla \phi),
\end{equation}
the Poisson equation
\begin{equation}\label{eq:NDP}
-2 \Lambda^2 \nabla^2\phi = \rho_e,
\end{equation}
and the Navier-Stokes equation
\begin{equation}\label{eq:NDNS}
\frac{1}{Sc}\frac{1}{\Lambda}\frac{d\boldsymbol{u}}{dt} + \frac{1}{Sc} \boldsymbol{u}\cdot\nabla\boldsymbol{u}
=-\nabla p + \nabla^{2}\boldsymbol{u}
- \frac{\kappa}{2\Lambda^2}\Sigma c_i z_i\nabla \phi
\end{equation}
\section{Additional results}
\label{app:WeakDEP}
We provide additional results illustrating cation distribution comparisons between strong and weak imposition of boundary conditions in ~\ref{fig:2DWeakComp}. We focus on the near boundary region ($0 \le x \le 0.1$), for the problem setup discussed in \ref{1D_IDZ} with \(\Lambda=0.01\). The simulation for the strong boundary conditions is performed on a mesh with $1000$ uniform elements ($h = 10^{-3}$) in the domain. Thus, there are about 10 elements across the boundary layer. In contrast, we use fairly coarse meshes with $100$ and $80$ uniform elements for simulations with weak imposition of the boundary conditions. A single element in this mesh is comparable to the boundary layer thickness.
As described in the main text, two types of weak BC are considered: Weak BC for both \(c+\) and \(\phi\), and weak BC only for \(c+\). We note that in both these cases (and meshes) the current flux matches very well (as shown in the main text). It is interesting to see that even with coarse meshes, the cation distribution matches with the highly resolved cation distribution within two elements from the boundary.
\begin{figure}[b!]
\centering
\begin{subfigure}[t]{0.45\linewidth}
\centering
\begin{tikzpicture}[]
\tikzstyle{every node}=[font=\footnotesize]
\begin{axis}[
width=\linewidth,
y label style={at={(axis description cs:0.1,0.5)},anchor=south},
xlabel=$x$,
ylabel=$c_+$,
legend style={at={(0.95,0.95)},anchor=north east},
x tick label style={rotate=0,anchor=north},
axis line style = thick,
cycle list name=color list,
legend cell align={left},
xmin=0,
xmax=0.1
]
\addplot[black, solid, line width=0.6mm]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/Str.txt};
\addplot[blue, dashed, line width=0.5mm, mark = o, mark size=4pt, mark options={solid}]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/PC100.txt};
\addplot[red, dash dot, line width=0.5mm, mark = x, mark size=4pt, mark options={solid}]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/C100.txt};
\legend{Strong BC,Weak BC \(c_+\) \& \(\phi\),Weak BC \(c_+\)}
\end{axis}
\end{tikzpicture}
\caption{100 elements}
\end{subfigure}
\begin{subfigure}[t]{0.45\linewidth}
\centering
\begin{tikzpicture}[]
\tikzstyle{every node}=[font=\footnotesize]
\begin{axis}[
width=\linewidth,
y label style={at={(axis description cs:0.1,0.5)},anchor=south},
xlabel=$x$,
ylabel=$c_+$,
legend style={at={(0.95,0.95)},anchor=north east},
x tick label style={rotate=0,anchor=north},
axis line style = thick,
cycle list name=color list,
legend cell align={left},
xmin=0,
xmax=0.1
]
\addplot[black, solid, line width=0.6mm]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/Str.txt};
\addplot[blue, dashed, line width=0.5mm, mark = o, mark size=4pt, mark options={solid}]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/PC80.txt};
\addplot[red, dash dot, line width=0.5mm, mark = x, mark size=4pt, mark options={solid}]
table[x expr={\thisrow{x}},y expr={\thisrow{cp}},col sep=space]{5.RESULTS/data/1DdepWeak/C80.txt};
\legend{Strong BC,Weak BC \(c_+\) \& \(\phi\),Weak BC \(c_+\)}
\end{axis}
\end{tikzpicture}
\caption{80 elements}
\end{subfigure}
\caption{1D depletion: comparison between weakly imposed BC both for \(c_+\) and \(\phi\) and only for \(c_+\). Note that only adjacent of the membran ($x<0.1$) is shown.}
\label{fig:1DWeakComp}
\end{figure}
\section{}
\label{}
\section{}
\label{}
\section{}
\label{}
\section*{References}
\bibliographystyle{model1-num-names.bst}
\section*{References}}
\begin{document}
\maketitle
We would like to thank the reviewers for the constructive comments, which has significantly helped improve the manuscript. We have incorporated all the suggestions from the reviewers. Comments from reviewer 1 are color coded in \textcolor{cyan}{cyan}, and comments from reviewer 2 are color coded in \textcolor{green}{green}. Same color code is used to annotate the revised manuscript for changes. This document details each reviewer suggestion and our response below:
\section{}
\subsection{}\label{comment:r1_1}
\begin{mdframed}[style=commentR1]
\emph{There are several reference to "Dirichlet-to-Neumann", I guess this is correct. But the formulation is also referred to as Nitsche's method and has great similarities with SIPG (symmetric interior penalty). To help the reader these terms should also be mentioned in the abstract and/or introduction.}
\end{mdframed}
\noindent We have added these terms in the manuscript.
\begin{mdframed}[style=manuscript]
\textit{Changes in the manuscript:} \\
The third line of the forth paragraph in Introduction.
\end{mdframed}
\subsection{}\label{comment:r1_2}
\begin{mdframed}[style=commentR1]
\emph{Eq 40: The blue SUPG term does not use the full residual. Is this a "typo" or is this trully a inconsistent method. If so, please elaborate: why? what are the consequences? particular wrt convergence?}
\end{mdframed}
This is not a typo, the full residual is not written in these equations, the excluded terms would require higher regularity of basis and test functions. Careful examination would throw light on the fact that the terms which are not included in the blue residual are higher order terms of type divergence of a flux. In the residual these terms cannot be weakened, therefore they cannot be discretized using discrete $H^1$ spaces used in this conforming Galerkin method. These terms are naturally zero for conforming Galerkin $H^1$ discretizations, which is why we omit them. We have added a remark in the manuscript explaining this omission.
\begin{mdframed}[style=manuscript]
\textit{Changes in the manuscript:} \textbf{Remark 4} in page 7.
\end{mdframed}
\newpage
\subsection{}
\label{comment:r1_3}
\begin{mdframed}[style=commentR1]
\emph{Eq 40 \& 42: both equations seem to use the same stabilization parameter tau, while eq 40 seems quite different as the "effective convection" is a u + grad phi. This grad phi should also be included in the tau definition, I believe? If these tau's are indeed the same please elavorate why grad phi should not be included in the tau definition in eq 40.}
\end{mdframed}
As correctly pointed out by the reviewer we do adjust the stabilization parameter $\tau$ to account for the "effective convection" which includes convection and drift using $\frac{\partial{\phi}}{\partial{\mathbf{x}}}$.
\subsection{}\label{comment:r1_4}
\begin{mdframed}[style=commentR1]
\emph{Eq 4 the consistency term includes grad-phi term. Does this have a knock-on effect? Should other terms change accordingly to assure stability and accuracy?}
\end{mdframed}
This term does not have a knock-on effect. The reason for this is that Nernst-Planck equation and the Poisson equation are solved in a block-iteration. Therefore, $\phi$ terms in the Nernst-Planck equation are known and do not need to be treated as unknown in the variational form.
\subsection{}\label{comment:r1_5}
\begin{mdframed}[style=commentR1]
\textit{ pg 8 lines 52/53: The dual consistency also improves the formal accuracy of the method. Given the inclusion of the grad-phi term in the consistency term is the dual consistency fullfilled? }
\end{mdframed}
Yes, the dual consistency term is fulfilled. This is again because all the $\phi$ terms are known as the Poisson equation is solved in a separate block. This is shown in our convergence analysis where expected convergence rates are observed.
\subsection{}\label{comment:r1_6}
\begin{mdframed}[style=commentR1]
\textit{Remark 5: Decoupling is fine, and it is fine to assume things are constant when it comes to linear/nonlinear iterations, but it does not circumvent the questions from the previous 2 points (4\&5) raised.}
\end{mdframed}
To address this question we would like to remind the reviewer that individual block iteration is run until a minimum tolerance is reached which preserves consistency, within each block iteration Poisson and Nernst-Planck is solved in a linear and Non-linear Newton iteration.
\subsection{}\label{comment:r1_7}
\begin{mdframed}[style=commentR1]
\textit{Why consider a simple first order method in time? Why not a second order (or higher order)? This seems more efficient.}
\end{mdframed}
As we do a block iteration, we anticipate the block iteration in addition to preserving consistency also improves order of the method. Therefore, to conserve effort we use a more robust first order method as the part of the block iteration. We are working on higher order methods, which is part of our future work.
\subsection{}\label{comment:r1_8}
\begin{mdframed}[style=commentR1]
\textit{Fig 1: The P and NP equations are linear -- due to the decoupling, but NS is still nonlinear. Please provide clarity whether "Solve NS" means a full converged Newton solve of NS, or 1 update for the NS part?
If it is the former (full-newton) would it be possible (and cheaper?) to step to an approach with only one update on NS each block iteration?
Please elaborate.}
\end{mdframed}
We solve NS with a full converged Newton solve in each block iteration. We have improved the clarity in the manuscript.
\begin{mdframed}[style=manuscript]
\textit{Changes in the manuscript:} The flow chart in figure 1.
\end{mdframed}
\subsection{}\label{comment:r1_8}
\begin{mdframed}[style=commentR1]
\textit{The flux calculation based in eq 48 and eq 13 results in an unfair comparison. For the strong BC a flux can also be postprocessed based on the same global conservation arguments on which eq 48 is based.
Comparing Eq 48 with Eq 43 leads to the conclusion that\\
$B(1;c_i,phi,u) + L(1;c_i,phi) = - j_i . n$ \\
This relation is identical to Eq 48, but can also be used for strong BCs. This effectively reconstructs the lagrange multiplier required to enforce the BC.
The LM is the conservative flux. Please make a like-to-like comparison and use this alternative flux. Perhaps keep the old flux and compare with the new one, making the point that the new one is superior(I believe it has a higher order of convergence as eq 13).
}
\end{mdframed}
We apologize for the confusion that a mistake in our explanation caused. We have now clarified that the first term in Eq 48 is used for calculating the strong form flux, while both terms in Eq 48 are used to compute the weak form flux.
Thus, the comparison is fair, with a comparison on how well the strong boundary condition resolves the flux vs the weak boundary condition. We note that the influx condition ($x = 1$) serves as our 'ground truth', since both concentration and potential exhibit low gradients, thus allowing accurate calculation of fluxes there.
We have also separated Figure 6 into two parts to make this visually clear.
\begin{mdframed}[style=manuscript]
\textit{Changes in the manuscript:} Revised text, Page 13 last paragraph. Also, Revised Figure 6
\end{mdframed}
\subsection{}\label{comment:r1_8}
\begin{mdframed}[style=commentR1]
\textit{Fig 6: I expected the red to be better then the blue curve: perhaps this is indicative to a subtle issue eluded to in point 4.
}
\end{mdframed}
Actually, the blue is clearly better than red only at one data point. In general, the red is better or they are close each other.
\subsection{}\label{comment:r1_8}
\begin{mdframed}[style=commentR1]
\textit{Tab 2 ,3\& 4: This only shows there is a difference between weak and strong. Please provide an analytical answer, or an overkill answer in order to provide a "exact" value. Particular for tab 3\&4: which is correct?
}
\end{mdframed}
The analytical answer for table 3 and 4 is zero. These tables compare the total (Net) flux (which is expected to be zero) for both the case of strong imposition of boundary conditions at the membrane versus weak imposition of boundary conditions at the membrane. We can clearly see that the weak imposition of boundary conditions results in significantly more accurate fluxes, even for relatively coarse meshes. The net flux (Table 4) resulting from the weak BC approach is significantly closer to zero, indicating a clear advantage in comparison
to a strong imposition of boundary conditions.
\newpage
\section{}
\subsection{}\label{comment:r2_1}
\begin{mdframed}[style=commentR2]
\emph{The authors of the reviewed manuscript tried to demonstrate that a previously developed method could be applied to the computational modeling of this electrokinetic phenomenon. However, they tested their approach only on extremely simplified physical situations. For instance, the values of the major control parameter -- the dimensionless Debye length -- used in the manuscript is two-three orders of magnitude lower than its physically realistic values.}
\end{mdframed}
We appreciate the reviewers comments on the practical parameters. Table 2 shows results for dimensionless Debye length down up to $\SI{1e-4}{}$ which corresponds to realistic scenarios. Additionally, as per the reviewers suggestions, we have now included a new sub-section of results illustrating simulations of electro-convective instabilities.
\begin{mdframed}[style=manuscript]
\textit{Changes in the manuscript:} New section 5.6
\end{mdframed}
\subsection{}\label{comment:r2_2}
\begin{mdframed}[style=commentR2]
\emph{The authors only consider the simplex fluid flow case and do not address the much more interesting and exciting case of nonlinear vortex flow. The novel non-equilibrium electro-osmotic instability discovered more than 20 years ago (see Zaltzman, B. \& Rubinstein, I. 2007 Electro-osmotic slip and electroconvective instability, J. Fluid Mech. 579, 173-226 and references therein) and the related nonlinear vortex flow are the central research objects in the field of electro-kinetics, both for experimentalists and theoreticians. I
think that the verification of the suggested computational approach should include the realistic and important physical situations like the one mentioned above. }
\end{mdframed}
We thank the reviewer for encouraging us to illustrate electro-convective instability. We have now added a sub-section. While this has undoubtedly strengthened the paper, we emphasize that the major claim of this paper is the utility of the Dirichlet-to-Neumann transformation. We have amply exhibited this with multiple examples.
\end{document}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,128
|
The 2011 Scottish Challenge Cup final was played between Queen of the South and Ross County at McDiarmid Park, Perth. Ross County won 2–0. The game had been postponed from November to April due to inclement weather.
Queen of the South beat Peterhead 2–1 in their semi-final and Ross County beat Partick Thistle 4–3 on penalties after their semi-final ended at 2–2.
Appearances in previous finals
Queen of the South have appeared in the final twice before, winning the 2002 final 2–0 against Brechin City, but losing the 1997 final 1–0 to Falkirk. Ross County have appeared in three Challenge Cup finals to date, defeating Clyde on penalties in the 2006 final but losing the 2004 final to Falkirk, and the 2008 final to Airdrie United on penalties.
Both teams have recently appeared in the Scottish Cup final. Queens were beaten 3–2 in 2008 Scottish Cup final by Rangers. County were beaten 3–0 by Dundee United two years later in the 2010 Scottish Cup final.
Postponement
The game was originally scheduled to be played on 28 November 2010. However the game was postponed at noon the day before the game after consultation with police voicing concerns over weather conditions particularly on the A9. Due to the Scottish football referee strike, the original fixture was scheduled to be officiated by foreign officials. The revised final date was 10 April 2011.
TV coverage
The match was televised live on BBC Alba.
Match summary
The game was played in unseasonally warm conditions with bright sunshine and a good natured atmosphere generated by both sets of fans. An early goal gave County a dream start but it was a nightmare for Queens and in particular goalkeeper David Hutton. Asked to deal with a routine passback by Queens captain David Lilley, a combination or poor decision making and poor ball control on Hutton's part allowed Andrew Barrowman to exert pressure and dispossess him. Barrowman easily rolled the ball into the empty net from one yard in the eighth minute to make the score 1–0 against his former club.
Queens only exerted pressure in the five-minute period leading up to County's second goal when they forced goalmouth scrambles. However, a swift County counterattack led to a ball from the right wing, with Iain Vigurs scoring from close range in 39 minutes to make it 2–0.
County were deserved winners without having to exert themselves against a Queens side who were easily second best in all departments and short of ideas other than aiming long balls at Derek Holmes.
Match Details
Road to the final
References
2011
Ross County F.C. matches
Queen of the South F.C. matches
Final
Finals
Sport in Perth, Scotland
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 316
|
Carl Johan Dyfverman kan syfta på:
* Carl Johan Dyfverman (konstnär) (1844–1892), svensk skulptör
Carl Johan Dyfverman (lantmätare) (1908–1995), svensk lantmätare
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,859
|
import { SearchMeta } from "v2/Apps/Search/Components/SearchMeta"
import { MockBoot } from "v2/DevTools"
import { mount } from "enzyme"
import { Link, Title } from "react-head"
jest.mock("sharify", () => ({
data: {
APP_URL: "test-url",
},
}))
describe("Meta tags", () => {
const getWrapper = () => {
return mount(
<MockBoot>
<SearchMeta term="cats" />
</MockBoot>
)
}
it("includes the proper title", () => {
const component = getWrapper()
const title = component.find(Title)
expect(title.at(0).text()).toContain("Search Results for 'cats' | Artsy")
})
it("includes the proper url", () => {
const component = getWrapper()
const link = component.find(Link).at(0).html()
expect(link).toEqual(
'<link rel="canonical" href="test-url/search?term=cats">'
)
})
})
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,479
|
Q: Chat + feed multicolumn I was wondering if it wouldn't be better to have an OPTION to put the tag feed in its own column on the same page.
The page is readable even with two columns. Maybe the feed could be pushed under the chat users in the room.
Only 1% of users still use resolutions below 1024*800. So room shouldn't be the issue.
A: Since there's now the option to send new feed items into a dedicated ticker area, I consider this status-completed, even if the problem was solved without adding another column (which, as [insert Welbog's name of the day here] pointed out correctly, would be a screen space real estate issue).
A: You can mute the feed user and use a plugin for your browser which shows the RSS feed separately. But maybe one of our greasemonkey-magicians will come up with an easier solution
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,516
|
{"url":"http:\/\/danielimms.blogspot.com\/2013\/10\/greatest-common-divisor-gcd-with-working.html","text":"Wednesday, 9 October 2013\n\n# Greatest common divisor (GCD) with working\n\nThe one thing I hated about maths in school and university was the fact that I had to show my working. Of course I knew that it helped the marker see that you understood the problem, but I just found it incredibly tedious. Particularly when I knew the answer right after reading the question.\n\nI recall back in university I was asked many times to find the greatest common divisor (GCD) of two integers using Euclid's algorithm. This is basically the exact situation I described above, you can work out the greatest common divisor in your head fairly easily with a smallish number but to actually show your working can take a quite a bit of writing.\n\nFind the greatest common divisor of 108 and 30\n\n108 = 30 x 3 + 18\n30 = 18 x 1 + 12\n18 = 12 x 1 + 6\n12 = 6 x 2 + 0\n^\n\ngcd(108, 30) = 6\n\n\nSo after doing it a couple of times I went ahead and spent a few minutes writing a little program that solved the problem with working shown. I lost the original source but have reproduced it for a little fun. :)\n\n## Code\n\nView on GitHub\n\npublic static int gcd(int a, int b) {\nint dividend;\nint divisor = (a > b ? a : b);\nint quotient;\nint remainder = (a < b ? a : b);\n\nSystem.out.format(\"Find gcd(%d, %d)\\n\", a, b);\n\ndo {\ndividend = divisor;\ndivisor = remainder;\n\nquotient = dividend \/ divisor;\nremainder = dividend % divisor;\n\nSystem.out.format(\n\"%d = %d x %d + %d\\n\",\ndividend, divisor, quotient, remainder);\n} while (remainder != 0);\n\nSystem.out.format(\n\"\\ngcd(%d, %d) = %d\\n\\n\",\na, b, divisor);\n\nreturn divisor;\n}","date":"2022-11-30 23:58:27","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\": 1, \"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\": 0.4805215299129486, \"perplexity\": 868.2081791982229}, \"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-2022-49\/segments\/1669446710777.20\/warc\/CC-MAIN-20221130225142-20221201015142-00472.warc.gz\"}"}
| null | null |
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\centerline{{\titlefont An exercise in ``anhomomorphic logic''}\footnote
{$^{^{\displaystyle\star}}$}%
{To appear in a special volume of {\it Journal of Physics}, edited by
L. Diosi, H-T Elze, and G. Vitiello, and devoted to the
Proceedings of the DICE2006 meeting,
held September 2006, in Piombino, Italia.
\eprint{arxiv quant-ph/0703276}}}
\bigskip
\singlespace
\author{Rafael D. Sorkin}
\address
{Perimeter Institute, 31 Caroline Street North, Waterloo ON, N2L 2Y5 Canada}
\furtheraddress
{Department of Physics, Syracuse University, Syracuse, NY 13244-1130, U.S.A.}
\email{sorkin@physics.syr.edu}
\AbstractBegins
A classical logic exhibits a threefold inner structure comprising
an algebra of propositions $\EA$,
a space of ``truth values'' $V$, and
a distinguished family of mappings $\f$
from propositions to truth values.
Classically $\EA$ is a Boolean algebra, $V=\Integers_2$, and the admissible maps
$\f:\EA\to\Integers_2$ are {\it homomorphisms}. If one admits a larger set of
maps, one obtains an anhomomorphic logic that seems better suited to
quantal reality (and the needs of quantum gravity). I explain these
ideas and illustrate them with three simple examples.
\AbstractEnds
\sesquispace
\vskip -30pt
\section{}
From a certain point of view, the phrase ``classical logic'' should be
used in the plural, not the singular, because the things with which
logic deals depend on the ``domain of discourse'', and this can vary
both with time and with the ``system'' one has in mind.
To each such domain corresponds
its own {\it Boolean algebra}, namely the
algebra $\EA$ of all ``questions'' one may ask about the
system.\footnote{$^{1}$}
{Instead of ``question'' one also says ``predicate'', ``proposition'' or
``event''. I will use these terms interchangeably, and will sometimes
refer to $\EA$ as the ``event algebra'', for lack of a better term.}
But a domain of questions
together with
rules for combining them via {\it and},
{\it xor}, {\it not}, etc, is not all there is to a logic.
In addition, one has the space of ``answers''\footnote{$^{2}$}
{also called ``truth values''.}
that a question may have, which classically is
$\Integers_2=\braces{0,1}=\braces{false,true}$.
And one has also the space of allowed ``answering maps'' $\f:\EA\to\Integers_2$,
which classically coincides with the space of {\it homomorphisms} from the
algebra $\EA$ to the algebra $\Integers_2$.
To provide such a $\f$
(which I will refer to as a {\it co-event} since it takes events to scalars)
is to answer every conceivable question in $\EA$,
and consequently to give as full a description of
the corresponding reality as is classically possible.
Seen in this way, logic has a threefold character, and one might
think to generalize the classical setup by altering any one of its
basic ingredients:
the algebra of propositions $\EA$,
the space of truth-values $\Integers_2$, or
the possible maps $\f$.
I have proposed elsewhere [1]
that the paradoxical features of the quantum world can be understood if
one fastens on the last of these three possibilities,
modifying the
nature of the
co-events
without
disturbing either
the space of truth-values
or
the Boolean character of
the
event algebra
$\EA$.
The change wrought by
such a modification
can be thought of in different ways.
One might say that
reality
remains what
it was
for classical logic
(namely an individual ``history'', in the sense of a collection of
particle worldlines, for example\footnote{$^{3}$}
{I am emphatically adopting a ``histories standpoint'', according
to which reality has a ``spacetime'' nature, not a ``spatial'' one.}),
but
one accepts that
it
will sometimes
manifest
contradictory attributes;
or one might say
(less provocatively?)
that the
conception of reality is no longer that of an individual history,
but rather of a ``non-classical'' co-event $\f:\EA\to\Integers_2$.
By terming $\f$ ``non-classical'',
I merely mean that it is no longer required to be a homomorphism.
According to classical logic, the truth or falsity of a
compound proposition $P$ like `$A$ or $B$' is unambiguously determined by
the truth or falsity of its individual constituents. In algebraic
language, if we know $\f(A_i)$ for all the constituents $A_i$
then we also know
$\f(P)$, and the rules for deriving $\f(P)$ from the $\f(A_i)$ say
precisely that $\f$ is a homomorphism of $\EA$ into $\Integers_2$.
In the type of generalization proposed in [1], this is no
longer the case.
One may therefore call such a generalized logic
``anhomomorphic''.
(The name ``quantal logic'' would also
be suitable were it not
already in use for a different sort of structural modification
that replaces
$\EA$
by the collection of subspaces of a Hilbert space,
which is a lattice but
not an algebra at all in the strict sense.\footnote{$^{4}$}
{One might ask with what ``quantum logic'' replaces the other two
logical ingredients, the space of truth-values and the homomorphism
$\f$. As far as I know, this question has never been answered, and
therefore no definite picture of reality has been given. Instead, one
has focused on maps from the lattice to the unit interval that
generalize the classical idea of {\it probability}, rather than that of
truth.})
By relaxing the demand that a possible coevent be a homomorphism, one can
accommodate contradictions such as that
of the Kochen-Specker gedankenexperiment,
but of course one needs to limit the coevents in some other manner in
order to arrive at a meaningful logical framework.
Otherwise one would be unable to infer the truth or falsity of any
statement about the world from that of any others,
and
theoretical predictions would become impossible.
What condition, then, should replace the requirement that co-events be
homomorphisms? But first, why do we need to replace it at all?
The reason, as explained in [1], is that we are assuming that
all dynamical truths can be deduced from the {\it preclusion} of certain
events $A\in\EA$, expressed symbolically as $\f(A)=0$.
Among these events are all those for which
$\mu(A)=0$, where $\mu$ is the ``quantal measure''
furnished by the path integral
(see [1]).
For example in
a diffraction experiment with silver atoms,
the event of the atom going to a dark
part of the interference pattern is precluded.
But in combination with the classical laws of inference
this preclusion rule is too powerful.
It ends up denying events that clearly do happen.
In order to accept all the preclusions furnished by quantum theory,
we must therefore give up some of the laws of classical logic.
But in doing so, it is natural
to be guided by the idea that $\f$ should remain as close to
being a homomorphism as it can.
The conditions explored briefly in [1] arose in this manner.
They dealt well with several of the simplest paradoxes, and they had the
virtue of reproducing classical logic when the pattern of preclusions
was classical, but it appears that they are still too restrictive
(specifically in connection with 4-slit diffraction [2]).
In this
paper, I will propose
a modified
set of rules, motivated by
the same underlying ideas, and then illustrate the resulting logical scheme by
working out
some
simple examples.
In fact I will describe two different
schemes,
both of which seem so far to be viable.
In proposing them, I am not trying to claim that either of the
new
schemes
will prove to be the last word. Rather, I feel that further
experimentation with the rules will have to precede any definitive
formulation. What I hope will prove to be lasting is the insight that
an ``objective'' interpretation of quantum mechanics can be founded on
the concept of preclusion,
provided that one generalizes one's conception
of reality by admitting anhomomorphic co-events into one's logic.
Before turning to the specific schemes, let us look at the question in a
somewhat different way. The problem we are faced with can be seen as a
clash between two ``tendencies of nature''.
On the one hand, events $E$ of very small measure $\mu(E)$ tend
not to happen. (This is one way to think about probability as a
``propensity'', in the classical case.) On the other hand, nature tends
to avoid ``contradictions'' among the events, which we can express
mathematically by saying that nature
favors
coevents
$\f:\EA\to\Integers_2$ that preserve the logical operations $and$, $not$,
etc.\footnote{$^{5}$}
{One could also express this by saying that nature tends to
observe
the
``laws of inference'' of classical logic. In the type of scheme I am
proposing,
there will in general be no universal laws of inference, but
only concrete inferential relationships that depend on which
system (and ``initial conditions'') one is dealing with.}
(This could seem an aesthetic requirement, since a map between two
algebras is ``most naturally a homomorphism''.)
Without seeking a deeper understanding of these two tendencies, we can
just accept them and ask what types of possible realities (as co-events)
they point to, given that the two tendencies oppose each other to some
extent.
If the above viewpoint is valid, then
the coevent $\f$ that actually
occurs
(i.e. the coevent that describes what actually happens)
results in part from a balancing of two opposite
tendencies. How this balancing takes place is something we know only in
part. But to the extent that we can guess the full scheme, we can
determine which coevents are possible and which are not (or are at least
``almost forbidden''). To do so would be to complete the path-integral
formalism (which defines $\mu$) by producing a predictive dynamical
scheme free of reference to ``external observers''.
(One might hope to go still farther by formulating the dynamical laws
directly in terms of the coevent itself, without referring to $\mu$ at
all; but no road toward that goal is discernible at present.)
To help us in our ``balancing act'', we have several guides. The
recovery of classical logic in the
classical limit (and ultimately of probability) is one such guide.
Another is the need to deal
adequately with ``product systems'', and still others are the need to
furnish a realistic account of what happens in a measurement and to
respect ``relativistic causality''. However, the best single source of
inspiration may be the ``quantal antinomies'', by which I mean the
paradoxical experiments and thought experiments that illustrate why it
is so difficult to come up with a satisfying interpretation of the
quantal formalism. These include the EPRB experiment, where
probabilistic correlations play a role, but there are other examples
in which
logic alone leads to the paradox, and the latter offer easier starting
points for exploring a scheme of ``anhomomorphic logic'' such as I am
proposing.
Before I propose any specific scheme, it would be a good idea to pause
to discuss the mathematical structures of $\EA$, with respect to
which the notion of homomorphism acquires a meaning. We will also need
to refer to some of the mathematical structures possessed by the space of
coevents, i.e. by the space of functions from $\EA$ to $\Integers_2$.
(I will call this space $\CE$ for lack of a better symbol.)
In the background of both the older and newer schemes is a space
$\Om$ of ``histories'' and a {\it quantal measure} $\mu$ or {\it
decoherence functional} $D$ on that space. For brevity, I will
not describe
any of this
in further detail,
referring
the reader to [1] (and references therein) for more explanation.
I will call $\Om$ the {\it sample space},
and its elements ``formal trajectories''
(by analogy with the case where
$\gamma\in\Om$ is a set of particle worldlines).
And for simplicity I will
always take $\Om$ to be finite.
On an ``extensional'' view, the event algebra $\EA$ is simply
(given that $\Om$ is finite) the collection of all subsets of
$\Om$. (So an element $A\in\EA$ is just a subset of $\Om$;
``intensionally'' it is the corresponding ``predicate'' or potential
``property of reality''.)
As such it supports a multitude of operations
that make it, among other things, a poset, a distributive lattice with
complement, a ring, and an algebra over the finite field $\Integers_2$. It is a
poset\footnote{$^{6}$}
{partially ordered set}
in an obvious way, with respect to the ordering given by set
inclusion. It is a lattice with respect to the operations of
intersection and union. (Indeed a lattice is a special case of a poset.)
And it becomes a ring if one interprets the product `$AB$' as `$A\cap B$'
and the sum `$A+B$' as
the symmetric difference `$A\less B \cup B\less A$'.
(Logically, `$AB$' is `$A \and B$', while `$A+B$' is `$A \xor B$' [$\xor$ being
``exclusive or''].)
The fact that $A+A=0$ makes $\EA$ not only a ring
but an algebra over the finite field $\Integers_2$, and the fact that $AA=A$
makes it a Boolean algebra.
Notice
in particular that with these definitions, $\EA$ is a vector space over $\Integers_2$,
which is something that could not have been deduced merely from the fact
that it is a lattice with respect to ``and'' and ``or''.
This is also a good place to point out that the
space $\CE$ of co-events $\f$ is also an algebra
(in fact a Boolean algebra once again),
simply because it is a function-space,
and one can
define addition and multiplication pointwise:
$(\f_1 \f_2)(A)=\f_1(A) \; \f_2(A)$
and
$(\f_1 + \f_2)(A)=\f_1(A) + \f_2(A)$.
The variety of ways in which we can conceive of $\EA$ engenders a
corresponding variety of notions of what it means for
a function $\f:\EA\to\Integers_2$
to be a homomorphism. All these definitions agree when $\f$
actually is a homomorphism, but when it deviates from being so, they can
give rise to different ways to judge by how much it has deviated.
This is one source of ambiguity in how best to balance ``preclusivity''
against ``homomorphicity''.
I will call a coevent $\f$
{\it preclusive} if it maps every precluded event $A$ to zero (= false),
and ``homomorphic'' if it preserves the logical operations,
or equivalently if
it preserves algebraic sum and product (and $\f(1)\ideq\f(\Om)=1$).
As explained in [1], it cannot
in general do both at once. In the schemes to be discussed, $\f$ will
be strictly preclusive,\footnote{$^{7}$}
{It seems harder to relax preclusivity in a controlled way than homomorphicity.}
so it will of necessity be anhomomorphic.
The question then becomes in what sense $\f$ can remain ``close'' to a
homomorphism without being literally so.
In the scheme proposed in [1]
(call it the ``linear scheme''),
the algebraic aspect of $\EA$'s
structure was taken as primary, meaning that preservation of sum
(linearity) and of product (``multiplicativity'') were the criteria for
it to be homomorphic. Linearity was retained exactly, but
multiplicativity was dropped. In place of the latter, $\f$ was to be
unital\footnote{$^{8}$}
{That $\f$ is unital says merely that $\f(1)=1$. For a homomorphism
this is automatic except for the trivial $\f$ that vanishes identically:
$\f=0$. With events $A\in\EA$ construed as questions, the event
$1=\Om\in\EA$ asks ``Does anything at all happen?'', and $\f$ is unital
iff it answers ``Yes'' to this question.
}
and {\it ``minimal''}. And of course it was to be {\it preclusive}, as we
are assuming always.
The word minimal here refers to the support of $\f$, which I will
define in a moment. One says that $\f$ is minimal if there is no
(preclusive, linear)
$\f$ with smaller support. For linear $\f$,
$\f$ is homomorphic iff its support is a single element of $\Om$.
Thus
one may claim that the smaller its support, the more nearly homomorphic
$\f$ is.
(The minimal such $\f$ also {\it generate} --- i.e. they span --- the
whole vector space of linear preclusive coevents.)
In order to define support, we need some more notation.
For $\gamma\in\Om$ a formal trajectory, let $\gamma^*:\EA\to\Integers_2$ be the
``containment'' map defined by
$\gamma^*(A)=1$ if $\gamma\in A$,
$\gamma^*(A)=0$ if $\gamma\notin A$.
(Instead of thinking of $\gamma$ as an element of $\Om$ one can think of
it as an
element of $\EA$ by identifying it with the
singleton set $\braces{\gamma}$.
As such it is what is called an {\it atom}
of $\EA$, meaning a
minimal element when $\EA$ is regarded as a lattice.
Algebraically, $x$ is an atom if for all $y$, $xy$ is either $0$ or $x$
itself.
In general it simplifies the notation to identify $\gamma$ with
the corresponding atom $\braces{\gamma}$,
and I will normally do so in the sequel.)
It is easy to verify that $\gamma^*$ is a unital homomorphism of $\EA$
onto $\Integers_2$. (It thus may be called a ``classical coevent''.)
In particular it is linear.
Moreover the $\gamma^*$ are a basis for the space ${\cal L}(\EA,\Integers_2)$ of
linear transformations from $\EA$ into $\Integers_2$. Thus every
$\f\in{\cal{L}}(\EA,\Integers_2)$
decomposes uniquely as a sum of the form
$$
\f = \sum_{\gamma\in S} \gamma^* \ ,
$$
where $S$ is some subset of $\Om$ that one may refer to as the {\it
support} of $\f$, $\mathop {\rm supp }\nolimits(\f)$.
More generally, any mapping $\f$ of $\EA$ into $\Integers_2$ whatsoever can be
expressed as a polynomial in the classical coevents $\gamma^*$ for
$\gamma\in\Om$.\footnote{$^{9}$}
{This leads to a useful graphical notation in which,
for $x,y,z\in\Om$,
$\Star{x}$ is represented as a vertex or 0-simplex,
$\Star{x}\Star{y}$ is an edge or 1-simplex,
$\Star{x}\Star{y}\Star{z}$ is a 2-simplex,
etc.
For $\f$ represented in this way and $A\subseteq\Om$, $\f(A)=1$ iff $A$
contains an odd number of such simplices.}
One may thus extend the notion of support by defining $\mathop {\rm supp }\nolimits(\f)$ to be
the set of all $\Star{\gamma}$ occurring in the polynomial.
The two schemes we will explore below are related in opposite ways to
the linear scheme.
In both of them reality can be
identified with a single\footnote{$^{10}$}
{Here I'm imagining that $\EA$ includes all possible predicates,
including ones pertaining to happenings arbitrarily far in the future
(or past). If this is not the case, then one will need to consider
more than just a single event-algebra $\EA$. There will then be a
coevent for each $\EA$ together with coherence conditions among
these ``partial coevents''.
Furthermore, a coevent which is ``minimal'' with respect to one
such $\EA$ can fail to remain so when restricted to a subalgebra. This
can lead to a kind of ``premonition'' phenomenon that shows up, for
example, in the Hardy gedankenexperiment discussed in [1].}
coevent $\f\in\Star{\EA}$.
As stated already, $\f$ will be preclusive
in both schemes ($\mu(A)=0\Rightarrow\f(A)=0$),
but anhomomorphic.
The first of the two schemes
will be in a sense complementary to the linear scheme.
Rather than preserving sum it will preserve product (so I'll call it the
``multiplicative scheme'').
The second scheme will
be a kind of augmented linear scheme, but it will
preserve strictly neither sum nor product.
For reasons that will become clear, I'll call it the ``ideal-based
scheme''. Since the multiplicative scheme is easier to define, let's
begin with it.
In this scheme, $\f$ preserves the product, $AB$, which in logical terms
means that it preserves conjunction, `$and$'.
Let us also exclude the trivial multiplicative coevents
$\f=1$ and $\f=0.$
The
axioms for the multiplicative scheme will then include:
\noindent \qquad $(i) \quad \f \not= 0, \, 1$
\noindent \qquad $(ii) \quad (\forall A,B\in \EA) \ \f(AB)=\f(A) \f(B)$
\noindent
It is relatively easy
to work out the
general form
of such a $\f$,
by asking which events are true according to $\f$,
i.e. for which $A\in\EA$ one has $\f(A)=1$.
Suppose $A\in\EA$, $\f(A)=1$
and $A\subseteq B$.
Then, since $AB=A$, we have by multiplicativity,
$\f(A)\f(B)=\f(A)=1\Rightarrow\f(B)=1$.
Thus $\f$ is monotone: any superset of a true event is also true.
Now suppose that $A$ and $B$ are both true with respect to $\f$.
It follows immediately that they have in common some true ``subevent''
(i.e. subset) $C\subseteq A,B$;
for $A\cap B=AB$ is such a subset and $\f(AB)=\f(A)\f(B)=1\times1=1$.
By induction, there must be a smallest true event $F\in\EA$ with the
property that the other true events
coincide with
its supersets:\footnote{$^{11}$}
{We are just using the fact that $\f^{-1}(1)$ is a {\it filter},
when $\f\not=0,1$ is multiplicative.}
$$
\f(A)=1 \iff F \subseteq A \eqno(1)
$$
In this scheme, then, a coevent can be construed as a subset $F$ of
$\Om$,
and the rule (1) tells us that, with respect to a given coevent
$\f$, reality ``has the property $A$''
iff all the atoms in $F$ ``share this property''.
Since (1) is a simple generalization of the above definition of
$\Star{\gamma}$, it is natural to write it as: $\f=\Star{F}$.
One can also see that, for any $F\in\EA$,
$$
\Star{F} = \prod_{\gamma\in F} \Star{\gamma}
$$
Thus a multiplicative coevent is simply a polynomial that reduces to a
monomial (Graphically it is a single simplex),
and the support of $\f$ is $F$ itself:
$$
F = \mathop {\rm supp }\nolimits(\f) \ . \eqno(2)
$$
Finally, remember that we want $\f$ to be as nearly homomorphic as it
can be. Recalling that $\f$ would be a homomorphism
if its support were
reduced to a single atom, let us postulate that $F=\mathop {\rm supp }\nolimits{\f}$ is as
small as possible. Our final axioms for this scheme are then:
\noindent \qquad $(iii)$ no precluded $A\in\EA$ contains $F$ as a subset
\noindent \qquad $(iv)$ $F$ is minimal subject to $(iii)$
\noindent
(Axiom $(iii)$ requires that $F$ meet the complement of every precluded
subset.)
I will write $\hat{\EA}$ for the set of all coevents that satisfy these
axioms. The elements of $\hat\EA$ are thus the ``possible realities'',
or ``possible bundles of attributes of reality'', depending on how we
think about a coevent.
Now consider a two-slit diffraction experiment distilled down to a set
of four trajectories joining either of two ``apertures'', $a_1$, $a_2$
to either of two ``detector locations'' $\ell_1$, $\ell_2$.
(We don't include any actual detectors.)
Calling $s$ the source, we have
$$
\Om = \braces{sa_1\ell_1, sa_1\ell_2, sa_2\ell_1, sa_2\ell_2}
\ideq \braces{\gamma_1, \gamma_2, \gamma_3, \gamma_4} \ .
$$
Suppose that $\gamma_1$ and $\gamma_3$ interfere destructively.
To each $\gamma_i$ corresponds an amplitude $\alpha_i$
(assuming unitary quantum mechanics), and, respecting unitarity, we may
take these amplitudes to be
$$
\pmatrix{\alpha_1 & \alpha_2 \cr \alpha_3 & \alpha_4}
= {1\over \sqrt{2}}
\pmatrix{1 & 1 \cr -1 & 1}
$$
The only precluded event is then
$\gamma_1 + \gamma_3$,
which I have written using the algebraic notation introduced earlier.
(Regarded as a subset of $\Om$ this event would be
$\braces{\gamma_1,\gamma_3}$,
which, strictly speaking, should be written as
$\braces{\gamma_1} + \braces{\gamma_3}$.
But the distinction disappears
when one identifies
$\gamma_i$ with $\braces{\gamma_i}$, as we are doing.)
In order to be preclusive, $\f$ must therefore
satisfy $\f(\gamma_1+\gamma_3)=0$.
In the multiplicative scheme, $F=\f^{-1}(1)$ must not be contained
within $\gamma_1+\gamma_3$ (axiom $(iii)$).
Hence it must contain either $\gamma_2$ or $\gamma_4$.
For example, $F=\gamma_2+\gamma_3$ will do, as will
$F=\gamma_4+\gamma_1+\gamma_3$. Clearly the {\it minimal} sets of this
sort are just $\gamma_2$ and $\gamma_4$ themselves,
corresponding to the coevents
$\Star{\gamma_2}$ and $\Star{\gamma_4}$.
These two coevents are the members of $\hat\EA$,
and both are purely
classical. In each, the particle goes through a single slit and
continues on to the ``bright spot'', avoiding the ``dark spot''.
A more interesting example is three-slit diffraction, as described in
[1]. For simplicity, let's limit ourselves to three
trajectories, $a$, $b$, $c$, all meeting at a common ``detector
location'', and let the corresponding amplitudes be respectively
$1$, $1$, $-1$.
Now both $a+c$ and $b+c$
are precluded,
whence no classical coevent can be preclusive,
since $a+c$ and $b+c$ together cover all of $\Om$.~\footnote{$^{12}$}
{Proving this by computation provides good practice in the algebraic
notation (even though the
set-theoretic notation happens to be considerably simpler in this case).
We have in general $X\cup Y=X+Y+XY$. Hence
$(a+c)\cup(b+c)$ = $(a+c)+(b+c)+(a+c)(b+c)$ = $a+b+2c+ab+ac+cb+c^2$
= $a+b+0+0+0+0+c$ = $a+b+c=\Om$.}
Classical logic leads to an impasse in this case.
In the multiplicative scheme,
$F=\f^{-1}(1)=\mathop {\rm supp }\nolimits(\f)$
must contain both $a$ and $b$ in order to avoid falling within either
$a+c$ or $b+c$.
The only possibilities are $F=a+b$ and $F=a+b+c$,
of which only the former is minimal.
Hence $\hat\EA$ contains a single coevent in this example, namely
$\f=\Star{(a+b)}=\Star{a}\Star{b}$;
and for it,
$\f(a)= \f(b)= \f(c)= \f(a+c)= \f(b+c)=0$, \
$\f(a+b)= \f(a+b+c)=1$.
Thus for example,
the answer to ``Does the particle go through slit $a$?'' is ``No'',
but
the answer to ``Does it go through {\it some} slit?'' is ``Yes''.
(One could perhaps imagine these questions in terms of idealized
``observations'' that discover no more or less than the question asked
for;
but of course it would be wrong to identify such ``observations''
with any ordinary physical operations except in very special cases.)
In this example, the important thing to notice is that there {\it is} a
viable coevent --- only one in this case, but nevertheless enough to
avoid the untenable conclusion that classical logic would have reached.
As a final example, consider one that figured heavily in an earlier
interpretation of the path-integral [3].
Here we have two variables $A$ and $B$, each of which can take only the
value $+1$ or $-1$. If we write $A$ for the event that $A=1$ and
${\bar{A}}$ for the event that $A=-1$,
and similarly for $B$, then our four-element sample space can be written
as
$$
\Om = AB + A{\bar{B}} + {\bar{A}} B + {\bar{A}} {\bar{B}} \ .
$$
Assume that $A$ and $B$ are perfectly correlated, in the
dynamical
sense that
$\mu(A{\bar{B}})=\mu({\bar{A}} B)=0$.
From this it follows as well that $\mu(A+B)=\mu( A{\bar{B}} +{\bar{A}} B)=0$,
assuming that $\mu$ is strongly positive.\footnote{$^{13}$}
{Strong positivity of the decoherence functional, as defined in
[4], holds automatically in
unitary quantum mechanics. Via an analog of the Schwarz inequality,
it implies $\mu(A\cup N)=\mu(A)$ whenever
$N$ has measure zero and is disjoint from $A$.}
So our precluded events are
$A{\bar{B}}$, ${\bar{A}} B$, and $A+B$.
(Notice that $A+B$ is the event
that $A$ and $B$ are {\it anti}-correlated.)
With our sample space of 4 elements, we have
$|\Om|=4$,
$|\EA|=2^{|\Om|}=16$,
$|\Star{\EA}|=2^{|\EA|}=65536$,
where $|\cdot|$ denotes cardinality.
Of these 65 thousand or so coevents,
sixteen are multiplicative,
since there are $2^4=16$ subsets of $\Om$
to play the role of $F=\mathop {\rm supp }\nolimits(\f)$.
Which of these sixteen coevents
are preclusive, and which of the preclusive ones are minimal?
Reasoning as before, we see that $F$ must contain either $AB$ or
${\bar{A}}{\bar{B}}$. But $\f=\Star{(AB)}$ is already preclusive, as is
$\f=\Star{({\bar{A}}{\bar{B}})}$. Hence these are the only minimal preclusive
multiplicative coevents. Once again, we've reached the classical
solution:
$$
\hat\EA = \braces{\Star{(AB)},\Star{({\bar{A}}{\bar{B}})}} \ .
$$
Indeed this had to happen, because the pattern of preclusions was
classical in the sense that it could have arisen from a classical
probability-measure $\mu$. Equivalently, every subset of a precluded
set
was
also precluded. One can prove that when this happens the minimal
$\f$ are just the classical coevents $\Star{\gamma}$, for non-precluded
$\gamma$. Hence the multiplicative scheme, like the linear one,
reproduces classical logic when quantal interference is absent.
Although this example of ``$A$-$B$-correlations'' turned out to be
fairly trivial in the end, it is important because it illustrates how
``anhomomorphic inference'' works. Classically we can conclude from
``$A+B$ is false'' that exactly one of $AB$, ${\bar{A}}{\bar{B}}$ is true.
Consequently, if $A$ is true then $B$ must be true and ${\bar{B}}$ false
(together with ${\bar{A}}$).
None of these deductions is guaranteed a priori in anhomomorphic
logic. But our analysis of the above example shows that if not only
$A+B$, but also ${\bar{A}} B$ and $A{\bar{B}}$ are false
(which classically would have followed from $A+B$ false),
then classical logic does apply,
whence the truth of $A$ does imply that of $B$ and conversely.
[proof: if $\f(A)=1$ then $\f$ cannot be $\Star{({\bar{A}}{\bar{B}})}$ because
$\Star{({\bar{A}}{\bar{B}})}(A)=0$ since ${\bar{A}}{\bar{B}}\not\subseteq A$. Hence
$\f=\Star{(AB)}$ (the only other possibility in $\hat\EA$), whence
$\f(B)=1$ and $\f({\bar{A}})=\f({\bar{B}})=0$.]
Finally, let's turn briefly to the ``ideal-based'' scheme that
generalizes the linear scheme of [1]. For lack of space, I
will only sketch this scheme and its application to the above examples.
Its advantage is its greater flexibility and generality, but its
disadvantage is that it is harder to state. The basic idea is that $\f$
should be preclusive (as always), and that the members of $\hat\EA$
should be the ``simplest'' that suffice to generate $\Star{\EA}_0$ as an
ideal.\footnote{$^{14}$}
{An ideal in an algebra is a linear subspace of the algebra which is
closed under multiplication by arbitrary algebra elements.
A subset $S$ of an ideal $I$ generates it if $I$ is the smallest ideal
including $S$. It is not difficult to verify that the preclusive
coevents form an ideal.}
Here $\Star{\EA}_0$ denotes the ideal of all preclusive coevents, and
``simple'' is yet another word meaning ``close to homomorphic''.
In the present context it seems best to interpret ``simplicity''
not in terms of the support of $\f$,
but rather in terms of --- say ---
the number of {\it operations}
needed to build up $\f$ as a polynomial $p$ in the classical coevents.
Thus defined, simplicity is measured by the sum of the degrees of the
monomials whose sum is $p$. The smaller is this sum, the ``simpler''
is $\f$.
We then want to take for $\hat\EA$ the generating set of ``maximum
simplicity'', or perhaps just the unital members of this set.
(In detail, there will be different ways to compare the simplicity of
coevents and sets of coevents;
in addition it could happen that the simplest generating set was not
unique. None of these potential ambiguities surfaces in any of our
three examples.)
Applying the ideal-based scheme
to our three examples, we find the following (limiting ourselves to
the generators that are unital):
\noindent\qquad {\it 2-slit}: $\hat\EA$ = same as above.\footnote{$^{15}$}
{There is also a non-classical generator, $\Star{a}+\Star{b}$, but it's not unital.}
\noindent\qquad {\it 3-slit}:
$\hat\EA = \braces{\Star{a}+\Star{b}+\Star{c}, \Star{a}\Star{b}}$
\noindent\qquad $A$-$B$-{\it correlations}: $\hat\EA$ = same as above
\noindent
Thus in these examples, the ideal-based scheme differs from the multiplicative
scheme only in the three-slit example, where it yields
a second coevent,
namely the unique coevent produced by the linear scheme of
[1].
With respect to this coevent, $a$, $b$ and $c$ all become true, while $a+b$
becomes false.
One pleasant feature of the ideal-based scheme is that (as one can
prove) if an event $A\in\EA$ is not precluded then there exists
$\f\in\hat{\EA}$ for which $A$ happens ($\f(A)=1$).
\noindent {\csmc Remark \ }
Notice that anhomomorphic logic shifts the emphasis from
individual histories $\gamma\in\Om$
to the
algebra of predicates $\EA$.
This shift could seem like a retreat from
reality, but it
is perhaps natural from a
``dialectical'' starting point that takes the whole as prior to its
parts.
To ``unexamined materialism'', reality is simply a single history
$\gamma\in\Om$, what I called earlier a ``formal trajectory''. Yet such
an element only begins to take shape when we subdivide the whole into
its (spatio-temporally separated) parts. To the extent that the
subdivision remains to be completed, as it always must, we recognize
only a ``coarse-grained world'' corresponding to the subalgebra of
$\EA$ generated by the coarse-grained variables.
Perhaps such musings lend a greater ``dignity'' to the elements of
$\EA$, as being in some sense logically prior to those of $\Om$.
Anhomomorphic logic is also ``dialectical'' in a second, more obvious
sense: it ``admits contradictions''.
\bigskip
\noindent
It's a pleasure to thank Fay Dowker and Yousef Ghazi-Tabatabai for
providing some key examples that helped give birth to the multiplicative
and ideal-based schemes.
Research at Perimeter Institute for Theoretical Physics is supported in
part by the Government of Canada through NSERC and by the Province of
Ontario through MRI.
This research was partly supported
by NSF grant PHY-0404646.
\ReferencesBegin
\reference [1]
Rafael D. Sorkin,
``Quantum dynamics without the wave function''
\journaldata{J. Phys. A: Math. Theor.}{40}{3207-3221}{2007}
(http://stacks.iop.org/1751-8121/40/3207)
\eprint{quant-ph/0610204}
http://physics.syr.edu/~sorkin/some.papers/
\reference [2] Yousef Ghazi-Tabatabai (unpublished)
\reference [3]
Rafael D.~Sorkin,
``Quantum Measure Theory and its Interpretation'',
in
{\it Quantum Classical Correspondence: Proceedings of the $4^{\rm th}$
Drexel Symposium on Quantum Nonintegrability},
held Philadelphia, September 8-11, 1994,
edited by D.H.~Feng and B-L~Hu,
pages 229--251
(International Press, Cambridge Mass. 1997)
\eprint{gr-qc/9507057}
\reference [4]
Xavier Martin, Denjoe O'Connor and Rafael D.~Sorkin,
``The Random Walk in Generalized Quantum Theory''
\journaldata {Phys. Rev.~D} {71} {024029} {2005}
\eprint{gr-qc/0403085}
\end
(prog1 'now-outlining
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;"\\\\reference....."
"\\\\end...."))
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Q: PHP hangs at uncompressing a GZipped file? I am uncompressing a .gz-file and putting the output into tar with php.
My code looks like
$tar = proc_open('tar -xvf -', array(0 => array('pipe', 'r'), 1 => array('pipe', 'w'), 2 => array('pipe', 'a')), &$pipes);
$datalen = filesize('archive.tar.gz');
$datapos = 0;
$data = gzopen('archive.tar.gz', 'rb');
while (!gzeof($data))
{
$step = 512;
fwrite($pipes[0], gzread($data, $step));
$datapos += $step;
}
gzclose($data);
proc_close($tar);
It works great (tar extracts a couple directories and files) until a bit more than halfway in (according to my $datapos) the compressed file, then the script will get stuck at the fwrite($pipes...) line forever (i waited a few minutes for it to advance).
The compressed archive is 8425648 bytes (8.1M) large, the uncompressed archive is 36720640 bytes (36M) large.
What am I possibly doing wrong here, since I havn't found any resources considering a similar issue?
I'm running php5-cli version 5.3.3-7+squeeze3 (with Suhosin 0.9.32.1) on a 2.6.32-5-amd64 linux machine.
A: 1 => array('pipe', 'w')
You have tar giving you data (file names) on stdout. You should empty that buffer. (I normally just read it.)
You can also send it to a file so you don't have to deal with it.
1 => array('file', '[file for filelist output]', 'a')
if you're on Linux, I like to do
1 => array('file', '/dev/null', 'a')
[Edit: Once it outputs enough, it'll wait for you to read from standard out, which is where you are hanging.]
A: Your problem is one of buffer, like @EPB said. Empty the stream buffer (e.g.: using fread on $pipes[1] in non-blocking mode; or simply remove the v switch).
I want to point out however, that $datalen will contain the compressed length of the data, while $datapos will contain the uncompressed one, because the $step passed to gzread is the uncompressed length to read in bytes. If you want to populate $datalen with the actual uncompressed archive size, use something like this:
$info = shell_exec('gzip -l archive.tar.gz');
$temp = preg_split('/\s+/', $info);
$datalen = $temp[6]; // the actual uncompressed filesize
Otherwise you'd end up with $datapos always being bigger than $datalen.
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"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,617
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{"url":"https:\/\/plainmath.net\/precalculus\/79764-for-all-x-b-in","text":"Mara Cook\n\n2022-06-26\n\nFor all $\\theta$ in $\\left[0,\\pi \/2\\right]$ I need to show that $\\mathrm{cos}\\left(\\mathrm{sin}\\theta \\right)>\\mathrm{sin}\\left(\\mathrm{cos}\\theta \\right)$\n\npheniankang\n\nExpert\n\nOver $I=\\left[0,\\frac{\\pi }{2}\\right]$ we have:\n$\\mathrm{sin}\\left(\\theta \\right)+\\mathrm{cos}\\left(\\theta \\right)=\\sqrt{2}\\mathrm{sin}\\left(\\theta +\\frac{\\pi }{4}\\right)\\le \\sqrt{2}<\\frac{\\pi }{2}$\nhence:\n$\\begin{array}{}\\text{(1)}& \\mathrm{\\forall }\\theta \\in I,\\phantom{\\rule{2em}{0ex}}\\mathrm{cos}\\theta <\\frac{\\pi }{2}-\\mathrm{sin}\\theta .\\end{array}$\nThe LHS of (1) belongs to [0,1], the RHS belongs to $\\left[\\frac{\\pi }{2}-1,\\frac{\\pi }{2}\\right]$; the sine function is increasing over $\\left[0,\\frac{\\pi }{2}\\right]$, hence:\n$\\begin{array}{}\\text{(2)}& \\mathrm{\\forall }\\theta \\in I,\\phantom{\\rule{2em}{0ex}}\\mathrm{sin}\\left(\\mathrm{cos}\\theta \\right)<\\mathrm{cos}\\left(\\mathrm{sin}\\theta \\right).\\end{array}$\n\nDo you have a similar question?","date":"2023-02-01 22:49:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 35, \"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\": 0.9846760034561157, \"perplexity\": 892.2625460540999}, \"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-2023-06\/segments\/1674764499953.47\/warc\/CC-MAIN-20230201211725-20230202001725-00015.warc.gz\"}"}
| null | null |
$config.framework = "4.5.2";
$config.buildFileName = "build\default.ps1";
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,455
|
var express = require('express');
var app = express();
var port = process.env.PORT || 8080;
var mongoose = require('mongoose');
var passport = require('passport');
var flash = require('connect-flash');
var morgan = require('morgan');
var bodyParser = require('body-parser'); // pull information from HTML POST (express4)
var methodOverride = require('method-override'); // simulate DELETE and PUT (express4)
var cookieParser = require('cookie-parser');
var session = require('express-session');
var configDB = require('./config/database.js')
mongoose.connect(configDB.url);
var Todo = mongoose.model('Todo', {
text: String
});
var db = mongoose.connection;
db.on('error', console.error.bind(console, 'connection error:'));
db.once('open', function (callback) {
console.log('OpenDatabase');
});
require('./config/passport')(passport);
app.use(express.static(__dirname + '/public'));
app.use(morgan('dev'));
app.use(bodyParser.urlencoded({ 'extended': 'true' })); // parse application/x-www-form-urlencoded
app.use(bodyParser.json()); // parse application/json
app.use(bodyParser.json({ type: 'application/vnd.api+json' })); // parse application/vnd.api+json as json
app.use(methodOverride());
app.use(cookieParser());
app.use(flash());
app.set('view engine', 'ejs');
app.use(session({secret:'sessionsecretitodo'}));
app.use(passport.initialize());
app.use(passport.session());
// app.use(express.cookieParser());
require('./app/routes.js')(app,passport,Todo);
// starting server
var server = app.listen(port, function () {
console.log('App listening on port' +port);
});
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,264
|
AI-driven robotics key to recycling's challenges
Image credit: Recycleye
By James Hayes
Published Wednesday, September 15, 2021
From Coke bottles to flatscreen displays, more of the raw materials from our massing mounds of waste can now be recovered and recycled using AI-driven technologies.
China's Operation National Sword policy initiative curbed the country's imports of most types of solid waste for disposal, and imposed stringent limits on the materials that it will accept for recycling. The policy's ramifications have hugely impacted the many foreign economies that for decades relied on China's materials recovery facilities (MRFs) to deal with the bulk of their recyclable waste materials, from plastics and packaging to glass, metals, and wood.
Before National Sword came into force in 2018, 70 per cent of plastics collected in the US and 95 per cent of plastics collected in the European Union (EU) were consigned to a slow boat to China, according to the Yale School of the Environment. A study by the University of Georgia estimated that by 2030, the policy could have 'displaced' some 111 million tonnes of discarded plastic.
As other eastern nations also impose strict limits on the amount of western refuse they will accept, the waste disposal problem exporters now face has caused many to fundamentally reconsider their collection, recovery and processing strategies for recyclables. In particular, it has highlighted the essential importance of ensuring that waste for recycling is as 'pure' as possible – at least 98 per cent in some instances. This means uncontaminated by use residues (such as food deposits), unmixed with non-recyclables, and reliably sorted into same-material silos.
To this end, MRFs in Europe and North America are investing in a new-generation scalable waste-processing plant. It will combine vision-assisted robotics with cloud-based artificial intelligence (AI) back ends to fully automate the way mixed waste is processed for recycling. The last year has seen a wave of new solutions installed and enter operation.
In November 2020, Texas-based waste services specialist Waste Connections announced the deployment of 24 AI-guided robotics solutions from AMP Robotics. Norwegian waste-management firm Bjorstaddalen opened the country's first municipal AI-powered robotic waste-sorting station in April 2021, running on technology from ZenRobotics.
In the UK, Coventry City Council has contracted another AI waste-management solutions provider, Machinex, to deliver an AI-backed MRF that will be able to process some 175,000 tonnes of recyclables per year. Operated by Sherbourne Recycling, the MRF will use 14 Machinex SamurAI sorting robots and 14 optical sorters.
In France, Machinex has sold six more SamurAIs to the Veolia Group as MRFs located at Portes-lès-Valence and Bègles are upgraded.
In November 2020, Texas-based waste services specialist Waste Connections announced the deployment of 24 AI-guided robotics solutions from AMP Robotics.
Integrated into existing MRF plants as modular units, this emergent technology class employs advanced vision systems that use machine intelligence to recognise broad ranges of waste types as they are conveyed through the facility. The various waste types are then crosschecked against datasets, which identify their material and other characteristics necessary for recycling.
However, before suitable waste is near ready to become reusable, some pre-processes must occur; it has to be picked and sorted. These processes are necessary if the recovered materials are to be turned into the raw materials that can be used to make new recyclable objects, which will help turn the economic circularity many countries aim for.
For this, robotic arms are guided to separate waste fractions from the conveyor, and put them into assigned collection chutes for aggregation. The arms work fast, at rates in the range of 2,000-4,200 picks-per-hour-per-sorting bay (depending on use requirements), compared to a typical manual (or human) waste-picker rate of 200 picks per hour.
"Traditionally, waste processors relied on manual pickers to identify and sort waste," says Peter Hedley, chief technology officer at waste management start-up Recycleye. "They are exposed to a multitude of occupational hazards, which has resulted in the waste-recovery industry facing an average of 50 per cent labour turnover every six months."
'The digitisation of the flow of recyclables provides the ability to measure material streams... Materials recovery facility managers can use this data to make more-informed decisions.'
Matanya Horowitz, AMP Robotics
Compounded by China's Operation National Sword and coronavirus workplace rules, the waste recovery industry is now overstretched.
Furthermore, most waste facilities use material recovery modules that were developed up to 20 years ago. Hedley says: "Due to the changing waste composition since then, the systems are forced to operate at a reduced capacity due to the inability to effectively sort more abundant materials."
Robotic picker arms work faster and longer than their human counterparts, and can lift heavier objects. Depending on the waste type involved, robotic arms can hold and lift objects that weigh anything between 1.25kg and 30kg, according to the model capacity and gripper type (e.g. air suction or mechanical claw).
Some solutions can be configured for secondary applications, such as quality control (removing unwanted items from a single waste stream that's mostly pure) and sucking out unrecyclable materials like plastic bags and film, which can jam up plant machinery and cause stoppages.
Growing interest in the intelligent waste-management market has opened opportunities for robotic automation specialists to join with AI specialists to create integrated modular solutions. One such collaboration is factory automation specialist FANUC UK, which in April 2021 partnered with Recycleye to create a robotic waste-picking system powered by cloud-based AI that runs on Microsoft Azure.
"At the start of a new installation the vision system is installed in the MRF," says Recycleye's Hedley. "This detects the waste passing on [the existing] conveyor belts. This creates millions of images of waste, millions of data points – data points that we use to teach our AI models what waste looks like. When the system goes into full operation our datasets grow bigger and bigger, and Azure scales to get as big as our datasets are."
The AI component of intelligent waste-management applications also feed analytics dashboards than run behind the materials management operations. These capture process data that, as datasets build up, provide MRF operators with more detailed understanding of waste dynamics. AI also informs an MRF's ability to offer value-added services to clients at either end of the waste-processing supply chain.
Suppliers of waste can gain insights into what their stuff contains, and data can be fed back up the waste chain to improve recyclability at the points of collection. While many waste materials are not suitable to be recycled, some waste fractions that can be recycled have negligible resale value, and to process them into recycled raw materials could be environmentally detrimental.
AI technology's ability to reconfigure waste sorting patterns in response to materials market demand fluctuations is another way for MRFs to add value to their operations, especially in situations where specific recyclables are ultimately more likely to be bought. Key to this is the AI's ability to include new material types in its datasets, and to recognise valued materials when they are in a dirty or damaged condition, says Matanya Horowitz, founder and CEO at AMP Robotics.
"AMP Robotics' AI has to learn many different material types, and deformations – as well as customer-specific material types, which vary in terms of end-market application," he explains. "AI enables the digitisation of objects in the material stream, which opens up many applications as this technology matures. The digitisation of the flow of recyclables provides the ability to measure material streams, and then our AMP Clarity portal surfaces the data and insights that MRF managers can use to make more-informed decisions."
Horowitz adds: "For example, they can better understand how much contamination enters the facility (and from what sources), the loss of valuable materials at the point-of-residue, and whether they can drive a higher price for scrap bales based on both the quantity and the quality of material."
Robotic sorting, along with the emergence of descriptive and diagnostic analysis through stand-alone sensors, should be seen as initial applications for AI-enabled waste-management technology, according to Horowitz.
"The distribution of these sensors throughout MRFs helps them become more data-driven," he points out. "Traditionally, MRFs are centralised material hubs, but the proliferation of these sensors begins to effectively transform recovery facilities into digital information hubs."
E-waste innovation
'Disassembly line' enables valued fraction recovery for the first time
Brand-new electronic goods like flatscreen TVs and computer displays present recyclers with a longstanding dilemma. They contain valued materials that can be recovered and reused. They also contain varying amounts of noxious substances that, released into the immediate vicinity by the recycling processes, could prove harmful to MRF personnel and to organisms further afield.
Until recently, the process for recycling flat-panel displays had not changed since the start of the Waste from Electrical and Electronic Equipment (WEEE) Regulations in 2006, says Craig Thompson, CEO at UK screen-based-device recycling specialist Areera.
"Shredding [has been] the main process for recycling flat-panel displays, with hazardous chemical particles – compounds of arsenic, cadmium, lead, mercury – covering the shredder and the recovery facilities," he says. "The shredded raw materials themselves – ferrous, nonferrous and circuit boards – also cause potential hazards on the downstream processing of the materials."
Shredding yields minimal recoverable value – there's almost no market for co-mingled metal, plastics, and glass – and it's a power-hungry process that does not comply with current low-energy/low-emission standards.
Areera is tackling the problem with newly installed solutions from robotic recycling system provider FPD Recycling. Its FPD PRO 'depollution machines' integrate AI with two ABB Robotics model IRB 2600 20kg-payload robotic arms – each fitted with additional cutting unit axes – that at full capacity can dissemble and process up to 100 screens or 200 laptop PCs per hour.
Processing happens in three stations. Defunct screen-based devices are placed vertically on the in-feed conveyor belt, and moved through the container. In the first station, the object is weighed. Data is collected and the object is identified and categorised.
It then gets conveyed to the next station, where it is held in position; the first robot arm scans the object's screen and determines the processing method, and then removes the screen.
If the screen is identified as a Cold Cathode Fluorescent Lamp (CCFL) TV, for instance, it is conveyed to the next station where the second robot takes an image to identify the location of CCFLs, and then removes the mercury hazards from the chassis. The depolluted display then exits the station safe for the next process step.
The scanner also looks for a manufacturer logo if it's visible on the front panel/bezel. All the information is fed into a continually building dataset that informs future object identification. In the next implementation of FPD PRO, a barcode scanner will look for the label and record information included there – barcode/QR Code and model number, for example.
"Obtaining specifics on any plastics component is important principally because many products combine polymers with a bromine flame retardant, which is now deemed to be hazardous over a given concentration," explains Paudy O'Brien, CEO at FPD Recycling. "Identification and separation mean that the bromine-free fraction can be recovered."
Waste recognition
Branding to improve AI logo detection
Despite the superabundance of mixed waste that potentially could be recycled, gaining knowledge of its key constituent statistics is an estimable challenge. "The largest challenge for AI is the sheer variety of waste," says Peter Hedley at Recycleye.
"Waste differs by country, for instance, and as waste objects can get crushed into strange shapes, get covered in dirt or discolour. AI systems must learn to see past these eventualities to identify the item consistently."
If initiatives such as Extended Producer Responsibility (a framework that would enfold the environmental costs associated with a product throughout its life cycle into its market price) are to succeed, they need greater transparency as to who – which producer – made it.
A development of EPR that AI-enabled waste management is investigating is in encouraging producers to design packaging so that it is more AI-friendly, i.e. by developing designs that makes it easier for vision systems to recognise specific objects for their recyclability.
Such initiatives are at early stages. Both Recycleye and AMP Robotics are trialling AI/computer vision for brand-level logo detection of retail waste in real-time operation. Recycleye's algorithm was trained with plastic drinks brands Coca Cola, Pepsi, and Heineken, using 1,399 images from the internet.
An overall accuracy of 93 per cent was obtained with varying lighting conditions, damaged and partially visible objects. Recycleye reports: "With improvement, this technology can be implemented [in MRFs] to support a closed-loop system of re-use. It also provides an Extended Producer Responsibility [for] brands [to] take greater accountability for the environmental impacts of their product-end-life."
AMP Robotics is working with consumer packaged goods companies to recover higher rates of these materials used in some of their products. One of AMP Robotics' first initiative partners is beverage brand Keurig Dr Pepper (KDP) in support of its introduction of recyclable K-Cup pods. Following KDP's conversion of its coffee pods to polypropylene – a valued material for recycled plastics – the companies trained AMP Robotics' technology to more exactly identify and sort K-Cup pods, with the aim of increasing waste recovery levels.
The bigger picture: Wall-climbing robot
Goldfish learns to drive lidar-equipped vehicle
View from Brussels: Atom-smashers and gas guzzlers
Czech Republic plans to phase out coal by 2033
AI camera can sort and separate 12 types of plastic
Sustainable batteries made with cellulose offer promising performance
Robot voices emote, even with minimal training data
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,781
|
Free to retransmit: time for a new model for PSB content?
What should the relationship be between public service broadcasters (PSBs) and distribution platforms such as Sky, and how can the existing model of sharing content best be reformed? In this post, Tom Evens, Senior Researcher at Ghent University and Visiting Fellow at LSE, reflects on the 2015 consultation paper issued by the UK Department for Culture, Media and Sport (DCMS).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,407
|
No beracha is said on vitamins or medicines unless they are pleasantly flavored, in which case the beracha is shehakol. A Holeh Sheyesh Bo Sakana who has been instructed by his doctor to eat non kosher food does not say a beracha on the food. However, if the food itself is permissible but the Holeh is not permitted to eat it at this time, such as on Yom Kippur, a beracha is said. One who is forced to eat food does not say a beracha even if the food is enjoyable. Likewise, even if he ate enough bread to require him to say Birkat Hamazon, he does not say it.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,273
|
Q: Mind + Action Ing? is it correct for ask anything to someone? I read somewhere that if I want to ask or request something (very politely), I should use "Mind + Action ing...?"
*
*Like If I want to ask pen to any one.
=> Mind giving me a pen?
*If I talk to some one to please go market very politely
=> Mind going to market?
So is this a correct way to ask someone to do something very politely/respectfully?
Please clarify when I can use this. I am confused.
A: Your examples are a shortened and less formal and thus not polite. They are NOT rude, but they are simply another way of asking for something.
The full polite/respectful version is
"Would + subject + mind [verb]ing"
e.g Would you mind lending me a pen?
e.g Would you mind going to the market?
Th
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,693
|
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- The above 3 meta tags *must* come first in the head; any other head content must come *after* these tags -->
<title>기본페이지 샘플</title>
<!-- bootstrap style -->
<link href="/k-cms/html/lib/bootstrap/css/bootstrap.default.min.css" rel="stylesheet">
<link href="/k-cms/html/css/main.default.css" rel="stylesheet">
<!-- 임시 적용 -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.2/jquery.min.js"></script>
<script src="/k-cms/html/lib/bootstrap/js/bootstrap.min.js"></script>
</head>
<body>
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<div id="top">
<header class="masthead hidden-xs">페이지 상단영역</header>
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<div id="menu" class="navbar-inverse" data-spy="affix" data-offset-top="232">
<div class="container">
<div class="row">
<nav class="navbar navbar-static-top">
<div class="container-fluid">
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<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#menu-navbar-collapse" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand visible-xs" href="<?=$site['r']?>">Brand</a>
</div>
<!-- Collect the nav links, forms, and other content for toggling -->
<div class="collapse navbar-collapse" id="menu-navbar-collapse">
<ul class="nav navbar-nav ">
<li><a href="#">메인메뉴1</a></li>
<li><a href="#">메인메뉴2</a></li>
<li><a href="#">메인메뉴3</a></li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li><a href="#">로그인</a></li>
</ul>
</div><!-- /.navbar-collapse -->
</div><!-- /.container-fluid -->
</nav>
</div>
</div>
</div>
</div>
<!-- content -->
<div id="content">
<div class="container">
<div class="row">
<!-- left menu -->
<div class="col-sm-3 hidden-xs">
<div class="list-group">
<a class="list-group-item active" href="#">사이드메뉴</a>
<a class="list-group-item" href="#">사이드메뉴2</a>
<a class="list-group-item" href="#">사이드메뉴3</a>
</div>
</div>
<div class="col-sm-9">
<?php for($i=0; $i<10; $i++) :?>
<p>
<h2>Content</h2>
Totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae
dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia cor magni dolores
eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit,
sed quia non numquam eius modi tempora incidunt ut labore et dolore magnam aliquam quaerat voluptatem.
Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur?
</p>
<?php endfor?>
</div>
</div>
</div>
</div>
<!-- footer -->
<div id="footer">
<div class="navbar-inverse">
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<div class="clearfix"><p class="navbar-text"><b>(주)회사이름</b></p></div>
<div class="clearfix"><p class="navbar-text">TEL : 02-123-4567</p><p class="navbar-text">FAX : 02-123-4567</p></div>
<div class="clearfix"><p class="navbar-text">서울특별시 영등포구 국회대로</p></div>
<div class="clearfix"><p class="navbar-text">Copyright © <?=date('Y')?> <?=$_SERVER['HTTP_HOST']?> All rights reserved.</p></div>
</div>
</div>
</div>
</body>
</html>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,406
|
91. AP Hopes to Improve Online Revenue Streams
newspapers ep six
93. Citizens As Budding Reporters And Editors (1999)
92. Upside of Disappearing Newspaper Advertising (Jan 2009)
90. The Associated Press
89. Newspaper and Citizen Journalism Reading List
88. Newspaper's Shift in Focus (Mar 2009)
Over the last several years the Associated Press has sought to move its content online. From the last segment we saw one such effort, with the AP teaming up with Microsoft to provide online video. With member newspapers threatening to leave, and profits failing, one place the AP is looking to improve its bottom line is the licensing deals it has with major Web sites,
"The Associated Press hopes to negotiate more lucrative licensing deals with major Web sites while mining new revenue from advertisers and readers as the 163-year-old news cooperative adapts to Internet-driven changes in the media."
Over the last year, the AP has reduced its fees for U.S. Newspapers by $30 Million dollars. Over the next year it plans to reduce those fees by another $45 Million. All of this is in an effort to keep member newspapers who can no longer afford to use the AP's content from leaving altogether. The AP states that they expect revenues to fall this year and next, after seeing them rise by 5% in 2008.
The biggest negotiation for the AP will be on its licensing deal with Google. They want to find a way to improve their terms, which they believe mostly benefit Google, which makes money by putting ads against the content. They are also looking for new ways to put advertising against their own photographs and news stories.
Will this work? I think the AP is asking the same questions the rest of the news industry is asking, what should their place be in the new landscape. Fortunately, the AP has the advantage that they are not directly tied to any platform, they have chosen to take a multi-channel approach which gives them more flexibility than the newspapers have (one example of this flexibility can be found in this segment's clip). This approach, however, does not hand them a new way to monetize this content once the services that typically paid for it run out of money.
What do you think? Can the AP survive and if so, what should they be doing?
6. Raising Questions
65. The Freedom Of Information Act
13. Look At Other Stories
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,291
|
set -x
set -e
export CLOUD_SDK_VERSION=209.0.0
export CHROME_DRIVER_VERSION=2.35
export LOCAL_USER=geode
export LOCAL_UID=93043
apt-get update
apt-get install -y --no-install-recommends \
apt-transport-https \
lsb-release
echo "deb [arch=amd64] http://dl.google.com/linux/chrome/deb/ stable main" > /etc/apt/sources.list.d/google-chrome.list
echo "deb [arch=amd64] https://download.docker.com/linux/ubuntu $(lsb_release -cs) stable" | tee -a /etc/apt/sources.list.d/google-cloud-sdk.list
echo "deb [arch=amd64] https://apt.bell-sw.com/ stable main" | sudo tee /etc/apt/sources.list.d/bellsoft.list
curl -fsSL https://dl.google.com/linux/linux_signing_key.pub | apt-key add -
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | apt-key add -
curl -fsSL https://download.bell-sw.com/pki/GPG-KEY-bellsoft | apt-key add -
apt-get update
set +e && apt-get purge -y google-cloud-sdk lxc-docker && set -e
DEBIAN_FRONTEND=noninteractive apt-get install -y --no-install-recommends \
aptitude \
ca-certificates \
cgroupfs-mount \
containerd.io \
docker-ce="5:19.03.14~3-0~ubuntu-bionic" \
docker-ce-cli="5:19.03.14~3-0~ubuntu-bionic" \
git \
google-chrome-stable \
htop \
jq \
less \
lsof \
net-tools \
python3 \
python3-pip \
rsync \
tcl \
tmux \
unzip \
vim
cp -R /etc/alternatives /etc/keep-alternatives
apt-get install -y --no-install-recommends \
bellsoft-java11 \
bellsoft-java17 \
bellsoft-java8
rm -rf /etc/alternatives
mv /etc/keep-alternatives /etc/alternatives
pip3 install --upgrade pip
pip3 install setuptools
pip3 install docker-compose
pushd /tmp
curl -fO https://dl.google.com/dl/cloudsdk/channels/rapid/downloads/google-cloud-sdk-${CLOUD_SDK_VERSION}-linux-x86_64.tar.gz
tar xzf google-cloud-sdk-${CLOUD_SDK_VERSION}-linux-x86_64.tar.gz -C /
rm google-cloud-sdk-${CLOUD_SDK_VERSION}-linux-x86_64.tar.gz
curl -fsSO https://dl.google.com/cloudagents/add-google-cloud-ops-agent-repo.sh
sudo bash add-google-cloud-ops-agent-repo.sh --also-install
rm add-google-cloud-ops-agent-repo.sh
popd
export PATH=/google-cloud-sdk/bin:${PATH}
gcloud config set core/disable_usage_reporting true
gcloud config set component_manager/disable_update_check true
gcloud config set metrics/environment github_docker_image
gcloud components install docker-credential-gcr --quiet
gcloud auth configure-docker --quiet
curl -fLo /usr/local/bin/dunit-progress https://github.com/jdeppe-pivotal/progress-util/releases/download/0.2/progress.linux
chmod +x /usr/local/bin/dunit-progress
wget --no-verbose -O /tmp/chromedriver_linux64.zip https://chromedriver.storage.googleapis.com/${CHROME_DRIVER_VERSION}/chromedriver_linux64.zip
rm -rf /opt/selenium/chromedriver
unzip /tmp/chromedriver_linux64.zip -d /opt/selenium
rm /tmp/chromedriver_linux64.zip
mv /opt/selenium/chromedriver /opt/selenium/chromedriver-${CHROME_DRIVER_VERSION}
chmod 755 /opt/selenium/chromedriver-${CHROME_DRIVER_VERSION}
ln -fs /opt/selenium/chromedriver-${CHROME_DRIVER_VERSION} /usr/bin/chromedriver
adduser --disabled-password --gecos "" --uid ${LOCAL_UID} ${LOCAL_USER}
usermod -G docker,google-sudoers -a ${LOCAL_USER}
echo "export PATH=/google-cloud-sdk/bin:${PATH}" > /etc/profile.d/google_sdk_path.sh
apt-get remove -y unattended-upgrades && apt-get -y autoremove
apt-get clean
rm -rf /var/lib/apt/lists/*
echo "kernel.pid_max=983040" > /etc/sysctl.d/99-geode.conf
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{
"redpajama_set_name": "RedPajamaGithub"
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{"url":"https:\/\/www.physicsforums.com\/threads\/the-fundamental-delusion-of-scientists.895799\/","text":"# The Fundamental Delusion of Scientists?\n\nTags:\n1. Dec 3, 2016\n\n### liometopum\n\nI was listening to a lecture by Peter Thiel. He argued that \"scientists never make any money\", and are \"always deluded into thinking they live in a just universe that will reward them for their work, and this is probably the fundamental delusion that scientists tend to suffer from in our society.\"\n\nIt certainly is an interesting concept, and well worth some reflection by scientists and engineers.\n\nIs it true? Close to true?\n\nat 28:00\nVideo and transcript: http:\/\/startupclass.samaltman.com\/courses\/lec05\/\n\n\"We've lived through centuries of enormous amounts of innovation in science as well, and the thing that I think people always miss when they think about these things is because X and Y are independent variables. Some of these things can be extremely valuable innovations, but the people invent them, who come up with them, do not get rewarded for this.\n\nIf you create X dollars in value, you capture Y percentage of X, I'd suggest that the history of science has generally been one where Y is 0% across the board.\n\nThe scientists never make any money. They are always deluded into thinking they live in a just universe that will reward them for their work and for their inventions, and this is probably the fundamental delusion that scientists tend to suffer from in our society. And even in technology there are many areas of technology where there were great innovations that created tremendous value for society, but people did not actually capture that much of the value.\n\nSo I think there is this sort of whole history of science and technology that can be told from the perspective of how much value was actually captured. And certainly there are entire sectors where people did not capture anything.\n\nSo you're the smartest physicist of the 20th century, and you came up with Special Relativity, and you come up with General Relativity. You don't get to be a billionaire. You don't even get to be a millionaire. It just somehow doesn't work that way.\"\n\n2. Dec 3, 2016\n\n### billy_joule\n\nI think the fundamental delusion of Peter Thiel is thinking that scientists and engineers want or expect to become billionaires from science and engineering.\n\n3. Dec 3, 2016\n\n### liometopum\n\nAlbert Einstein\u2019s patents\nabout 50 patents.....no, he did not want to make money from his ideas; he was above that.\n\nBut that is not the point Peter Thiel is making.\n\n4. Dec 3, 2016\n\n### phinds\n\nAnd Theil is deluded into thinking that everyone is driven by greed as he apparently is. Besides, why would you think he has any particularly valid take on scientists? He's NOT a scientist. He's not even an engineer, he's a philosophy major turned investment banker. He's into greed, not scientific recognition and I doubt he'd really understand the thrill of invention and discovering new scientific knowledge even if you explained it to him.\n\nHe's very successful at what he does but like many guys who are very successful in one field he thinks that makes him an expert in other fields where he doesn't necessarily know his bum from his brain.\n\nLast edited: Dec 4, 2016\n5. Dec 4, 2016\n\n### liometopum\n\nPeter Thiel is giving a lecture on Startups. He discusses the difference between X and Y, where X is the value produced by a business and Y is the percentage you capture of X; they are independent variables.\n\nTechnology startups, often based on innovative, scientific breakthroughs, do not necessarily lead to high Y values. People usually think that if they develop a new technology, they will get rich. But they often don\u2019t make any money. He gives examples.\n\nHe then extends the idea to scientific breakthroughs, and the greatest one was Einstein\u2019s work. The theories of Special and General Relativity have high X value, but Einstein captured almost no Y value. Thiel laments it, and states \u201cIt just somehow doesn't work that way.\u201d\n\nMaybe that is why billionaire Yuri Milner gives the Fundamental Prize in Physics, or Alfred Nobel, who was also very rich., set up the Nobel Prize: it is a way to give cash to the creators of great X, as a way of compensating them for the low Y. Apparently Milner and Nobel already understood the comment \u201cIt just somehow doesn't work that way.\u201d\n\nThe point of the lecture is that to create a high-value company, you want both high X and high Y. You get high Y with a monopoly; that should be your goal. Capturing a great return is not a given, despite producing a high X. Scientists and engineers, as creators of high X, should be aware that X and Y are independent of each other; they can then plan more intelligently.\n\nWhat if you came up with an idea that lead to a billion dollar industry, that made many millionaires, even billionaires, but you made essentially nothing from it?\n\nWhat if you came up with a great idea, but others took credit for it, and your role was diminished, even ignored, and you received no credit or recognition?\n\nThe thrill of discovery is likely to be overshadowed by other, negative, feelings. That is pretty common, I am guessing.\n\n6. Dec 4, 2016\n\n### ZapperZ\n\nStaff Emeritus\nIn science? No, it is my guess that it is not common. This is because we publish our ideas and discoveries. While there are instances where the initial discoverer may be overlooked or not credited, it is a lot more often now that the persons who are responsible for the significant advancement are recognized. And by its nature, such publications are open to everyone in the sense that it is adding to the body of knowledge that anyone can use.\n\nI think you missed the point here. While we certainly want to be well-off, there is a difference between making money as the central occupation, versus it being a means to another ends. Many of us want to make a living by doing science, versus doing science to make a living. And if you are good at it and successful at it, you might even make quite a good living out of it. It is why tenured professor positions are such desirable. It has nothing to do with being millionaires or billionaires, as if THAT in itself can be an \"ambition\".\n\nI would also point out that if Tim Berners-Lee actually decided to either copyright or patent his idea of the World Wide Web just so he can make money out of it, it would probably NOT take off and shaped the internet the way we have it today. So you could say now that he missed a financial opportunity to become a \"billionaire\", but there's nothing there in that parallel universe to say that if he did not do what he did, it would have become as popular and revolutionary.\n\nA lot of science is done via public funds. This can be via direct public grants, or using facilities that were built using public money. While scientists certainly get rewarded financially for important discoveries, work, or long-term careers, this is different than private individual or companies producing their own products or services and are able to reap all the rewards of such success. It is by its nature that publically-funded work belongs to the public as dictated by the funding agencies. One may be compensated for a discovery, invention, or a patent, but one does not own that work. The people who paid you to do that work do.\n\nZz.\n\n7. Dec 4, 2016\n\n### zoobyshoe\n\nOne can make the case scientists and engineers are deluded about being rewarded, but that isn't really what prevents them from becoming wealthy. There is a fundamental difference between the mindset of a scientist and the mindset of a billionaire which makes it impossible for either to be the other. The scientist's efforts will go nowhere unless he agrees to submit completely to the tyranny of physical reality. The billionaire doesn't have that restriction; he can spin, bully, obfuscate, misdirect, subvert, bribe, etc. The scientist is working with nature, the billionaire is essentially manipulating people.\n\nWhen you try to run science like a business, it doesn't work. When you push medical engineers to create a drug by some deadline that cures X disease so you can sell that drug, you often get something that works in 1 out of 25 patients and causes unwanted side effects in 20 out of 25. You get smart diesel engines that know how to subvert the pollution tests. Above all, you get the holy grail of science-as-business: planned obsolescence.\n\n8. Dec 4, 2016\n\n### liometopum\n\nI need to work now, and will vanish for some time, but first...\n\nZoobyshoe, yes, the mindset is different. Many scientists and engineers presumably want to commercialize their ideas, but they need to study some business ideas, to help align their thinking better. Peter Thiel's comments should be valuable to them; that is why I shared it. As a venture capitalist, he sees this delusional thinking.\n\nFor ZapperZ, a survey of discontent might be revealing. I did find this survey that concluded scientists were happy with their jobs but worried about money. See http:\/\/www.nature.com\/naturejobs\/science\/articles\/10.1038\/nj7413-685a\n\nDigressing somewhat, I'd not seen this until now, or had forgotten it. Here is a billionaire Russian helping a Nobel laureate: \"On 4 December 2014, Usmanov paid $4.9m for Dr James Watson's Nobel Prize Medal in Physiology or Medicine, which was auctioned at Christie's in New York City. Watson was selling his prize to raise money to support scientific research. After auctions fees, Watson received$4.1m. Usmanov subsequently returned the medal to Watson, stating \"in my opinion, a situation in which an outstanding scientist sells a medal recognizing his achievements is unacceptable. Watson's work contributed to cancer research, the illness from which my father died. It is important for me that the money that I spent on this medal will go to supporting scientific research, and the medal will stay with the person who deserved it.\" https:\/\/en.wikipedia.org\/wiki\/Alisher_Usmanov\n\nBut think, James Watson.... wow, that was super high X value. And he has to sell his medal? Watson created high X, but Usmanov created high X and Y.\n\nFor the billionaire to get a concept to be a commercial success requires way more than manipulating people. And you don't think scientists fight? They are just as human. Here is a famous quote from Henry Kissinger: \"University politics are vicious precisely because the stakes are so small.\"\n\n9. Dec 4, 2016\n\n### liometopum\n\nHe does not think it, he sees it. He is a venture capitalist. http:\/\/foundersfund.com\/team\/peter-thiel\/\nThe guy is talking from experience. This is wisdom he is offering to those who can listen.\n\n10. Dec 4, 2016\n\n### zoobyshoe\n\nI understand this. What I'm saying is that, if you're authentically good at science or engineering you will automatically be handicapped in understanding \"business ideas,\" because business is fundamentally about manipulating people's perception of reality rather than about understanding physical reality.\nLike what? A \"vision\" of what things could be? Those are a dime a dozen. Convincing large numbers of people, or simply the 'right' people, to share your vision is where you make billions.\nAre you equating fighting to manipulating people?\n\n11. Dec 4, 2016\n\n### collinsmark\n\nAgain, at the risk of repeating what others have been saying in this thread (i.e., @zoobyshoe, @ZapperZ, @billy_joule, @phinds) the problem is Peter Thiel's presumption that scientists pursue academic research -- including long years of effort in the lab or study, the publishing of academic papers to peer reviewed journals, etc. -- for the primary purpose of becoming billionaires. That's not true, and that's where the objections are targeting.\n\nThey [scientists] do it because they are curious about universe in which we live. A bit of notoriety might be a close second for some scientists. Of course they need enough money to feed themselves and their families, and that comes from modest grants -- but nobody expects billions of dollars for a academic paper or two.\n\nStart listening in the video at about 29:00 and continue to around 31:00 or so.\n\n\"They're always deluded into thinking that they live in a just universe that will reward them for their work and for their inventions and this is probably the fundamental delusion that scientists tend to suffer from in our society.\" Then he goes on a little later, \"So you're the smartest physicist of the twentieth century, you come up with special relativity, you come up with general relativity, you don't get to be a billionaire, you don't even get to be a millionaire.\"\n\nEinstein never expected to receive billions of dollars, or even millions of dollars for his work on special and general relativity. He never deluded himself into thinking that he would. The claim that Peter Thiel is implying, that Einstein developed his theories of relativity primarily because he had big dollar signs (\\$) in his eyes (or Deutsche Marks, or whatever currency symbol) is a false claim.\n\n12. Dec 4, 2016\n\n### phinds\n\nYep. We've all been saying the same thing basically, and it's clear that liometopum has the same delusions that Theil has and we are wasting our time.\n\n13. Dec 4, 2016\n\n### ZapperZ\n\nStaff Emeritus\nRead the survey carefully. They are worried about FINANCES.\n\nI never said we don't care about making a living. We do! But this is different than what Thiel is urging us to do. The issue in that survey is what is happening lately where science funding has been severely affected due to various policies and economic decision. This isn't the need to make tons of money!\n\nThiel should put his money where is mouth is. As a venture capitalist, he will be the LAST person to invest in the type of work that many scientists do! Has he put money into the LHC, the research on topological insulators, etc... etc.? Heck, I'm sure if he was alive back then, would he had put money into Watson and Crick's work? On Einstein's work while he was sitting all by himself in the Swiss Patent office? On the beginnings of quantum mechanics even though there was ZERO indication of any beneficial application of it back then? No, because many of these require govt. agencies who do not have the short-term and short-sighted need to make money and get immediate return on their investments!\n\nWhen Bell Labs split and became Lucent, and there was then pressure start producing marketable product (i.e. now the stock holders want something for their investments), the FIRST thing to go is basic research. Now, Bell Labs is a shadow of what it was before when some of the most innovative ideas in physics made it into a premier research center of the world. Point to Thiel and show him that this is what happens when making money becomes a primary motive. This is what happens when one live to eat rather than eat to live.\n\nNo venture capitalists have invested their money in basic physics research. Period!\n\nZz.\n\n14. Dec 4, 2016\n\n### Stephen Tashi\n\nI agree. The presentation is not about scientists in general. The topic is how to recognize which businesses will profitable. The pitfalls Thiel describes are pitfalls that people make when they try to recognize such businesses. Not all scientists and inventors are focused on recognizing good business opportunities. Thiel is only talking about mistakes that those particular scientists and inventors who are trying to develop businesses make.\n\n15. Dec 4, 2016\n\n### zoobyshoe\n\nNo, he is saying all scientists have chronically failed to understand they must reap their own Y from X instead of buying into the \"delusion\" they will be rewarded by \"a just universe\":\n\nHe's right that Y has been about 0% across the board, but wrong that scientists were\/are, or should be, out to harvest their lion's share, Y.\n\n16. Dec 4, 2016\n\n### rootone\n\nThe subliminal message here seems to be that research into anything that has no guarantee of leading to a profitable technology is a waste of time.\nSo I guess in his view (just thinking of an example), almost all the exploration missions of NASA + other space agencies are a waste of time and money.\n\n17. Dec 4, 2016\n\n### Stephen Tashi\n\nIt's not a subliminal message. The information in the talk entails how a person should spend his time if his purpose is to find profitable businesses. For the purpose of pursuing that goal, Thiel explicitly says that innovation in itself is not a guarantee of a profitable business.\n\nFrom the point of view of a person investing his own money in ventures in order to get a financial return, that is a correct conclusion. Whether space missions have a benefit because they satisfy peoples' curiosity, or strengthen the nation is a different question. That wasn't the topic of Thiel's presentation.\n\n18. Dec 4, 2016\n\n### zoobyshoe\n\nI think the \"subliminal\" message is that scientists can be deluded, and this is their \"fundamental\" delusion, there being others he doesn't go into. It's a taint that primes the receptive listener for other bad news about scientist's beliefs. If you catch my drift.\n\n19. Dec 4, 2016\n\n### rootone\n\nOK, but modern science strictly involves a review process, the point of which is to exclude irrational\/delusional\/biased\/silly propositions.\nI guess there are some that have a political agenda to discourage that, but I can't really see why they would.\n\n20. Dec 4, 2016\n\n### zoobyshoe\n\nWhat I'm talking about is all over the news, but it's a forbidden subject on PF: too many arguments erupted. Perhaps I can get away with saying Thiel is a supporter of a certain orange-faced personage who leans toward certain attitudes about certain scientific things.","date":"2017-08-21 21:00:27","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\": 0.3043670058250427, \"perplexity\": 1762.671983694458}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"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-2017-34\/segments\/1502886109525.95\/warc\/CC-MAIN-20170821191703-20170821211703-00405.warc.gz\"}"}
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{"url":"http:\/\/rxiv.org\/math\/","text":"# General Mathematics\n\nPrevious months:\n2010 - 1003(1) - 1005(2) - 1008(2) - 1009(1) - 1010(2) - 1011(2) - 1012(1)\n2011 - 1101(2) - 1103(3) - 1105(1) - 1108(1) - 1109(1) - 1111(2)\n2012 - 1202(2) - 1203(3) - 1204(2) - 1205(2) - 1206(2) - 1207(1) - 1208(3) - 1211(2) - 1212(1)\n2013 - 1301(1) - 1302(4) - 1303(4) - 1304(3) - 1305(2) - 1306(4) - 1309(3) - 1310(2) - 1311(2) - 1312(2)\n2014 - 1401(2) - 1402(3) - 1403(639) - 1404(85) - 1405(60) - 1406(1) - 1407(4) - 1408(1) - 1409(2) - 1411(59) - 1412(19)\n2015 - 1501(7) - 1502(18) - 1503(6) - 1504(8) - 1505(1) - 1506(7) - 1507(1) - 1508(114) - 1509(18) - 1510(144) - 1511(16) - 1512(182)\n2016 - 1601(65) - 1602(28) - 1603(35) - 1604(39) - 1605(18) - 1606(24) - 1607(45) - 1608(36) - 1609(39) - 1610(9) - 1611(21) - 1612(25)\n2017 - 1701(259) - 1702(11) - 1703(13) - 1704(21)\n\n## Recent submissions\n\nAny replacements are listed further down\n\n[2142] viXra:1704.0354 [pdf] submitted on 2017-04-26 11:52:19\n\n### Formalization of Multivariate Lagrange Interpolation\n\nAuthors: Le Fay Yvann\n\nWe generalize a simple formula for constructing the multinomial function f which interpolates a set of (d+1) points in IR^N. We also provide an example of application of this method.\nCategory: General Mathematics\n\n[2141] viXra:1704.0329 [pdf] submitted on 2017-04-25 03:19:00\n\n### An Isolated Interval Valued Neutrosophic Graph\n\nAuthors: Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache\n\nThe interval valued neutrosophic graphs are generalizations of the fuzzy graphs, interval fuzzy graphs, interval valued intuitionstic fuzzy graphs, and single valued neutrosophic graphs. Previously, several results have been proved on the isolated graphs and the complete graphs. In this paper, a necessary and sufficient condition for an interval valued neutrosophic graph to be an isolated interval valued neutrosophic graph is proved.\nCategory: General Mathematics\n\n[2140] viXra:1704.0327 [pdf] submitted on 2017-04-25 03:22:04\n\n### Applications of Fuzzy and Neutrosophic Logic in Solving Multi-criteria Decision Making Problems\n\nAuthors: Abdel Nasser H. Zaied, Hagar M. Naguib\n\nIn daily life, decision makers around the world are seeking for the appropriate decisions while facing many challenges due to conflicting criteria and the presence of many alternatives.\nCategory: General Mathematics\n\n[2139] viXra:1704.0325 [pdf] submitted on 2017-04-25 03:25:49\n\n### The 3n + p Conjecture: A Generalization of Collatz Conjecture\n\nAuthors: W.b. Vasantha Kandasamy, Ilanthenral Kandasamy, Florentin Smarandache\n\nThe Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n \uf02b1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried.\nCategory: General Mathematics\n\n[2138] viXra:1704.0323 [pdf] submitted on 2017-04-25 03:52:27\n\n### Fuzzy Logic vs. Neutrosophic Logic: Operations Logic\n\nAuthors: Salah Bouzina\n\nThe goal of this research is first to show how different, thorough, widespread and effective are the operations logic of the neutrosophic logic compared to the fuzzy logic\u2019s operations logical. The second aim is to observe how a fully new logic, the neutrosophic logic, is established starting by changing the previous logical perspective fuzzy logic, and by changing that, we mean changing the truth values from the truth and falsity degrees membership in fuzzy logic, to the truth, falsity and indeterminacy degrees membership in neutrosophic logic; and thirdly, to observe that there is no limit to the logical discoveries.\nCategory: General Mathematics\n\n[2137] viXra:1704.0322 [pdf] submitted on 2017-04-25 03:53:42\n\n### An Application on Standard Neutrosophic Information Systems\n\nAuthors: Nguyen Xuan Thao, Bui Cong Cuong, Florentin Smarandache\n\nA rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets, standard neutrosophic information system and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.\nCategory: General Mathematics\n\n[2136] viXra:1704.0321 [pdf] submitted on 2017-04-25 03:55:07\n\n### Some Aggregation Operators For Bipolar-Valued Hesitant Fuzzy Information\n\nAuthors: Tahir Mahmood, Florentin Smarandache, Kifayat Ullah, Qaisar Khan\n\nIn this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-making problem on these operation.\nCategory: General Mathematics\n\n[2135] viXra:1704.0299 [pdf] submitted on 2017-04-22 16:51:50\n\n### Multi Criteria Decision Making Based on Projection and Bidirectional Projection Measures of Rough Neutrosophic Sets\n\nAuthors: Surapati Pramanik, Rumi Roy, Tapan Kumar Roy\n\nIn this paper, we define projection and bidirectional projection measures between rough neutrosophic sets. Then two new multi criteria decision making methods are proposed based on neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multiple criteria group decision making problems. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the proposed methods.\nCategory: General Mathematics\n\n[2134] viXra:1704.0292 [pdf] submitted on 2017-04-23 05:21:47\n\n### One Step Forecasting Model\n\nIn this research investigation, the author has detailed two models of One Step Forecasting\nCategory: General Mathematics\n\n[2133] viXra:1704.0257 [pdf] submitted on 2017-04-20 08:14:31\n\n### The Real Root of the Equation: X^5+x^4+x-1=0\n\nAuthors: Edgar Valdebenito\n\nthis note presents some representations for the real root of the equation: x^5+x^4+x-1=0.\nCategory: General Mathematics\n\n[2132] viXra:1704.0241 [pdf] submitted on 2017-04-19 11:32:41\n\n### Trigonometric Interpolation Based on Summation of Fourier Series F_{i}^{\\delta} with Data-Related Delta-Function Property F_{i}^{\\delta}\\left(x_{j}\\right)=y_{j}\\delta_{ij} (Analogy to Lagrange Form of Interpolation Polynomial)\n\nAuthors: Andrej Liptaj\n\nFull analogy to the Lagrange form of the interpolation polynomial is constructed for Fourier series. As a straightforward consequence one gets the ability to extend an existing trigonometric interpolation to additional data point(s).\nCategory: General Mathematics\n\n[2131] viXra:1704.0201 [pdf] submitted on 2017-04-15 19:16:00\n\n### \u03d6\n\nAuthors: Soerivhe Iriene\n\nFinite.\nCategory: General Mathematics\n\n[2130] viXra:1704.0197 [pdf] submitted on 2017-04-15 10:09:35\n\n### Introduction to Complementary Analysis\n\nAuthors: Fran\u00e7ois Mendzina Essomba, Gael Dieudonn\u00e9 Essomba Essomba\nComments: 48 Pages. analyse, differentielle, compl\u00e9mentaire, analyse compl\u00e9mentaire\n\nWe introduce a new notion in the analysis, the notion of complementarity, which completes the work of Newton-Leibniz by defining all the elements.\nCategory: General Mathematics\n\n[2129] viXra:1704.0193 [pdf] submitted on 2017-04-14 19:06:31\n\n### Universal Optimization and Its Application\n\nAuthors: Alexander Bolonkin\n\nThe book consists of three parts. The first part describes new method of optimization that has the advantages at greater generality and flexibility as well as the ability to solve complex problems which other methods cannot solve. This method, called the \u201cMethod of Deformation of Functional (Extreme)\u201d, solves for a total minimum and finds a solution set near the optimum. Solutions found by this method can be exact or approximate. Most other methods solve only for a unique local minimum. The ability to create a set of solutions rather than a unique solution has important practical ramifications in many designs, economic and scientific problems because a unique solution usually is difficult to realize in practice. This method has the additional virtue of a simple proof, one that is useful for studying other methods of optimization, since most other methods can be delivered from the Method of Deformation. The mathematical methods used in the book allow calculating special slipping and breaking optimal curves, which are often encountered in problems of optimal control. The author also describes the solution of boundary problems in optimization theory. The mathematical theory is illustrated by several examples. The book is replete with exercises and can be used as a text-book for graduate courses. In fact the author has lectured on this theory using this book for graduate and post-graduate students in Moscow Technical University. The second part of the book is devoted to applications of this method to technical problems in aviation, space, aeronautics, control, automation, structural design, economic, games, theory of counter strategy and etc. Some of the aviation, aeronautic, and control problems are examined: minimization of energy, exact control, fuel consumption, heating of re-entry space ship in the atmosphere of planets, the problems of a range of aircraft, rockets, dirigibles, and etc. Some of the economic problems are considered, for example, the problems of a highest productivity, the problem of integer programming and the problem of linear programming. Many economic problems may be solved by the application of the Method to the Problems of non-cooperative games. The third part of the book contains solutions of complex problems: optimal thrust angle for different flight regimes, optimal trajectories of aircraft, aerospace vehicles, and space ships, design of optimal regulator, linear problems of optimal control. This book is intended for designers, engineers, researchers, as well as specialists working on problems of optimal control, planning, or the choosing of optimal strategy. For engineers the book provides methods of computation of the optimal construction and control mechanisms, and optimal flight trajectories. In addition, the book will be useful to students of mathematics, general engineering, and economic. English translation is not full. Full text is in Russian referances.\nCategory: General Mathematics\n\n[2128] viXra:1704.0171 [pdf] submitted on 2017-04-13 04:13:42\n\n### Mathematics, the Continuous or the Discrete Which is Better to Reality of Things\n\nAuthors: Linfan Mao\n\nThere are 2 contradictory views on our world, i.e., continuous or discrete, which results in that only partially reality of a thing T can be understood by one of continuous or discrete mathematics because of the universality of contradiction and the connection of things in the nature, just as the philosophical meaning in the story of the blind men with an elephant. Holding on the reality of natural things motivates the combination of continuous mathematics with that of discrete, i.e., an envelope theory called mathematical combinatorics which extends classical mathematics over topological graphs because a thing is nothing else but a multiverse over a spacial structure of graphs with conservation laws hold on its vertices. Such a mathematical object is said to be an action flow. The main purpose of this report is to introduce the powerful role of action flows, or mathematics over graphs with applications to physics, biology and other sciences, such as those of G-solution of non-solvable algebraic or differential equations, Banach or Hilbert G-flow spaces with multiverse, multiverse on equations, and with applications to, for examples, the understanding of particles, spacetime and biology. All of these make it clear that holding on the reality of things by classical mathematics is only on the coherent behaviors of things for its homogenous without contradictions, but the mathematics over graphs G is applicable for contradictory systems because contradiction is universal only in eyes of human beings but not the nature of a thing itself.\nCategory: General Mathematics\n\n[2127] viXra:1704.0149 [pdf] submitted on 2017-04-12 07:47:23\n\n### Progressive Fourier (Or Trigonometric) Interpolation\n\nAuthors: Andrej Liptaj\n\nMethod of progressive trigonometric interpolation is presented.\nCategory: General Mathematics\n\n[2126] viXra:1704.0124 [pdf] submitted on 2017-04-11 03:37:54\n\n### Mathematical Beauty with Prime Numbers: Elegant Sieve-Based Primality Test Formula Constructed with Periodic Functions\n\nAuthors: Andrej Liptaj\n\nFormulas which relate basic mathematical constants, operations and prime numbers are presented. Some related ideas are explored.\nCategory: General Mathematics\n\n[2125] viXra:1704.0122 [pdf] submitted on 2017-04-10 07:38:09\n\n### Unsuccessful Attempt to Speed-up Numerical Integration of Functions with Peaks and Some Related Topics\n\nAuthors: Andrej Liptaj\nComments: 3 Pages. Publication of a negative result.\n\nAn (unsuccessful) attempt to use \u201cdamping\u201d functions for sharp peak integration is made. Some related comments about Monte Carlo \u201carea\u201d integration and speeding a uniform random number generator are made.\nCategory: General Mathematics\n\n[2124] viXra:1704.0117 [pdf] submitted on 2017-04-09 19:42:00\n\n### University Mathematics for Intelligent Teenagers.\n\nAuthors: Johan Noldus\n\nMany topics are touched upon at a fair level of sophistication.\nCategory: General Mathematics\n\n[2123] viXra:1704.0066 [pdf] submitted on 2017-04-06 04:00:32\n\n### Cosine Interpolation, Sine Interpolation, Interpolation of Arbitrary Series with Multiplicative Coefficients\n\nAuthors: Andrej Liptaj\n\nThis text summarizes methods for (pure) cosine and sine interpolations and reminds the reader of the matrix-inversion method valid for any interpolation using series with multiplicative coefficients.\nCategory: General Mathematics\n\n[2122] viXra:1704.0048 [pdf] submitted on 2017-04-05 03:42:02\n\n### Short Notice on (Exact) Trigonometric Interpolation.\n\nAuthors: Andrej Liptaj\n\nAbstract Method of trigonometric interpolation is presented in details and summarized. New ideas related to the high-frequency cutoff in the case of an even number of data points are presented.\nCategory: General Mathematics\n\n[2121] viXra:1703.0279 [pdf] submitted on 2017-03-29 12:53:24\n\n### Question 2345 : Integral , Fractals , Pi\n\nAuthors: Edgar Valdebenito\n\nAn Integral for pi\nCategory: General Mathematics\n\n[2120] viXra:1703.0255 [pdf] submitted on 2017-03-27 10:44:14\n\n### The Answer to Riemann is Giant.\n\nAuthors: Nicholas R. Wright\n\nWe prove the Riemann Hypothesis, by means of the Extended Riemann Hypothesis, the Generalized Riemann Hypothesis, and the Grand Riemann Hypothesis. Quasicrystals are the answer to the Riemann Hypothesis. A solution could be found using Russell\u2019s Paradox. Measurement is possible through nominative determinism. Deuring\u2013Heilbronn repulsion phenomenon was useful in regression analysis. An index method of forecasting was overlooked for centuries. In summary, the Grand Riemann Hypothesis should be seen as the standard. Grand Riemann Hypothesis improves on the basics of more simplified Riemann Hypotheses.\nCategory: General Mathematics\n\n[2119] viXra:1703.0195 [pdf] submitted on 2017-03-20 13:17:51\n\n### The Polynomial P(x)=x^8+x^7-7x^6-6x^5+15x^4+10x^3-10x^2-4x+1\n\nAuthors: Edgar Valdebenito\n\nIn this note give some formulas related with the polynomial:p(g)=g^8+g^7-7g^6-6g^5+15g^4+10g^3-10g^2-4g+1\nCategory: General Mathematics\n\n[2118] viXra:1703.0160 [pdf] submitted on 2017-03-16 08:59:13\n\n### Logarithmic Extension of Real Numbers and Hyperbolic Representation of Generalized Lorentz Transforms\n\nAuthors: Grushka Ya.I.\nComments: 6 Pages. Mathematics Subject Classification: 12D99; 83A05\n\nWe construct the logarithmic extension for real numbers in which the numbers, less then $-\\infty$ exist. Using this logarithmic extension we give the single formula for hyperbolic representation of generalized tachyon Lorentz transforms.\nCategory: General Mathematics\n\n[2117] viXra:1703.0156 [pdf] submitted on 2017-03-15 23:21:37\n\nAuthors: Clive Jones\n\nColourizing the Complex-Plane\nCategory: General Mathematics\n\n[2116] viXra:1703.0127 [pdf] submitted on 2017-03-13 12:58:37\n\n### Integrals\n\nAuthors: Edgar Valdebenito\n\nthis note presents a collection of integrals involving pi.\nCategory: General Mathematics\n\n[2115] viXra:1703.0126 [pdf] submitted on 2017-03-13 13:32:26\n\n### The Numbers: K1,k2,pi\n\nAuthors: Edgar Valdebenito\n\nThis note presents the numbers k1 and k2.\nCategory: General Mathematics\n\n[2114] viXra:1703.0088 [pdf] submitted on 2017-03-09 12:25:43\n\n### On Fermat's Last Theorem\n\nAuthors: R. Wayte\n\nA solution of Fermat\u2019s Last Theorem is given, using elementary function arithmetic and inference from worked examples.\nCategory: General Mathematics\n\n[2113] viXra:1703.0071 [pdf] submitted on 2017-03-07 22:59:43\n\n### On the Link Between Finite Differences and Derivatives of Polynomials (Vixra)\n\nAuthors: Kolosov Petro\nComments: 12 Pages. Final revised paper, text overlap with previous versions\n\nThe main aim of this paper to establish the relations between for- ward, backward and central finite(divided) differences (that is discrete analog of the derivative) and partial & ordinary high-order derivatives of the polyno- mials.\nCategory: General Mathematics\n\n[2112] viXra:1703.0053 [pdf] submitted on 2017-03-07 02:13:29\n\n### A Type D Breakdown of the Navier Stokes Equation in D=3 Spatial Dimensions\n\nAuthors: Han Geurdes\n\nIn this paper a type D breakdown of the Navier Stokes equation in d=3 dimensions is demonstrated.\nCategory: General Mathematics\n\n[2111] viXra:1703.0052 [pdf] submitted on 2017-03-06 12:20:58\n\n### Fractal,Polynomial,pi\n\nAuthors: Edgar Valdebenito\n\nThis note presents formulas and fractals related with the polynomial:p(x)=x^8+4x^7-10x^6-16x^5+19x^4+16x^3-10x^2-4x+1.\nCategory: General Mathematics\n\n[2110] viXra:1703.0017 [pdf] submitted on 2017-03-02 12:03:30\n\n### Ramanujan's Issues N\u00b01: the Radical R = (5^(1\/4)-1)\/(5^(1\/4)+1)\n\nAuthors: Edgar Valdebenito\n\nIn this note we presents some formulas related with the radical:r=(5^(1\/4)-1)\/(5^(1\/4)+1).\nCategory: General Mathematics\n\n[2109] viXra:1702.0330 [pdf] submitted on 2017-02-27 12:42:03\n\n### Newton-Julia Set for Some Polynomials Related with Number pi\n\nAuthors: Edgar Valdebenito\n\nNewton-Julia fractals and pi formulas\nCategory: General Mathematics\n\n[2108] viXra:1702.0324 [pdf] submitted on 2017-02-26 23:40:12\n\n### Why Finite Mathematics Is The Most Fundamental and Ultimate Quantum Theory Will Be Based on Finite Mathematics\n\nAuthors: Felix M. Lev\nComments: 10 Pages. Published in Physics of Particles and Nuclei Letters\n\nClassical mathematics (involving such notions as infinitely small\/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.\nCategory: General Mathematics\n\n[2107] viXra:1702.0239 [pdf] submitted on 2017-02-19 05:54:26\n\n### Energy and Laplacian Energy of a Single Value Neutrosophic Graph\n\nAuthors: Sumera Naz, Hossein Rashmanlou, M. Aslam Malik\n\nSingle valued neutrosophic model as an instance of a neutrosophic model provide an additional possibility to represent imprecise, uncertainty, inconsistent and incomplete information which exist in real situations. In this paper, the concept of energy of a graph is introduced in the context of a single valued neutrosophic environment, where for each element the truth-membership, indeterminacy-membership and falsity-membership degree, in [0, 1], are independently assigned. Firstly, the novel concepts of energy of a single valued neutrosophic graph (SVNG) are proposed and their properties are investigated, then Laplacian energy of a SVNG is introduced. Between the properties of energy and Laplacian energy of a SVNG, there is a great deal of analogy, but also some significant differences.\nCategory: General Mathematics\n\n[2106] viXra:1702.0238 [pdf] submitted on 2017-02-18 14:00:18\n\n### Certain Types of Graphs in Interval-Valued Intuitionistic Fuzzy Setting\n\nAuthors: S. Naz, M. A. Malik, H. Rashmanlou\n\nInterval-valued intuitionistic fuzzy set (IVIFS) as a generalization of intuitionistic fuzzy set (IFS) increase its elasticity drastically. In this paper, some important types of interval-valued intuitionistic fuzzy graphs (IVIFGs) such as regular, irregular, neighbourly irregular, highly irregular and strongly irregular IVIFGs are discussed. The relation among neighbourly irregular, highly irregular and strongly irregular IVIFGs is proved. The notion of interval-valued intuitionistic fuzzy clique (IVIFC) is introduced. A complete characterization of the structure of the IVIFC is presented.\nCategory: General Mathematics\n\n[2105] viXra:1702.0237 [pdf] submitted on 2017-02-18 14:33:00\n\n### Measurement of Planarity in Product Bipolar Fuzzy Graphs\n\nAuthors: S. Naz, S. Ashraf, H. Rashmanlou\n\nBipolar fuzzy set theory provides a basis for bipolar cognitive modeling and multiagent decision analysis, where in some situations, the product operator may be preferred to the min operator, from theoretical and experimental aspects. In this paper, the definition of product bipolar fuzzy graphs (PBFGs) is modified. The concepts of product bipolar fuzzy multigraphs (PBFMGs), product bipolar fuzzy planar graphs (PBFPGs) and product bipolar fuzzy dual graphs (PBFDGs) are introduced and investigated. Product bipolar fuzzy planarity value of PBFPG is introduced. The relation between PBFPG and PBFDG is also established. Isomorphism between PBFPGs is discussed. Finally, an application of the proposed concepts is provided.\nCategory: General Mathematics\n\n[2104] viXra:1702.0183 [pdf] submitted on 2017-02-16 07:59:31\n\n### Hybrid Vector Similarity Measure of Single Valued Refined Neutrosophic Sets to Multi-Attribute Decision Making Problems\n\nAuthors: Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri\n\nThis paper proposes hybrid vector similarity measures under single valued refined neutrosophic sets and proves some of its basic properties. The proposed similarity measure is then applied for solving multiple attribute decision making problems. Lastly, a numerical example of medical diagnosis is given on the basis of the proposed hybrid similarity measures and the results are compared with the results of other existing methods to validate the applicability, simplicity and effectiveness of the proposed method.\nCategory: General Mathematics\n\n[2103] viXra:1702.0180 [pdf] submitted on 2017-02-15 07:33:20\n\n### An Elliptic Integral\n\nAuthors: Edgar Valdebenito\n\nThis note presents some formulas related with the elliptic integrals.\nCategory: General Mathematics\n\n[2102] viXra:1702.0173 [pdf] submitted on 2017-02-14 19:38:12\n\n### On the Squaring of the Circle\n\nAuthors: Clive Jones\n\nAn Exploration of Circle-Square Properties & Identities\nCategory: General Mathematics\n\n[2101] viXra:1702.0140 [pdf] submitted on 2017-02-11 13:12:03\n\n### Bipolar Neutrosophic Projection Based Models for Multi-attribute Decision Making Problems\n\nAuthors: Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri\n\nBipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modeling real life decision making problems. In the paper, we have defined projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets and the proposed measures are then applied to multi-attribute decision making problems. The ratings of performance values of the alternatives with respect to the attributes are expressed by bipolar neutrosophic values. We calculate projection, bidirectional projection, and hybrid projection measures between each alternative and ideal alternative with bipolar neutrosophic information and then all the alternatives are ranked to identify best option. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the developed method. Comparison analysis with other existing methods is also provided.\nCategory: General Mathematics\n\n[2100] viXra:1702.0082 [pdf] submitted on 2017-02-06 11:01:59\n\n### Infinite Tetration of Euler\u2019s Number and the Z-Exponential\n\nAuthors: C. A. Laforet\n\nIt is shown that the infinite tetration of Euler\u2019s number is equal to any complex number. It is also found that starting with any complex number except 0 and 1, we can convert the complex number into an exponential with a complex exponent. If this is done recursively for each successive exponent, we find that the complex exponent converges to a constant number, which is named the Z-Exponential (Z_e). Derivatives for the Z-Exponential function are derived as well as its relationship to the exponential and natural logarithm.\nCategory: General Mathematics\n\n[2099] viXra:1702.0050 [pdf] submitted on 2017-02-03 11:54:49\n\nAuthors: Edgar Valdebenito\n\nIn this note we briefly examine some elementary radical identities found in Ramanujan's work.\nCategory: General Mathematics\n\n[2098] viXra:1701.0685 [pdf] submitted on 2017-01-31 05:28:31\n\n### Optional Model\n\nvery temptive model.\nCategory: General Mathematics\n\n[2097] viXra:1701.0671 [pdf] submitted on 2017-01-30 11:39:16\n\n### On Certain Infinite Products\n\nAuthors: Edgar Valdebenito\n\nIn this note we presents infinite products for some classical constants.\nCategory: General Mathematics\n\n[2096] viXra:1701.0670 [pdf] submitted on 2017-01-30 11:45:58\n\n### A Collection of Double Integrals Involving pi , Bailey's Issue\n\nAuthors: Edgar Valdebenito\n\nIn this note presents a collection of double integrals involving constant pi.\nCategory: General Mathematics\n\n[2095] viXra:1701.0626 [pdf] submitted on 2017-01-26 13:54:34\n\n### Two Sequences\n\nAuthors: Edgar Valdebenito\n\nIn this note we presents some formulas related with the recurrences:(i)u(n+5)=u(n+3)+u(n+2)+u(n), u(0)=u(1)=u(2)=u(3)=0,u(4)=1; (ii)v(n+5)=v(n+4)+v(n+1)+v(n), v(0)=v(1)=v(2)=v(3)=0,v(4)=1\nCategory: General Mathematics\n\n[2094] viXra:1701.0616 [pdf] submitted on 2017-01-26 02:05:30\n\n### Bipolar Neutrosophic Planar Graphs\n\nAuthors: Muhammad Akram, K. P. Shum\n\nFuzzy graph theory is used for solving real-world problems in different fields, including theoretical computer science, engineering, physics, combinatorics and medical sciences. In this paper, we present conepts of bipolar neutrosophic multigraphs, bipolar neutrosophic planar graphs, bipolar neutrosophic dual graphs, and study some of their related properties. We also describe applications of bipolar neutrosophic graphs in road network and electrical connections.\nCategory: General Mathematics\n\n[2093] viXra:1701.0462 [pdf] submitted on 2017-01-11 05:45:26\n\n### Numbers in Base B that Generate Primes with Help the Luhn Function of Order \u03c9\n\nAuthors: Octavian Cira, Florentin Smarandache\n\nWe put the problem to determine the sets of integers in base b \u2265 2 that generate primes with using a function.\nCategory: General Mathematics\n\n[2092] viXra:1701.0457 [pdf] submitted on 2017-01-11 05:51:19\n\n### On Soft Mixed Neutrosophic N-Algebraic Structures\n\nAuthors: Florentin Smarandache\n\n: Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly de\ufb01ned objects. In this paper we introduced soft mixed neutrosophic N-algebraic with the discussion of some of their characteristics. We also introduced soft mixed dual neutrosophic N-algebraic structures, soft weak mixed neutrosophic N-algebraic structures, soft Lagrange mixed neutrosophic N-algebraic structures, soft weak Lagrange mixed neu trosophic and soft Lagrange free mixed neutosophic N-algebraic structures. the so called soft strong neutrosophic loop which is of pure neutrosophic character. We also introduced some of new notions and some basic properties of this newly born soft mixed neutrosophic N-structures related to neutrosophic theory.\nCategory: General Mathematics\n\n[2091] viXra:1701.0452 [pdf] submitted on 2017-01-11 05:55:50\n\n### Relations on Neutrosophic Multi Sets with Properties\n\nAuthors: Said Broumi, Irfan Deli, Florentin Smarandache\n\nIn this paper, we \ufb01rst give the cartesian product of two neutrosophic multi sets(NMS). Then, we de\ufb01ne relations on neutrosophic multi sets to extend the intuitionistic fuzzy multi relations to neutrosophic multi relations. The relations allows to compose two neutrosophic sets. Also, various properties like re\ufb02exivity, symmetry and transitivity are studied.\nCategory: General Mathematics\n\n[2090] viXra:1701.0449 [pdf] submitted on 2017-01-11 06:00:01\n\n### Robot System Identification using 3D Simulation Component Applied on VIPRO Platform\n\nAuthors: Luige Vl\u0103d\u0103reanu, Florentin Smarandache, Mumtaz Ali, Victor Vl\u0103d\u0103reanu, Mingcong Deng\n\nThe paper presents automated estimation techniques for robot parameters through system identification, for both PID control and future implementation of intelligent control laws, with the aim of designing the experimental model in a 3D virtual reality for testing and validating control laws in the joints of NAO humanoid robots.\nCategory: General Mathematics\n\n[2089] viXra:1701.0448 [pdf] submitted on 2017-01-11 06:02:38\n\n### Rough Standard Neutrosophic Sets: an Application on Standard Neutrosophic Information Systems\n\nAuthors: Nguyen Xuan Thao, Bui Cong Cuong, Florentin Smarandache\n\nA rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets, standard neutrosophic information system and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.\nCategory: General Mathematics\n\n[2088] viXra:1701.0447 [pdf] submitted on 2017-01-11 06:03:45\n\n### Shortest Path Problem under Bipolar Neutrosphic Setting\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache, Mumtaz Ali\n\nThis main purpose of this paper is to develop an algorithm to find the shortest path on a network in which the weights of the edges are represented by bipolar neutrosophic numbers. Finally, a numerical example has been provided for illustrating the proposed approach.\nCategory: General Mathematics\n\n[2087] viXra:1701.0446 [pdf] submitted on 2017-01-11 06:04:50\n\n### Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache, Luige Vl\u0102d\u0102reanu\n\nIn this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.\nCategory: General Mathematics\n\n[2086] viXra:1701.0445 [pdf] submitted on 2017-01-11 06:05:51\n\n### Shortest Path Problem Under Trapezoidal Neutrosophic Information\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache\n\nIn this study, we propose an approach to determine the shortest path length between a pair of specified nodes s and t on a network whose edge weights are represented by trapezoidal neutrosophic numbers. Finally, an illustrative example is provided to show the applicability and effectiveness of the proposed approach.\nCategory: General Mathematics\n\n[2085] viXra:1701.0444 [pdf] submitted on 2017-01-11 06:06:52\n\n### Simulation Environment for Mobile Robots Testing Using ROS and Gazebo\n\nAuthors: Kenta Takaya, Toshinori Asai, Valeri Kroumov, Florentin Smarandache\n\nIn the process of development a control strategy for mobile robots, simulation is important for testing the software components, robot behavior and control algorithms in different surrounding environments. In this paper we introduce a simulation environment for mobile robots based on ROS and Gazebo. We show that after properly creating the robot models under Gazebo, the code developed for the simulation process can be directly implemented in the real robot without modi\ufb01cations. In this paper autonomous navigation tasks and 3D-mapping simulation using control programs under ROS are presented. Both the simulation and experimental results agree very well and show the usability of the developed environment.\nCategory: General Mathematics\n\n[2084] viXra:1701.0439 [pdf] submitted on 2017-01-11 06:10:57\n\n### Single Valued Neutrosophic Trapezoid Linguistic Aggregation Operators Based Multi-Attribute Decision Making\n\nAuthors: Said Broumi, Florentin Smarandache\n\nMulti-attribute decision making (MADM). Play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, single valued neutrosophic sets is widely used to model indeterminate information.\nCategory: General Mathematics\n\n[2083] viXra:1701.0438 [pdf] submitted on 2017-01-11 06:11:57\n\n### Sisteme Vibrante Trilobice\n\nAuthors: Florentin Smarandache, Mircea Eugen \u015eelariu\n\nTrilobele sunt func\u0163ii supermatematice circulare excentrice (FSM-CE) de excentricitate unghiular\u0103.\nCategory: General Mathematics\n\n[2082] viXra:1701.0435 [pdf] submitted on 2017-01-11 06:15:54\n\n### Some Mathematical Aspects on Walking Robots Stable Evolution\n\nAuthors: Marcel Migdalovici, Luige Vladareanu, Gabriela Vladeanu, Said broumi, Daniela Baran, Florentin Smarandache\n\nA survey of some author\u2019s concepts on the dynamic systems stability regions, in the general case of dynamic systems, that depend on parameters, is related in the paper. The property of separation of stable regions in the free parameters domain is assumed in the paper as an important property of the environment that is carry out and in the specified case of walking robot analyzed in the paper.\nCategory: General Mathematics\n\n[2081] viXra:1701.0433 [pdf] submitted on 2017-01-11 06:17:59\n\n### The 3n\u00b1p Conjecture: A Generalization of Collatz Conjecture\n\nAuthors: W.B. Vasantha Kandasamy, Ilanthenral Kandasamy, Florentin Smarandache\n\nThe Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried.\nCategory: General Mathematics\n\n[2080] viXra:1701.0424 [pdf] submitted on 2017-01-11 06:27:41\n\n### Trilobic Vibrant Systems\n\nAuthors: Florentin Smarandache, Mircea Eugen \u0218elariu\n\nThe trilobes are ex-centric circular supermathematics functions (EC-SMF) of angular excentricity.\nCategory: General Mathematics\n\n[2079] viXra:1701.0423 [pdf] submitted on 2017-01-11 06:28:41\n\n### Triple Re\ufb01ned Indeterminate Neutrosophic Sets for Personality Classi\ufb01cation\n\nAuthors: Ilanthenral Kandasamy, Florentin Smarandache\n\nPersonality tests are most commonly objective type where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A person may not be in general capable to judge his\/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved. The results of the test depend a lot on the circumstances under which the test is taken, the amount of time that is spent, the past experience of the person, the emotion the person is feeling and the person\u2019s self image at that time and so on.\nCategory: General Mathematics\n\n[2078] viXra:1701.0422 [pdf] submitted on 2017-01-11 06:29:23\n\n### Un Indicator DE Incluziune cu APLICA\u0162II \u00ceN Computer Vision\n\nAuthors: Ovidiu Ilie \u015eandru, Florentin Smarandache\n\n\u00cen aceasta lucrare vom prezenta un procedeu de algoritmizare a operatiilor necesare deplasarii automate a unui obiect predefinit dintr-o imagine video data intr-o regiune tinta a acelei imagini, menit a facilita realizarea de aplicatii software specializate in rezolvarea acestui gen de probleme.\nCategory: General Mathematics\n\n[2077] viXra:1701.0419 [pdf] submitted on 2017-01-10 10:38:19\n\n### \u03b1-D MCDM-Topsis Multi-Criteria Decision Making Method for N-Wise Criteria Comparisons and Inconsistent Problems\n\nAuthors: Azeddine ELHASSOUNY, Florentin SMARANDACHE\n\nThe purpose of this paper is to present an extension and alternative of the hybrid approach using Saaty\u2019s Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called \u03b1-D MCDM-TOPSIS(\u03b1-Discounting Method for Multi-Criteria Decision Making-TOPSIS). The proposed method works not only for preferences that are pairwise comparisons of criteria as AHP does, but for preferences of any n-wise (with n \u2265 2) comparisons of criteria. Finally the \u03b1-D MCDM-TOPSIS methodology is veri\ufb01ed by some examples to demonstrate how it might be applied in di\ufb00erent types of matrices and is how it allwos for consistency, inconsistent, weak inconsistent, and strong inconsistent problems.\nCategory: General Mathematics\n\n[2076] viXra:1701.0418 [pdf] submitted on 2017-01-10 10:41:59\n\n### Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy\n\nAuthors: Ilanthenral Kandasamy, Florentin Smarandache\n\nDouble Refined Indeterminacy Neutrosophic Set(DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache [1], which provides the additional possibility to represent with sensitivity and accuracy the uncertain,imprecise,incomplete,and inconsistent information which are available in real world.\nCategory: General Mathematics\n\n[2075] viXra:1701.0417 [pdf] submitted on 2017-01-10 10:48:31\n\n### Neutrosophic Cubic Ideals in Semigroups\n\nAuthors: Muhammad Gulistan, Majid Khan, Young Bae Jun, Florentin Smarandache, Naveed Yaqoob\n\nWe generalize the concept of fuzzy point, intutionistic fuzzy point, cubic point by introducing the concept of neutrosophic cubic point.\nCategory: General Mathematics\n\n[2074] viXra:1701.0415 [pdf] submitted on 2017-01-10 12:06:01\n\n### Neutrosophic Combination Rules Based on Dempster-Shafer Theory and Dezert-Smarandache Theory\n\nAuthors: Gao Jian, Xinhan Huang, Min Wang, Xinde Li\n\nSeveral neutrosophic combination reles based on the Dempster-Shafer Theory and Dezert-Smarandache Theory are presented in the study.\nCategory: General Mathematics\n\n[2073] viXra:1701.0413 [pdf] submitted on 2017-01-10 12:08:23\n\n### Neutrosophic\ufb01ltersinBE-Algebras\n\nAuthors: Akbar Rezaei, Arsham Borumand Saeid, Florentin Smarandache\n\nIn this paper, we introduce the notion of (implicative)neutrosophic \ufb01lters in BE-algebras. The relation between implicative neutrosophic \ufb01lters and neutrosophic \ufb01lters is investigated and we show that in self distributive BEalgebras these notions are equivalent.\nCategory: General Mathematics\n\n[2072] viXra:1701.0412 [pdf] submitted on 2017-01-10 12:09:13\n\n### Neutrosophic Indetermination and Fiction in Negative Journalistic Communication\n\nAuthors: Florentin Smarandache, \u0218tefan Vl\u0103du\u021bescu\n\nThe study highlights persuasive-fictional inductions that are recorded in journalistic discourse. Subsequently it constitutes an application of Neutrosophic on journalistic communication. The theoretical premise is that journalism is impregnated persuasion.\nCategory: General Mathematics\n\n[2071] viXra:1701.0411 [pdf] submitted on 2017-01-10 12:10:09\n\n### Neutrosophic Logic Applied in the Statistical Indicators Theory\n\nAuthors: Florentin Smarandache, Gheorghe S\u0103voiu\n\nNeutrosophic numbers easily allow modeling uncertainties of prices universe, thus justifying the growing interest for theoretical and practical aspects of arithmetic generated by some special numbers in our work. At the beginning of this paper, we reconsider the importance in applied research of instrumental discernment, viewed as the main support of the final measurement validity.\nCategory: General Mathematics\n\n[2070] viXra:1701.0410 [pdf] submitted on 2017-01-10 12:10:53\n\n### Neutrosophic Modal Logic\n\nAuthors: Florentin Smarandache\n\nWe introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic.\nCategory: General Mathematics\n\n[2069] viXra:1701.0407 [pdf] submitted on 2017-01-10 12:14:36\n\n### Neutrosophic Set and Logic\n\nAuthors: Mumtaz Ali, Florentin Smarandache, Luige Vladareanu\n\nNeutrosophic sets and Logic plays a significant role in approximation theory. It is a generalization of fuzzy sets and intuitionistic fuzzy set. Neutrosophic set is based on the neutrosophic philosophy in which every idea Z, has opposite denoted as anti(Z) and its neutral which is denoted as neut(Z). This is the main feature of neutrosophic sets and logic.\nCategory: General Mathematics\n\n[2068] viXra:1701.0406 [pdf] submitted on 2017-01-10 12:15:32\n\n### Neutrosophic Set Approch for Characterizations of Left Almost Semigroups\n\nIn this paper we have dened neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them.\nCategory: General Mathematics\n\n[2067] viXra:1701.0404 [pdf] submitted on 2017-01-10 12:19:28\n\n### Neutrosophic Social Structures Specificities\n\nAuthors: Florentin Smarandache\n\nThis paper is an extention of (t,i,f)-Neutrosophic Structures applicability, where were introduced for the first time a new type of structures.\nCategory: General Mathematics\n\n[2066] viXra:1701.0403 [pdf] submitted on 2017-01-10 12:20:21\n\n### Neutrosophic Soluble Groups, Neutrosophic Nilpotent Groups and Their Properties\n\nAuthors: Mumtaz Ali, Florentin Smarandache\n\nThe theory of soluble groups and nilpotent groups is old and hence a generalized on. In this paper, we introduced neutrosophic soluble groups and neutrosophic nilpotent groups which have some kind of indeterminacy. These notions are generalized to the classic notions of soluble groups and nilpotent groups. We also derive some new type of series which derived some new notions of soluble groups and nilpotent groups. They are mixed neutrosophic soluble groups and mixed neutrosophic nilpotent groups as well as strong neutrosophic soluble groups and strong neutrosophic nilpotent groups.\nCategory: General Mathematics\n\n[2065] viXra:1701.0402 [pdf] submitted on 2017-01-10 12:21:37\n\n### Neutrosophic Triplet Group\n\nAuthors: Florentin Smarandache, Mumtaz Ali, Muhammad Shabir\n\nIn this paper, for the first time the authors introduced the notions of neutrosophic triplet group which is completely different from the classical group. In neutrosophic triplet group, we apply the fundamental law of neutrosophy that for an idea A, we have neut(A) and anti(A) and we capture the picture of neutrosophy in algebraic structures.\nCategory: General Mathematics\n\n[2064] viXra:1701.0400 [pdf] submitted on 2017-01-10 12:26:05\n\n### New Class of Soft Linear Algebraic Codes and Their Properties Using Soft Sets\n\nAuthors: Mumtaz Ali, Florentin Smarandache, W. B. Vasantha Kandasamy\n\nAlgebraic codes play a signicant role in the minimisation of data corruption which caused by deffects such as inference, noise channel, crosstalk, and packet loss.In this paper, we introduce soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes.\nCategory: General Mathematics\n\n[2063] viXra:1701.0394 [pdf] submitted on 2017-01-10 07:43:01\n\n### An Economic Analogy with Maxwell Equations in Fractional Space\n\nAuthors: Victor Christianto, Florentin Smarandache\n\nHyman Minsky pioneered the idea of the financial instability hypothesis to explain how swings between robustness and fragility in financial markets generate business cycles in the economic system. Therefore, in his model business cycles and instability are endogenous. The problem now is how to put his idea of financial instability into a working model which can be tested with empirical data. Such a Minskyan model is quite rare, though some economists have proposed have tried to achieve that. For example, Toichiro Asada suggested generalized Lotka-Volterra nonlinear systems of equations as a model for Minskyan cycles.\nCategory: General Mathematics\n\n[2062] viXra:1701.0393 [pdf] submitted on 2017-01-10 07:44:18\n\n### An Evidence Fusion Method with Importance Discounting Factors Based on Neutrosophic Probability Analysis in DSmT Framework\n\nAuthors: Qiang Guo, You He, Yong Deng, Tao Jian, Florentin Smarandache\n\nTo obtain effective fusion results of multi source evidences with different importances, an evidence fusion method with importance discounting factors based on neutrosopic probability analysis in DSmT framework is proposed. First, the reasonable evidence sources are selected out based on the statistical analysis of the pignistic probability functions of single focal elements.\nCategory: General Mathematics\n\n[2061] viXra:1701.0392 [pdf] submitted on 2017-01-10 07:45:51\n\n### A New 3n\u22121 Conjecture Akin to Collatz Conjecture\n\nAuthors: W.B. Vasantha Kandasamy, Ilanthenral Kandasamy, Florentin Smarandache\n\nThe Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutani\u2019s problem (after Shizuo Kakutani) and so on.\nCategory: General Mathematics\n\n[2060] viXra:1701.0391 [pdf] submitted on 2017-01-10 07:47:02\n\n### A New Approach to Algebraic Coding Theory Through the Applications of Soft Sets\n\nAuthors: Mumtaz Ali, Florentin Smarandache\n\nAlgebraic codes play a signicant role in the minimisation of data corruption which caused by de\u2044ects such as inference, noise channel, crosstalk, and packet loss.In this paper, we introduce soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discuss several types of soft codes such as type-1 soft codes, complete soft codes etc. Further, we constrcut the soft generator matrix and soft parity check matrix for the soft linear codes. Moreover, we develop two techinques for the decoding of soft codes.\nCategory: General Mathematics\n\n[2059] viXra:1701.0390 [pdf] submitted on 2017-01-10 07:48:31\n\n### A New Similarity Measure Based on Falsity Value Between Single Valued Neutrosophic Sets Based on the Centroid Points of Transformed Single Valued Neutrosophic Values with Applications to Pattern Recognition\n\nAuthors: Mehmet \u015eahin, Necati Olgun, Vakkas Ulu\u00e7ay, Abdullah Karg\u0131n, Florentin Smarandache\n\nIn this paper, we propose transformations based on the centroid points between single valued neutrosophic values. We introduce these transformations according to truth, indeterminacy and falsity value of single valued neutrosophic values. We propose a new similarity measure based on falsity value between single valued neutrosophic sets.\nCategory: General Mathematics\n\n[2058] viXra:1701.0384 [pdf] submitted on 2017-01-10 08:29:52\n\n### An Introduction to Bipolar Single Valued Neutrosophic Graph Theory An Introduction to Bipolar Single Valued Neutrosophic Graph Theory\n\nAuthors: Said Broumi, Florentin Smarandache, Mohamed Talea, Assia Bakali\n\nIn this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.\nCategory: General Mathematics\n\n[2057] viXra:1701.0383 [pdf] submitted on 2017-01-10 08:31:27\n\n### An Operational View in Computational Construction of Information\n\nAuthors: Florentin Smarandache, \u0218tefan Vl\u0102du\u021aescu, Ioan Constantin Dima, Dan Valeriu Voinea\n\nThe paper aims to explain the technology of emergence of information. Our research proves that information as communicational product is the result of processing within some operations, actions, mechanisms and strategies of informational material meanings. Are determined eight computational-communicative operations of building information.\nCategory: General Mathematics\n\n[2056] viXra:1701.0381 [pdf] submitted on 2017-01-10 08:33:59\n\n### Application of Dijkstra Algorithm for Solving Interval Valued Neutrosophic Shortest Path Problem\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache\n\nIn this paper, the authors propose an extended version of Dijkstra\u2019 algorithm for finding the shortest path on a network where the edge weights are characterized by an interval valued neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.\nCategory: General Mathematics\n\n[2055] viXra:1701.0380 [pdf] submitted on 2017-01-10 08:43:21\n\n### Applications of Complex Neutrosophic Sets in Medical Diagnosis Based on Similarity Measures\n\nAuthors: Kalyan Mondal, Surapati Pramanik, Florentin Smarandache\n\nThis paper presents some similarity measures between complex neutrosophic sets. A complex neutrosophic set is a generalization of neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex valued falsity membership functions are the combinations of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term respectively. In the present study, we have proposed complex cosine, Dice and Jaccard similarity measures and investigated some of their properties. Finally, complex neutrosophic cosine, Dice and Jaccard similarity measures have been applied to a medical diagnosis problem with complex neutrosophic information.\nCategory: General Mathematics\n\n[2054] viXra:1701.0377 [pdf] submitted on 2017-01-10 08:51:57\n\n### Applying Dijkstra Algorithm for Solving Neutrosophic Shortest Path Problem\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache\n\nThe selection of shortest path problem is one the classic problems in graph theory. In literature, many algorithms have been developed to provide a solution for shortest path problem in a network. One of common algorithms in solving shortest path problem is Dijkstra\u2019s algorithm. In this paper, Dijkstra\u2019s algorithm has been redesigned to handle the case in which most of parameters of a network are uncertain and given in terms of neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm\nCategory: General Mathematics\n\n[2053] viXra:1701.0376 [pdf] submitted on 2017-01-10 08:54:44\n\n### A Situation Assessment Method in Conditional Evidential Networks based on DSm-PCR5\n\nAuthors: GUO Qiang, HE You, LI Xian, Florentin Smarandache, XU Shi-you\n\nAiming to solving the problem that the evidence information based on Dezert-Smarandache (DSm) model cannot be effectively conditionally reasoned in multi-source heterogeneous network which leads to the low rate of situation assessment, a situation assessment method in Conditional Evidential Network based on DSm-Proportional Conflict Redistribution No.5 (PCR5) is proposed. First, the conditional reasoning formula in Conditional Evidential Network based on DSm model is given. Then, the Disjunctive Rule of Combination(DRC) based on DSm-PCR5 is proposed and the Generalized Bayesian Theorem (GBT) for multiple intersection sets of focal elements can be obtained in the premise that the conditional mass assignments functions of focal elements in refinement of hyper-power set is known. Finally, through the simulation experiments results of situation assessment, the effectiveness of the proposed method is verified.\nCategory: General Mathematics\n\n[2052] viXra:1701.0374 [pdf] submitted on 2017-01-10 09:16:25\n\n### Classical Logic and Neutrosophic Logic. Answers to K. Georgiev.\n\nAuthors: Florentin Smarandache\n\nIn this paper we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to respond to K. Georgiev [1]\u2019s criticism. We recall that if an axiom is true in a classical logic system, it is not necessarily that the axiom be valid in a modern (fuzzy, intuitionistic fuzzy, neutrosophic etc.) logic system.\nCategory: General Mathematics\n\n[2051] viXra:1701.0373 [pdf] submitted on 2017-01-10 09:19:44\n\n### Clustering Algorithm of Triple Re\ufb01ned Indeterminate Neutrosophic Set for Personality Grouping\n\nAuthors: Ilanthenral Kandasamy, Florentin Smarandache\n\nTriple Re\ufb01ned Indeterminate Neutrosophic Set (TRINS) which is a case of the re\ufb01ned neutrosophic set was introduced. It provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world.\nCategory: General Mathematics\n\n[2050] viXra:1701.0371 [pdf] submitted on 2017-01-10 09:22:27\n\n### Clustering of Personality using Indeterminacy Based Personality Test\n\nAuthors: Ilanthenral Kandasamy, Florentin Smarandache\n\nTriple Re\ufb01ned Indeterminate Neutrosophic Set (TRINS) a case of the re\ufb01ned neutrosophic set was introduced in [8]. The uncertain and inconsistent information which are available in real world is represented with sensitivity and accuracy by TRINS.\nCategory: General Mathematics\n\n[2049] viXra:1701.0368 [pdf] submitted on 2017-01-10 09:28:40\n\n### Complex Neutrosophic Similarity Measures in Medical Diagnosis\n\nAuthors: Kalyan Mondal, Mumtaz Ali, Surapati Pramanik, Florentin Smarandache\n\nThis paper presents some similarity measures between complex neutrosophic sets. A complex neutrosophic set is a generalization of neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex valued falsity membership functions are the combinations of realvalued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term respectively.\nCategory: General Mathematics\n\n[2048] viXra:1701.0366 [pdf] submitted on 2017-01-10 09:32:05\n\n### Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache\n\nIn this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node.\nCategory: General Mathematics\n\n[2047] viXra:1701.0364 [pdf] submitted on 2017-01-10 09:37:38\n\n### CSP and \u201comics\u201d Technology Apllied on Versatile and Intelligent Portable Platform for Modeling Complex Bio-medical Data\n\nAuthors: Luige Vladareanu, Mihaiela Iliescu, Hongbo Wang, Feng Yongfei, Victor Vladareanu, Hongnian Yu, Florentin Smarandache\n\nThis paper presents relevant aspects of the idea of using the digital medicine in cancer, so that to shape a viable strategy for creating and implementing an interactive digital platform, NEO-VIP, that should be the basic support to design the strategy for integration of basic, clinical and environmental research on neoplasia progression to cancer.\nCategory: General Mathematics\n\n[2046] viXra:1701.0363 [pdf] submitted on 2017-01-10 09:39:32\n\n### CURIOZIT\u0102\u0162I Ale FUNC\u0162IILOR Supermatematice\n\nAuthors: Florentin Smarandache, Mircea Eugen \u015eelariu\n\nFunc\u0163iile beta excentrice de variabil\u0103 excentric\u0103 bex\u03b8 \u015fi de variabil\u0103 centric\u0103 Bex\u03b1 stau la baza edificiul func\u0163iilor supermatematice circulare excentrice (FSM\u2212CE).\nCategory: General Mathematics\n\n[2045] viXra:1701.0362 [pdf] submitted on 2017-01-10 09:42:09\n\n### Decision-Making Method based on the Interval Valued Neutrosophic Graph\n\nAuthors: Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache\n\nIn this article, we extend the concept of neutrosophic graph-based multicriteria decision making method (NGMCDM) to the case of interval valued neutrosophic graph theory. The new concept is called interval valued neutrosophic graph-based multicriteria decision making method (IVNGMCDM for short).\nCategory: General Mathematics\n\n[2044] viXra:1701.0356 [pdf] submitted on 2017-01-10 09:54:12\n\n### Interval Valued Bipolar Neutrosophic Sets and Their Application in Pattern Recognition\n\nAuthors: Irfan Deli, Yusuf \u015euba\u015f, Florentin Smarandache, Mumtaz Ali\n\nInterval valued bipolar neutrosophic set(IVBN-set) is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making.\nCategory: General Mathematics\n\n[2043] viXra:1701.0354 [pdf] submitted on 2017-01-10 09:56:56\n\n### Interval-Valued Neutrosophic Soft Rough Sets\n\nAuthors: Said Broumi, Florentin Smarandache\n\nWe first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets(IVIF-soft rough sets).\nCategory: General Mathematics\n\n[2042] viXra:1701.0351 [pdf] submitted on 2017-01-10 10:04:37\n\n### Luhn Primes of Order \u03c9\n\nAuthors: Octavian Cira, F, Smarandache\n\nCategory: General Mathematics\n\n[2041] viXra:1701.0340 [pdf] submitted on 2017-01-10 03:55:52\n\n### On the General Solution of Initial Value Problems of Ordinary Differential Equations Using the Method of Iterated Integrals\n\nAuthors: Ahsan Amin\n\nOur goal is to give a very simple, effective and intuitive algorithm for the solution of initial value problem of ODEs of 1st and arbitrary higher order with general i.e. constant, variable or nonlinear coefficients and the systems of these ordinary differential equations. We find an expansion of the differential equation\/function to get an infinite series containing iterated integrals evaluated solely at initial values of the dependent variables in the ordinary differential equation. Our series represents the true series expansion of the closed form solution of the ordinary differential equation. The method can also be used easily for general 2nd and higher order ordinary differential equations. We explain with examples the steps to solution of initial value problems of 1st order ordinary differential equations and later follow with more examples for linear and non-linear 2nd order and third order ODEs. We have given mathematica code for the solution of nth order ordinary differential equations and show with examples how to use the general code on 1st, 2nd and third order ordinary differential equations. We also give mathematica code for the solution of systems of a large number of general ordinary differential equations each of arbitrary order. We give an example showing the ease with which our method calculates the solution of system of three non-linear second order ordinary differential equations.\nCategory: General Mathematics\n\n[2040] viXra:1701.0337 [pdf] submitted on 2017-01-09 12:02:34\n\n### AVRO: Real Flying Saucer\n\nAuthors: Desire Francine Gobato, Ricardo Gobato\nComments: 1 Page. Panel presented in the THIRD INTERNATIONAL SATELLITE CONFERENCE ON MATHEMATICAL METHODS IN PHYSICS, Londrina - PR (Brazil), October 21 - 26, 2013.\n\nOne of the most unusual V\/STOL aircraft programs was the Avro VZ-9 \u201cAvrocar\u201d. Designed to be a true flying saucer, the Avrocar was one of the few V\/STOL aircraft to be developed in complete secrecy. Despite significant design changes during flight test, the Avrocar was unable to achieve its objectives and the program was ultimately canceled after the expenditure of over $10 million (1954-61). The concept of a lift fan driven by a turbojet engine did not die either, and lives on today as a key component of the Lockheed X-35 Joint Strike Fighter contender. While the Avrocar was under development, Peter Kappus of General Electric independently developed a lift fan propulsion system which evolved into the GE\/Ryan VZ-11 (later XV-5) \u201cVertifan\u201d. Category: General Mathematics [2039] viXra:1701.0280 [pdf] submitted on 2017-01-04 06:57:26 ### Fixed Point Method , Number pi , Fractals Authors: Edgar Valdebenito Comments: 6 Pages. In this note we present:Real solutions of the polynomial equations:x^5+x^4+x-1=0 , x^5+x^3+x^2-1=0 , via fixed point method , Relations for pi number, Fractal connection. Category: General Mathematics [2038] viXra:1701.0279 [pdf] submitted on 2017-01-03 13:45:09 ### Static Versus Dynamic Data Information Fusion Analysis Using Dddas for Cyber Security Trust Authors: Erik Blasch, Youssif Al-Nashif, Salim Hariri Comments: 15 Pages. Information fusion includes signals, features, and decision-level analysis over various types of data including imagery, text, and cyber security detection. With the maturity of data processing, the explosion of big data, and the need for user acceptance; the Dynamic Data-Driven Application System (DDDAS) philosophy fosters insights into the usability of information systems solutions. Category: General Mathematics [2037] viXra:1701.0278 [pdf] submitted on 2017-01-03 13:46:09 ### Structural Properties of Neutrosophic Abel-Grassmanns Groupoids Authors: Madad Khan, Misbah Comments: 25 Pages. In this paper, we have introduced the notion of neutrosophic (2;2)regular, neutrosophic strongly regular neutrosophic AG-groupoids and investigated these structures. We have shown that neutrosophic regular, neutrosophic intraregular and neutrosophic strongly regular AG-groupoid are the only generalized classes of an AG-groupoid. Category: General Mathematics [2036] viXra:1701.0277 [pdf] submitted on 2017-01-03 13:47:23 ### Studies on Finite Semigroups, Semigroup Semirings, Group Semirings on Semirings as Distributive Lattices Authors: Jayshree K. Comments: 219 Pages. As the name suggests, a semigroup is a generalization of a group; because a semigroup need not in general have an element which has an inverse. The algebraic structure enjoyed by a semigroup is a non-empty set together with an associative closed binary operation. Category: General Mathematics [2035] viXra:1701.0276 [pdf] submitted on 2017-01-03 13:48:38 ### Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field Authors: Mumtaz Ali, Mohsin Khan Comments: 8 Pages. This article is a study on the development of neutrosophic triplet ring and neutrosophic triplet field. Category: General Mathematics [2034] viXra:1701.0275 [pdf] submitted on 2017-01-03 13:49:23 ### Supervised Pattern Recognition Using Similarity Measure Between Two Interval Valued Neutrosophic Soft Sets Authors: Anjan Mukherjee, Sadhan Sarkar Comments: 8 Pages. F. Smarandache introduced the concept of neutrosophic set in 1995 and P. K. Maji introduced the notion of neutrosophic soft set in 2013, which is a hybridization of neutrosophic set and soft set. Category: General Mathematics [2033] viXra:1701.0274 [pdf] submitted on 2017-01-03 13:50:16 ### Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space Authors: G\u00fclnur Saffak Atalay, Emin Kasap Comments: 11 Pages. In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Category: General Mathematics [2032] viXra:1701.0273 [pdf] submitted on 2017-01-03 13:51:26 ### Survey on Fusion of Multimodal Biometrics Using Score Level Fusion Authors: S.mohana Prakash, P.betty, K.sivanarulselvan Comments: 10 Pages. Biometrics is used to uniquely identify a person\u2019s individual based on physical and behavioural characteristics. Unimodal biometric system contains various problems such as degree of freedom, spoof attacks, non-universality, noisy data and error rates. so the need of multimodal biometrics system occurred, a multimodal biometric system combines the different biometric traits and provides better performance as compared to a single biometric trait. Category: General Mathematics [2031] viXra:1701.0272 [pdf] submitted on 2017-01-03 13:52:20 ### Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set Authors: Edmundas Kazimieras Zavadskas, Romualdas Bau\u0161ys, Marius Lazauskas Comments: 14 Pages. The principles of sustainability have become particularly important in the construction, real estate maintenance sector, and all areas of life in recent years. The one of the major problem of urban territories that domestic and construction waste of generated products cannot be removed automatically. Category: General Mathematics [2030] viXra:1701.0271 [pdf] submitted on 2017-01-03 13:53:15 ### Texture Segmentation Based on Gabor Filters and Neutrosophic Graph Cut Authors: Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo Comments: 4 Pages. Image segmentation is the \ufb01rst step of image processing and image analysis. Texture segmentation is a challenging task in image segmentation applications. Category: General Mathematics [2029] viXra:1701.0269 [pdf] submitted on 2017-01-03 13:54:47 ### The Generalized Dice Measures for Multiple Attribute Decision Making Under Simpli\ufb01ed Neutrosophic Environments Authors: Yun Ye Comments: 9 Pages. A simpli\ufb01ed neutrosophic set (SNS) is a subclass of neutrosophic set and contains a single-valued neutrosophic set (SVNS) and an interval neutrosophic set (INS). Category: General Mathematics [2028] viXra:1701.0268 [pdf] submitted on 2017-01-03 13:57:03 ### The Generalized Golden Proportion, a New Theory of Real Numbers, and Ternary Mirror-Symmetrical Arithmetic Authors: Alexey Stakhov Comments: 20 Pages. We consider real important Generalized Golden proportion. Category: General Mathematics [2027] viXra:1701.0267 [pdf] submitted on 2017-01-03 13:57:58 ### The Impact of the Quality Assessment of Optimal Assignment for Data Association in a Multitarget Tracking Context Authors: J. Dezert, A. Tchamova, P. Konstantinova Comments: 11 Pages. The main purpose of this paper is to apply and to test the performance of a new method, based on belief functions, proposed by Dezert et al. in order to evaluate the quality of the individual association pairings provided in the optimal data association solution for improving the performances of multisensormultitarget tracking systems. Category: General Mathematics [2026] viXra:1701.0265 [pdf] submitted on 2017-01-03 13:58:52 ### The Knee Wear Prediction of UHMWPE Tibial Insert Using VIPRO Platform Authors: Lucian Capitanu, Luige Vladareanu, Virgil Florescu Comments: 10 Pages. The failure mechanism was postulated as a combination of the high level of loading during normal activities and a non-conforming contact mechanism between the femoral condyles and the tibial insert. Category: General Mathematics [2025] viXra:1701.0263 [pdf] submitted on 2017-01-03 14:01:39 ### The Smarandache Bryant Schneider Group Of A Smarandache Loop Authors: Temitope Gbolahan Jaiyeola Comments: 14 Pages. The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced. Relationship(s) between the Bryant Schneider Group and the Smarandache Bryant Schneider Group of an S-loop are discovered and the later is found to be useful in \ufb01nding Smarandache isotopy-isomorphy condition(s) in S-loops just like the formal is useful in \ufb01nding isotopy-isomorphy condition(s) inloops. Category: General Mathematics [2024] viXra:1701.0255 [pdf] submitted on 2017-01-04 03:26:39 ### The Weighted Distance Measure Based Method to Neutrosophic Multi-Attribute Group Decision Making Authors: Chunfang Liu, YueSheng Luo Comments: 12 Pages. Neutrosophic set (NS) is a generalization of fuzzy set (FS) that is designed for some practical situations in which each element has di\ufb00erent truth membership function, indeterminacy membership function and falsity membership function. Category: General Mathematics [2023] viXra:1701.0254 [pdf] submitted on 2017-01-04 03:28:13 ### Three-Way Fuzzy Concept Lattice Representation Using Neutrosophic Set Authors: Prem Kumar Singh Comments: 11 Pages. Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. Category: General Mathematics [2022] viXra:1701.0253 [pdf] submitted on 2017-01-04 03:29:17 ### Topsis Approach to Chance Constrained Multi Objective Multi Level Quadratic Programming Problem Authors: Surapati Pramanik, Durga Banerjee, B. C. Giri Comments: 18 Pages. This paper presents TOPSIS approach to solve chance constrained multi \u2013 objective multi \u2013 level quadratic programming problem. The proposed approach actually combines TOPSIS and fuzzy goal programming. Category: General Mathematics [2021] viXra:1701.0251 [pdf] submitted on 2017-01-04 03:33:20 ### Toward Trustworthy Cloud Service Selection: a Time-Aware Approach Using Interval Neutrosophic Set Authors: Hua Ma, Zhigang Hu, Keqin Li, Hongyu Zhang Comments: 20 Pages. Toward trustworthy cloud service selection: A time-aware approach using interval neutrosophic set. Category: General Mathematics [2020] viXra:1701.0250 [pdf] submitted on 2017-01-04 03:34:42 ### Toward Wisdom: A Hierarchical Wisdom Ontology based on Chinese Classics Authors: Feng Liu Comments: 14 Pages. Based on extensive exploration in Chinese classics, this paper \u00afnds a fresh new perspective for KM philosophy especially in pyramid issue: The primary role in knowledge ontology should be consciousness rather than IT aspects, in which the former determines the perceived results such as data, information, knowledge or wisdom. Category: General Mathematics [2019] viXra:1701.0245 [pdf] submitted on 2017-01-04 03:42:47 ### Uncertainty Measure Method of Evidence and Its Application Authors: CHEN Jinguang, ZHANG Fen, MA Lili. Comments: 6 Pages. Conflict of evidence is one of the most important factor which leads to the fusion result of evidence theory unsatisfactory. Thus the evidence conflict has been the key issue to be solved in evidence theory. By using a linear combination of ambiguity measure, discord measure and nonspecificity measure, a new uncertainty measurement method of evidence is presented. Category: General Mathematics [2018] viXra:1701.0244 [pdf] submitted on 2017-01-04 03:44:01 ### Vector Similarity Measures for Simplied Neutrosophic Hesitant Fuzzy Set and Their Applications Authors: Jun Ye, Tahir Mahmood, Qaisar Khan Comments: 24 Pages. In this article we present three similarity measures between simplied neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space. Category: General Mathematics [2017] viXra:1701.0243 [pdf] submitted on 2017-01-04 03:45:30 ### \u0410\u041d\u0410\u041b\u0418\u0417 \u041f\u0420\u0410\u0412\u0418\u041b \u041a\u041e\u041c\u0411\u0418\u041d\u0418\u0420\u041e\u0412\u0410\u041d\u0418\u042f \u0413\u0420\u0423\u041f\u041f\u041e\u0412\u042b\u0425 \u042d\u041a\u0421\u041f\u0415\u0420\u0422\u041d\u042b\u0425 \u041e\u0426\u0415\u041d\u041e\u041a \u0412 \u041a\u041e\u041d\u0424\u041b\u0418\u041a\u0422\u041d\u042b\u0425 \u0421\u0418\u0422\u0423\u0410\u0426\u0418\u042f\u0425 Authors: KOVALENKO Igore Ivanovich, ShVED Alena Vladimirovna, PUGAChENKO Ekaterina Sergeevna Comments: 7 Pages. \u041f\u0440\u0438 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u0433\u0440\u0443\u043f\u043f\u043e\u0432\u044b\u0445 \u044d\u043a\u0441\u043f\u0435\u0440\u0442\u043d\u044b\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u044d\u0444\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u044b \u043f\u0440\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u043c \u0443\u0447\u0435\u0442\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u041d\u0415\u2013\u0444\u0430\u043a\u0442\u043e\u0440\u043e\u0432 (\u043d\u0435\u043f\u043e\u043b\u043d\u043e\u0442\u0430, \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c, \u043d\u0435\u0447\u0435\u0442\u043a\u043e\u0441\u0442\u044c, \u043d\u0435\u0434\u043e\u0441\u0442\u043e\u0432\u0435\u0440\u043d\u043e\u0441\u0442\u044c, \u043d\u0435\u043e\u0434\u043d\u043e\u0437\u043d\u0430\u0447\u043d\u043e\u0441\u0442\u044c \u0438 \u0434\u0440.), \u0447\u0442\u043e \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c \u0441\u043e\u0437\u0434\u0430\u0435\u0442 \u043e\u0441\u043d\u043e\u0432\u0443 \u0434\u043b\u044f \u0432\u044b\u0431\u043e\u0440\u0430 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0445 \u043f\u043e\u0434\u0445\u043e\u0434\u043e\u0432 \u0438 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438 \u044d\u043a\u0441\u043f\u0435\u0440\u0442\u043d\u043e\u0439 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438. Category: General Mathematics [2016] viXra:1701.0242 [pdf] submitted on 2017-01-04 03:47:03 ### \u0412\u042b\u0411\u041e\u0420 \u0420\u0415\u0428\u0415\u041d\u0418\u0419 \u041d\u0410 \u041c\u041d\u041e\u0416\u0415\u0421\u0422\u0412\u0415 \u042d\u041a\u0421\u041f\u0415\u0420\u0422\u041d\u042b\u0425 \u0421\u0412\u0418\u0414\u0415\u0422\u0415\u041b\u042c\u0421\u0422\u0412 \u0421 \u0418\u0421\u041f\u041e\u041b\u042c\u0417\u041e\u0412\u0410\u041d\u0418\u0415\u041c \u041f\u0420\u0410\u0412\u0418\u041b \u041f\u0415\u0420\u0415\u0420\u0410\u0421\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u042f \u041a\u041e\u041d\u0424\u041b\u0418\u041a\u0422\u041e\u0412 Authors: Igore KOVALENKO, Ekaterina ANTIPOVA, Sergey BORDUN Comments: 5 Pages. \u0412 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u044d\u043a\u0441\u043f\u0435\u0440\u0442\u0438\u0437\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u0443\u0436\u0434\u0435\u043d\u0438\u044f\u043c\u0438 \u044d\u043a\u0441\u043f\u0435\u0440\u0442\u043e\u0432 \u043c\u043e\u0433\u0443\u0442 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0442\u044c \u043a\u043e\u043d\u0444\u043b\u0438\u043a\u0442\u043d\u044b\u0435 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 \u043e\u0446\u0435\u043d\u043a\u0438 \u0434\u0432\u0443\u0445 \u0438 \u0431\u043e\u043b\u0435\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445 \u044d\u043a\u0441\u043f\u0435\u0440\u0442\u043d\u044b\u0445 \u0433\u0440\u0443\u043f\u043f \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f. Category: General Mathematics [2015] viXra:1701.0239 [pdf] submitted on 2017-01-03 11:09:03 ### Lean Supplier Selection based on Hybrid MCGDM Approach using Interval Valued Neutrosophic Sets: A Case Study Authors: Rajeswara Reddy P., Naga Raju I., Diwakar Reddy V., Krishnaiah G. Comments: 6 Pages. In any manufacturing industry 60% - 70% of total cost of product pertains raw materials cost. Therefore selec material supplier is very significant factor to improve quality of product as well as reducing total cost. Supplier selection considers various factors and numerous alternatives. Category: General Mathematics [2014] viXra:1701.0238 [pdf] submitted on 2017-01-03 11:10:21 ### Liar Liar, Pants on \ufb01re; or How to Use Subjective Logic and Argumentation to Evaluate Information from Untrustworthy Sources Authors: Andrew Koster, Ana L. C. Bazzan, Marcelo de Souza Comments: 18 Pages. This paper presents a non-prioritized belief change operator, designed speci\ufb01cally for incorporating new information from many heterogeneous sources in an uncertain environment. We take into account that sources may be untrustworthy and provide a principled method for dealing with the reception of contradictory information. Category: General Mathematics [2013] viXra:1701.0235 [pdf] submitted on 2017-01-03 11:15:39 ### Medical Treatment Options Selection Using Extended Todim Method with Single Valued Trapezoidal Neutrosophic Numbers Authors: Hong-yu Zhang, Pu Ji, Jian-qiang Wang Comments: 36 Pages. The selection process of medical treatment options is a multi-criteria decision-making (MCDM) one, and single valued trapezoidal neutrosophic numbers (SVTNNs) are useful in depicting information and fuzziness in selection processes. Category: General Mathematics [2012] viXra:1701.0234 [pdf] submitted on 2017-01-03 11:16:49 ### Merging of Semilattices and Their Special Properties Authors: M. Reehana Parveen, P. Sekar Comments: 16 Pages. In this paper for the first time authors define the new notion of merging of semilattices. The properties of merged semilattices is studied and several interesting results are proved in this direction. Category: General Mathematics [2011] viXra:1701.0233 [pdf] submitted on 2017-01-03 11:18:32 ### M\u00e9thode D\u2019aide \u00e0 la D\u00e9cision Bas\u00e9e Sur un Raisonnement \u00e9videntiel Pour \u00e9valuer L\u2019ef\ufb01cacit\u00e9 D\u2019un Ouvrage Torrentiel de Stabilisation Authors: Simon CARLADOUS, Jean-Marc TACNET, Jean DEZERT, Corinne CURT, Mireille BATTON-HUBERT Comments: 7 Pages. Assessment of structural, functional and economic effectiveness of civil protective works against natural hazard, such as torrential check dams, is a key issue for infrastructures assets owners and managers such as French government who owns many of them. This assessment relies on imperfect information (imprecise, incomplete, uncertain), provided by several sources, which relates as far to structures themselves than to natural phenomena scenarios. Category: General Mathematics [2010] viXra:1701.0232 [pdf] submitted on 2017-01-03 11:22:24 ### MRI Brain Tumor Segmentation Methods- A Review Authors: Gursangeet Kaur, Jyoti Rani Comments: 5 Pages. Medical image processing and its segmentation is an active and interesting area for researchers. It has reached at the tremendous place in diagnosing tumors after the discovery of CT and MRI. MRI is an useful tool to detect the brain tumor and segmentation is performed to carry out the useful portion from an image. The purpose of this paper is to provide an overview of different image segmentation methods like watershed algorithm, morphological operations, neutrosophic sets, thresholding, K-means clustering, fuzzy C-means etc using MR images. Category: General Mathematics [2009] viXra:1701.0231 [pdf] submitted on 2017-01-03 11:24:55 ### Multi-Camera People Tracking Using Evidential Filters Authors: Rafael Munoz-Salinas, R. Medina-Carnicer, F.J. Madrid-Cuevas, A. Carmona-Poyato Comments: 18 Pages. Multi-camera people tracking using evidential filters. Category: General Mathematics [2008] viXra:1701.0230 [pdf] submitted on 2017-01-03 11:42:01 ### Multi-Criteria Decision Making Method Based on Similarity Measures Under Single Valued Neutrosophic Refined and Interval Neutrosophic Refined Environments Authors: Faruk Karaaslan Comments: 15 Pages. In this paper, we propose three similarity measure methods for single valued neutrosophic re\ufb01ned sets and interval neutrosophic re\ufb01ned sets based on Jaccard, Dice and Cosine similarity measures of single valued neutrosophic sets and interval neutrosophic sets. Category: General Mathematics [2007] viXra:1701.0229 [pdf] submitted on 2017-01-03 11:42:59 ### Multi \u2013 Criteria Group Decision Making Model in Neutrosophic Refined Set and Its Application Authors: Surapati Pramanik, Durga Banerjee, B. C. Giri Comments: 7 Pages. In the paper, multi criteria group decision making model has been presented based on tangent similarity measure of neutrosophic refined set. Simplified form of tangent similarity measure in neutrosophic refined set has been presented. New ranking method has been proposed based on refined tangent similarity measure. The proposed approach has been illustrated by solving a teacher selection problem in neutrosophic refined set environment. Category: General Mathematics [2006] viXra:1701.0227 [pdf] submitted on 2017-01-03 11:44:43 ### Multicriteria Decision Making Approach by Vikor Under Interval Neutrosophic Set Environment Authors: Romualdas Bausys, Edmundas-Kazimieras Zavadskas Comments: 16 Pages. The paper presents the extension of VIKOR method for the solution of the multicriteria decision making problems, namely VIKOR-IVNS. The original VIKOR method was proposed for the solution of the decision problems with the conflicting and non-common measurable criteria. In this paper, a new extension of the crisp VIKOR method has been proposed. This extension is developed in the context of interval-valued neutrosophic sets. Category: General Mathematics [2005] viXra:1701.0226 [pdf] submitted on 2017-01-03 11:46:18 ### Multi-Objective Neutrosophic Optimization Technique and its Application to Structural Design Authors: Mridula Sarkar, Samir Dey, Tapan Kumar Roy Comments: 7 Pages. In this paper, a multi-objective non-linear neutrosophic optimization (NSO) approach for optimizing the design of plane truss structure with multiple objectives subject to a specified set of constraints has been developed. Category: General Mathematics [2004] viXra:1701.0225 [pdf] submitted on 2017-01-03 11:47:18 ### Multiple Attribute Decision-Making Method under Hesitant Single Valued Neutrosophic Uncertain Linguistic Environment Authors: Yun Ye Comments: 20 Pages. Motivated by the idea of single valued neutrosophic uncertain linguistic sets (SVNULSs) and hesitant fuzzy sets (HFSs), in this article we combine SVNULSs with HFSs to present the idea of hesitant single valued neutrosophic uncertain linguistic sets (HSVNULSs), hesitant single valued neutrosophic uncertain linguistic elements (HSVNULEs) and defined some basic operational laws of HSVNULEs. Category: General Mathematics [2003] viXra:1701.0223 [pdf] submitted on 2017-01-03 11:48:29 ### Multiple Attribute Group Decision Making Method Based on Some Normal Neutrosophic Number Heronian Mean Operator Authors: Peide Liu, Fei Teng Comments: 27 Pages. In this paper, similar to the extension from intuitionistic fuzzy numbers (IFNs) to neutrosophic numbers (NNs), we propose the normal neutrosophic numbers (NNNs) based on the normal intuitionistic fuzzy numbers (NIFNs) to handle the incompleteness, indeterminacy and inconsistency of the evaluation information. Category: General Mathematics [2002] viXra:1701.0222 [pdf] submitted on 2017-01-03 11:49:40 ### Multiple Moving Targets Tracking Research in Cluttered Scenes Authors: Yingwu Fang, Yi Wang, Wei Jin Comments: 5 Pages. Traditional particle filter (PF) will have bad effect when the target\u2019s color is similar to the background or the target is blocked, and an improved tracking algorithm is presented in the framework of PF and DSmT. Category: General Mathematics [2001] viXra:1701.0221 [pdf] submitted on 2017-01-03 11:51:02 ### Multisource Fusion\/Classification Using ICM and DSmT with New Decision Rule Authors: Azeddine Elhassouny, Soufiane Idbraim, Aissam Bekkarri, Driss Mammass, Danielle Ducrot Comments: 9 Pages. In this paper we introduce a new procedure for classification and change detection by the integration in a fusion process using hybrid DSmT model, both, the contextual information obtained from a supervised ICM classification with constraints and the temporal information with the use of two images taken at two different dates. Category: General Mathematics [2000] viXra:1701.0220 [pdf] submitted on 2017-01-03 11:53:32 ### Multitarget Tracking Performance based on the Quality Assessment of Data Association Authors: Jean Dezert, Albena Tchamova, Pavlina Konstantinova Comments: 8 Pages. The main objective of this paper is to present, to apply, and to test the effectiveness of the new method, based on belief functions, proposed by Dezert et al. in order to evaluate the quality of the individual association pairings provided in the classical optimal data association solution for improving the performances of multitarget tracking systems in clutter, when some of the association decisions given in the optimal assignment solution are unreliable and doubtful and lead to potentially critical mistake. Category: General Mathematics [1999] viXra:1701.0217 [pdf] submitted on 2017-01-03 11:56:40 ### Neutrosophic Complex N Continuity Authors: R. Narmada Devi Comments: 14 Pages. In this paper, the concept of N-open set in neutrosophic complex topological space is introduced. Some of the interesting properties of neutrosophic complex N-open sets are studied. The idea of neutrosophic complex N-continuous function and its characterization are discussed. Also the interrelation among the sets and continuity are established. Category: General Mathematics [1998] viXra:1701.0216 [pdf] submitted on 2017-01-03 11:57:44 ### Neutrosophic Cubic Ideals Authors: Majid Khan, Muhammad Gulistan Comments: 21 Pages. Operational properties of neutrosophic cubic sets are investigated.The notion of neutrosophic cubic subsemigroups and neutrosophic cubic left (resp.right) ideals are introduced, and several properties are investigated. Category: General Mathematics [1997] viXra:1701.0215 [pdf] submitted on 2017-01-03 12:00:04 ### Neutrosophic Functions of the Joint Roughness Coefficient and the Shear Strength: A Case Study from the Pyroclastic Rock Mass in Shaoxing City, China Authors: Jun Ye, Rui Yong, Qi-Feng Liang, Man Huang, Shi-Gui Du Comments: 10 Pages. Many studies have been carried out to investigate the scale effect on the shear behavior of rock joints. Category: General Mathematics [1996] viXra:1701.0214 [pdf] submitted on 2017-01-03 12:01:01 ### Neutrosophic Hypergraphs Authors: Muhammad Akram, Sundas Shahzadi, A. Borumand Saeid Comments: 16 Pages. In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties. Category: General Mathematics [1995] viXra:1701.0213 [pdf] submitted on 2017-01-03 12:01:53 ### Neutrosophic Hyperideals of \u0393-Semihyperrings Authors: Debabrata Mandal Comments: 12 Pages. Hyperstructures, in particular hypergroups, were introduced in 1934 by Marty [12] at the eighth congress of Scandinavian Mathematicians. The notion of algebraic hyperstructure has been developed in the following decades and nowadays by many authors, especially Corsini [2, 3], Davvaz [5, 6, 7, 8, 9], Mittas [13], Spartalis [16], Stratigopoulos [17] and Vougiouklis [20]. Basic de\ufb01nitions and notions concerning hyperstructure theory can be found in [2]. Category: General Mathematics [1994] viXra:1701.0210 [pdf] submitted on 2017-01-03 12:08:30 ### Neutrosophic Linear Programming Authors: Surapati Pramanik Comments: 11 Pages. This paper proposes the framework of neutrosophic linear programming approach for solving multi objective optimization problems involving uncertainty and indeterminacy. Category: General Mathematics [1993] viXra:1701.0209 [pdf] submitted on 2017-01-03 12:09:10 ### Neutrosophic Logic Based Inconsistent Relational Database for Normalizing Data and Accurate Decision Authors: Soumitra De Comments: 7 Pages. In this paper the author propose a new method of search called Neutrosophic search to find the most suitable match for the predicates to answer any imprecise query made by the database users. Neutrosophic search is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or vague relation can only handle incomplete information. Neutrosophic logic is an extension of classical logic. Category: General Mathematics [1992] viXra:1701.0207 [pdf] submitted on 2017-01-03 12:10:59 ### Neutrosophic Multi-Objective Linear Programming Authors: Surapati Pramanik Comments: 11 Pages. For modeling imprecise and indeterminate data for multi-objective decision making, two different methods: neutrosophic multi-objective linear\/non-linear programming, neutrosophic goal programming, which have been very recently proposed in the literatuire. Category: General Mathematics [1991] viXra:1701.0206 [pdf] submitted on 2017-01-03 12:12:26 ### Neutrosophic Refined Similarity Measure Based on Tangent Function and Its Application to Multi Attribute Decesion Making Authors: Kalyan Mondal, Surapati Pramanik Comments: 10 Pages. In the paper, tangent similarity measure of neutrosophic refined set is proposed and its properties are studied. The concept of this tangent similarity measure of single valued neutrosophic refined sets is an extension of tangent similarity measure of single valued neutrosophic sets. Category: General Mathematics [1990] viXra:1701.0201 [pdf] submitted on 2017-01-03 12:16:38 ### Neutrosophic Technique and Its Application Authors: A. A. Salama Comments: 13 Pages. The fundamental concepts of neutrosophic set, introduced by Smarandache in [ 38, 39, 40], and Salama et al. in [20-37], provides a natural foundation for treating mathematically the neutrosophic phenomena which exist pervasively in our real world and for building new branches of neutrosophic mathematics. Category: General Mathematics [1989] viXra:1701.0200 [pdf] submitted on 2017-01-03 12:17:25 ### Neutrosophic Vague Soft Expert Set Theory Authors: Ashraf Al-Quran, Nasruddin Hassan Comments: 12 Pages. In this paper, we \ufb01rst introduce the concept of neutrosophic vague soft expert sets (NVSESs for short) which combines neutrosophic vague sets and soft expert sets to be more effective and useful. We also de\ufb01ne its basic operations, namely complement, union, intersection, AND and OR along with illustrative examples, and study some related properties with supporting proofs. Lastly, this concept is applied to a decision making problem and its effectiveness is demonstrated using a hypothetical example. Category: General Mathematics [1988] viXra:1701.0199 [pdf] submitted on 2017-01-03 12:18:06 ### Neutrsophic Complex N-Continuity Authors: R. Narmada Devi Comments: 14 Pages. In this paper, the concept of N-open set in neutrosophic complex topological space is introduced. Some of the interesting properties of neutrosophic complex N-open sets are studied. The idea of neutrosophic complex N-continuous function and its characterization are discussed. Also the interrelation among the sets and continuity are established. Category: General Mathematics [1987] viXra:1701.0198 [pdf] submitted on 2017-01-03 12:19:08 ### New Algebraic Properties of Middle Bol Loops Authors: Temitope Gbolahan Jaiyeola, S.P. David Comments: 23 Pages. In this paper, some new algebraic properties of a middle Bol loop are established. Category: General Mathematics [1986] viXra:1701.0197 [pdf] submitted on 2017-01-03 12:19:56 ### New Distance Measure of Single-Valued Neutrosophic Sets and Its Application Authors: Han-Liang Huang Comments: 12 Pages. A single-valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which can be used to handle uncertainty, imprecise, indeterminate, and inconsistent information in real life. In this paper, a new distance measure between two SVNSs is de\ufb01ned by the full consideration of truthmembership function, indeterminacy-membership function, and falsity-membership function for the forward and backward differences. Category: General Mathematics [1985] viXra:1701.0196 [pdf] submitted on 2017-01-03 12:20:43 ### New Type Surfaces in Terms of B-Smarandache Curves in Sol3 Authors: Talat K\u00f6rp\u0131nar Comments: 5 Pages. Analisa-se novos tipos de superf\u00edcies conforme as curvas B- Smarandache TM1 das h\u00e9lices com inclina\u00e7\u00e3o B bi-harmonica. Caracterizam-se as curvas B- Smarandache TM1 conforme as curvaturas de Bishop, acresentando outras rela\u00e7\u00f5es interessantes. Category: General Mathematics [1984] viXra:1701.0195 [pdf] submitted on 2017-01-03 12:21:37 ### N-Fold Filters in Smarandache Residuated Lattices, Part (I) Authors: Somayeh Motamed, Mahsa Sadeghi Kosarkhizi Comments: 12 Pages. In this paper we introduce the notions of n-fold BL-Smarandache positive implicateve \ufb01lter and n-fold BL-Smarandache implicateve \ufb01lter in Smarandache residuated lattices and study the relations among them. Category: General Mathematics [1983] viXra:1701.0194 [pdf] submitted on 2017-01-03 12:22:24 ### N-Fold Filters in Smarandache Residuated Lattices, Part (Ii) Authors: Somayeh Motamed, Mahsa Sadeghi Kosarkhizi Comments: 12 Pages. In this paper we introduce the notions of n-fold BL-Smarandache n-fold BL-Smarandache fantastic \ufb01lter and n-fold BL-Smarandache easy \ufb01lter in Smarandache residuated lattices and study the relations among them. Category: General Mathematics [1982] viXra:1701.0193 [pdf] submitted on 2017-01-03 12:23:19 ### Non-Overlapping Matrices Authors: Elena Barcucci, Antonio Bernini, Stefano Bilotta, Renzo Pinzani Comments: 16 Pages. Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the k-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational. Category: General Mathematics [1981] viXra:1701.0192 [pdf] submitted on 2017-01-03 12:24:17 ### N\u00f6trosofik Benzerlik \u00d6l\u00e7\u00fcs\u00fc Ile Pid Katsay\u0131lar\u0131n\u0131n Ayarlanmas\u0131 Metodunda \u00dc\u00e7gen, Gauss ve \u00c7an E\u011frisi \u00dcyelik Fonksiyonlar\u0131n\u0131n Etkilerinin \u0130ncelenmesi Authors: Mehmet Serhat Can, \u00d6mer Faruk \u00d6zg\u00fcven Comments: 7 Pages. PID denetleyici ile bulan\u0131k mant\u0131k denetleyici ve bunlardan olu\u015fturulmu\u015f karma tasar\u0131mlar, kontrol uygulamalar\u0131nda s\u0131k\u00e7a kullan\u0131lan denetleyici t\u00fcrlerindendir. Category: General Mathematics [1980] viXra:1701.0191 [pdf] submitted on 2017-01-03 12:25:01 ### N\u00f6trosofik \u00dcyelik Fonksiyonlu Bulan\u0131k Mant\u0131k Denetleyici Ile Sabit M\u0131knat\u0131sl\u0131 Do\u011fru Ak\u0131m Motor Milinin D\u00f6n\u00fc\u015f A\u00e7\u0131s\u0131n\u0131n Kontrol\u00fc Authors: Mehmet Serhat Can, \u00d6mer Faruk \u00d6zg\u00fcven Comments: 6 Pages. Bu bildiride, hatan\u0131n ve hata de\u011fi\u015fiminin n\u00f6trosofik \u00fcyelik fonksiyonlar\u0131yla de\u011ferlendirildi\u011fi bir bulan\u0131k kontrol yakla\u015f\u0131m\u0131 sunulmu\u015ftur. Category: General Mathematics [1979] viXra:1701.0190 [pdf] submitted on 2017-01-03 12:25:44 ### Novel Multiple Criteria Decision Making Methods Based on Bipolar Neutrosophic Sets and Bipolar Neutrosophic Graphs Authors: Muhammad Akram, Musavarah Sarwar Comments: 20 Pages. In this research study, we introduce the concept of bipolar neutrosophic graphs. We present the dominating and independent sets of bipolar neutrosophic graphs. We describe novel multiple criteria decision making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs. We also develop an algorithm for computing domination in bipolar neutrosophic graphs. Category: General Mathematics [1978] viXra:1701.0189 [pdf] submitted on 2017-01-03 12:26:45 ### N-Valued Re\ufb01ned Neutrosophic Soft Set Theory Authors: Shawkat Alkhazaleh Comments: 6 Pages. In this paper as a generalization of neutrosophic soft set we introduce the concept of n-valued re\ufb01ned neutrosophic soft set and study some of its properties. We also, de\ufb01ne its basic operations, complement, union intersection, \"AND\" and \"OR\" and study their properties. Category: General Mathematics [1977] viXra:1701.0188 [pdf] submitted on 2017-01-03 12:29:06 ### N-Valued Re\ufb01ned Neutrosophic Soft Sets and Its Applications in Decision Making Problems and Medical Diagnosis Authors: Shawkat Alkhazaleh Comments: 12 Pages. In this work we use the concept of a n-valued re\ufb01ned neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two n-valued re\ufb01ned neutrosophic soft sets are proposed. Category: General Mathematics [1976] viXra:1701.0187 [pdf] submitted on 2017-01-03 12:30:51 ### On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra Authors: Husein Hadi Abbass, Qasim Mohsin Luhaib Comments: 11 Pages. In this paper, the notions of Q-Smarandache fuzzy commutative ideal and Q-Smarandache fuzzy sub-commutative ideal of a Q-Smarandache BH-Algebra are introduced, examples and related properties are investigated. Also, the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied. Category: General Mathematics [1975] viXra:1701.0186 [pdf] submitted on 2017-01-03 12:31:47 ### On a Q- Smarandache Implicative Ideal with Respect to an Element of a Q-Smarandache BH-algebra Authors: Husein Hadi Abbass, Hayder Kareem Gatea Comments: 9 Pages. In this paper, we define the concept of a Q-Smarandache implicative ideal with respect to an element of a Q-Smarandache BH-algebra. We state and prove some theorems which determine the relationships among this notion and other types of ideals of a Q-Smarandache BH-algebra. Category: General Mathematics [1974] viXra:1701.0184 [pdf] submitted on 2017-01-03 12:38:43 ### On Neutrosophic Normal Soft Groups Authors: Tuhin Bera, Nirmal Kumar Mahapatra Comments: 20 Pages. The concepts of neutrosophic normal soft group,neutrosophic soft cosets, neutrosophic soft homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established. Category: General Mathematics [1973] viXra:1701.0183 [pdf] submitted on 2017-01-03 12:39:55 ### On Neutrosophic Soft Function Authors: Tuhin Bera, Nirmal Kumar Mahapatra Comments: 19 Pages. In this paper, the cartesian product and the relations on neutrosophic soft sets have been de\ufb01ned in a new approach. Some properties of this concept have been discussed and veri\ufb01ed with suitable real life examples. Category: General Mathematics [1972] viXra:1701.0182 [pdf] submitted on 2017-01-03 12:40:54 ### On Neutrosophic Submodules of a Module Authors: Vildan Cetkin, Banu Pazar Varol, Halis Aygun Comments: 9 Pages. The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept. Category: General Mathematics [1971] viXra:1701.0181 [pdf] submitted on 2017-01-03 12:41:41 ### On Parallel Curves Via Parallel Transport Frame in Euclidean 3-Space Authors: Muhammed T. Sariaydin, Vedat Asil Comments: 7 Pages. In this paper, we study the parallel curve of a space curve according to parallel transport frame. Then, we obtain new results according to some cases of this curve by using parallel transport frame in Euclidean 3-space. Additionally, we give new examples for this characterizations and we illustrate this examples in gures. Category: General Mathematics [1970] viXra:1701.0180 [pdf] submitted on 2017-01-03 12:44:32 ### On Pseudospherical Smarandache Curves in Minkowski 3-Space Authors: Esra Betul Koc Ozturk, Ufuk Ozturk, Kazim Ilarslan, Emilija Ne\u0161ovic Comments: 15 Pages. In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. Category: General Mathematics [1969] viXra:1701.0179 [pdf] submitted on 2017-01-03 12:46:08 ### On Solutions of Some of Unsolved Problems in Number Theory, Speci\ufb01cally on the Distribution of Primes Authors: Ahmad Sabihi Comments: 19 Pages. We solve some famous conjectures on the distribution of primes. These conjectures are to be listed as Legendre\u2019s, Andrica\u2019s, Oppermann\u2019s, Brocard\u2019s,Cramer\u2019s, Shanks\u2019, and \ufb01ve Smarandache\u2019s conjectures. We make use of both Firoozbakht\u2019s conjecture (which recently proved by the author) and Kourbatov\u2019s theorem on the distribution of and gaps between consecutive primes. Category: General Mathematics [1968] viXra:1701.0178 [pdf] submitted on 2017-01-03 12:47:38 ### On The Darboux Vector Belonging To Involute Curve A Different View Authors: S\u00fcleyman SENYURT, Yasin ALTUN, Ceyda CEVAHIR Comments: 8 Pages. In this paper, we investigated special Smarandache curves in terms of Sabban frame drawn on the surface of the sphere by the unit Darboux vector of involute curve. We created Sabban frame belonging to this curve. It was explained Smarandache curves position vector is composed by Sabban vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the base curve. We also gave example belonging to the results found. Category: General Mathematics [1967] viXra:1701.0176 [pdf] submitted on 2017-01-03 12:49:38 ### Paradoxismul Economic \u015eI Economia MESONIC\u0102 Authors: Gheorghe S\u0103voiu, Vasile Dinu Comments: 23 Pages. Structura articolului reune\u015fte trei sec\u0163iuni majore, urm\u00e2nd demersul general al impactului paradoxurilor \u00een cadrul teoriei economice. O prim\u0103 sec\u0163iune descrie o necesar\u0103 investiga\u0163ie \u00een universul sintetizat al paradoxurilor, pentru a valorifica taxonomia paradoxurilor lui Quine \u015fi a releva importan\u0163a paradoxului cu adev\u0103rat paraconsistent, delimit\u00e2nd relativ \u015fi inovativ paradoxismul economic in sensul excesului valorific\u0103rii creative a paradoxurilor din arealul \u015ftiin\u0163ific, a\u015fa cum l-a ini\u0163iat matematicianul \u015fi logicianul Florentin Smarandache. Category: General Mathematics [1966] viXra:1701.0174 [pdf] submitted on 2017-01-03 12:51:46 ### Performance \u0415valuation of \u0422racking \u0410lgorithm Incorporating Attribute Data Processing Via DSmT Authors: Jean Dezert, Albena Tchamova, L. Bojilov, Pavlina Konstantinova Comments: 5 Pages. The main objective of this paper is to investigate the impact of the quality of attribute data source on the performance of a target tracking algorithm. An array of dense scenarios arranged according to the distance between closely spaced targets is studied by different confusion matrices. Category: General Mathematics [1965] viXra:1701.0173 [pdf] submitted on 2017-01-03 12:53:14 ### PID Tuning with Neutrosophic Similarity Measure Authors: Mehmet Serhat Can, Omerul Faruk Ozguven Comments: 15 Pages. In this paper, a method for adjusting the proportional-integral-derivative (PID) coef\ufb01cients based on the neutrosophic similarity measure is proposed. First, rough PID coef\ufb01cients were determined by the Ziegler\u2013 Nichols method, and the upper and lower limit values for the search range of the PID coef\ufb01cients were determined. Category: General Mathematics [1964] viXra:1701.0170 [pdf] submitted on 2017-01-03 13:00:35 ### Q-Single Valued Neutrosophic Soft Sets Authors: Tahir Mahmood, Qaisar Khan, Mohsin Ali Khan Comments: 16 Pages. In this paper, we have introduced the concept of Q-single value neutrosophic soft set, multi Qsingle valued neutrosophic set and defined some basic results and related properties. We have also defined the idea of Q-single valued neutrosophic soft set, which is the genralizations of Q-fuzzy set, Q-intuitionistic fuzzy set, multi Q-fuzzy set , Multi Q-intuitionistic fuzzy set, Q-fuzzy soft set, Q-intuitionistic fuzzy soft set. We have also defined and discussed some properties and operations of Q-single valued neutrosophic soft set. Category: General Mathematics [1963] viXra:1701.0169 [pdf] submitted on 2017-01-03 13:01:40 ### Quantitative Analysis of Particles Segregation Authors: Ting Peng, Aiping Qu, Xiaoling Wang Comments: 7 Pages. Segregation is a popular phenomenon. It has considerable e\ufb00ects on material performance. To the author\u2019s knowledge, there is still no automated objective Quantitative indicator for segregation. In order to full \ufb01ll this task, segregation of particles is analyzed. Edges of the particles are extracted from the digital picture. Then, the whole picture of particles is splintered to small rectangles with the same shape. Category: General Mathematics [1962] viXra:1701.0168 [pdf] submitted on 2017-01-03 13:02:22 ### Recognition and Classification of Ancient Dwellings based on Elastic Grid and GLCM Authors: Yang-Fan, Shen Lai-xin Comments: 12 Pages. Rectangle algorithm is designed to extract ancient dwellings from village satellite images according to their pixel features and shape features. For these unrecognized objects, we need to distinguish them by further extracting texture features of them. In order to get standardized sample, three pre-process operations including rotating operation, scaling operation, and clipping operation are designed to unify their sizes and directions. Category: General Mathematics [1961] viXra:1701.0165 [pdf] submitted on 2017-01-03 13:06:49 ### Research on Dynamic Targets Tracking Based on Color Cues Under Complicated Scene Authors: Yi Wang, Yingwu Fang, Xinyu Da, Shuxin Chen, Hui Wang Comments: 6 Pages. Compared with DST, DSmT can be good evidence of contradictions to resolve the issue of evidence portfolios, In view of the occluding in tracking dynamic targets in complex background, a new anti-occluding target tracking algorithm based on DSmT and particle filter is proposed by color cues. The simulation results show that the proposed algorithm is effective and practicable in tracking occluded target and intersected target. Compared with the existing combination rules, the newly proposed rule is applied to both cases of conflicting and coincidence. Category: General Mathematics [1960] viXra:1701.0164 [pdf] submitted on 2017-01-03 13:08:18 ### Research Project Evaluation and Selection: an Evidential Reasoning Rule-Based Method for Aggregating Peer Review Information with Reliabilities Authors: Wei-dong Zhu, Fang Liu, Yu-wang Chen, Jian-bo Yang, Dong-ling Xu, Dong-peng Wang Comments: 22 Pages. Research project evaluation and selection is mainly concerned with evaluating a number of research projects and then choosing some of them for implementation. It involves a complex multiple-experts multiple-criteria decision making process. Category: General Mathematics [1959] viXra:1701.0163 [pdf] submitted on 2017-01-03 13:09:14 ### Rough Bipolar Neutrosophic Set Authors: Surapati Pramanik, Kalyan Mondal Comments: 11 Pages. Bipolar neutrosophic set theory and rough neutrosophic set theory are emerging as powerful tool for dealing with uncertainty, and indeterminate, incomlete, and inprecise information. In the present study we develop a hybrid structure called \u201crough bipoar neutrsophic set\u201d. In the study, we define rough bipoar neutrsophic set and define union, complement, intersection and containment of rough bipolar neutrosophic sets. Category: General Mathematics [1958] viXra:1701.0162 [pdf] submitted on 2017-01-03 13:10:06 ### Rough Neutrosophic Relation on Two Universal Sets Authors: I. Arockiarani, C. Antony Crispin Sweety Comments: 14 Pages. In this paper, we define the rough neutrosophic relation of two universe sets and study the algebraic properties of two rough neutrosophic relations that are interesting in the theory of rough sets. Finally, we present the similarity rough neutrosophic relation with an example. Category: General Mathematics [1957] viXra:1701.0161 [pdf] submitted on 2017-01-03 13:12:18 ### Segmentation of Breast Masses in Local Dense Background using Adaptive Clip Limit-CLAHE Authors: Shelda Sajeev, Mariusz, Gobert Lee Comments: 9 Pages. Segmentation of Breast Masses in Local Dense Background using Adaptive Clip Limit-CLAHE. Category: General Mathematics [1956] viXra:1701.0160 [pdf] submitted on 2017-01-03 13:13:15 ### Selection of Lead-Zinc Flotation Circuit Design by Applying Waspas Method with Single-Valued Neutrosophic Set Authors: Edmundas Kazimieras Zavadskas, Romualdas Bau\u0161ys, Dragisa Stanujkic, Marija Magdalinovic-Kalinovic Comments: 8 Pages. In this paper, selection of adequate circuit design of lead-zinc froth flotation, which has a significant impact on the processing costs and useful minerals utilization, is considered. Category: General Mathematics [1955] viXra:1701.0157 [pdf] submitted on 2017-01-03 13:16:50 ### Similarity Measures of Bipolar Neutrosophic Sets and Their Application to Multiple Criteria Decision Making Authors: Vakkas Ulucay, Irfan Deli, Mehmet Sahin Comments: 10 Pages. In this paper, we introduced some similarity measures for bipolar neutrosophic sets such as; Dice similarity measure, weighted Dice similarity measure, Hybrid vector similarity measure and weighted Hybrid vector similarity measure. Category: General Mathematics [1954] viXra:1701.0156 [pdf] submitted on 2017-01-03 13:19:06 ### Simpli\ufb01ed Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development Authors: Zhang-peng Tian, Jing Wang, Jian-qiang Wang, Hong-yu Zhang Comments: 31 Pages. For many companies, green product development has become a key strategic consideration due to regulatory requirements and market trends. In this paper, the life cycle assessment technique is used to develop an innovative multi-criteria group decision-making approach that incorporates power aggregation operators and a TOPSIS-based QUALIFLEX method in order to solve green product design selection problems using neutrosophic linguistic information. Category: General Mathematics [1953] viXra:1701.0155 [pdf] submitted on 2017-01-03 13:19:54 ### Single-Valued Neutrosophic Graph Structures Authors: Muhammad Akram, Muzzamal Sitara Comments: 9 Pages. A graph structure is a generalization of undirected graph which is quite useful in studying some structures, including graphs and signed graphs. In this research paper, we apply the idea of single-valued neutrosophic sets to graph structure, and explore some interesting properties of single-valued neutrosophic graph structure. We also discuss the concept of \u03c6-complement of single-valued neutrosophic graph structure. Category: General Mathematics [1952] viXra:1701.0154 [pdf] submitted on 2017-01-03 13:21:51 ### Smarandache BE-Algebra Authors: A. Borumand Saeid, A. Ahadpanah, L.Torkzadeh Comments: 9 Pages. In this article we define theSmarandache BE-Algebra. Category: General Mathematics [1951] viXra:1701.0152 [pdf] submitted on 2017-01-03 13:27:11 ### Smarandache's Concurent Lines Theorem Authors: M. Khoshnevian Comments: 7 Pages. In this paper we present the Smarandache's Concurent Lines Theorem in the geometry of polygon. Category: General Mathematics [1950] viXra:1701.0151 [pdf] submitted on 2017-01-03 13:29:01 ### Smarandache Curves According to Sabban Frame of Fixed Pole Curve Belonging to the Bertrand Curves Pair Authors: S\u00fcleyman \u015eenyurt, Yasin Altun, Ceyda Cevahir Comments: 5 Pages. In this paper, we investigate the Smarandache curves according to Sabban frame of \ufb01xed pole curve which drawn by the unit Darboux vector of the Bertrand partner curve. Some results have been obtained. These results were expressed as the depends Bertrand curve. Category: General Mathematics [1949] viXra:1701.0150 [pdf] submitted on 2017-01-03 13:32:14 ### Smarandache Curves in the Galilean 4-Space G 4 Authors: M. Elzawy, S. Mosa Comments: 4 Pages. In this paper,we study Smarandache curves in the 4-dimensional Galilean space G4. We obtain Frenet Serret invariants for the Smarandache curve in G4. Category: General Mathematics [1948] viXra:1701.0146 [pdf] submitted on 2017-01-03 13:37:19 ### An Example of a Smarandache Geometry Authors: Ion Patrascu Comments: 6 Pages. An example of a Smarandache geometry. Category: General Mathematics [1947] viXra:1701.0144 [pdf] submitted on 2017-01-03 13:40:12 ### Some Algebraic Properties of Picture Fuzzy T-Norms and Picture Fuzzy T \u2013 Conorms on Standard Neutrosophic Sets Authors: Bui Cong Cuong, Roan Thi Ngan, Le Chi Ngoc Comments: 20 Pages. In 2013 we introduced a new notion of picture fuzzy sets (PFS), which are direct extensions of the fuzzy sets and the intuitonistic fuzzy sets. Category: General Mathematics [1946] viXra:1701.0143 [pdf] submitted on 2017-01-03 13:41:00 ### Some Characterizations of Smarandache Special Definite Groups Authors: P.A.Hummadi, H.M.Yassin Comments: 7 Pages. In this paper, we study Smarandache special definite groups. We give necessary and sufficient conditions for a group to be Smarandache special definite group(S-special definite group). Moreover we study Smarandache special definite subgroups, Smarandache special definite maximal ideals, Smarandache special definite minmal ideals. Category: General Mathematics [1945] viXra:1701.0141 [pdf] submitted on 2017-01-03 13:44:11 ### Special Smarandache Curves in R Authors: Nurten Gurses, Ozcan Bektas\u201a Salim Yuce Comments: 18 Pages. In differential geometry, there are many important consequences and properties of curves studied by some authors [1, 2, 3]. Researchers always introduce some new curves by using the existing studies. Category: General Mathematics [1944] viXra:1701.0140 [pdf] submitted on 2017-01-03 07:25:38 ### Approaches for Combination of Interval-Valued Belief Structures Authors: Sun Wei-cha, Xu Ai-qiang, J. Wen-hui Comments: 9 Pages. Approaches for Combination of Interval-Valued Belief Structures. Category: General Mathematics [1943] viXra:1701.0138 [pdf] submitted on 2017-01-03 07:27:57 ### Approaches for Managing Uncertainty in Learning Management Systems Authors: Nouran M. Radwan, M. Badr Senousy, Alaa El Din M. Riad Comments: 10 Pages. The notion of uncertainty in expert systems is dealing with vague data, incomplete information, and imprecise knowledge. Different uncertainty types which are imprecision, vagueness, ambiguity, and inconsistence need different handling models. Category: General Mathematics [1942] viXra:1701.0137 [pdf] submitted on 2017-01-03 07:29:31 ### A Projection-Based Todim Method Under Multi-Valued Neutrosophic Environments and Its Application in Personnel Selection Authors: Pu Ji, Hong-yu Zhang, Jian-qiang Wang Comments: 14 Pages. The personnel selection is a vital activity for companies, and multi-valued neutrosophic sets (MVNSs) can denote the fuzziness and hesitancy in the processes of the personnel selection. Category: General Mathematics [1941] viXra:1701.0136 [pdf] submitted on 2017-01-03 07:33:47 ### A Ranking Method of Single Valued Neutrosophic Numbers and Its Applications to Multi-Attribute Decision Making Problems Authors: I. Deli, Y. \u015euba\u015f Comments: 14 Pages. The concept of a single valued neutrosophic number (SVN-number) is of importance for quantifying an ill-known quantity and the ranking of SVN-numbers is a very dif\ufb01cult problem in multi-attribute decision making problems. Category: General Mathematics [1940] viXra:1701.0134 [pdf] submitted on 2017-01-03 07:35:36 ### A Study on Neutrosophic Graphs Authors: M.Rajeswari, J.Parveen Banu Comments: 9 Pages. In this paper, we are study about some basic definitions related to Graphs and Neutrosophic graphs. Some properties for the neutrosophic graphs associated with the Neutrosophic bigraphs. By applying some neutrosophic cognitive map and techniques in Neutrosophic models. Category: General Mathematics [1939] viXra:1701.0133 [pdf] submitted on 2017-01-03 07:36:53 ### A Survey on Trust Modeling Authors: Jin-Hee Cho, Kevin Chan, Sibel Adali Comments: 40 Pages. The concept of trust and\/or trust management has received considerable attention in engineering research communities as trust is perceived as the basis for decision making in many contexts and the motivation for maintaining long-term relationships based on cooperation and collaboration. Category: General Mathematics [1938] viXra:1701.0132 [pdf] submitted on 2017-01-03 07:38:28 ### A Survey on Various Approaches to Fingerprint Matching for Personal Verification and Identification Authors: Shoba Dyre, C.P. Sumathi Comments: 17 Pages. Automatic Fingerprint authentication for personal identification and verification has received considerable attention over the past decades among various biometric techniques because of the distinctiveness and persistence properties of fingerprints. Category: General Mathematics [1937] viXra:1701.0131 [pdf] submitted on 2017-01-03 07:39:42 ### A Unified Framework for Human Activity Detection and Recognition for Video Surveillance Using Dezert Smarandache Theory. Authors: Srilatha V., Veeramuthu Venkatesh Comments: 7 Pages. Trustworthy contextual data of human action recognition of remotely monitored person who requires medical care should be generated to avoid hazardous situation and also to provide ubiquitous services in home-based care. It is difficult for numerous reasons. At first level, the data obtained from heterogeneous source have different level of uncertainty. Category: General Mathematics [1936] viXra:1701.0130 [pdf] submitted on 2017-01-03 07:41:02 ### Automatic Liver Tumor Segmentation on Computed Tomography for Patient Treatment Planning and Monitoring Authors: Mehrdad Moghbel, Syamsiah Mashohor, Rozi Mahmud, M. Iqbal Bin Saripan Comments: 18 Pages. Segmentation of liver tumors from Computed Tomography (CT) and tumor burden analysis play an important role in the choice of therapeutic strategies for liver diseases and treatment monitoring. In this paper, a new segmentation method for liver tumors from contrast-enhanced CT imaging is proposed. Category: General Mathematics [1935] viXra:1701.0129 [pdf] submitted on 2017-01-03 07:43:57 ### Basic Properties Of Second Smarandache Bol Loops Authors: Temitope Gbolahan Jaiyeola Comments: 10 Pages. The basic properties of S2ndBLs are studied. These properties are all Smarandache in nature. The results in this work generalize the basic properties of Bol loops, found in the Ph.D. thesis of D. A. Robinson. Some questions for further studies are raised. Category: General Mathematics [1934] viXra:1701.0128 [pdf] submitted on 2017-01-03 07:47:02 ### Biological N-System with Global Stability Authors: Linfan Mao Comments: 28 Pages. However, even if it is non-solvable, it charac terizes biological systems also if it can be classi\ufb01ed into solvable subsystems. The main purpose of this paper is to characterize the biological behavior of such systems with global stability by a combinatorial approach, i.e., establish the relationship between solvable subsystems of a biological n-system with Eulerian subgraphs of la beling bi-digraph of\u2192 G, characterize n-system with linear growth rate and the global stability on subgraphs. Category: General Mathematics [1933] viXra:1701.0127 [pdf] submitted on 2017-01-03 08:49:03 ### Bipolar Neutrosophic Refined Sets and Their Applications in Medical Diagnosis Authors: I. Deli, Y. \u015euba\u015f Comments: 12 Pages. This paper proposes concept of bipolar neutrosophic refined set and its some operations. Firstly, a score certainty and accuracy function to compare the bipolar neutrosophic refined information is defined. Secondly, to aggregate the bipolar neutrosophic refined information, a bipolar neutrosophic refined weighted average operator and a bipolar neutrosophic refined weighted geometric operator is developed. Category: General Mathematics [1932] viXra:1701.0126 [pdf] submitted on 2017-01-03 08:50:11 ### Bipolar Neutrosophic Soft Expert Sets Authors: Mehmet \u015eahin, \u0130rfan Deli, Vakkas Ulu\u00e7ay Comments: 10 Pages. In this paper, we introduce concept of bipolar neutrosophic soft expert set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic soft expert sets. We give examples for these concepts. Category: General Mathematics [1931] viXra:1701.0125 [pdf] submitted on 2017-01-03 08:51:45 ### Brain Tumor Segmentation Using Hybrid of Both Netrosopic Modified Nonlocal Fuzzy C-Mean and Modified Level Sets Authors: Shaima Elnazer, Mohamed Morsy, Mohy Eldin A.Abo-Elsoud Comments: 7 Pages. An improved segmentation approach based on Neutrosophic sets (NS) and Modified Non local Fuzzy c-mean clustering (NLFCM) is proposed. The brain tumor MRI image is transformed into NS domain, which is described using three subsets namely; the percentage of truth in a subset T%, the percentage of indeterminacy in a subset I% , and the percentage of falsity in a subset F%. Category: General Mathematics [1930] viXra:1701.0124 [pdf] submitted on 2017-01-03 08:52:53 ### Broken Lines Signals and Smarandache Stepped Functions Authors: Mircea Eugen \u015eelariu Comments: 11 Pages. The evolutive supermathematical functions (FSM \u2500 Ev) are discussed in the papers [1], [2], [3], [4], [5], [6], [7], [8].They are combinations of the four types of FSM (centric functions (FC), excentric functions (FE), elevated functions (FEl) and exotic functions (FEx), taken by two, called centricoexcentric functions, elevatoexotic functions, centricoelevated functions, and so forth). Category: General Mathematics [1929] viXra:1701.0123 [pdf] submitted on 2017-01-03 08:55:39 ### Causal Models and Exploratory Analysis in Heterogeneous Information Fusion for Detecting Potential Terrorists Authors: Paul K. Davis, David Manheim, Walter L. Perry, John S. Hollywood Comments: 24 Pages. We describe research fusing heterogeneous information in an effort eventually to detect terrorists, reduce false alarms, and exonerate those falsely identified. The specific research is more humble, using synthetic data and first versions of fusion methods. Both the information and the fusion methods are subject to deep uncertainty. Category: General Mathematics [1928] viXra:1701.0122 [pdf] submitted on 2017-01-03 08:56:31 ### Certain Networks Models Using Single-valued Neutrosophic Directed Hypergraphs Authors: Muhammad Akram, Anam Luqman Comments: 20 Pages. A directed hypergraph is powerful tool to solve the problems that arises in di\ufb00erent \ufb01elds, including computer networks, social networks and collaboration networks. In this research paper, we apply the concept of single-valued neutrosophic sets to directed hypergraphs. Category: General Mathematics [1927] viXra:1701.0121 [pdf] submitted on 2017-01-03 08:58:17 ### Change Detection by New DSmT Decision Rule and Icm with Constraints :Application to Argan Land Cover Authors: Azeddine Elhassouny, Sou\ufb01ane Idbraim, Driss Mammass, Danielle Ducrot Comments: 6 Pages. The objective of this work is, in the \ufb01rst place, the integration in a fusion process using hybrid DSmT model, both, the contextual information obtained from a supervised ICM classi\ufb01cation with constraints and the temporal information with the use of two images taken at two different dates. Category: General Mathematics [1926] viXra:1701.0120 [pdf] submitted on 2017-01-03 08:59:21 ### Characterization of Smarandache-Soft Neutrosophic Near-Ring by Soft Neutrosophic Quasi-Ideals Authors: N. Kannappa, B. Fairosekani Comments: 6 Pages. In this paper, we introduce the Smarandache-2-algebraic structure of soft neutrosophic near-ring, namely Smarandache-soft neutrosophic near-ring. Category: General Mathematics [1925] viXra:1701.0119 [pdf] submitted on 2017-01-03 09:03:57 ### Characterization of Weak Bi-Ideals in Bi-Near Rings Authors: S. Maharasi, V. Mahalakshmi, S. Jayalakshmi Comments: 10 Pages. In this paper, with a new idea, we define weak bi-ideal and investigate some of its properties. We characterize weak bi-ideal by biideals of bi-near ring. Category: General Mathematics [1924] viXra:1701.0118 [pdf] submitted on 2017-01-03 09:05:05 ### Classi\ufb01cation multi\u00ad\u00e9chelle d\u2019images \u00e0 tr\u00e8s haute R\u00e9solution spatiale bas\u00e9e sur une nouvelle approche Texturale Authors: Alexandre Delahaye Comments: 159 Pages. Face \u00e0 l\u2019accroissement de la r\u00e9solution spatiale des capteurs optiques satellitaires, de nouvelles strat\u00e9gies doivent \u00eatre d\u00e9velopp\u00e9es pour classifier les images de t\u00e9l\u00e9d\u00e9tection. Category: General Mathematics [1923] viXra:1701.0117 [pdf] submitted on 2017-01-03 09:06:23 ### Combination of Uncertain Ordinal Expert Statements: the Combination Rule Eidmr and Its Application to Low-Voltage Grid Classi\ufb01cation with SVM Authors: Sebastian Breker, Bernhard Sick Comments: 10 Pages. The use of expert knowledge is always more or less af\ufb02icted with uncertainties for many reasons: Expert knowledge may be imprecise, imperfect, or erroneous, for instance. Category: General Mathematics [1922] viXra:1701.0116 [pdf] submitted on 2017-01-03 09:08:25 ### Concatenated Problems Authors: Henry Ibstedt Comments: 21 Pages. This study has been inspired by questions asked by Ch. Ashbacher in the Journal of Recreational Maathematics. Category: General Mathematics [1921] viXra:1701.0112 [pdf] submitted on 2017-01-03 09:29:04 ### Context Assumptions for Threat Assessment Systems Authors: Steven A. Israel, Erik Blasch Comments: 26 Pages. Decision support systems enable users to quickly assess data, but they require signi\ufb01cant resources to develop and are often relevant to limited domains. This chapter identi\ufb01es the implicit assumptions that require contextual analysis for decision support systems to be effective for providing a relevant threat assessment. Category: General Mathematics [1920] viXra:1701.0111 [pdf] submitted on 2017-01-03 09:32:34 ### Context-dependent Combination of Sensor Information in Dempster-Shafer Theory for BDI Authors: Sarah Calderwood, Kevin McAreavey, Weiru Liu, Jun Hong Comments: 26 Pages. There has been much interest in the Belief-Desire-Intention (BDI) agentbased model for developing scalable intelligent systems, e.g. using the AgentSpeak framework. However, reasoning from sensor information in these large-scale systems remains a signi\ufb01cant challenge. Category: General Mathematics [1919] viXra:1701.0110 [pdf] submitted on 2017-01-03 09:34:10 ### Correlated Aggregation Operators for Simpli\ufb01ed Neutrosophic Set and Their Application in Multi-Attribute Group Decision Making Authors: Chunfang Liua, YueSheng Luo Comments: 7 Pages. The simpli\ufb01ed neutrosophic set (SNS) is a generalization of the fuzzy set that is designed for some incomplete, uncertain and inconsistent situations in which each element has different truth membership, indeterminacy membership and falsity membership functions. Category: General Mathematics [1918] viXra:1701.0109 [pdf] submitted on 2017-01-03 09:36:18 ### Correlation Coefficient of Simplified Neutrosophic Sets for Bearing Fault Diagnosis Authors: Lilian Shi Comments: 17 Pages. In order to process the vagueness in vibration fault diagnosis of rolling bearing, a new correlation coefficient of simplified neutrosophic sets (SNSs) is proposed. Vibration signals of rolling bearings are acquired by an acceleration sensor, and a morphological filter is used to reduce the noise effect. Category: General Mathematics [1917] viXra:1701.0108 [pdf] submitted on 2017-01-03 09:37:36 ### Correlation Coef\ufb01cient of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Its Applications in Decision Making Authors: R\u0131dvan Sahin, Peide Liu Comments: 9 Pages. As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truthhesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coef\ufb01cient have been applied widely in many research domains and practical \ufb01elds. Category: General Mathematics [1916] viXra:1701.0107 [pdf] submitted on 2017-01-03 09:38:36 ### Correlation Coe\ufb03cients of Interval Neutrosophic Hesitant Fuzzy Sets and Its Application in a Multiple Attribute Decision Making Method Authors: Jun YE Comments: 24 Pages. This paper proposes the concept of an interval neutrosophic hesitant fuzzy set (INHFS) and the operational relations of INHFSs. Then, we develop correlation coe\ufb03cients of INHFSs and investigate the relation between the similarity measures and the correlation coe\ufb03cients. Category: General Mathematics [1915] viXra:1701.0103 [pdf] submitted on 2017-01-03 09:43:16 ### Cosine Similarity Measures of Neutrosophic Soft Set Authors: I. R. Sumathi, I.Arockiarani Comments: 10 Pages. In this paper we have introduced the concept of cosine similarity measures for neutrosophic soft set and interval valued neutrosophic soft set.An application is given to show its practicality and e\ufb00ectiveness. Category: General Mathematics [1914] viXra:1701.0102 [pdf] submitted on 2017-01-03 09:45:00 ### Cross-Entropy and Prioritized Aggregation Operator with Simpli\ufb01ed Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems Authors: Xiao-hui Wu, Jian-qiang Wang, Juan-juan Peng, Xiao-hong Chen Comments: 13 Pages. Simpli\ufb01ed neutrosophic sets (SNSs) can effectively solve the uncertainty problems, especially those involving the indeterminate and inconsistent information. Considering the advantages of SNSs, a new approach for multi-criteria decision-making (MCDM) problems is developed under the simpli\ufb01ed neutrosophic environment. Category: General Mathematics [1913] viXra:1701.0101 [pdf] submitted on 2017-01-03 09:46:24 ### Decision-Making with Belief Interval Distance Authors: Jean Dezert, Deqiang Han, Jean-Marc Tacnet, Simon Carladous, Yi Yang Comments: 9 Pages. In this paper we propose a new general method for decisionmaking under uncertainty based on the belief interval distance. We show through several simple illustrative examples how this method works and its ability to provide reasonable results. Category: General Mathematics [1912] viXra:1701.0100 [pdf] submitted on 2017-01-03 09:48:11 ### Designing an Approach to Building the Teams of High Technological Projects Performers at Virtual Instrumentmaking Enterprises Authors: A. Sobchak, E. Shostak, T. Tseplyaeva, O. Popova, A. Firsova Comments: 8 Pages. Under conditions of post-industrial society, a steady trend is the formation and support of the functioning of virtual instrument-making enterprises (VIE) in the field of high technologies. Category: General Mathematics [1911] viXra:1701.0098 [pdf] submitted on 2017-01-03 09:51:13 ### Design of the Neutrosophic Membership Valued Fuzzy-PID Controller and Rotation Angle Control of a Permanent Magnet Direct Current Motor Authors: Mehmet Serhat CAN, \u00d6mer\u00fcl Faruk \u00d6ZG\u00dcVEN Comments: 13 Pages. In this paper, we propose a method based on the fuzzy logic controller (FLC) method, created by using neutrosophic membership values. This method is named as proportional integral derivative-neutrosophic valued fuzzy logic controller (PID-NFLC). Category: General Mathematics [1910] viXra:1701.0097 [pdf] submitted on 2017-01-03 09:52:40 ### Dezert- Smarandache Theory based Classification of EMG Signals Authors: Preeti Meena, Malti Bnasal Comments: 6 Pages. This research paper proposes an intellectual method for the classification of different types of Electromyography (EMG) signals like normal, myopathy and neuropathy signals. Inside the human body, contraction of muscles and nerves occur at every second. Category: General Mathematics [1909] viXra:1701.0096 [pdf] submitted on 2017-01-03 09:53:45 ### Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm Authors: Ilanthenral Kandasamy Comments: 20 Pages. Neutrosophy (neutrosophic logic) is used to represent uncertain, indeterminate, and inconsistent information available in the real world. Category: General Mathematics [1908] viXra:1701.0095 [pdf] submitted on 2017-01-03 09:56:04 ### Driver Behavior Assessment Based on the G-G Diagram in the Dve System Authors: Oussama Derbel, Rene Jr. Landry Comments: 6 Pages. This paper proposes a driving risk model based on the information given from the driver-vehicle-enviroment entities. Category: General Mathematics [1907] viXra:1701.0094 [pdf] submitted on 2017-01-03 09:57:19 ### DSm Evidence Modeling and Radar Emitter Fusion Recognition Method Based on Cloud Model Authors: Guo Qiang, He You Comments: 7 Pages. To improve the correct radar emitter recognition rate in cases that radar emitter characteristic parameters are overlapped with each other and existence of multiple modes, a DSm (Dezert-Smarandache) evidence modeling and radar emitter fusion recognition method based on cloud model is proposed. Category: General Mathematics [1906] viXra:1701.0093 [pdf] submitted on 2017-01-03 09:59:09 ### Dual Curves of Constant Breadth According to Bishop Frame in Dual Euclidean Space Authors: Suha Y\u0131lmaz, Umit Ziya Savc\u0131 Comments: 4 Pages. In this work, curves of constant breadth are de\ufb01ned and some characterizations of closed dual curves of constant breadth according to Bishop frame are presented in dual Euclidean space. Also, it has been obtained that a third order vectorial differential equation in dual Euclidean 3-space. Category: General Mathematics [1905] viXra:1701.0092 [pdf] submitted on 2017-01-03 10:01:00 ### Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere Authors: Tanju Kahraman, Hasan H\u00fcseyin Ugurlu Comments: 13 Pages. In this paper, we give Darboux approximation for dual Smarandache curves of time like curve on unit dual Lorentzian sphere. Category: General Mathematics [1904] viXra:1701.0091 [pdf] submitted on 2017-01-03 10:02:17 ### Econometric Micro and Macroeconomic Modelling in Romania:finding Simplicity in Complexity and Generating Statistical Simplexity Authors: Gheorghe S\u0103voiu, Vasile Dinu, Emilia Gogu, Hosney Zurub Comments: 16 Pages. This paper describes, in its introduction, its main objective and some of its investigative premises,emphasizing the need to address micro- and macroeconomic models using the major principles of statistical thinking. Category: General Mathematics [1903] viXra:1701.0088 [pdf] submitted on 2017-01-03 10:04:18 ### Ef\ufb01cientProcessingofUncertainDataUsingDezert-SmarandacheTheory: ACaseStudy Authors: Hossein Jafari, Xiangfang Li, Lijun Qian Comments: 8 Pages. Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning has excellent performance when the data contain uncertainty or con\ufb02icting. Category: General Mathematics [1902] viXra:1701.0087 [pdf] submitted on 2017-01-03 10:06:01 ### Enhanced Fuzzy C-Means Based Segmentation Technique for Brain Magnetic Resonance Images Authors: A.S. Shankar, A. Asokan, D. Sivakumar Comments: 9 Pages. Brain tumor is most vital disease which commonly penetrates in the human beings. Studies based on brain tumor confirm that people affected by brain tumors die due to their erroneous detection. In this paper, an enhancedFuzzy C- Means segmentation (FCM) technique is proposed for detecting brain tumor. Category: General Mathematics [1901] viXra:1701.0086 [pdf] submitted on 2017-01-03 10:09:09 ### Evaluation of Ef\ufb01ciency of Torrential Protective Structures With New BF-TOPSIS Methods Authors: Simon Carladous, Jean-Marc Tacnet, Jean Dezert, Deqiang Han, Mireille Batton-Hubert Comments: 8 Pages. Real life Decision-Making Problems (DMPs) depend on several criteria for which precise or imperfect evaluation can be provided. Economic aspects are also of main importance to compare and choose strategies or measures. For instance, in mountainous areas, risk managers must rank several protective actions against torrential \ufb02oods to choose the best one. Category: General Mathematics [1900] viXra:1701.0085 [pdf] submitted on 2017-01-03 10:10:02 ### Exponential Operations And aggregation Operators Of interval Neutrosophic Sets And their Decision Making Methods Authors: Yun Ye Comments: 18 Pages. An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. Category: General Mathematics [1899] viXra:1701.0084 [pdf] submitted on 2017-01-03 10:14:23 ### Fault and Event Tree Analyses for Process Systems Risk Analysis: Uncertainty Handling Formulations Authors: Refaul Ferdous, Faisal Khan, Rehan Sadiq, Paul Amyotte, Brian Veitch Comments: 22 Pages. Process systems in chemical engineering are infamous for fugitive emissions, toxic releases, \ufb01re and explosions, and operation disruptions. These incidents have considerable potential to cause an accident and incur environmental and property damage, economic loss, sickness, injury, or death of workers in the vicinity. Category: General Mathematics [1898] viXra:1701.0083 [pdf] submitted on 2017-01-03 10:15:43 ### Fault Diagnoses of Hydraulic Turbine Using the Dimension Root Similarity Measure of Single-Valued Neutrosophic Sets Authors: Yun Ye Comments: 14 Pages. This paper proposes a dimension root distance and its similarity measure of single-valued neutrosophic sets (SVNSs), and then develops the fault diagnosis method of hydraulic turbine by using the dimension root similarity measure of SVNSs. Category: General Mathematics [1897] viXra:1701.0082 [pdf] submitted on 2017-01-03 10:18:45 ### Fingerprint Quality Assessment: Matching Performanceand Image Quality Authors: Zhigang Yao, Jean-Marie Le Bars, Christophe Charrier, Christophe Rosenberger Comments: 18 Pages. This article chie\ufb02y focuses on Fingerprint Quality Assessment(FQA)applied to the Automatic Fingerprint Identi\ufb01cation System (AFIS). In our research work, different FQA solutions proposed so far are compared by using several quality metrics selected from the existing studies. Category: General Mathematics [1896] viXra:1701.0081 [pdf] submitted on 2017-01-03 10:20:43 ### Foundation For Neutrosophic Mathematical Morphology Authors: E.M.El-Nakeeb, Hewayda El Ghawalby, A.A.Salama, S.A.El-Hafeez Comments: 23 Pages. The aim in this paper is to introduce a new approach to mathematical morphology based on neutrosophic set theory. Basic definitions for neutrosophic morphological operations are extracted and a study of its algebraic properties is presented. In our work we demonstrate that neutrosophic morphological operations inherit properties and restrictions of fuzzy mathematical morphology. Category: General Mathematics [1895] viXra:1701.0079 [pdf] submitted on 2017-01-03 10:23:09 ### Fusion of Multimodal Biometrics using Feature and Score Level Fusion Authors: S.Mohana Prakash, P.Betty, K.Sivanarulselvan Comments: 5 Pages. Abstract-Biometrics is used to uniquely identify a person\u2018s individual based on physical and behavioural characteristics. Unimodal biometric system contains various problems such as degree of freedom, spoof attacks, non-universality, noisy data and error rates. Category: General Mathematics [1894] viXra:1701.0078 [pdf] submitted on 2017-01-03 10:24:55 ### Fuzzy Neutrosophic Equivalence Relations Authors: J. Martina Jency, I. Arockiarani Comments: 9 Pages. This paper introduces the concept of fuzzy neutrosophic equivalence relations and discuss some of their properties.Also we define fuzzy neutrosophic transitive closure and investigate their properties. Category: General Mathematics [1893] viXra:1701.0076 [pdf] submitted on 2017-01-03 10:27:24 ### Fuzzy Neutrosophic Relations Authors: I. Arockiarani, J. Martina Jency Comments: 14 Pages. The focus of this paper is to present the concept of fuzzy neutrosophic relations. Further we study the composition of fuzzy neutrosophic relations with the choice of t-norms and tconorms and characterize their properties. Category: General Mathematics [1892] viXra:1701.0075 [pdf] submitted on 2017-01-03 10:28:27 ### Fuzzy Neutrosophic Soft Set Measures Authors: I.R.Sumath, I.Arockiarani Comments: 7 Pages. In this paper we propose the three types of similarity measures between fuzzy neutrosophic soft sets based on value matrix of fuzzy neutrosophic soft sets. Furthermore, we demonstrate the efficiency of the proposed similarity measures through the application in decision making. Category: General Mathematics [1891] viXra:1701.0074 [pdf] submitted on 2017-01-03 10:29:19 ### Fuzzy Neutrosophic Subgroups Authors: J. Martina Jency, I.arockiarani Comments: 12 Pages. In this paper we introduce the notion of fuzzy neutrosophic subgroups. Also we obtain the fuzzy neutrosophic subgroups generated by fuzzy neutrosophic set and investigate some of their properties. Category: General Mathematics [1890] viXra:1701.0073 [pdf] submitted on 2017-01-03 10:30:31 ### Fuzzy Topsis: a General View Authors: Sorin Nadaban, Simona Dzitac, Ioan Dzitac Comments: 9 Pages. The aim of this survey paper is to o\ufb00er a general view of the developments of fuzzy TOPSIS methods. We begin with a literature review an we explore di\ufb00erent fuzzy models that have been applied to the decision making \ufb01eld. Finally, we present some applications of fuzzy TOPSIS. Category: General Mathematics [1889] viXra:1701.0072 [pdf] submitted on 2017-01-03 10:31:36 ### Fuzzy Uncertainty Assessment in RBF Neural Networks Using Neutrosophic Sets for Multiclass Classi\ufb01cation Authors: Adrian Rubio-Solis, George Panoutsos Comments: 8 Pages. In this paper we introduce a fuzzy uncertainty assessment methodology based on Neutrosophic Sets (NS). This is achieved via the implementation of a Radial Basis Function Neural-Network (RBF-NN) for multiclass classi\ufb01cation that is functionally equivalent to a class of Fuzzy Logic Systems (FLS). Category: General Mathematics [1888] viXra:1701.0071 [pdf] submitted on 2017-01-03 10:39:35 ### Generalizedfibonaccisequencesin Groupoids Authors: Hee Sik Kim Neggers, Keum Sook So Comments: 10 Pages. In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents.Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences. Category: General Mathematics [1887] viXra:1701.0070 [pdf] submitted on 2017-01-03 10:41:07 ### Generalized Fuzzy Cognitive Maps: a New Extension of Fuzzy Cognitive Maps Authors: Bingyi Kang, Hongming Mo, Rehan Sadiq, Yong Deng Comments: 11 Pages. A fuzzy cognitive maps (FCM) is a cognitive map within the relations between the elements. FCM has been widely used in many applicati Category: General Mathematics [1886] viXra:1701.0068 [pdf] submitted on 2017-01-03 10:44:15 ### Genetic Algorithm Based on Similarity for Probabilistic Transformation of Belief Functions Authors: Yilin Dong, Xinde Li, Jean Dezert, Pei Li, Xianghui Li Comments: 41 Pages. Recent studies of alternative Probabilistic Transformation (PT) in Dempster Shafer (DS) theory have mainly focused on investigating various schemes for assigning the mass of compound focal elements to each singleton in order to obtain Bayesian belief function for decision making problems. Category: General Mathematics [1885] viXra:1701.0067 [pdf] submitted on 2017-01-03 05:02:46 ### A Bayesian Approach to Fusing Uncertain, Imprecise and Con\ufb02icting Information Authors: Simon Maskell Comments: 19 Pages. The Dezert\u2013Smarandache theory (DSmT) and transferable belief model (TBM) both address concerns with the Bayesian methodology as spplied to applications involving the fusion of uncertain, imprecise and con\ufb02icting information. In this paper, we revisit these concerns regarding the Bayesian methodology in the light of recent developments in the context of the DSmT and TBM. We show that, by exploiting recent advances in the Bayesian research arena, one can devise and analyse Bayesian models that have the same emergent properties as DSmT and TBM. Speci\ufb01cally, we de\ufb01ne Bayesian models that articulate uncertainty over the value of probabilities (including multimodal distributions that result from con\ufb02icting information) and we use a minimum expected cost criterion to facilitate making decisions that involve hypotheses that are not mutually exclusive. We outline our motivation for using the Bayesian methodology and also show that the DSmT and TBM models are computationally expedient approaches to achieving the same endpoint. Our aim is to provide a conduit between these two communities such that an objective view can be shared by advocates of all the techniques. Category: General Mathematics [1884] viXra:1701.0066 [pdf] submitted on 2017-01-03 05:06:21 ### A Clustering-Based Evidence Reasoning Method Authors: Xinde Li, Fengyu Wang Comments: 24 Pages. Aiming at the counterintuitive phenomena of the Dempster\u2013Shafer method in combining the highly con\ufb02ictive evidences, a combination method of evidences based on the clustering analysis is proposed in this paper. At \ufb01rst, the cause of con\ufb02icts is disclosed from the point of view of the internal and external contradiction. Andthen,a new similarity measure based on it is proposed by comprehensively considering the Pignistic distance and the sequence according to the size of the basic belief assignments over focal elements. Category: General Mathematics [1883] viXra:1701.0065 [pdf] submitted on 2017-01-03 05:12:15 ### A Double Cryptography Using The Smarandache Keedwell Cross Inverse Quasigroup Authors: Temitope Gbolahan Jaiyeola Comments: 7 Pages. The present study further strengthens the use of the Keedwell CIPQ against attack on a system by the use of the Smarandache Keedwell CIPQ for cryptography in a similar spirit in which the cross inverse property has been used by Keedwell. This is done as follows. By constructing two S-isotopic S-quasigroups(loops) U and V such that their Smarandache automorphism groups are not trivial, it is shown that U is a SCIPQ(SCIPL) if and only if V is a SCIPQ(SCIPL). Explanations and procedures are given on how these SCIPQs can be used to double encrypt information. Category: General Mathematics [1882] viXra:1701.0064 [pdf] submitted on 2017-01-03 05:13:40 ### Aggregation Operators Of neutrosophic Linguistic Numbers For multiple Attribute Group Decision Making Authors: Yun Ye Comments: 11 Pages. Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties. Further, we establish a multiple attribute group decision-making (MAGDM) method by using the NLNWAA and NLNWGA operators under NLN environment. Finally, an illustrative example on a decision-making problem of manufacturing alternatives in the flexible manufacturing system is given to show the application of the proposed MAGDM method. Category: General Mathematics [1881] viXra:1701.0063 [pdf] submitted on 2017-01-03 05:15:40 ### A Hybrid Fuzzy C-Means and Neutrosophic for Jaw Lesions Segmentation Authors: Mutasem K. Alsmadi Comments: 10 Pages. It is really important to diagnose jaw tumor in its early stages to improve its prognosis. A differential diagnosis could be performed using X-ray images; therefore, accurate and fully automatic jaw lesions image segmentation is a challenging and essential task. The aim of this work was to develop a novel, fully automatic and effective method for jaw lesions in panoramic X-ray image segmentation. The hybrid Fuzzy C-Means and Neutrosophic approach is used for segmenting jaw image and detecting the jaw lesion region in panoramic X-ray images which may help in diagnosing jaw lesions. Category: General Mathematics [1880] viXra:1701.0062 [pdf] submitted on 2017-01-03 05:18:40 ### Algorithms for Neutrosophic Soft Decision Making Based on Edas and New Similarity Measure Authors: Xindong Peng, Chong Liu Comments: 11 Pages. This paper presents two novel single-valued neutrosophic soft set (SVNSS) methods. First,we initiate a new axiomatic de\ufb01nition of single-valued neutrosophic simlarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory. Combining objective weights with subjective weights, we present the combined weights, which can re\ufb02ect both the subjective considerations of the decision maker and the objective information. Later, we present two algorithms to solve decision making problem based on Evaluation based on Distance from Average Solution (EDAS) and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by a numerical example. Category: General Mathematics [1879] viXra:1701.0061 [pdf] submitted on 2017-01-03 05:22:36 ### Alternating Iterations of the Sum of Divisors Function and the Pseudo-Smarandache Function Authors: Henry Ibstedt Comments: 13 Pages. This study is an extentionof work done by Ch. Ashbacher.Iteration results have been refined in terms of invariants and loops. Category: General Mathematics [1878] viXra:1701.0060 [pdf] submitted on 2017-01-03 05:23:52 ### A Method of Disease Detection and Segmentation of Retinal Blood Vessels using Fuzzy C-Means and Neutrosophic Approach Authors: Ishmeet Kaur, Lalit Mann Singh Comments: 7 Pages. Diabetic Retinopathy is a disease which causes a menace to the eyesight. The detection of this at an early stage can aid the person from vision loss. The examination of retinal blood vessel structure can help to detect the disease, so segmentation of retinal blood vessel vasculature is important and is appreciated by the ophthalmologists. In this paper, we present the approach of blood vessel segmentation using computer intelligence by deploying fuzzy c-means and neutrosophic set. Category: General Mathematics [1877] viXra:1701.0059 [pdf] submitted on 2017-01-03 05:25:42 ### A Model for Medical Diagnosis Via Fuzzy Neutrosophic Soft Sets Authors: Yildiray Celik Comments: 9 Pages. The concept of neutrosophic soft set is a new mathematical tool for dealing with uncertainties that is free from the di\ufb03culties a\ufb00ecting existing methods. The theory has rich potential for applications in several directions. In this paper, a new approach is proposed to construct the decision method for medical diagnosis by using fuzzy neutrosophic soft sets. Also, we develop a technique to diagnose which patient is su\ufb00ering from what disease. Our data with respect to the case study has been provided by the a medical center in Ordu, Turkey. Category: General Mathematics [1876] viXra:1701.0058 [pdf] submitted on 2017-01-03 05:26:46 ### A Multi-Criteria Decision-Making Method Using Power Aggregation Operators for Single-valued Neutrosophic Sets Authors: Lihua Yang, Baolin Li Comments: 10 Pages. As a generalization of intuitionistic fuzzy sets, neutrosophic sets (NSs) can be better handle the incomplete, indeterminate and inconsistent information, which have attracted the widespread concerns for researchers. Category: General Mathematics [1875] viXra:1701.0057 [pdf] submitted on 2017-01-03 05:28:31 ### An Adaptive Color Similarity Function Suitable for Image Segmentation and its Numerical Evaluation Authors: Rodolfo Alvarado-Cervantes, Edgardo M. Felipe-Riveron, Vladislav Khartchenko, Oleksiy Pogrebnyak Comments: 17 Pages. In this article, we present an adaptive color similarity function de\ufb01ned in a modi\ufb01ed hue-saturationintensity color space, which can be used directly as a metric to obtain pixel-wise segmentation of color images among other applications. The color information of every pixel is integrated as a unit by an adaptive similarity function thus avoiding color information scattering. Category: General Mathematics [1874] viXra:1701.0056 [pdf] submitted on 2017-01-03 05:32:36 ### AnAlgorithmforMedicalMagneticResonanceImage Non-LocalMeansDenoising Authors: Stefan Korolija, Eva Tuba, Milan Tuba Comments: 8 Pages. Digital images and digital image processing were widely researched in the past decades and special place in this \ufb01eld have medical images. Magnetic resonance images are a very important class of medical images and their enhancement is very signi\ufb01cant for diagnostic process. Category: General Mathematics [1873] viXra:1701.0055 [pdf] submitted on 2017-01-03 05:34:01 ### Analysis of Side Effects of Chemotheraphy Treatment for Cancer Patients Using Neutrosophic Cognitive Graphs (NCG) Authors: .Ashit Kumar Dutta Comments: 3 Pages. Cancer is considered as a most dangerous disease in the world. The research shows that there is no medicine to cure the disease. Chemotherapy is one of the treatments to prolong the patient life time but the side effects cause more problems for the patient. Cognitive maps discovered many solutions for the complex problems. Category: General Mathematics [1872] viXra:1701.0054 [pdf] submitted on 2017-01-03 05:35:29 ### An Automatic Segmentation & Detection of Blood Vessels and Optic Disc in Retinal Images Authors: Anchal Sharma, Shaveta Rani Comments: 5 Pages. \u2014Conceptual Segmentation is a critical technique in medical imaging. The Processes of identification and division of optic circle and veins are the fundamental strides for the analysis of a few infections that causes visual deficiency like diabetic retinopathy, hypertension, glaucoma and different visual deficiency ailment. Category: General Mathematics [1871] viXra:1701.0053 [pdf] submitted on 2017-01-03 05:38:14 ### A DSmT Approximate Reasoning Method on the Condition of Non-zero Mutiple Focal Elements Authors: Guo Qiang, He You, Guan Xin, Gai Ming-jiu. Comments: 7 Pages. A DSmT Approximate Reasoning Method on the Condition of Non-zero Mutiple Focal Elements. Category: General Mathematics [1870] viXra:1701.0052 [pdf] submitted on 2017-01-03 05:50:29 ### An Efficient Image Denoising Approach Based on Dictionary Learning Authors: Mohammadreza Karimipoor, Vahid Abolghasemi, Saideh Ferdowsi Comments: 7 Pages. In this paper, a denoising method based on dictionary learning has been proposed. With the increasing use of digital images, the methods that can remove noise based on image content and not restrictedly based on statistical properties has been widely extended. The major weakness of dictionary learning methods is that all of these methods require a long training process and a very large storage memory for storing features extracted from the training images. Category: General Mathematics [1869] viXra:1701.0051 [pdf] submitted on 2017-01-03 05:53:10 ### AnEfficientSoftSet-BasedApproachfor ConflictAnalysis Authors: Edi Sutoyo, Mungad Mungad, Suraya Hamid, Tutut Herawan Comments: 31 Pages. Conflict analysis has been used as an important tool in economic,business,governmental and political dispute, games, management negotiations, military operations and etc. Category: General Mathematics [1868] viXra:1701.0050 [pdf] submitted on 2017-01-03 05:54:33 ### An Ensemble Data Preprocessing Approach for Intrusion Detection System Using Variant Firefly and Bk-NN Techniques Authors: D. Shona, M. Senthilkumar Comments: 6 Pages. The Hasty intensification of Internet communication and accessibility of systems to infringe the network, network security has become requisite. This paper focuses on development of efficient IDS in MANET. Category: General Mathematics [1867] viXra:1701.0049 [pdf] submitted on 2017-01-03 05:59:26 ### An Ensemble Designof Intrusion Detection System Using for Handling Uncertainty Using Neutrosophic Logic Classifier Authors: B. Kavitha, D. Karthikeyan, P. Sheeba Maybell Comments: 9 Pages. In the real word it is a result that one most deal with uncertainty when security is concerned. Category: General Mathematics [1866] viXra:1701.0048 [pdf] submitted on 2017-01-03 06:00:59 ### A Neutrosophic Recommender System for Medical Diagnosis Based on Algebraic Neutrosophic Measures Authors: Mumtaz Ali, Nguyen Van Minh, Le Hoang Son Comments: 76 Pages. Neutrosophic set has the ability to handle uncertain, incomplete, inconsistent, indeterminate information in a more accurate way. In this paper, we proposed a neutrosophic recommender system to predict the diseases based on neutrosophic set which includes single-criterion neutrosophic recommender system (SCNRS) and multi-criterion neutrosophic recommender system (MC-NRS). Category: General Mathematics [1865] viXra:1701.0047 [pdf] submitted on 2017-01-03 06:05:13 ### An Evidence Clustering DSmT Approximate Reasoning Method Based on Convex Functtions Analysis Authors: Qiang Guo, You He, Xin Guan, Li Deng, Lina Pan, Tao Jian Comments: 11 Pages. The computetional complexity of Dezert-Smarandache Theory increases exponentially with the linear increment of element number in the discernment frame, and it limits the wide applications and development of DSmT. Category: General Mathematics [1864] viXra:1701.0046 [pdf] submitted on 2017-01-03 06:09:12 ### An Evidence Clustering DSmT Approximate Reasoning Method Based for More Than Two Sources Authors: Qiang Guo, You He, Tao Jian, Haipeng Wang, Shutao Xia Comments: 14 Pages. Due to the huge computation complexity of Dezert-Smarandache Thery, its applications especiall for multi-source (more than two sources) complex fusion problems have been limited. Category: General Mathematics [1863] viXra:1701.0045 [pdf] submitted on 2017-01-03 06:11:37 ### A New Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment Authors: A. Thamaraiselvi, R. Santhi Comments: 10 Pages. Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain,inconsistent,and incomplete information about areal world problem. For the first time, this paper attempts to introduce the mathematical representation of a transportation problem in neutrosophic environment. Category: General Mathematics [1862] viXra:1701.0044 [pdf] submitted on 2017-01-03 06:16:44 ### A New De\ufb01nition of Entropy of Belief Functions in the Dempster-Shafer Theory Authors: Radim Jirousek, Prakash P. Shenoy Comments: 29 Pages. We propose a new de\ufb01nition of entropy for basic probability assignments (BPA) in the Dempster-Shafer (D-S) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our de\ufb01nition is di\ufb00erent from the de\ufb01nitions proposed by H\u00a8ohle, Smets, Yager, Nguyen, Dubois-Prade, Lamata-Moral, Klir-Ramer, Klir-Parviz, Pal et al., MaedaIchihashi, Harmanec-Klir, Jousselme et al., and Pouly et al. We state a list of \ufb01ve desired properties of entropy for D-S belief functions theory that are motivated by Shannon\u2019s de\ufb01nition of entropy for probability functions together with the requirement that any de\ufb01nition should be consistent with the semantics of D-S belief functions theory. Category: General Mathematics [1861] viXra:1701.0043 [pdf] submitted on 2017-01-03 06:20:41 ### A New Expert System for Learning Managment Systems Evaluation Based on Neutrosophic Sets Authors: Nouran M. Radwan, M.Badr Senousy, Alaa El M. Riad Comments: 11 Pages. There has been a sudden increase in the usage of Learning Managment Systems applicatios to support learner's learning process in higher education. Category: General Mathematics [1860] viXra:1701.0041 [pdf] submitted on 2017-01-03 06:22:34 ### A New Fuzzy Based Algorithm for Solving Stereo Vagueness in Detecting and Tracking People Authors: Rui Pa\u00fal, Eugenio Aguirre, Miguel Garc\u00eda-Silvente, Rafael Mu\u00f1oz-Salinas Comments: 16 Pages. This paper describes a system capable of detecting and tracking various people using a new approach based on color, stereo vision and fuzzy logic. Initially, in the people detection phase, two fuzzy systems are used to \ufb01lter out false positives of a face detector. Category: General Mathematics [1859] viXra:1701.0040 [pdf] submitted on 2017-01-03 06:28:31 ### A New Non-Specificity Measure in Evidence Theory Based on Belief Intervals Authors: Yang Yi, Han Deqiang, Jean Dezert Comments: 10 Pages. In the theory based on belief functions, the measure of uncertainty is an important concept, which is used for representing some types of uncertainty incorporated in bodies of evidence such as the discord and the non-specificity. Category: General Mathematics [1858] viXra:1701.0039 [pdf] submitted on 2017-01-03 06:30:33 ### A New Probabilistic Transformation in Generalized Power Space Authors: HU Lifanga, HE You, GUAN Xin, DENG Yong, HAN Deqiang Comments: 12 Pages. The mapping from the belief to the probability domain is a controversial issue, whose original purpose is to make (hard) decision, but for contrariwise to erroneous widespread idea\/claim, this is not the only interest for using such mappings nowadays. Category: General Mathematics [1857] viXra:1701.0038 [pdf] submitted on 2017-01-03 06:32:52 ### A New Similarity Measure on Npn-Soft Set Theory and Its Application Authors: \u015eerif \u00d6zl\u00fc, \u0130rfan Deli Comments: 6 Pages. In this paper, we give a new similarity measure on npn-soft set theory which is the extension of correlation measure of neutrosophic refined sets. By using the similarity measure we propose a new method for decision making problem. Finally, we give an example for diagnosis of diseases could be improved by incorporating clinical results and other competing diagnosis in npn-soft environment. Category: General Mathematics [1856] viXra:1701.0036 [pdf] submitted on 2017-01-03 06:36:38 ### An Extended Grey Relational Analysis Based Interval Neutrosophic Multi Attribute Decision Making for Weaver Selection Authors: Partha Pratim Dey, Surapati Pramanik, Bibhas Chandra Giri Comments: 12 Pages. The paper proposes a multi-attribute decision making method based on extended grey relation analysis under interval neutrosophic environment. The interval neutrosophic set is an important decision making apparatus that can handle imprecise, indeterminate, inconsistence information. Category: General Mathematics [1855] viXra:1701.0035 [pdf] submitted on 2017-01-03 06:38:10 ### An Extended Multiple Criteria Decision Making Method Based on Neutrosophic Hesitant Fuzzy Information Authors: Peide Liu, Lili Zhang Comments: 15 Pages. Neutrosophic hesitant fuzzy set is the generalization of neutrosophic set and the hesitant fuzzy set, which can easily express the uncertain, incomplete and inconsistent information in cognitive activity, and the VIKOR (from Serbian:VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximum \u2018\u2018group utility\u2019\u2019 and minimum of an \u2018\u2018individual regret\u2019\u2019 with cognitive computation. Category: General Mathematics [1854] viXra:1701.0032 [pdf] submitted on 2017-01-03 06:43:09 ### An Improved Focal Element Control Rule Authors: JIN Hong-bin, LAN Jiang-qiao Comments: 5 Pages. The computational complexity of evidence theory is a hot issue in current research. Dezert-Smarandache theory (DSmT) introduces conflicting focal element, which makes the calculation complexity increases sharply. This paper starts with the focal element control rule used by the approximate calculation method mostly. The examples show that the improved rule is effective and feasible in both Shafer model and DSm model. Category: General Mathematics [1853] viXra:1701.0031 [pdf] submitted on 2017-01-03 06:46:34 ### An Improved Multimoora Approach for Multi-Criteria Decision-Making Based on Interdependent Inputs of Simpli\ufb01ed Neutrosophic Linguistic Information Authors: Zhang-peng Tian, Jing Wang, Jian-qiang Wang, Hong-yu Zhang Comments: 13 Pages. Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the \ufb02exibility and robustness it introduces into the decision process. Category: General Mathematics [1852] viXra:1701.0030 [pdf] submitted on 2017-01-03 06:50:50 ### An Improved Partial Haar Dual Adaptive Filter for Rapid Identification of a Sparse Echo Channel Authors: P. Kechichian, B. Champagne Comments: 14 Pages. Recently, a coupled echo canceller was proposed that uses two short adaptive filters for sparse echo cancellation. Category: General Mathematics [1851] viXra:1701.0029 [pdf] submitted on 2017-01-03 06:52:16 ### An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multicriteria Decision-making Problems Authors: Hong-yu Zhang, Pu Ji, Jian-qiang Wang, Xiao-hong Chen Comments: 18 Pages. This paper presents a new correlation coefficient measure, which satisfies the requirement of this measure equaling one if and only if two interval neutrosophic sets (INSs) are the same. And an objective weight of INSs is presented to unearth and utilize deeper information that is uncertain. Category: General Mathematics [1850] viXra:1701.0028 [pdf] submitted on 2017-01-03 06:53:41 ### An Integrated MCGDM Approach based Lean Faclitator Selection under Neutrosophic Environment Authors: P. Rajeswara Reddy, I. Naga Raju, V. Diwakar Reddy, G. Krishnaiah Comments: 7 Pages. In today\u2019s practical work environment group decision making is essential to choose best alternative from set of alternatives which are characterized by multiple criteria. In manufacturing environment frequent group decision making is common practice which involves conflicting and multiple criteria problems. Category: General Mathematics [1849] viXra:1701.0027 [pdf] submitted on 2017-01-03 06:54:53 ### An Interval Neutrosophic Linguistic Multi-Criteria Group Decision-Making Method and Its Application in Selecting Medical Treatment Options Authors: Yin-xiang Ma, Jian-qiang Wang, Jing Wang, Xiao-hui Wu Comments: 21 Pages. Selecting medical treatments is a critical activity in medical decision-making. Usually, medical treatments are selected by doctors, patients, and their families based on various criteria. Category: General Mathematics [1848] viXra:1701.0026 [pdf] submitted on 2017-01-03 06:59:41 ### A Novel Breast Tumor Classification Algorithm Using Neutrosophic Score Features Authors: K.M. Amin, A.I.Shahin, Yanhui Guo Comments: 11 Pages. A lot of studies confurmed the seriousness of brest cancer as the most tumors lethal to women worldwide. Category: General Mathematics [1847] viXra:1701.0025 [pdf] submitted on 2017-01-03 07:04:28 ### A Novel Decision Support Model for Satisfactory Restaurants Utilizing Social Information: a Case Study of Tripadvisor.com Authors: Hong-yu Zhang, Pu Ji, Jian-qiang Wang, Xiao-hong Chen Comments: 17 Pages. Decision support model for satisfactory restaurants have attracted numerous researcher's attention. Category: General Mathematics [1846] viXra:1701.0024 [pdf] submitted on 2017-01-03 07:06:00 ### A Novel Object Tracking Algorithm by Fusing Color and Depth Information Based on Single Valued Neutrosophic Cross-Entropy Authors: Keli Hu, Jun Ye, En Fan, Shigen Shen, Longjun Huang, Jiatian Pi Comments: 13 Pages. Although appearance based trackers have been greatly improved in the last decade, they are still struggling with some challenges like occlusion, blur, fast motion, deformation, etc. As known, occlusion is still one of the soundness challenges for visual tracking. Category: General Mathematics [1845] viXra:1701.0023 [pdf] submitted on 2017-01-03 07:07:13 ### An Overview of Technological Revolution in Satellite Image Analysis Authors: Jenice Aroma R., Kumudha Raimond Comments: 5 Pages. The satellite image based applications are highly utilized nowadays from simple purposes like vehicle navigation to complex surveillance and virtual environment modeling projects. On increased population rate, the depletion of natural resources is highly unavoidable and it leads to increased threats on natural hazards. In order to protect and overcome the physical losses on devastation of properties, the risk mapping models such as weather forecasts, drought modeling and other hazard assessment models are in need. Category: General Mathematics [1844] viXra:1701.0021 [pdf] submitted on 2017-01-03 07:13:01 ### Application of DSmT-Icm with Adaptive Decision Rule to Supervised Classi\ufb01cation in Multisource Remote Sensing Authors: A. Elhassouny, S. Idbraim, A. Bekkari, D. Mammass, D. Ducrot Comments: 11 Pages. In this paper, we introduce a new procedure called DSmT-ICM with adaptive decision rule, which is an alternative and extension of Multisource Classi\ufb01cation Using ICM (Iterated conditional mode) and DempsterShafer theory (DST). Category: General Mathematics [1843] viXra:1701.0019 [pdf] submitted on 2017-01-03 07:16:19 ### Application of Fuzzy Neutrosophic Relation in Decision Making Authors: .J. Martina Jency, I. Arockiarani Comments: 4 Pages. In this paper a new approach is proposed to meet the challenges in medical diagnosis using fuzzy neutrosophic c ompositionrelation. Category: General Mathematics [1842] viXra:1701.0018 [pdf] submitted on 2017-01-03 07:19:33 ### Application of Neutrosophic Set to Multicriteria Decision Making by Copras Authors: Romualdas Bausys, Edmundas Kazimieras Zavadskas, Art\u016bras Kaklauskas Comments: 15 Pages. The paper presents multicriteria decision making method with single value neutrosophic sets (SVNS), namely COPRAS-SVNS. The complex proportional assessment method (COPRAS) has shown accurate results for the solution of various multicriteria decision making problems in the engineering field. Category: General Mathematics [1841] viXra:1701.0017 [pdf] submitted on 2017-01-03 07:22:23 ### Applying ER-MCDA and BF-TOPSIS to Decide on E\ufb00ectiveness of Torrent Protection Authors: Simon Carladous, Jean-Marc Tacnet, Jean Dezert Comments: 10 Pages. Experts take into account several criteria to assess the e\ufb00ectiveness of torrential \ufb02ood protection systems. In practice, scoring each criterion is imperfect. Category: General Mathematics [1840] viXra:1612.0412 [pdf] submitted on 2016-12-31 00:28:51 ### TRL Universal Recursive Sub-Sets And Super-Sets Of A Set In Completion. (Universal Engineering Series). Authors: Ramesh Chandra Bagadi Comments: 7 Pages. In this research investigation, the author has detailed about 'Universal Recursive Sub-Sets And Super-Sets Of A Set In Completion'. Category: General Mathematics ## Replacements of recent Submissions [81] viXra:1704.0354 [pdf] replaced on 2017-04-28 14:41:46 ### Formalization of Multivariate Lagrange Interpolation Authors: Yvann Le Fay Comments: 4 Pages. We generalize a simple formula for constructing the multinomial function f which interpolates a set of (d+1) points in IR^N. We also provide an example of application of this method. Category: General Mathematics [80] viXra:1703.0160 [pdf] replaced on 2017-04-04 06:42:10 ### Logarithmic Extension of Real Numbers and Hyperbolic Representation of Generalized Lorentz Transforms Authors: Grushka Ya.I. Comments: 6 Pages. Mathematics Subject Classification: 12D99; 83A05 We construct the logarithmic extension for real numbers in which the numbers, less then$-\\infty$exist. Using this logarithmic extension we give the single formula for hyperbolic representation of generalized tachyon Lorentz transforms. Category: General Mathematics [79] viXra:1703.0073 [pdf] replaced on 2017-03-30 02:27:52 ### On The Riemann Zeta Function Authors: Jonathan Tooker Comments: 13 Pages. 13 figures, fixed some stuff We discuss the Riemann zeta function, the topology of its domain, and make an argument against the Riemann hypothesis. While making the argument in the classical formalism, we discuss the material as it relates to the theory of infinite complexity (TOIC). We extend Riemann's own (planar) analytic continuation$\\mathbb{R}\\to\\mathbb{C}$into (bulk) hypercomplexity with$\\mathbb{C}\\to\\,^\\star\\mathbb{C}$. We propose a solution to the Banach--Tarski paradox. Category: General Mathematics [78] viXra:1703.0073 [pdf] replaced on 2017-03-25 15:03:46 ### On The Riemann Zeta Function Authors: Jonathan Tooker Comments: 13 Pages. 13 figures We discuss the Riemann zeta function, the topology of its domain, and make an argument against the Riemann hypothesis. While making the argument in the classical formalism, we discuss the material as it relates to the theory of infinite complexity. We extend Riemann's own (planar) analytic continuation$\\mathbb{R}\\to\\mathbb{C}^2$into (bulk) hypercomplexity with$\\mathbb{C}^2\\to\\,^\\star\\mathbb{C}\\$. We propose a solution to the Banach--Tarski paradox.\nCategory: General Mathematics\n\n[77] viXra:1701.0597 [pdf] replaced on 2017-02-15 12:59:03","date":"2017-04-29 17:33:14","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\": 0.5632966160774231, \"perplexity\": 5652.681240434896}, \"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-2017-17\/segments\/1492917123549.87\/warc\/CC-MAIN-20170423031203-00502-ip-10-145-167-34.ec2.internal.warc.gz\"}"}
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Okręg południowy – jeden z trzech okręgów diecezji południowej Kościoła Adwentystów Dnia Siódmego w RP. Terytorialnie obejmuje zbory i grupy znajdujące się na terenie Śląska Cieszyńskiego i południowo-zachodniej Małopolski, w granicach powiatów: cieszyńskiego, bielskiego i żywieckiego oraz miasta Bielska-Białej z województwa śląskiego, a także powiatu suskiego i gminy Andrychów z województwa małopolskiego. Siedziba okręgu znajduje się w Bielsku-Białej.
Adwentyzm dotarł do Bielska w 1903 roku, skąd rozprzestrzenił się na okolicę m.in. do Cieszyna (1908) czy Wisły (1911), gdzie powstały później zbory. Władze austriackie nie uznawały ani nie tolerowały adwentystów, więc funkcjonowały one jako stowarzyszenia. W okresie międzywojennym istniały zbory m.in. w Wiśle (kilka), Cieszynie, Jaworzu, Nierodzimiu, Skoczowie. Podlegały diecezji śląsko-galicyjskiej.
Śląsk Cieszyński i obejmujący zbory tego regionu okręg południowy jest dziś najgęstszym i największym skupiskiem wyznawców adwentyzmu w Polsce, przy czym sam okręg jest najmniejszym terytorialnie okręgiem senioralnym Kościoła w Polsce, jedynym, który został wydzielony z większego obszaru województwa jako oddzielna jednostka administracyjna.
Aktualnie do okręgu południowego należy 12 zborów i 1 grupa.
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Zbory
Grupy
Przypisy
Bibliografia
Południowy
Protestantyzm na Śląsku Cieszyńskim
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,382
|
Bennebroek este o localitate în Țările de Jos, în comuna Bloemendaal din provincia Olanda de Nord, Țările de Jos. Până în 2009 localitatea era o comună separată fiind pentru mult timp cea mai mică comună olandeză.
Foste comune din Olanda de Nord
Localități din Olanda de Nord
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 360
|
Q: sql split field by comma delimiter Given the following.
Products_Joined.METATAG_Keywords AS Keyword,
This returns this for "keyword"
shoe,sneaker,boot,slipper
I am tying to split this into separate fields as so.
keyword1 shoe
keyword2 sneaker
keyword3 boot
keyword4 slipper
Something like a Javascript split function on comma delimiter.
Unfortunately this is how this field is stored in the database.
EDIT: Although I do not think it matters much I have provided the full sql query, perhaps someone can tell which version of SQL this is.
SELECT
'home-and-garden-products > home decorations > rugs' AS Category,
SUBSTRING(Products_Joined.ProductName, 6,LEN(Products_Joined.ProductName)) AS [stripHTML-Title],
'Config_FullStoreURL' + 'ProductDetails.asp?ProductCode=' + Products_Joined.IsChildOfProductCode AS Link,
Products_Joined.ProductCode AS SKU,
CAST(IsNull(Products_Joined.SalePrice,Products_Joined.ProductPrice) AS VARCHAR(30)) AS Price,
Products_Joined.ProductManufacturer AS Brand,
Products_Joined.UPC_code AS UPC,
'Config_FullStoreURLConfig_ProductPhotosFolder/' + IsNull(Products_Joined.IsChildOfProductCode,Products_Joined.ProductCode) + '-2T.jpg' AS Image,
Products_Joined.ProductDescription AS [stripHTML-DESCRIPTION],
Products_Joined.ProductManufacturer AS Manufacturer,
Products_Joined.vendor_partno AS [Mfr part number],
'0' AS [Shipping Cost],
Products_Joined.Google_Color AS Color,
Products_Joined.Google_Material AS Material,
Products_Joined.ProductWeight AS [Shipping Weight],
Products_Joined.Google_Size AS Size,
Products_Joined.METATAG_Keywords AS Keyword,
Products_Joined.ProductWeight AS Weight
FROM Products_Joined WITH (NOLOCK)
WHERE (Products_Joined.ProductPrice > 0)
AND (Products_Joined.IsChildOfProductCode IS NOT NULL)
ORDER BY Products_Joined.ProductCode
A: You may find that this page contains the solution you're looking for.
Hope it helps!
A: Check out this SPLIT Function which I hope would provide the solution you are looking for - http://vadivel.blogspot.com/2011/10/how-to-split-delimited-string-values-in.html
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,029
|
package org.gradle.process.internal;
import org.gradle.api.GradleException;
import org.gradle.internal.exceptions.Contextual;
@Contextual
public class WorkerProcessException extends GradleException {
public WorkerProcessException(String message, Throwable cause) {
super(message, cause);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,466
|
Vishay Intertechnology, Inc. launched four new Gen. 5.0 high-performance 45 and 100V Schottky diodes which the company states set a new standard in the industry by extending the D-Pak current capability up to 20A. Built on submicron trench technology, Vishay says the devices are suitable as stand-alone packages for high-efficiency, high-density solutions, as well as offering a cost-effective and compact replacement for the D2-Pak package.
According to the company, the 6CWT04FN, 10WT10FN, 20CWT10FN, and 20WT04FN offer a maximum junction temperature to +175°C, extremely low forward voltage drop, and low reverse leakage, allowing designers to increase power density in automotive, solar energy, and other high-temperature applications. All four devices are also available in I-Pak versions.
The Schottky diodes released today feature maximum forward voltage drops at +125°C of < 0.54 V typical at 6 and 20A for the 45V devices, and < 0.65V at 10 and 20A for the 100V devices. Reverse leakage at +125°C is 3 and 7mA for the 45V diodes and 4mA for the 100V diodes, with very tight parameter distribution. The devices offer optimized VF versus IR trade-off for increased system efficiency.
The diodes are optimized for ac-to-dc secondary rectification, flyback, buck and boost converters, half-bridge, reverse battery protection, freewheeling, dc-to-dc module, and solar photovoltaic bypass diode applications. Typical end products include high power density SMPS; adaptors for desktop PCs; servers; consumer electronics like PDPs, LCDs, and high-efficiency audio systems; and mobile electronics such as notebook computers, cell phones, and portable media players. The diodes are AEC-Q101 qualified for automotive drives and controls.
A high and stable breakdown voltage of 57V typical for the 45V devices, and 118V typical for the 100V devices, accommodates voltage spikes and optimizes power density, which is increased in the diodes by 25%. The devices feature 30% increased ruggedness for reverse avalanche capability, with parts 100% screened in avalanche, and negligible switching losses.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,204
|
Q: SQLSTATE[HY000] [1045] Access denied for user 'wymtavvh_admin'@'localhost' (using password: YES) I am using laravel on a live shared hosting and I am getting the error above despite using the right database connection credentials.
I have edited the .env and the database.php files and added the necessary credentils. My problem is that the same credentials are working on a raw php file that I have written to test but not on laravel.
the laravel project works correctly though on localhost
here is a sample of the .env file code
DB_CONNECTION=mysql
DB_HOST=127.0.0.1
DB_PORT=3306
DB_DATABASE=wymtav_food
DB_USERNAME=wymtav_admin
DB_PASSWORD=PasswordNce
BROADCAST_DRIVER=log
CACHE_DRIVER=file
QUEUE_CONNECTION=sync
SESSION_DRIVER=file
SESSION_LIFETIME=120
and here is a snippet of the edited database.php file
'mysql' => [
'driver' => 'mysql',
'url' => env('DATABASE_URL'),
'host' => env('DB_HOST', '127.0.0.1'),
'port' => env('DB_PORT', '3306'),
'database' => env('DB_DATABASE', 'wymtav_food'),
'username' => env('DB_USERNAME', 'wymtav_admin'),
'password' => env('DB_PASSWORD', 'PasswordNce'),
'unix_socket' => env('DB_SOCKET', ''),
'charset' => 'utf8mb4',
'collation' => 'utf8mb4_unicode_ci',
'prefix' => '',
'prefix_indexes' => true,
'strict' => true,
'engine' => null,
'options' => extension_loaded('pdo_mysql') ? array_filter([
PDO::MYSQL_ATTR_SSL_CA => env('MYSQL_ATTR_SSL_CA'),
]) : [],
],
Note that on local environment, the database port was 3309 and I have changed it to 3306 as per the production environment port.
What could I be doing wrong?
A: You are not required to update database connection both at .env and database.php files. You can either do at .env file or database.php file.
It is recommended to do in .env file like below :-
DB_CONNECTION=mysql
DB_HOST=localhost
DB_PORT=3306
DB_DATABASE=wymtav_food
DB_USERNAME=wymtav_admin
DB_PASSWORD=PasswordNce
Some of the hosting servers provide localhost as DB_HOST but some provides their own host url so you need to check with your hosting account for that.
A: 'host' => env('DB_HOST', '127.0.0.1'),
This is not the correct IP address of your database. You should check your host and get the IP of your db.
A: As it turned out my host had set the database password and username to be the same as the ones for accessing the cpanel. No other user created could do read or write the db directly unless logged into the phpmyadmin. Therefore anyone who experiences this problem especially in directadmin, can try changing the credentials to the ones for login into directadmin
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,105
|
{"url":"https:\/\/www.db-thueringen.de\/receive\/dbt_mods_00010902","text":"# Edge-injective and edge-surjective vertex labellings\n\nFor a graph G = (V,E) we consider vertex-k-labellings f : V \\rightarrow {1,2,...,k} for which the induced edge weighting w : E \\rightarrow {2,3,..., 2k} with w(uv) = f(u) + f(v) is injective or surjective or both. We study the relation between these labellings and the number theoretic notions of an additive basis and a Sidon set, present a new construction for a so-called restricted additive basis and derive the corresponding consequences for the labellings. We prove that a tree of order n and maximum degree \\triangle has a vertex-k-labelling f for which w is bijective if and only if \\triangle \\leq k = n\/2. Using this result we prove a recent conjecture of Ivan\u010do and Jendrol' concerning edge-irregular total labellings for graphs that are sparse enough.\n\nCitation style:\n\n### Rights\n\nUse and reproduction:","date":"2021-04-23 17:55:18","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\": 0.9783039093017578, \"perplexity\": 1279.0754717123937}, \"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-2021-17\/segments\/1618039596883.98\/warc\/CC-MAIN-20210423161713-20210423191713-00320.warc.gz\"}"}
| null | null |
{"url":"http:\/\/www.jmlr.org\/papers\/v18\/15-481.html","text":"## Probabilistic preference learning with the Mallows rank model\n\nValeria Vitelli, \u00d8ystein S\u00f8rensen, Marta Crispino, Arnoldo Frigessi, Elja Arjas; 18(158):1\u221249, 2018.\n\n### Abstract\n\nRanking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational complexity has limited its use to a particular form based on Kendall distance. We develop new computationally tractable methods for Bayesian inference in Mallows models that work with any right-invariant distance. Our method performs inference on the consensus ranking of the items, also when based on partial rankings, such as top-$k$ items or pairwise comparisons. We prove that items that none of the assessors has ranked do not influence the maximum a posteriori consensus ranking, and can therefore be ignored. When assessors are many or heterogeneous, we propose a mixture model for clustering them in homogeneous subgroups, with cluster-specific consensus rankings. We develop approximate stochastic algorithms that allow a fully probabilistic analysis, leading to coherent quantifications of uncertainties. We make probabilistic predictions on the class membership of assessors based on their ranking of just some items, and predict missing individual preferences, as needed in recommendation systems. We test our approach using several experimental and benchmark datasets.\n\n[abs][pdf][bib]\u00a0\u00a0\u00a0\u00a0[supplementary 1][supplementary 2]","date":"2018-06-23 15:45:23","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\": 0.1861667037010193, \"perplexity\": 2575.0823948481543}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"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-2018-26\/segments\/1529267865098.25\/warc\/CC-MAIN-20180623152108-20180623172108-00227.warc.gz\"}"}
| null | null |
Select this title You Be Mother [Electronic Resource] Mason, Meg 2017 Electronic Resource Available.
Select this title All together now [Book] McInerney, Monica 2008 Shelf Location: F.
Select this title Alphabet sisters [Book] McInerney, Monica 2004 Shelf Location: F.
McInerney, Monica 2009 Shelf Location: Audio MP3 Adult.
Select this title At home with the Templetons [Book] McInerney, Monica 2010 Shelf Location: F.
McInerney, Monica 2015 Shelf Location: Audio Adult.
Select this title Hello from the Gillespies [Book] McInerney, Monica 2014 Shelf Location: F.
Select this title Hello from the Gillespies [Electronic Resource] McInerney, Monica 2014 Electronic Resource Available.
Select this title Hello from the Gillespies [Book] McInerney, Monica 2018 Shelf Location: L.
Select this title The House of memories [Book] McInerney, Monica 2012 Shelf Location: F.
Available at: Maitland library, Thornton library.
McInerney, Monica 2012 Shelf Location: Audio MP3 Adult.
Select this title Lola's secret [Book] McInerney, Monica 2011 Shelf Location: F.
McInerney, Monica 2011 Shelf Location: Audio Adult.
Select this title Spin the bottle [Electronic Resource] McInerney, Monica 2010 Shelf Location: Online.
Available at: Maitland library Not for Loan.
McInerney, Monica 2002 Shelf Location: Audio Adult.
Select this title A Taste for it [Book] McInerney, Monica 2008 Shelf Location: F.
Select this title A taste for it [Electronic Resource] McInerney, Monica 2010 Electronic Resource Available.
Select this title Those Faraday girls [Book] McInerney, Monica 2007 Shelf Location: F.
Select this title The Trip of a lifetime [Book] McInerney, Monica 2017 Shelf Location: F.
Available at: East Maitland library, Thornton library, Maitland library.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,299
|
Основна категория е термин от когнитивната психология и представлява категория на дадено ниво, включваща йерархията (тоест дадено ниво на всеобщност), която е предпочитана от хората в задачите за учене и памет. Терминът се асоциира с работата на психолога Елеонор Рош, която демонстрира преимуществата на основната категория в редица класически експерименти.
Когнитивна психология
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,892
|
{"url":"https:\/\/www.semanticscholar.org\/paper\/Finiteness-Theorems-for-Gromov-Hyperbolic-Spaces-Besson-Courtois\/08e1ec8ca943f7de9a193e01f50588015ce4f732","text":"Corpus ID: 237940173\n\n# Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups\n\n@inproceedings{Besson2021FinitenessTF,\ntitle={Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups},\nauthor={G'erard Besson and Gilles Courtois and Sylvestre Gallot and Andrea Sambusetti},\nyear={2021}\n}\nIn this article we prove that the set of torsion-free groups acting by isometries on a hyperbolic metric space whose entropy is bounded above and with a compact quotient is finite. The number of such groups can be estimated in terms of the hyperbolicity constant and of an upper bound of the entropy of the space and of an upper bound of the diameter of its quotient. As a consequence we show that the set of non cyclic torsion-free \u03b4-hyperbolic marked groups whose entropy is bounded above by a\u2026\u00a0Expand\n\n#### References\n\nSHOWING 1-10 OF 59 REFERENCES\nTH\n\u2022 Dictionary of Upriver Halkomelem\n\u2022 2019\nDentro de las facultades de la Superintendencia previstas en el art\u00edculo 36 de la Ley 454 de 1998, se encuentran entre otras, la se\u00f1alada en el numeral 22 que prev\u00e9:.. \u201c22. Instruir a lasExpand\nA Lower Bound on the Growth of Word Hyperbolic Groups\n\u2022 Mathematics\n\u2022 2006\nWe give a linear lower bound on the exponential growth rate of a non-elementary subgroup of a word hyperbolic group, with respect to the number of generators for the subgroup.\nMetric Spaces of Non-Positive Curvature\n\u2022 Mathematics\n\u2022 1999\nThis book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces byExpand\nThree-dimensional geometry and topology\n\u2022 Mathematics\n\u2022 1997\nPreface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289Expand\nCurvature-Free Margulis Lemma for Gromov-Hyperbolic Spaces\n\u2022 Mathematics\n\u2022 2017\nWe prove curvature-free versions of the celebrated Margulis Lemma. We are interested by both the algebraic aspects and the geometric ones, with however an emphasis on the second and we aim at givingExpand\nCompactness and Finiteness Theorems for Gromov-Hyperbolic spaces\n\u2022 Preprint\n\u2022 2021\nEntropy and finiteness of groups with acylindrical splittings\n\u2022 Mathematics\n\u2022 Groups, Geometry, and Dynamics\n\u2022 2021\nWe prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\\mathrm{Ent}(G,S)<E$, weExpand\nOn Scalar and Ricci Curvatures\n\u2022 Mathematics\n\u2022 Symmetry, Integrability and Geometry: Methods and Applications\n\u2022 2020\nThe purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3,Expand","date":"2021-12-08 19:58:15","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\": 1, \"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\": 0.7462071180343628, \"perplexity\": 1400.8374252914546}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"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-2021-49\/segments\/1637964363520.30\/warc\/CC-MAIN-20211208175210-20211208205210-00328.warc.gz\"}"}
| null | null |
Q: How to detect when project is run by Add-Migration I have a .net Core 3.1 Web API solution, using EF Core for the database. When I execute Add-Migration to generate database migrations, the tool runs the startup project. I want to skip some code that executes when the startup project starts (it will not impact the migration generation). Is there a way to tell, in the project code, that it has been launched from the EF tool?
A: While not completly reliable, a workarround could be to use #if DEBUG directive :
public static void Main(string[] args)
{
#if DEBUG
// Debug mode: stop here
return;
#endif
// other stuff
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,034
|
from sparts.vservice import VService
from sparts.tasks.thrift import NBServerTask
from sparts.tasks.fb303 import FB303HandlerTask
from sparts.tasks.thrift.handler import ThriftHandlerTask
from sparts.gen.sparts_examples import SpartsFooService, SpartsBarService
class FooServiceHandler(ThriftHandlerTask):
MODULE = SpartsFooService
def foo(self):
return "foo is better!"
FooServiceHandler.register()
class BarServiceHandler(ThriftHandlerTask):
MODULE = SpartsBarService
def bar(self):
return "bar is better!"
BarServiceHandler.register()
NBServerTask.register()
NBServerTask.MULTIPLEX = True
FB303HandlerTask.register()
if __name__ == '__main__':
VService.initFromCLI()
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,750
|
A sea of people, paintings, and musical instruments saturated Bishop Moore Catholic High School's gym for the Orlando Catholic Schools 2nd Annual Fine Arts Extravaganza. Our schools offer a wide variety of extracurricular activities that encourage students to explore and develop their God-given, artistic talents, and this day celebrated these gifts.
Fourteen schools from Orange, Seminole, and Osceola counties participated. Ninety-seven pieces of artwork were entered in the show, ranging from a recreation of Van Gogh's "Irises" to a Chagall-inspired painting that depicted feeling God's love in a first communion. Marion M., a student from Holy Family Catholic School, incorporated fallen palm branches from Hurricane Irma to create a unique, brightly-colored piece inspired by traditional African tribal masks. She won 1st place for grades 6-8 in Three-Dimensional Art.
Sofia C. from St. James Cathedral School took home 3rd place for grades 6-8 in Three-Dimensional Art after bringing "Seussical" and "The Cat in the Hat" to life. She won the People's Choice award as well. Susie M. from St. Margaret Mary Catholic School won the Best of Show and Anton F. from Morning Star Catholic School received an Honorable Mention.
Meanwhile, Annunciation Catholic Academy left with three ribbon winners: Mary H. won 1st place for grades 6-8 in Painting, Sarah Z. won 1st place for grades 2-5 in Three-Dimensional Art, and Mauricio H. won 2nd place for grades 2-5 in Mixed Media. From All Souls Catholic School, James C. and Karalyna L. showcased vibrant, Kandinsky-inspired artwork. Emmalyn D. and Sarai R. received Honorable Mention ribbons for their paintings, and Soledad A. won second place for her Mixed Media entry.
The youngest artists were also very successful. For K-2 Drawing, Jamar B. from St. Andrew Catholic School took home 1st place while Marly L. took home 3rd. In Mixed Media K-2, St. Mary Magdalen Catholic School's students claimed 1st, 2nd, and 3rd place, and Chloe C. from St. Thomas Aquinas Catholic School won 1st place in K-2 Three-Dimensional Art.
A special display of artwork created by Bishop Moore Catholic High School students offered inspiration to the younger students, showing them where their artistic talents could take them at the high school level.
Throughout the morning, there were 16 musical performances from 10 schools, with more than 400 students performing as musicians, singers, or actors. The band from St. Charles Borromeo Catholic School, the Pride of St. Charles, played a Star Wars Medley that would make George Lucas proud. The Voices of St. Charles sang beautifully as well! Later on, Holy Redeemer Catholic School's second-grade choir stole the audience's hearts with their sweet rendition of Louis Armstrong's "What a Wonderful World," and the eighth graders from Good Shepherd Catholic School enacted a scene from "High School Musical." St. John Vianney Catholic School's newly formed Stage Band had toes tapping and hands clapping to "We Got the Beat," by the GoGos.
All of the students involved did a marvelous job of using their artistic talents to further God's kingdom. At Orlando Catholic schools, we embrace our students' God-given gifts and encourage them to excel academically, spiritually, and socially. To learn more about what makes our schools different, contact us online or at 407-246-4800.
Next Post: What is Your Student's Learning Style?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,336
|
using System.Collections.Generic;
using System.Linq;
using EncompassRest.Schema;
using EncompassRest.Utilities;
using EnumsNET;
using Newtonsoft.Json;
namespace EncompassRest.Settings.Loan
{
/// <summary>
/// CustomFieldDefinition
/// </summary>
public sealed class CustomFieldDefinition : DirtyExtensibleObject, IIdentifiable
{
private string? _id;
private string? _description;
private StringEnumValue<LoanFieldFormat> _format;
private int _maxLength;
private string? _calculation;
private FieldAudit? _audit;
private List<string>? _options;
private NeverSerializeValue<string?>? _modelPath;
private NeverSerializeValue<bool>? _isCalculatedField;
/// <summary>
/// Loan custom field name.
/// </summary>
[JsonRequired]
public string? Id { get => _id; set => SetField(ref _id, value); }
/// <summary>
/// Description for loan custom field.
/// </summary>
public string? Description { get => _description; set => SetField(ref _description, value); }
/// <summary>
/// Indicates the range and format of values the custom field can store.
/// </summary>
public StringEnumValue<LoanFieldFormat> Format { get => _format; set => SetField(ref _format, value); }
/// <summary>
/// Indicates the maximum length of the value for the custom field.
/// </summary>
[JsonProperty(DefaultValueHandling = DefaultValueHandling.Ignore)]
public int MaxLength { get => _maxLength; set => SetField(ref _maxLength, value); }
/// <summary>
/// A custom calculation is an expression that returns a number or text value, which is then saved into the associated custom field.
/// </summary>
[JsonProperty(NullValueHandling = NullValueHandling.Ignore)]
public string? Calculation { get => _calculation; set => SetField(ref _calculation, value); }
/// <summary>
/// Defines the audit data to return.
/// </summary>
[JsonProperty(NullValueHandling = NullValueHandling.Ignore)]
public FieldAudit? Audit { get => _audit; set => SetField(ref _audit, value); }
/// <summary>
/// If the format is DROPDOWNLIST or DROPDOWN, provide the values that will appear in the drop-down list.
/// </summary>
[JsonProperty(NullValueHandling = NullValueHandling.Ignore)]
public IList<string>? Options { get => _options; set => SetField(ref _options, value?.ToList()); }
/// <summary>
/// Model path for loan custom field.
/// </summary>
public string? ModelPath { get => _modelPath; internal set => SetField(ref _modelPath!, value); }
/// <summary>
/// A value of <c>true</c> indicates the field has a calculation associated.
/// </summary>
public bool IsCalculatedField { get => _isCalculatedField; internal set => SetField(ref _isCalculatedField!, value); }
/// <summary>
/// Custom field definition constructor.
/// </summary>
/// <param name="id">Loan custom field name.</param>
/// <param name="description">Description for loan custom field.</param>
/// <param name="format">Indicates the range and format of values the custom field can store.</param>
public CustomFieldDefinition(string id, string description, LoanFieldFormat format)
: this(id, description, format.Validate(nameof(format)).GetValue()!)
{
}
/// <summary>
/// Custom field definition constructor.
/// </summary>
/// <param name="id">Loan custom field name.</param>
/// <param name="description">Description for loan custom field.</param>
/// <param name="format">Indicates the range and format of values the custom field can store.</param>
public CustomFieldDefinition(string id, string description, string format)
{
Preconditions.NotNullOrEmpty(id, nameof(id));
Preconditions.NotNullOrEmpty(description, nameof(description));
Preconditions.NotNullOrEmpty(format, nameof(format));
Id = id;
Description = description;
Format = format;
}
[JsonConstructor]
private CustomFieldDefinition(string id, string description, string format, int maxLength)
{
Preconditions.NotNullOrEmpty(id, nameof(id));
Preconditions.NotNull(description, nameof(description));
Preconditions.NotNullOrEmpty(format, nameof(format));
Preconditions.GreaterThanOrEquals(maxLength, nameof(maxLength), 0);
Id = id;
Description = description;
Format = format;
MaxLength = maxLength;
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,407
|
from django.conf import settings
from django.core.signals import got_request_exception
from rest_framework import status
from rest_framework.exceptions import APIException
from rest_framework.response import Response
from rest_framework.views import exception_handler
class AlreadyPurchased(Exception):
pass
class Conflict(APIException):
status_code = status.HTTP_409_CONFLICT
default_detail = 'Conflict detected.'
def __init__(self, detail=None):
self.detail = detail or self.default_detail
class NotImplemented(APIException):
status_code = status.HTTP_501_NOT_IMPLEMENTED
default_detail = 'API not implemented.'
def __init__(self, detail=None):
self.detail = detail or self.default_detail
class ServiceUnavailable(APIException):
status_code = status.HTTP_503_SERVICE_UNAVAILABLE
default_detail = 'Service unavailable at this time.'
def __init__(self, detail=None):
self.detail = detail or self.default_detail
def custom_exception_handler(exc):
"""
Custom exception handler for DRF, which doesn't provide one for HTTP
responses like tastypie does.
"""
# If propagate is true, bail early.
if settings.DEBUG_PROPAGATE_EXCEPTIONS:
raise
# Call REST framework's default exception handler first,
# to get the standard error response.
response = exception_handler(exc)
# If the response is None, then DRF didn't handle the exception and we
# should do it ourselves.
if response is None:
# Start with a generic default error message.
data = {"detail": "Internal Server Error"}
# Include traceback if API_SHOW_TRACEBACKS is active.
if getattr(settings, 'API_SHOW_TRACEBACKS', settings.DEBUG):
import traceback
import sys
data['error_message'] = unicode(exc)
data['traceback'] = '\n'.join(
traceback.format_exception(*(sys.exc_info())))
request = getattr(exc, '_request', None)
klass = getattr(exc, '_klass', None)
# Send the signal so other apps are aware of the exception.
got_request_exception.send(klass, request=request)
# Send the 500 response back.
response = Response(data, status=status.HTTP_500_INTERNAL_SERVER_ERROR)
return response
class HttpLegallyUnavailable(APIException):
status_code = 451
default_detail = 'Legally unavailable.'
def __init__(self, detail=None):
self.detail = detail or self.default_detail
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,436
|
Quintus Fabius Maximus († zwischen etwa 207 und 203 v. Chr.) entstammte als Sohn des Quintus Fabius Maximus Verrucosus dem altrömischen Patriziergeschlecht der Fabier und war 213 v. Chr. Konsul.
Leben
Fabius Maximus Verrucosus war als schon bejahrter Mann während des Zweiten Punischen Krieges, den Rom gegen Hannibal führte, einer der einflussreichsten Senatoren und bedeutendsten Persönlichkeiten Roms. Die Karriere seines Sohnes Quintus Fabius Maximus fiel auch gänzlich in die Zeit des Kampfes gegen Hannibal.
In den Quellen erscheint Quintus Fabius Maximus erstmals 217 v. Chr., als er unter der Diktatur seines Vaters militärisch aktiv war. Bei diesen Erwähnungen handelt es sich um zwei Anekdoten, die vom ältesten und glaubwürdigsten Gewährsmann des Zweiten Punischen Krieges, Polybios, nicht erwähnt werden. Laut der ersten Erzählung hatte der Diktator mit Hannibal einen Gefangenenaustausch vereinbart, wobei die Römer Geld für all jene Gefangenen bezahlen sollten, die sie mehr als die Punier zurückerhielten. Da der Senat dazu nicht vorher um Erlaubnis gefragt worden war, stimmte er diesem Übereinkommen nicht zu. Deshalb habe der Diktator seinen Sohn beauftragt, die Finanzierung der Zahlungsverpflichtung durch den Verkauf seiner eigenen Güter zu ermöglichen. Weiters wird von Quintus Fabius Maximus erzählt, dass er für eine Expedition wegen der nur geringen zu erwartenden Verluste plädiert habe, aber von seinem Vater mit der Bemerkung gemaßregelt worden sei, ob er zu den wenigen ihr Leben verlierenden Soldaten gehören wolle.
In der für die Römer mit einer verheerenden Niederlage gegen die Punier endenden Schlacht bei Cannae (216 v. Chr.) fungierte Quintus Fabius Maximus als Militärtribun. Er konnte in die apulische Stadt Canusium (heute Canosa di Puglia) entkommen. Dann stieg er ungewöhnlich schnell zu den höchsten Ämtern des cursus honorum auf, offenbar weniger aufgrund eigener Leistungen als wegen des Einflusses seines Vaters. 215 v. Chr. übte er das Amt eines kurulischen Ädils aus. Im nächsten Jahr war er in der Funktion eines Prätors militärisch in Apulien im Einsatz, wobei er seine Stellung zuerst in Luceria, dann in Herdonia bezog.
Den Höhepunkt seiner Laufbahn erreichte Quintus Fabius Maximus 213 v. Chr., in welchem Jahr er gemeinsam mit Tiberius Sempronius Gracchus das Konsulat bekleidete. Er erhielt Apulien als Provinz zugewiesen und löste seinen Vater als Oberbefehlshaber der dortigen römischen Truppen ab. Dabei soll er von seinem Vater die ihm als Konsul zustehende Ehrerbietung verlangt haben; dieses Ansinnen sei auch auf völlige Zustimmung des ehemaligen Diktators gestoßen. Eine bedeutsame Leistung gelang dem Konsul vor allem mit der Rückeroberung der apulischen Stadt Arpi, die 216 v. Chr. auf Hannibals Seite gewechselt hatte.
Wahrscheinlich hielt sich Quintus Fabius Maximus noch 212 v. Chr. als Kommandant eines Truppenkontingents in Arpi auf, wenn er auch den Oberbefehl über seine Armee dem neuen Konsul übergeben hatte. In den nächsten Jahren dürfte er an einer Krankheit laboriert haben, da er seitdem kaum noch bei wichtigen Staatsangelegenheiten hervortrat und vor seinem Vater starb. Als dieser 209 v. Chr. zum fünften Mal das höchste Staatsamt innehatte, befahl er seinem Sohn, Truppen von Etrurien zum Prokonsul Marcus Valerius Laevinus nach Sizilien zu überführen. Im Folgejahr wurde Quintus Fabius Maximus sodann für einige Zeit Kommandant der Armee des in seinem ebenfalls fünften Konsulat gefallenen Marcus Claudius Marcellus. Am Ende des Sommers 207 v. Chr. kam er nach Rom mit der Mitteilung an den Senat, dass der Konsul Marcus Livius Salinator und dessen Heer nach dem entscheidenden Erfolg gegen Hannibals Bruder Hasdrubal in der Schlacht am Metaurus bald heimzukehren wünschten. Da ein Enkel des Fabius Maximus Verrucosus bezeugt ist, der den gleichen Namen wie der hier behandelte Sohn trug, könnte vor allem der zuletzt genannte Auftrag nach Ansicht des Althistorikers Friedrich Münzer auch von diesem Enkel (und nicht von Verrucosus' Sohn) ausgeführt worden sein.
Nach dem Tod des Quintus Fabius Maximus (vor 203 v. Chr.) hielt ihm sein Vater eine von diesem publizierte, heute aber verschollene Leichenrede, die der römische Redner und Politiker Marcus Tullius Cicero möglicherweise aus eigener Lektüre kannte.
Literatur
Anmerkungen
Konsul (Römische Republik)
Maximus, Quintus Fabius
Geboren im 3. Jahrhundert v. Chr.
Gestorben im 3. Jahrhundert v. Chr.
Mann
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,620
|
Q: moving the image from one activity to other in android in my app i am using camera to capture an image and i want to send it to other activity.
following is the code which explains about the path it gets stored and how it is moved to next activity
String path = String.format("/sdcard/%d.jpg",System.currentTimeMillis());
outStream = new FileOutputStream(path);
Intent i=new Intent();
i.setClassName("com.rest.gis","View");
i.putExtra("image", path);
startActivity(i);
here com.rest.gis is the my package name and View is the class name where I want send the image.
now in the view class how to get these datas
A: Intent intent = getIntent();
String path = intent.getExtras().getString("image");
A: In another activity if you have to get data then use bundle for that.
Bundle extra=getIntent().getExtras();
String imagePath=extra.getString("image");
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,321
|
We are a Cornwall based business providing landscaping, garden design and maintenance to both individuals and businesses. We work across the county in urban and rural settings and challenging coastal locations creating low maintenance beautiful gardens.
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,410
|
Win 2 Free Nights at a Gaylord Hotels Resort!
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Ready to enter and get our latest news, offers and more? Sign up below. We'll send you an email newsletter about once a week.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,163
|
\section{Introduction}
One of the principal aims of the upgrade of the Ooty Radio Telescope (ORT) to OWFA\citep{Prasad2011,
Subrahmanya2017a, Subrahmanya2017b} is to enable the detection of {H{\sc i}}~emission from large scale
structures in the post-EoR universe at redshifts $\sim 3$. Theoretical
calculations of the expected emission tuned to the projected parameters of
OWFA indicate that the telescope should have sufficient sensitivity
to detect the power spectrum of the redshifted {H{\sc i}}~21-cm emission, in integration times
of a few hundred hours\citep{Ali2014, Bharadwaj2015, Sarkar2017a}.
Currently, a number of
experiments are in various stages of progress that aim to directly
detect the brightness temperature
fluctuations $\delta T_b$ of the 21-cm post-reionisation cosmological signal
like the Canadian Hydrogen Intensity Mapping Experiment (CHIME;
\citealt{Bandura2014}), Baryon Acoustic Oscillation Broadband and Broad-beam
Array (BAOBAB; \citealt{Pober2013b}) and
the Tianlai Cylinder Radio Telescope (CRT; \citealt{Chen2011, Xu2015}).
These experiments would each operate at different frequency ranges; BAOBAB
has been proposed to specifically detect the Baryon Acoustic Oscillation (BAO) feature in the redshifted {H{\sc i}}~21-cm line in the
600-900 MHz band. The Tianlai CRT also is gearing up to
detect the BAO features and constrain dark energy through redshifted {H{\sc i}}~21-cm
observations in the 700-1400 MHz band\citep{Chen2011, Xu2015}. CHIME would
overlap with both these experiments in the range $\sim 400-800$ MHz. The OWFA
cosmology experiment is expected to fill a significant gap in understanding the
evolution of post-reionisation neutral hydrogen at large scales in an important redshift
interval of $z\sim 3.35$.
While the raw sensitivity of the telescope would be sufficient to detect
the {H{\sc i}}~emission from redshifts $z\sim 3.35$\citep{Ali2014, Bharadwaj2015}, the expected signal
is many orders of magnitude fainter than the other astrophysical signals,
i.e. the ``foregrounds''\citep[see e.g.][]{Santos2005, Ali2008}. These include
emission from the diffuse ionised galactic interstellar medium (``diffuse Galactic
synchrotron emission'' and ``galactic free-free emission'') and emission from
the extragalactic radio sources(called ``the
extragalactic foreground'') that the telescope is sensitive to.
Many instrumental effects come into play when the signal of interest is
buried several in orders of magnitude brighter foregrounds:
systematics introduced by uncalibrated antenna gains, interference
from terrestrial sources and effects of the complex intrinsic interaction between the
instrument and the foregrounds, due to the chromatic response of the telescope, are
thought to be the dominant contributors.
A good understanding of all of these issues is required to enable a robust
prediction of the cosmological signal that could be detected through
observations with OWFA.
The first step to understanding the instrumental systematics is to develop a thorough understanding of
the instrument itself, and capture it in a software model
that would include all the expected instrumental effects. All of the
astrophysical signals(e.g. the diffuse Galactic and the extragalactic point
source foregrounds) can then be suitably parametrized and
included in the model. One of the expected by-products of the exercise to detect the
cosmological {H{\sc i}}~signal is a better understanding
of some of the foregrounds, particularly of the diffuse Galactic foreground, which is the dominant foreground from within the Galaxy
and of interest in itself\citep[see e.g.][]{Iacobelli2013a, Iacobelli2013b, Iacobelli2014}.
The ability to characterise the foregrounds and the fundamental limitations set by the
instrument are both crucial to enable realistic predictions for the redshifted
{H{\sc i}}~21-cm detection. The software model described in this paper was developed
in order to help better understand
the systematics, as well as devise methods to devise foreground characterisation
and subtraction methods.
\section{The rationale for a software model}\label{sec:rationale}
The OWFA {H{\sc i}}~experiment is a
challenging one in terms of both the special hardware requirements as
well as the methods and algorithms that eventually enable us to
measure the {H{\sc i}}~power spectrum. A significant component of the design
of an experiment, especially in modern low frequency radio cosmology,
has been the investment in simulating the
instrument and the experiment itself based purely on a software
model. The results from simulations can often
influence the course of the experiment through valuable insight. This
has been the driving philosophy for an emulator based on a software
model for the OWFA {H{\sc i}}~experiment.
For OWFA, traditional interferometric data analysis software packages are not useful as they do not provide
sufficient functionality for redundancy
calibration, or for the final processing which, in this case, is not imaging.
A complete software suite has been developed consisting of several
standalone programs that serve two simultaneous purposes:
\begin{itemize}
\item to simulate visibilities as obtained from OWFA, based on the
instrument and sky description. The instrument description should
naturally lead to all the effects and systematics that are
expected to be present in an actual interferometric
observation. Simulated data can provide a test bed for devising
and refining RFI mitigation algorithms, calibration algorithms and
statistical estimators for signal characterisation, etc.
\item to function as the observatory software pipeline that is used to
process real data from the telescope, so that the
simulations above inform us to refine and adopt the optimal
strategies for working with real data.
\end{itemize}
Given that a software model for the telescope and
the sky would serve as a very useful guide to
the experiment, I shall now set up the preliminaries for describing the
emulator in some detail, and list its various features with examples.
\section{The programming philosophy}
The software suite that has been developed for OWFA
simulations is a C-based collection of utilities and algorithm
implementations. Visualisation of data is almost
the first step in data handling and a standard format definition
should therefore be the first choice.
The suite was conceived from the early days as one that would grow
organically to accommodate observatory needs. Therefore, the choice
was to adhere to an international standard for the visibility data, so
that a team of astronomers stationed in widely separated geographical
locations can handle these data using this software suite.
The following considerations were kept in mind during the development of the emulator.
\begin{itemize}
\item The Flexible Image Transport
System(FITS; \citealt{FITS}) or the Measurement Set(MS; \citealt{MS})
format definitions were the obvious formats to choose
from.
The fact that FITS is the data format
at the GMRT and hence is familiar to astronomers both within NCRA and users of
the GMRT played a significant role in the decision to adopt it. However, it is
worth mentioning that the Hierarchical Data Format (HDF) \citep[see e.g.][for
advantages of HDF5 over UVFITS]{Price2015} could be considered in the future due to its advantages over FITS, such as
compressibility and parallel I/O. The availability of conversion libraries from
FITS to HDF5 makes this an attractive alternative if the full potential of
parallel processing is to be harnessed. Pre-conversion of UVFITS observatory
data to HDF5 is then the only extra step in the offline processing necessitated
by this choice. UVFITS will therefore currently remain the
observatory data format of choice.
\item The second major factor was the ability to add new
utilities to the suite by anyone familiar with the FITS
definition. Therefore, the suite comes with a very rich set of
subroutine functions that do standard operations in a transparent
manner. A new utility that has to operate on the FITS data at the
level of individual records can hence draw on this library of
subroutines.
\item Finally, a high level of ease with which utilities can be added
to the suite is achieved by making the chore of passing arguments to
function calls a trivial operation. Instead of passing specific
arguments to functions, the pointer to a global superstructure is
passed uniformly to all function calls. The superstructure itself is a
structure of many structures, which are defined in different header
files depending on their functionality. Therefore, any user would be
able to add her own function definition to the existing
subroutines by passing a single argument.
\end{itemize}
Figure~\ref{fig:philosophy} captures the spirit of the programming
philosophy. The main call merely initialises a few variables
specific to the program.
\begin{figure}
\begin{center}
\includegraphics[scale=0.33]{philosophy.eps}
\end{center}
\caption{The general model for each program in the OWFA simulator
suite}
\label{fig:philosophy}
\end{figure}
Subroutines, variables and structures are segregated according to
their functionality and defined in appropriate header
files. Similarly, subroutine functions are defined in functionally
separable C program files. For example, all function definitions
related to the instrument are available in the \textbf{inc/sysdefs.h} and
\textbf{src/syssubs.c} files. FITS-related definitions and structures
are to be found in \textbf{inc/fitsdefs.h} and \textbf{src/fitssubs.c}
files. Sky simulations are grouped under \textbf{inc/skydefs.h} and
\textbf{src/skysubs.c}. Mathematical function definitions and
structures are grouped under \textbf{inc/matdefs.h} and
\textbf{src/matsubs.c}. The global superstructure, which holds all the variables
and structures is defined to be of type \textbf{ProjParType}, which is defined
in \textbf{inc/sysdefs.h}\footnote{\textbf{Prowess} is continually evolving, but
is available on request.}.
\section[Prowess - OWFA emulator]{\textbf{Prowess} - a \textbf{Pr}ogrammable \textbf{OW}FA \textbf{E}mulator \textbf{S}y\textbf{s}tem}
The software suite is given the name ``Programmable OWFA Emulator System'', and it is self-explanatory. Programmable, because
adding new utilities or functionality is made easy as described in the
previous section, and the emulator is specific to OWFA. I shall now describe the preliminaries required to capture the
instrument in a software model.
\subsection{Antennas and baselines}
OWFA\citep{Subrahmanya2017a, Subrahmanya2017b} would operate
in two concurrent modes - Phase-I and Phase-II. Phase-I is a 40-antenna interferometer and Phase-II is a
264-antenna interferometer. Only Phase-II refers to an operational system and
Phase-I is achieved in software. The Ooty Radio Telescope(ORT)
is a $\sim 530$ m long cylinder that is 30 m wide\citep{Swarup1971}.
The telescope consists of 1056 dipoles arranged regularly along its
length. These 1056 dipoles are grouped into 22 modules, each module being
supported mechanically by a parabolic frame. All the 22 frames are steered in
unison through a common drive shaft. Each of the 22 modules is the sum of a
contiguous group of 48 dipoles, combined through a passive combiner network. The
signals from the dipoles are summed hierarchically, and the second smallest unit
in this hierarchy is the output of the 4-way combiner\citep{Subrahmanya2017b}.
The signals from six Phase-II apertures are again summed in two stages to give the Phase-I aperture.
Correspondingly, the two interferometer modes provide two different aperture settings:
\begin{itemize}
\item The output of the 4-way combiner forms the aperture of the Phase-II
system. Every group of 4 dipoles, or a sixth of a half-module, would operate as a
single element in Phase-II. This corresponds to 1.92 m of the 530 m
long cylinder, equivalent to 2$\lambda$. This results in 264
apertures throughout the length of the telescope.
\item The output of the sum of six 4-way combiners forms the aperture of the Phase-I
system, equivalent to one half-module. Therefore, every group of 24 dipoles
would operate as a single element in Phase-I. This corresponds to 11.5 m of the 530 m
long cylinder, equivalent to 12.5$\lambda$. This results in 40 apertures
throughout the length of the telescope.
\end{itemize}
\begin{figure}
\begin{center}
\begin{verbatim}
#AntId Ant bx by bz ddly fdly
#------------------------------------------------------------
ANT00 N10N 0.0 0.0 10.0 0.0 0.0
ANT01 N10S 0.0 0.0 21.5 0.0 0.0
. . . . . . .
. . . . . . .
. . . . . . .
ANT38 S10N 0.0 0.0 447.0 0.0 0.0
ANT39 S10S 0.0 0.0 458.5 0.0 0.0
#END
\end{verbatim}
\end{center}
\caption{The antenna definition file Antenna.Def.40 for Phase-I of the
OWFA interferometer.}
\label{fig:ant-def}
\end{figure}
To begin with, the emulator has to be initialised with the
antenna positions. This is done through an input
Antenna Definition file, ``Antenna.Def.40'' for Phase-I and
``Antenna.Def.264'' for Phase-II. The parsing section of the code then
figures out which of the two modes the telescope is being operated
in. Accordingly, it sets the aperture dimensions. The user has the
option to switch off certain antennas in the ``Antenna.Def'' file to
simulate a situation when some antennas are not available. These are then omitted from the
simulations as well as the output visibility data. This
not only obviates the need to maintain a running log of the invalid
antennas, but also eases memory and storage requirements.
Figure~\ref{fig:ant-def} shows the antenna definition for Phase-I. The
file has seven columns:
\begin{enumerate}
\item Column 1 shows the antenna identifier used by the FITS standard.
\item Column 2 is the antenna name; the name of each antenna is tied
to its identifier. This helps in unambiguous bookkeeping even when
switching off certain antennas.
\item Columns 3, 4 and 5 respectively give the antenna $x, y$ and $z$
co-ordinates in a right-handed co-ordinate system, which shall be described shortly.
\item Columns 6 and 7 respectively denote the delay in seconds, corresponding to
the number of integer and fractional clock cycles offset with respect to a reference antenna. At the moment, these fields are not being used,
hence their values are all set to zero. In practice, these would
represent the fixed delays arising from differences in cable lengths.Therefore
they can be measured reasonably accurately and are unlikely to change in an
undisturbed setup. These fields would be used to correct for the phase ramps
in the visibilities across the band for each baseline.
\end{enumerate}
Since the dipoles are regularly spaced, the equivalent apertures in Phase-I and
Phase-II are also regularly spaced. This results in an interferometer in which
the separation between any pair of apertures is an integral multiple of the
shortest separation between adjacent apertures,
\begin{equation}
d_{\mathrm{n}} = nd
\label{eqn:physical-baseline}
\end{equation}
where $d$ is the both the size of the aperture as well as the shortest
spacing. The 40-antenna Phase-I has twenty half-modules in the northern half and twenty in
the southern half. The northern ones are
named N01 to N10 outwards from the midpoint of the telescope, and
similarly the southern modules. The two half-modules within each
module are given a ``N'' or ``S'' identifier. The antenna definition
file is parsed and the values are stored in the antenna structure
within the superstructure(\textbf{ProjParType}).
In the co-ordinate system chosen for OWFA,
the antennas are placed along the $z$-axis.
\begin{figure}
\begin{center}
\begin{verbatim}
### Antenna Re(gain) Im(gain) abs(gain) arg(gain)
###
0 N10N 2.111527 -1.651020 2.680375 -38.022146
1 N10S -0.769040 2.448255 2.566198 107.438412
. . . . . .
. . . . . .
. . . . . .
38 S10N 0.112905 1.564518 1.568587 85.872353
39 S10S 1.386609 -1.809840 2.279958 -52.542475
\end{verbatim}
\end{center}
\caption{The antenna initialiser log, with the complex gain assigned
to each antenna.}
\label{fig:ant-init.info}
\end{figure}
Each antenna $i$ is assigned a complex, frequency dependent, electronic gain $g_i$, obtained
as a random complex number distributed around a mean gain $|g|$,
referred to the central frequency $\nu_0$ = 326.5 MHz. The observing
band is split into $N$ channels. It is possible to introduce slowly time-varying
gains in the simulations about the mean antenna gains described above, but such
gain variations are automatically handled at the time of calibration.
\begin{figure}
\begin{center}
\begin{verbatim}
### Ant1 Ant2 FITSbl Ant1 Ant2
###
1 0 1 257 N10N N10S
2 0 2 258 N10N N09N
. . . . . .
. . . . . .
. . . . . .
38 0 38 294 N10N S10N
39 0 39 295 N10N S10S
\end{verbatim}
\end{center}
\caption{The log ``baselines.info'' that lists the baselines counted
as pairs of the available antennas. Only the first 39 baselines of
Phase-I are shown as an example.}
\label{fig:baselines.info}
\end{figure}
The antenna structure initialization information is written out
in a log called ``ant-init.info''. The real and imaginary parts of the
complex gains, as well as its amplitude and phase(in degrees) at $\nu_0$
are written out in the file. An example is shown in Figure~\ref{fig:ant-init.info}.
Baselines are then obtained as antenna pairs, and each baseline is
written into a structure that holds the baseline number, the
participating antenna pair, the three dimensions of the baseline and its length
in wavelength units at the reference frequency. A log of the baselines is
written out to ``baseline.info'', part of which is shown in
Figure~\ref{fig:baselines.info}. An $N_A$ antenna interferometer results in $^{N_A}C_2$
baselines, giving 780 for Phase-I and 34716 for Phase-II.
The baseline vectors are obtained from the physical antenna
separations, defined at the central frequency $\nu_0$
but at each channel it is appropriately scaled when computing the
visibilities.
\begin{equation}
\mathbf{d}_{|a-b|} = \mathbf{x}_a - \mathbf{x}_b
\label{eqn:baseline-phy}
\end{equation}
\begin{equation}
\mathbf{U}_{|a-b|} = \mathbf{d}_{|a-b|}\ \frac{\nu}{c}
\label{eqn:lambda-baseline}
\end{equation}
Equation~\ref{eqn:baseline-phy} shows the physical separation between
antenna pairs, whereas equation~\ref{eqn:lambda-baseline} shows the baseline in
wavelength units at any given frequency $\nu$.
The regular spacing of the antennas results in baselines with
redundant spacings. As a result, we obtain $N_A-n$ copies of the baseline with a
separation of $n$ units.
In this case of an $N_A$-antenna linear array, only
$N_A-1$ baselines out of $^{N_A}C_2$ are unique and non-redundant. All of these
$N_A-1$ baselines have redundant copies, except the longest one.
\subsection{A co-ordinate system suitable for OWFA}
A generalised framework for computing the visibilities is presented here.
Consider a right-handed Cartesian coordinate system, shown in Figure~\ref{fig:owfa_coord},
tied to the telescope, in which the $z$-axis is along the N-S direction, parallel to the
axis of the parabolic cylinder, the $x$-axis is aligned with the normal to the
telescope aperture which is directed towards $(\alpha_0,0)$ on the celestial
equator, and the $y$ axis is in the plane of the telescope's aperture, perpendicular
to both the $x$ and $z$ axes respectively. $\mathbf{\hat{i}}, \mathbf{\hat{j}}$ and $\mathbf{\hat{k}}$ denote the
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{owfa_new.eps}
\caption{A schematic of the co-ordinate system for computing the visibilities,
in which $\mathbf{n}$ is an arbitrary direction and $\mathbf{m}$ is the
direction of pointing. The visibilities are computed over the entire solid
angle of the celestial hemisphere.}
\label{fig:owfa_coord}
\end{center}
\end{figure}
unit vectors along $x, y$ and $z$. In this coordinate system, we have
\begin{equation}
\mathbf{U}= v \mathbf{\hat{k}}
\end{equation}
Observations are centered on a position
$(\alpha_0,\delta_0)$ on the celestial sphere: let the unit vector $\mathbf{\hat{m}}$
denote this position on the celestial sphere. $\mathbf{\hat{m}}$ always lives on the
$x\!-\!z$ plane, and is given by
\begin{equation}
\mathbf{\hat{m}}=\sin(\delta_o) \, \mathbf{\hat{k}} + \cos(\delta_0) \, \mathbf{\hat{i}}
\end{equation}
The measured visibility for a baseline of length $\mathbf{U}$ at a frequency $\nu$
can be written as
\begin{equation}
\mathbf{M}(\mathbf{U},\nu)=\int d \Omega_{\mathbf{\hat{n}}} \, I(\mathbf{n},\nu) \, A(\Delta \mathbf{n},\nu) \,
e^{2 \pi i \mathbf{U} \cdot \Delta \mathbf{n}}
\label{eqn:model_RIME}
\end{equation}
where $\mathbf{\hat{n}}$ refers to an arbitrary direction in the celestial sphere,
given by
\begin{equation}
\mathbf{\hat{n}}=\sin(\delta) \, \mathbf{\hat{k}} + \cos(\delta) \left[ \cos(\alpha-\alpha_0) \, \mathbf{\hat{i}} +
\sin(\alpha-\alpha_0) \mathbf{\hat{j}} \right]
\end{equation}
The solid angle integral here is over the entire celestial hemisphere, and
\begin{equation}
\Delta n = \mathbf{\hat{n}} - \mathbf{\hat{m}}
\end{equation}
We finally have
\begin{equation}
\mathbf{M}(\mathbf{U},\nu)=\int [d \sin(\delta) \, d \alpha ] \,
I(\alpha,\delta, \nu) \, e^{2 \pi i v [\sin(\delta-\delta_0)] } A(\Delta n_y,\Delta n_z)
\end{equation}
where
$\Delta n_y=\cos(\delta) \, \sin(\alpha-\alpha_0)$ and
$\Delta n_z= \sin(\delta-\delta_0)$.
Note that in this co-ordinate system the argument of the exponent depends only
on the baseline length and the declination, reflecting the 1D geometry of OWFA.
\subsection{Aperture and the primary beam}
We may write the general beam pattern for a rectangular aperture as $A(\Delta \mathbf{n})\equiv
A(\Delta n_y,\Delta n_z)$ where $(\Delta n_y,\Delta n_z)$ are respectively
the $y$ and $z$ components of $\Delta \mathbf{n}$. The Phase-I
aperture is $11.5 \mathrm{m} \times 30 \mathrm{m}$ and the Phase-II
aperture is $1.92 \mathrm{m} \times 30 \mathrm{m}$ in $d \times b$.
For the rectangular aperture approximated in this paper for OWFA, if we assume for the
moment uniform illumination, $A(\Delta n_y,\Delta n_z)$ can be modelled as a
product of ${\rm sinc}^2$ functions:
\begin{equation}
A(\Delta n_y,\Delta n_z)={\rm sinc}^2 \left( \frac{\pi b\, \Delta n_y}{\lambda} \right) {\rm sinc}^2 \left( \frac{\pi d \, \Delta n_z }{\lambda} \right)
\end{equation}
However, the primary beam should infact be written as
\begin{equation}
\mathbf{A}(\boldsymbol{\theta}, \nu) =
\left(\frac{\sin\left(\pi\ \!\frac{d\nu}{c}\ \!\left(\delta - \delta_0\right)\ \!\cos\ \!\delta_0\right)}{\pi\ \!\frac{d\nu}{c}\ \!\left(\delta
- \delta_0\right)\ \!\cos\ \!\delta_0}\right)^2
\left(\frac{\sin\left(\left(\pi\ \!\frac{b\nu}{c}\right)\ \!\left(\alpha -
\alpha_0\right)\right)}{\pi\ \!\frac{b\nu}{c}\ \!\left(\alpha - \alpha_0\right)}\right)^2
\end{equation}
The $\cos\ \!\delta_0$ factor in the primary beam function arises from
the fact that the aperture is foreshortened in the $d$ direction as
seen from the source at $\delta_0$. This effective reduction in the
aperture size results in a broader primary beam as the declination
increases, as well as reduced sensitivity. In \textbf{Prowess}, by default for
Phase-I, the beam is computed out upto $\sim 18^{\circ}$ from the phase centre in each
direction. This corresponds to three sidelobes north-south, and 10
sidelobes east-west at $\delta_0 = 0^\circ$. The beam is computed and stored as
an array, with a pixel resolution $\sim 1.0' \times
1.0'$, and $2048 \times 2048$ pixels across. The resolution of these maps is
finer than OWFA's resolution of $2^\circ \times 0.1^\circ$.
The simulated foreground maps, elaborated in \citet{Marthi2017a}, are also
computed and stored in an identical sized array. The sinc-squared beam used
here is considered only as a
worst-case scenario, i.e., as having the most pronounced sidelobes. In practice, the beam is a
Gaussian in the east-west dimension as confirmed independently from
slew-scan measurements. To quantify the instrumental chromatic effects described in Section~\ref{sec:PS_estim}, the sinc-squared beam
would give rise to the strongest signatures. Besides, the effects of representing the primary beam as a
sinc-function in hour-angle are expected to be sub-dominant to the extent that
ORT cannot resolve in that direction: unlike in the declination direction, the
hour-angle term is absent from the Fourier exponent term of the van
Cittert-Zernike theorem.
The full extent of the simulated
primary beam power pattern is shown in Figure~\ref{fig:PRBEAM-vs-dec}
at four different declinations. Having said that, \textbf{Prowess}
can accommodate any definition for the primary beam power pattern, and
need not be constrained to the two-dimensional $\mathrm{sinc}^2$ alone.
\begin{figure}
\begin{center}
\begin{minipage}{190mm}
\subfigure[$\delta_0 =
0^\circ$]{\includegraphics[scale=0.25,angle=270]{PRBEAM.DEC0-lowres.eps}}
\hskip 0.3in
\subfigure[$\delta_0 =
20^\circ$]{\includegraphics[scale=0.25,angle=270]{PRBEAM.DEC20-lowres.eps}}\\
\vskip 0.3in
\subfigure[$\delta_0 =
40^\circ$]{\includegraphics[scale=0.25,angle=270]{PRBEAM.DEC40-lowres.eps}}
\hskip 0.4in
\subfigure[$\delta_0 =
60^\circ$]{\includegraphics[scale=0.25,angle=270]{PRBEAM.DEC60-lowres.eps}}
\end{minipage}
\end{center}
\caption{The primary beam power pattern at declinations (a) $\delta_0
= 0^\circ$, (b) $20^\circ$, (c) $40^\circ$ and (d) $60^\circ$. The
beam widens noticeably in declination extent at higher declination
as the projected aperture size shrinks as $\cos\ \!\delta_0$.}
\label{fig:PRBEAM-vs-dec}
\end{figure}
\subsection{Sky and model visibilities}\label{ssec:sky-and-model}
The model visibilities are computed as described below. In the model for the
foregrounds, only two components are considered here as they are the most
dominant at 326.5 MHz. The diffuse Galactic
synchrotron foreground dominates the emission from within the
Galaxy at very large scales($ \> 2^{\circ}$), while the extragalactic
sources dominate at scales typically
smaller than a degree\citep{Ali2014}.
Random realisations of the foreground emission are obtained from the assumed power
spectrum of the emission: the details of how they are generated are
explained in \citet{Marthi2017a}, however a very brief description follows.
For the Galactic diffuse foreground, a random realisation of the angular power
spectrum is generated on a Fourier grid, the values of which are given by
\begin{equation}
\Delta \tilde{S}(u,\nu)=\left(\frac{\partial B}{\partial T}\right) \sqrt{\frac{\Omega \, C_{\ell}(\nu)}{2}}\left(x+iy\right)
\label{eqn:ran222}
\end{equation}
where $\Delta \tilde{S}(u,\nu)$ represents the Fourier transform of the
intensity fluctuations. $\Omega$ is the solid angle of the sky to be simulated,
$C_\ell$ is the angular power spectrum, $x$ and $y$ are Gaussian random variables
with zero mean and unit variance. An inverse Fourier transform of the populated Fourier
grid now gives a single random realisation of the diffuse foreground.
The extragalactic foreground is similarly obtained from an angular power
spectrum, but it is more involved than the simple Fourier inversion in the
diffuse foreground case. We therefore follow the method of \citet{Gonzalez2005}
by modifying the Poisson density contrast field by the clustering power spectrum
and populating the modified density field with sources drawn from the radio source
counts at 325 MHz \citep{Wieringa1991}.
Once the maps
are available, their individual components are superimposed in
sky-coordinates to obtain the total emission from the sky.
\begin{figure}
\begin{center}
\includegraphics[scale=0.22]{flowchart.eps}
\end{center}
\caption{This flowchart gives an overall picture of the part of the
simulator that produces the model and observed visibilities.}
\label{fig:flowchart}
\end{figure}
The specific intensity function is then given by
\begin{equation}
I(\alpha, \delta, \nu) = \Delta I_D(\alpha, \delta, \nu)\ +\ \sum\limits^L_{k=1}
I_k(\alpha_k, \delta_k, \nu)
\end{equation}
where $\Delta I_D(\alpha, \delta, \nu)$ is the fluctuation in the
specific intensity of the diffuse foreground
emission, and the $L$ distinct extragalactic radio sources are
identified by their co-ordinates $(\alpha, \delta)$ and specific intensities $I_k$.
The discrete sources are each confined to a pixel, so that the specific intensity
of each source is equal to its flux density. For the diffuse foregrounds, the
simulated maps are already pixelised, and the specific intensity in each pixel
has already been scaled by the solid angle of the pixel. The flux density of the
sky is
\begin{equation}
S(\alpha, \delta, \nu) = \Delta S_D(\alpha, \delta, \nu) +\ \sum\limits^L_{k=1}
S_k(\alpha_k, \delta_k, \nu)
\end{equation}
Since the model visibilities $M(\mathbf{U}, \nu)$ for the
non-redundant set of baselines are obtained as a pixel-by-pixel
Fourier sum of the primary-beam weighted specific intensity
distribution, we finally have
\begin{equation}
\mathbf{M}(\mathbf{U}, \nu) = \sum\limits_{\alpha, \delta}\ S(\alpha, \delta,\nu)\ \mathbf{A}(\alpha, \delta,\nu)\ e^{-i 2\pi \mathbf{U}.\mathbf{\hat{n}}}
\label{eqn:modelvis}
\end{equation}
which is the discretized version of equation~\ref{eqn:model_RIME}.
The observing band is centered at 326.5 MHz with a bandwidth of $\sim39$ MHz split
into 312 channels in the simulations. The frequency resolution in this case is
125 kHz per channel.
Based on our understanding
of the distribution of the neutral gas around the redshift of $z\sim3.35$, it is
expected that the {H{\sc i}}~signal at two redshifted frequencies, separated by more
than $\Delta\nu$ of 1 MHz, decorrelates rapidly\citep[see e.g.][]{
Bharadwaj2005}. This means that with a channel
resolution of 125 kHz, the {H{\sc i}}~signal correlation is adequately sampled over the
1-MHz correlation interval. In reality, the channel resolution is
likely to be much finer($\sim 50 \mathrm{kHz}$), with about 800 channels across the
$\sim$39-MHz band. This is useful for the identification and excision of narrow line
radio frequency interference. Beyond the need to handle RFI, there is no real
incentive to retain the visibility data at this resolution at the cost of
downstream computing and storage requirements. Eventually, we may smooth the
data to a resolution of 125 kHz, keeping in mind the decorrelation bandwidth of
the {H{\sc i}}~signal. The emulator itself is indeed capable of running at any
frequency resolution, including the actual final configuration of the Phase-I and Phase-II
systems. But the 125-kHz resolution used in the simulations allows for rapid
processing, especially if they are to be run repetitively for a wide range of different parameters.
The model visibilities $\mathbf{M(U)}$ need be obtained only
for the set of distinct non-redundant baselines, denoted by
$\mathbf{U}_{|i-j|}$. The observed visibility $V_{ij}$ for a
baseline with antennas $i$ and $j$ depends on the model
visibility for that particular spacing $M(_{|i-j|})$, as well the gains of the individual antennas:
\begin{equation}
V_{ij}\left(U_{|i-j|}\right) = g_i\ g_j^*\ M\left(U_{|i-j|}\right) + N_{ij}\left(\nu\right)
\label{eqn:RIME}
\end{equation}
where $M$ is the model visibility including the primary beam as
described above, $g_i$ and $g_j$ are the complex antenna
gains and $N_{ij}$ is the complex Gaussian random noise equivalent to the system
temperature $T_{\mathrm{sys}}$. The real and
imaginary parts of the noise $N_{ij}$ in equation~\ref{eqn:RIME} have a
RMS fluctuation
\begin{equation}
\sigma_{ij} = \frac{\sqrt{2}k_B T_{\mathrm{sys}}}{\eta A
\sqrt{\Delta\nu\Delta t }}
\label{eqn:T_sys}
\end{equation}
per channel, where $k_B$ is the Boltzmann constant, $\eta$ is the
aperture efficiency, $A = b \times d$ is the aperture area,
$\Delta\nu$ the channel width and $\Delta t$ the integration time.
The foreground maps give the flux in Jy units at every
pixel, therefore the Fourier sum directly produces the model
visibilities in Jy units as well. The flowchart in Figure~\ref{fig:flowchart} gives a bird's eye
view of the part of the simulator pipeline used to obtain the
visibilities, and summarises the emulator part of \textbf{Prowess}.
The dashed box in the flowchart represents the functionality that simulates the
foreground maps. The emulator also has the functionality to accept an external
FITS image(e.g.~via observations from some other telescope) of the foreground.
\subsection{Redundancy calibration}\label{ssec:calibration}
Due to the highly redundant configuration of OWFA, the number of independent
Fourier modes measured on the sky is small, given by a small number of
baselines, $N_A-1$. All other baselines give copies of these measurements. As a
result, we obtain a system of equations in which the number of unknowns is much
smaller than the number of measurements. This allows us to not only solve for
the gains of the antennas but, unlike routine interferometric calibration, also
solve for the true sky visibilities. This class of calibration algorithms is
called redundancy calibration\citep[see][for examples]{Wieringa1992,
Liu2010}. \textbf{Prowess} implements a highly efficient, fast and
statistically optimal non-linear least squares minimisation based steepest
descent calibration, that is capable of running in real time. This calibration
algorithm, detailed in \citet{Marthi2014}, is the algorithm of choice for
OWFA. Denoting the antenna gains as $g_i$, the true visibilities as $M_{|i-j|}$
and the observed visibilities as $V_{ij}$, the gains and the true visibilities
are solved for iteratively using the equations
\begin{equation}
g_k^{n+1} = (1 - \alpha) g_k^n + \alpha \mathbf{Q_k}^n
\label{giter}
\end{equation}
and
\begin{equation}
M_{|k-j|}^{n+1} = (1 - \alpha) M_{|k-j|}^n + \alpha \mathbf{R_{kj}}^n
\label{miter}
\end{equation}
where
\begin{equation}
\mathbf{Q_k} = \frac{\sum\limits_{j \neq
k} w_{kj} g_j M_{|k-j|}^* V_{kj}}{\sum\limits_{j \neq
k} w_{kj} |g_j|^2\ |M_{|k-j|}|^2},
\label{itergainsol}
\end{equation}
\begin{equation}
\mathbf{R_{kj}} = \frac{\sum\limits_{j > k} g_k^* g_j V_{kj}}{\sum\limits_{j >
k}w_{kj} |g_k|^2 |g_j|^2}
\label{itervissol}
\end{equation}
and $0<\alpha<1$ is the step size. The gains and true visibilities at the
present instant are obtained as updates to those obtained in the previous instant.
The simulated visibilities are therefore calibrated using this algorithm
to obtain the true visibilities. Redundancy calibration is a model-independent
calibration procedure; hence the sky model is a natural product of
calibration.
\subsection{Power spectrum estimation}\label{sec:PS_estim}
The calibrated visibility data are processed directly to obtain the power
spectrum. A visibility-based angular power spectrum estimator has been
implemented in \textbf{Prowess}. The estimator has been studied in earlier
works\citep{Begum2006, Datta2007, Choudhuri2014}, but it has been recast for
OWFA. \textbf{Prowess} implements the estimator to take advantage
of the redundant baseline configuration of OWFA, allowing us to add the
visibilities from all the redundant copies of a baseline of a given length. The
implementation of the estimator is detailed in \citet{Marthi2017a}.
Denoting the calibrated visibility as $\mathcal{V}(\mathbf{U}_n,\nu)$,
let us define the quantity
\begin{equation}
\mathcal{V}^\prime(\mathbf{U}_n,\nu) = \sum_{i=0}^{N_n} |\mathcal{V}^{(i)}(\mathbf{U}_{n}, \nu)|^2
\end{equation}
We can now define our estimator, $\mathbf{S}_2$, as
\begin{equation}
\mathbf{S}_2(\mathbf{U}_n, \nu_i, \nu_j) = \frac{\mathcal{V}(\mathbf{U}_n,
\nu_i)\mathcal{V}^*(\mathbf{U}_n, \nu_j) - \delta_{ij}\mathcal{V}^\prime(\mathbf{U}_n,
\nu_i)}{N_n^2 - \delta_{ij}N_n}
\label{eqn:S2_compute}
\end{equation}
The second term in the numerator corrects for the bias contributed by the
self-correlated noise.
For an N-channel visibility dataset, the real-valued $\mathbf{S}_2(\mathbf{U}_n,
\nu_i, \nu_j)$ is a $N \times N$ matrix as implemented in \textbf{Prowess}.
This representation in the $\nu-\nu$ plane has its
advantages in the study of systematics as it retains the full spectral
information of the foregrounds and those introduced by the instrument. The
estimator matrix cube is available in FITS format that can be visulaised either
through standard FITS visualisation programs or through the tool implemented in
\textbf{Prowess}.
The study of foreground power spectra through simulations, enabled by
\textbf{Prowess}, inform us that per-baseline spectral features arising in the estimator within the
observing band are caused by (i) the effect of the
frequency-dependent primary beam and (ii) the frequency dependence of the
baseline vector. These effects have been studied in some detail in the context
of EoR experiments, such as by \citet{Vedantham2012} for example. We have
carried out exhaustive studies of instrumental chromatic effects on the power
spectrum for OWFA \citep{Marthi2017a}. Importantly, simulations using
\textbf{Prowess} appear to indicate that the instrinsic chromatic properties of
the sky are less important, but such chromatic effects are compounded by the
chromatic instrument response. These effects would eventually play a limiting
role in the detectability of the {H{\sc i}}~signal.
\subsection{Data visualisation}
The simulated visibilities are written into a FITS file in the UVFITS
data format. This is a standard format for reading and writing the
radio interferometric visibility data, and is the format being used at the GMRT. However, \textbf{Prowess} has
its own interface that helps in visualising the visibility data, which is
explained here. The data are available in time-baseline-frequency
order. That is, the coarsest data identifier is the record number,
which is tagged to the timestamp. At each timestamp, all the $^{N_A}C_2$
baselines are sorted in a specific order, indexed by the FITSbl
\begin{figure}
\begin{center}
\includegraphics[scale=0.55]{displaybuf.eps}
\end{center}
\caption{The display buffer with gridded Time, Frequency and Baseline axes,
where the complex visibility resides.}
\label{fig:displaybuf}
\end{figure}
number shown in Figure~\ref{fig:baselines.info}. Each baseline has $N$
channels, and each channel has a real and imaginary number for the
visibility, and an associated weight. The visibility data therefore reside in a
\begin{figure}
\begin{center}
\includegraphics[scale=0.27,angle=270]{imagtifr.eps}
\end{center}
\caption{A time-frequency view of the visibility data on the $T-N$
plane for $B=1$.}
\label{fig:imagtifr}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.27,angle=270]{imagtibl.eps}
\end{center}
\caption{A time-baseline view of the visibility data on the $T-B$
plane for $N=156$.}
\label{fig:imagtibl}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[scale=0.27,angle=270]{imagfrbl.eps}
\end{center}
\caption{A frequency-baseline view of the visibility data on the $N-B$
plane for $T=30$.}
\label{fig:imagfrbl}
\end{figure}
gridded three-dimensional co-ordinate system where the three axes are time,
baseline and frequency. There are $T \times B \times N$ grid cells,
where $T$ is the number of records, $B$ is the number of baselines and
$N$ is the number of channels, shown in Figure~\ref{fig:displaybuf}. This
arrangement is very convenient; therefore
the native structure that holds these visibility data in a display
buffer is similarly defined. For visualising the data, they are therefore
read from the FITS record into the display buffer. The visualisation
programs hence access one of the planes parallel to the $T-B$, $B-N$
or $T-N$ planes. Figures~\ref{fig:imagtifr}, ~\ref{fig:imagtibl} and
~\ref{fig:imagfrbl} show the simulated visibility accessed
from the display buffer for an example run with a particular
realisation for the diffuse Galactic foreground, with the 312-channel, 40-antenna,
780-baseline Phase-I observed for 60 seconds with a record being
written to disk every second. There is an option to dynamically switch
between a real/imaginary or an amplitude/phase view, and dynamically switch
between linear, square-root and logarithmic image transfer functions. A dynamic
zooming feature is available in these interfaces as well. Besides the
colour-coded plan view, these plane data from the display buffer can
also be viewed in a line-plot format, again, with the
option to dynamically switch between real/imaginary and
amplitude/phase view formats.
\section{The observatory data processing pipeline}
\textbf{Prowess} is not an emulator alone, as the name may suggest. It
was described in Section~\ref{sec:rationale} why the emulator was
conceived: it serves the dual purpose of an emulator and
would potentially become the standard post-correlation data processing
pipeline at the observatory. It would be useful now to dwell a little
on the data processing pipeline aspect of \textbf{Prowess} and state
what functionality it is meant to provide.
The data pooled from the antennas would terminate in the eight
high-performance compute nodes through eleven copper ethernet links
each. These nodes correlate the signal from every pair of antennas and
accumulate the products upto an interval of time, usually
programmable. The typical integration time, called the Long Term
Accumulation(LTA), is of the order of $1-10$ seconds.
Once the data are available in FITS format, \textbf{Prowess} can
completely take over downstream processing, which include
calibration and power spectrum estimation. The uncalibrated FITS
data can as well be stored in the disks for offline calibration. The enormous
redundancy of the measurements and the structure of
OWFA are best exploited by calibrating the visibilities using the non-linear least
squares redundancy calibration algorithm, described in
Section~\ref{ssec:calibration}.
The calibrated visibilities are later processed to obtain the power spectrum of observed
sky.
\section{Summary}
A software model that captures the instrumental and geometric
details of OWFA has been described. This detailed model is an important aid to understanding the
systematics introduced by the instrument and to make robust and meaningful
predictions for the foregrounds and the {H{\sc i}}~signal. The programming philosophy
allows for modular function definitions and easy addition of new
functionality. The suite features a rich and interactive visual environment to
play back the visibility data. These programs comprise not just an emulator for OWFA, but they
are also designed to serve as observatory data analysis software. Prowess has greatly
aided our understanding of the instrument and the systematics expected in the OWFA cosmology
experiment.
\bibliographystyle{mnras}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,665
|
Knowledge Strategy
Knowledge-based Benchmarking
Kings Road
Ascot, England, SL5 9AB
Putting knowledge to work, wisely.
How the stiff upper lip is the enemy of knowledge sharing
January 31, 2013 Chris Collison
Here's a quote from a BBC news article yesterday:
The UK's "stiff upper lip" culture may explain why it lags behind other countries when it comes to beating cancer, say experts.
Researchers, who surveyed nearly 20,000 adults in six high-income countries, said they found embarrassment often stopped Britons visiting the doctor. Respondents in the UK were as aware of cancer symptoms as those in Australia, Canada, Denmark, Norway and Sweden, but more reluctant to seek help, they said.
When you drill down to the underlying reason behind "embarrassment" or "reluctance to ask for help", you usually end up with "pride".
This reminds me of one of my "seven deadly syndromes of knowledge-sharing". I called it "Real men don't ask directions", or "TomTom syndrome"
Imagine the scene: You're on your way to a dinner party at a friend's house; you left home a little late, so now you're in a hurry and the quality of your driving is deteriorating. Your partner is unsettled and tells you that "she'd prefer to get there in one piece than not at all". Now, just to add to the tension, you have a nagging thought that you might have taken a wrong turn. You carry on though, hoping that you'll happen upon a road-sign or a landmark, but none appear. Finally, your partner breaks the silence and tells you what you already know. You're lost! "No problem", she says triumphantly pronouncing the solution; "pull over by that man over there and we'll ask for directions".
Of course, it's not exclusively a male problem, but it does seem to be the case that men suffer from this syndrome more than women. It's hard to ask for help.
We have all had times when we have that nagging sense that "there might be a better way to do this", or "perhaps someone else has already figured this one out". What stops us from asking around for solutions and ideas for improvement? Sometimes it's a sense that we're supposed to know the answers.
Why would I want to show everyone else that I'm incompetent? That doesn't seem like a route to promotion. However, once I've solved my problem, I'll be happy to share my solution.
The truth is, the biggest challenge to organisations who want to get more from what they know, isn't that they have a knowledge sharing problem. It's that they have an asking problem.
It's also true to say that we often turn to technology for help when a conversation would be more timely, more accurate and more helpful – whether that's with a doctor, a local resident or a knowledgeable colleague who would be only too willing to help.
In Behaviours, Health, KM, Knowledge Management, Knowledge Sharing, Organizational learning, Peer Assist
Does Social Networking makes your brain grow?
October 19, 2011 Chris Collison
Ten year ago, we were hearing that London Taxi drivers have an enlarged hippocampus because of their encyclopedic (or should that be atlassian?) knowledge of London's roads.
Now the same research team in UCL are questioning whether social networking has a similar impact although the researchers do confess:
It's not clear whether using social networks boosts grey matter or if those with certain brain structures are good at making friends.
...so perhaps slightly cyclic reasoning?
I've wondered for a while whether we have a finite "namespace" in our brains, and once it's full (see why I didn't make it as a neuroscientist!), it starts to overflow and we forget people's names.
I can testify that changing my work relationship pattern from a single slowly-evolving large corporation to short assignments in 100 client organisations over the last 6 years has certainly helped to fill it up. My wife reports similar name-overflow challenges working a supply teacher.
Or perhaps it's just that we're just getting older!
In Health, KM, Knowledge Management, Web 2-0
Judgement day...
May 14, 2007 Chris Collison
It's been a healthy last couple of weeks.I attended a "Patient Harm Conference" last week (provocative title, eh?) - organised by Tricordant, for the NHS and a number of health-related organisations all focused on improving patient safety. I had the privilege of hearing leadership speaker Alistair Mant discuss complex systems (using frogs and bicycles) the subject of Judgement (not in the biblical sense - that's another story!)
Alistair came out with a couple of quotes which made me think:
Judgement is what you do when you don't know (and can't know) what to do - and you know you need to do something fast!
Good judgement is based on experience; experience is based on bad judgement...
I guess I'd better be the judge of that!
In Health, Learning
Lights, Camera, (after) Action (review)!
I spent a fascinating day last week with some senior NHS clinical staff at a Leadership Development Centre in Leicester. From the outside, the building looks like any other office in the city, and as you go past the smart reception, it still looks relatively familiar, although signs pointing to areas like "Narrative Centre" hint at a something out of the ordinary. Then, turning the corner and pushing though a pair of double doors, you suddenly find yourself in the middle of an NHS hospital ward, - it even has that disinfectant-like smell like a hospital ward! This one, however is devoid of any staff or patients, but has a number of hidden cameras. Kind of like Big Brother meets ER. In fact, it was built by the same company that constructs the set for the British medical drama-soap, Holby City.
This elaborate and incredibly lifelike environment has been built as part of an "immersive" senior management development programme. Professional role-players act out scenarios involving the real professional staff - often tough, highly emotional scenes, whilst the other delegates observe the video relay, debrief and discuss . Speaking with some of the participants, they were all amazed at how quickly they found themselves "believing" what was happening during the role plays.
My role was to provide some input relating to After Action Reviews (AARs), and to use the role-plays to help the clinicians translate this input into real life - well, it felt real to us!
I was really struck by the power of simulation in learning - we don't use this nearly enough in business. I was also really encouraged that parts of the NHS are sufficiently progressive to develop their senior staff through such innovative approaches - and are committed to learning-whilst-doing.
In AAR, Health, Organizational learning
Contact Chris on +44 (0)7841 262900
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,567
|
{"url":"https:\/\/brilliant.org\/practice\/integration-of-logarithmic-functions\/","text":"Calculus\n\n# Integration of Logarithmic Functions\n\nIf $$xf'(x)=24\\ln x,$$ what is the function $$f(x)?$$ (Use $$C$$ as the constant of integration.)\n\nIf $$f(x)$$ is a function such that $f(x)=\\int \\frac{1}{x \\sqrt{\\ln x+3}} dx$ and $$f(e)=21,$$ what is the value of $$f(e^{5})?$$\n\nWhat is the indefinite integral$\\int \\frac{1}{x}\\left(7(\\ln x)^{6}+5\\right) dx?$ (Use $$C$$ as the constant of integration.)\n\nLet $$N = \\displaystyle \\int_{1}^{e^ 8} \\ln \\left( \\dfrac {1}{x} \\right) \\, dx$$. If $$N = -ae^b - c$$, where $$a$$, $$b$$ and $$c$$ are positive integers and $$e$$ is the base of the natural logarithm, what is the value of $$a + b + c$$?\n\nIf $$f(x)$$ is a function satisfying $f(x)=\\int \\frac{6(\\ln x)^{5}}{x} dx$ and $$f(e)=8,$$ what is the value of $$f(e^2)?$$\n\n\u00d7","date":"2018-05-22 21:40:58","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\": 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\": 0.921875, \"perplexity\": 79.19984450037116}, \"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-2018-22\/segments\/1526794864968.11\/warc\/CC-MAIN-20180522205620-20180522225620-00221.warc.gz\"}"}
| null | null |
Little Lulu: Working Girl by John Stanley
4-col
The first in a five-volume best-of series, featuring an introduction from Margaret Atwood!
Lulu Moppet is an outspoken and brazen young girl who doesn't follow any rules—whether they've been set by her parents, the neighborhood boys, or society itself. In 2019 D+Q begins a landmark full-color reissue series collecting five volumes of Lulu's funniest suburban hijinks: she goes on picnics, babysits, and attempts to break into the boys' clubhouse again and again. Cartoonist John Stanley's expert timing and constant gags made these stories unbelievably enjoyable, ensuring that Marge's Little Lulu was a defining comic of the post-war period.
First released in the 1940s and 1950s as Dell comics, Little Lulu as helmed by Stanley remains one of the most entertaining works in the medium. In this first volume, Little Lulu: Working Girl, we meet the series' mainstay characters: Lulu, Tubby, Alvin, and oodles more neighbourhood kids. Little Lulu's comedy lies in the hilarious dynamic between its cast of characters.
Lulu's assertiveness, individuality, and creativity is empowering to witness—the series is powerfully feminist despite the decades in which the stories were created. It's the character's strong personality that made her beloved by such feminist icons as Patti Smith, Eileen Myles, and more. Lovingly restored to its original full color, complete with knee-slapping humor and an introduction by Margaret Atwood that explains the vitality of Lulu herself, Little Lulu: Working Girl is a delight for classic comics fans and the uninitiated.
(Past Event) Free Comic Book Day 2019
Margaret Atwood Introduces Little Lulu in the New Yorker
The New Yorker / November 29, 2019
Youth Services Book Review Features Little Lulu
Youth Services Book Review / November 15, 2019
Lifehacker lists Little LuLu under FBCD 2019
Lifehacker / January 17, 2019
Visit John Stanley's Author Page!
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,798
|
package edu.berkeley.compbio.sequtils;
import com.davidsoergel.dsutils.ChainedError;
import org.apache.log4j.Logger;
/**
* @version 1.0
*/
public class SequenceError extends ChainedError
{
// ------------------------------ FIELDS ------------------------------
private static final Logger logger = Logger.getLogger(SequenceError.class);
// --------------------------- CONSTRUCTORS ---------------------------
public SequenceError(String s)
{
super(s);
}
public SequenceError(Exception e)
{
super(e);
}
public SequenceError(Exception e, String s)
{
super(e, s);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,466
|
The 2018 Campeonato Brasileiro Série C was a football competition held in Brazil, equivalent to the third division. The competition started on 14 April and ended on 22 September 2018.
Twenty teams competed in the tournament, twelve returning from the 2017 season, four promoted from the 2017 Campeonato Brasileiro Série D (Operário Ferroviário, Globo, Atlético Acreano and Juazeirense), and four relegated from the 2017 Campeonato Brasileiro Série B (Luverdense, Santa Cruz, ABC and Náutico).
Botafogo-SP, Bragantino, Cuiabá and Operário Ferroviário qualified for the semi-finals and were promoted to the 2019 Campeonato Brasileiro Série B.
Operário Ferroviário won the title after defeating Cuiabá in the final.
Teams
Number of teams by state
Personnel
Group stage
In the group stage, each group was played on a home-and-away round-robin basis. The teams were ranked according to points (3 points for a win, 1 point for a draw, and 0 points for a loss). If tied on points, the following criteria would be used to determine the ranking: 1. Wins; 2. Goal difference; 3. Goals scored; 4. Head-to-head (if the tie is only between two teams). If tied on aggregate, the away goals rule would be used (except if both teams shared the same stadium); 5. Fewest red cards; 6. Fewest yellow cards; 7. Draw in the headquarters of the Brazilian Football Confederation (Regulations Article 15).
The top four teams of each group advanced to the quarter-finals of the knockout stages.
Group A
Results
Group B
Results
Final Stages
Starting from the quarter-finals, the teams played a single-elimination tournament with the following rules:
Each tie was played on a home-and-away two-legged basis, with the higher-seeded team hosting the second leg (Regulations Article 17).
If tied on aggregate, the away goals rule would not be used, extra time would not be played, and the penalty shoot-out was used to determine the winner (Regulations Article 16).
Starting from the semi-finals, the teams were seeded according to their performance in the tournament. The teams were ranked according to overall points. If tied on overall points, the following criteria would be used to determine the ranking: 1. Overall wins; 2. Overall goal difference; 3. Draw in the headquarters of the Brazilian Football Confederation (Regulations Article 17).
Bracket
Quarter-finals
The matches were played between 18 and 27 August 2018.
|}
Group C
Bragantino won 4–2 on aggregate and advanced to the semi-finals
Group D
Operário Ferroviário won 3–1 on aggregate and advanced to the semi-finals
Group E
Cuiabá won 4–2 on aggregate and advanced to the semi-finals
Group F
Tied 1–1 on aggregate, Botafogo-SP won on penalties and advanced to the semi-finals
Semi-finals
The matches were played between 1 and 9 September 2018.
|}
Group G
Tied 0–0 on aggregate, Operário Ferroviário won on penalties and advanced to the finals
Group H
Cuiabá won 3–0 on aggregate and advanced to the finals
Finals
The matches were played on 16 and 22 September 2018.
|}
Group I
Top goalscorers
References
Campeonato Brasileiro Série C seasons
3
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 683
|
The Naked Dietitian: a true radical
September 6, 2017 - by Joe Turnbull
The Naked Dietitian is a one-woman spoken word piece which explores an unorthodox approach to health and dietetics, written and performed by fully qualified dietitian, Lucy Aphramor. It played Quaker Meeting House at the Edinburgh Festival Fringe throughout the month of August.
Lucy Aphramor in the Naked Dietitian. Photograph (c) Linda Marshall LPRS
Lucy Aphramor is a radical dietitian. I know what you may be thinking. How radical can a dietitian really be? No, Lucy doesn't advocate some bizarre fad diet of only eating netils, or fasting for days then stuffing your face the next. She is radical in that she posits ill-health outside the individual – at societal level with prejudice, trauma and inequality. She is a dietitian who says we cannot tackle ill-health without first acknowledging and tackling the root causes of discrimination.
Whilst this is not a show about disability per se, her fight against a 'medical model' of ill-health which disregards the socio-political context within which it occurs has deep parallels with the ongoing battle for disabled people's civil rights. Unsurprisingly, this subversive approach has made her the bane of her profession. She is ostracised. She is ignored. But she will not be silenced.
The Naked Dietitian is a spoken word piece which takes you on a journey, from personal experiences of abuse, through solidarity with others facing prejudice and pointing to a more hopeful and healthy future, via Grenfell and the Black Lives Matter movement. All with lyrical abandon and astute acuity. The piece is also sprinkled with nuggets of advice gleaned from a lived experience of dealing with shit.
The mantra that 'just because things are crap doesn't mean you are' is one that will resonate across groups marginalised by class, race, gender, body shape, sexuality or disability. Lucy suggests when things are completely overwhelming to just grab onto every breath ('even if you don't have a hand or fingers to grasp with'). This is coupled with the ethos of being present in every moment. There are moments like these in the show where it threatens to fall into new-age platitudes on wellness, but Lucy treads the line masterfully and it always feels sincere and never cliché.
She also teeters on the brink in other ways. 'I'm tearing my heart out on stage for you because I know it regrows and I'm shit scared you don't.' In the most vulnerable sections where Lucy is laying her pain and experience of abuse bare she looks like she could genuinely break down at any minute. But she doesn't. It keeps you gripped and also somehow makes you feel she is connecting to you directly.
At 45 minutes, with no props (save some train tickets), no music and no set of any kind, it runs a little on the long side for a spoken word piece. But Lucy holds your attention, breathlessly throughout. That is a real skill.
For Lucy, the dietetic profession is just an instrument of neoliberalism which places the blame for being overweight and other health problems on the individual with its relentless creed of 'eat less, move more'; as she describes it, 'a joyless treadmill'. It also disciplines and enforces a warped sense of 'normality' onto any form of bodily difference. Sound familiar? For disabled people, it should.
The performance weaves in vignettes on other experiences of oppression, from children made to question their bodies or sexuality, to a young black man who is constantly stopped on the tube to prove he has a valid ticket. Apparently, there is a direct link between increased rates of hypertension and being of non-majority ethnicity. Racism, not diet may be the primary cause. There's also a nod to the disabled child who may feel invisible because they don't see themselves represented in their toys or on screen.
Lucy's self-care and social justice approach known as Well Now has been adopted by NHS Highland Public Health as their healthy weight policy, which shows real impact. But her art is just as powerful.
Lucy implores anyone to love their body, embrace and be comfortable in their fleshy contours. 'You are enough. Ample, plenty'. Her message is one of pure compassion. Of emphatic empathy. There lies the path to a more healthy and happy world.
For more information about Lucy Aphramor and the Radical Dietitian movement, visit her website.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,856
|
\section{#1}\setcounter{equation}{0}}
\newcommand{\ra}{\rangle}
\newcommand{\la}{\langle}
\newcommand{\p}{\partial}
\newcommand{\hp}{{\Phi}}
\newcommand{\hq}{{Q_B}}
\newcommand{\he}{{\eta_0}}
\newcommand{\ha}{{{A}}}
\newcommand{\rrr}{\big\rangle\big\rangle}
\newcommand{\lllb}{\Bigl\langle\Bigl\langle}
\newcommand{\rrrb}{\Bigr\rangle\Bigr\rangle}
\begin{document}
\begin{center}
\large {\bf Dirac equation of spin particles and tunneling radiation from an Kinnersly black hole}
\end{center}
\begin{center}
Guo-Ping Li $^1$
$\footnote{E-mail: Corresponding author, gpliphys@yeah.net}$
Zhong-Wen Feng $^2$
$\footnote{E-mail: \texttt{zwfengphy@163.com}}$
Hui-Ling Li $ ^{1, 3}$
$\footnote{E-mail: \texttt{LHL51759@126.com}}$
Xiao-Tao Zu ${^1}$
$\footnote{E-mail: \texttt{xtzu@uestc.edu.cn}}$
\end{center}
\begin{center}
\textit{1. School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, 610054, China\\
2. Department of Astronomy, China West Normal University, Nanchong, 637009, China\\
3. College of Physics Science and Technology, Shenyang Normal University, Shenyang, 110034, China}
\end{center}
\noindent
{\bf Abstract:} In curved space-time, Hamilton-Jacobi equation is a semi-classical particle's motion equation, which plays an important role in the research of black hole physics. In this paper, starting from Dirac equation describing the spin 1/2 fermion and Rarita-Schwinger equation describing the spin 3/2 fermion respectively, we derive a Hamilton-Jacobi equation of the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling behavior of a charged spherically symmetric black hole is investigated by using this Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful for people to understand the thermodynamic properties and the radiation characteristics of a black hole.
\noindent
{\bf Keywords:} Hamilton-Jacobi equation; non-stationary spherically black hole; tunneling radiation
\section{Introduction}
\label{section1}
\setlength{\parindent}{2em}
In 1974, considering quantum effects, Hawking proved that a black hole has the thermal radiation \cite{1}. After that, people have carried out a series of research for various types of black hole radiation \cite{2,3,4,5,7}. About the origin of Hawking radiation, a kind of viewpoint is that the virtual particles inside a black hole via the quantum tunneling effect reach the event horizon of a black hole and materialize real particles, and radiate out, which called Hawking thermal radiation \cite{7+}. (About the source of Hawking radiation, a common viewpoint believes that, due to vacuum fluctuation near the event horizon where a virtual particle pair could be created or annihilated, a negative energy particle falls in since there exists a negative energy orbit inside black hole, however the positive energy particle left outside is radiated to infinite, which causes Hawking radiation \cite{8}). In 2000, Parikh and Wilczek \emph{et al}. put forward that a quantum tunneling theory to study the thermal radiation of a black hole. By taking into account the background change before and after radiation particles tunneling, they have carried out modification to the previous tunneling probability \cite{9}. Thus, in recent years, a series of significant studies have been made on the tunneling radiation of black holes \cite{10}. Zhang and Zhao \emph{et al.} have developed this tunneling theory, and studied the relationship between the tunneling radiation and the black hole entropy, which provides a reasonable explanation for information loss paradox of a black hole. Further research of Lin and Yang \emph{et al.} showed that the tunneling rate of the event horizon from a dynamic black hole is not only related to the black hole entropy, but also related to an integral function \cite{11}. Therefore, information loss paradox of a black hole still needs further research. According to the literature \cite{12,13,131+,131a+,131b+,13+,14+,15+,16+,17+,add1}, the Hamilton-Jacobi equation in curved space-time is the basic equation describing the dynamic characteristics of all kinds of particles. For the Dirac equation describing the spin particle and the equation describing the spin 3/2 particle, the Dirac equation and the tunneling radiation of a stationary black hole have been studied. However, a black hole in the universe is due to radiation, accretion, merging and other reasons, which leads to be dynamic change of the black hole. Therefore, it is a practical significance to study the tunneling radiation characteristics of a dynamic black hole.
For a dynamic black hole, the Dirac equation describing the spin $1/2$ and the $3/2$ particles is more complex than that of a stationary black hole. In this paper, according to the space-time linear element of a Kinnersley black hole, using the advanced Eddington coordinate to represent its dynamic characteristics, we study the tunneling radiation of spin $1/2$ and $3/2$ particles in this space-time background.
The rest of the paper is organized as follows. Due to the Dirac equation for spin $1/2$ particle and the Rarita-Schwinger equation for spin $3/2$ particle, we derived the Hamilton-Jacobi equation in Section~\ref{section2}. In Section~\ref{section3}, according to the Hamilton-Jacobi equation, the fermion tunnelling behavior in a non-stationary Kinnersley black hole is addressed. Section~\ref{section4} is devoted to our discussion and conclusion.
\section{Dirac equation of spin particles and the Hamilton-Jacobi equation}
\label{section2}
\setlength{\parindent}{2em} The Dirac equation for spin $1/2$ particle can be described by \cite{14}
\begin{eqnarray}
\gamma ^\mu D_\mu \Psi + \left( {{m \mathord{\left/
{\vphantom {m \hbar }} \right.
\kern-\nulldelimiterspace} \hbar }} \right)\Psi = 0,
\label{eq1}
\end{eqnarray}
where
\begin{eqnarray}
D_\mu = \partial _\mu + \frac{1}{2}i\Gamma _\mu ^{\alpha \beta } \Pi _{\alpha \beta } ,
\label{eq2}
\end{eqnarray}
\begin{eqnarray}
\Pi _{\alpha \beta } = \frac{i}{4}\left[ {\gamma ^\alpha ,\gamma ^\beta } \right],
\label{eq3}
\end{eqnarray}
here the relationship between gamma matrices and the space-time metric is
\begin{eqnarray}
\left\{ {\gamma ^\mu ,\gamma ^\nu } \right\} = 2g^{\mu \nu } I,
\label{eq4}
\end{eqnarray}
Before solving the equation Eq.~(\ref{eq1}), one must know the space-time background. Let us consider a dynamic Kinnersley black hole of arbitrarily variably accelerated rectilinear motion. In the advanced Eddington coordinate, the space-time linear element of the black hole can be written as \cite{15}
\begin{eqnarray}
ds^2 = & - & \left( {1 - 2ar\cos \theta - r^2 f^2 - 2Mr^{ - 1} } \right)d\upsilon ^2 - 2d\upsilon dr + 2r^2 fd\upsilon d\theta
\nonumber \\
& - &r^2 d\theta ^2 - r^2 \sin ^2 \theta d\varphi ^2 ,
\label{eq5}
\end{eqnarray}
where $f = - a\left( \upsilon \right)\sin \theta$, $M = M\left( \upsilon \right)$. $a\left( \upsilon \right)$ stands for the magnitude of acceleration. $M\left( \upsilon \right)$ is the mass of the black hole. From Eq.~(\ref{eq2}), one gets the metric determinant and the non-zero components of the inverse metric tensor
\begin{eqnarray}
g = - r^4 \sin ^2 \theta,
\label{eq6}
\end{eqnarray}
and
\begin{eqnarray}
g^{01} = g^{10} = - 1,g^{11} = - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right),g^{12} = g^{21} = f,g^{22} = - {1 \mathord{\left/
{\vphantom {1 {r^2 }}} \right.
\kern-\nulldelimiterspace} {r^2 }}, g^{33}=r^{-2}\sin ^{-2} \theta.
\label{eq7}
\end{eqnarray}
According to Eq.~(\ref{eq5}) - Eq.~(\ref{eq7}), the gamma matrices of Eq.~(\ref{eq4}) can be constructed as follows
\begin{eqnarray}
\gamma ^\upsilon =\sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} } \left[ {i\left( {\begin{array}{*{20}c}
I & 0 \\
0 & { - I} \\
\end{array}} \right) + \left( {\begin{array}{*{20}c}
0 & {\sigma ^3 } \\
{\sigma ^3 } & 0 \\
\end{array}} \right)} \right],
\label{eq8}
\end{eqnarray}
\begin{eqnarray}
\gamma ^r =\sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)} \left( {\begin{array}{*{20}c}
0 & {\sigma ^3 } \\
{\sigma ^3 } & 0 \\
\end{array}} \right),
\label{eq9}
\end{eqnarray}
\begin{eqnarray}
\gamma ^\theta = \frac{f}{{\sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} } }}\left( {\begin{array}{*{20}c}
I & 0 \\
0 & { - I} \\
\end{array}} \right) + \sqrt {\frac{{\chi \left( { - {1 \mathord{\left/
{\vphantom {1 {r^2 }}} \right.
\kern-\nulldelimiterspace} {r^2 }}} \right) - f^2 }}{{ - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} }}} {\rm{ }}\left( {\begin{array}{*{20}c}
0 & {\sigma ^1 } \\
{\sigma ^1 } & 0 \\
\end{array}} \right),
\label{eq10}
\end{eqnarray}
\begin{eqnarray}
\gamma ^\varphi = \sqrt {r^{ - 2} \sin ^{ - 2} \theta } \left( {\begin{array}{*{20}c}
0 & {\sigma ^2 } \\
{\sigma ^2 } & 0 \\
\end{array}} \right),
\label{eq11}
\end{eqnarray}
and in gamma matrices Eq.~(\ref{eq8}) - Eq.~(\ref{eq11}), the Pauli matrices are
\begin{eqnarray}
\sigma ^1 = \left( {\begin{array}{*{20}c}
0 & 1 \\
1 & 0 \\
\end{array}} \right),\sigma ^2 = \left( {\begin{array}{*{20}c}
0 & { - i} \\
i & 0 \\
\end{array}} \right),\sigma ^3 = \left( {\begin{array}{*{20}c}
1 & 0 \\
0 & { - 1} \\
\end{array}} \right),
\label{eq12}
\end{eqnarray}
where, $\chi = - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)$. The wave function is expressed as
\begin{eqnarray}
\Psi = \zeta \exp \left( {\frac{i}{\hbar }S} \right),
\label{eq13}
\end{eqnarray}
Where $S$ is the main function, the coefficient term can be decomposed into
\begin{eqnarray}
\zeta = \left( {\begin{array}{*{20}c}
A \\
B \\
\end{array}} \right).
\label{eq14}
\end{eqnarray}
Substituting Eq.~(\ref{eq12}) - Eq.~(\ref{eq13}) into Eq.~(\ref{eq11}) and neglecting the terms with $\hbar$, one can get a matrix equation, i.e.
\begin{eqnarray}
\left( {\begin{array}{*{20}c}
C & D \\
D & G \\
\end{array}} \right)\left( {\begin{array}{*{20}c}
A \\
B \\
\end{array}} \right) = 0,
\label{eq15}
\end{eqnarray}
In Eq.~(\ref{eq15}), $C$, $D$ and $G$ are closely related to Eq.~(\ref{eq5})-Eq.~(\ref{eq12}). The expressions are respectively,
\begin{eqnarray}
C = m - \sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} } \frac{{\partial S}}{{\partial \upsilon}}I - \frac{f}{{\sqrt { - \left( {1 - 2ar\cos \theta, - 2Mr^{ - 1} } \right)^{ - 1} } }}\frac{{\partial S}}{{\partial \theta }}I,
\label{eq16}
\end{eqnarray}
\begin{eqnarray}
D & = &i\left[ {\sqrt { - \left( {1 - 2ar\cos \theta - 2M r^{ - 1} } \right)^{ - 1} } \frac{{\partial S}}{{\partial \upsilon }} + \sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)} \frac{{\partial S}}{{\partial r}}} \right]\sigma ^3
\nonumber \\
& +& i\sqrt {\frac{{ - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} \left( { - {1 \mathord{\left/
{\vphantom {1 {r^2 }}} \right.
\kern-\nulldelimiterspace} {r^2 }}} \right) + f^2 }}{{ - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} }}} \frac{{\partial S}}{{\partial \theta }}\sigma ^1 + i\sqrt {r^{ - 2} \sin ^{ - 2} \theta } \frac{{\partial S}}{{\partial \phi }}\sigma ^2 ,
\label{eq17}
\end{eqnarray}
\begin{eqnarray}
G = m + \sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} } \frac{{\partial S}}{{\partial \upsilon}}I + \frac{f}{{\sqrt { - \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)^{ - 1} } }}\frac{{\partial S}}{{\partial \theta }}I,
\label{eq18}
\end{eqnarray}
Because of $C D = D C$, in order to obtain non-trivial solutions, it is necessary to have
\begin{eqnarray}
\det \left( {CG - DD} \right) = 0,
\label{eq19}
\end{eqnarray}
Taking into account the anti-commute relationship of Pauli matrices
\begin{eqnarray}
\left\{ {\sigma ^\mu ,\sigma ^\nu } \right\} = 2\delta _{\mu \nu },
\label{eq20}
\end{eqnarray}
According to Eq.~(\ref{eq16}) - Eq.~(\ref{eq18}), we can concretely express Eq.~(\ref{eq19}) as
\begin{eqnarray}
- \left( {1 - 2ar\cos \theta - 2Mr^{ - 1} } \right)\left( {\frac{{\partial S}}{{\partial r}}} \right)^2 - 2\frac{{\partial S}}{{\partial r}}\frac{{\partial S}}{{\partial \upsilon }} + 2f\frac{{\partial S}}{{\partial r}}\frac{{\partial S}}{{\partial \theta }} - \frac{1}{{r^2 }}\left( {\frac{{\partial S}}{{\partial \theta }}} \right)^2 + \frac{1}{{r^2 \sin ^2 \theta }}\left( {\frac{{\partial S}}{{\partial \phi }}} \right)^2 + m^2 = 0
\label{eq21}
\end{eqnarray}
This is the kinetic equation that only for a spin $1/2$ particle. That is to say, we derive the equation Eq.~(\ref{eq21}) from the equation Eq.~(\ref{eq1}). Eq.~(\ref{eq21}) is just the Hamilton-Jacobi equation of the dynamic Kinnersley black hole of the variably accelerated rectilinear motion, which is described by the equation Eq.~(\ref{eq7}). One can simplify it as $g^{\mu \nu } \left( {{{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial \mu }}} \right. \kern-\nulldelimiterspace} {\partial \mu }}} \right)\left( {{{\partial S} \mathord{\left/
{\vphantom {{\partial S} {\partial \nu }}} \right. \kern-\nulldelimiterspace} {\partial \nu }}} \right) + m^2 = 0$.
At the same time, it is needed to explain that, the dynamical behavior of the spin $3/2$ particles is described by Rarita-Schwinger equation of the curved space-time. Its concrete expression is
\begin{eqnarray}
\gamma ^\mu D_\mu \Psi _\nu + \left( {{m \mathord{\left/
{\vphantom {m \hbar }} \right.
\kern-\nulldelimiterspace} \hbar }} \right)\Psi _\nu = 0,
\label{eq22}
\end{eqnarray}
\begin{eqnarray}
\gamma ^\mu \Psi _\nu = 0,
\label{eq23}
\end{eqnarray}
where every $\Psi _\nu$ is a matrix. The expressions Eq.~(\ref{eq2}) and Eq.~(\ref{eq23}) together can determine every wave function. In the semi-classical theory, the wave function in the equation Eq.~(\ref{eq22}) can be expressed as
\begin{eqnarray}
\Psi_\nu = \left( {\begin{array}{*{20}c}
{A_\nu } \\
{B_\nu } \\
\end{array}} \right)\exp \left( {\frac{i}{\hbar }S} \right),
\label{eq24}
\end{eqnarray}
where $A = \left( {\begin{array}{*{20}c} {a_\nu } & {b_\nu } \\\end{array}} \right)^{TM}$ and $B = \left( {\begin{array}{*{20}c} {b_\nu } & {d_\nu } \\
\end{array}}\right)^{TM}$ and $a_\upsilon$,$b_\upsilon$,$c_\upsilon$,$d_\upsilon$ express the corresponding matrix. Thus, for the spin $3/2$ particles, the gamma matrix can be chosen to be consistent with Eq.~(\ref{eq9}) - Eq.~(\ref{eq11}). In the same way, we can still discuss the tunneling radiation of spin $3/2$ particles in the expression~(\ref{eq7}), which describes a dynamic Kinnersley black hole of the variably accelerated rectilinear motion. In the semi classical approximation, we can still get
\begin{eqnarray}
\left( {\begin{array}{*{20}c}
C & D \\
D & G \\
\end{array}} \right)\left( {\begin{array}{*{20}c}
{A_\nu } \\
{B_\nu } \\
\end{array}} \right) = 0,
\label{eq25}
\end{eqnarray}
In the above expression $C$, $D$ and $G$ are shown such as expressions Eq.~(\ref{eq16}) - Eq.~(\ref{eq18}). Taking into account non-trivial solution conditions in Eq.~(\ref{eq25}), we can obtained
\begin{eqnarray}
\det \left( {CG - DD} \right) = 0,
\label{eq26}
\end{eqnarray}
By the calculation, the Hamilton-Jacobi equation which is consistent with the Eq.~(\ref{eq21}) can still be obtained. So, for the Rarita-Schwinger equation of spin $3/2$ fermion particles, we can also obtain the dynamic equation Eq.~(\ref{eq21}). This further shows that the Hamilton-Jacobi equation of curved space-time is a basic dynamic equation of the radiation particles.
\section{Hamilton-Jacobi equation and the tunneling from Non-Stationary Kinnersly black hole}
\label{section3}
\setlength{\parindent}{2em} The event horizon of a non-stationary Kinnersley black hole described by the expression~(\ref{eq2}) satisfies the null hypersurface condition
\begin{eqnarray}
\label{eq27}
g^{\mu \nu } \frac{{\partial F}}{{\partial x^\mu }}\frac{{\partial F}}{{\partial x^\nu }} = 0.
\end{eqnarray}
Because of the acceleration direction of a non-uniformly rectilinearly accelerating black hole is always pointing to the north pole, namely $\theta = 0$, the space-time described by Eq.~(\ref{eq2}) is axial symmetry. From the expression~(\ref{eq9}) and Eq.~(\ref{eq27}), we can get the null hypersurface equation that the black hole event horizon satisfying
\begin{eqnarray}
r_H^2 - 2\dot r_H r_H^2 - 2a r_H^3 \cos \theta - 2M r_H - 2a r'_H r_H^2 \sin \theta + {r'_H}^2 = 0,
\label{eq28}
\end{eqnarray}
where$\dot r_H = {{\partial r} \mathord{\left/ {\vphantom {{\partial r} {\partial \upsilon }}} \right. \kern-\nulldelimiterspace} {\partial \upsilon }}
$, $r'_H = {{\partial r} \mathord{\left/ {\vphantom {{\partial r} {\partial \theta }}} \right. \kern-\nulldelimiterspace} {\partial \theta }}$ . From Eq.~(\ref{eq28}) we can see that, the event horizon $r_H$ is a function which depends not only on time $\upsilon$, but also on angle $\theta$. In order to calculate the temperature of a black hole, here we introduce a new generalized tortoise coordinate transformation \cite{16}
\begin{eqnarray}
r_* = r + r_H \left( {\upsilon _0 ,\theta _0 } \right) \ln \left[ \frac{ {r - r_H \left( {\upsilon ,\theta } \right)}}{r_H \left( {\upsilon ,\theta } \right)} \right]^{\alpha},\upsilon _* = \upsilon - \upsilon _0 ,\theta _* = \theta - \theta _0,
\label{eq29}
\end{eqnarray}
in which $\alpha$ is an adjustable coefficient, $\upsilon _0$ and $\theta _0$ are arbitrary constants. The differential forms for above expression become
\begin{eqnarray}
\frac{\partial }{{\partial r}} = \left[ {1 + \frac{\alpha r_H \left( {\upsilon _0 ,\theta _0 } \right)}{{ \left( {r - r_H } \right)}}} \right]\frac{\partial }{{\partial r_* }},
\frac{\partial }{{\partial \upsilon }} = \frac{\partial }{{\partial \upsilon _* }} - \frac{{\alpha r_H \left( {\upsilon_0 ,\theta_0 } \right) r \dot r_H }}{{ r_H \left( {r - r_H } \right)}}\frac{\partial }{{\partial r_* }},
\frac{\partial }{{\partial \theta }} = \frac{\partial }{{\partial \theta _* }} - \frac{ \alpha r_H \left( {\upsilon_0 ,\theta_0 } \right) r {r'_H }}{{ r_H \left( {r - r_H } \right)}}\frac{\partial }{{\partial r_* }}.
\label{eq30}
\end{eqnarray}
Substituting Eq.~(\ref{eq30}) into the Eq.~(\ref{eq21}), we have
\begin{flalign}
& g^{11} \left[ {1 + \frac{\alpha r_H \left( {\upsilon _0 ,\theta _0 } \right)}{{ \left( {r - r_H } \right)}}} \right]^2 \left( {\frac{{\partial S}}{{\partial r_* }}} \right)^2 + 2g^{01} \left[ {1 + \frac{\alpha r_H \left( {\upsilon _0 ,\theta _0 } \right)}{{ \left( {r - r_H } \right)}}} \right] \frac{{\partial S}}{{\partial r_* }} \left[ \frac{\partial S }{{\partial \upsilon _* }} - \frac{{\alpha r_H \left( {\upsilon_0 ,\theta_0 } \right) r \dot r_H }}{{ r_H \left( {r - r_H } \right)}}\frac{\partial S }{{\partial r_* }} \right]
\nonumber \\
& + 2g^{12} \left[ {1 + \frac{\alpha r_H \left( {\upsilon _0 ,\theta _0 } \right)}{{ \left( {r - r_H } \right)}}} \right] \frac{{\partial S}}{{\partial r_* }}\left[ {P_\theta - \frac{ \alpha r_H \left( {\upsilon_0 ,\theta_0 } \right) r {r'_H }}{{ r_H \left( {r - r_H } \right)}} \frac{{\partial S}}{{\partial r_* }}} \right] + g^{22} \left[ {P_\theta - \frac{ \alpha r_H \left( {\upsilon_0 ,\theta_0 } \right) r {r'_H }}{{ r_H \left( {r - r_H } \right)}} \frac{{\partial S}}{{\partial r_* }}} \right]^2
\nonumber \\
& +g^{33} j^2 + m_0^2 = 0,
\label{eq31}
\end{flalign}
In the above expression, we define $P_\theta = {{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial \theta _* }}} \right. \kern-\nulldelimiterspace} {\partial \theta _* }}$ and $P_\varphi = {{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial \varphi }}} \right. \kern-\nulldelimiterspace} {\partial \varphi }} = j$. $P_\theta$ stands for the generalized momentum, $j$ is a constant that is related to the Killing $\left( {{\partial \mathord{\left/ {\vphantom {\partial {\partial \varphi }}} \right. \kern-\nulldelimiterspace} {\partial \varphi }}} \right)$ vector \cite{5}. After processing the above expression, we can get
\begin{flalign}
& \frac{{g^{11} r_H^2 \mathcal{R}^2 + \alpha r r'_H r_H\left( {\upsilon_0 ,\theta_0 } \right) \left\{ {g^{22} \alpha r r'_H r_H\left( {\upsilon_0 ,\theta_0 } \right) - 2g^{12} r_H \mathcal{R}} \right\} - 2 g^{01} \alpha r r_H r_H\left( {\upsilon_0 ,\theta_0 } \right) \mathcal{R} \dot r_H }}{{g^{01} r_H^2 \left( {r - r_H } \right)\mathcal{R} }}\left( {\frac{{\partial S}}{{\partial r_* }}} \right)^2
\nonumber \\
&+ 2\frac{{\partial S}}{{\partial r_* }}\frac{{\partial S}}{{\partial \upsilon _* }} - \frac{{2\left\{ {g^{22} \alpha r r'_H r_H\left( {\upsilon_0 ,\theta_0 } \right) - g^{12} r_H \mathcal{R}} \right\}}}{{g^{01} r_H \mathcal{R}}}P_\theta \frac{{\partial S}}{{\partial r_* }} + \frac{{ {r - r_H } }}{{g^{01} \mathcal{R}}} g^{33} j^2 + \frac{{{r - r_H } }}{{g_{01} \mathcal{R}}} g^{22} P_\theta ^2 + \frac{{ {r - r_H } }}{{g_{01} \mathcal{R}}}m_0^2 = 0,
\label{eq32}
\end{flalign}
where, $\mathcal{R} = r - r_H + \alpha r_H\left( {\upsilon_0 ,\theta_0 } \right)$.
According to the conformally flat condition, here we ask that the limit of the coefficients of the $r_H$ in Eq.~(\ref{eq32}) is $1$ when the radius of the black hole approaches the event horizon $r_H$, namely
\begin{eqnarray}
\mathop {\lim }\limits_{\scriptstyle r \to r_H \hfill \atop
{\scriptstyle \upsilon \to \upsilon _0 \hfill \atop
\scriptstyle \theta \to \theta _0 \hfill}} \frac{{g^{11} r_H^2 \mathcal{R}^2 + \alpha r r'_H r_H\left( {\upsilon_0 ,\theta_0 } \right) \left\{ {g^{22} \alpha r r'_H r_H\left( {\upsilon_0 ,\theta_0 } \right) - 2g^{12} r_H \mathcal{R}} \right\} - 2 g^{01} \alpha r r_H r_H\left( {\upsilon_0 ,\theta_0 } \right) \mathcal{R} \dot r_H }}{{g^{01} r_H^2 \left( {r - r_H } \right)\mathcal{R} }}
\nonumber \\
= r_H\left( {\upsilon_0 ,\theta_0 } \right).
\label{eq33}
\end{eqnarray}
But we can find that, when $r \to r_H$, an infinite limit of $0/0$-type arises from the above expression. In order to study the tunneling radiation on the event horizon, we use the L'Hospital rule, thus we have
\begin{eqnarray}
\alpha = \frac{r_H \left[4M + r_H (-2 + 2 \dot r_H + r_H\left( {\upsilon_0 ,\theta_0 } \right) ) + 2 a r_H ( 2 r_H \cos \theta + r'_H \sin \theta ) \right]}{2 r_H\left( {\upsilon_0 ,\theta_0 } \right) \left[ M- r_H \dot r_H - a r_H \left( r_H \cos \theta - r'_H \sin \theta \right)\right]}.
\label{eq34}
\end{eqnarray}
In the above equation $\kappa$ is the coefficient of surface gravity of a variably rectilinearly accelerating black hole. Therefore, on the event horizon, Eq.~(\ref{eq32}) can be expressed as
\begin{eqnarray}
\left( {\frac{{\partial S}}{{\partial r_* }}} \right)^2 + \frac{2}{r_H\left( {\upsilon_0 ,\theta_0 } \right)} \frac{{\partial S}}{{\partial r_* }}\frac{{\partial S}}{{\partial \upsilon _* }} + \frac{AP_\theta}{r_H\left( {\upsilon_0 ,\theta_0 } \right)} \frac{{\partial S}}{{\partial r_* }} = 0,
\label{eq35}
\end{eqnarray}
where the limit of the coefficient $A$ is
\begin{eqnarray}
\left. A \right|_{r \to r_H } = \tilde A = \left. {{{2\left( {g_{12} - g_{22} \alpha r'_H } \right)} \mathord{\left/
{\vphantom {{2\left( {g_{12} - g_{22} r'_H } \right)} {g_{01} }}} \right.
\kern-\nulldelimiterspace} \left({g_{01} \alpha }\right)}} \right|_{\scriptstyle \upsilon \to \upsilon _0 \hfill \atop
\scriptstyle \theta \to \theta _0 \hfill}.
\label{eq36}
\end{eqnarray}
By simplifying Eq.~(\ref{eq35}), we can get
\begin{eqnarray}
\left( {\frac{{\partial S}}{{\partial r_* }}} \right)^2 + 2\frac{{\partial S}}{{\partial r_* }}\left( \frac {\omega + \omega _0 } {r_H\left( {\upsilon_0 ,\theta_0 } \right)}\right) = 0.
\label{eq37}
\end{eqnarray}
In Eq.~(\ref{eq37}), we order $\omega _0 = {{AP_\theta } \mathord{\left/ {\vphantom {{AP_\theta } 2}} \right. \kern-\nulldelimiterspace} 2}$. At the same time, in the previous work, we proved the relationship ${{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial \upsilon _* }}} \right. \kern-\nulldelimiterspace} {\partial \upsilon _* }} = \omega$, where $\omega$ is the energy of the radiation particles. So, by solving the above equation, we can get
\begin{eqnarray}
{{\partial S} \mathord{\left/
{\vphantom {{\partial S} {\partial r}}} \right.
\kern-\nulldelimiterspace} {\partial r}} = \left[ {1 + \frac {\alpha r_H\left( {\upsilon_0 ,\theta_0 } \right)}{r-r_H}} \right]{{\partial S} \mathord{\left/
{\vphantom {{\partial S} {\partial r_* }}} \right.
\kern-\nulldelimiterspace} {\partial r_* }} = \left[ {1 + \frac {\alpha r_H\left( {\upsilon_0 ,\theta_0 } \right)}{r-r_H}} \right] {\left[ \frac{{\left( {\omega - \omega _0 } \right) \pm \left( {\omega - \omega _0 } \right)}}{r_H\left( {\upsilon_0 ,\theta_0 } \right)} \right]}.
\label{eq38}
\end{eqnarray}
In the expression, it can be found that there is only one singularity, that is $r_H$. After integration, the result can be expressed as
\begin{eqnarray}
S_ \pm = \int {\left[ {1 + \frac {\alpha r_H\left( {\upsilon_0 ,\theta_0 } \right)}{r-r_H}} \right] {\left[ \frac{{\left( {\omega - \omega _0 } \right) \pm \left( {\omega - \omega _0 } \right)}}{r_H\left( {\upsilon_0 ,\theta_0 } \right)} \right]} dr} = {{i\pi \alpha \left[ {\left( {\omega - \omega _0 } \right) \pm \left( {\omega - \omega _0 } \right)} \right]} },
\label{eq39}
\end{eqnarray}
where $ + \left( - \right)$ is a outgoing (ingoing) solution. In order to obtain the tunneling rate, we have to consider both the outgoing and the ingoing solutions. As a result, the tunneling rate of the particle becomes
\begin{eqnarray}
\Gamma = \frac{{\Gamma _{out} }}{{\Gamma _{in} }} = \frac{{\exp \left( { - 2{\mathop{\rm Im}\nolimits} S_ + } \right)}}{{\exp \left( { - 2{\mathop{\rm Im}\nolimits} S_ - } \right)}} = \exp \left[ {{{- 4 \pi \alpha \left( {\omega - \omega _0 } \right)}}} \right].
\label{eq40}
\end{eqnarray}
Using the Boltzmann factor expression, the Hawking temperature of the black hole is given by
\begin{eqnarray}
T_H = \frac{1 }{{4 \pi \alpha}} = \frac {1}{4 \pi}\frac{{2 r_H\left( {\upsilon_0 ,\theta_0 } \right) \left[ M- r_H \dot r_H - a r_H \left( r_H \cos \theta - r'_H \sin \theta \right)\right]}}{{r_H \left[4M + r_H (-2 + 2 \dot r_H + r_H\left( {\upsilon_0 ,\theta_0 } \right) ) + 2 a r_H ( 2 r_H \cos \theta + r'_H \sin \theta ) \right]}}.
\label{eq41}
\end{eqnarray}
In the above expression, while ignoring the angular momentum $a$ and the coefficients $r'_H$, $\dot r_H$, meanwhile setting $r_H=2M$, we can find that the surface gravity of a dynamic Kinnersley black hole reduces to the case of Schwarzschild hole. Therefore, Eq.~(\ref{eq41}) also reduces to the Hawking temperature of a Schwarzschild black hole. Furthermore, it is well-known that the relationship between the temperature and the surface gravity is $T=\kappa /(2 \pi)$, where the $\kappa$ is the surface gravity of the black hole. Combined with this fact, we find from Eq.(\ref{eq41}) that the value of $\alpha$ is equal to $ 1 / ( 2 \kappa)$.
In the calculation of the above process, by using the Hamilton-Jacobi equation, we study the tunneling behavior of spin $1/2$ and $3/2$ particles in a dynamic Kinnersley black hole, and get the Hawking temperature of the black hole. In fact, in previous work, we have proved that the Hamilton-Jacobi equation can describe the movement behavior in curved spacetime for scalar particles with spin $0$, fermions with spin $1/2$ and $3/2$, boson with spin $1$ and graviton \cite{13}. For instance, the Klein-Gordon equation for the scalar particle can be described by
\begin{eqnarray}
\frac{1}{\sqrt{-g}} \frac{\partial}{\partial x^{\mu}} \left(\sqrt{-g} g^{\mu \nu} \frac{\partial}{\partial x^{\mu}} \right) \Psi - \frac{m^2}{\hbar^2} \Psi=0.
\label{eq42}
\end{eqnarray}
In a similar way, after substituting the wave function
\begin{eqnarray}
\Psi = \zeta \exp \left( {\frac{i}{\hbar }S} \right),
\label{eq43}
\end{eqnarray}
into Eq.(\ref{eq42}), and neglecting the terms with $\hbar$, then it is easy for us to obtain the Hamilton-Jacobi equation
\begin{eqnarray}
g^{\mu \nu } \left( {{{\partial S} \mathord{\left/ {\vphantom {{\partial S} {\partial \mu }}} \right. \kern-\nulldelimiterspace} {\partial \mu }}} \right)\left( {{{\partial S} \mathord{\left/
{\vphantom {{\partial S} {\partial \nu }}} \right. \kern-\nulldelimiterspace} {\partial \nu }}} \right) + m^2 = 0.
\label{eq44}
\end{eqnarray}
This means, by using the Hamilton-Jacobi equation, the tunneling rate and the Hawking temperature for scalar particles can also be addressed in the non-stationary black hole. In a word, we confirm from Eq.(\ref{eq21},\ref{eq26},\ref{eq42},\ref{eq44}) that the Hamilton-Jacobi equation is a basic equation, and it can be used to study the tunneling behavior of any particle in curved space-time.
\section{Conclusions}
\label{section4}
\setlength{\parindent}{2em} In this paper, starting from both Dirac equation of spin $1/2$ fermion and Rarita-Schwinger equation of spin $3/2$ fermion, we can obtain a Hamilton-Jacobi equation. Moreover, making use of this equation, we investigate the fermion tunneling rate and the Hawking temperature of a non-stationary Kinnersly black hole. According to our research conclusion, the Hamilton-Jacobi equation can be derived from the kinetic equations of arbitrary spin particles. This shows that the Hamilton-Jacobi equation is a basic semi-classical equation, which can be used to study the quantum tunneling behavior of arbitrary spin particles. Furthermore, through the comparison of the previous work, we can obviously see that, it is very convenient to study tunneling radiation by using the Hamilton-Jacobi equation. Especially for the fermion tunneling, since there is no need to construct complex gamma matrix for tedious calculation, which greatly reduces the workload. It is better for people to carry out the creative research in depth.
\vspace*{3.0ex}
{\bf Acknowledgements}
\vspace*{1.0ex}
This work is supported by the Natural Science Foundation of China (Grant No. 11573022).
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The War College building in Bydgoszcz is a historical building in Bydgoszcz, at 190 Gdańska Street, property of Polish MOD. It is registered on the Kuyavian-Pomeranian Voivodeship Heritage List.
Location
The building stands on the eastern side of Gdanska Street, in the area delimitated by:
Dwernicki street;
Żołnierska street;
Czerkaska street;
Gdańska Street.
This whole area lies within the Forest district in Bydgoszcz.
History
The building was built between 1913 and 1914 and designed by German architects Arnold Hartman and Robert Schlezinger.
The 1913 initial footprint of the project covered an area of approximately 22 hectares within the administrative boundaries of the city.
The estate was planned to be the seat of the German War College (), but the start of World War I changed it all, and the edifice housed during the conflict a German military hospital.
In 1920 the building was taken over by the Polish authorities of the city. After lengthy negotiations and efforts of General Kazimierz Sosnkowski, then Deputy Minister of Military Affairs, the city agreed to hand over the edifice to the Polish Ministry of Military Affairs.
On July 11, 1920, the building housed the High School of Infantry which had moved from Poznań due to the Polish–Soviet War.
On August 1, 1922, the school was converted into an Officer Academy for Non-Commissioned Officers (NCOs) and on August 9, 1928, it has been renamed the NCO Cadet School.
In the first half 1939, the building housed the Naval Cadet School.
From July 1, 1943 to January 17, 1945 the building, seized by Nazi armed forces, has accommodated the Intelligence and Cavalry School (). After the liberation of Bydgoszcz in January 1945, Soviet troops were billeted here.
From 1947 to 2007, the edifice housed the Pomeranian Military District Command, and since 2007 it is the seat of the Inspectorate of Armed Forces Support.
In an adjacent building is open a military museum.
Architecture
The massive building has a E-shaped foot print, following eclecticism style with a clear predominance of neo-Baroque elements.
The building has a prominent avant-corps on its center and wings: all is topped with high Mansard roofs with dormers.
The front portico, with Tuscan styled columns is prominent and topped by a balcony crowned with an elliptical pediment. The facade is divided by a series of decorative cornices and wide pilasters.
Among the noteworthy elements of architectural decoration and stucco are:
stone balusters and helmets;
flaming vases;
pelmets and Bydgoszcz's coats of arms.
The interiors still preserve the original layout: adorned staircases, arcade hall, tiled corridors and walls with panelling and pilasters, and stucco ceilings.
Next to the War College is the former Directorate building (). It is an impressive villa with a portico, terraces, balconies and stylised pediments. The whole area is surrounded by a cast-iron fence, decorated with stone trophies.
The building and its architectural environment has been put on the Kuyavian-Pomeranian Voivodeship Heritage List Nr.601325 Reg.A/30/1-6, on December 28, 2000.
Gallery
See also
Bydgoszcz
Gdanska Street in Bydgoszcz
Downtown district in Bydgoszcz
References
External links
Poslish Armed Forces Logistics Inspectorate
Army Museum of Bydgoszcz
Bibliography
Cultural heritage monuments in Bydgoszcz
Buildings and structures on Gdańska Street, Bydgoszcz
Government buildings in Poland
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GOD UNION
Kriya in Sanskrit means action, deed, effort and includes personal work and spiritual efforts. True spiritual efforts always are efforts of selfless love. Yoga to join, to unite, thus to reunite mankind with God. Kriya Yoga as a combined word thus means to act with love and work in a loving way until all our karma is dissolved and we are reunited with God. ____________________________________________ The world, it tells them, is without permanence or purpose, other than that of expiation; the body is "a nest of disease" and the seat of "desire"; the mind itself is subject to decay, and capricious, easily led away after false pursuits.
PÁGINA INICIAL – PORTUGUÊS
BUSCA POR PALAVRAS
04 – THE LEGEND OF OSIRIS.
THE LEGEND OF OSIRIS.
The main features of the Egyptian religion constant.
The chief features of the Egyptian religion remained unchanged from the Vth and VIth dynasties down to the period when the Egyptians embraced Christianity, after the preaching of St. Mark the Apostle in Alexandria, A.D. 69, so firmly had the early beliefs taken possession of the Egyptian mind; and the Christians in Egypt, or Copts as they are commonly called, the racial descendants of the ancient Egyptians, seem never to have succeeded in divesting themselves of the superstitious and weird mythological conceptions which they inherited from their heathen ancestors. It is not necessary here to repeat the proofs, of this fact which M. Amélineau has brought together,[1] or to adduce evidence from the lives of the saints, martyrs and ascetics; but it is of interest to note in passing that the translators of the New Testament into Coptic rendered the Greek {Greek a!'dhs} by ###, amenti, the name which the ancient Egyptians gave to the abode of man after death,[3] and that the Copts peopled it with beings whose prototypes are found on the ancient monuments.
Persistence of the legend of Osiris and the belief in the resurrection.
The chief gods mentioned in the pyramid texts are identical with those whose names are given on tomb, coffin and papyrus in the latest dynasties; and if the names of the great cosmic gods, such as Ptah and Khnemu, are of rare occurrence, it should be remembered that the gods of the dead must naturally occupy the chief place in this literature which concerns the dead. Furthermore, we find that the doctrine of eternal life and of the resurrection of a glorified or transformed body, based upon the ancient story of the resurrection of Osiris after a cruel death and horrible mutilation, inflicted by the powers of evil, was the same in all periods, and that the legends of the most ancient times were accepted without material alteration or addition in the texts of the later dynasties.
[1. Le Christianisme chez les anciens Coptes, in Revue des Religions, t, xiv., Paris, 1886, PP, 308-45
2. I.e., ###.
3. See St. Matthew xi., 23; Acts ii., 27, etc.]
{p. xlix}
Plutarch's version of the legend.
The story of Osiris is nowhere found in a connected form in Egyptian literature, but everywhere, and in texts of all periods, the life, sufferings, death and resurrection of Osiris are accepted as facts universally admitted. Greek writers have preserved in their works traditions concerning this god, and to Plutarch in particular we owe an important version of the legend as current in his day. It is clear that in some points he errs, but this was excusable in dealing with a series of traditions already some four thousand years old.[1] According to this writer the goddess Rhea [Nut], the wife of Helios [Ra], was beloved by Kronos [Seb]. When Helios discovered the intrigue, he cursed his wife and declared that she should not be delivered of her child in any month or in any year. Then the god Hermes, who also loved Rhea, played at tables with Selene and won from her the seventieth part of each day of the year, which, added together, made five whole days. These he joined to the three hundred and sixty days of which the year then consisted.[2] Upon the first of these five days was Osiris brought forth;[3] and at the moment of his birth a voice was heard to proclaim that the lord of creation was born. In course of time he became king of Egypt, and devoted himself to civilizing his subjects and to teaching them the craft of the husbandman; he established a code of laws and bade men worship the gods. Having made Egypt peaceful and flourishing, he set out to instruct the other nations of the world. During his absence his wife Isis so well ruled the state that Typhon [Set], the evil one, could do no harm to the realm of Osiris. When Osiris came again, Typhon plotted with seventy-two comrades, and with Aso, the queen of Ethiopia, to slay him; and secretly got the measure of the body of Osiris, and made ready a fair chest, which was brought into his banqueting hall when Osiris was present together with other guests. By a ruse Osiris was induced to lie down in the chest, which was immediately closed by Typhon and his fellow conspirators, who conveyed it to the Tanaitic mouth of the Nile.[4] These things happened on the seventeenth day of
[1. For the text see De Iside et Osiride, ed. Didot (Scripta Moralia, t. iii., pp. 429-69), § xii. ff.
2. The days are called in hieroglyphics ###, "the five additional days of the year," e?pago'menai!hme'rai pe'nte; see Brugsch, Thesaurus Inscriptionum Aegytiacarum, Abt. ii. (Kalendarische Inschriften), Leipzig, 1883, pp. 479, 480; Brugsch, Aegyptologie, p. 361 Chabas, Le Cálendrier, Paris (no date), p. 99 ff.
3. Osiris was born on the first day, Horus on the second, Set on the third, Isis on the fourth, and Nephthys on the fifth; the first, third, and fifth of these days were considered unlucky by the Egyptians.
4. The mouths of the Nile are discussed and described by Strabo, XVII., i., 18 (ed. Didot, p. 681) and by Diodorus, I., 33, 7 (ed. Didot, p. 26).]
{p. l}
Plutarch's version.
the month Hathor,[1] when Osiris was in the twenty-eighth year either of his reign or of his age. The first to know of what had happened were the Pans and Satyrs, who dwelt hard by Panopolis; and finally the news was brought to Isis at Coptos, whereupon she cut off a lock of hair[2] and put on mourning apparel. She then set out in deep grief to find her husband's body, and in the course of her wanderings she discovered that Osiris had been united with her sister Nephthys, and that Anubis, the offspring of the union, had been exposed by his mother as soon as born. Isis tracked him by the help of dogs, and bred him up to be her guard and attendant. Soon after she learned that the chest had been carried by the sea to Byblos, where it had been gently laid by the waves among the branches of a tamarisk tree ({Greek e?pei'khj tini`}), which in a very short time had grown to a magnificent size and had enclosed the chest within its trunk. The king of the country, admiring the tree, cut it down and made a pillar for the roof of his house of that part which contained the body of Osiris. When Isis heard of this she went to Byblos, and, gaining admittance to the palace through the report of the royal maidens, she was made nurse to one of the king's sons, Instead of nursing the child in the ordinary way, Isis gave him her finger to suck, and each night she put him into the fire to consume his mortal parts, changing herself the while into a swallow and bemoaning her fate. But the queen once happened to see her son in flames, and cried out, and thus deprived him of immortality. Then Isis told the queen her story and begged for the pillar which supported the roof. This she cut open, and took out the chest and her husband's body,[3] and her lamentations were so terrible that one of the royal children died of fright. She then brought the
[1. In the Calendar in the fourth Sallier papyrus (No. 10,184) this day is marked triply unlucky, and it is said that great lamentation by Isis and Nephthys took place for Un-nefer (Osiris) thereon. See Chabas, Le Calendrier, p. 50. Here we have Plutarch's statement supported by documentary evidence. Some very interesting details concerning the festivals of Osiris in the month Choiak are given by Loret in Recueil de Travaux, t. iii., p. 43 ff; t. iv., p. 21 ff.; and t. v., p. 85 ff. The various mysteries which took place thereat are minutely described.
2 On the cutting of the hair as a sign of mourning, see W. Robertson Smith, The Religion of the Semites, p. 395; and for other beliefs about the hair see Tylor, Primitive Culture, vo1. ii., p. 364, and Fraser, Golden Bough, pp. 193-208.
3 The story continues that Isis then wrapped the pillar in fine linen and anointed it with oil, and restored it to the queen. Plutarch adds that the piece of wood is, to this day, preserved in the temple of Isis, and worshipped by the people of Byblos. Prof. Robertson Smith suggests (Religion of the Semites, p. 175) that the rite of draping and anointing a sacred stump supplies the answer to the unsolved question of the nature of the ritual practices connected with the Ashera. That some sort of drapery belonged to the Ashera is clear from 2 Kings xxiii., 7. See also Tylor, Primitive Culture, vol. ii., p. 150; and Fraser, Golden Bough, vol. i., p. 304 ff.]
{p. li}
chest by ship to Egypt, where she opened it and embraced the body of her husband, weeping bitterly. Then she sought her son Horus in Buto, in Lower Egypt, first having hidden the chest in a secret place. But Typhon, one night hunting by the light of the moon, found the chest, and, recognizing the body, tore it into fourteen pieces, which he scattered up and down throughout the land. When Isis heard of this she took a boat made of papyrus[1]–a plant abhorred by crocodiles–and sailing about she gathered the fragments of Osiris's body.[2] Wherever she found one, there she built a tomb. But now Horus had grown up, and being encouraged to the use of arms by Osiris, who returned from the other world, he went out to do battle with Typhon, the murderer of his father. The fight lasted many days, and Typhon was made captive. But Isis, to whom the care of the prisoner was given, so far from aiding her son Horus, set Typhon at liberty. Horus in his rage tore from her head the royal diadem; but Thoth gave her a helmet in the shape of a cow's head. In two other battles fought between Horus and Typhon, Horus was the victor.[3]
Identity of the deceased with Osiris.
This is the story of the sufferings and death of Osiris as told by Plutarch. Osiris was the god through whose sufferings and death the Egyptian hoped that his body might rise again in some transformed or glorified shape, and to him who had conquered death and had become the king of the other world the Egyptian appealed in prayer for eternal life through his victory and power. In every funeral inscription known to us, from the pyramid texts down to the roughly written prayers upon coffins of the Roman period, what is done for Osiris is done also for the deceased, the state and condition of Osiris are the state and condition of
[1. The ark of "bulrushes" was, no doubt, intended to preserve the child Moses from crocodiles.
2. {Greek Mo'non de` tw^n merw^u tou^ O?si'ridos th`n I?^sin ou`x e`urei^n to` ai?doi^n e`uðu`s ga`r ei's to`n potamo`n r!ifh^nai kai` geu'sasðai to'n te lepidwto`n au`tou^ kai` to`n fa'gron kai` to`n o?ksu'rugxon. k.t.l.}. By the festival celebrated by the Egyptians in honour of the model of the lost member of Osiris, we are probably to understand the public performance of the ceremony of "setting up the Tet in Tattu", which we know took place on the last day of the month Choiak; see Loret, Les Fêtes d'Osiris au mois de Khoiak (Recueil de Travaux, t. iv., p. 32, § 87); Plutarch, De Iside, § xviii.
3. An account of the battle is also given in the IVth Sallier papyrus, wherein we are told that it took place on the 26th day of the month Thoth. Horus and Set fought in the form of two men, but they afterwards changed themselves into two bears, and they passed three days and three nights in this form. Victory inclined now to one side, and now to the other, and the heart of Isis suffered bitterly. When Horus saw that she loosed the fetters which he had laid upon Set, he became like a "raging panther of the south with fury," and she fled before him; but he pursued her, and cut off her head, which Thoth transformed by his words of magical power and set upon her body again in the form of that of a cow. In the calendars the 26th day of Thoth was marked triply deadly. See Chabas, Le Calendrier, p. 28 ff.]
{p. lii}
the deceased; in a word, the deceased is identified with Osiris. If Osiris liveth for ever, the deceased will live for ever; if Osiris dieth, then will the deceased perish.[1]
[1. The origin of Plutarch's story of the death of Osiris, and the Egyptian conception of his nature and attributes, may be gathered from the following very remarkable hymn. (The text is given by Ledrain, Les Monuments Égyptiens de la Bibliothèque Nationale, Paris, 1879, pll. xxi-xxvii. A French translation of it was published, with notes, by Chabas, in Revue Archéologique, Paris, 1857, t. xiv., p. 65 ff.; and an English version was given in Records of the Past, 1st series, vol. iv., p. 99 ff. The stele upon which it is found belongs to the early part of the XVIIIth dynasty, by which is meant the period before the reign of Amenophis IV.; this is proved by the fact that the name of the god Amen has been cut out of it, an act of vandalism which can only have been perpetrated in the fanatical reign of Amenophis IV.):
Hymn to Osiris.
"(1) Hail to thee, Osiris, lord of eternity, king of the gods, thou who hast many names, thou disposer of created things, thou who hast hidden forms in the temples, thou sacred one, thou KA who dwellest in Tattu, thou mighty (2) one in Sekhem, thou lord to whom invocations are made in Anti, thou who art over the offerings in Annu, thou lord who makest inquisition in two-fold right and truth, thou hidden soul, the lord of Qerert, thou who disposest affairs in the city of the White Wall, thou soul of Ra, thou very body of Ra who restest in (3) Suten-henen, thou to whom adorations are made in the region of Nart, thou who makest the soul to rise, thou lord of the Great House in Khemennu, thou mighty of terror in Shas-hetep, thou lord of eternity, thou chief of Abtu, thou who sittest upon thy throne in Ta-tchesert, thou whose name is established in the mouths of (4) men, thou unformed matter of the world, thou god Tum, thou who providest with food the ka's who are with the company of the gods, thou perfect khu among khu's, thou provider of the waters of Nu, thou giver of the wind, thou producer of the wind of the evening from thy nostrils for the satisfaction of thy heart. Thou makest (5) plants to grow at thy desire, thou givest birth to . . . . . . . ; to thee are obedient the stars in the heights, and thou openest the mighty gates. Thou art the lord to whom hymns of praise are sung in the southern heaven, and unto thee are adorations paid in the northern heaven. The never setting stars (6) are before thy face, and they are thy thrones, even as also are those that never rest. An offering cometh to thee by the command of Seb. The company of the gods adoreth thee, the stars of the tuat bow to the earth in adoration before thee, [all] domains pay homage to thee, and the ends of the earth offer entreaty and supplication. When those who are among the holy ones (7) see thee they tremble at thee, and the whole world giveth praise unto thee when it meeteth thy majesty. Thou art a glorious sahu among the sahu's, upon thee hath dignity been conferred, thy dominion is eternal, O thou beautiful Form of the company of the gods; thou gracious one who art beloved by him that (8) seeth thee. Thou settest thy fear in all the world, and through love for thee all proclaim thy name before that of all other gods. Unto thee are offerings made by all mankind, O thou lord to whom commemorations are made, both in heaven and in earth. Many are the shouts of joy that rise to thee at the Uak[*] festival, and cries of delight ascend to thee from the (9) whole world with one voice. Thou art the chief and prince of thy brethren, thou art the prince of the company of the gods, thou stablishest right and truth everywhere, thou placest thy son upon thy throne, thou art the object of praise of thy father Seb, and of the love of thy mother Nut. Thou art exceeding mighty, thou overthrowest those who oppose thee, thou art mighty of hand, and thou slaughterest thine (10) enemy. Thou settest thy fear in thy foe, thou removest his boundaries, thy heart is fixed, and thy feet are watchful. Thou art the heir of Seb and the sovereign of all the earth;
[* This festival took place on the 17th and 18th days of the month Thoth; see Brugsch, Kalendarische Inschriften, p. 235.]
{footnote page liii}
Seb hath seen thy glorious power, and hath commanded thee to direct the (11) universe for ever and ever by thy hand.
"Thou hast made this earth by thy hand, and the waters thereof, and the wind thereof, the herb thereof, all the cattle thereof, all the winged fowl thereof, all the fish thereof, all the creeping things thereof, and all the four-footed beasts thereof. (12) O thou son of Nut, the whole world is gratified when thou ascendest thy father's throne like Ra. Thou shinest in the horizon, thou sendest forth thy light into the darkness, thou makest the darkness light with thy double plume, and thou floodest the world with light like the (13) Disk at break of day. Thy diadem pierceth heaven and becometh a brother unto the stars, O thou form of every god. Thou art gracious in command and in speech, thou art the favoured one of the great company of the gods, and thou art the greatly beloved one of the lesser company of the gods.
"Thy sister put forth her protecting power for thee, she scattered abroad those who were her enemies, (14) she drove back evil hap, she pronounced mighty words of power, she made cunning her tongue, and her words failed not. The glorious Isis was perfect in command and in speech, and she avenged her brother. She sought him without ceasing, (15) she wandered round and round the earth uttering cries of pain, and she rested[*] not until she had found him. She overshadowed him with her feathers, she made wind with her wings, and she uttered cries at the burial of her brother. (16) She raised up the prostrate form of him whose heart was still, she took from. him of his essence, she conceived and brought forth a child,[+] she suckled it in secret (?) and none knew the place thereof; and the arm of the child hath waxed strong in the great house of Seb. (17) The company of the gods rejoiceth and is glad at the coming of Osiris's son Horus, and firm of heart and triumphant is the son of Isis, the heir of Osiris."[++]
[*. Literally, "she alighted not,"; the whole passage here justifies Plutarch's statement (De Iside Osiride, 16) concerning Isis: {Greek Au?th`n de` genome'nhn xelido'na tu~j ki'oni peripi'tesðai kai` ðrhnei~n}.
+. Compare Plutarch, op. cit., §19: {Greek T`hn d' I?'sin th`n teleuth`n e`ks O?si'ridos suggenome'nou tekei~n h?li'to'mhnon kai` a?sðenh~ toi~s ka'twðen gui'ois to`n A?rpokra'thn}.
++. The remainder of the hymn refers to Horus.]]
{p. liii}
Osiris invested with the attributes of Ra.
Later in the XVIIIth, or early in the XIXth dynasty, we find Osiris called "the king of eternity, the lord of everlastingness, who traverseth millions of years in the duration of his life, the firstborn son of the womb of Nut, begotten of Seb, the prince of gods and men, the god of gods, the king of kings, the lord of lords, the prince of princes, the governor of the world, from the womb of Nut, whose existence is for everlasting,[1] Unnefer of many forms and of many attributes, Tmu in Annu, the lord of Akert,[2] the only one, the lord of the land on each side of the celestial Nile."[3]
In the XXVIth dynasty and later there grew up a class of literature
[1. For the text see the papyrus of Ani, pl. ii., and pl. xxxvi., 1. 2.
2. I.e., the underworld.
3. neb atebui; see Ani, pl. xix., 1. 9.]
{p. liv}
Osiris the god of the resurrection.
represented by such works as "The Book of Respirations,"[1] "The Lamentations of Isis and Nephthys,"[2] "The Festival Songs of Isis and Nephthys,"[3] "The Litanies of Seker,"[4] and the like, the hymns and prayers of which are addressed to Osiris rather as the god of the dead and type of the resurrection[5] than as the successor of the great cosmic god Tmu-Ra. He is called "the soul that liveth again,"[6] "the being who becometh a child again," "the firstborn son of unformed matter, the lord of multitudes of aspects and forms, the lord of time and bestower of years, the lord of life for all eternity."[7] He is the "giver of life from the beginning;"[8] "life springs up to us from his destruction,"[9] and the germ which proceeds from him engenders life in both the dead and the living.[10]
[1. ###. The text of this work, transcribed into hieroglyphics, was published, with a Latin translation, by Brugsch, under the title, Sai an Sinsin sive Aber Metempsychosis veterum Aegyptiorum, Berlin, 1851; and an English translation of the same work, but made from a Paris MS., was given by p. J. de Horrack in Records of the Past, 1st series, vol., iv., p. 121 ff. See also Birch, Facsimiles of Two Papyri, London, 1863, p. 3; Devéria, Catalogue des MSS. Égyptiens, Paris, 1874, pp. 130 ff., where several copies of this work are described.
2. The hieratic text of this work is published with a French translation by p. J. de Horrack, Les Lamentations d'Isis et de Nephthys, Paris, 1886.
3. A hieroglyphic transcript of these works, with an English translation, was given in Archælogia, vol. iii., London, 1891.
4. What Devéria says with reference to the Book of Respirations applies to the whole class: "Toutefois, on remarque dans cet écrit une tendance à la doctrine de la résurrection du corps plus marquée que dans les compositions antérieures" (Catalogue, p. 13).
5. ###. Festival Songs, iv., 33.
6. ###. Ibid., viii., 21, ix., 8.
7. Litanies of Seker, col. xviii.
8. ###. Festival Songs, vi., 1.
9. ###. Ibid., iii., 18.
10. ###. Ibid., ix., 26.]
{p. lv}
Next: The Doctrine Of Eternal Life.
BEING PURE PILLARS OF LIGHT
Dion Fortune (1890 -… em THE MYSTICAL QABALAH by Dion…
WHO IS GOD? | Pukira… em NOTE #160 – Verily, ther…
HOW TO AVOID BOREDOM… em NOTE #160 – Verily, ther…
NOTAS DO KITAB-I-AQD… em NOTAS DO KITAB-I-AQDAS – …
NOTAS DO KITAB-I-AQD… em O KITAB-I-AQDAS – T17
BEAR SUTRA
KITAB-I-AQDAS
NOTAS DO KITAB-I-AQDAS
O TABLET DE ISHRAQAT
QABALAH
SACRED BOOKS
A ÁRVORE DA VIDA
A BUDDHIST BIBLE
A FORMA DE DEUS
AMITABHA, A STORY OF BUDDHIST THEOLOGY
BOOK OF CREATION
BUDDHA – AVOIDING THE TEN EVILS
EGYPTIAN IDEAS OF THE FUTURE LIFE
ERA OF PEACE
FIVE TIBETAN RITES, THE EYE OF REVELATION
GOD'S FORM
I N T R O D U C T I O N T O Y A N T R A
O CAMINHO DA VIRTUDE DE BUDA
O ESPLENDOR DE DEUS
O KITAB-I-AQDAS
O MAHÂVAGGA.
O MANTRA GAYATRI
O PODER DOS YANTRAS
SACRED BOOKS OF THE EAST: DHAMMAPADA AND SUTTA NIPATA
SELECTIONS FROM THE WRITINGS OF THE BAB.
SMOKEY THE BEAR SUTRA
SPIRITUAL TREASURES
SUTRA OF TRANSCENDENTAL WISDOM
THE BOOK OF FILIAL DUTY
THE BOOK OF THE DEAD
00 – TITLE PAGE
01 – PREFACE.
02 – CONTENTS.
03 – INTRODUCTION.
05 – THE DOCTRINE OF ETERNAL LIFE.
06 – THE EGYPTIANS' IDEAS OF GOD.
07 – THE LEGEND OF RA AND ISIS.
08 – THE ABODE OF THE BLESSED.
09 – THE GODS OF THE BOOK OF THE DEAD.
10 – THE PRINCIPAL GEOGRAPHICAL AND MYTHOLOGICAL
11 – FUNERAL CEREMONIES.
12 – THE PAPYRUS OF ANI.
13 – PLATE I.
14 – PLATE II.
15 – PLATE III.
16 – PLATE IV.
17 – PLATES V. AND VI.
18 – PLATES VII.-X.
19 – PLATES XI. AND XII.
20 – PLATE XIII.
21 – PLATE XIV.
22 – PLATE XV.
23 – PLATE XVI.
24 – PLATE XVII.
25 – PLATE XVIII.
26 – PLATE XIX.
27 – PLATE XX.
28 – PLATE XXI.
29 – PLATE XXII.
30 – PLATE XXIII. AND PLATE XXIV.
31 – PLATE XXV.
32 – PLATE XXVI.
33 – PLATE XXVII.
34 – PLATE XXVIII.
35 – PLATES XXIX. AND XXX.
36 – PLATES XXXI. AND XXXII.
37 – PLATE XXXII.
38 – PLATE XXXIII.
39 – PLATES XXXIII AND XXXIV.
40 – PLATES XXXV. AND XXXVI.
41 – PLATE XXXVII.
THE BUDDHA'S WAY OF VIRTUE
THE BURDEN OF ISIS
THE KITAB-I-AQDAS
THE MAHÂVAGGA.
THE MERKABA FORMATION – YOU SHALL BECOME PURE PILLARS OF LIGHT
THE MYSTICAL QABALAH
THE PATH OF LIGHT
THE SPLENDOUR OF GOD
TRANSCENDENTAL WISDOM
VOCÊ É O CAPITÃO DA SUA ALMA
WELCOME TO ERA OF PEACE
YOU ARE THE CAPTAIN OF YOUR SOUL
כיתב-אני-אקדס
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{{ Ficha de título nobiliario
|imagen=Corona de conde.svg
|texto imagen=Corona condal
|primer titular=Juan Antonio Gamazo y Abarca
|rey=Alfonso XIII de España
|fecha=30 de agosto de 1909
|actual titular=Germán Gamazo y Hohenlohe
|}}
El condado de Gamazo es un título nobiliario español creado por el
rey Alfonso XIII en favor de Juan Antonio Gamazo y Abarca, político y empresario, mediante real decreto del 22 de junio de 1909 y despacho expedido el 30 de agosto del mismo año, para hacer memoria de los servicios prestados por su padre Germán de Gamazo y Calvo, ministro de Fomento, Hacienda y Ultramar y presidente de la Academia de Jurisprudencia.
Condes de Gamazo
Historia de los condes de Gamazo
Juan Antonio Gamazo y Abarca (Madrid, 1883-10 de julio de 1968), I conde de Gamazo, III marqués de Soto de Aller, III vizconde de Miravalles, diputado a Cortes (1909-1923), subsecretario del Ministerio de Gracia y Justicia (1919), gobernador del Banco de España (1930), miembro fundador de Acción Española y de Renovación Española (partido por el que fue diputado en las elecciones de 1936).
Casó con Marta Arnús y Gayón, sobrina del marqués de Comillas. El 17 de enero de 1970, previa orden del 7 de octubre de 1969 para que se expida la correspondiente carta de sucesión (BOE del día 16), le sucedió su hijo:
Juan Antonio Gamazo y Arnús (1920-1998), II conde de Gamazo, IV vizconde de Miravalles.
Sin descendientes. El 12 de mayo del 2000, previa orden del 12 de abril del mismo año para que se expida la correspondiente carta de sucesión (BOE del día 28), le sucedió un hijo de su hermano Claudio Gamazo y Arnús, IV marqués de Soto de Aller —casado con María Francisca Hohenlohe-Langenburg e Ytube, III marquesa de Belvís de las Navas— y por tanto su sobrino:
Germán Manuel Gamazo y Hohenlohe-Langenburg (n. 1951), III conde de Gamazo''', V marqués de Soto de Aller, V vizconde de Miravalles.
Casó con Isabelle Sourdeau Couadau.
Referencias
Gamazo
España en 1909
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Jeffrey William Sarwer (Kingston, Ontario, 1978. május 14. –) kanadai-finn kettős állampolgár, egykori csodagyerek, sakkzseni, akit karizmatikus személyisége és sakktehetsége tett ismert médiaszemélyiséggé. A sakk-karrierje és a családja szokatlan életmódja sok cikk és TV-műsor témájául szolgált.
Sarwer támadó játékstílusát gyakran hasonlították Bobby Fischeréhez, és egy másik fiatal játékos, Joshua Waitzkin ellen játszott mérkőzése szolgált A bajnok (Searching for Bobby Fischer) című film alapjául.
1986-ban Sarwer megnyerte a 10 év alatti ifjúsági sakkvilágbajnokságot Puerto Ricóban, ahol Kanadát képviselte.
Amikor Sarwer nyolcéves volt, sokan azt hitték, ő az egyik legerősebb zseni a játék történetében. Allen Kaufman, az Amerikai Sakk Alapítvány elnöke azt mondta, "Jeff 9 évesen erősebb, mint Bobby volt 11 évesen." Bruce Pandolfini szerint, "A sok ezer gyerek közül, akiket tanítottam, Jeff a legfantasztikusabb fiatal játékos, akit valaha láttam."
Korai karrier
Anyja finn, apja kanadai. Sarwer négy évesen tanulta meg a sakk szabályait hatéves nővérétől, Juliától, és hatévesen kezdett el játszani a Manhattan Chess Club nevű klubban, amely az egyik legnagyobb presztízsű sakk-klub volt a világon abban az időben. Bruce Pandolfini, a klub menedzsere le volt nyűgözve az ő és a nővére teljesítményétől, ezért mindkettőjüknek életre szóló ingyenes tagságot biztosított, amelyet általában csak a nagymesterek élvezhettek.
Sarwer hétéves korától hozzászokott, hogy minden Canada Day alkalmával nagy tömegeket szórakoztasson egy szimultán sakkparti keretében, amikor 40 ember ellen játszott egyszerre a Parliament Hillen, Ottawában. Ahhoz is hozzászokott, hogy villám sakkmérkőzéseket játsszon a Washington Square Parkban, New York Cityben, ahol nagy számú néző gyűlt össze, hogy élvezze a játékát.
Média
Hétévesen Sarwer játék iránti szenvedélye felkeltette Edmar Mednis nagymester figyelmét, aki meghívta őt, hogy elemezze az 1986-os világbajnokság meccsét Kaszparov és Karpov között a PBS-en. Sarwer és a nővére, Julia (aki szintén világbajnok volt a 10 év alatti lányok között) folytatták ezt a visszavágó találkozón, 1987-ben is. Ezek után Jeff és Julia ismertté váltak a média köreiben, számos talk show-ban és egy dokumentumfilmben is szerepeltek.
Az olyan magazinok, mint a GQ és a Sports Illustrated cikkeket írtak Sarwerről és a családjáról, gyakran kiemelve a bizarr életstílusukat, és megkérdőjelezve az apai gondozás alatti biztonságát és sakk-karrierjét.
A Vanity Fair-cikk
Jeff apja nem engedte neki, hogy folytassa a sakk-karrierjét, amikor bebizonyosodott, hogy nem tudna teljes kontrollt gyakorolni az élete felett. Elköltöztette a családját New York Cityből, és vitás helyzetbe került az ontariói Gyermekgondozó Társasággal (The Children's Aid Society of Ontario). Egy cikk, amely a Vanity Fair magazinban jelent meg John Colapinto tollából, rávilágított a Jeff és Julia által elszenvedett gyermekbántalmazásra, és arra indította a C.A.S.-t, hogy védő felügyelet alá vegyék őket.
Jeff és Julia elszöktek a C.A.S.-től, vissza az apjukhoz, és elrejtőztek a hatóságok elől, nehogy ismét felügyelet alá kerüljenek. A Sarwer család számos országban élt, és hozzászokott az anonim életmódhoz.
A bajnok – Bobby Fischer nyomában (Searching For Bobby Fischer)
1993-ban megjelent A bajnok – Bobby Fischer nyomában című film és Jeff Sarwer karaktere "Jonathan Poe" néven szerepelt benne. A film végső játszmájában Poe elutasítja a döntetlen ajánlatot, és végül veszít. A valóságban Sarwer elutasította a döntetlent Josh Waitzkintől, de végül a játék döntetlennel ért véget (egyéb okok miatt), néhány lépéssel később. A torna holtversenyt eldöntő szabályai szerint Waitzkin több kihívást jelentő ellenfél ellen játszott az egész verseny során, ezért ő kapta meg az első helyet, de mindketten amerikai általános iskolai bajnokok lettek. Mikor a találkozót játszották, Sarwer hétéves volt, Waitzkin pedig kilenc.
Sarwer vs. Waitzkin, 1986 (eredeti, angol nyelvű lépések) 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.f4 0-0 6.Nf3 Nbd7 7.e5 Ne8 8.Bd3 c5 9.dxc5 Nxc5 10.Bc2 a5 11.0-0 b6 12.Be3 Bb7 13.Qd4 dxe5 14.Nxe5 Qxd4 15.Bxd4 Rd8 16.Bxc5 bxc5 17.Na4 Bxe5 18.fxe5 Rd2 19.Rf2 Rxf2 20.Kxf2 f6 21.e6 Nd6 22.Nxc5 Rc8 23.Nxb7 Nxb7 24.b3 Nc5 25.Re1 Rc6 26.Be4 Ra6 27.Bc2 Rxe6 28.Rxe6 Nxe6 29.Ke3 Kf8 30.Ke4 Ke8 31.g3 Kd7 32.Kd5 f5 33.a3 h6 34.b4 axb4 35.axb4 Nc7+ 36.Kc5 e5 37.Ba4+ Kc8 38.Bc6 e4 39.b5 e3 40.Bf3 Ne6+ 41.Kd5 Ng5 42.Be2 Kc7 43.Ke5 Ne4 44.Kd4 Kd6 45.Kxe3 Kc5 46.g4 Nd6 47.Kf4 g5+ 48.Ke5 fxg4 49.Kf6 g3 50.hxg3 Ne4+ 51.Kg6 Nxg3 52.Bd3 Nh1 53.Kxh6 g4 54.Kg5 g3 55.Be4 Nf2 56.Bd5 Nd1 57.Kf4 Nc3 58.Bc6 Ne2+ 59.Kf3 Nd4+ 60.Kxg3 Nxc6 61.bxc6 Kxc6 62.Kf3 Kc5 63.Ke3 Kxc4 ½–½
Ismételt felbukkanása
Miután nagyon fiatalon eltűnt, sokan úgy gondolták, hogy Sarwer nem fog többet sakkozni. 2007 szeptemberében azonban ismét felbukkant a sakkszíntéren, edzés nélkül, és benevezett a harmincperces félvillámtornára Malbork kastélyában, Lengyelországban. Mint utólag elárulta, egy hirtelen ötlet vezérelte, mikor elindult a versenyen.
Harmadik helyen végzett 7 ponttal a 9-ből, a 86 játékost számláló csoportban, ahol négy nagymester is versenyzett. Mivel nem volt aktív sakkminősítése, ideiglenes Élő-minősítést kapott 2250 FIDE-ponttal, bár úgy tűnt, hogy ezen a szinten felül teljesített. 2010 januárjában Sarwer hosszú interjút adott a Chess Life Online oldalnak, ahol a tornán szerzett tapasztalatát részletezte, és az európai életéről beszélt. 2010 augusztusában Sarwer megjelent a Sunday Times Magazine hasábjain is, ahol az apja módszereiről beszélt, a saját sakk-karrierjéről és a nyilvánosság előtti újabb felbukkanásáról. Sarwer azt mondta, ha úgy döntene, hogy a sakkot választja prioritásnak, azt csak azért tenné, hogy nagymester lehessen. "Ehhez viszont legalább két év kemény tanulásra és gyakorlásra lenne szükségem" - mondta. "Különösen, ami a nyitásokra való felkészülést illeti".
2015 nyarán Sarwer részt vett a VI. Shakkinet tornán Finnországban, ahol 5 pontot szerzett a 9-ből, ami elegendő volt a nemzetközi mesteri normához.
Póker
Jeff Sarwer bebizonyította, hogy egy sakkmester kiváló pókerjátékos is lehet. A pókervilág akkor figyelt fel rá igazán, amikor 2009-ben harmadik helyen végzett a European Masters of Poker (Európai Pókermesterek) tornán, amelyet Tallinnban rendeztek meg. Ezek után számos más pókerversenyen is részt vett, és a magas pénzdíjak mellett egyéb elismeréseket is bezsebelt. A legmagasabb helyezést 2010-ben érte el Berlinben, ahol az EPT bajnokságon megszerezte a második helyet.
Bár ezek után Sarwer kevésbé ért el jó eredményeket, úgy tűnik, hogy a sakkban edzett taktikai érzéke és türelme végül ismét győzelemre segíti majd őt a jövő pókertornáin.
Rádióinterjú
Sarwer szerepelt a BBC World Service The Interview című programjában 2010. december 19-én, ahol őszintén beszámolt az életéről, a gyerekkori tapasztalatairól és a bántalmazó apjával való kapcsolatáról. Beszélt a sikeres éveiről az USA-ban, a húszas éveiben és a jelenlegi sikereiről az európai pókerkörökben, a harmincas éveiben.
Jegyzetek
1978-ban született személyek
Élő személyek
Kanadai sakkozók
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Q: Bounded function ${f_n}$ is a sequence of continuous functions on $\Bbb R$, and $f_n \rightarrow f$ uniformly on every finite interval $[a,b]$. If each $f_n$ is bounded, is it true that $f$ must be bounded?
A: Here is a counterexample:
$f_n(x) = |x|$ if $|x| < n$
$f_n(x) = n$ otherwise
A: Answer is NO. For example, Let $f(x)=x$, $f_n(x)=x$ if $-n\leq x\leq n$, $f_n(x)=-n$ if $ x\leq -n$, and $f_n(x)=n$ if $ x\geq n$.
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ACC AD's Vote to Keep Eight-Game Schedule Plus Play Power Five or Notre Dame
By Kevin Kelley - May 12, 2014
ACC commissioner John Swofford in Oct. 2013. (Sam Sharpe-USA TODAY Sports)
ACC commissioner John Swofford announced today that the conference athletic directors have voted to keep an eight-game football schedule. In addition, the ACC will vote to add a strength of schedule requirement similar to the SEC.
The requirement, if passed, stipulates that each ACC team must play a non-conference game against a team from the power five conferences (Big 12, Big Ten, Pac-12, SEC) or Notre Dame beginning in 2017.
The vote is reportedly set to take place on Thursday and is said to merely be a "formality." The SEC adopted a similar football scheduling format last month.
Four ACC teams meet that requirement already due to annual in-state rivalry games. Clemson plays South Carolina, Florida State plays Florida, Georgia Tech plays Georgia, and Louisville plays Kentucky.
Five teams will also meet the strength of schedule requirement each year due to the conference's partnership with Notre Dame. But in some seasons, Clemson, Florida State, Georgia Tech, and Louisville will have Notre Dame plus their annual SEC rival on their schedule.
That is likely one of the main factors in keeping an eight-game conference schedule. With 10 games set in any given year, a few teams would have little flexibility in scheduling the remaining two games.
Also, a nine-game schedule is unbalanced because teams have only four conference home games every other season.
On the other hand, the Big 12 and Pac-12 already have a nine-game schedule and the Big Ten will move in that direction in 2016. There doesn't seem to be much griping from them about nine-games, and the Pac-12 coaches have even resorted to slamming the SEC for its chosen format.
A few other notes on the ACC scheduling format:
The ACC's new scheduling requirements will not forbid teams from playing games against the FCS.
It hasn't been determined if games against BYU, Army or Navy will fulfill the power five requirement (Navy likely won't because they join the AAC in 2015).
Games against Notre Dame scheduled as part of the ACC partnership will fulfill the power five requirement.
Commissioner Swofford said the ACC will keep the existing divisions and permanent crossover rivalries.
va. born says:
good move…..
Actually, four ACC teams already meet the requirement. Georgia Tech plays Georgia every year in addition to the other three annual SEC-ACC pairings.
Kevin Kelley says:
Right, how could I forget?
Navy will be in the AAC by then, so they wouldn't fulfill the requirement
Notre Dame WILL NOT be in the ACC.
That's correct but they play five ACC teams per year (actually 4 in 2014, 6 in 2015, then 5 thereafter).
Ricky W says:
SEC leads the way and the ACC follows. Both the ACC and SEC's decision to remain at an 8-game conference schedule appears to only impact lower tier programs in the two conferences (NC St, WF, Vandy, Miss St, as well as Misso and Missi).
ACC:
2014 – WF and NC St are the only two ACC programs to not have scheduled a P5 program for OOC play.
2015 – NC St has yet to schedule a P5 to OOC, but still has one TBA.
2016 – both NC St and BC do not have P5 on their OOC schedules, but each still has a TBA.
2017 – Miami FL has yet to schedule P5 to OOC, but still has one TBA.
2014 – Missi, TAM, Vandy and Miss St have not scheduled a P5 program for OOC play.
2015 – Missi has not scheduled a P5 program for OOC play. Same for Misso, Vandy, and Miss St but the three programs still have a TBA.
2016 – Much of the SEC OOC schedule is yet to be announced. At this time, Auburn, Alabama, and Misso have no OOC games scheduled. Both Missi and Miss St do not have P5 on OOC schedule, but each has a TBA.
2017 – Much of the SEC OOC schedule is yet to be announced. At this time, Auburn, and Alabama have no OOC games scheduled. Both Vandy and Miss St do not have P5 on OOC schedule, but each has a TBA.
Unless something changes, it appears the overwhelmingly majority of SEC programs will continue to schedule THREE OOC games with G5 or FCS programs.
Whereas, after 2014, future schedules show half of ACC programs scheduled OOC games with THREE G5 or FCS programs, the other half opting to play TWO OOC games with P5 programs. I suspect you will see the entire ACC move towards scheduling TWO OOC games with P5 programs every season.
It will be interesting to watch how the SEC's effectively non-decision to remain at the status quo pans out.The Playoff Committee will definitely take this into consideration.
P5 = Power Conference
G5 = Group of Five Conference
It will be interesting to see if the strength of the SEC as a whole will be enough to counteract the cupcake non-conference schedules. In recent years most FBS teams must go undefeated to get a shot at the title. The exception has been teams coming out of the SEC. There is a tremendous amount of respect for those that can navigate through the SEC gauntlet with only a few blemishes. Schools in other conferences have been afforded no such luxuries.
With the introduction of the College Football Playoff, non-conference schedules will probably be a factor when deciding which 1-loss (or perhaps 2-loss) teams are more deserving. That being said, a typical SEC schedule consists of so many quality teams to the point that it doesn't really matter who they play out of conference. The other P5 teams are in a position where they need to beef up their schedule in order to catch up. The SEC will stick with the status quo as long as they keep getting a shot at the title. If after a few years their strength of schedule keeps them out of the playoffs (highly unlikely) then we could see a 9 game conference schedule or perhaps a limit on lower tier competition. Until then, why would they make the path to the championship any more difficult than it already is?
"Why change the ingredients of success?"
Compare to the three conferences with 9-game conferences schedules (including B1G in 2016),
Future OOC schedules NOT including at least one P5 program:
B12:
2014 – Baylor*.
2015 – Baylor*, Ok St, Kan St.
2016 – Baylor*, Kansas. (Kan St and WV still have a TBA).
2017 – (Kan St, WV and Kansas still has a TBA).
2018 – (OK St. Kan St and Tex Tech still have a TBA).
2019 – Baylor*. (Ok St, WV, Kan St, Tex Tech and Kansas still have a TBA).
*Baylor – annual game with SMU injures the Bears OOC, unless Baylor adds a P5 program to their OOC schedules. None are scheduled through 2016 or in 2019. Baylor's only P5 OOC games through 2019 is a home and home with Duke in 2017-18.
P12:
2014 – Colo$, Arizona, Ore St.
2015 – Colo$, Wash. (Arizona still has a TBA).
2016 – Utah#, Wash St. (Arizona still has a TBA).
2017 – Utah#, Wash St, Colo$. (Arizona and Cal still have a TBA).
2018 – Arizona. (Arizona St. Cal, Wash, Utah#, Oregon St and Wash St still have a TBA).
2019 – (Arizona St, Utah#, Cal, Wash St, Arizona and Oregon St still have a TBA).
$Colorado – annual rivalry game with Colo State will injure Buffalo OOC. The Buffs however are visting Michigan in 2016 and home and home with Nebraska in 2019-19 and 2023-24 and home and home with Minnesota in 2021-22.
#Utah – annual rivalry game with BYU injures Ute OOC. Utah has home and home scheduled with Michigan in 2014-15.
B1G:
2014 – %
2016 – Maryland, Purdue.
2017 – Illinois. (Wisconsin and Indiana still have a TBA).
2018 – Illinois. (Wisconsin, Mich St, Minn and Indiana still have a TBA).
2019 – (Mich St, Minn, Purdue, Illinois and Indiana still have a TBA).
2020 – (Nebraska, Minn, Illinois and Indiana still have a TBA).
2021 – (Penn St and Indiana still have a TBA).
%note: 9-game conf schedule takes effect in 2016. Thus NW and Minnesota Will have to cancel OOC games currently on 2016 schedules.
The B1G will play 8-game conf schedules in 2014 & 2015 and B1G programs will play FOUR OOC games each. Only FOUR B1G programs are playing TWO OOC games each against P5 programs in both 2014 and 2015, whereas the other TEN B1G programs will each play THREE OOC games against G5 or FCS programs. The Playoff Committee will definitely include this in their evaluations for 2014 and 2015.
bradleysmith1212 says:
BYU does not hurt Utah's out of conference schedules. Northern Colorado, Weber St., Idaho St., Southern Utah, and San Jose St. hurt their out of conference schedules.
JoeShmoetheRagman says:
Wait what? Why would Army potentially count as one of the required group of 5 games and Navy wouldn't just b/c Navy is joining the AAC? Navy has been far better than Army as of late winning 12 straight and 15 of the last 17. vs Army. BYU probably wont even get the Notre Dame like exception so there is just no way Army would and Navy wouldnt.
Reporters mentioned Army and Navy with BYU and Notre Dame because they are all independents right now. There's no way Army and Navy will count as a Power Five game.
BYU should absolutely get the P5 inclusion. They schedule more and compete better against P5 schools than any other Group of Five school…and than many mediocre P5 schools. They have a 30,000+ student body and average around 64K in home game attendance (this would be #3 in the Big 12, #5 in the PAC 12, #6 in the ACC, and #8 in the Big Ten).
Regardless, any ACC team that schedules BYU knows that it helps their strength of schedule. The real issue is whether the risk of losing to BYU, even at home, will scare off ACC teams from scheduling the Cougars.
As an independent, BYU is actually well-situated to fill in some late season scheduling holes created by Notre-ACC and ACC-SEC matchups. PAC 12 have already seen this value and have started to schedule BYU in November.
Travis B says:
The best thing for the B10, B12, and PAC to do now is make a scheduling agreement of 9 conference games + 1 mandatory game against Power 5 teams.
Basically just saying we can do the same thing you are doing, with the extra conference game. No problem whatsoever.
Absolutely! The only way to have a beauty contest (aka, CFP selection process) is if the contestants actually compete with each other.
As is, teams are saying – my conference championship and my undefeated home record against Group of Five and FCS opponents is better than yours! It's ridiculous.
Play the games on the field. Why in the world don't the Big 10, Big 12, and PAC 12 just schedule each other out of conference? THAT would help to actually determine who deserves the CFP selections and who the true championship is!
ACC Atlantic fan: Hey guys! Nice of you to come to town and play us. What conference are you from?
ACC Coastal fan: We are in the ACC Conference.
ACC Atlantic fan: Really? We are in the ACC Conference too. That's funny, I've been going here for 6 years and have yet to see you guys here.
You can take the above story and replace it with SEC East and SEC West too!
This article should actually say Power 5.
Group of 5 means the other 5 conferences that are not power conferences.
Power 5 = ACC/B10/B12/PAC/SEC
Group of 5 = AAC/MWC/MAC/CUSA/SBELT
Just throwing it out there, this article is all over and I think they confused a few people with their wording on this matter.
bwburke94 says:
Seriously, how many times do we have to clear this up?
It's actually all over the place wherever you look. I was under the impression that "Group of Five" and "Power Five" were the same thing. Hopefully this will be fleshed out soon.
"Power 5" = 1-A
Other 1-A's >>>>> 1-AA
current 1-AA's >>>>>> 1-AAA
"Group of Five" is commonly used by major news reporting sites to refer to the American, Mountain West, MAC, Conference USA, and Sun Belt conference. The highest rated champion from among these conferences will receive an invitation to play in one of the CFP's "access" bowls. I think it's pretty standard. Here are links to articles using this "Group of Five" reference from: ESPN, CBSSports, Sports Illustrated, USAToday, and Sporting News…
http://espn.go.com/blog/ncfnation/post/_/id/94936/college-football-playoff-qa
http://www.cbssports.com/collegefootball/writer/jeremy-fowler/24547508/in-playoff-era-group-of-five-sees-big-payouts-and-big-expenses
http://sportsillustrated.cnn.com/college-football/news/20140310/college-football-playoff-mid-majors/
http://www.usatoday.com/story/sports/ncaaf/2014/05/09/college-football-playoff-cinderellas-power-conferences/8917705/
http://www.sportingnews.com/ncaa-football/story/2014-04-29/college-football-playoff-conference-games-sec-acc-big-ten-12-pac-committee-league-selection
Thanks. I can show you several examples of major news sites using Group of Five for the BCS, but most are from last year. Looks like they changed to power five along the way.
Yeah, it wasn't your fault Kevin. It was how the article was worded. I just see it confusing so many people, especially ones who don't follow CFB as closely…
The one thing they missed, in my opinion, was switching the VT & BC crossover games with the UVA & Louisville. VT & Louisville seem like a more natural paring and so does UVA & BC. UVA (#23) and BC (#31) are closer in academic rankings, and so are VT (#69) and Louisville (#161). The switched pairs are closer in distance, which I think helps rivalries. Not a lot of games between BC and UVA (5), but there are only 2 games between UVA and Louisville. VT and Louisville have played 7 times, not a lot, but I think a better long term fit. VT and BC do have 22 games, but I know some VT they like the switch. I have even seen on some forums that BC guys would like the switch.
jst5 says:
The ACC staying with 8 games makes perfect sense. 4 teams already play their P5 rival each year. And 5 teams play Notre Dame which (basically acts as a 9th conference game). Clemson and Georgia Tech who both play Notre Dame in 2015. Their schedules would be 9 Conf games their SEC rival and Notre Dame. That would leave them with 1 OOC game to schedule.
The pro 9 game arguments are that you dont play everyone in your conference enough with 8 games and therefore you need 9 to shorten the time between playing every team. This is the best argument for 9 games IMO. But this problem has more to do with going to 14 team conferences. As the conferences get bigger the regularity at which all schools play each other gets smaller. Also having every team pay 4 home and 4 away each year is more fair than 4 – 5 for some and 5-4 for others. The 9th game vs Notre Dame or another P5 will not affect your conference standings.
IMO the B1G will follow the lead of the ACC and SEC and never actually go to 9 conference games. And instead they will require 1 P5 OOC game per year (just a prediction). This will help push to keep rivalries such as Iowa – Iowa St. And help keep Michigan Michigan St. and Purdue to regularly play Notre Dame.
The only conference that should play 9 conference games is the Big 12. As long as they maintain 10 schools and a true round robin format they should keep the 9 game schedule. But if and when they expand I think that they should go back to 8 games. I also think that all P5 schools should play the 8 conf and 1 p5 OOC model. And that they should add BYU to the list of the acceptable P5 games. BYU can help fill a spot when the ACC or Pac 12 are playing Notre Dame (as they are in playing Cal this year). Also the fact that BYU is a better program than at least 1/3 of P5 programs makes them viable.
That noise you hear, are the Athletic Director's phonelines at Kansas & University of Utah blowing up!
If you get the same credit for playing Texas or USC in a 100k seat stadium as you do playing Utah or Kansas in a 30k+ stadium, why not just pick the conference doormats?
I agree and disagree.
This whole 8+1 model isn't anything special. Teams should already be following this requirement. Shame on the ones who don't. I think CFB would be better off if everyone had a 9+1 or 8+2 format. Teams should challenge themselves more.
ONLY 9 games required against P5 schools with a 12 game schedule? Should be at least 10 games for everybody. In my opinion, 9 just isn't anything special when you have room for 12 games on your schedule. Do you really need 3 games against schools from lower conferences or from the FCS?
My point does apply to all teams in P5 conferences too, not just the ACC and SEC.
Fair enough on the B10 prediction. But, just so you know, they already have schedules made all the way out until 2019.
I agree that schools shouldn't shy away from playing other P5 schools. Take Clemson and FSU they will play 8 conf + SEC rival every year + Notre Dame every 3 years or so. So they have 9 P5 every year and 10 in a lot of others. And FSU has future home/home series with USF and Boise St. and playing those games are a bigger challenge then scheduling P5 schools like Indiana Kansas Colorado etc. So you can still play quality non P5 teams in your remaining games.
Most P5 programs want to schedule 7 homes games each year. And the top programs are doing this. This becomes the main reason why the P5 needs the G5 and the FCS. Without those games everyone would be forced to play 6-6. And teams that play annual neutral site games like Oklahoma – Texas and Florida – Georgia would play a 5-6-1 or a 6-5-1 home-away-neutral schedule. And that just wont happen.
Also the lower tier P5 programs Indiana, Kansas, Wake Forest, Ole Miss, Colorado etc. they want to win and go bowling. So they will try to create schedules that give them the best chance to do so.
And that is what is wrong with college football my friend. Teams have to get what they want. Nobody NEEDS 7 home games, they want it, but they will try to tell you they need it. Like you said, teams will try to schedule easier in order to make a bowl. It's a shame but it's true. Some teams don't want to challenge themselves.
RickyW says:
Bradley BYU fan said "BYU should absolutely get the P5 inclusion". Please quit drinking the koolaid.
Until BYU plays a schedule equivalent to Power Conference programs (that is, a minimum of nine games per season against other power conference programs) BYU should not be considered of Power conference quality as Notre Dame is.
Number of power conference programs BYU has currently scheduled
2015 (2) (1 TBA remaining)
Theoretically, in 2019, BYU could still play nine games against power conference programs. But I don't see that happening.
Nothing against the BYU. Indeed the Cougars are attempting to improve their schedule. But those are the facts.
Bradly, I mistyped. I meant to type SOS (instead of OOC)…
Utah – annual rivalry game with BYU injures the Ute's SOS
Colorado – annual rivalry game with Colo State injures the Buffaloes SOS
Baylor – annual game with SMU injures the Bears SOS
To clarify each of the rivalry game above does not necessarily have a significant negative impact on the SOS. But when the rivalry game replaces a game against a power conference program, that is where the likely SOS injury comes into play.
ddl65 says:
Actually, you can add another In a few years. Pitt and Penn State are renewing there rivalry, that was one of the best in the 70's, 80's and early 90's. Slated for 16 through 19 now, but both athletic directors have said that they are working on making it become permanent again.
Pitt is losing it's every year game against Notre Dame which we don't like, but understand, and thankfully Pitt's A.D. has added Penn State as said above, and a series staring with
Oklahoma St. in a few years, so we'll have 8 conf. and 2 BCS conf games every year.
Now to get the program up to the task.
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\section*{Introduction}
Let $G$ be a finite graph on the vertex set $[N]=\{1,\ldots,N\}$
with no loops, no multiple edges and no isolated vertices.
A {\it vertex cover} of $G$ is a subset $C \subset [N]$ such that,
for each edge $\{i,j\}$ of $G$, one has either $i \in C$ or $j \in C$.
Such a vertex cover $C$ is called {\it minimal} if
no subset $C' \subsetneqq C$
is a vertex cover of $G$.
We say that a finite graph $G$ is {\it unmixed} if all minimal vertex covers of $G$
have the same cardinality.
Let $A = K[z_1, \ldots, z_N]$ the polynomial ring in $N$ variables
over a field $K$.
The {\em edge ideal} of $G$ is
the monomial ideal $I(G)$ of $A$ generated by those quadratic
monomials $z_iz_j$ such that $\{ i, j \}$ is an edge of $G$.
It is well-known that
the primary decomposition of the edge ideal of $G$ is
$$
I(G) = \bigcap_{C \in {\mathcal M}(G)} \left< z_i \ | \ i \in C \right>
$$
where ${\mathcal M}(G)$ is the set of all minimal vertex covers of $G$.
We say that $G$ is {\em Cohen--Macaulay} (over $K$) if
the quotient ring $A / I(G)$ is Cohen--Macaulay.
Every Cohen--Macaulay graph is unmixed.
A graph theoretical characterization of
Cohen--Macaulay bipartite graphs was given in \cite{HH}
and that of unmixed bipartite graphs was given in \cite{V}.
In Sections 1 and 2, we study the correspondence between
unmixed bipartite graphs and sublattices of the
Boolean lattice ${\mathcal L}_n$ on $\{x_1,\ldots,x_n\}$:
\begin{itemize}
\item
There exists a one-to-one correspondence between
unmixed bipartite graphs on $\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
and sublattices ${\mathcal L}$ of ${\mathcal L}_n$
with $\emptyset \in {\mathcal L}$ and $\{x_1,\ldots,x_n\} \in {\mathcal L}$.
(Theorem \ref{unmixed}.)
\item
There exists a one-to-one correspondence between
Cohen--Macaulay bipartite graphs on $\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
and full sublattices of ${\mathcal L}_n$.
(Theorem \ref{CM}.)
\end{itemize}
In Section 3, we study toric ideals arising from
the set of minimal vertex covers of unmixed bipartite graphs.
Let $G$ be an unmixed bipartite graph on the vertex set
$\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
and let
$K[x_1,\ldots,x_n,y_1,\ldots,y_n]$ the polynomial ring in $2n$ variables
over a field $K$ with each $\deg x_i = \deg y_i=1$.
We associate each minimal vertex cover $C$ of $G$ with the squarefree monomial
$
u_C = \prod_{v \in C} v
\in K[x_1,\ldots,x_n,y_1,\ldots,y_n]$ of degree $n$.
Let ${\mathcal R}_G$ denote the semigroup ring
generated by all monomials $u_C$ with $C \in {\mathcal M}(G)$
over $K$.
Let $S_G = K[\{ z_C \}_{C \in {\mathcal M}(G)}]$ denote the polynomial ring
of $|{\mathcal M}(G)|$ variables over $K$.
The {\it toric ideal} $I_G$ of ${\mathcal R}_G$ is the kernel of the
surjective homomorphism $\pi: S_G \rightarrow {\mathcal R}_G$
defined by $\pi (z_C) = u_C$.
In Section 3,
by using the correspondence given in Section 1,
we show that:
\begin{itemize}
\item
The toric ideals arising from an unmixed bipartite graph possesses
a squarefree quadratic initial ideal.
(Theorem \ref{quadratic}.)
\end{itemize}
\section{Minimal vertex covers of unmixed bipartite graphs}
First we recall a fact stated in \cite[p.300]{HH}.
Let $G$ be a bipartite graph without isolated vertices
and let $V(G) = \{x_1,\ldots,x_m\} \cup \{y_1,\ldots,y_n\}$ denote the set of vertices of $G$.
Suppose that $G$ is unmixed.
Since $\{x_1,\ldots,x_m\}$ and $\{y_1,\ldots,y_n\}$ are minimal vertex covers
of $G$, we have $m = n$.
Moreover, by virtue of the ``marriage theorem,"
we may assume that $\{x_i,y_i\} \in E(G)$ for all $i$.
Thanks to this fact, it follows that
each minimal vertex cover of $G$ is of the form
$\{x_{i_1},\ldots,x_{i_s},y_{i_{s+1}},\ldots,y_{i_n}\}$
where
$\{i_1,\ldots, i_n \} = [n] $.
For a minimal vertex cover $C=\{x_{i_1},\ldots,x_{i_s},y_{i_{s+1}},\ldots,y_{i_n}\}$
of $G$, we set $\overline{C} = \{x_{i_1},\ldots,x_{i_s}\}$.
Let ${\mathcal L}_n$ denote the Boolean lattice on the set $\{x_{1},\ldots,x_{n}\}$
and let
$${\mathcal L}_G = \{\overline{C} \ | \ C \mbox{ is a minimal vertex cover of } G\}
\ (\subset {\mathcal L}_n).$$
\begin{Remark}
{\rm
Let $G$ and $G'$ be unmixed bipartite graphs on
$\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$.
\begin{enumerate}
\item[(i)]
Both
$\emptyset$ and $\{x_{1},\ldots,x_{n}\}$
belong to ${\mathcal L}_G$.
\item[(ii)]
If $G \neq G'$, then we have $I(G) \neq I(G')$.
Hence ${\mathcal L}_G \neq {\mathcal L}_{G'}$ follows from
the primary decomposition of the edge ideals.
\end{enumerate}
}
\end{Remark}
\begin{Theorem}
\label{unmixed}
Let ${\mathcal L}$ be a subset of ${\mathcal L}_n$.
Then
there exists a (unique) unmixed bipartite graph $G$
on $\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
such that ${\mathcal L} = {\mathcal L}_G$
if and only if
$\emptyset$ and
$\{x_{1},\ldots,x_{n}\}$ belong to ${\mathcal L}$ and
${\mathcal L}$ is a sublattice of ${\mathcal L}_n$.
\end{Theorem}
\begin{proof}
{\bf (``Only if")}
Suppose that both
$C= \{x_{i_1},\ldots,x_{i_s},y_{i_{s+1}},\ldots,y_{i_n}\}$
and
$C'=\{x_{j_1},\ldots,x_{j_t},y_{j_{t+1}},\ldots,y_{j_n}\}$
are minimal vertex covers of $G$.
Then
$$\{ y_k \ | \ x_k \notin \overline{C} \cap \overline{C'} \} = \{y_{i_{s+1}},\ldots,y_{i_n}\} \cup \{ y_{j_{t+1}},\ldots,y_{j_n}\},$$
$$\{ y_k \ | \ x_k \notin \overline{C} \cup \overline{C'} \}=\{y_{i_{s+1}},\ldots,y_{i_n}\} \cap \{ y_{j_{t+1}},\ldots,y_{j_n}\}.$$
First we show that $\overline{C} \cap \overline{C'} \in {\mathcal L}_G$, that is,
$C_1=( \overline{C} \cap \overline{C'} ) \cup \{ y_k \ | \ x_k \notin \overline{C} \cap \overline{C'} \}$
is a minimal vertex cover of $G$.
Suppose that an edge $\{x_i,y_j\}$ of $G$
satisfies
$y_j \notin \{ y_k \ | \ x_k \notin \overline{C} \cap \overline{C'} \}= \{y_{i_{s+1}},\ldots,y_{i_n}\} \cup \{ y_{j_{t+1}},\ldots,y_{j_n}\}$.
Since $C$ (resp. $C'$) is a vertex cover of $G$, we have $x_i \in \overline{C}$ (resp. $x_i \in
\overline{C'}$).
Hence $x_i \in \overline{C} \cap \overline{C'}$.
Thus $C_1$ is a minimal vertex cover of $G$.
Second we show that $\overline{C} \cup \overline{C'} \in {\mathcal L}_G$, that is,
$C_2= (\overline{C} \cup \overline{C'})
\cup \{ y_k \ | \ x_k \notin \overline{C} \cup \overline{C'} \}$
is a minimal vertex cover of $G$.
Suppose that an edge $\{x_i,y_j\}$ of $G$
satisfies
$x_i \notin \overline{C} \cup \overline{C'}$.
Since $C$ (resp. $C'$) is a vertex cover of $G$, we have $y_j \in \{y_{i_{s+1}},\ldots,y_{i_n}\}$ (resp. $y_j \in
\{ y_{j_{t+1}},\ldots,y_{j_n}\}$).
Thus
$
y_j \in \{y_{i_{s+1}},\ldots,y_{i_n}\} \cap \{ y_{j_{t+1}},\ldots,y_{j_n}\}
= \{ y_k \ | \ x_k \notin \overline{C} \cup \overline{C'} \}$
and hence $C_2$ is a minimal vertex cover of $G$.
\bigskip
{\bf (``If")}
For each element $S \in {\mathcal L}$, let $S^*$ denote
the set $\{y_j \ | \ x_j \notin S\}$.
Let $I$ be an ideal
$
\bigcap_{S \in {\mathcal L}} \left< S \cup S^* \right>
$.
We will show that
there exists an unmixed bipartite graph $G$ such that
$I = \left< x_i y_j \ | \ \{x_i,y_j\} \in E(G) \right>$.
Since $\emptyset \in {\mathcal L}$ and $\{x_{1},\ldots,x_{n}\} \in {\mathcal L}$,
$I \subset \left< x_i y_j \ | \ 1 \leq i,j \leq n \right> $.
Suppose that a monomial $M$ of degree $\geq 3$ belongs to the minimal set of generators of $I$.
If $M = x_i x_j u$ where $i \neq j$ and $u$ is a (squarefree) monomial,
then there exist $S, S' \in {\mathcal L}$ such that
$x_i \in S \setminus S'$,
$x_j \in S' \setminus S$,
$u \notin \left< S \cup S^* \right>$ and
$u \notin \left< S' \cup {S'}^* \right>$.
Since ${\mathcal L}$ is a sublattice of ${\mathcal L}_n$,
$S \cap S' \in {\mathcal L}$.
Note that $(S \cap S')^* = S^* \cup {S'}^*$.
Hence we have
$$
I \subset
\left<
(S \cap S') \cup (S^* \cup {S'}^*)
\right>
.$$
However,
none of the variables in $M$ appears in
the set
$(S \cap S') \cup (S^* \cup {S'}^*).$
If $M = y_i y_j u$ where $i \neq j$ and $u$ is a (squarefree) monomial,
then there exist $S, S' \in {\mathcal L}$ such that
$y_i \in S^* \setminus {S'}^*$,
$y_j \in {S'}^* \setminus S^*$,
$u \notin \left< S \cup S^* \right>$ and
$u \notin \left< S' \cup {S'}^* \right>$.
Since ${\mathcal L}$ is a sublattice of ${\mathcal L}_n$,
$S \cup S' \in {\mathcal L}$.
Note that $(S \cup S')^* = S^* \cap {S'}^*$.
Hence we have
$$
I \subset
\left<
(S \cup S') \cup (S^* \cap {S'}^*)
\right>
.$$
However,
none of the variables in $M$ appears in
the set
$(S \cup S') \cup (S^* \cap {S'}^*).$
Thus the minimal set of generators of $I$ is a subset of
$\{x_i y_j \ | \ 1 \leq i,j \leq n\}$
and hence there exists a bipartite graph $G$ such that
$I = I(G)$.
Since the primary decomposition of the edge ideal $I(G)$ of $G$ is
$I = \bigcap_{C \in {\mathcal M}(G)} \left< C \right>$,
it follows that ${\mathcal M}(G) = \{ S \cup S^* \ | \ S \in {\mathcal L} \}$.
Thus we have
${\mathcal L} = {\mathcal L}_G$.
Since the cardinality of
each $S \cup S^*$ with $S \in {\mathcal L}$
is $n$, $G$ is unmixed as desired.
\end{proof}
\section{Minimal vertex covers of Cohen--Macaulay bipartite graphs}
Let, as before, $G$ be a finite graph on $[N]$ and
$A = K[z_1, \ldots, z_N]$ the polynomial ring in $N$ variables
over a field $K$. The {\em edge ideal} of $G$ is
the monomial ideal $I(G)$ of $A$ generated by those quadratic
monomials $z_iz_j$ such that $\{ i, j \}$ is an edge of $G$.
We say that $G$ is {\em Cohen--Macaulay} (over $K$) if
the quotient ring $A / I(G)$ is Cohen--Macaulay.
Every Cohen--Macaulay graph is unmixed.
Given a finite poset (partially ordered set)
$P = \{ p_1, \ldots, p_n \}$,
we introduce the bipartite graph $G_P$
on the vertex set
$\{ x_1, \ldots, x_n \} \cup \{ y_1, \ldots, y_n \}$
whose edges are those 2-element subsets $\{ x_i, y_j \}$
with $p_i \leq p_j$.
In particular for each $i \in [n]$ the edge $\{ x_i, y_i \}$
belongs to $G_P$.
It is known \cite{HH} that $G_P$
is Cohen--Macaulay. Conversely, given a Cohen--Macaulay
bipartite graph $G$, there is a finite poset $P$ with
$G = G_P$.
A subset $\alpha \subset P$ is called a {\em poset ideal}
of $P$ if $\alpha$ enjoys the property that
if $p_i \in \alpha$ and $p_j \leq p_i$, then
$p_j \in \alpha$. In particular
the empty set and $P$ itself
are poset ideals of $P$.
For each poset ideal $\alpha$ of $P$,
we set
$\alpha_x =
\{ x_i \, | \, p_i \in \alpha \}$
and
$\alpha_y =
\{ y_j \, | \, p_j \not\in \alpha \}$.
\begin{Lemma}
\label{Oberwolfach}
The set $\alpha_x \cup \alpha_y$ is a minimal vertex cover
of $G_P$. Conversely, every minimal vertex cover of $G_P$
is of the form $\beta_x \cup \beta_y$
for some poset ideal $\beta$ of $P$.
\end{Lemma}
\begin{proof}
Let $\alpha$ be a poset ideal of $P$. We show that
$C = \alpha_x \cup \alpha_y$ is a minimal vertex cover
of $G_P$. Let $\{ x_i, y_j \}$ be an edge of $G$.
Then $p_i \leq p_j$. Suppose $x_i \not\in \alpha_x$.
Then $p_i \not\in \alpha$. Since $\alpha$ is a poset ideal of $P$,
it follows that $p_j \not\in \alpha$. Thus $y_j \in \alpha_y$.
Hence $C$ is a vertex cover of $G$. Since
$G_P$ is unmixed and $|C| = n$, it follows that
$C$ is a minimal vertex cover.
Conversely, given a minimal vertex cover
$C = \{ x_{i_1}, \ldots, x_{i_s} \}
\cup \{ y_{i_{s+1}}, \ldots, y_{i_{n}} \}$ of $G_P$,
where $\{ i_1, \ldots, i_n \} = [n]$, we prove that
$\alpha = \{ p_{i_1}, \ldots, p_{i_s} \}$
is a poset ideal of $P$.
Let $p_{i_j} \in \alpha$ and $p_{a} < p_{i_j}$ in $P$.
Then $\{ x_a, y_{i_j} \}$ is an edge of $G_P$.
Suppose $p_a \not\in \alpha$. Then $x_a \not\in C$.
Since $x_{i_j} \in C$, one has $y_{i_j} \not\in C$.
Thus neither $x_a$ nor $y_{i_j}$ belongs to $C$.
However, $\{ x_a, y_{i_j} \}$ is an edge of $G_P$.
Thus $C$ cannot be a vertex cover of $G_P$.
Hence $p_a \in \alpha$. Consequently,
$\alpha$ is a poset ideal of $G_P$, as desired.
\end{proof}
Let, as before, ${\mathcal L}_n$ denote the Boolean lattice
on $\{x_1, \dots, x_n\}$. A sublattice ${\mathcal L}$
of ${\mathcal L}_n$ is called {\em full} if the rank of
${\mathcal L}$ is equal to $n$. Here the rank of
${\mathcal L}$ is defined to be the nonnegative integer
$\ell - 1$, where
$\ell$ is the maximal cardinality of chains
(totally ordered subsets) of ${\mathcal L}$.
Let $P$ be a finite poset with $|P| = n$ and
${\mathcal J}(P)$ the set of all poset ideals of $P$.
It turns out that the subset ${\mathcal J}(P)$
of ${\mathcal L}_n$ is a full
sublattice of ${\mathcal L}_n$.
Conversely, the classical fundamental structure theorem
for finite distributive lattices
\cite[pp. 118--119]{Hibibook}
guarantees that every full sublattice of ${\mathcal L}_n$
is of the form ${\mathcal J}(P)$ for a unique poset
$P$ with $|P| = n$.
\begin{Theorem}
\label{CM}
A subset ${\mathcal L}$ of ${\mathcal L}_n$
is a full sublattice of ${\mathcal L}_n$
if and only if
there exists a Cohen--Macaulay bipartite graph $G$
on $\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
with ${\mathcal L} = {\mathcal L}_G$.
\end{Theorem}
\begin{proof}
{\bf (``If")}
Let $G$ be a Cohen--Macaulay bipartite graph
on the set $\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$ and
$P$ a poset with $G = G_P$, where $|P| = n$.
Lemma \ref{Oberwolfach} says that
${\mathcal L}_G$ coincides with ${\mathcal J}(P)$.
Thus ${\mathcal L}_G$ is a full sublattice of ${\mathcal L}_n$.
{\bf (``Only if")}
Suppose that ${\mathcal L}$ is a full sublattice of ${\mathcal L}_n$.
One has ${\mathcal L} = {\mathcal J}(P)$ for a unique poset
$P$ with $|P| = n$. Let $G = G_P$.
Then $G$ is a Cohen--Macaulay bipartite graph.
Lemma \ref{Oberwolfach} says that
${\mathcal L}_G$ coincides with ${\mathcal J}(P)$.
Thus ${\mathcal L}_G = {\mathcal L}$, as required.
\end{proof}
\section{Toric ideals arising from minimal vertex covers}
Let $G$ be an unmixed bipartite graph on the vertex set
$\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$
and let
$K[x_1,\ldots,x_n,y_1,\ldots,y_n]$ the polynomial ring in $2n$ variables
over a field $K$ with each $\deg x_i = \deg y_i=1$.
Let ${\mathcal M}(G)$ denote the set of all minimal vertex covers of $G$.
We associate each minimal vertex cover $C$ of $G$ with the squarefree monomial
$
u_C = \prod_{v \in C} v
\in K[x_1,\ldots,x_n,y_1,\ldots,y_n]$ of degree $n$.
Let ${\mathcal R}_G$ denote the semigroup ring
generated by all monomials $u_C$ with $C \in {\mathcal M}(G)$
over $K$.
Let $S_G = K[\{ z_C \}_{C \in {\mathcal M}(G)}]$ denote the polynomial ring
of $|{\mathcal M}(G)|$ variables over $K$.
The {\it toric ideal} $I_G$ of ${\mathcal R}_G$ is the kernel of the
surjective homomorphism $\pi: S_G \rightarrow {\mathcal R}_G$
defined by $\pi (z_C) = u_C$.
\begin{Theorem}
\label{quadratic}
Let $G$ be an unmixed bipartite graph.
Then the toric ideal $I_G$ of ${\mathcal R}_G$ has a squarefree quadratic initial ideal
with respect to a reverse lexicographic order.
\end{Theorem}
\begin{proof}
Let $G_0$ denote the (unmixed) bipartite graph with the edge set
$E(G) = \{ \{x_1,y_1 \} ,\ldots, \{x_n,y_n \}\}$.
Then ${\mathcal L}_{G_0}$ is the Boolean lattice on $\{x_1,\ldots,x_n\}$.
It is known \cite{Hibipaper} that
the reduced Gr\"obner basis of toric ideal of ${\mathcal R}_{G_0}$
with respect to a suitable reverse lexicographic order is
$$
{\mathcal G}_0=
\{
\ \underline{z_C z_{C'}} - z_{C \cap C'} z_{C \cup C'} \ | \ C, C' \in {\mathcal M}(G) , \ C \neq C' \
\}
$$
where the initial monomial of each binomial of ${\mathcal G}_0$ is
the first monomial.
Let $G$ be an unmixed bipartite graph on the vertex set
$\{x_1,\ldots,x_n\} \cup \{y_1,\ldots,y_n\}$.
Then ${\mathcal L}_G$ is a sublattice of ${\mathcal L}_{G_0}$.
Hence we have the following:
\begin{itemize}
\item[(i)]
$I_G = I_{G_0} \cap S_G$
(by \cite[Proposition 4.13 (a)]{Stu});
\item[(ii)]
If $C$ and $C'$ belong to ${\mathcal M}(G)$,
then ${C \cap C'}$ and ${C \cup C'}$ belong to ${\mathcal M}(G)$.
Thus, if $z_C z_{C'} \in S_G$, then we have $z_{C \cap C'} z_{C \cup C'} \in S_G$.
\end{itemize}
Thanks to the elimination property above,
${\mathcal G}_0 \cap S_G$
is a Gr\"obner basis of the toric ideal $I_G$ of ${\mathcal R}_G$ as desired.
\end{proof}
\begin{Corollary}
Let $G$ be an unmixed bipartite graph.
Then the semigroup ring ${\mathcal R}_G$ is normal and Koszul.
\end{Corollary}
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Patricia Lynne Mitchell
Patricia Mitchell currently specializes in protecting employees rights. Ms. Mitchell works with Ms. Lauren Abrams, Law Office of Lauren Abrams representing employees' interests in California. Her practice includes wrongful termination, retaliation, class action lawsuits, disability discrimination, age discrimination, race discrimination, national origin discrimination, sexual harassment and wage and hour violations. Ms. Mitchell was a member of the Plaintiffs' Steering Committee, In Re: Prempro Products Liability, MDL Case Number 1507. She has also practiced as an employment defense attorney for several years. She is a member of the Consumer Attorneys Assn of Los Angeles, and the Los Angeles County Bar Association. Ms. Mitchell was designated as a "Rising Star" by Super Lawyers from 2013 through 2016.
Ms. Mitchell earned her J.D. in 2001 from Loyola Law School, her B.S. in Political Science, with honors, in 1998 from the University of California at Santa Barbara. In Law School Ms. Mitchell was awarded the Scott Moot Court Team Top Ten Appellate Brief, and placed 2nd on the Scott Moot Court team in 2001.
Litigation Percentage
100% of Practice Devoted to Litigation
U.S. District Court Central District of California, 2001
Supreme Court of California, 2001
Loyola Law School, Los Angeles, California
University of California at Santa Barbara, California
B.S. - 1998
Honors: With High Honors
Honors: Dean's List
CAALA
LACBA, Employment Section, 2008 - 2017
Meet Attorney Lauren Abrams
© 2019 by Law Offices of Lauren Abrams. All rights reserved. Disclaimer | Site Map
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{
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Virxilio Viéitez Bértolo (Forcarei, Galiza, 23 de outubro de 1930 — ibid., 15 de julho de 2008) foi um fotógrafo espanhol.
Biografia
Nasceu em 23 de outubro de 1930 em Soutelo de Montes, no município galego de Forcarei. Aos dezesseis anos consegue seu primeiro emprego, nas obras de construção do Aeroporto de Santiago-Rosalía de Castro, mas devido às más condições de trabalho emigra aos Pireneus dois anos depois, onde trabalha como mecânico em um teleférico e compra sua primeira câmera, uma Kodak. Anos mais tarde muda-se a Palamós, em Catalunha, onde conheceu a Julio Pallí, de quem aprendeu o ofício da fotografia. Nessa época trabalha fazendo retratos de turistas na Costa Brava.
Em 1955 regressa a Galiza e abre um estúdio fotográfico na sua vila natal. Desta forma teve a oportunidade de retratar a muitas gerações de vizinhos da Terra de Montes, de forma quase anônima. Suas fotografías são retratos de pessoas e grupos em eventos sociais como comunhões, velórios e batismos, mas tambén actividades cotidianas. Em relação à sua técnica, a maioría das suas fotos são em branco e preto, mas na década de 1970 tirou algumas coloridas.
Morreu na sua vila natal em 15 de julho de 2008.
Ligações externas
Galeria de fotografias, em El Mundo
Fotógrafos da Espanha
Nascidos em 1930
Mortos em 2008
Naturais de Pontevedra (província)
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{"url":"https:\/\/brilliant.org\/discussions\/thread\/an-olympiad-maths-problem\/","text":"\u00d7\n\nHi everybody,I have a question on olympiad maths (Not from brilliant's problems) that I'm unable to solve.The question is:If $$a+b=432$$ and $$(a,b)+[a,b]=7776$$,find $$ab$$.Please help me.Thanks!\n\nNote by Tan Li Xuan\n4\u00a0years, 7\u00a0months ago\n\nSort by:\n\na=210, b=222, ab=46620.\n\n- 4\u00a0years, 7\u00a0months ago\n\nCan you explain why?\n\n- 4\u00a0years, 7\u00a0months ago\n\nGcd of a and b must divide 432,so their Gcd must be a divisor of 432.We see that higher divisors of 432 like 216,108 cant be the Gcd and lower one like 2,3 also can't be the Gcd,so checking the middle ones we get Gcd = 6 so,further simplification gives us the answer...........\n\n- 4\u00a0years, 7\u00a0months ago\n\nThanks!\n\n- 4\u00a0years, 7\u00a0months ago\n\nyeah\n\n- 4\u00a0years, 7\u00a0months ago\n\ncan u explain me the meaning of - (a,b)+[a,b]=7776\n\n- 4\u00a0years, 7\u00a0months ago\n\n$$(a,b)$$ is the greatest common divisor of integers $$a,b$$. Similarly, $$[a,b]$$ is the least common multiple of $$a,b$$.\n\n- 4\u00a0years, 7\u00a0months ago\n\nwhat is the book?\n\n- 4\u00a0years, 7\u00a0months ago\n\nIt's not a book.It's from the 2012 IMAS upper primary question paper.I was practicing for this year's IMAS.\n\n- 4\u00a0years, 7\u00a0months ago\n\nHint: Use the fact that $$(a,b)[a,b]=ab$$ for positive integers $$a,b$$.\n\n- 4\u00a0years, 7\u00a0months ago","date":"2017-10-17 20:56:05","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\": 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\": 0.9877150058746338, \"perplexity\": 3498.2949268955017}, \"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-2017-43\/segments\/1508187822488.34\/warc\/CC-MAIN-20171017200905-20171017220905-00257.warc.gz\"}"}
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\section{Introduction}
The paper has a dual aim; first to prove finiteness theorems for Kolchin's constrained cohomology (or what we are now calling differential Galois cohomology), over suitable differential fields $(K,\delta)$. Secondly to apply these finiteness theorems to the so-called Parameterized Picard-Vessiot (PPV) theory; namely to show the existence of PPV-extensions of differential fields $(K,\delta_x, \delta_t)$ for linear equations $\delta_x Y = AY$ over $K$, under conditions on the $\delta_t$ field of $\delta_x$-constants of $K$, and where we may demand more properties of the PPV-extension.
The first is modelled on the {\em triviality} result from \cite{Pillay2017}, but requires some new ideas. The second is a relatively routine adaptation of \cite{KP}, but building on and depending on \cite{LSN}, and with a few delicate points.
The constrained cohomology set $H^{1}_{\delta}(K,G)$ (for $(K,\delta)$ a differential field and $G$ a differential algebraic group over $K$), was defined in \cite{KolchinBook2}. It parameterizes differential algebraic principal homogeneous spaces $X$ for $G$ over $K$, up to isomorphism over $K$ in the appropriate category.
We will work in characteristic $0$. Recall that a field $K$ is called {\em bounded} if it has only finitely many algebraic extensions of any given degree. A field $K$ is called {\em large} if whenever $V$ is a $K$-irreducible variety over $K$ with a smooth $K$-point then $V$ has a Zariski-dense set of $K$-points. A rather strong notion of {\em differentially large} was given in \cite{LSTressl2018}: $(K,\delta)$ is differentially large if $K$ is large (as a field) and for any differential extension $(L,\delta)$ of $(K,\delta)$ if $K$ is existentially closed in $L$ as fields, then $(K,\delta)$ is existentially closed in $(L,\delta)$. Other weaker notions of differential largeness will be discussed later. Many examples of differentially large fields come from models of Tressl's uniform model companion \cite{Tressl}; namely suppose that $T$ is a model-complete theory of large fields, then $T \cup\{\delta$ is a derivation\} has a model companion, and any model will be differentially large.
As mentioned above, the basic template for our finiteness proof comes from \cite{Pillay2017}, where {\em triviality} of the relevant cohomology sets is shown, assuming that $(K,\delta)$ is algebraically closed and Picard-Vessiot closed. We are weakening the algebraically closed assumption on $K$ to boundedness, and strengthening the PV-closed assumption to ``differentially large", and obtaining finiteness of the relevant cohomology sets. We will discuss possible refinements and improvements of our results later.
\section{Preliminaries}
We will here be working mainly with (ordinary) differential fields $(K,\delta)$ of characteristic $0$, although two commuting derivations will appear in Section 5. $(\mathcal U,\delta)$ denotes a saturated differentially closed field containing $(K,\delta)$, and where needed $(K^{diff},\delta)$ denotes a differential closure of $(K,\delta)$.
We begin with a quick recollection on the $\tau$-functor, $\nabla$ map, D-varieties, $D$-groups, sharp points etc. as well as on differential Galois (or constrained) cohomology.
(And again in Section 5 on applications to the PPV theory we will need to deal with relative or parameterized versions of these notions, as in \cite{LSN}.)
Many of these notions are due to Buium \cite{Buium} and have been discussed in many papers, such as \cite{Pillay-2remarks}, \cite{Kowalski-Pillay}, and \cite{LSTressl2018} with varying viewpoints.
If $X \subseteq {\mathbb A}^{n}$ is an affine variety over $K$ whose ideal is generated by polynomials $P_{1}({\bar x}),...., P_r({\bar x})$ then the prolongation $\tau(X)\subseteq {\mathbb A}^{2n}$ of $X$ is the variety over $K$ defined by $P_{i}({\bar x}) = 0$ for $i=1,..,r$ as well as $\sum_{j=1,..,n}( \partial P_{i}/\partial x_{j})u_{j} + P_{i}^{\partial} = 0$ for $i=1,..,r$ where $P_{i}^{\delta}$ is the polynomial in ${\bar x}$ obtained from $P_{i}$ by applying $\delta$ to its coefficients. If $X$ is an abstract variety over $K$ then working locally in the affine charts, gives a well-defined variety $\tau(X)$.
Alternatively one can use Weil descent as in Definition 2.7 of \cite{LSTressl2018}.
When $X$ is defined over the constants of $K$ then $\tau(X)$ coincides with the tangent bundle $T(X)$ of $X$. In general $\tau(X)$ is a {\em torsor} for $T(X)$: each fibre $\tau(X)_{a}$ is a principal homogeneous space for the tangent space $T(X)_{a}$ at $a\in X$ (and uniformly so).
When $X$ is affine, and $a$ is a point in $X(\mathcal U)$ then $\delta(a)$ is the tuple obtained by applying $\delta$ to the coordinates of $a$ and one sees readily that $(a,\delta(a))\in \tau(X)(\mathcal U)$. We call this map $\nabla_{X}:X\to \tau(X)$. It makes sense for any algebraic variety $X$ over $K$, and is of course a map only in the sense of {\em differential algebraic geometry}.
An important observation is that $\tau$ is a (covariant) functor that commutes with products and preserves fields of definition, from which one concludes:
\begin{remark} If $G$ is an algebraic group over $K$, then $\tau(G)$ has a natural structure of algebraic group over $K$, and the natural projection $\pi: \tau(G)\to G$ is a homomorphism. Moreover $\nabla_{G}:G\to \tau(G)$ is a homomorphic section for $\pi$.
\end{remark}
If $G$ is an algebraic group over $K$, then by an (algebraic) torsor for $G$ over $K$, also called an (algebraic) PHS for $G$ over $K$, we mean an algebraic variety $X$ over $K$ together with a regular (strictly transitive) action of $G(\mathcal U)$ on $X(\mathcal U)$ over $K$ (in the sense of algebraic geometry).
\begin{remark} Suppose $X$ is an algebraic torsor for the algebraic group $G$ over $K$. Then
\begin{enumerate}
\item $\tau(X)$ is an algebraic torsor for $\tau(G)$ over $K$.
\item For $g\in G(\mathcal U)$, $x\in X(\mathcal U)$, $\nabla_{X}(g\cdot x) = \nabla_{G}(g)\cdot \nabla_{X}(x)$.
\end{enumerate}
\end{remark}
Now for the notions of {\em algebraic D-variety} and {\em algebraic D-group}.
An algebraic D-variety over $K$ is an algebraic variety $X$ equipped with a regular (in the sense of algebraic geometry) section $s:X\to \tau(X)$ of the projection $\pi:\tau(X) \to X$, all over $K$. The data $s$ is equivalent to a lifting of the derivation $\delta$ on $K$ to a derivation of the structure sheaf of $X$.
An algebraic D-group over $K$ is an algebraic D-variety $(G,s)$ over $K$ where $G$ is an algebraic group and $s:G\to\tau(G)$ a homomorphism. There is a natural category of D-varieties. In particular a D-subvariety of a D-variety $(X,s)$ is a subvariety $Y$ such that $s|Y: Y\to \tau(Y)$.
\begin{remark}\label{factsDvar} \
Suppose $(V,s)$ is an algebraic D-variety over $K$. If $W$ is a $K$-irreducible component of $V$, then $W$ is a D-subvariety of $V$
\end{remark}
Let $(G,s_G)$ be an algebraic D-group over $K$. By a D-torsor for $(G,s_G)$ over $K$ we mean a D-variety $(X,s_X)$ over $K$ such that $X$ is an algebraic torsor for $G$ and for all $g\in G$ and $x\in X$ we have
$$s_X(g\cdot x)=s_G(g)\cdot s_X(x)$$
where the latter action is the (regular) action of $\tau(G)$ on $\tau(X)$ (mentioned earlier).
The analogues of algebraic varieties for differential algebraic geometry are {\em differential algebraic varieties}, which are modelled locally on solution sets of systems of differential polynomial equations in $\mathcal U$ (see \cite{KolchinBook2}, \cite{Buium}). In place of the Zariski topology we have the Kolchin topology, where on affine $n$-space for example, the Kolchin closed sets are the common zero sets of finite systems of differential polynomial equations. In this paper we will be only concerned with differential algebraic groups and their differential algebraic torsors, which coincide with groups and their torsors in the definable category, i.e. in the structure $(\mathcal U,+,\times,\delta)$. For example, any definable group (over $K$) has the structure of a differential algebraic group over $K$, giving an equivalence of categories. An exhaustive account of all of this appears in \cite{Pillay-foundational}, which also gives an introduction to model theory. We will be concerned mainly with linear differential algebraic groups over $K$, namely differential algebraic subgroups of some $GL_{n}$, defined over $K$ (or rather with an embedding, definable over $K$ into some $GL(n,\mathcal U)$).
In any case we have the obvious notion of a differential algebraic torsor $X$ for a differential algebraic group, all over $K$.
There is a close connection between ``finite-dimensional" (finite Morley rank) differential algebraic varieties and algebraic D-varieties via the $\sharp$-points functor. Let $(X,s)$ be an algebraic D-variety over $K$. Then $(X,s)^{\sharp}$ (also called $(X,s)^{\delta}$) is $\{a\in X(\mathcal U): s(a) = \nabla(a)\}$, and is a finite-dimensional differential algebraic variety, and any finite-dimensional differential algebraic variety essentially arises this way (see \cite{Pillay-2remarks}). For finite-dimensional differential algebraic groups and their differential algebraic torsors we have a closer relationship.
\begin{remark}\label{equivcat}
\begin{enumerate}
\item There is an equivalence of categories between algebraic D-groups over $K$ and differential algebraic groups of finite Morley rank over $K$. The functor is given by taking sharp points.
\item More generally, consider the following categories. Let $\mathcal C$ be the category of algebraic D-torsors for algebraic D-groups over $K$ with morphisms between $X^G$ and $Y^G$ being D-morphisms over $K$ that preserve the $G$-actions (i.e., $G$-morphisms). On the other hand, let $\mathcal D$ be the category of differential torsors for differential algebraic groups of finite Morley rank over $K$ with morphisms being differential morphisms over $K$ preserving the action. The $\sharp$-points functor yields an equivalence of categories.
\end{enumerate}
\end{remark}
For arbitrary, not necessarily finite-dimensional differential algebraic torsors, we have (see \cite{Pillay-foundational}):
\begin{remark} Suppose $X$ is a differential algebraic torsor of a differential algebraic group $G$, over $K$.
Then there is a definable over $K$ embedding of $(G, X)$ into some $(G_{1},X_{1})$ where $G_{1}$ is an algebraic group over $K$, $X_{1}$ an algebraic torsor for $G_{1}$ over $K$ and the action of $G_{1}$ on $X_{1}$ restricts to the action of $G$ on $X$.
\end{remark}
Now for (differential) Galois cohomology. The usual Galois cohomology (pointed) set $H^{1}(K,G)$ classifies algebraic torsors $X$ for $G$ over $K$ up to isomorphism over $K$ (as $G$-torsors). Here $K$ is a field and $G$ is an algebraic group over $K$. The generalization to differential algebraic groups over $K$ was carried out by Kolchin (in Chapter VII of \cite{KolchinBook2}). $G$ is now a differential algebraic group over a differential field $K$ and the set of differential algebraic torsors for $G$ over $K$, up to differential algebraic over $K$ isomorphism can be described in terms of certain 1-cocycles from $Aut(K^{diff}/K)$ to $G(K^{diff})$. Hence the expression ``constrained cohomology", as Kolchin referred to $K^{diff}$ as the constrained
closure of $K$. The set-up was generalized in \cite{Pillay-Galois} to a model-theoretic setting. In any case $H^{1}_{\delta}(K,G)$ classifies the differential algebraic PHS's over $K$ for $G$.
As a matter of notation the expression ``differential Galois cohomology" was used in Kolchin's first book \cite{KolchinBook1} for a distinct, but related, notion (related to the Galois theory of strongly normal extensions). The various cohomology theories of Kolchin and their interrelations, are discussed in \cite{Chatzidakis-Pillay}. Anyway we hope that our identification of ``constrained cohomology" and ``differential Galois cohomology", is acceptable.
The following lemma yields, in particular, an \emph{inductive principle} in cohomology sequences (similar to Lemma 2.1 of \cite{Pillay2017}) which is one of the key points in the proof of Theorem~\ref{mainfinite} below. The proof of the lemma makes use of results of Kolchin appearing in Chapter VII of \cite{KolchinBook2} and also arguments from \cite{Pillay-Galois} and \cite{PR}. We recall that given a differential algebraic group $N$ over $K$, by a $K$-form of $N$ one means a differential algebraic group over $K$ which is definably isomorphic to $N$ over $K^{diff}$. One way to build $K$-forms is as follows: Suppose $N$ is differential algebraic subgroup of a differential algebraic group $G$, both over $K$. Let $X$ be a differential algebraic torsor for $G$ over $K$, by \cite{Pillay-Galois} $X$ can be identified with a (constrained) definable 1-cocycle $\mu$ over $K$ in $G$ (so the cohomology class of $\mu$ is an element of $H^{1}_\delta (K,G)$). Consider the map $\Phi$ from $Aut(K^{diff}/K)$ to the group of $K^{diff}$-definable group automorphisms of $N$ given by taking any $\sigma$ to conjugation of $N$ by $\mu(\sigma)$. This map $\Phi$ is also a definable cocycle in the sense of \S4 of \cite{Pillay-Galois} and furthermore, by an adaptation of the arguments in that section, $\Phi$ gives rise to a $K$-form of $N$ that we denote by $N_\mu$. We note that if $\mu$ is a definable 1-coboundary over $K$ in $G$ (namely $\mu$ is cohomologous to the trivial cocycle) then $N_\mu$ is isomorphic to $N$ over $K$.
\begin{lemma} \label{inductive}
\begin{enumerate}
\item Let $G$ be an algebraic group over the differential field $K$. Then $H^{1}(K,G) = H^{1}_{\delta}(K,G)$.
\item Let $1\to N \to G\to H\to 1$ be a normal short exact sequence of differential algebraic groups over $K$.
Then the sequence
$$H^{1}_{\delta}(K,N) \to H^{1}_{\delta}(K,G) \to H^{1}_{\delta}(K,H)$$
of pointed sets is exact. Furthermore, if $H^{1}_{\delta}(K,H)$ is finite and for every $\mu\in H^{1}_{\delta}(K,G)$ the cohomology $H^{1}_{\delta}(K,N_\mu)$ is also finite, then $H^{1}_{\delta}(K,G)$ is finite as well.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) is Theorem 4 from Chapter VII of Kolchin's book \cite{KolchinBook2}.
\vspace{2mm}
\noindent
(2) By Theorem 2 in Chapter VII of Kolchin's book \cite{KolchinBook2}, the short exact sequence of groups gives rise to the exact sequence (of pointed sets) in cohomology. We observe that when the group $G$ is abelian the sequence in cohomology is an exact sequence of groups and the ``furthermore clause'' follows immediately in this case. However, in general ($G$ not necessarily abelian) the sequence is only an exact sequence of pointed sets and the finiteness of $H^{1}_{\delta}(K,G)$ in the ``furthermore clause'' needs to be justified~\footnote{We thank an anonymous referee for pointing out this subtle issue}. We remark that the analogue of (2) is well-known for the usual Galois cohomology of fields and algebraic groups; see for instance Theorem 6.16 of Platonov\&Rapinchuk's book \cite{PR}. The proof in the algebraic case adapts to the differential algebraic environment. Here we simply point out where the adaptations are needed and leave details to the interested reader. So we are now assuming that $H^{1}_{\delta}(K,H)$ is finite and for every $\mu\in H^{1}_{\delta}(K,G)$ the cohomology $H^{1}_{\delta}(K,N_\mu)$ is also finite. As remarked above we already have $\pi:H^{1}_{\delta}(K,G) \to H^{1}_{\delta}(K, H)$. Hence the image $\pi(H^{1}_{\delta}(K,G))$ is finite, as it is contained in $H^{1}_{\delta}(K,H)$. So there are $
\mu_{1},\dots,\mu_{r}\in H^{1}_{\delta}(K,G)$ with $\pi(H^{1}_{\delta}(K,G))= \pi(\{\mu_{1},\dots,\mu_{r}\})$. Now the key point, which comes from adapting the arguments in \S1.3.2 of Platonov\&Rapinchuk book \cite{PR}, is that, for each $i=1,\dots,r$, $H^{1}_{\delta}(K,N_{\mu_i})$ maps onto $\pi^{-1}(\pi(\mu_{i}))$. Thus, by our hypothesis, each $\pi^{-1}(\pi(\mu_{i}))$ is finite, and so $H^{1}_{\delta}(K,G)$ is finite as well.
\end{proof}
A basic theorem of Serre \cite{Serrebook} is that if the field $K$ is bounded (finitely many extensions of degree $n$ for any $n$), then $H^{1}(K,G)$ is finite for any linear algebraic group $G$ over $K$. A motivating theme of this paper and future work is to generalize Serre's theorem in suitable ways to finiteness theorems for the differential Galois cohomology of linear differential algebraic groups.
\smallskip
Finally let us discuss ``differential largeness" more. As mentioned earlier a field $K$ is called large if any $K$-irreducible variety over $K$ with a smooth $K$-point has a Zariski-dense set of $K$-points. One of the points of largeness of $K$ is that the condition that a variety over $K$ has a dense set of $K$-points becomes first order, in definable families.
Largeness (of the field of constants of a given differential field) played a role in the strong existence theorems for strongly normal extensions in \cite{KP} and \cite{BCPP}. Analogous notions of ``differential largeness" of a differential field should give denseness, in the sense of the Kolchin topology, of the set of $K$-points of a differential algebraic variety $X$ over $K$, under appropriate assumptions. The question is what the assumptions should be. One natural idea is to define the notion of a ``smooth point" on the differential algebraic variety $X$, and take as our assumption that $X$ has a smooth $K$-point. This idea was pursued in \cite{Cousins-thesis}. Another idea is to take rather a weaker assumption that certain {\em algebraic} varieties attached to $X$ have many $K$-points. This was pursued by the first author and Marcus Tressl in \cite{LSTressl2018} and is the notion of differential largeness used in the current paper.
A convenient definition from \cite{LSTressl2018} (also appearing in \cite{Cousins-thesis}) is:
\begin{definition} Let $(K,\delta)$ be a differential field. We call $K$ differentially large, if $K$ is large as a field, and for any differential field extension $(L,\delta)$ of $(K,\delta)$, if $K$ is existentially closed in $L$ as a field, then it is existentially closed in $L$ as a differential field.
\end{definition}
An equivalent condition (see Corollary 6.5 of \cite{LSTressl2018}) is a slight variant on the geometric axioms for $DCF_{0}$:
\begin{fact} $(K,\delta)$ is differentially large iff $K$ is large as a field, and whenever $(V,s)$ is an algebraic D-variety over $K$ such that $V$ is $K$-irreducible, and has a smooth $K$-point, then for any nonempty Zariski open subset $U$ of $V$, over $K$, there is a $K$-point $a$ in $U$ such that $s(a) = \nabla_{V}(a)$.
\end{fact}
\begin{remark}
\
\begin{enumerate}
\item The conclusion on the right hand side of Fact 2.8 says precisely that $(V,s)^{\sharp}(K)$ is Kolchin dense in $(V,s)^{\sharp}$.
\item Assuming that $T$ is a model-complete theory of large fields (in the ring language), then $T\cup\{\delta$ is a derivation\} has a model companion which is axiomatized by $T \cup \{\delta$ is a derivation\} $\cup$ the axioms scheme given by the right hand side of Fact 2.8. This is Tressl's ``Uniform Model Companion" \cite{Tressl}, and provides a large source of differentially large, but not differentially closed fields, such as closed ordered differential fields, and closed $p$-adic differential fields.
\item As pointed out in \cite{LSTressl2018}, algebraically closed and differentially large implies differentially closed.
\end{enumerate}
\end{remark}
As in \cite{Pillay2017} we will make use of model-theoretic dimensions, Morley rank and $U$-rank, in the context of $DCF_{0}$. (And as mentioned in \cite{Pillay2017} our arguments could be replaced by ``purely differential algebraic" arguments using Cassidy and Singer \cite{Cassidy-Singer-Holder}.) We refer to \cite{Poizat} for facts, background, and references about definable groups and dimensions in stable theories. We have already mentioned ``finite rank" or ``finite-dimensional" differential algebraic groups a few times. Finite rank can be taken to be finite Morley rank or finite $U$-rank and coincides with finite-dimensional in the sense of \cite{Buium} or ``differential type $0$" in the sense of \cite{Cassidy-Singer-Holder}.
In $DCF_{0}$, the Morley rank of $G$ coincides with the $U$-rank of $G$ and is of the form $\omega\cdot m + k$, for $m, k$ nonnegative integers. $G$ is said to be $1$-connected if it has no proper, nontrivial, normal definable subgroup $N$ such that $G/N$ has finite rank (this coincides with the notion of strongly connected for differential algebraic groups \cite{Cassidy-Singer-Holder}). From \cite[Corollary 6.3 and Theorem 6.7]{Poizat}$, G$ being $1$-connected is equivalent to $U(G) = \omega\cdot m$ (some $m\geq 0$) and $G$ being connected (no definable subgroup of finite index). For any $G$, there is a maximal $1$-connected definable subgroup $N$ of $G$ (necessarily normal) such that $G/N$ has finite rank. $N$ is called the $1$-connected component of $G$.
In the bulk of this paper we are concerned with linear differential groups, that is differential algebraic (equivalently definable in $(\mathcal U,\delta)$) subgroups of some $GL(n,\mathcal U)$. We will be using repeatedly the fact \cite{Cassidy} that if $G$ is a linear differential algebraic group over $K$ and $N$ is a normal definable subgroup of $G$ defined over $K$, then $G/N$ is also linear over $K$, specifically $G/N$ is definably embeddable (over $K$) in some $GL(n,\mathcal U)$.
Let us remark briefly that an arbitrary differential algebraic group $G$ defined over $K$, definably over $K$ embeds in an algebraic group $H$. And we conclude from this that $G$ has a normal definable subgroup $N$ such that $N$ is linear and $G/N$ embeds in an abelian variety. (See \cite{Pillay-foundational}).
\vspace{5mm}
\noindent
A crucial technical result will be proved in Section 3.
In Section 4 the finiteness theorem is proved (Theorem 4.1). In Section 5 we state and discuss the PPV existence theorem, and sketch the proof.
\section{The D-variety structure on $G$-maps}\label{modeltheory}
From now on we work inside a large saturated model $(\mathcal U,\delta)\models \operatorname{DCF}_0$. Fix a differential field $(K,\delta)$ of characteristic zero. Let $(G,s_G)$ be an algebraic D-group over $K$, and let $(X,s_X)$ and $(Y,s_Y)$ be $D$-torsors for $G$ also over $K$.
We set
$$\mathcal B(G;X\times Y)=\{f:X\to Y: f \text{ is a $G$-isomorphism}\}.$$
When the context is clear we simply write $\mathcal B$ in place of $\mathcal B(G;X\times Y)$. Recall that a $G$-isomorphism $f$ is an isomorphism between $X$ and $Y$ (as algebraic varieties) such that $f(g\cdot x)=g\cdot f(x)$ for all $g\in G$, $x\in X$ and $y\in Y$; i.e., $f$ preserves the $G$-action. In this section we show that $\mathcal B$ has naturally the structure of a $D$-variety over $K$, and that its sharp $K$-points correspond to $G$-isomorphisms defined over $K$ that are $D$-morphisms.
First note that a $G$-isomorphism $f:X\to Y$ is completely determined by what it does to a single point of $X$; that is, fixing $a\in X$ once we know $f(a)$ then $f(x)$ must equal $g\cdot f(a)$ where $g\in G$ is such that $x=g\cdot a$. Thus, to any pair $(a,b)\in X\times Y$ we can associate a $G$-isomorphism $f:X\to Y$ given by
$$f(x)=g\cdot b$$
where $g\in G$ is the unique element of $G$ with $x=g\cdot a$. Also, note that the graph of such an $f$ is simply given by the orbit of $(a,b)$ under the natural action of $G$ on $X\times Y$; namely, $g\cdot (x,y)=(g\cdot x,g\cdot y)$. In other words, each orbit determines uniquely a $G$-isomorphism and distinct orbits yield distinct maps. We thus have that the set $\mathcal B$ is in bijection, and we identify it, with the algebraic variety
$$(X\times Y)/G$$
which is defined over $K$.
Moreover, the canonical $D$-structure on $X\times Y$, namely
$$s_{X\times Y}:=(s_x,s_Y):X\times Y \to \tau (X\times Y),$$
induces a $D$-structure on $\mathcal B$. Indeed, given $f\in \mathcal B$, let $(a,b)\in X\times Y$ be any point such that $\pi(a,b)=f$ where $\pi$ is the canonical (surjective) morphism $X\times Y\to \mathcal B$. Note that this is equivalent to $b=f(a)$. Let
$$s_\mathcal B(f):=\tau \pi(s_{X\times Y}(a,b))\in \tau \mathcal B$$
and one just needs to show that this map is independent of the choice of $(a,b)$. So let $(a',b')\in X\times Y$ be in the fibre of $\pi$ above $f$. Note that $\tau \mathcal B$ is given as
$$\tau(X\times Y)/\tau G$$
where the action of $\tau G$ on $\tau(X\times Y)=\tau(X)\times \tau(Y)$ is coordinate-wise. Thus, all we need to show is that there is $u\in \tau G$ such that
$$s_{X\times Y}(a,b)=u\cdot s_{X\times Y}(a',b').$$
Since $(a,b)$ and $(a',b')$ are in the same $\pi$-fibre, there is $g\in G$ such that $(a,b)=g\cdot (a',b')$. We then have
\begin{align*}
s_{X\times Y}(a,b) & = (s_X(g\cdot a'),s_Y(g\cdot b')) \\
& = (s_G(g)\cdot s_X(a'),s_G(g)\cdot s_Y(b')) \\
& = s_G(g)\cdot s_{X\times Y}(a',b'). \\
\end{align*}
This shows that $s_\mathcal B:\mathcal B\to \tau \mathcal B$ as defined above is well-defined.
Note that we actually showed that there is a (necessarily unique) map $s_\mathcal B$ that makes the following diagram commute.
$$\xymatrix{
\tau (X\times Y) \ar[rr]^{\tau \pi}&&\tau \mathcal B\\
X\times Y \ar[u]^{s_{X\times Y}}\ar[rr]^{\pi}&&\mathcal B \ar[u]_{s_\mathcal B}
}$$
\begin{remark}\label{smooth}
Note that, as an algebraic variety, $\mathcal B$ becomes isomorphic to $Y$ after naming a point in $X$. Indeed, fixing $a\in X$, the morphism that assigns $f\in \mathcal B$ to $f(a)\in Y$ is an isomorphism. In particular, each $K$-irreducible component of $\mathcal B$ is a smooth algebraic variety. We will use this latter fact in Corollary \ref{tosharp} below.
\end{remark}
So far we have shown that the algebraic variety $\mathcal B$ (defined over $K$) has a $D$-variety structure. We now prove further properties of this structure.
\begin{proposition}\label{Bproperties}
For $(\mathcal B,s_\mathcal B)$ as above, we have
\begin{itemize}
\item [(i)] $K$-points of $\mathcal B$ correspond to $G$-isomorphisms defined over $K$, and
\item [(ii)] Sharp points of $(\mathcal B,s_\mathcal B)$ correspond to $G$-isomorphisms that are $D$-morphisms.
\end{itemize}
\end{proposition}
\begin{proof}
(i) One just has to note that $f\in \mathcal B$ is a $K$-point of $\mathcal B$ if and only if the preimage $\pi^{-1}(f)$ is defined over $K$ (this uses that $\pi$ is a morphism over $K$). Note that this preimage is precisely the graph of $f$.
(ii) Suppose $f$ is a sharp point of $(\mathcal B,s_\mathcal B)$. To prove that $f$ is a D-morphism, it suffices to show that if $a$ is a sharp point of $(X,s_X)$ then $f(a)$ is a sharp point of $(Y,s_Y)$. We have that $s_\mathcal B(f)=\nabla_B(f)$. In other words, there is $u\in \tau G$ such that
$$s_{X\times Y}(a,f(a))=u\cdot \nabla_{X\times Y}(a,f(a)).$$
This means that $s_X(a)=u\cdot \nabla_X(a)$ and $s_Y(f(a))=u\cdot \nabla_Y(f(a)).$ As $a$ is a sharp point of $(X,s_X)$, then $u=\nabla_G(e)$ the identity of $\tau G$. Hence, $s_Y(f(a))=\nabla_X(f(a))$; i.e., $f(a)$ is a sharp point of $(Y,s_Y)$.
Now assume that $f\in \mathcal B$ is a $D$-morphism. We argue that it must be a sharp point of $(\mathcal B,s_\mathcal B)$. Let $(a,f(a))\in X\times Y$ be such that $a$ is sharp point of $(X,s_X)$. Then, as $f$ is a D-morphism, $(a,f(a))$ is a sharp point of $(X\times Y, s_{X\times Y})$. It follows, by definition of $s_\mathcal B$, that $s_\mathcal B(f)=\nabla_\mathcal B(f)$, as desired.
\end{proof}
The following is an important consequence of Proposition ~\ref{Bproperties}.
\begin{corollary}\label{tosharp}
Assume $(K,\delta)$ is differentially large. With $(G,s_{G})$, $(X,s_{X})$ and $(Y,s_{Y})$ as above, if there is a $G$-isomorphism $f:X\to Y$ defined over $K$, then there is a differential $G^\sharp$-isomorphism $g:X^\sharp\to Y^\sharp$ defined over $K$.
\end{corollary}
\begin{proof}
Let $(\mathcal B,s_\mathcal B)$ be the $D$-variety over $K$ of $G$-isomorphisms between $X$ and $Y$ as above. As we are assuming that there is a $G$-isomorphism over $K$, Proposition~\ref{Bproperties}(i) implies that $\mathcal B$ has a $K$-point. Let $\mathcal B_1$ be the $K$-irreducible component of $\mathcal B$ that contains this $K$-point. Recall that by Remark \ref{factsDvar}, $\mathcal B_1$ is a D-subvariety of $\mathcal B$ and by Remark \ref{smooth} it is also a smooth algebraic variety. As $(K,\delta)$ is differentially large, there is a sharp $K$-point of $(\mathcal B_1,s_{\mathcal B_1})$, and in particular also of $(\mathcal B,s_\mathcal B)$. Call it $f$.
By Proposition~\ref{Bproperties}, $f$ is a $G$-isomorphism over $K$ that is also a $D$-morphism between $X$ and $Y$. Hence, the restriction of $f$ to $X^\sharp$ yields the desired $G^\sharp$-isomorphism.
\end{proof}
\section{Finiteness of $H^1_\delta(K,G)$}\label{finiteH1}
We now prove the first main result.
\begin{theorem}\label{mainfinite}
Suppose $(K,\delta)$ is differentially large and also that $K$ is bounded as a field. Then, for any linear differential algebraic group $G$ over $K$, the differential Galois cohomology set $H^1_\delta(K,G)$ is finite.
\end{theorem}
\begin{proof}
We split the proof into two cases; namely, when $G$ is of finite rank and the general case.
\medskip
\noindent {\bf Case 1. $G$ has finite Morley rank.}
By Remark~\ref{equivcat}(1), we may assume that $G$ is of the form $H^\sharp$ for a linear algebraic $D$-group $(H,s_H)$ over $K$. We will prove that
$$|H^1_\delta(K,G)| \leq |H^1(K,H)|$$
The result follows from this inequality. Indeed, as $K$ is bounded as a field, the right-hand-side is finite (see \cite[Chapter III, \S4.3]{Serrebook}).
Let $X$ and $Y$ be differential torsors for $G$ over $K$. By Remark~\ref{equivcat}(2), we may assume $X$ and $Y$ are of the form $V^\sharp$ and $W^\sharp$, respectively, for $(V,s_V)$ and $(W,s_W)$ algebraic $D$-torsors for $H$ over $K$. Now, if there is a $H$-isomorphism over $K$ between $V$ and $W$, then, by Corollary~\ref{tosharp}, there is a differential $G$-isomorphism over $K$ from $X$ and $Y$. This establishes the desired inequality.
\bigskip
\noindent {\bf Case 2. $G$ is arbitrary.}
The proof in this case is similar in strategy to that in \cite[\S 2]{Pillay2017}, although we must take additional care as $K$ is not assumed to be algebraically closed. We will make heavy use use of Lemma~\ref{inductive}.
\medskip
By the inductive principle (Lemma~\ref{inductive}) and Case 1, we may assume that $G$ is 1-connected; namely, $G$ has no proper differential algebraic subgroup $N$ such that the homogeneous space $G/N$ is of finite rank.
Exactly as in \cite{Pillay2017}, let $N$ be the (unique) maximal normal solvable definable $1$-connected subgroup of $G$. Then $H= G/N$ is almost semisimple in the sense that $H$ has no proper nontrivial normal commutative definable $1$-connected subgroup. By uniqueness $N$ (so also $H$) is defined over $K$.
Moreover, as mentioned earlier $H$ is also linear. By Lemma~\ref{inductive} it is enough to deal with the cases where $G = N$ and $G = H$.
\medskip
{\bf Case 2(a). $G = N$.}
Let $\bar G$ be the Zariski closure of $G$ (inside the ambient $GL_{n}(\mathcal U)$). Then $\bar G$ is a connected solvable linear algebraic group defined over $K$. By Theorems 2.3 and 2.4 of \cite{PR}, $\bar G$ is the semidirect product of connected algebraic subgroups $T$ and $U$ of $\bar G$, both defined over $K$, where $U$ is unipotent, and normal in $\bar G$, and $T$ is an algebraic torus (that is, $T$ is isomorphic, over the algebraic closure of $K$, to some product of copies of the multiplicative group, as an algebraic group).
$U\cap G$ is normal in $G$ and defined over $K$, and $G/(U\cap G)$ is also defined over $K$ and embeds in $T$. By Lemma~\ref{inductive} (2) it suffices to prove that each of $U\cap G$ and $G/(U\cap G)$ has finite $H^{1}_{\partial}(K,-)$.
Now by \cite{PR} $U$ has a central series defined over $K$ where each quotient is isomorphic over $K$ to the additive group $(\mathcal U, +)$. Intersecting with $G$, $U\cap G$ has a central series defined over $K$ where each quotient $U_{i}$ say, definably over $K$, embeds in $(\mathcal U,+)$. We may assume by Case 1, that each such quotient $U_{i}$ has infinite Morley rank, so must be definably isomorphic over $K$ to $(\mathcal U,+)$. But $H^{1}(K,\mathbb{G}_{a})$ is trivial, hence by Lemma~\ref{inductive}(1) so is $H^{1}_{\partial}(K, U_{i})$. We have shown that $H^{1}_{\partial}(K,(U\cap G))$ is finite.
Now we should deal with $T_{1} = G/(U\cap G)$. There are different approaches. The first is as follows: $T$ itself, as a connected algebraic torus, over $K$, may not be isomorphic over $K$ to some power of $\mathbb{G}_{m}$. But it is isomorphic over $K$ to a finite product of connected $1$-dimensional algebraic tori. Such a connected $1$-dimensional algebraic torus has in $DCF_{0}$ Morley rank $\omega$ and all proper differential algebraic subgroups have finite Morley rank. So we can proceed, as in the previous paragraph, to show that $H^{1}_{\partial}(K,T_{1})$ is finite, using the hypothesis that $K$ is bounded as a field, Serre's theorem, and Lemma~\ref{inductive}.
Alternatively, one can use the standard logarithmic derivative, $dlog$, to reduce to the case of (commutative) unipotent groups, which is dealt with above. (And this method may be useful in other situations.) We have seen that $T_{1}$ is definably embeddable over $K$ into $T$ which is a commutative subgroup of $GL_{n}(\mathcal U)$. This logarithmic derivative takes a matrix $X\in GL_{n}(\mathcal U)$ to $X'\cdot X^{-1}$, and restricted to $T$, takes $T$ into a commutative (differential algebraic) unipotent group, defined over $K$. The kernel of $dlog|T_{1}$ has finite Morley rank, and the image is contained in a commutative unipotent algebraic group, all defined over $K$. Induction, together with the earlier methods yield that
$H^{1}_{\partial}(K,T_{1})$ is finite, as required.
\vspace{2mm}
\noindent
{\bf Case 2(b). $G = H$ (is almost semisimple).}
The centre $Z$ of $G$ is finite-dimensional, by almost simplicity of $G$, so by Lemma~\ref{inductive} (2) and Case 1, we may quotient by $Z$ (i.e. assume $Z$ is trivial), and so $G$ is semisimple in the sense of \cite{Cassidy-semisimple}: no normal definable nontrivial connected commutative subgroup. In fact $G$ will also have trivial centre (but we will not use this).
Let $\bar G$ be the Zariski closure of $G$. By \cite[Theorem 14]{Cassidy-semisimple}, $\bar G$ is a connected semisimple algebraic group, defined over $K$. We will prove that $G = \bar G$. We are in the situation of Theorem 15 of Cassidy \cite{Cassidy-semisimple}. This Theorem 15 of Cassidy depends on an earlier paragraph from Cassidy's paper which cites a result, Theorem 27.5 of Humphreys \cite{Humphreys} on semisimple algebraic groups defined over a field $K$. Cassidy is working with arbitrary $K$, but Humphreys is assuming $K$ to be algebraically closed. So in fact this Theorem 15 from \cite{Cassidy-semisimple}, to be correct, should be stated under an assumption that $K$ is algebraically closed. We conclude:
\newline
(i) there are normal, nontrivial, simple (in the sense of algebraic groups), pairwise commuting, algebraic subgroups $A_{1},...,A_{r}$ of $\bar G$ such that the induced morphism $\pi$ from $A_{1}\times ... \times A_{r}$ to $\bar G$ is surjective with finite kernel (and moreover any normal simple algebraic subgroup of $\bar G$ is among the $A_{i}$), and
\newline
(ii) let $G_{i}$ be the connected component of $G\cap A_{i}$ (in the sense of groups definable in $(\mathcal U,\delta)$) for $i=1,..,r$. Then each $G_{i}$ is simple (as a differential algebraic group), and Zariski-dense in $A_{i}$, and of course the $G_{i}$ pairwise commute. Moreover the natural homomorphism which we call also $\pi$ from $G_{1}\times ...\times G_{r}$ to $G$ is surjective with finite kernel.
Both the $A_{i}$ (and so $G_{i}$) will in general be defined only over the algebraic closure of $K$.
As $G$ is $1$-connected, it is easy to see that each $G_{i}$ is $1$-connected too, so has infinite Morley rank. But $G_{i}$ is Zariski-dense in the simple algebraic group $A_{i}$, so by Theorem 17 of \cite{Cassidy-semisimple} or Proposition 5.1 of \cite{Pillay-fields}, $G_{i} = A_{i}$ for $i=1,..,r$. It follows easily that $G = \bar G$. Namely $G$ is already an algebraic group over $K$. Our assumption that $K$ is bounded as a field implies that $H^{1}(K,G)$ is finite (by Serre's theorem) so by Lemma~\ref{inductive} (1), $H^{1}_{\partial}(K, G)$ is also finite.
\end{proof}
\begin{remark}
Some final comments.
\begin{enumerate}
\item [(i)] We have focused here on linear differential algebraic groups, but the results should extend to arbitrary differential algebraic groups $G$ over $K$ with the conclusion that $H^{1}_{\delta}(K,G)$ is countable, rather than finite.
\item [(ii)] The differential largeness assumption in Theorem 4.1 is rather strong and we would like to replace it by weaker conditions, eventually finding the appropriate differential analogue of boundedness of a field. A first approximation would be the condition that every system of linear differential equations over $K$ has a fundamental system of solutions in $K$. This should be tractable although the proofs in \cite{Pillay2017} will not go through directly (as $K$ is no longer assumed to be algebraically closed). The ``right" differential analogue of boundedness should be that for each $n$ there are only finitely many linear DE's (in vector form) over $K$ of the form $\delta Y = AY$ where $Y$ is a $n\times 1$ vector of indeterminates, up to gauge transformation over $K$ (together with boundedness of $K$ as a field). Deducing the finiteness theorem for the differential Galois cohomology of linear differential algebraic groups over $K$, using this (tentative) notion of differentially bounded, seems to be substantially more difficult.
\item [(iii)]Also note from the proofs in this section that the main case is when $G$ is finite-dimensional. Namely, assuming that $K$ is bounded as a field, it follows that if $H^{1}_{\delta}(K,G)$ is finite for every finite rank linear differential algebraic group over $K$, then the same holds without the finite rank assumption.
\item [(iv)] The results in this section also go through for fields with several commuting derivations (differential largeness having been formulated in \cite{LSTressl2018} in the partial case). But for the sake of exposition we focused on the ordinary case.
\end{enumerate}
\end{remark}
\section{Existence of parameterized Picard Vessiot (PPV) extensions}
In this section we present the application of Theorem \ref{mainfinite} to the existence of PPV extensions, with prescribed properties (as described in the abstract). We now assume that $(K,\delta_x,\delta_t)$ is a differential field (of characteristic zero) with two commuting derivations. We refer to \cite{LS} and \cite{LSN} for some model theory of differentially closed fields with respect to several commuting derivations (in our case two). $K^{\delta_x}$ denotes the field of $\delta_x$-constants of $K$. We sometimes use $\Pi$ to refer to the set $\{\delta_x, \delta_t\}$ of (commuting) derivations.
Consider a homogeneous linear $\delta_x$-equation of order $n$ in matrix form:
\begin{equation}\label{lineareq}
\delta_x (Z)=A Z
\end{equation}
where $Z$ is an indeterminate varying in $GL_n$ and $A$ is in $Mat_n(K)$.
A PPV extension of $K$ for the equation is precisely a $\Pi$-field $L$ extending $K$ which is generated, as a $\Pi$-field by a solution $Z$ of the equation \eqref{lineareq}, and such that $L^{\delta_x} = K^{\delta_x}$, where as above, $K^{\delta_x}$ denotes the field of $\delta_x$-constants of $K$ (which note is a $\delta_t$-field).
With the above notation we show:
\begin{theorem} Suppose that $(K^{\delta_x},\delta_t)$ is existentially closed in $(K,\delta_t)$ as $\delta_t$-fields, $K^{\delta_x}$ is bounded as a field, and $(K^{\delta_x},\delta_t)$ is differentially large (in the sense of Definition 2.7). Then there is a PPV extension $(L,\delta_x,\delta_t)$ of $(K,\delta_x,\delta_t)$ for the equation \eqref{lineareq} such that $(K^{\delta_x},\delta_t)$ is existentially closed in
$(L,\delta_t)$ as $\delta_t$-fields.
\end{theorem}
This is the PPV generalization of Theorem 1.5 of \cite{KP}.
In \cite{KP} the context was simply a linear $DE$
\begin{equation}\label{linearordinary}
\delta Z = AZ
\end{equation}
over a differential field $(K,\delta)$ where the constants $K^{\delta}$ are asssumed to be bounded, large, and existentially closed in the field $K$. And we produced in Theorem 1.5 of \cite{KP} a PV extension $(L,\delta)$ of $K$ for the equation such that $K^{\delta}$ is existentially closed in $L$ as fields. We have chosen here to summarize the steps involved in the proof of Theorem 1.5 of \cite{KP}, and then show how these adapt/generalize to the PPV case, partly for pedagogical reasons, relevant to future generalizations. Although just going through the required steps in the new situation with references to \cite{KP} may have been sufficient. In any case, until the end of Remark 5.2 we will be working in the case of one derivation.
\vspace{2mm}
\noindent
(I) (Interpretations.) Let $\mathcal Y$ be the solution set of the equation \eqref{linearordinary} in the universal domain $(\mathcal U,\delta)$.
Consider the $2$-sorted structure $(\mathcal U^{\delta},{\mathcal Y})$ equipped with all $K$-definable structure from $(\mathcal U,\delta)$.
Then in a suitable language $L_{\delta,K}$, $(\mathcal U^{\delta},{\mathcal Y})$ is proved in \cite{KP} to be an elementary substructure of $(\mathcal U, GL(n,\mathcal U))$, where the latter is a suitable reduct of the algebraically closed field $\mathcal U$. More precisely the language $L_{\delta,K}$ consists of symbols $R_{X}$ for D-subvarieties of $\mathcal U^{r} \times (GL(n,\mathcal U))^{s}$ over $K$, namely subvarieties $X$ of $\mathcal U^{r} \times (GL(n,\mathcal U))^{s}$ which are defined over $K$ and such that $((\mathcal U^{\delta})^{r} \times {\mathcal Y}^{s})\cap X$ is Zariski-dense in $X$. The interpretation of $R_{X}$ in $(\mathcal U, GL(n,\mathcal U))$ is the tautolological one, and its interpretation in $(\mathcal U^{\delta},\mathcal Y)$ is $((\mathcal U^{\delta})^{r} \times {\mathcal Y}^{s})\cap X$. What is important is that the subsets of $(\mathcal U^{\delta})^{r} \times {\mathcal Y}^{s}$ which are definable over $K$ in the differentially closed field $(\mathcal U,\delta)$ are precisely the sets which are (quantifier-free) definable without parameters in the $L_{\delta,K}$-structure $(\mathcal U^{\delta},{\mathcal Y})$.
The map assigning to each relation symbol $R_{X}$ of $L_{\delta,K}$ the formula over $K$ defining $X$ in the algebraically closed field $\mathcal U$ yields an interpretation of $Th(\mathcal U^{\delta},\mathcal Y)_{L_{\delta,K}}$ in $ACF_{K}$ ($ACF$ with constants for elements of $K$) and we call this interpretation $\omega$.
\vspace{2mm}
\noindent
(II) (Galois group and PV extensions.) This is a construction of a certain $K$-definable function $f$ from ${\mathcal Y}$ to some power of $\mathcal U^{\delta}$ which, in a sense to be made precise later, classifies
Picard-Vessiot extensions of $K$ for \eqref{linearordinary}. Let $Aut({\mathcal Y}/K(\mathcal U^{\delta}))$ be the group of permutations of ${\mathcal Y}$ induced by automorphisms of the differential field $(\mathcal U,\delta)$ which fix pointwise both $K$ and the constants $\mathcal U^{\delta}$. Let $b\in {\mathcal Y}$. Then the map $\rho_{b}$ taking $\sigma$ to $\sigma(b)b^{-1}$ is an isomorphism between $Aut({\mathcal Y}/K(\mathcal U^{\delta}))$ and a differential algebraic subgroup $H^{+}$ of $GL(n,\mathcal U)$ which is defined over $K$. Moreover $\rho_{b}$ does not depend on the choice of $b$ so we just call it $\rho$. Let ${\mathcal Y}/H^{+}$ denote the set of right cosets of $H^{+}$ in ${\mathcal Y}$, equivalently the set of orbits under the action of $H^{+}$ on ${\mathcal Y}$ by left multiplication in $GL(n,\mathcal U)$. Then ${\mathcal Y}/H^{+}$ is in $K$-definable bijection with a subset $\mathcal O$ of some Cartesian power of $\mathcal U^{\delta}$, definable over $K\delta$. And $f:{\mathcal Y} \to {\mathcal O}$ is the function that we wanted to construct. So $f(b_{1}) = f(b_{2})$ iff $b_{1} = hb_{2}$ for some $h\in H^{+}$.
Moreover $b$ generates over $K$ a Picard-Vessiot extension for \eqref{linearordinary} iff $f(b)$ is a tuple of constants belonging to $K$, i.e. in $K^{\delta}$.
\vspace{2mm}
\noindent
(III) (Galois groupoid.) Given the map $f:{\mathcal Y} \to {\mathcal O}$, and $a\in {\mathcal O}$, ${\mathcal Y}_{a}$ denotes the fibre $f^{-1}(a)$ which is precisely $H^{+}b$ for some/any $b$ in the fibre. For $a_{1},a_{2}\in {\mathcal O}$, $H_{a_{1},a_{2}}$ denotes $\{b_{1}^{-1}b_{2}: b_{1}\in {\mathcal Y}_{a_{1}}, b_{2}\in {\mathcal Y}_{a_{2}}\}$. And $H_{a_{1}}$ denotes $H_{a_{1},a_{1}}$. Note that multiplication is meant always in the sense of $GL(n,\mathcal U)$. For $a\in {\mathcal O}$, $H_{a}$ is an algebraic subgroup of $GL(n, \mathcal U^{\delta})$, and is the ``usual" Galois group of the equation \eqref{linearordinary}, as an algebraic group in the constants.
The Galois groupoid ${\mathcal G}$ of \eqref{linearordinary} has as objects the set $\mathcal O$, and for each $a_{1}, a_{2}$ the set $Mor(a_{1},a_{2})$ of morphisms between $a_{1}$ and $a_{2}$ is precisely $H_{a_{1},a_{2}}$. Lemma 4.3 of \cite{KP} explains why this is a groupoid, and why and how it is (quantifier-free) definable over $K^{\delta}$ in the algebraically closed field $\mathcal U^{\delta}$.
If $C$ is a field of constants containing $K^{\delta}$ then ${\mathcal G}(C)$ denotes the groupoid with objects ${\mathcal O}(C)$ and for $a_{1}, a_{2}\in {\mathcal O}(C)$, the morphisms between $a_{1}$ and $a_{2}$ consists of the set $Mor(a_{1},a_{2})(C)$. (Namely just take $C$ points of everything.) The main point is Proposition 4.6 of \cite{KP} which states that the set of Picard-Vessiot extensions of $K$ for \eqref{linearordinary} is in natural one-to-one correspondence with the set of connected components of the groupoid ${\mathcal G}(K^{\delta})$.
\vspace{2mm}
\noindent
(IV) (Galois cohomology.) The connection with Galois cohomology is as follows: Using the construction in (III), assume that ${\mathcal G}(K^{\delta})$ is nonempty which means that there is $a\in {\mathcal O}(K^{\delta})$. So $H_{a}$ is a linear algebraic group, defined over $K^{\delta}$. Then the proof of Corollary 5.3 of \cite{KP} yields an injection of the set of connected components of ${\mathcal G}(K^{\delta})$ into $H^{1}(K^{\delta},H_{a})$. So boundedness of the field $K^{\delta}$ implies, via Serre's theorem, that ${\mathcal G}(K^{\delta})$ has finitely many connected components.
\vspace{2mm}
\noindent
(V) (End of proof.)
Lemma 4.7 of \cite{KP} gives more information about the interpretation $\omega$ constructed in (I). Recall that for a set $Z$, say, $\emptyset$-definable in the $L_{K,\delta}$-structure $(\mathcal U^{\delta},{\mathcal Y})$, $\omega(Z)$ is the corresponding set $\emptyset$-definable in the $L_{K,\delta}$-structure $(\mathcal U,GL(n,\mathcal U))$. And this of course extends to sets definable with parameters.
For notation: Following \cite{KP} we define ${\mathcal O}(\mathcal U)$ to be $\omega({\mathcal O})$. Let $f:{\mathcal Y}\to {\mathcal O}$, be as given in (II), then $F$ denotes $\omega(f)$, and note that $F$ is a function from $GL(n,\mathcal U)$ onto ${\mathcal O}(\mathcal U)$ (of course definable over $K$ in the algebraically closed field $\mathcal U$). Let $X_{a}$ denote $F^{-1}(a)$ for $a\in {\mathcal O}(\mathcal U)$. We write $H$ for the Zariski closure of $H^{+}$ in $GL(n,\mathcal U)$. (In fact as $H^{+}$ is $\emptyset$-definable in the $eq$ of the $L_{K,\delta}$-structure $(\mathcal U^{d}, {\mathcal Y})$ we could also define $H$ to be $\omega(H^{+})$.) We also write ${\mathcal G}(\mathcal U)$ for $\omega({\mathcal G})$. And likewise we write $Mor(\mathcal U)$ for $\omega(Mor)$ where $Mor$ is the set of morphisms of ${\mathcal G}$.
Let $h:{\mathcal Y}\times {\mathcal Y} \to GL(n, \mathcal U^{\delta})$ be $h(x,y) = x^{-1}y$. Then Lemma 4.7 of \cite{KP} says:
\newline
(i) $\omega(h):GL(n,\mathcal U)\times GL(n,\mathcal U) \to GL(n,\mathcal U)$ is precisely $\omega(x,y) = x^{-1}y$.
\newline
(ii) The fibres $X_{a}$ for $a\in {\mathcal O}(\mathcal U)$ are precisely the right cosets of $H$ in $GL(n,\mathcal U)$, so ${\mathcal O}(\mathcal U)$ is the homogeneous space $GL(n,\mathcal U)/H$.
\newline
(iii) If $a\in {\mathcal O}(K^{\delta})$ then $X_{a}$ is $K$-irreducible, is the Zariski closure of ${\mathcal Y}_{a}$ and the Picard-Vessiot extension of $K$ corresponding to $a$ and \eqref{linearordinary} is precisely the function field $K(X_{a})$ of $X_{a}$.
\newline
(iv) For $a_{1}, a_{2}\in {\mathcal O}(\mathcal U)$, $Mor(\mathcal U)(a_{1},a_{2}) = \{b_{1}^{-1}b_{2}: b_{1}\in X_{a_{1}}, b_{2}\in X_{a_{2}}\}$.
(This basically follows by transfer from $(\mathcal U^{d},{\mathcal Y})$ via $\omega$. )
\vspace{2mm}
\noindent
Now, assuming that $K^{\delta}$ is existentially closed in $K$ (as a field) and that $K^{\delta}$ is bounded and large, Theorem 1.5 of \cite{KP} is proved by first showing, using Lemma 4.7:
\vspace{2mm}
\noindent
(v) For some elementary extension (as fields) $K^{1}$ of $K^{\delta}$ which contains $K$, there is $a\in {\mathcal O}(K^{\delta})$ such that $X_{a}$ has a $K_{1}$-rational point.
\vspace{2mm}
\noindent
Now assuming for simplicity that $X_{a}$ is also $K_{1}$-irreducible (otherwise replacing it by a $K_{1}$-irreducible component which has a $K_{1}$-point), $K_{1}$ is existentially closed in the function field $K_{1}(X_{a})$ (as fields). Hence $K^{\delta}$ is existentially closed in $K^{1}(X_{a})$ as fields. But $K^{\delta} \leq K(X_{a})\leq K_{1}(X_{a})$, whereby $K^{\delta}$ is existentially closed in $K(X_{a})$. By (iii) from (V) above, we have found a Picard-Vessiot extension $L$ of $K$ for \eqref{linearordinary} such that $K^{\delta}$ is existentially closed in $L$ (as fields).
\vspace{1mm}
\begin{remark}
\begin{enumerate}
\item[(i)] Crespo, Hajto and van der Put \cite{CHvdP} prove the conclusion of Theorem 1.5 of \cite{KP} (in the linear case) when $K^{\delta}$ is real closed or $p$-adically closed (and $K^{\delta}$ is existentially closed in $K$) but their proof works only assuming boundedness (and largeness) of $K^{\delta}$, and goes through the Tannakian formalism.
\newline
\item [(ii)] In fact Theorem 1.5 of \cite{KP} is stated in the more general context of a logarithmic differential equation $dlog_{G}(y) = a$ on a not necessarily linear algebraic group $G$ defined over the constants of $K$ and where $a\in LG(K)$. In this situation the Tannakian theory (which is a linear theory) is not available, and so the technology in (I) to (V) above was really needed.
On the other hand from boundedness of $K^{\delta}$ we only have countability (rather than finiteness) of $H^{1}(K^{\delta}, G)$ for arbitrary algebraic groups over $K^{\delta}$, but this implies finiteness of ``definable" chunks of $H^{1}(K^{\delta},G)$, which was enough to obtain finitely many connected components of the set of $K^{\delta}$ points of the relevant groupoid.
\newline
\item [(iii)] The paper \cite{KP} also included a simple existence theorem for PV (or strongly normal extensions), Theorem 1.3, as well as a certain uniqueness theorem, Theorem 1.4. The existence theorem said that assuming only that $K^{\delta}$ is existentiallly closed in $K$ as fields then there is a Picard-Vessiot extension of $K$ for \eqref{linearordinary}. This used just steps (I) and (II) above, and was proved as follows: Let $F: GL(n,\mathcal U) \to {\mathcal O}(\mathcal U)$ be $\omega(f)$. Then $F$ applied to the identity of $GL(n,\mathcal U)$ is in ${\mathcal O}(K)$. So by existential closedness, ${\mathcal O}(K^{\delta})$ is nonempty, yielding our Picard-Vessiot extension. In fact as discussed in more detail below, this part of \cite{KP} was already extended to the $PPV$ (in fact the more general parameterized strongly normal) theory by the first author and Nagloo \cite{LSN}.
\newline
\item [(iv)] In the linear/PV case of Theorem 1.5 of \cite{KP}, actually the largeness assumption on $K^{\delta}$ is not needed. This was pointed out by the first author to the second author, and due to the fact that if $G$ is a connected linear algebraic group over a field $K$, then $G(K)$ is Zariski-dense in $G$. So if $X$ is a PHS over $K$ for $G$ with a $K$-rational point then $X(K)$ is Zariski-dense in $X$. This is not necessarily the case for arbitrary algebraic groups such as abelian varieties. So the more general case of Theorem 1.5 of \cite{KP} as discussed in (ii) above {\em does} need the largeness assumption on $K^{\delta}$ (in addition to boundedness).
\end{enumerate}
\end{remark}
\vspace{5mm}
\noindent
We will now begin going through the adaptation of steps (I) - (V) above to the PPV situation so as to prove Theorem 5.1 above.
In the new situation of the equation \eqref{lineareq}, there is also a universal domain $(\mathcal U,\delta_x, \delta_t)$, a saturated model of $DCF_{0,2}$ the theory of differentially closed fields with two commuting derivations. As mentioned earlier we let $\Pi = \{\delta_x,\delta_t\}$.
$(K,\delta_x, \delta_t)$ is a differential subfield of $\mathcal U$ and we are given the equation \eqref{lineareq} above. ${\mathcal Y}$ now denotes the solution of \eqref{lineareq} in $\mathcal U$, and note again
${\mathcal Y}\subseteq GL(n,\mathcal U)$.
The role of the $\delta$ constants of $K$ and of the universal domain is now played by $K^{\delta_x}$ and $\mathcal U^{\delta_x}$. In fact the first author and Nagloo already carried out the generalizations of Steps (I) and (II) in \cite{LSN}, leading to the theorem that if $(K^{\delta_x},\delta_t)$ is existentially closed in $(K,\delta_t)$ as $\delta_t$-fields, then there is a PPV extension of $K$ for \eqref{lineareq}. (Actually \cite{LSN} works in the more general context of a commmuting set $\Pi$ of $m$ derivations and a partition of $\Pi$ into nonempty sets ${\mathcal D}$ and $\Delta$, as well as with $GL_{n}$ replaced by an arbitrary $\Delta$-algebraic group $G$ defined over $K^{\mathcal D}$.)
The generalization of the notion of an algebraic $D$-variety from Section 1, is that of a {\em parameterized} or {\em relative} $D$-variety from \cite{LS} and \cite{LSN}. We will follow the notation in \cite{LSN}.
By a $\delta_t$-variety (or differential $\delta_t$-variety) over $K$ we mean a subset $V$ of $\mathcal U^{n}$ defined by a finite system of $\delta_t$-polynomials in indeterminates $\bar y=(y_1,\dots,y_n)$ say. Then by the {\em parameterized prolongation}
$\tau_{\delta_x}(V)$ of $V$ is meant the $\delta_t$-subvariety of $\mathcal U^{2n}$ defined by
the following (differential) equations in indeterminates $y_{1},..,y_{n}, u_{1},..,u_{n}$: First the set of $f(\bar y) = 0$ for all $\delta_t$-polynomials over $K$ vanishing on $V$.
Secondly the set of $\sum_{i\geq 0, j=1,\dots,n} (\partial f/\partial(\delta^i y_j))\delta^i u_j + f^{\delta_x}(\bar y)=0$
where $f$ ranges over the $\delta_t$-polynomials above, and where $f^{\delta_t}$ means the resulting of hitting the coefficients of $f$ with $\delta_t$. A {\em parameterized} $D$-variety over $K$ is a pair $(V,s)$ where $V$ is a $\delta_t$-variety over $K$, and $s: V\to \tau_{\delta_t}(V)$ is a $\delta_t$-polynomial section of the projection $\tau_{\delta_t}(V)\to V$ on the first $n$-coordinates.
By $\nabla_{\delta_x}$ (or $\nabla_{V,\delta_x}$) we mean the map taking $(v_{1},..,v_{n})\in V$ to $(v_{1},..,v_{n},\delta_x(v_1),...,\delta_x(v_n))\in \tau_{\delta_t}(V)$.
$(V,s)^{\sharp}$ denotes $\{ {\bar v}\in V: s({\bar v}) = \nabla({\bar v})\}$, a (differential) $\Pi$-algebraic subvariety of $V$ (defined over $K$, if $(V,s)$ is). There is a natural notion of a parameterized $D$-subvariety of $(V,s)$. Several key facts (analogues of facts about algebraic $D$-varieties) are given in Section 2 of \cite{LSN}, including the following characterization:
Let $(V,s)$ be a parameterized $D$-variety, and let $W$ be a $\delta_t$-subvariety of $V$. Then $W$ is a parametrized $D$-subvariety of $(V,s)$ iff $W\cap (V,s)^{\sharp}$ is Kolchin-dense in $W$.
\vspace{2mm}
\noindent
(I)' (Interpretations.) \cite{LSN} establishes the interpretation of the theory of the two sorted structure $(\mathcal U^{\delta_x},{\mathcal Y})$ equipped with all relations definable with parameters from $K$ in $(\mathcal U,\delta_x,\delta_t)$ in the theory $Th(\mathcal U,\delta_t)$ with parameters for elements of $K$. The details of the interpretation and of the language chosen are somewhat delicate, and this is maybe the most tricky part of the generalization of the single derivation situation. In the case at hand we have, in analogy with (I), relation symbols $R_{X}$ for $\delta_t$-algebraic subvarieties $X$ of $\mathcal U^{r}\times GL(n,\mathcal U)^{t}$ defined over $K$ such that $X\cap ((\mathcal U^{\delta_x})^{r}\times {\mathcal Y}^t)$ is Kolchin-dense in $X$. We call this language $L_{\Pi,K}$.
So
\begin{lemma} (\cite{LSN}, Corollary 4.3) Consider both $(\mathcal U^{\delta_x},{\mathcal Y})$ and $(\mathcal U, GL(n,\mathcal U))$ as $L_{\Pi,K}$-structures, where $R_{X}$ is interpreted as $X$ itself in $(\mathcal U, GL(n,\mathcal U))$ and as $X\cap ((\mathcal U^{\delta_x})^{r}\times {\mathcal Y}^t)$ in $(\mathcal U^{\delta_x},{\mathcal Y})$. Then $(\mathcal U^{\delta_x},{\mathcal Y})$ is an elementary substructure of $(\mathcal U, GL(n,\mathcal U))$.
\end{lemma}
As previously we call the interpretation $\omega$.
\vspace{2mm}
\noindent
(II)' (Galois group and PPV extensions.)
This is discussed in Section 5 of \cite{LSN}, see Lemma 5.2 and Proposition 5.3 there, and is a straightforward adaptation of (II). $Aut({\mathcal Y}/K\langle\mathcal U^{\delta_x}\rangle)$ denotes the group of permutations of ${\mathcal Y}$ induced by automorphisms of the ambient differential closed field $(\mathcal U, \delta_x, \delta_t)$ which fix $K$ and $\mathcal U^{\delta_x}$ pointwise (and there are other descriptions). Here $K\langle\mathcal U^{\delta_x}\rangle$ denotes the $\{\delta_x, \delta_t\}$-field generated over $K$ by
$\mathcal U^{\delta_x}$.
Claims 1 and 2 in the proof of Proposition 5.3 of \cite{LSN} establish that for $\sigma\in Aut({\mathcal Y}/K\langle\mathcal U^{\delta_x}\rangle)$ and $\alpha\in {\mathcal Y}$, $\sigma(\alpha)\alpha^{-1}$ (multiplication in the sense of $GL(n,\mathcal U)$) does not depend on the choice of $\alpha$, and that the map taking $\sigma$ to $\sigma(\alpha)\alpha^{-1}$ establishes an isomorphism between $Aut({\mathcal Y}/K\langle\mathcal U^{\delta_x}\rangle)$ and a $K$-definable subgroup of $GL(n,\mathcal U)$ which we again call $H^{+}$, the intrinsic Galois group. By elimination of imaginaries let ${\mathcal O}$ again be the set of orbits under the action of $H^{+}$ on ${\mathcal Y}$ by left multiplication, a $K$-definable set in $(\mathcal U,\delta_x,\delta_t)$ which up to $K$-definable bijection can be assumed to be a subset of some Cartesian power of $\mathcal U^{\delta_x}$. So, just as before, we get a $K$-definable function $f:\mathcal Y\to \mathcal O$ such that $f(b_1)=f(b_2)$ iff $b_1=h b_2$ for some $h\in H^+$. The following is a mixture of Proposition 5.3 from \cite{LSN} and its proof.
\begin{fact} If $b\in {\mathcal Y}$ and $a= f(b)\in K^{\delta_x}$ then $K\langle b\rangle$ (the $\Pi$-differential field generated by $K$ and $b$) is a PPV extension of $K$ for \eqref{lineareq}, and in fact the formula $y\in {\mathcal Y} \wedge f(y) = a$ isolates the type of $b$ over $K\langle\mathcal U^{\delta_x}\rangle$.
\end{fact}
And Theorem 5.4 of \cite{LSN} says:
\begin{corollary} Suppose $(K^{\delta_x},\delta_t)$ is existentially closed in $(K,\delta_t)$ as $\delta_t$-fields. Then there is a PPV extension of $K$ for \eqref{lineareq}
\end{corollary}
Again this holds and is stated in \cite{LSN} for the more general situation of $\delta_x$-log differential equations over $K$ on an algebraic group $G$ defined over $K^{\delta_x}$. This reproves and generalizes the main results of \cite{GGO}.
\vspace{2mm}
\noindent
(III)' (Galois groupoid.) This goes through identically to (III) except that now the Galois groupoid is (quantifier-free) definable over $K^{\delta_x}$ in the differentially closed $\delta_t$-field $(\mathcal U, \delta_t)$. Here are some details. We feel free to identify $H^{+}$ acting by left multiplication on ${\mathcal Y}$ with $Aut({\mathcal Y}/K\langle\mathcal U^{\delta_x}\rangle)$.
We start with the obvious:
\begin{fact} ${\mathcal Y}$ is a left coset of $GL(n,\mathcal U^{\delta_x})$ in $GL(n,\mathcal U)$, namely of the form $bGL(n,\mathcal U^{\delta_x})$ for some/any $b\in {\mathcal Y}$. In particular for all $b_{1},b_{2}\in {\mathcal Y}$, $b_{1}^{-1}b_{2} \in GL(n,\mathcal U^{\delta_x})$.
\end{fact}
Now, for $a\in {\mathcal O}$, note that ${\mathcal Y}_{a} = f^{-1}(a)$ is precisely an orbit under left multiplication by $H^{+}$, i.e. of the form $H^{+}b$ for some/any $b\in {\mathcal Y}_{a}$.
Exactly as in Definition 4.1 and Remark 4.2 of \cite{KP} we have:
(*) For $a_{1}, a_{2}\in {\mathcal O}$, define $H_{a_{1},a_{2}} = \{b_{1}b_{2}^{-1}: b_{1}\in {\mathcal Y}_{a_{1}}, b_{2}\in
{\mathcal Y}_{a_{2}}\}$, which as in Remark 4.2 of \cite{KP} equals $\{b_{1}^{-1}b: b\in {\mathcal Y}_{a_{2}}\} =
\{b^{-1}b_{2}: b\in {\mathcal Y}_{a_{1}}\}$ for any fixed $b_{1}\in {\mathcal Y}_{a_{1}}$ and $b_{2}\in {\mathcal Y}_{a_{2}}$.
With this notation we have:
\begin{lemma} (i) $H_{a_{1}, a_{2}}$ is a subset of $GL(n,\mathcal U^{\delta_x})$ (uniformly) definable over $K^{\delta_x}$, $a_{1}, a_{2}$.
\newline
(ii) For any $c\in H_{a_{1},a_{2}}$, right multiplication by $c$ gives a bijection between ${\mathcal Y}_{a_{1}}$ and ${\mathcal Y}_{a_{2}}$.
\newline
(iii) For $a\in {\mathcal O}$, $H_{a}$ (which is by definition $H_{a,a}$) is a $\delta_t$-algebraic subgroup of $GL(n,\mathcal U^{\delta_x})$, and is the ``usual" Galois group of \eqref{lineareq}. For any $b\in {\mathcal Y}$, $bH_{a} = {\mathcal Y}_{a} = H^{+}b$, so in particular $bH_{a}b^{-1} = H^{+}$.
\newline
(iv) For $a\in {\mathcal O}$, and any $b\in {\mathcal Y}_{a}$, the map taking $\sigma$ to $b^{-1}\sigma(b)$ is an isomorphism of groups between $Aut({\mathcal Y}/K\langle\mathcal U^{\delta_x}\rangle)$ and $H_{a}$.
\newline
(v) $H_{a_{1},a_{2}}\cdot H_{a_{2},a_{3}} = H_{a_{1},a_{3}}$. In particular $H_{a_{1},a_{2}}$ is a right coset (left torsor) of $H_{a_{1}}$ and a left coset (right torsor) of $H_{a_{2}}$.
\end{lemma}
\begin{proof}
(i) is Fact 5.6.
\newline
(ii) follows from (*).
\newline
(iii) $H_{a}$ is clearly closed under inverses and and by (*) the product of two elements in $H_{a}$ has the form $b_{1}b_{2}^{-1}b_{2}b_{3}^{-1} = b_{1}b_{3}^{-1} \in H_{a}$ (where $b_{1}, b_{2}, b_{3}\in H_{a}$).
Now $H_{a}$ is a subgroup of $GL(n,\mathcal U^{\delta_x})$ and is definable over $K$ in $(\mathcal U,\delta_x,\delta_t)$. As $(\mathcal U^{\delta_x},\delta_t)$ with the induced structure from $(\mathcal U,\delta_x,\delta_t)$ is just a $\delta_t$-differentially closed field, and the definable closure of $K^{\delta_x}$ in
$\mathcal U^{\delta_x}$ is $K^{\delta_x}$, we obtain the first sentence of (iii). The rest is a simple computation using the definitition of $H^{+}$ as well as Fact 5.4 (that all elements of ${\mathcal Y}_{a}$ have the same type over $K\langle\mathcal U^{\delta_x}\rangle$).
\newline
Both (iv) and (v) are routine (and well-known).
\end{proof}
The Galois groupoid attached to \eqref{lineareq} has ${\mathcal O}$ as its set of objects, and for $a_{1}, a_{2}\in {\mathcal O}$, $Mor(a_{1},a_{2})$ is precisely $H_{a_{1}, a_{2}}$. Composition of morphisms is just multiplication in $GL(n,\mathcal U^{\delta_x})$. We call this groupoid ${\mathcal G}$. We see from Lemma 5.7 that:
\begin{lemma} ${\mathcal G}$ is (quantifier-free) definable over $K^{\delta_x}$ in the $\delta_t$-differentially closed field $(\mathcal U^{\delta_x},\delta_t)$. It is moreover connected (namely for each $a_{1}, a_{2}\in {\mathcal O}$, $Mor(a_{1},a_{2}) \neq \emptyset$).
\end{lemma}
Now for any $\delta_t$-differential field $(L,\delta_t)$ (e.g. differential subfield of $(\mathcal U^{\delta_x}, \delta_t)$) containing $K^{\delta_x}$, we can, by Lemma 5.8, consider the groupoid ${\mathcal G}(L)$, the set of objects ${\mathcal O}(L)$ being the interpretation in $L$ of the quantifier-free over $K^{\delta_x}$-formula which defines ${\mathcal O}$ in $(U^{\delta_x}, \delta_t)$, and likewise for $H_{a_{1},a_{2}}(L)$ for $a_{1}, a_{2}\in {\mathcal O}(L)$ (which now may be empty). Nevertheless it is easy to see that ${\mathcal G}(L)$ is a groupoid, although possibly has more than one connected component.
\begin{lemma} The set of PPV extensions of $K$ (up to isomorphism over $K$ as $\Pi$-fields) for the equation \eqref{lineareq} is parameterized by, or in natural one-one correspondence with, the set of connected components of the groupoid ${\mathcal G}(K^{\delta_x})$.
\end{lemma}
\begin{proof} Every PPV extension of $K$ for \eqref{lineareq} is generated over $K$ by some $b\in {\mathcal Y}$ and clearly $f(b)\in {\mathcal O}(K^{\delta_x})$. And conversely if $b\in {\mathcal Y}$ and $f(b)\in {\mathcal O}(K^{\delta_x})$ then by Fact 5.4, $K\langle b\rangle$ is a PPV extension of $K$.
Now suppose that $b_{1}, b_{2}\in {\mathcal Y}$, $f(b_{i})\in {\mathcal O}(K^{\delta_x})$, and that $K\langle b_{1}\rangle$ and $K\langle b_{2}\rangle$ are isomorphic over $K$ as $\Pi$-fields.. After applying an automorphism of $(\mathcal U,\Pi)$ which fixes pointwise $K$ (so fixes pointwise ${\mathcal G}(K^{\delta_x})$) we may assume that $K\langle b_{1}\rangle = K\langle b_{2}\rangle = L$ say.
So working in $GL(n,\mathcal U)$, $b_{2}^{-1}b_{1}\in GL(n,L^{\delta_x}) = GL(n,K^{\delta_x})$, whereby $Mor(a_{1},a_{2})$ in ${\mathcal G}(K^{\delta_x})$ is nonempty.
Conversely, suppose that $f(b_{i}) = a_{i}\in {\mathcal O}(K^{\delta_x})$ for $i=1,2$ and $Mor(a_{1},a_{2})$ is nonempty in ${\mathcal G}(K^{\delta_x})$. So there exist $b_{i}' \in {\mathcal Y}_{a_{i}}$, such that $b_{2}'^{-1}b_{1}'\in GL(n,K^{\delta_x})$. Then $K\langle b_{1}'\rangle = K\langle b_{2}'\rangle$.
But by Fact 5.4, $b_{1}$ and $b_{1}'$ have the same type over $K$, whence there is an isomorphism over $K$ between $K\langle b_{1}\rangle$ and $K\langle b_{1}'\rangle$. Likewise there is an isomorphism over $K$ between $K\langle b_{2}\rangle$ and $K\langle b_{2}'\rangle$. Hence $K\langle b_{1}\rangle$ and $K\langle b_{2}\rangle$ are isomorphic over $K$. This concludes the proof.
\end{proof}
\vspace{2mm}
\noindent
(IV') (Differential Galois cohomology.) We are in the above situation of \eqref{lineareq} and its Galois groupoid $\mathcal G$, definable over $K^{\delta_x}$ in $(\mathcal U^{\delta_x}, \delta_t)$.
\begin{lemma} Assume that $(K^{\delta_x},\delta_t)$ is differentially large, and that $K^{\delta_x}$ is bounded as a field. Then ${\mathcal G}(K^{\delta_x})$ has finitely many connected components.
\end{lemma}
\begin{proof} We may assume that ${\mathcal O}(K^{\delta_x}) \neq \emptyset$. So fix $a\in {\mathcal O}(K^{\delta_x})$, and consider $H_{a}$, a $\delta_t$-algebraic subgroup of $GL(n,\mathcal U^{\delta_x})$ defined over $K^{\delta_x}$.
The Claim in Corollary 5.3 of \cite{KP} goes through with no change, showing that for $b,c\in {\mathcal O}(K^{\delta_x})$, $Mor(a,b)$ and $Mor(a,c)$ are isomorphic over $K^{\delta_x}$, as left torsors for $H_{a}$ in the category of $\delta_t$-algebraic varieties, if and only if $Mor(b,c)(K^{\delta_x})$ is nonempty. This gives an embedding of the set of connected components of ${\mathcal G}(K^{\delta_x})$ into $H^{1}_{\delta_t}(K^{\delta_x}, H_a)$ (where $K^{\delta_x}$ is considered as a $\delta_t$-field, and $H_{a}$ as a $\delta_t$-algebraic group over $K^{\delta_x}$). So we conclude by Theorem 4.1.
\end{proof}
\vspace{2mm}
\noindent
(V') (End of proof of Theorem 5.1.) We go back to the interpretation $\omega$ of $Th(\mathcal U^{\delta_x}, {\mathcal Y})$ (with all induced structure from sets definable over $K$ in $(\mathcal U,\Pi)$), in $Th(\mathcal U, \delta_t)$, using the precise formalism in (I)'. Remember this gave $(\mathcal U^{\delta_x}, {\mathcal Y})$ as an elementary substructure of $(\mathcal U, GL(n,\mathcal U))$ in the common language we called $L_{\Pi,K}$.
Let $f:{\mathcal Y} \to {\mathcal O}$ be as given in (II)'. As remarked earlier ${\mathcal O}(\mathcal U) = \omega({\mathcal O})$. Let $F = \omega(f)$ which is a map from $GL(n,\mathcal U)$ to ${\mathcal O}(\mathcal U)$, which we know to be $K$-definable in the differentially closed field $(\mathcal U, \delta_t)$.
Again we write $X_{a}$ for $F^{-1}(a)$, where $a\in {\mathcal O}(\mathcal U)$.
Recall that $H^{+}$ (the intrinsic Galois group of \eqref{lineareq}) is a $\Pi$-definable subgroup of $GL(n,\mathcal U)$, and we now let $H$ denote the $\delta_t$-Kolchin closure of $H^{+}$, namely the smallest $\delta_t$-definable subgroup of $GL(n,\mathcal U)$ containing $H^{+}$ (which exists by $\omega$-stability of $Th(\mathcal U,\delta_t)$).
We write ${\mathcal G}(\mathcal U)$ for $\omega({\mathcal G})$ which makes sense functorially. We write $Mor(\mathcal U)$ for $\omega(Mor)$. And we record the analogous facts about the interpretation $\omega$, to what was said earlier in (V).
\begin{lemma}
(i) Let $h:{\mathcal Y}\times {\mathcal Y} \to GL(n,\mathcal U^{\delta_x})$ be $h(x,y) = x^{-1}y$. Then it is the same for $\omega(h): GL(n,\mathcal U)\times GL(n,\mathcal U) \to GL(n,\mathcal U)$.
\newline
(ii) The family of $X_{a}$ for $a\in {\mathcal O}(\mathcal U)$ is precisely the family of right cosets of $H$ in $GL(n,\mathcal U)$. So ${\mathcal O}(\mathcal U)$ identifies with $G/H$.
\newline
(iii) Let $a\in {\mathcal O}(K^{\delta_x})$. Then $X_{a}$ is $K$-irreducible as a $\delta_t$-algebraic set defined over $K$. Moreover the PPV extension of $K$ corresponding to $a$ (given by Fact 5.4) is precisely the $\delta_t$-function field of $X_{a}$ over $K$, $K\langle X_{a}\rangle$, namely the $\delta_t$-subfield of $(\mathcal U,\delta_t)$ generated over $K$ by a generic point of $X_{a}$.
\newline
(iv) For $a_{1}, a_{2}\in {\mathcal O}(\mathcal U)$, $Mor(\mathcal U)(a_{1},a_{2}) = \{b_{1}^{-1}b_{2}: b_{1}\in X_{a_{1}}, b_{2}\in X_{a_{2}}\}$.
\end{lemma}
\begin{proof} (i) ${\mathcal Y}$ is the set of sharp points of a parameterized $D$-variety structure $s$ on $GL(n,\mathcal U)$ over $K$. Hence we can find $b_{1}, b_{2} \in {\mathcal Y}$ which are
$\delta_{t}$-generic and independent over $K$ in $GL(n,\mathcal U)$. Then $b_{1}^{-1}b_{2}\in GL(n,\mathcal U^{\delta_x})$, and we see that if $Z$ is the graph of the map taking $(x,y)\in GL(n,\mathcal U)\times GL(n,\mathcal U)$ to
$x^{-1}y\in GL(n,\mathcal U)$, then $Z\cap ({\mathcal Y}\times {\mathcal Y} \times GL(n,\mathcal U^{\delta_x}))$ is $\delta_t$-Kolchin dense in $Z$, which yields that $Z = \omega(graph(h))$ as required.
\newline
(ii) Fix $b\in {\mathcal Y}$. Let $h_{b}:{\mathcal Y} \to GL(n,\mathcal U^{\delta_x})$ be left multiplication by $b^{-1}$. Then by part (i), $\omega(h_{b})$ is left multiplication by $b^{-1}$ from $GL(n,
\mathcal U)$ to $GL(n,\mathcal U)$. Let $f_{1}$ be the composition $f\circ h_{b}^{-1}: GL(n,\mathcal U^{\delta_x}) \to {\mathcal O}$. By Lemma 5.3, $F_{1} :=\omega(f_{1}) = F\circ \omega(h_{b}^{-1}):GL(n,\mathcal U) \to {\mathcal O}(\mathcal U)$.
Let $a=f(b)\in {\mathcal O}(\mathcal U^{\delta_x})$. Then the fibres of $f_{1}$ are the right cosets of $H_{a}$. All of this being definable in the differentially closed field $(\mathcal U^{\delta_x}, \delta_t)$, the fibres of $F_{1}$ are the right cosets of $H_{a}(\mathcal U)$. Hence the fibres of $F$ are the right cosets of $bH_{a}(\mathcal U)b^{-1}$. By Lemma 5.7 (iii), $bH_{a}b^{-1} = H^{+}$. Taking $\delta_t$- Kolchin closures, we obtain that $bH_{a}(\mathcal U)b^{-1} = H$, as required.
\newline
(iii) Let $a\in {\mathcal O}(K^{\delta_x})$, and let $b\in {\mathcal Y}_{a}$. From the proof of (ii), $X_{a} = F^{-1}(a) = Hb$ which is the $\delta_t$-Kolchin closure of $H^{+}b = {\mathcal Y}_{a}$ (see Lemma 5.7 (iii)). So $X_{a}$ is the Kolchin closure of ${\mathcal Y}_{a}$. Now all elements of ${\mathcal Y}_{a}$ have the same type over $K$ (in $(\mathcal U,\Pi)$), see Fact 5.4, which implies that $X_{a}$ is $K$-irreducible, as a $\delta_t$-algebraic variety (over $K$). Hence $b$ is the generic point of $X_{a}$ over $K$ as a $\delta_t$-variety, and the $\delta_t$-function field of $X_{a}$ over $K$ is precisely $K\langle b\rangle_{\delta_t}$ the $\delta_{t}$-field generated by $K$ and $b$. As $b$ is a solution of \eqref{lineareq}, we see that $K\langle b\rangle_{\delta_t} = K\langle b\rangle_{\Pi} =K\langle b\rangle$ (with earlier notation).
\newline
(iv) In the $L_{\Pi,K}$-structure $(\mathcal U^{\delta_x}, {\mathcal Y})$ the following holds: for all $a_{1},a_{2}\in {\mathcal O}$, $Mor(a_{1},a_{2}) = \{b_{1}^{-1}b_{2}: b_{1}\in f^{-1}(a_{1}), b_{2}\in f^{-1}(a_{2})\}$. Applying the interpretation $\omega$, Fact 5.4, and parts (i) and (ii) gives the required conclusion.
\end{proof}
\vspace{2mm}
\noindent
We now finish the proof of Theorem 5.1. We are assuming that $(K^{\delta_x}, \delta_{t})$ is existentially closed in $(K,\delta_t)$, that $K^{\delta_x}$ is bounded as a field, and that $(K^{\delta_x}, \delta_t)$ is differentially large (in the sense of \cite{LSTressl2018}). First:
\begin{lemma} There is $a\in {\mathcal O}(K^{\delta_x})$ such that the $\delta_t$-variety $X_{a}$ has a point in some elementary extension $(K_{1},\delta_t)$ of $(K^{\delta_x}, \delta_t)$ which contains (extends) $(K, \delta_t)$.
\end{lemma}
\begin{proof} By Corollary 5.5, ${\mathcal O}(K^{\delta_x})$ is nonempty, giving rise to a PPV extension of $K$, but we need more.
Considering $F:GL(n,\mathcal U) \to {\mathcal O}(\mathcal U)$, let $a' = F(e)$ where $e$ is the identity of $GL(n,\mathcal U)$, So $a'\in {\mathcal O}(K)$. By 5.11 (ii), $X_{a'} = H$. As $(K^{\delta_x}, \delta_t)$ is e.c. in $(K,\delta_t)$ there is, on general grounds, an elementary extension $(K_{1},\delta_t)$ of $(K^{\delta_x},\delta_t)$ which contains $(K,\delta_t)$, and we may assume that $(K_{1},\delta_t)$ is also a differential subfield of $(\mathcal U,\delta_t)$. Now ${\mathcal G}(K^{\delta_x})$ has only finitely many connected components, by Lemma 5.10. Hence, as $(K_{1},\delta_t)$ is an elementary extension of $(K^{\delta_x},\delta_t)$, there is $a\in {\mathcal O}(K^{\delta_x})$ such that $Mor(a,a')(K_{1})$ is nonempty. Now $X_{a'}(K_{1})$ is nonempty as it contains the identity of $H$. Hence $X_{a}(K_{1})$ is nonempty, finishing the proof of the lemma.
\end{proof}
Let $a$ and $K_{1}$ be as in Lemma 5.12. $X_{a}$ is a right coset of $H$, which is $K$-irreducible (as a $\delta_t$-algebraic variety over $K$). Let $Z$ be a $K_{1}$-irreducible component of $X_{a}$ which has a $K_{1}$-point. Then $Z$ is a coset of the connected component $H^{0}$ of the $\delta_t$-algebraic group $H$.
Consider the $\delta_t$-function field $K_{1}\langle Z\rangle_{\delta_t}$. Now general model-theoretic considerations imply that this $K_{1}\langle Z\rangle_{\delta_t}$ is the function field of a coset $C$ of a proalgebraic group over $K_{1}$ such that $C$ has a $K_{1}$-rational point. As $K^{\delta_x}$ is large as a field, so is $K_{1}$, whereby $K_{1}$ is existentially closed in $K_{1}\langle Z\rangle_{\delta_t}$ as fields. As $(K^{\delta_x}, \delta_t)$ is differentially large, so is $(K_{1},\delta_t)$ which implies that $K_{1}$ is existentially closed in $K_{1}\langle Z\rangle_{\delta_t}$, as $\delta_t$-fields. As $K^{\delta_x}$ is an elementary substructure of $K_{1}$, as $\delta_t$-fields, it follows that $K^{\delta_x}$ is existentially closed in $K_{1}\langle Z\rangle_{\delta_t}$ as $\delta_t$-fields.
Finally, as the embedding of $K$ in $K_{1}$ extends to an embedding of $K\langle X_{a}\rangle_{\delta_t}$ in $K_{1}\langle Z\rangle_{\delta_t}$ as $\delta_t$-fields, it follows that $K^{\delta_x}$ is existentially closed in $K\langle X_{a}\rangle_{\delta_t}$ as $\delta_t$-fields. As we know from Lemma 5.11 (iii) that $K\langle X_{a}\rangle_{\delta_t}$ is a PPV extension of $K$ for \eqref{lineareq}, we are finished with the proof of Theorem 5.1.
\vspace{5mm}
\noindent
As mentioned in Remark 2.9 (2), Theorem 5.1 applies to the situation where $T$ is a model complete theory of bounded large fields (in the language of unitary rings), and $(K^{\delta_x},\delta_t)$ is a model of the model companion of $T\cup\{\delta_t$ is a derivation\} (in the language of differential unitary rings). When $T$ is the theory of real closed fields, this model companion coincides with Singer's theory $CODF$ of closed ordered differential fields \cite{Singer1978} after adding a symbol for the unique ordering.
\begin{corollary} Suppose $(K,\delta_x,\delta_t)$ is a field with commuting derivations $\delta_x, \delta_t$. Suppose that $K$ is formally real, and that $(K^{\delta_x},\delta_t)$ is a ``closed ordered differential field" (i.e. a model of CODF). Then, for any parameterized linear DE $\delta_x(Z) = AZ$ over $K$ (as in \eqref{lineareq}) there is a PPV extension $(L,\delta_x,\delta_t)$ for the equation such that $L$ is formally real.
\end{corollary}
\begin{proof}
As $(K,\delta_t)$ is a formally real differential field and $(K^{\delta_x},\delta_t)$ is a model of CODF, we see that $(K^{\delta_x},\delta_t)$ is existentially closed in $(K,\delta_t)$ as $\delta_t$-fields.
Apply Theorem 5.1 to find a PPV extension $(L,\delta_x,\delta_t)$ such that $(K^{\delta_x},\delta_t)$ is existentially closed in $(L,\delta_t)$. It follows that $L$ must be formally real.
\end{proof}
Another example is when the theory $T$ is the theory of $p$-adically closed fields of rank $d$. In this case the model companion of $T\cup \{\delta_t$ is a derivation\} is the theory of closed $p$-adic differential fields of rank $d$ introduced by Tressl in \cite{Tressl}. Similar to the above corollary we have:
\begin{corollary} Suppose $(K,\delta_x,\delta_t)$ is a field with commuting derivations $\delta_x, \delta_t$. Suppose that $K$ is a $p$-adic field of rank $d$, and that $(K^{\delta_x},\delta_t)$ is a ``closed $p$-adic differential field of rank $d$". Then, for any parameterized linear DE $\delta_x(Z) = AZ$ over $K$ (as in \eqref{lineareq}) there is a PPV extension $(L,\delta_x,\delta_t)$ for the equation such that $L$ is a $p$-adic field of rank $d$.
\end{corollary}
These two corollaries are parameterized versions of the main result of \cite{CHvdP}.
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Q: Solving 80-20-20 triangle problem I am trying to understand the solution of 80-20-20 triangle problem as stated here http://www.cut-the-knot.org/triangle/80-80-20/Classical4.shtml#Knop
One thing I cannot get understand from the solution is how BP = CD. Pointers on this is appreciated. The rest of the solution is fine.
A: You know that $\angle CBD = 50$ degrees and $\angle ACB = 80$ degrees, so that gives you $\angle BDC=50$ degrees.From this, you know that $\triangle BCD$ is isosceles, so $BC=CD$ and hence $BP=CD$. Then, $P$ is constructed as the third vertex of an equilateral triangle with base $BC$, so $BP=BC$ and so $BP=BC=BD$.
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The Power of New Energy
World Stage for Sustainable Technologies & Innovations
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BELOW (FOR SAMPLE PURPOSES ONLY) IS A LIST OF PAST WGES SPEAKERS - PLEASE CONTACT WGES (event@wges.us) FOR MORE INFORMATION
The WGES Host Ambassadors, Co-Hosts & Partners Proudly Announce Invited
Master Class Lecturers & Session Speakers
U.S. Federal Government, District of Columbia,
Global & U.S. Industry Leaders
"Latest Programs, Policies, Advancements & Opportunities"
Dan Utech is the Deputy Assistant to the President for Energy and Climate Change
Dan Utech is the Deputy Assistant to the President for Energy and Climate Change. Prior to joining the White House, Dan served as a Senior Advisor to Energy Secretary Steven Chu. He joined the Administration after 10 years in the Senate, where he worked on a wide range of energy and environmental policy issues.
Kevin Kampschroer, Deputy Senior Sustainability Official, U.S. General Services Administration, Federal Director, Office of Federal High-Performance Green Buildings - Master Class (confirmed)
Kevin Kampschroer has worked for GSA for more than 39 years and is a graduate of Yale University. He manages the government's implementation of a comprehensive improvement in the training and certification of facility managers and personnel across the entire Federal government. Mr. Kampschroer was the Project Manager for the Ronald Reagan Building & International Trade Center, and he has lectured at various universities such as MIT, Harvard, Georgia Tech, and Yale. His most recent publication as a contributing author is the first medical study showing the link between building characteristics on office worker stress and heart function-which showed the beneficial results of good lighting, natural light and IEQ. He has created the framework for which GSA responds to the challenges of greenhouse gas emissions reductions and of the American Recovery and Reinvestment Act's mandate to move GSA's Federal building inventory toward high-performance green buildings.
Tommy Wells, Acting Director of the District Department of Environment (DDOE) (confirmed)
Mr. Wells is chiefly responsible for protecting the environment and conserving the natural resources of the District of Columbia. His team is comprised of approximately 300 environmental professionals collectively working to improve the quality of life for residents and the natural inhabitants of the Nation's Capital. Mr. Wells career in public service spans 32 years. He earned his law degree from the Columbus School of Law at Catholic University and a master's degree in social work from the University of Minnesota.
DDOE is comprised of several agencies; The Energy Administration (EA) is a single resource for energy efficiency and renewable energy programs, products and services for residential, commercial, institutional, and government sectors in the District of Columbia. The EA develops energy-related policies and plans, and coordinates and facilitates the overall effort of the District Government to achieve reliable, clean and affordable energy. The Environmental Services Administration (ESA) protects public health and the environment in areas related to air quality, hazardous waste, lead, pesticides, and underground storage of petroleum products. The Natural Resources Administration's (NRA) core function is to conserve, protect, and improve the soil, water, and living resources of the District of Columbia, and to protect its aquatic resources from pollution and degradation.
Dr. Sonny Ramaswamy, director of the National Institute of Food and Agriculture (NIFA), United States Department of Agriculture (confirmed)
Dr. Sonny Ramaswamy was appointed by President Barack Obama
to serve as director of the National Institute of Food and
Agriculture (NIFA), United States Department of Agriculture. NIFA
provides funding to catalyze transformative discoveries, education,
and engagement to solve societal challenges.
Prior to starting at NIFA on May 7, 2012, Dr. Ramaswamy held a
number of academic positions, including: dean of Oregon State's
College of Agricultural Sciences; director of Purdue's Agricultural
Research Programs; university distinguished professor and head of
Kansas State's Entomology Department; and professor of
entomology at Mississippi State.
Sonny has been a successful scientist, educator, and administrator. He has received research
grants from many federal agencies, including NIFA, NSF, NIH, EPA, and USAID, as well as from
state agencies, commodity groups, and industry for his research in the area of integrative
reproductive biology of insects. He has published over 150 journal articles, book chapters, and a
book. He is an award-winning teacher, and has mentored a number of high school,
undergraduate, graduate, and post-doctoral students. He has received a number of awards and
honors, including being named Fellow of the American Association for the Advancement of
Science and Fellow of the Entomological Society of America.
Dr. Ramaswamy has had excellent success in capital campaigns and fund-raising to create
endowments for faculty professorships, student scholarships and fellowships, including creation
of the Leadership Academy at Oregon State University, support of research, extension, and
outreach, infrastructure improvements, construction of new facilities for research, education,
and outreach, including the Kansas State University Insect Zoo.
Dr. Ramaswamy received his Bachelor of Science degree in agriculture and Master of Science
degree in entomology from the University of Agricultural Sciences, Bangalore, India. His
doctorate is in entomology from Rutgers University. He is also a graduate of Harvard
University's Management Development Program.
Dr. Sonny Ramaswamy was appointed by President Barack Obama to serve as director of the National Institute of Food and Agriculture (NIFA), United States Department of Agriculture. NIFA provides funding to catalyze transformative discoveries, education, and engagement to solve societal challenges. Prior to starting at NIFA on May 7, 2012, Dr. Ramaswamy held a number of academic positions, including: dean of Oregon State's College of Agricultural Sciences; director of Purdue's Agricultural Research Programs; university distinguished professor and head of Kansas State's Entomology Department; and professor of entomology at Mississippi State.
Sonny has been a successful scientist, educator, and administrator. He has received research grants from many federal agencies, including NIFA, NSF, NIH, EPA, and USAID, as well as from state agencies, commodity groups, and industry for his research in the area of integrative reproductive biology of insects. He has published over 150 journal articles, book chapters, and a book. He is an award-winning teacher, and has mentored a number of high school, undergraduate, graduate, and post-doctoral students. He has received a number of awards and honors, including being named Fellow of the American Association for the Advancement of Science and Fellow of the Entomological Society of America.
Dr. Sabine O'Hara,Dean of Urban Sustainability and Environmental Sciences University of D.C. (confirmed)
Dr. Sabine O'Hara is Dean and Director of Land Grant Programs for the College of Agriculture, Urban Sustainability and Environmental Sciences (CAUSES) of the University of the District of Columbia (UDC). As Dean of CAUSES, she is responsible for academic, research and community outreach programs in the tradition of landgrant universities, and is leading UDC's efforts to building a cutting edge model for urban agriculture that improves the quality of life and economic opportunity for urban populations. Dr. O'Hara is a respected author, researcher annd higher education executive, and is well known for her expertise in sustainable economic development, global education and executive leadership. She has experience in virtually every aspect of university administration including curriculum development, strategic planning, program accreditation, international partnerships and research collaborations.
Paul R. Puckorius, CEO and President of Puckorius & Associates, Inc. a Water & Waste Water Consulting Firm with corporate offices in Westminster Colorado (confirmed)
Paul R. Puckorius, has provided energy, water, and green water consulting to all major Industrial, commercial and institutional facilities all over the world since 1976. Over 50 years experience with water systems, including cooling water, boiler water, waste and process water. Principal expertise is in cooling water corrosion, scale and microbiological program development, problem solving, treatment selection, and system startup. Expertise in water use, reuse, root cause analysis, and water impact on water using equipment and water treatment requirements for utility power plants both fossil and nuclear, refineries, chemical plants, paper mills, tire plants, mining and ore refining, as well as HVAC air conditioning systems. Considerable practical knowledge and experience in identifying the potential for Legionnaires Disease and its control. Extensive knowledge of boiler water treatment programs as well as water pretreatment, potable water protection, use of reuse water, and water conservation.
Michael Jones-Bey - Director of Supplier Diversity Con Edison (confirmed)
Michael Jones-Bey
Michael Jones-Bey is Director of the Con Edison Supplier Diversity Program and is responsible for developing and implementing activities that increase contract opportunities for qualified Minority and Women-owned business enterprises (MWBEs) in ways that strategically support the company's mission and promote economic growth within the communities it serves.
Prior to joining Con Edison, Michael served as Executive Director of one of the nation's largest public sector supplier diversity programs, where he was responsible for revitalizing the New York State certification program, agency compliance, and business development initiatives. Targeted industry sector capacity building and market access programs resulted in hundreds of millions of dollars of additional contract opportunities for MWBEs in the construction, renewable energy, and information technology industries. New opportunities in
the financial services industry surpassed $1 billion. Michael also spearheaded the State's disparity study and worked on historic legislation to create one of the strongest MWBE laws in the nation. This legislation has made it possible for New York State agencies and authorities to more than double MWBE expenditures.
Michael Jones-Bey is Director of the Con Edison Supplier Diversity Program and
is responsible for developing and implementing activities that increase contract
opportunities for qualified Minority and Women-owned business enterprises
(MWBEs) in ways that strategically support the company's mission and promote
economic growth within the communities it serves.
Prior to joining Con Edison, Michael served as Executive Director of one of the
nation's largest public sector supplier diversity programs, where he was
responsible for revitalizing the New York State certification program, agency
compliance, and business development initiatives. Targeted industry sector
capacity building and market access programs resulted in hundreds of millions
of dollars of additional contract opportunities for MWBEs in the construction,
renewable energy, and information technology industries. New opportunities in
the financial services industry surpassed $1 billion. Michael also spearheaded
the State's disparity study and worked on historic legislation to create one of the
strongest MWBE laws in the nation. This legislation has made it possible for
New York State agencies and authorities to more than double MWBE
expenditures.
Mr. Ronald Uba (confirmed)
Ronald Uba has earned a BA in Physical Chemistry/ Psychology at the University of Colorado in Boulder and worked at U.S. Geological Survey Western Water Quality Radiation and Trace Mineral Toxin Research Labs. After a student internship at Columbine High School in Littleton, Colorado, Ron completed a Clean Water Irrigation Study at the U.S. DoC International Trade Administration. PetroIMAGE Corp had Ron encrypting Remote Satellite Images data for petroleum geo mapping for Mineral Exploration Research . Ron landed roles as an Assistant Principal and a AP Math, Science, and Computer Education Specialist for young TV Screen Actors. With an Instructional Technology Computer Statistics MS from the University of Southern California LA, Ron's 23 year career has evolved from his devotion of program development in community advocacy to cultivating business development technology training at the United Nations International School, KUMON USA & North America, PBS, Prudential, U.S. Census Bureau Census 2000 NY/NJ, and the Minority Business Development Agency/ USDOC to prepare Federal Government Contracting Opportunities for larger scale M/WBE's, NABE's, and SDVOB's. Ron provides strategic guidance to entrepreneurs on the Advisory Board of the Diversity Alliance for Science Pharmaceuticals & BioSciences Group and Miracles Corners of the World where they build villages and infrastructure for communities in Africa. Recipient of the Government Advocacy Award in 2006 for NY/NJ Minority Supplier Development Council's and the 2001 State of New Jersey Governor's Community Leadership Award, Ron continues to coordinate Matchmaker events for entrepreneurs, present and moderate public/ private partnership panels.
Ms. Virginia Gibson
With more than 20 years in the industry; Virginia Gibson President of Reliant Water Management, is one of only a handful of woman-owned companies in the entire Nation who are currently approved as federal contractors, in the water treatment, water reclamation & green energy category. Reliant Water Management is located in California and provides services in corrosion reduction, MIC testing & mitigation, control & remediation of waterborne pathogens, energy efficiency and sustainability programs, tower treatment, hot water boiler and steam treatment, non-chemical service providers, process water, filtration & softening to the Mining Industry, Ship / Marine & Water Pollution Control Plants working with local, state and federal agencies, on a national and international scale. Gibson is an expert in the industry, partnering with the U.S. EPA, U. S. NAVY, BAE, other agencies & organizations while overseeing the implementation of environmentally responsible products. She currently serves on The National Board of (AFE) The Association for Facilities Engineering and has served on the local non-profit boards of ASHRAE (American Society of Heating Refrigeration & Air-conditioning), RETA (Refrigerating Engineers & Technicians Assoc.), International Green Industry Hall of Fame, USGBC (United States Green Building Council).
WAYNE P. SAYA
WAYNE P. SAYA (confirmed)
Executive Director and former Chairman of the Board for the Association for Facilities Engineering
Wayne is a Certified Plant Engineer (CPE) and Department of Public Safety multi-license holder within Massachusetts, and currently moderates the AFE National Corporate Relations Council, and is a CPE and CPMM course instructor for AFE. As a member of the United Inventors Association, Wayne is a patented electronic design engineer and published author with over 30 years of all-around building operations, energy and facilities engineering experience.
Executive Chairman of the WGES Council
Professor Robert J. Gallagher
Professor Robert J. Gallagher serves as the Executive Chairman of the World Green Energy Symposium (WGES) Council. As a respected leader and educator, Professor Gallagher works in tandem with leading experts from education, government, industry and environment in the development of master lectures and speakers for the Symposium.
Professor Gallagher is a multi-faceted visionary, educator and senior advisor who has dedicated his entire career to education and public service. His background as an expert in health, economic development and sustainable programs has led to his engagement in working with top leaders and officials. He oversees the world energy sustainable programs which have earned a global footprint attracting top echelon of leaders in the industry while serving as a World Stage and platform of education and information exchange and as a vantage point for economic development and a healthier planet.
Professor Gallagher concurrently serves as a University Professor and Senior Advisor. He earned his Post Graduate Degrees from Adelphi University and his Bachelor's degree from Manhattan College. He has received numerous awards and recognitions during his longstanding career and holds several certifications.
WGES PAST PRESENTERS include;
Landon Van Dyke, U. S. State Department, Senior MA Executive Coordinator of Sustainability
Landon Van Dyke currently serves as the executive coordinator of sustainability at the U.S. Department of State. In this capacity, he oversees Department efforts to operate in an efficient and environmentally sustainable manner. Working both with U.S. and foreign missions, Mr. Van Dyke collaborates with the diplomatic community to promote best practices and to minimize its environmental footprint. Previously, he served at the White House Council on Environmental Quality as the Associate Director of International Affairs and Climate Change, where he was responsible for environmental and energy policy development and programs as they related to U.S. international relations. In addition, he has advised on several multilateral efforts, including the G20, APEC, S&ED and the WTO. Mr. Van Dyke holds several graduate degrees including an MA in Asian Studies and an MBA.
Dr. Leo S Mackay, Jr. Lockheed Martin - Vice President Ethics and Sustainability (confirmed)
Dr. Mackay is Corporate Vice President Ethics and Sustainability and an elected Officer of Lockheed Martin Corporation. He reports directly to the Chief Executive Officer and to the Ethics & Sustainability Committee of the Board of Directors. He oversees Lockheed Martin's award-winning ethics program; the corporation's compliance training/ procurement integrity/anti-corruption efforts; and as the Chief Sustainability Officer is responsible for ensuring responsible growth and global corporate citizenship. He is an independent director of Cognizant Technology Solutions Corporation, a $25B+ leading global provider of business and technology services. His previous assignments at Lockheed Martin have included: Vice President, Corporate Domestic Business Development (2007-2011) leading strategic customer relationship development; and management of Lockheed Martin's US field offices; President of ICGS, LLC (2005-2007) – a $1billion joint venture of Lockheed Martin and Northrop Grumman with simultaneous service as Lockheed Martin's Vice President/General Manager of Coast Guard Systems (CGS). CGS provided program management, systems integration, aircraft systems, C4ISR and integrated logistics for the U.S. Coast Guard's modernization.
Michael Wells, Partner and Vice President IBM (confirmed)
Michael F. Wells is a Partner and Vice President in IBM's Global Business Services (GBS) Organization. Specifically, he is responsible for IBM's Smarter Planet/Cities initiative. Michael is the IBM GBS World-Wide Leader for Smarter Buildings and Water. Additionally, he is responsible for Smarter Cities for North America (Public and Commercial Industries) and, lastly, leads the cross-brand Smarter Cities Federal Team. Michael and his team ensure that IBM's Services, Solutions and Strategies are aligned with customers in both the Public and Commercial Sectors.
Thomas Kakovitch, Professor of Environmental Science, Principal Kakovitch Industries.
Mr. Kakovitch is an accomplished professor, business leader, inventor and author in the field of environmental science and applied physics. He holds 26 national and international patents in areas as diverse as the energy efficiency of power plants, aerating water for use in fish production, improving the water quality of open water bodies, and improving the efficiency of shipping. This theoretical work includes the discoverer of an invariant scalar force field that he termed 'the fifth force' and that is currently being studied, and the invention of a new statistical model for four-quadrant analysis of economic production using the random motion of photons. In addition, he has developed more than ten university courses ranging from applied mathematics, to applied physics, and environmental science and technology. He conducted Post Master and Doctoral studies in Applied Mathematics, at American University, received an M.S. degree in Environmental Engineering/Civil Engineering from the University of Maryland, and a B.S. degree in Aerospace Engineering also from the University of Maryland. Kakovitch is fluent in English, Russian, French, Iranian (Farsi), and Afghan Assyrian (Aramaic) In addition to his service as a faculty member at the University of the District of Columbia, he founded Kakovitch Industries LLC, Flo-Vex LLC, and Millennium Technologies Inc., and is the Director of Applied Sciences and Technology of the McLean Project in McLean, Virginia".
Harry Wingo, President & CEO, DC Chamber of Commerce (confirmed)
Harry Wingo is the President & CEO of the DC Chamber of Commerce, a Veteran U.S. Navy SEAL Officer. He is a graduate of the U.S. Naval Academy and Yale Law School. Prior to the DC Chamber, he was Managing Partner of West River Solutions, a DC-based technology consulting firm focused on cybersecurity and also spent five years in Google's DC office, where he was Senior Policy Counsel and managed a program to hire military veterans. Mr. Wingo has served as Counsel to the U.S. Senate Commerce Committee, Special Counsel to the General Counsel of the Federal Communications Commission, held the position of Communications Law Associate at the firm of Skadden Arps, and was Judicial Clerk to the Hon. James Robertson, U.S. District Court for the District of Columbia. Mr. Wingo was born in Washington, DC, where he currently lives with his wife, Magistrate Judge Elizabeth Wingo and three daughters.
Advanced Manufacturing Office, U. S. Department of Energy (invited)
The Advanced Manufacturing Office (AMO) partners with industry, small business, universities, and other stakeholders to identify and invest in emerging technologies with the potential to create high-quality U.S. manufacturing jobs, enhance global competitiveness, and reduce energy use by encouraging a culture of continuous improvement in corporate energy management. EERE'S INVESTMENTS IN ADVANCED MANUFACTURING - R&D that has high impact, uses project diversity to spread risk, targets nationally important innovation at critical decision points, and contributes to quantifiable energy savings.
Mr. Samuel K. Burlum, CEO, Extreme Energy Solutions (confirmed)
As CEO/President of Extreme Energy Solutions, he worked with the New York City Taxi and Limo Commission in approving the SMART Emissions Reducer for use on all vehicles under their regulation. He developed a manufacturing plan, where the Company., would manufacture all of its products in the USA. Mr. Burlum currently is Vice President of SMART Air Fuel Saver LLC. (FL.). Mr. Burlum serves as Board Secretary for the non-profit Spirit of the Arts Foundation (501c3)(NJ), while also serving as a Director on Board for ESLC Inc. (NJ). He graduated from Berkeley College with an Associates Degree in Business Management & Entrepreneurship in 1998. He is an active participant in the Employer Legislative Committee, part of the Sussex County Chamber of Commerce.
(full bio)
Kristine M. Kingery, Director Army Sustainability Policy, Office of the Assistant Secretary of Army
(Installations, Energy and Environment) - Master Class (confirmed)
Ms. Kristine Kingery serves as the Director, Army Sustainability Policy, Office of the Deputy Assistant Secretary of the Army for Energy and Sustainability, with overall responsibility for Army-wide sustainability initiatives. She provides program oversight, strategic planning, policy recommendations, and establishes goals, objectives, and metrics for sustainability initiatives. She is responsible for the vertical and horizontal coordination of programs from installations to Headquarters, Department of the Army with full authority for management decisions related to program initiatives. She serves as subject matter expert on the Army's Net Zero Installations Initiative to develop the strategy, identify installations, and monitor progress towards achieving Net Zero Energy, Net Zero Water, and Net Zero Waste. Before joining the Army secretariat, Ms. Kingery served as the Chief, Cleanup Branch, Assistant Chief of Staff for Installation Management (ACSIM). She was responsible for oversight and leadership of the Army's environmental cleanup. Ms. Kingery completed her undergraduate studies at Texas A&M University as a Distinguished Military Graduate with a Bachelor of Science Degree in Chemistry and holds a Master of Applied Science in Environmental Engineering from the University of Delaware, and Master of Science Degree in National Resource Strategy from the National Defense University, Industrial College of the Armed Forces.
She is married to Colonel Michael Doherty, U.S. Army retired.
Ian Portnoy Phillips Lytle LLP
Ian has played a significant role in many high profile projects throughout the United States. Highlights among Ian's background are major economic development and infrastructure development and finance projects, including public/private joint ventures, in conjunction with airports and mass transit facilities throughout the U.S. and extensive work regarding public private partnerships involving privatization of facilities on military bases. These projects often involved extensive coordination with federal, state and local governmental authorities including having the local laws changed to accommodate the projects. Several of these projects also involved the development of energy generation facilities, including green energy.
Kaila Santiago - Global Energy Efficiency
Kaila Santiago is the Chief Operation Officer of Global Energy Efficiency, an energy services company delivery a comprehensive turnkey suite of energy efficiency products and services. Kaila has contributed to the company's success including recognition by the New York State Energy Research and Development Authority (NYSERDA) and Consolidated Edison as a top producer of energy savings. Kaila managed the over 2,000 project implemented for clients in the New York City Metropolitan Area. Kaila has helped grow the company into one of the most influential energy efficient advocates in NYC through her strategic partnerships with various utility and state programs. Kaila is a certified energy (CEM) through the Association of Energy Engineers (AEE) Her goal is to foster education on energy related issues incentive program participation in order to reduce fossil fuel dependence and have a significant impact on future generations.
Sven-Erik Prytz - HydroInfra Technologies, Stockholm Sweden (confirmed)
Sven-Erik Prytz, is the founder and strategy leader at the HydroInfra Technologies, Stockholm Sweden. The mind blowing innovative climate concept that the company represents has its base 40 years ago. The interest in energy development started during the early employment in Volvo Cars AB. Then in 1970-80 the general interest for new energy sources to cars were limited but Sven-Erik was keeping the active engagement in this area. Inspired by meeting with Nobel Prize winner in Chemistry 1986-Yuan T. Lee, his work became a friendly inspiration for developments to come. With this as a base Sven Erik states the company has an impressive formula for future energy handling and elimination of disturbing emissions in traditional Power Plants or Industries as well as turning this fuel climate neutral. Sven-Erik was part writer in a book regarding Africa and the future infrastructure. It is published in Italian soon to be translated and distributed in English. Todays work within HydroInfra technologies is based on years of experience and knowledge networking with extended laboratory and real world solutions
David Flynn - Phillip Lytle's Energy
Mr. Flynn is the Practice Team Leader for Phillips Lytle's Energy, Environment, Marcellus Shale, and Nanotechnology Practice Teams. With respect to environmental law, Mr. Flynn concentrates on brownfield redevelopment, regulatory compliance and remediation of complex contaminated sediment sites. He was involved in the first successful conversion of a former industrial brownfield into a modern manufacturing facility in New York State. In addition, Mr. Flynn advises clients on the development and regulation of energy projects before state and federal authorities. He also advises clients on the development and siting of renewable energy projects and licensing of hydropower projects, and Marcellus formation natural gas opportunities.
Phillips Lytle LLP and Mr. Flynn have been recognized by Chambers USA for excellence in environmental law.
Jan Fox, will serve as the 2015 WGES Celebrity Anchor Host of Ceremonies. Ms. Fox is the recipient of 4 Emmys. Although today she is an author and global speaker, while at WUSA TV9 in Washington DC she earned 3 Emmys and another for a talk show she hosted on ABC in Boston. She came from a small Indiana town, however, she says that somehow she ended up on TV, interviewing many celebrities and US Presidents – a life she never could have imagined. TV and the speaking stage are a far cry from her first jobs – sweeping out her uncle's old shoe repair. Her book GET YOURSELF on TV focus is on getting the producer's attention and exactly what to do to get yourself or our business to the studio. She holds a Masters' Degree from Lesley University.
Speakers and Sponsors - Previous WGES include:
Randy Solomon
Randall (Randy) is a Lead Program Engineer in the Energy Efficiency Group at the New York Power Authority (NYPA). He manages NYPA's distributed generation program and energy efficiency work for New York City Department of Correction (DOC). He is the project manager for a 15 MW cogeneration plant at DOC's Rikers Island correctional facility which is scheduled to be completed in 2014.
Before joining NYPA, Randy held engineering positions in the fields of aerospace and industrial products. He holds a Bachelor of Industrial Engineering from the Pennsylvania State University. He is a New York State Licensed Professional Engineer, a Certified Energy Manager, and a Project Management Professional. He is a member of the Association of Energy Engineers and Project Management Institute.
Mr. Kala Henry
Mr. Henry works in the Clean Energy Technology Group at the New York Power Authority as an R&TD Engineer. He is a Certified Energy Manager and a graduate of the City College of New York with Master and Bachelor of Engineering Degrees in Electrical Engineering. In his day to day operations at the New York Power Authority, Mr. Henry manages projects in the areas of energy storage, distributed generation, renewable energy and electric transportation. Prior to joining the Power Authority, Mr. Henry worked as a Junior Designer with Consolidated Edison Company of New York where he performed engineering analysis in support for the addition of new services to the NYC electric distribution gridral Energy Management.
Charles Barr
Charles Barr is a 25 year employee of the GSA Public Buildings Service. Currently, Charles is working as a Procurement Analyst in the Acquisition Management Division Policy and Compliance. His duties include pre- and post award contract review. Prepares and conducts monthly acquisition policy briefings. Prepares in-house training to assure new policies are implemented, and assist Contracts Specialist maintain skills levels. Advise acquisition staff on federal, GSA and PBS regulation and practices.
He began his career as a Buildings Management Trainee in the Boston Facility Support Center. As a trainee he served in the Building's Manger's Office in both Boston Field office as well as the Providence Rhode Island Field Office. Upon completion of the trainee program, he was assigned as Buildings Manager for the <?xml:namespace prefix = "st1" />Waltham Federal Center, Waltham Mass. He handled most of the field office major programs, such as mechanical maintenance, elevator maintenance janitorial, lease administration, reimbursable work authorization, and Small Purchases. His responsibilities covered Federal Buildings in Bridgeport, New Haven, Waterbury as well as Hartford. During this period, he earned a Real Property Administrators designation for the Buildings Owner's and Manager's Association.
Dr. Kevin T. Geiss
A member of the Senior Executive Service, is the Deputy Assistant Secretary of the Air Force for Energy, Office of the Assistant Secretary of the Air Force for Installations, Environment and Logistics, Washington, D.C. Dr. Geiss is responsible for providing oversight and direction for all matters pertaining to the formulation, review, and execution of plans, policies, programs, and budgets for the effective and efficient use of energy to support the global Air Force mission.
Wes Kennedy
Wes Kennedy is an application engineer for the Hybrid Energy Solutions group at SMA America, the U.S.-based subsidiary of solar inverter leader SMA Solar Technology AG, headquartered in Germany.
In this role, his project scope ranges from residential PV with battery back-up to MW-scale stand-alone microgrids, primarily in North America and the Caribbean. This includes design and installation work on the 53 kW solar PV array at the Zanmi Beni Home for Children, a safe haven for children in Haiti, built after the 2010 earthquake destroyed the hospital that housed them.
Kennedy, a Colorado resident, has nearly 20 years of experience in the solar industry. He began his career in 1996, when virtually all projects were built around batteries, with pioneering solar companies Jade Mountain and Real Goods. Kennedy went on to establish Colorado EPC firm Namaste Solar, manage engineering staff for Gro Solar, and provide engineering services for Abound Solar. His skill set includes engineering, design, training, education, installation, service, O&M, software modeling, sales, marketing and management.
Ms. Eleni Reed
Eleni Reed serves as Chief Greening Officer at the U.S. General Services Administration's Public Buildings Service (PBS).Eleni works with PBS business lines and regions to integrate sustainability practices in all aspects of real estate operations to increase the environmental performance of GSA's portfolio in support of the agency's sustainability plan. She also leads the agency's Green Proving Ground (GPG), a program that utilizes GSA's real estate portfolio to test and evaluate innovative building technologies and practices. The GPG program aims to drive innovation in environmental performance in federal buildings and help lead market transformation through deployment of new technologies. Prior to coming to GSA, Eleni was Director of Sustainability Strategies with Cushman and Wakefield. Her past public service includes working with the City of New York's Mayor's Office of Operations.
Sergio Fernandez De Cordova
Sergio is Co-Chairman of the World Energy Forum's Next Generation Energy Leaders, a board member of the United Nations Foundation's Global Entrepreneurs Council, an official delegate for the US Department of State's Global Entrepreneurship Program, Co-Chairman of the G8 Young Summit, a member of the Council of Underserved Communities for the US Small Business Administration, and he is Co-Chairman of the Young Leaders Board for the Global Center for Development and Democracy; a group made up of 20 past Presidents of Latin America. Sergio is also sits on the board and or advises over 10 media related companies, such as DELL EIR, Cross Commerce Media and others. He is graduate of Rutgers University. Sergio also completed an MIT Executive Program for 60 worldwide business leaders under the age of 40. He lives in New York City
Mr. Kenneth Adams
Kenneth Adams has served as President & CEO of Empire State Development and Commissioner of the New York State Department of Economic Development since February 2011. Empire State Development, or "ESD", is the economic development agency of New York State. Commissioner Adams and his colleagues manage a broad range of programs, incentives and services designed to increase private sector investment and job creation in New York. The organization has a staff of over 400 people located in 12 offices across the State.
Ms. Kelly Tyler
Economic Development and Community Outreach, Energy $mart Communities Program, EDGE Program, Manager of Buffalo Regional Office.
Mr. Robert McFarlane
McFarlane has more than 35 years of experience in communications consulting, including data center power and cooling, cable design, audio, video, telephony, computer communications, and acoustics. He majored in physics and engineering at Colorado State University, subsequently serving as Research Engineer in the Department of Hearing and Speech Science and lecturing on Psychoacoustics and Bio-acoustic Instrumentation at the graduate level. He has also taught telecommunications as a member of the adjunct faculty at NYU.
Mr. Jeremy Kingsley
Inspirational speaker and author Jeremy Kingsley is one of the most sought after speakers in the country. Since 1995 he has spoken to over 500,000 people at live events around the world. He has given over 2000 keynote speeches and his messages have reached millions through radio, television, and the Internet. He is a master storyteller and connects with audiences through the perfect blend of humor, inspiration, and relevant principles to help each individual. He believes that inspired people produce results and that people can change, grow, and fulfill their personal and professional dreams.
Mr. John C. Sheptor
Sheptor's business career spans diverse industries including agriculture, food ingredients, pharmaceuticals, automotive parts, chemicals, plastics, mining and healthcare. He is a leader of change building enterprise capacity through strategy, business process effectiveness and execution. Sheptor has developed and successfully launched many consumer products. He is an advocate for managerial systems including Lean Six Sigma and integrates their benefits into his organizations.
C.R. Herro
C.R. Herro is the President of the Board for the Energy and Environmental Building Alliance (EEBA), a national nan-profit focused on collaboration and education to manifest sustainable and responsible building principles. C.R. is also the Vice President of Environmental Affairs for Meritage Homes, the 7th largest home builder in the US. and leader in energy efficient building. C.R. earned a Bachelors of Science at Arizona State University in Physical and Life Science, a Masters in Environmental Science from Governors State, and a Doctorate in Environmental Engineering from Illinois Institute of Technology.
Mr. Edward S. Kowalewski
Currently serves as the Director of International Investments at Empire State Development's Strategic Business Division. Ed manages international investment operations out of Empire State Development's Buffalo-based office. He is formerly the Director of International Trade Programs for the New York. Ed has a proven record of success in effectively encouraging foreign firms to invest in New York State to create jobs. His broad based experience includes business development, strategic marketing, leadership and community/government relations. Ed previously has testified before the Congressional advisory US-China Economic and Security Commission. In addition to his 14 years of government experience, Ed has over 20 years of international business experience. Mr. Kowalewski's responsibilities have included technical/engineering assignments, international sales, business development, market entry strategies, strategic partnering, and contract management assignments. Mr. Kowalewski entered the international field by working in the private sector for large technology firm specializing in computer and communications systems design and systems engineering. Ed's international business experience includes 8 years in the Middle East Markets, 5 years in Asian markets and 5 years in European Markets. With 10 Years of active and reserve military service. Ed has had various assignments worldwide which developed international skills by requiring interactions with international diplomatic, military & corporate clients. His military career included being a senior technical instructor at the USAF Interceptor Weapons School, (Air Force version of TOP GUN).
Mr. Kowalewski has a Bachelors degree in Legal Studies and Masters in International Business. He also holds a diploma's from George Washington University Federal Contracting Program. He is an adjunct faculty member at the State University of NY at Buffalo and Niagara University teaching international business and strategy courses.
Mr. John P. Dienna, Jr.
Mr. DiEnna, the Executive Director & Founder of the Geothermal National & International Initiative (GEO-NII), is a business development and marketing professional with over forty years combined experience in the electric utility industry and the renewable energy industry. He is a nationally recognized authority on all aspects of renewable technology and specifically geothermal heat pumps (ghp), including marketing, creative financing, and the resulting positive economic and environmental impact that can be derived from the use of renewable technologies. His expertise is internationally acknowledged as a valued resource by not only the renewable & geothermal heat pump industry but also by government officials, both national and international, trade allies, and all major market segment associations in the promotion of renewable technologies.
Dr. William Acker, Executive Director, NY-BEST
Dr. William Acker is a well known and highly regarded scientist and entrepreneur in the field of Energy. He currently serves as the first Executive Director of NY-BEST, the New York Battery and Energy Storage Consortium. He is a serial entrepreneur who has been instrumental in the founding of several energy-related businesses, including Optiwind Corporation, MTI MicroFuel Cells, and Taconic Energy. Dr. Acker previously served as Vice President of Technology at Plug Power, Inc. and held managerial and scientific positions at Texaco Fuel and Lubricants Technology. He serves on the advisory board of the Center for Future Energy Systems at RPI and Cornell University and recently served as a commissioner to the NY Ready Commission by Governor Cuomo. He received a Ph.D, in Applied Physics and Engineering from Yale University and a B.S. in Physics from Rensselaer Polytechnic University.
Dr. Esther S. Takeuchi
Dr. Esther S. Takeuchi is a SUNY Distinguished Professor in the Departments of Materials Science and Engineering and Chemistry at Stony Brook University. She also has a joint appointment at Brookhaven National Laboratory as Chief Scientist in the Global and Regional Solutions Directorate. Prior to her academic appointment, she was employed at Greatbatch, Inc., where her achievements in lithium battery research, particularly on cells for implantable applications, led to a number of key technological developments, including the lithium/silver vanadium oxide (Li/SVO) battery, which powers the majority of implantable cardiac defibrillators (ICDs). A prolific inventor, she holds over 140 patents. Dr. Takeuchi received a bachelor's degree from the University of Pennsylvania with a double major in chemistry and history and completed a Ph.D. in chemistry at the Ohio State University.
Mr. William C. Anderson
William C. "Bill" Anderson serves as Strategic Development Executive for Eaton Corporation, based in Washington, DC. His duties encompass business and market development in the government sector, focused primarily on sustainability and energy. Most recently, he served as President and Chief Executive Officer of Anderson Global Innovation Group, Inc.; a firm that specialized in energy technology commercialization, environmental sustainability, defense, real estate asset optimization and business development, while also holding several senior advisory positions in organizations serving the defense, aerospace, sustainability and energy markets. He is a founding member/director of the ArchAngels of Washington, DC, a network of angel investors in the Mid Atlantic region. Previously, Anderson served as Assistant Secretary of the United States Air Force for Installations, Environment and Logistics, and the Air Force's Senior Energy Executive, based at the Pentagon in Washington, DC. As Assistant Secretary, he led an organization with responsibilities that included installations, military construction, base closure and realignment, environment, energy, safety and occupational health issues, and all logistical matters. Most notably, Anderson led Air Force efforts to test, certify and fly alternative aviation fuels, and to develop renewable electric generation facilities for U.S. military installations. For his efforts, Bill was presented the Decoration for Exceptional Civilian Service and the Presidential Award for Leadership in Federal Energy Management.
John Cerveny, Director of Resource Development, NY-BEST
At NY-BEST, John Cerveny facilitates connections between and among members, funding opportunities and the community at large. Cerveny's expertise lies in understanding emerging technologies and the benefits they provide in sufficient detail to then attract investment, talent and resources through a broad array of partnerships. As an engineer, he has the ability to understand technologies that enable products in the cleantech space. As an experienced entrepreneur, he has led successful efforts to transform startups and their promising technologies into profitable businesses with successful products.
Arlene White
Arlene White, is the former Executive Director of the Bi-national Alliance, a bi-national membership-based trade organization, and served as Business Development Officer, Southern Ontario for the Ministry of Tourism in Ontario Canada. For more than two decades she was with Scotiabank serving in a variety of Management positions in Executive Office and branches throughout Toronto and Southern Ontario.
White is currently the Principal of Cross-Border Business Exports, a consulting and training organization specializing in exports/imports between Canada and the U.S. as well as International trade into both countries. She and her partner, Maryann Stein, have more than 30 years experience in trade development and work closely with other trade professionals from across North America to deliver concierge business services and exceptional results
Maryann Stein
Maryann Stein is a proud veteran of the U.S. Army where she served as an Intelligence Analyst and received her M.S. in Global Business from Daemen College in Amherst NY. She is past president and board member of the Buffalo World Trade Association, former VP and board member of the Binational Alliance, assisted in the development of the 5 year strategic plan for the Buffalo CVB, and currently serves on the Advisory Board of the Women's Business Center at Canisius College in Buffalo and as VP of the International Weather Experience Center @ Buffalo.
Ms. Stein is the U.S. Partner of Cross-Border Business Experts, a consulting and training organization specializing in exports/imports between Canada and the U.S. as well as International trade into both countries. She and her partner, Arlene White, have more than 30 years experience in trade development and work closely with other trade professionals from across North America. Prior to starting this business, Ms. Stein was Director of International Programs at the Erie County Industrial Development Agency in Buffalo, NY. She was responsible for all aspects of global trade for businesses in Erie County, and assisted other counties with their international development needs. Programs she facilitated included Erie County's Foreign Trade Zones, partnerships with the Export-Import Bank of the U.S., and operating an innovative Worldwide Credit Reporting Service.
2013 WGES Invited Symposium Keynotes, Speakers and Moderators World Green Energy Symposium (please note: the bios below are cached and reflect the presenters organizations and positions they held at the time of their affiliation & presentation at the WGES)
Mr. Bill Toth
Director, Office of Motor Vehicle Management, GSA. Bill manages the largest fleet in existence today, that being the US Government.
Mr. Toth oversees GSA's Fleet and vehicle acquisition programs, which earn $2.6 billion annually in business volume. The GSA Fleet leasing program provides safe, reliable, low-cost leased vehicles and economical fleet management services to most Federal agencies. The program manages over 205,000 vehicles, providing non-tactical support to civilian and military customer agencies. GSA Fleet manages all aspects of a full service leasing program, including vehicle acquisition, maintenance and repair, and accident management. The GSA vehicle acquisition program acquires all non-tactical vehicles for Federal agencies, purchasing 55,000 vehicles annually. By consolidating all Federal agency requirements, this program is able to leverage the government's buying power to achieve significant discounts of 30 percent or more below manufacturer's invoice prices.
Bill has worked for the Federal government for 22 years and he brings a diverse background of management and operational experience, serving in various positions across the former Federal Supply Service (FSS) and in the Federal Acquisition Service (FAS). Bill previously served as the Director of the Planning and Performance Division in the Office of Strategic Business Planning and Process Improvement. Prior to this, he was the Director of the Service Contract Division in the FSS Office of Commercial Acquisition; and Chief of the Program Operations Branch in the Office of Transportation and Property Management.
Mr. Toth earned a bachelor's degree in finance from Towson University in 1990, and a master's degree in business administration in 2005 from Marymount University.
Mr. Greg Nadeau
Deputy Administrator Nadeau has focused significant attention on spearheading the development and administration of Every Day Counts (EDC) on behalf of Administrator Mendez since the Administrator launched his initiative in 2010. EDC is FHWA's Innovation Initiative which is designed to address shortening project delivery time and accelerate the rapid deployment of innovative technology using a state based model. Partnering with FHWA teams across the nation on the implementation of EDC are our state DOT and local partners, as well as stakeholders in the private and non-profit transportation sectors.
Mayor Vincent C. Gray
A native Washingtonian, Mayor Vincent Gray was sworn in as the sixth elected Mayor of the District of Columbia. In April of 2012, DC launched A Vision for a Sustainable D.C. The plan is an ambitious initiative to transform Washington D.C. into "the healthiest, greenest, most livable city" in the country by 2032. The plan was developed after seven months of community outreach and engagement. Mayor Gray stated "We will demonstrate how enhancing our natural and built environments, investing in a diverse clean economy, and reducing disparities among residents can create an educated, equitable and prosperous society."
Mr. Kevin Boshears
Director of the Department of Homeland Security's Office of Small and Disadvantaged Business Utilization (OSDBU) in May 2003. He is responsible for the overall implementation of the department's small business procurement program. Mr. Boshears was the Director of the Treasury Departments OSDBY since February 1999. He served in the same office as a procurement analyst since June 1995 and was responsible for providing guidance to the small business specialists located in the Treasury's twelve bureaus. Mr. Boshears brings a wealth of knowledge and experience in the procurement field, having served as a contracting officer for the Justice Department prior to his duties with the Treasury Department. Mr.Boshears is a well known instructor in the federal small business procurement arena.
Mr. Lanny Bates
Lanny Bates is Assistant Laboratory Director for Facilities & Operations (F&O) at the U.S. Department of Energy's Brookhaven National Laboratory. Named to that position in 2007, Mr. Bates oversees the directorate responsible for the operations, protection and modernization of the Laboratory's physical plant and Infrastructure, which includes more than 350 buildings on an almost 5,300-acre campus. He manages some 540 employees and an annual budget of approximately $100 million. At BNL, Mr. Bates initially completed a significant reorganization of his directorate, to focus more strategically on modernization of the lab along with better integrated operations and protective services. More recently he has led the implementation of Integrated Facility Management which is a best practice "landlord/tenant" approach to managing the Laboratory's facility portfolio. This has resulted in deployment of Directorate staff to geographic "complexes" to improve customer service, work control, and facility planning. Coming to Brookhaven Lab with 30 years of experience within the DOE laboratory system, Mr. Bates previously served as the Director of the Facilities Development Division at Oak Ridge National Laboratory (ORNL) in Tennessee, where he oversaw a $300-million, one-million-square-foot infrastructure modernization program. Bates also served as the Executive Vice President of University of Tennessee-Battelle Development Corporation, the not-for-profit established to facilitate private-sector investment in ORNL's modernization. Mr. Bates holds a 1975 B.S. in nuclear engineering from Mississippi State University and completed graduate courses in nuclear engineering at the University of Tennessee. He has been honored with the 1998 American Academy of Environmental Engineers Superior Achievement Award, the 1990 and 1998 Lockheed Martin Energy Systems Management Achievement Award, and the 2005 and 2007 ORNL Small Business Advocate Award.
Ms. Barbara Lang
Barbara Lang has been president and chief executive officer of the District of Columbia Chamber of Commerce since March 2002. She has complete responsibility for the operations and the strategic direction of the organization – the premier advocate of business in the District of Columbia. The Chamber is an approximate 1700+ member organization that advances the interests and prosperity of its members through advocacy, education, information and business development. Ms. Lang has transformed the organization into the most powerful and respected business group in the region through her aggressive leadership on key public policy business issues and by working diligently on education (Pre-K-12) and workforce development issues and projects, small business/entrepreneurial development initiatives like the Chamber's signature Executive leadership Development Program (ELDP). Her goal is to have the Chamber pave the way to make the District of Columbia "a better place to work, play, live and of course, do business". She has developed several initiatives that put the DC Chamber of Commerce on the leading edge of non-traditional programming and non-dues revenue generation. Under Ms. Lang's leadership, the DC Chamber of Commerce has been ranked the #1 Chamber of Commerce for six consecutive years by the Washington Business Journal, and has truly distinguished itself as the "Voice of Business in the District of Columbia".
Mr. Kurt E. Yeager
Mr. Kurt E.Yeager was named the 2003 Technology Policy Leader for Energy by Scientific American. He has authored more than 200 technical publications on energy and environmental topics. Yeager previously served as President of the Electric Power Research Institute (EPRI), during his time at EPRI he guided an industry-wide collaborative effort know as "The Electricity Technology Roadmap" and the "Electricity Sector Framework of the Future" which have since become the foundation of utility industry progress.
Before joining EPRI, Yeager was director of energy research and development planning for the Environmental Protection Agency's (EPA) Office of Research. Yeager served seven years, active duty in the U.S. Air Force and is a distinguished graduate of the Air Force Nuclear Research Officer's Program. Yeager is a fellow of the American Society of Mechanical Engineers and its Industry Advisory Board, trustee of the Committee for Economic Development, and served on the Energy Research Advisory Board to the Secretary of Energy. Yeager currently serves as Vice Chairman Galvin Electricity Initiative.
Ms. Michelle Desiderio
Michelle Desiderio leads the national green building certification program based on the ANSI-approved National Green Building Standard™ (ICC 700-2008). The program includes training and accreditation of Green Verifiers and certification of single family, multi-family, renovations, additions, and land development. As a related service to product manufacturers, the Green Approved Products program pre-approves certification points for products that meet green building practices.
James A. Momoh Ph.D.
James Momoh received a BSEE degree (1975) from Howard University, a MSEE degree (1976) from Carnegie Mellon University, a MS degree (1980) in Systems Engineering from the University of Pennsylvania and a Ph.D. degree (1983) in Electrical Engineering from Howard University. He was Chair of the Electrical Engineering Department at Howard University and Director of the Center for Energy Systems and Control. In 1987, Momoh received a National Science Foundation (NSF) Presidential Young Investigator Award. He was Program Director of the Power program in the Electrical and Communications Systems (ECS) Division at NSF from 2001-2004. Momoh is a Fellow at the Institute of Electronics and Electrical Engineering (IEEE) and a Distinguished Fellow at the Nigerian Society of Engineers (NSE). He was inducted as a Fellow Member of Nigerian Academy of Engineering (NAE) in 2004.
Mr. Ron Perry
President of the National 8(a) Association - President of Teya Technologies LLC. – 8(a) Certified Alaska Native Corporation
Ron Perry an Alaskan Native, is a nationally recognized expert in 8(a) and minority contracting to include; Mentor Protégé, JV, teaming, equity buyouts and national trends. With 25 years of federal business experience. Ron has years of experience navigating the ever continuing changes of government contracting to include; HUB Zone, Service Disabled Vet, and Women Owned businesses. Over the last 25 years Ron has help facilitate hundreds of meetings between both large and small businesses. You grow by enlarging your network and increasing your capabilities. Teya Technologies is a subsidiary of Salamatof Native Association located in Kenai Alaska. Teya Technologies was listed as the Alaska Native Corporation of the year 2006 by Northwest American Indian Development and National Center of American Indian Enterprise Development, Teya Technologies was named the 2012 Teaming Partner of the Year by American Express Open. Mr. Perry obtained his bachelors degree from Oregon State University and has attended 8(a) training through Loyola University and a pilot program between Howard University and the University of Alaska Anchorage.
Mr. Rich Zuccaro
Power Factor Program Manager for Staco Energy Products Company. Staco Energy Products Company manufactures voltage control, VAR compensation, uninterruptible power supplies and engineered power quality solutions. For more than 70 years, customers worldwide have relied on Staco as their dependable source for standard and tailored solutions to a wide range of electrical power problems. Headquartered in Dayton, Ohio, Staco Energy Products is a wholly owned subsidiary of Component Corporation of America, located in Dallas, Texas. Zuccaro is responsible for working with customers and reps to identify opportunities for cost savings due to power factor penalties and other electric utility billing tariff rates. In addition, he works with utilities to identify those which have incentives available to curb energy demand. Rich Zuccaro holds a BEE from Manhattan College and an MBA from the Rutgers Graduate School of Business. He has extensive experience in the power factor/capacitor industry. Prior to Staco Energy he was with GE.
Ms. Janice Bracey
Janice Bracey is the Director, for the Northeast and Caribbean's Regional Office of Small Business Utilization. In this position, Ms. Bracey manages and oversees GSA's Regional Small Business program; which includes making sure that Small Businesses participate in government contracting. During her 17 year tenure in this position, Ms. Bracey has counseled thousands of small business owners regarding possible contracting opportunities within GSA and the federal Government; as well as educating them on GSA procurement policies and methods. Ms. Bracey also conducted hundreds of presentations regarding doing business with GSA and the federal government. Ms. Bracey is also responsible for planning workshops, seminars and procurement conferences for small business participation. Ms. Bracey studied Business at New York City Technical College and Marymount Manhattan College in New York City, NY.
Mr. Richard J. Sobelsohn
Richard J. Sobelsohn is the Director of Lexis® Practice Advisor's Real Estate Content. Richard brings more than 14 years of legal experience to LexisNexis® in the area of real estate. When he began his legal career, Richard worked as a solo practitioner while at the same time running an adult business school specializing in real estate, insurance and accounting. He then went in-house as general counsel to a real estate development firm. After working in-house, Richard worked at the law firms Stroock, Stroock & Lavan, LLP, Kaye Scholer LLP, and Moses & Singer LLP, where he advised developers, corporations, financial institutions and individuals concerning a variety of real estate transactions including sustainable development, acquisitions, dispositions, financing, condominium offerings and leasing. Richard has extensive experience in negotiating, drafting and closing various types of real estate and business transactions. Richard earned his J.D. from Brooklyn Law School and his A.B. from Colgate University. He is currently an adjunct professor of law at Brooklyn Law School and New York Law School where he teaches Sustainable Building Law and Commercial Leasing. Richard is a LEED Accredited Professional and is an authority on the subject of sustainable development, a topic on which he speaks and writes extensively. Richard is a member of the New York, New Jersey, Connecticut, District of Columbia and United States Supreme Court Bars.
Mr. Lawrence Silverman
At the young age of 16, Lawrence Silverman was accepted into MIT where he majored in Physics and Computer Science/Cybernetics. Mr. Silverman currently serves as Chairman and Chief Scientist at Gridplex Networks, an advanced EnergySmart LED lighting company delivering energy conservation & sustainability solutions. He is a leading innovator in intelligent electronics & energy automation and holds numerous patents. Mr. Silverman conceived, developed, and manufactured technology which has made an impact worldwide. In 1972, he developed and patented THE FIRST ENERGY CONSERVATION AUTOMATION SYSTEM for digital lighting control. For the following three decades he continued to produce a series of advanced building automation, energy and lighting management and communications systems. He has also led co-development projects with Raytheon, EPRI, Oracle, IBM & others.
Mr. Silverman has spent most of the last decade focusing his talents on developing internet-based lighting, energy and smart grid automation technology utilizing advanced M2M communications and adaptive artificial intelligence techniques for utilities and energy consumers, to deliver mass-deployable user-friendly software, applications and system to conserve energy and water and create sustainable structures and communities worldwide.
Ms. Jill Clough-Johnston
Utilizing her many years of procurement experience, Jill Clough-Johnston has reached her current position of Small Business Liaison Officer (SBLO) at Brookhaven Science Associates/Brookhaven National Laboratory (BSA/BNL), where she manages the laboratories Small Business Program.BSA/BNL is one of ten national laboratories overseen and primarily funded by the Office of Science of the U.S. Department of Energy (DOE). BSA/BNL conducts research in the physical, biomedical, and environmental sciences, as well as in energy technologies and national security. In Jill's capacity as SBLO, she is responsible for all activities relating to BSA/BNL's prime contract with the DOE, as it pertains to the procurement of supplies and/or services from all types of small businesses. In 2009, as a result of Jill's efforts, BSA/BNL won the distinguished national Dwight D. Eisenhower Award for Excellence from the U. S. Small Business Administration. She received her B.S. in Business Administration from Adelphi University in Garden City, New York, in 1986.
Mr. George Davis
A professor emeritus at Rutgers University, where, for 10 years, he conducted the Spiritual Intelligence Action Research Project, focused on how to be spiritually intelligent in everyday life. The entire Green Movement has for him a spiritual basis that translates into action. He has been a journalist with The Washington Post and The New York Times. He is the author of 8 books including a new novel called The Melting Points. He blogs regularly for The Huffington Post, Psychology Today, and other popular blogging sites.
Ms. Megan McCluer
Ms. McCluer started her career as a civil engineer for her home town of Acton, Massachusetts. She returned to school to study aerospace engineering, and upon graduation became an aerodynamics engineer at NASA Ames Research Center in California where she worked for 12 years in rotorcraft research and wind tunnel testing. She then joined the Air Force Civilian ranks at Edwards Air Force Base where she was the Flight Test Manager for Development Test and Evaluation of the CV-22 tilt rotor aircraft. In 2005, following Hurricane Katrina, Ms. McCluer volunteered for a tour of duty in New Orleans to assist FEMA with Disaster Relief. This experience inspired her to transition to the energy sector and she became the Senior Engineering Program Manager at Clipper WindPower, Inc. in Santa Barbara, California. In 2008, Ms. McCluer returned to the Federal government by joining the Department of Energy (DOE) in the Office of Energy Efficiency and Renewable Energy in Washington DC. On February 1st, 2012, to leverage both her AF and DOE experience, she joined the Air Force Energy office (SAF/IEN). Ms. McCluer has an Associate's Degree in Civil Engineering from Franklin Institute of Boston, a Bachelor's degree in Aerospace Engineering from San Jose State University, and a Master's Degree in Aerospace Engineering from the University of Maryland, College Park.
Mr. Kevin V. G. Wells, Esq
Is both General Counsel and the Director of MBE Services for the New York & New Jersey Minority Supplier Development Council ("The Council") focusing on procurement concerns of multi-ethnic business enterprises (MBEs), which range from start-ups to companies with revenues over $1billion. As a practicing attorney with over 18 years with extensive Environmental and global corporate compliance experience, Mr. Wells now focuses on Sustainability practices of both CSR teams and innovative diverse small businesses by assisting them in both obtaining and facilitating procurement opportunities to create supply chain transparency without risk for the Fortune 500.
Mr. Frank Basile - National Anthem
Frank Basile, Basso-contante, has sung in some of the most prestigious houses and stages in the world. As a member of the United States Air Force Singing Sergeants in Washington D.C. he was one of America's musical ambassadors singing frequently at the White House and before foreign heads of State. He has sung with such opera companies as The Metropolitan Opera, Washington Opera, Baltimore Opera, Sarasota Opera, Nevada Opera, Utah Opera, Augsburg Opera and been a featured soloist with such distinguished orchestras as the National Symphony Orchestra, the New York Philharmonic, The Mormon Tabernacle Choir, and the Boston Pops. Mr Basile recently returned from Istanbul where he sang concerts showcasing areas from the opera "The Leonardo Bridge" scheduled to make its world premier with Mr Basile singing the title role. WGES DC is honored to have Mr. Basile peform the U.S. National Anthem on its stage.
Mr. Thomas Kenney
Is vice president of the NAHB Research Center, an engineering and consulting firm that is also a subsidiary of the National Association of Home Builders. As vice president, Mr. Kenney helps to bring the Research Center's many assets – including its state-of-the-art laboratory and market research facility; its numerous third-party testing and certification credentials; and its depth of staff expertise – together to help accomplish the mission of improving the quality, affordability, and durability of housing.
Mr. Kenney is the NAHB Research Center's most senior engineer with over 25 years of service at the Research Center. His broad range of managerial and technical experience has allowed him to touch and influence virtually every technical capability within the company. His extensive experience with a wide range of engineering disciplines and housing product and system issues give him a depth of knowledge and a practical perspective that is unmatched in the home building research industry. He has lead research projects ranging from the integration of high-tech materials such as electrochromic window glazing and photovoltaic panels into housing, to research on more traditional housing systems and cutting-edge issues such as green building, moisture management, indoor air quality, renewable energy and energy conservation, wastewater treatment, low impact land development, and a variety of structural engineering projects.
Ms. Dee Wallace
World Green Energy Symposium DC
Celebrity Host & Master of Ceremonies
Ms. Dee Wallace has appeared in more than 85 films and achieved over 100 credits as an actor in film, television and theater. She is perhaps most known as the Star of Steven Spielberg's Academy Award nominated movie "ET". Ms. Wallace is a rarity in Hollywood, a young actress who immediately found success and is still in demand three decades later as an accomplished veteran in her craft. Ms. Wallace attended the University of Kansas and taught high school English while directing plays. She has also been featured in or contributed articles for many publications including People, US, Guideposts, Family, TV Guide, LA Times and the Washington Post. Ms. Wallace has authored three books, speaks world-wide, and is currently the host of two weekly international radio shows.
WGES Point of Reference 2011-2009
World Green Energy Symposium
World Green Energy Symposium (please note: the bios below are cached and reflect the presenters organizations and positions they held at the time of their affiliation & presentation at the WGES)
2011 WGES
Welcome - WGES Host City - Mayor Michael Nutter Mayor of Philadelphia
Michael A. Nutter, the 98th mayor of Philadelphia, has set a course for America's sixth largest city aimed at growing the regional economy in a sustainable manner, dramatically improving public safety and investing in education and workforce development. With a pledge to make Philadelphia the greenest city in America, Mayor Nutter has launched an aggressive strategy, Greenworks Philadelphia that will reduce the city's carbon footprint and train Philadelphians for new green collar jobs, from weatherization to solar panel installation. Long committed to careful planning of development, Mayor Nutter has reoriented city government, giving primacy to planning as the city prepares for future development along the Delaware River, the Navy Yard and Philadelphia International Airport. He has reorganized the city's Commerce Department to improve its assistance to small businesses and to foster minority- and women-owned business.
Secretary Gary Locke Former Secretary of Commerce / Current U.S. ambassador to China.(invited)
Former U.S. Department of Commerce Secretary Gary Locke has been appointed as U.S. ambassador to China, the first Chinese American to hold the post in American history. At the Department of Commerce, Locke was charged with helping implement President Obama's ambitious agenda to turn around the economy and put people back to work. In particular, Locke is the administration's point person for achieving the President's National Export Initiative, which seeks to double U.S. exports by 2015, in support of several million American jobs.
DR. KEVIN T. GEISS Deputy Assistant Secretary of the Air Force for Energy
Dr. Kevin T. Geiss, a member of the Senior Executive Service, is the Deputy Assistant Secretary of the Air Force for Energy, Office of the Assistant Secretary of the Air Force for Installations, Environment and Logistics, Washington, D.C. Dr. Geiss is responsible for providing oversight and direction for all matters pertaining to the formulation, review, and execution of plans, policies, programs, and budgets for the effective and efficient use of energy to support the global Air Force mission.
Richard G. Kidd IV Deputy Assistant Secretary of the Army (Energy & Sustainability)
Office of the Assistant Secretary of the Army Installations, Energy & Environment
Mr. Richard Kidd became the DASA (E&S) on October 25, 2010. This is his third assignment as a Senior Executive within the Federal Government. In this position he is responsible for overall program direction, establishment of policies, development and refinement of strategies, and oversight for implementation of all programs and initiatives related to Energy Security and Sustainability within the Army. As the Army's Senior Energy Executive, Mr. Kidd coordinates and integrates both installation (traditional as well as expeditionary) and operational energy programs and strategies.
Winslow Sargeant Chief Counsel for Advocacy of the U.S. Small Business Administration's Office of Advocacy
Dr. Winslow Sargeant is the sixth Chief Counsel for Advocacy of the U.S. Small Business Administration's Office of Advocacy, appointed by the President August 19, 2010. The Office of Advocacy is an independent voice for small business within the federal government with a mission of encouraging policies that support small business start-up, growth, and development.As chief counsel, Dr. Sargeant directs Advocacy's operations, which include conducting research on the U.S. small business sector, advocating for small businesses within the federal government's agencies and rulemaking processes, reaching out to regional and state small business advocates and policymakers, and fostering public awareness of small business contributions and concerns.
CAROL ANN BEDA, Director of Energy Policy in the Office of the Deputy Assistant Secretary of the Air Force for Energy (IEN).
Ms. Carol Ann Beda is the Director of Energy Policy in the Office of the Deputy Assistant Secretary of the Air Force for Energy (IEN). She leads the development of the Air Force Energy Strategy, creating innovative Air Force energy policy, directives and guidance for integration and implementation across the Air Force – from operations to installations and within the corporate business process for the effective and efficient use of energy to support the global Air Force mission.
Carol Eicher, Business Group Vice President, Dow Building & Construction
Carol Eicher is business group vice president for Dow Building & Construction, a business group within Dow's Advanced Materials Division that includes the following businesses: Dow Building Solutions, Dow Solar and Construction Chemicals. Dow Building & Construction specializes in the development and production of materials and technologies enhancing energy efficient and sustainable building. Before joining Dow (in 2009), Eicher spent 10 years at Rohm and Haas where she held multiple vice president and director roles. Most recently, she was business director for the Performance Monomers unit which provides essential raw materials to the company's coatings, construction and adhesives markets. Carol Eicher has extensive chemical industry experience, having previously worked at companies such as Ashland Inc., and DuPont.
Michael Kontranowski, Strategic Market Director - Dow Chemical
Mike joined Dow in 1990 as an Engineering Technician in Michigan Operations. He has held roles in Purchasing, Sales, and Marketing in Midland and San Francisco. From 2000-2006, Mike was responsible for growing the California and Nevada markets for Dow Building Solutions as well as being instrumental in developing a commercial roof strategy for growing STYROFOAMTM extruded polystyrene foam insulation sales in the west. Mike also represented Dow as Vice President of Industry on the board for Construction Specification Institute in San Francisco.
TONY CEBALLOS, Director, Philadelphia U.S. Export Assistance Center, US Commercial Service
As the Director the Philadelphia U.S. Export Assistance Center, Tony Ceballos oversees programs in Pennsylvania and Delaware, which provide customized overseas services to evaluate global opportunities, identify and qualify potential business partners. Mr. Ceballos also establishes program partnerships with state and federal agencies and other public and private sector entities to create an efficient export assistance network for U.S. companies. Mr. Ceballos transferred from the West Los Angeles office, where he developed the services sector-a primary industry concentration in the LA area. Mr. Ceballos received his Master's of Arts in International Studies from the Claremont Graduate University. Mr. Ceballos also holds a Bachelor of Arts in Political Science with a Minor in International Relations from the University of California, Riverside.
Jim Shih-Jiun Chen, Ph.D. Professor of mechanical engineering at Temple University
Dr. Chen is a professor of mechanical engineering at Temple University. He received his BSME degree from National Taiwan University in 1976 and his Ph.D. degree in mechanical engineering from Drexel University in 1985. He had three years of industrial working experience in piping system design and one year engineering experience in a US Naval Research Laboratory. His teaching interests are in the areas of Statics, Dynamics, Fluid Mechanics, Heat Transfer, and Technology Transformations. He has published more than 100 refereed articles in temperature measurement and control, film cooling, jet impingement, accelerated/controlled cooling, melt spinning, electronics cooling, cryoablation, wind energy, and heat pumps. In education, he has advised students winning national and international competitions. In 1996, Dr. Chen received the Distinguished Faculty Award from the College of Engineering at Temple University. He has been a member of ASME since 1986. His current research interests and wind turbines and geothermal heat pumps.
Erika Diamond, Vice President of Business Development at ThinkEco
Erika is VP of Business Development at ThinkEco, a NY based start-up developing smart plug-load technologies, as well as the Co-Founder and President of the Harvard Business School Green Business Alumni Association. She has 10+ years in business development and marketing for green companies and investors. Previously, Erika consulted for an environmentally focused private investor group as well as various online businesses, developing market opportunities, sourcing companies and managing partner relationships. She worked with the strategy and marketing consulting firm Green Order, where her clients included GE and Office Depot. Erika worked in Belize for the Toledo Institute for Development and Environment, including three years as the Director of Tourism Business and Development. She earned a BA in environmental studies from Vassar College, a MESc from the Yale School of Forestry and Environmental Studies, and an MBA from the Harvard Business School.
David C. Dickson, District Director for the Philadelphia District Office of the Small Business Administration.
District Director for the Philadelphia District Office of the Small Business Administration. As District Director, Dickson is responsible for the delivery and management of the Agency's financial and business development programs throughout the eastern 40 counties of Pennsylvania.For 4.5 years prior to his permanent appointment in January 2006, Dickson was the Plant Manager for Stanley LaBounty, in Two Harbors, Minnesota; a major part of The Stanley Works' Hydraulic Division. In that position he was responsible for the management and all operations for the manufacture and distribution of hydraulic excavator attachments (shears, universal processors, concrete pulverizers, and grapples) for the scrap, demolition, and general contractor markets.
John P.(JACK) Dienna, Jr., Executive Director & Founder of the Geothermal National & International Initiative (GEO-NII)
Sephen D. Eule, Vice President for Climate and Technology at the U.S. Chamber of Commerce, former Director of the Office of Climate Change Policy & Technology at the U.S. Department of Energy
Stephen D. Eule is vice president for climate and technology at the U.S. Chamber of Commerce's Institute for 21st Century Energy.Previously, Eule was director of the Office of Climate Change Policy & Technology at the U.S. Department of Energy. His prior experience includes a decade working in various public policy positions. He was a subcommittee staff director on the House Science Committee and also served as legislative director for Rep. Nick Smith. In addition, Eule was an environmental analyst in the Washington, D.C., office of New Jersey Gov. Christine Todd Whitman. Earlier, he worked for eight years as an Orkand Corporation consultant to the Energy Information Administration and at the Heritage Foundation, where he was assistant editor of the book Free Market Energy.
Peter L. Hagelstein., Associate Professor of Electrical Engineering
Professor Peter L. Hagelstein is a principal investigator in the Research Laboratory of Electronics (RLE) at the Massachusetts Institute of Technology (MIT). He received the B.S. and the M.S. in 1976, and the Ph.D. in electrical engineering in 1981, from MIT. He was a staff member of Lawrence Livermore National Laboratory from 1981 to 1985 before joining the MIT faculty in the Department of Electrical Engineering and Computer Science in 1986.
Timothy H. Haahs, P.E., AIA, President
Timothy Haahs & Associates, Inc. (TimHaahs) understands the important role parking plays in development. A multi-disciplined engineering and architectural firm, TimHaahs specializes in planning - masterplanning for campuses, urban and high density areas, and transit related projects - and providing design services for parking and mixed-use buildings.
Jason B. Kindt, LEED Green Associate Energy & Sustainability Analyst
Jason is focused on improving and promoting sustainability. His career consists of eleven years in project and client relationship management as well as business development in the fields of energy and emissions management and sustainable development. At Johnson Controls he provides subject matter expertise to public and private clients as well as manages sustainability initiatives including tracking and reducing energy and water consumption, reducing and reporting greenhouse gas emissions and addressing waste disposition. He assesses clients' needs, develops custom solutions and assists in change management.
Xing Zhong Li, PhD(eq.)
Xing Zhong Li (PhD(eq.), Tsinghua University, Beijing, China, 1962; PhD, University of Wisconsin (Madison), 1983) is a professor in the department of Physics at the Tsinghua University. In addition, he serves as a member of the Fusion Research Advisory Committee of China, and the head of the Fusion Physics Laboratory at Tsinghua University. His current research interests are fusion physics and industrial plasma engineering.
Dr. George H. Miley
Professor Emeritus Nuclear & Electrical Engineering University of Illinois
Dr. George H. Miley, Professor Emeritus Nuclear & Electrical Engineering University of Illinois, Fellow American Nuclear Society, Fellow Institute & Electrical Engineers, Senior NATO Fellow NSF, award winning published author of hundreds of articles in journals and books in the field. The subject of Cold Fusion technologies problems and possible solutions has been re-addressed in recent articles, at energy colloquiums and in recent segments on CNN and 60 Minutes.
Terry Penney, Principal Laboratory Program Manage, Advanced Vehicle and Fuel Technologies.
Terry Penney joined the National Renewable Energy Laboratory in 1979. Prior to joining NREL, he worked for Concentration, Heat and Momentum (CHAM) a consulting group headed by Prof. Brain Spalding based in London developing unique finite element computational codes for multiphase heat and mass transfer problems. He also worked Von Karmen Facility at the Arnold Engineering Development Center in middle Tennessee where he worked on the Space Shuttle program. At NREL he has worked on Ocean Energy, Buildings research, Optical and Thermal Fluid Science. More recently, he launched the Hybrid Vehicle program in 1992, which grew into a $300M Partnership for New Generation Vehicles (PNGV) between the government and GM, Ford and Daimler Chyrsler. Currently he is NREL's Laboratory Program Manager for Advanced Vehicle and Fuel Technologies responsible for both light and heavy-duty hybrid platforms. He has more than 50 technical publications to his credit, including energy-related articles in Scientific American and the Encyclopedia Britannica.
Sarah Wu, Policy and Outreach Manager in the City of Philadelphia Mayor's Office of Sustainability.
Prior to joining the Office of Sustainability, Sarah helped implement Opportunity NYC, an incentive program working to improve the health, employment, and education of New Yorkers in poverty. Sarah also served on New York University's Sustainability Task Force to help the University make green choices in its long-term planning and facilities management. Before moving to New York, Sarah researched national environmental policies at a non-partisan organization in Washington, DC. Sarah holds an undergraduate degree from Williams College and a Masters in Urban Planning from New York University.
Ngozi Bell, Region III Advocate
Most recently, Bell served as vice president of Birchmere Ventures, an early stage venture capital firm that focuses on investing in and developing startup companies in the medical, cleantech, and technoloogy sectors. Prior to that Bell was a senior director of technology and marketing at LSI, Agere Systems, and Lucent Technologies. She has also worked extensively on small business technology initiatives in the telecom and wireless sectors. In 2005, Bell cofounded a not-for-profit Nigerian-American organization in Pennsylvania that focuses on education, cultural exchange, and economic development. She has also operated a small business in the fashion and small transportation sector. Bell received her master's degree in electrical engineering from Florida A&M/Florida State University and her bachelor's degree in physics from University of Port Harcourt in Nigeria.
CHUCK MILLER, General Manager UGI Performance Solutions and General Manager of Thermmax ScientificRegion III Advocate
Chuck is responsible for the ongoing development and management of the flagship performance environments brand Thermmax Scientific as well as the creation of the UGI Performance Solutions business. Leveraging expert resources from the UGI HVAC Enterprises organization as well as key engineering and project management resources from within the UGI organization, Chuck will be responsible for the growth of the site based sustainability effort within UGI.
Joseph E. Barron
Joe Barron has over 30 years of experience growing and managing technology businesses from start-ups to multinational corporations and advising early stage technology companies at the executive level in the areas of funding strategy, business plan development and strategic alliances.
Rami Mikhail, Solar Business Development Specialist, Siemens Industry, Inc.
Rami Mikhail joined Siemens to oversee the development of Photovoltaic (PV) projects and the Siemens power purchase agreement (PPA). Prior to joining Siemens, Mr. Mikhail served as Vice President of a Solar Integration Company that resulted in an IPO in 2007. Mr. Mikhail was responsible for sales, marketing, engineering and operations for the company across the country.
Michael Choi, Korea trade specialist, ITA U.S. Department of Commerce
Michael Choi works as a Korea trade specialist in the Office of Japan and Korea within the Market Access and Compliance unit of the International Trade Administration (ITA) of the U.S. Department of Commerce (DOC) since 2006. He focuses on identifying barriers U.S. companies face in the Korean market and working with his ITA and USG colleagues to reduce them and increase market access for American businesses and workers. Since his start in 2006, Michael has been a member of the U.S. delegation to the U.S.-Korea Free Trade Agreement (KORUS) negotiations, and he has traveled to Korea on numerous occasions to help address market access barriers. He has been an acting Commercial Attaché at the U.S. Embassy in Seoul in 2008 and 2010. He is also part of a team that frequently advises DOC senior leadership on KORUS and the U.S.-Korea commercial relationship. Michael's past experience includes working as a foreign relations advisor to a Korean lawmaker, a legislative analyst at the New Mexico Senate, and as part of the staff at JP Morgan.
Ivan Bragin, Managing Director at LED Engineering Co. Ltd.
Mr. Bragin is working in the field of energy efficient technology and renewable energy sources as the Managing Director at LED Engineering Co. Ltd., where he is developing the Russian market for innovative energy efficient technology, especially LED based lighting solutions. He is also working with a couple of companies through a partnership that aims to provide new independent energy systems based on solar panels and wind turbines. Mr. Bragin completed his studies at the Saint Petersburg State Institute of Information Technology Mechanics and Optics with a specialization in Automatic Control Systems in 2006, at the Saint Petersburg State University of Economic and Finance with a specialization in Finance and Credit in 2009, and additionally at the Saint Petersburg State Academy of Economic and Management with a specialization in Management in 2011.
John Heon, Ph.D.
Educational Coordinator and a Founding Executive Board Member of the China Partnership of Greater Philadelphia, Programming Director and Founding Advisor of the Penn International Sustainability Association John Heon, Ph.D, is the Educational Coordinator and a Founding Executive Board Member of the China Partnership of Greater Philadelphia, a nonprofit that promotes collaboration on public/private cleantech and sustainable building initiatives between Philadelphia and the People's Republic of China. He is also the Programming Director and Founding Advisor of the Penn International Sustainability Association, an interdisciplinary group at the University of Pennsylvania that helps students launch green careers and entrepreneurial ventures through an extensive network of academic, corporate, and government organizations.
Timothy Kim, Senior Loan Officer and founding member of the Renewable Energy & Environmental Finance Division at US Export-Import Bank.
Timothy Kim is a Senior Loan Officer and founding member of the Renewable Energy & Environmental Finance Division at US Export-Import Bank. In this capacity, he originates and structures credits across the broad spectrum of the industry including solar, wind, gasification and biomass. To date, Timothy has closed more than sixty international transactions, with an aggregate total of over $3 billion across the public and private sectors.
Steven Chan, Deputy Director of the Office of China and Mongolia (OCM)
Steven Chan is the Deputy Director of the Office of China and Mongolia (OCM). OCM is part of the Market Access and Compliance unit in the International Trade Administration at the U.S. Department of Commerce. OCM also covers Hong Kong and Macau. Before Mr. Chan joined OCM in February 2009, he served as a Foreign Service Officer for the U.S. Department of State with overseas assignments in China and Mexico, and a domestic assignment at the Office of Korean Affairs in Washington, DC. From 2006 to 2009, Mr. Chan worked for Deloitte Consulting and Booz Allen Hamilton. He received a Master of Arts in International Economics and China Studies from the Johns Hopkins University, School of Advanced International Studies, and a Bachelor of Arts in International Relations from Lewis & Clark College.
Governor of Pennsylvania Edward G. Rendell, Welcome to State of PA
Edward G. Rendell, Pennsylvania's 45th Governor, began a second term of office on January 16, 2007, following a landslide re-election victory. As Governor, Rendell serves as chief executive of the nation's 6th-most-populous state and oversees a $28.3 billion budget.
Mayor of Philadelphia Michael A. Nutter, Welcome to Host City
Michael A. Nutter, the 98th mayor of Philadelphia, has set a course for America's sixth largest city aimed at growing the regional economy in a sustainable manner, dramatically improving public safety and investing in education and workforce development.
Michelle Moore, The Federal Environmental Executive (The White House)
Michelle Moore is the Obama Administration's Federal Environmental Executive, and is responsible for promoting sustainability and environmental stewardship throughout the federal government's operations. Housed within the White House Council on Environmental Quality, the Office stewards the implementation of President Obama's Executive Order on Federal Sustainability (EO 13514) and the GreenGov initiative. Prior to joining CEQ, Michelle was Senior Vice President of Policy and Public Affairs at the U.S. Green Building Council, a non-profit organization that developed and oversees the LEED certification system. She holds a Master's of Science in Foreign Service from Georgetown University and a BA from Emory University.
Kevin Kampschroer, Director, Office of Federal High-Performance Green Buildings
Kevin Kampschroer is the Director of the Office of Federal High-Performance Green Buildings at the U.S. General Services Administration (GSA). This new office within GSA has consolidated and is coordinating Federal efforts in the broad realm of building sustainability, acceleration of industry capability and adoption of sustainable principles across all aspects of asset creation, operation, maintenance and disposal. In response to the 2005 and 2007 Energy Bills & Executive Order on Federal Leadership in Environmental, Energy and Economic Performance, he has created the framework for which GSA responds to the challenges of greenhouse gas emissions reductions and of the American Recovery and Reinvestment Act's mandate to move GSA's Federal building inventory toward high-performance green buildings.
Kevin T. Geiss, PH.D.
Office of the Assistant Secretary of the Army for Installations & Environment.
Dr. Kevin Geiss is the Program Director for Energy Security in the Office of the Assistant Secretary of the Army for Installations and Environment. Dr. Geiss joined the office in 2008 and works on the development, coordination and implementation of the Army's energy security strategy. Prior to this position, he served as the Assistant Director for National Defense in the Office of Science and Technology Policy (OSTP) in the Executive Office of the President. During his 3 years at OSTP, he conducted policy and budget review of the Department of Defense science and technology efforts and led interagency S&T committees to support national policy development.
Dr. Steven Chu, Secretary of Energy (invited)
As United States Secretary of Energy, Dr. Steven Chu is charged with helping implement President Obama's ambitious agenda to invest in clean energy, reduce our dependence on foreign oil, address the global climate crisis, and create millions of new jobs. Dr. Chu is a distinguished scientist and co-winner of the Nobel Prize for Physics (1997). He has devoted his recent scientific career to the search for new solutions to our energy challenges and stopping global climate change - a mission he continues with even greater urgency as Secretary of Energy.
Marc LePage, Advisor Climate Change and Energy, Canada
Marc LePage was appointed Special Advisor, Climate Change and Energy in September 2009. Prior to his appointment Marc was the Consul General at the Consulate General of Canada, San Francisco | Silicon Valley with responsibility for northern California, Nevada and Hawaii. Formerly with Genome Canada, Marc brings extensive experience in the pharmaceutical industry, biotechnology, and venture capital. Mr. LePage joined the Trade Commissioner Service of the Department of Industry, Trade and Commerce in 1980 and has served abroad in Stockholm, Havana and at San Diego, California. In 1994, Mr. LePage moved to the Medical Research Council of Canada (now the Canadian Institutes of Health Research) to serve as Director of Business Development. Upon its launch in July of 2000, he joined Genome Canada as Executive Vice-President of Corporate Development, the capacity in which he has served to date. He holds a degree in Political Science from the University of Moncton, New Brunswick.
Ronald H. Bowman, Jr., Executive Vice President Tishman Technologies Corporation
As Executive Vice President of Tishman Technologies Corporation, Bowman is responsible for the organization's operations and its project management and construction management assignments, as well as providing services to its clients in all aspects of Mission Critical Data Centers: strategic site location and evaluation, life-span assessment, total cost of ownership, sustainable design and construction, alternative energy implementation, and commissioning. He has served as a project manager on trading floor and data center installations in some of the world's most competitive markets, including New York, London, Tokyo, Frankfurt, Paris, and Shanghai. He has managed 50 trading floor and 100 data center installations for such companies as Morgan Stanley, Goldman Sachs, E-Speed, Cantor Fitzgerald, DLJ, Mitsubishi, and Charles Schwab. Tishman Technologies
Dr. Greg Caplan, Director for Energy & Environment in Lockheed Martin
Dr. Greg Caplan is Director for Energy & Environment in Lockheed Martin Washington Operations, gathering policy-driven market intelligence to align and inform the pursuit of the business objectives of the corporation's Energy & Environment division. In this capacity, he manages relationships with Federal agencies involved in clean energy policies and programs, as well as with relevant stakeholder associations, and supports product line business development efforts to shape and capture opportunities in the Federal energy market. Previously, he worked in business development and program operations for Lockheed Martin in the homeland security market, managing capture efforts and program start-up on Department of Defense and Department of Homeland Security programs. Before joining Lockheed Martin, he worked in government relations and strategic development for nonprofit organizations, domestically and internationally, and on the presidential campaign of General Wes Clark (ret.). Dr. Caplan earned his Ph.D. in European history and his Master of Arts in European Studies from Georgetown University.
Michael Amante, Evening Gala Special Performance, Opening Ceremony (National Anthem), World-Renowned Recording Artist
World-renowned recording artist has performed to sold out audiences across the country. He has also given performances to countless dignitaries including former US Presidents Gerald Ford, George H.W. Bush, and Bill Clinton, UN Secretary General Kofi Annan, Pope John Paul II, Luciano Pavarotti, to name a few. He performs to sold-out audiences across the country including New York's Lincoln Center. He has performed for a myriad of nationally televised events and at well known arenas including Camden Yards, Shea Stadium, Madison Square Garden, Fox borough Field, The US Open, The Belmont Park Raceway, and Giants Stadium. Michael's latest project is focused on the production of a patriotic album, providing financial support to organizations benefiting United States Disabled Veterans.
John L. Banks
Lead Business Development Specialist
John L. Banks, a native of Philadelphia, PA has over 29 years working for the Small Business Administration (SBA). John is currently serving as the Lead Business Development Specialist overseeing SBA's Economic Development, Government Contracting, and Lending Programs for various counties throughout the Philadelphia District. Prior to this appointment, John has served as the head of the 8(a) Business Development Program. This program provides contractual, financial, management and technical assistance to firms that are owned, controlled and managed by socially and economically disadvantaged individuals.
Keith Blakely
CEO of NanoMech, LLC
Keith Blakely is a life-long entrepreneur who has been involved in energy, environmental, and infrastructure technologies throughout his career. He is, at present, the CEO of NanoMech, LLC, an award-winning technology commercialization company focused on the development and manufacturing of patented and proprietary application-specific nanomaterials, nanoparticle-based coatings and coating deposition systems, and nano-enabled products. He also serves as the cofounder and Director of R3 Fusion – a company focused on disruptive water purification technology being exploited in frac water, biofuel synthesis, and desalination.
John Costlow
CET, CRM Director of Technical Services Sustainable Energy Fund
John Costlow is the Director of Technical Services for Sustainable Energy Fund (SEF). Prior to joining SEF, Mr. Costlow has been employed as Vice President of Operations for Energy Control Companies, Marketing and Energy Conservation Manager for Florida Public Utilities, Technical Support Manager for Johnson Controls, and Nuclear Reactor Operator. Mr. Costlow is a Graduate student at NYIT, has a Bachelor of Science in Organizational Management from Palm Beach Atlantic University, is an honor graduate of Naval Nuclear Power School, and 1 of 38 Certified Carbon Reduction Managers in the North America. Mr. Costlow is also a member of Association of Energy Engineers, Association of Energy Service Professionals, and Alternative & Renewable Energy Development Institute.
David C. Dickson - Class moderator
District Director U.S. Small Business Administration
David C. Dickson, a native of Youngstown, Ohio, is serving as the District Director for the Philadelphia District Office of the Small Business Administration. As District Director, Dickson is responsible for the delivery and management of the Agency's financial and business development programs throughout the eastern 40 counties of Pennsylvania. In 1975, he graduated as an Industrial Engineer from Youngstown State University in Ohio, after which he served honorably for over 11 years as an officer in the United States Army. While in the Army, Dickson earned his Masters of Business Administration from Florida Institute of Technology and attended the Defense Systems Management College in Ft. Belvoir, Virginia.
John F. Fleming
John F. Fleming, a native of Springfield, Pennsylvania, is serving as a Lead Business Development Specialist for the Philadelphia District Office of the U.S. Small Business Administration. As a Lead Business Development Specialist, Fleming is responsible for the delivery and management of the Agency's financial and business development programs throughout 18 counties of Pennsylvania. Mr. Fleming started his SBA career in 1992, and has served in various positions including Chief Credit Officer, Marketing Specialist, and Public Information Officer.
Keith J. Forbes
Senior Climate Change and Sustainability Analyst, Science Applications International Corporation (SAIC)
Mr. Forbes has fifteen years in climate change, corporate sustainability reporting, and sustainable development. His expertise developed in the public and private sector in the U.S., Europe, and Africa, includes developing, managing, financing, and implementing project and programmatic work. His domain knowledge includes global climate change (impacts, adaptation measures, stakeholder outreach, mitigation, GHG inventories, climate change and land use, biofuels), corporate sustainability reporting (CSR) and strategy, and environmental governance.
Jennaphr Frederick - RoundtABLE MODERATOR
Co-host "Good Day"
Jennaphr Frederick joined the "Good Day" team in September, 2003. Prior to becoming a morning person, Jennaphr was a general assignment reporter for Fox 29.
Before joining the FOX family in October 1999, she worked for two years as an investigative reporter for WKBW-TV, the ABC affiliate in Buffalo, NY. A diverse background has helped Jennaphr to develop a proficiency in newsgathering. Before working at WKBW-TV, she was part of the morning team for WTVR-TV in Richmond, VA, a CBS affiliate. She speaks Spanish fluently and takes pride in having worked as an anchor and investigative reporter for KGNS-TV in Laredo, TX, an NBC affiliate and bilingual station. It was there that she started her career and frequently reported stories in Spanish.
Adam Garber
Penn Environment
As the field director for PennEnvironment, Adam helps to coordinate PennEnvironment's efforts to heighten public education about the state's most pressing environmental issues, increase civic participation, and garner media coverage to inform concerned Pennsylvanians. Before joining PennEnvironment in the fall of 2007, Adam worked as the energy and consumer associate for the New Jersey Public Interest Research Group (NJPIRG). During his tenure at NJPIRG he helped to pass one of the nation's strongest renewable energy standards, promote energy efficiency, and promote clean, safe energy production in New Jersey. In addition, Adam has run citizen outreach office in New Jersey and Georgia to mobilize citizens around environmental issues. Adam graduated from St. John's College- Annapolis in 2005 with a degree in liberal arts.
Joann Garbin
Johnson Controls INC.
JoAnn Garbin is the Program Director of Energy & Sustainability Information Services for Johnson Controls. She has 10 years experience in information technology development and deployment and sustainability business analysis and consulting. She serves as a Subject Matter Expert for organizations developing sustainability strategies that include creating inventories, mitigation plans, education and outreach programs, and internal and external reporting for domestic and foreign, voluntary and regulatory programs.
Patricia Griffin
President and Founder "Green" Hotels Association®
Patricia is an avid traveler, and a self-appointed cheerleader for all "green" hotels. She is very enthusiastic about protecting our environment especially through simple, good practice methods. She is particularly interested in encouraging the greening of the hospitality industry by informing not only hoteliers, but also travel agents, meeting planners, tour guides, business and pleasure travelers and government agencies. Ms. Griffin is a native Texan, owns a farm in Central Texas where she has wild horses and gentle cows. She is a graduate of The University of Texas at Austin with a Business degree.
Jennifer Hazelman
GSA Business Development Specialist
Jennifer Hazelman is a business development specialist with the GSA Center for Facilities Maintenance and Hardware. She is the team leader for the Energy Management Services Strategic Team and has led the team in their efforts to build the energy management services offered through the schedules program into a more comprehensive energy management services solution.
Kent L. Hibben
Mr. Kent L. Hibben serves as the US Department of Energy's (DOE) HQ Office of Small and Disadvantaged Business Utilization (OSDBU) subject matter expert and spokesperson on energy efficiency and renewable energy (EERE) issues. His accounts include the DOE EERE and Science offices, and the DOE SBIR/STTR program. He is also Team Leader of the OSDBU Business Opportunity Session activities, advocating for small companies seeking to do business with the US Department of Energy. In his previous (EERE) position he served as a contracting officer representative (COR) for several support service contracts for both the Research and Development (R&D), and the Business Administration sides of the Department of Energy's (DOE) Energy Efficiency and Renewable Energy (EERE) Office. These $25 million in contracts were for a range of business sizes and ownership structures, including small/8(a) firms and Mentor-Protege teaming arrangements.
Parsaoran Hutapea
Associate Professor of Mechanical Engineering and the Director of Composites Laboratory at Temple University
Dr. Parsaoran Hutapea is an Associate Professor of Mechanical Engineering and the Director of Composites Laboratory at Temple University, Philadelphia, Pennsylvania. He received his BS (1995), MSc (1997) and PhD (2000) all in Aerospace Engineering from North Carolina State University, Raleigh, North Carolina. He has authored and co-authored over sixty research articles, most of which have been published in international journals or presented at international conferences in the fields of mechanics of composite materials and structures, smart materials, and proton exchange membrane fuel cells. His primary research interest in energy is fuel cells and their applications for transportation.
U.S. General Services Administration
Gary Jenkins has been with the General Services Administration for 20 years. As a Business Development Specialist for the GSA Center for Facilities Maintenance and Hardware, his experience includes advertising and promoting the Center's 2 Multiple Award Schedules 51V & 03FAC, Develop Marketing Material for the Center, Attend Events/Shows and conferences, Train Federal Agencies, Assist Contractors in getting a GSA Contract and marketing their services and products, and Business Development for the Center. The GSA Center for Facilities Maintenance and Hardware (CFMH) provides federal agencies with a streamlined procurement tool to acquire all of the services necessary to maintain and manage a facility or marine vessels.
David Kaiser
Temple University Fox School of Business
David Kaiser has served as the Director of Enrollment Management for the Fox School of Business since July 2004. He is responsible for all recruitment and retention activities for the Undergraduate Programs at the Fox School. He also serves as the advisor for the Fox School College Council of Presidents, a cooperative council of the student professional organizations.
Hunter McIntosh
Vice President and Chief Operating Officer at The Boat Company
As Vice President and Chief Operating Officer at The Boat Company – a company started by his father with the purpose of conserving and protecting the largest remaining temperate rain forest in the Northern Hemisphere – Hunter considers himself an honored guardian of this founding mission. His work there takes him from Alaska's Tongass National Forest, carting eco-adventure travelers; to Capitol Hill, where he lobbies for the preservation of the forest and remaining pristine wildernesses found in Southeast Alaska.
Jeremy Peang-Meth
Partner of Blue Sun Renew
Jeremy Peang-Meth is partner of Blue Sun Renew, a firm specializing in the building and site integration of wind energy and other renewable energy systems. Blue Sun Renew has focused on vertical-axis wind turbines (VAWTs), managing projects in the US and abroad, including installations for the State Department, US Air Force, NC Museum of Science and United Nations. Current projects include the design and CFD studies for a roof-mounted VAWT installation in New York City, and assistance with the use of VAWT technology for a research study underway at California Institute of Technology. Mr. Peang-Meth's combined experience in architecture, commercial development and high-end construction has provided the expertise to incorporate clean energy technologies in more complex projects.
Emile Monette
GSA FAS Director
Mr. Emile Monette currently serves as the Director, Program Analysis Division the Federal Acquisition Service at the United States General Services Administration (GSA). In this position, he provides leadership for the GSA's initiatives to create and promote a more sustainable federal supply chain. Mr. Monette has broad experience in the field of federal procurement, in both the legislative and executive branches of the U.S. federal government, including active duty military service in Operation Iraqi Freedom, as a Senior Procurement Advisor to the Executive Office of the President, and as a Professional Staff Member with the House Oversight and Government Reform Committee. He is a graduate of The George Washington University Law School, in Washington D.C, and San Diego State University, in San Diego, CA.
Natalia Olson Urtecho
Director of Global Initiatives
Chair, Philadelphia 2010 WGES Planning Committee
Natalia Olson-Urtecho is the founder and President/CEO of the Ecolibrium Group, a company dedicated to helping public and private entities become more profitable through environmentally friendly and socially responsible planning and strategies. She serves on the Wharton/UPENN Initiative for Global Environmental Leadership Faculty Advisory Committee, the Philadelphia's Urban Sustainability Forum Committee, the Delaware Valley Green Building Council Policy Committee, Mayor's International Task Force and is one of the founding members of the Philadelphia Green Economy Task Force where she serves as the Co-Chair of the Policy Committee. She is also the representative for a new program of the U.S. DOE, US-India-China Integrated Cities for Energy and Environment.
Dino Ramos
Chief Operating Officer, World Trade Center of Greater Philadelphia
Dino Ramos oversees implementation of such programs as the Pennsylvania Export Program, Developing International Opportunities for Industry Clusters, the International Design and Engineering Consortium, and the American Business Practices for International Students. Dino has over 25 years experience in international trade management. As Export Sales Manager for the Hunt Corporation, Dino was responsible for sales and marketing in over 50 countries. His long tenure at Hunt included managing all international sales, export sales forecasting, sales and operational planning, export administration, international marketing, and marketing services. Prior to Hunt, Dino spent five years working in Singapore as Far East Sales Manager for King Press Inc. and another five-year assignment in Vietnam and Thailand for the U.S. General Accounting Office. Dino holds a Bachelor of Science degree in Business Management from East Tennessee State University and attended George Washington Graduate School of Business Management. He is familiar with Greek and French and has some understanding of Vietnamese, Thai, Chinese, and Arabic.
Cody A. Ray
President of Drexel Smart House
Cody A. Ray has served as President of Drexel Smart House since December 2008. He is responsible for leading renovation efforts to transform an abandoned, historic home into a living laboratory for student research, and for collaborating with faculty, staff, and industry to establish a sustainable design and technology incubator. He leads project teams in developing sustainable technologies that simultaneously enhance occupant well-being and decrease their environmental footprint. Mr. Ray is a sustainability researcher and a LEED AP. He is also a graduate student of electrical engineering at Drexel University, concentrating in intelligent systems and controls.
David Restaino
Partner Fox Rothschild
David provides dynamic litigation, transaction, regulatory, and strategic counsel for complex commercial matters in state and federal jurisdictions. He focuses his practice in environmental matters, including development, permitting, compliance, recycling, and reporting, as well as real estate matters. David has also litigated a variety of insurance contribution and subrogation cases.
Jerry Skaggs, P.E
Professional Civil Engineer
Jerry, a Registered Professional Civil Engineer in the UL DQS Programs and Business Line Manager - Environmental including: ISO 14001; Occupational Health and Safety Assessment System (OHSAS 18001); Responsible Care (RC14001 and RCMS); and Leadership in Energy and Environmental Design (LEED) review team, a member of the American Water Works Association's standards writing committee for the G100 – G300 Series, General Interest, Utility Management System Standard and the US TAG ISO/PC 242 for the emerging ISO 50001, Energy Management Standard. Jerry also audits ISO 9001 and the International Bottled Water Association standards. He has over 25 years of experience in environmental engineering and program management. Jerry joined UL in 1999 and has brought his knowledge of environmental management and compliance to our Assessment Team.
Richard J. Sobelsohn Esq.
Leadership in Energy and Environmental Design Accredited Professional (LEED AP)
Richard J. Sobelsohn Esq., Attorney earned his accreditation from the U.S. Green Building Council as a Leadership in Energy and Environmental Design Accredited Professional (LEED AP). As a LEED AP, Richard has in-depth knowledge of the LEED Green Building Rating System, the globally accepted rating and certification program for design, construction, operation, and maintenance of green buildings. He represents developers, corporations, financial institutions and individuals concerning a variety of commercial real estate transactions including sustainable development, acquisitions, dispositions, financing, condominium offerings and leasing. Richard is a Fellow in the Institute of Green Professionals, serves as a member of the National Legal Working Group of the U.S. Green Building Council, an adjunct professor of law at both Brooklyn Law School and New York Law School, and lectures extensively on the subject of sustainable development.
David Walls
Managing Director, Energy
Emerging Energy Technology
David Walls earned his Masters in Mechanical Engineering from MIT and has over 28 years experience in emerging energy technologies, business planning and strategy. Mr. Walls is currently leading a major project for the US DOE Office Electricity to support the $4 billion Smart Grid Investment Grant and Smart Grid Demonstration programs. Navigant's role involves developing the processes; approaches and analysis of the project build metrics, impact metrics and overall benefits. This will be a 5 year program involving approximately 140 major smart grid and energy storage projects aimed at understanding the benefits and business case for smart grid and energy storage technologies and investments
WGES 2009
Mayor Michael A Nutter
Morning Keynote Address
Maribel Aber, Former Vice President NASDAQ, host and spokesperson
World Green Energy Class Session Moderator
Maribel Aber is a television presenter, host and spokesperson covering a wide range of areas including: financial markets, women's issues, and the environment. She began her career on Wall Street, where she became the first female Asian executive to rise to the level of officer at the NASDAQ OMX Group. At NASDAQ OMX Aber was a key member of the Green Committee that focused on bringing environmental issues to the forefront of the exchange and its listed companies. This Committee worked with leading environmentally focused consultants towards innovating the way public companies approach green initiatives to maximize environmental efficiencies and drive towards bottom-line benefits.
Michael Amante Opening Ceremony (National Anthem)
World-Renowned Recording Artist
Nikos Avlonas, PhD Centre for Sustainability & Excellence
World Green Energy Symposium Presenter Nikos Avlonas is one of the founders and Managing Director of the Centre for Sustainability & Excellence - CSE, a global Think Tank and Sustainable Development Strategic advisory Network, based in Athens ,Chicago and Brussels been active in more than 12 countries. Avlonas is a well known international speaker in topics related to Sustainable Development and CSR and has delivered speeches all over the world (in Chicago, Kolkata, Beijing, Istanbul, London, Paris, Cairo, Madrid, Barcelona, Brussels, Rome, Budapest, Lisbon, Frankfurt, Hague, Moscow, Tehran, Luxemburg, Warsaw, Athens, Nicosia, Singapore and Dubai). He has carried out numerous projects in leading organizations including Fortune Global 500 Companies like BP, Dell Computers, Mc Cain, TNT, DHL, Lafarge, Deutsche Post, HSBC, Βank of Cyprus, TECOM ,DIFC and many others including the European Investment Bank. In addition he is the advisor of Lloyds TSB Bank in Corporate Social Responsibility. Since 2000 he has served as adjunct professor at the American College Of Greece and lectured at a variety of Universities including the Kellogg School of Management (Chicago) and Sheffield Hallam University (U.K). He is frequently interviewed on Sustainability matters on international TV, including CNBC, CCTV (China), and others.
Dan Birns, Advisor, International Activities Office of Energy Efficiency and Renewable Energy U.S. Department of Energy
Dan Birns is an advisor in DOE's Office of Energy Efficiency and Renewable Energy (EERE), where he co-manages EERE's portfolio of bilateral and multilateral initiatives. In addition, Dan provides recommendations to EERE leadership on new opportunities for international engagement. Previously, Dan served as an advisor to EERE's Deputy Assistant Secretary for Energy Efficiency. Dan is a former Presidential Management Fellow. He received a Master's degree in International Relations from the Johns Hopkins University, and a bachelor's degree from Wesleyan University.
David Blumenfeld - Founder and President of UEE
World Green Energy Symposium Saturday Program Speaker
David Blumenfeld, is a real estate investor with 20+ years of experience in residential, office and retail properties. David was an initial partner in a real estate company that developed and managed over $500,000,000 of real property. David's sales and marketing abilities have earned him industry recognition for operating prowess including the Philadelphia best luxury high-rise apartment building award, and a marketing award for the fastest lease up of a new building. He has a wide range of permitting, financing, and construction experience including single-family developments, new construction, historic renovations using federal tax credits, and HUD 221(d)(4) projects in Pennsylvania, New Jersey, and Delaware totaling over 1,500 residential units. David is a graduate of Northwestern University and the University Of Miami School Of Law. David is a member of the Pennsylvania and New York Bar and holds Pennsylvania and New York Real Estate Brokerage Licenses. David was recently certified as a Solar Installer under Pennsylvania licensing requirements and is a member of the Mid-Atlantic Solar Energy Industries Association and the Philadelphia Sustainable Business Network.
Michel Boufadel, Ph.D.
World Green Energy Symposium Speaker
Dr. Michel Boufadel is Professor and Chair of the Department of Civil and Environmental Engineering at Temple University, Philadelphia, Pennsylvania, USA. He is a Professional Engineer (Environmental Engineering) in the Commonwealth of Pennsylvania (USA). He is also a Professional Hydrologist as accredited by the American Institute of Hydrology (USA). His area of expertise is Environmental Hydrology and Ecohydrology, where he develops methods to account for changes in the environment due to natural and anthropogenic stressors. He has been the lead researcher on various projects funded by the Oil Spill Research program within the United States Environmental Protection Agency (USEPA). He is currently investigating the lingering of the Exxon Valdez oil (1989) in the beaches of Prince William Sound, where he and his team conducted field studies on various beaches and are exploring remediation technologies for dealing with the 20-year old spill. He also conducted floodplain delineation studies for the Federal Emergency Management Agency (FEMA) using hydrologic and hydraulic models developed by the US Army Corps of Engineers and Geographic Information System (GIS). He also conducted vulnerability studies of watersheds in a project funded by the Commonwealth of Pennsylvania. He is the author of numerous articles in publications such as the Journal of Environmental Engineering, Environmental Geology, Journal of the American Water Resources Association, Journal of Contaminant Hydrology, and Water Resources Research.
As Executive Vice President of Tishman Technologies Corporation, Bowman is responsible for the organization's operations and its project management and construction management assignments, as well as providing services to its clients in all aspects of Mission Critical Data Centers: strategic site location and evaluation, life-span assessment, total cost of ownership, sustainable design and construction, alternative energy implementation, and commissioning. He has served as a project manager on trading floor and data center installations in some of the world's most competitive markets, including New York, London, Tokyo, Frankfurt, Paris, and Shanghai. He has managed 50 trading floor and 100 data center installations for such companies as Morgan Stanley, Goldman Sachs, E-Speed, Cantor Fitzgerald, DLJ, Mitsubishi, and Charles Schwab. As an author, Bowman has written two books, his newest about energy options off the traditional grid and alternative power, entitled The Green Guide to Power, Thinking Outside the Grid. He has been quoted regularly in The Wall Street Journal, the New York Times, Crain's New York Business, Real Estate Weekly, USA Today, New York Daily News, and Real Estate Forum.
John Costlow, CET, CRM Director of Technical Services Sustainable Energy Fund
World Green Energy Symposium Presenter
Rita Cosby Veteran TV Host, Radio Host, Best-Selling Author
World Green Energy Symposium Roundtable Moderator
Emmy award-winning journalist Rita Cosby currently is a Special Correspondent for CBS' highly rated syndicated primetime show, "Inside Edition," where she secures exclusive interviews with the most sought-after newsmakers and key political figures. She previously hosted primetime shows on MSNBC and Fox News, and has interviewed more than a dozen world leaders, including Yasser Arafat, Ariel Sharon, Pervez Musharraf, and Slobodan Milosevic who called her while he was imprisoned at the Hague. Cosby has received numerous awards and honors for her reporting, including the National Foundation for Women Legislators' Media Award for Excellence, the Association of Women in Communications Headliner Award, and also the Matrix Award and Jack Anderson Award, both for journalism distinction. A first-generation American and daughter of a Polish ex-POW father, in 2006 she was presented with the Ellis Island Medal of Honor.
Dickson D. Despommier, Ph.D.,
Professor of Public Health in Environmental Health Sciences (and Microbiology)
Dickson D. Despommier is a professor at Columbia University, Mailman School of Public Health and a Sustainability Subject Matter Expert. He established "The Vertical Farm" to look at the possibility of agricultural sustainability within cities. The idea grew out of a class project to measure the effects of rooftop gardening in New York City on reducing the dome of heat that develops over us each year. From that original idea, he expanded the concept to include urban agriculture and finally to multi-story indoor farming. Sustainable urban life is now a major interest, Despommier believes that with enough input from multiple disciplines (e.g., industrial and soil microbiology, engineering, public health, policy making, urban planning, architecture, agronomy, plant genetics, economics), vertical farming could become a reality and thus replace most of what now passes for agriculture in many parts of the developed and under-developed world
David C. Dickson, District Director U.S. Small Business Administration
World Green Energy Symposium Ambassador Host, Presenter
Brennan Downes, Director Government and DoD Development GE Energy Infrastructure
World Green Energy Symposium Master Class Speaker
Brennan Downes manages GE's strategy and implementation of efficient solutions for the Department of Defense. An expert in the integration of energy efficiency-based solutions, he has led business development in a variety of industrial spaces, including power generation, cogeneration, energy recovery and gasification. Additionally, he has significant experience with operations groups in thermodynamics, fluids, and other mechanical or economic feasibility analyses. Downes is also the co-author of "Economic Growth and the Central Generation Paradigm," published by the International Association of Energy Economists in 2004. The paper highlights the last thirty years of decision-making by utilities and independent power producers. More recently, he authored, "Steel Appeal Potential of Energy Recycling and CHP in the US Steel Industry," published by Cogeneration and Onsite Power Production in 2006. The article discusses the economics of existing potential for CHP, recycled energy and third party involvement. Downes has a Master of Science degree in Mechanical Engineering with specific studies in combined heat and power (CHP) analysis from the University of Illinois at Chicago. He currently resides in Chicago, Illinois, with his wife, Liz.
Alan Edwards Program Manager
Alan Edwards is the program manager for the electronic business group solar program at the Federal Prison Industries (FPI). Mr. Edwards innovative approach in cutting edge federal financing has assisted many agencies in reaching renewable goals set forth by the current Energy Policy Act and Executive Orders. His focus is the installation of renewable energy projects both nationally and internationally. He is a subject matter expert for national energy policies, an awarded problem solver, and mentor for other agencies on energy and renewable energy projects. His efforts on a national level have been recognized with the following awards: 2008 Public Service Award shared by the Assistant Secretary of Energy, Andy Karsner, 2008 DOE Champion Award, 2007 Presidential Energy Award, 2007 GSA Sustainability Award, and 2006 DOE Energy/Water Management Award. He is an active member in the Department of Energy/Federal Energy Management Program (FEMP) Steering Committee, United Nations Framework Convention on Climate Change, World Energy Council, and US House of Representatives Congressional High Performance Building Caucus.
He is currently working on his MBA from Edinburgh Business School, Heroit Watt University, Scotland.
Adam Garber, Field Organizer for PennEnvironment
Adam Garber is the field organizer for PennEnvironment. Adam helps to coordinate PennEnvironment's efforts to heighten public education about the state's most pressing environmental issues, mobilize members, and garner media coverage to inform concerned Pennsylvanians. Before joining PennEnvironment in the fall of 2007, Adam worked as the energy and consumer associate for the New Jersey Public Interest Research Group (NJPIRG). During his tenure at NJPIRG he helped to pass one of the nation's strongest renewable energy standards, promote energy efficiency, and promote clean, safe energy production in New Jersey. In addition, Adam has run citizen outreach office in New Jersey and Georgia to mobilize citizens around environmental issues. Adam graduated from St. John's College- Annapolis in 2005 with a degree in liberal arts.
Kevin T. Geiss, Ph.D. Office of the Assistant Secretary of the Army for Installations & Environment.
Dr. Kevin Geiss is the Program Director for Energy Security in the Office of the Assistant Secretary of the Army for Installations and Environment. Dr. Geiss joined the office in 2008 and works on the development, coordination and implementation of the Army's energy security strategy. Prior to this position, he served as the Assistant Director for National Defense in the Office of Science and Technology Policy (OSTP) in the Executive Office of the President. During his 3 years at OSTP, he conducted policy and budget review of the Department of Defense science and technology efforts and led interagency S&T committees to support national policy development. Before joining OSTP, Dr. Geiss was a senior research scientist in the Air Force Research Laboratory at Wright-Patterson AFB, Ohio. Dr. Geiss earned both his M.S. and Ph.D. from Miami University of Ohio.
Kent L. Hibben United States Department of Energy World Green Energy Symposium Class Presenter
Mr. Kent L. Hibben serves as the US Department of Energy's (DOE) HQ Office of Small and Disadvantaged Business Utilization (OSDBU) subject matter expert and spokesperson on energy efficiency and renewable energy (EERE) issues. His accounts include the DOE EERE and Science offices, and the DOE SBIR/STTR program. He is also Team Leader of the OSDBU Business Opportunity Session activities, advocating for small companies seeking to do business with the US Department of Energy. In his previous (EERE) position he served as a contracting officer representative (COR) for several support service contracts for both the Research and Development (R&D), and the Business Administration sides of the Department of Energy's (DOE) Energy Efficiency and Renewable Energy (EERE) Office. These $25 million in contracts were for a range of business sizes and ownership structures, including small/8(a) firms and Mentor-Protege teaming arrangements. Prior to his COR tenure, Mr. Hibben worked as a legal assistant, program analyst and special investigator for the DOE Office of Hearings and Appeals, resolving cases involving legal claims of businesses and educational organizations of various sizes. Launching his DOE tenure in 1991 as a budget analyst for EERE, Mr. Hibben ensured that R&D activities of DOE National Labs and their subcontractors stayed fully funded. He maintained work continuity throughout the fiscal years for the various renewable energy programs. Prior to his Federal career, Mr. Hibben was a systems analyst, researching legislation and conducting applied research projects at a small business defense contractor in Aberdeen Maryland. He was a licensed stockbroker in a Co-Op Program during his studies at the University of Maryland, including a year of study in Germany. He graduated in 1987 with Bachelor Degrees in Economics, French, German, and Linguistics.
Gary Jenkins, U.S. General Services Administration, World Green Energy Symposium Class Presenter
Gary Jenkins has been with the General Services Administration for 20 years. As a Business Development Specialist for the GSA Center for Facilities Maintenance and Hardware, his experience includes advertising and promoting the Center's 2 Multiple Award Schedules 51V & 03FAC, Develop Marketing Material for the Center, Attend Events/Shows and conferences, Train Federal Agencies, Assist Contractors in getting a GSA Contract and marketing their services and products, and Business Development for the Center. The GSA Center for Facilities Maintenance and Hardware (CFMH) provides federal agencies with a streamlined procurement tool to acquire all of the services necessary to maintain and manage a facility or marine vessels. The CFMH is GSA's home to Energy Management Support and Services, under GSA MAS Schedule 03FAC Facilities Maintenance and Management, provides agencies with expert advice in all areas of energy management improvement and support services, including training, metering, building commissioning, energy audits, resource efficiency management services, turnkey innovation in energy(Innovative approaches to renewable and/or sustainable energy, sustainability services, and energy management technology and services) and water management.
David Kaiser; Director of Enrollment Management for the Fox School of Business
David Kaiser has served as the Director of Enrollment Management for the Fox School of Business since July 2004. He is responsible for all recruitment and retention activities for the Undergraduate Programs at the Fox School. He also serves as the advisor for the Fox School College Council of Presidents, a cooperative council of the student professional organizations. David completed his undergraduate degree in communications in the summer of 1998 and began his career as an Admission Counselor at Temple University Ambler in September 1998. He joined the Fox School in January 2000 as Assistant Director of Enrollment Management and also served as Associate Director of Enrollment Management. He is currently enrolled in the Fox School's MBA program. He received the James McKeever Promising Professional Award from the Pennsylvania Association for College Admission Counseling in 2002. He was also recognized as the 2004-2005 Fox School Administrative Service Award winner.
Kevin Kampschroer Acting Director, Office of Federal High-Performance Green Buildings
Kevin Kampschroer is the Acting Director, Office of Federal High-Performance Green Buildings, created by the Energy Independence & Security Act of 2007, in the US General Services Administration's Public Buildings Service. Mr. Kampschroer has been leading GSA's activities in response to the 2005 and 2007 Energy Bills & Executive Order on the Environment, Sustainability & Energy Conservation. He is creating a new Office within GSA intended to consolidate and coordinate Federal efforts in the broad realm of building sustainability, influence and accelerate industry capability and adoption of sustainable principles across all aspects of asset creation, operation, maintenance and disposal. He created the framework for GSA to respond to the challenges of the American Recovery and Reinvestment Act's mandate to move the GSA Federal building inventory toward high-performance green building. He has worked on developing new energy conservation legislation, in expanding the scope of sustainable design and training, as well as the creation of rigorous environmental management system. Recently, focusing on the relationships among the physical environment, individual and group behavior and organizational performance, Mr. Kampschroer developed a unique framework - of building + behavior + business - tested in real office conditions.
Allen K. Martin, GSA, FAS Contract Specialist
World Green Energy Symposium Class Presenter
Allen joined the GSA team in 2009 and is a retired military officer with over twenty five years of service as an enlisted member of the U.S. Air Force and as a Wing Plans Officer and Contracting Officer. Eleven years of his military career involved contracting assignments as a Contract Specialist, Contracting Officer and Flight Commander at various locations. His final military assignment was with Defense Contract Management Agency-Middle East as Chief of Contracting Policy. Allen achieved a B.S. degree from the University of Maryland, University College and an M.B.A. from the University of Phoenix. He is also a graduate of the U.S. Air Force's Air Command and Staff College. He has held multiple contracting warrants.
Hameed G. Nezhad, Ph.D.
Dr. Nezhad has more than 29 years experience in energy management. He has worked on energy projects in Armenia, China, Georgia, Ghana, India, Indonesia, Iran, Malaysia, Japan, Latvia, Philippines, Pakistan, Syria, Taiwan, Thailand, Ukraine, United Kingdom, and United States. The project sponsors included USAID, UNDP, and ADB. Dr. Nezhad has developed and managed energy research and evaluation programs, and has worked in close collaboration with local utilities, industry, and academic institutions, implementing DSM and ESCO training and development programs. As the project leader He was instrumental in the design and implementation of ADB-funded DSM and ESCO development programs in two provinces in China: Zhejiang and Guandong. In India, Dr. Nezhad designed, implemented, and evaluated USAID-funded energy efficiency projects for several electricity companies. Ph.D. Energy Management and Policy, University of Pennsylvania, Philadelphia, PA. 1979 Ph.D. Dissertation: Critical Choices for the United States and OPEC Member. A summary of dissertation was published in the Journal of Conflict Resolution. Vol. 25. No. 1:115-143.
Natalia Olson Urtecho,
World Green Energy Symposium Ambassador Host, Moderator
Commissioner Olson Urtecho was appointed by Mayor Michael Nutter to serve on the Philadelphia City Planning Commission and Zoning Code Commission on January 2008 and she serves as the Vice-chair of the Zoning Code Commission Natalia is the Director of Global Initiatives at H2L2, a Philadelphia based architecture, infrastructure and planning firm and has over 17 years of experience working with international, regional and local entities in the Philadelphia region and abroad in Latin America and Eastern Europe. She is also the President of the Ecolibrium Group a new social entrepreneurial venture created to drive fiscally responsible sustainability principles and initiatives into business and public policy. Before joining H2L2 and starting the Ecolibrium Group she was a transportation planner at the Delaware Valley Regional Planning Commission and previously before coming to Philadelphia she worked for the U.S State Department in Budapest, Hungary, on NATO accession, international policies, flood relief and evacuation missions, human rights and environmental issues.
Anne Papageorge Vice President for Facilities and Real Estate Services at the University of Pennsylvania
Anne Papageorge is the Vice President for Facilities and Real Estate Services at the University of Pennsylvania. Anne joined the University in October 2006 and has responsibility for Planning; Design and Construction; Facilities Operations, Maintenance, and Utilities; and Real Estate Operations and Development. She oversees a department of approximately 900 staff, $153M in operating expenses and a capital budget averaging approximately $250M per year, the Penn Connects campus development plan, and the Environmental Sustainability Advisory Committee responsible for developing a climate action plan for the university. Anne is a licensed landscape architect and was previously the Senior Vice President and Memorial Design Director for the Lower Manhattan Development Corp., managing the planning, design and construction of the nearly $1 billion project encompassing the World Trade Center Memorial, Memorial Museum, Visitor's Center and related facilities. Prior to joining the LMDC in 2004, she worked in design and construction for the City of New York, where she served as first deputy commissioner of the Department of Design and Construction, managing a staff of 1,200 and overseeing 750 projects valued at $4.4 billion. Anne holds a bachelor's degree in landscape architecture from the State University of New York College of Environmental Science and Forestry School of Landscape Architecture, where she currently serves on the Faculty Landscape Architecture Advisory Council, and an M.B.A. from the City University of New York Baruch College. She has been appointed to the Philadelphia Zoning Code Commission, the mayor's Sustainability Advisory Board, the University City Green Board as well as the Board of the Morris Arboretum of the University of Pennsylvania.
Dino Ramos, Chief Operating Officer, World Trade Center of Greater Philadelphia
Martin J. Weiland, P.E, Director of Subject Matter Expertise U.S. General Services Administration
Martin Weiland is Director of Subject Matter Expertise at GSA's Program Management Office for the American Recovery and Reinvestment Act (ARRA). Martin is accountable for assuring that the ARRA-funded projects actually deliver high performance green buildings. Previous to employment at GSA, Martin worked for the American Society of Heating, Refrigerating, and Air-conditioning Engineers (ASHRAE) as Manager of Government Outreach in Washington, DC, and Manager of Technical Services in Atlanta, GA. Martin has worked as a facilities director and construction project manager for Charlotte County, Florida, as energy manager for Georgetown University, and as a building mechanical/ plumbing/fire system designer for Leo A. Daly Co. He holds a B.S. in Mechanical Engineering and B.A. in Studio Art from Bucknell University, and is a registered professional engineer in Virginia.
Kate Zaiden, Clean Air Council
World Green Energy Symposium Presenter - Sustainability
Kate Zaidan joined the Clean Air Council in October 2008. As the Green Ports Initiative Coordinator, she has worked with her CAC team to unite a diverse group of stakeholders to address environmental issues in air, land and water at Philadelphia ports. Of particular importance in the emerging green ports movement in Philadelphia are the emissions released from short-haul trucks taking cargo from the ports to the distribution centers, and much of Kate's work with the Council has been devoted to designing an effective emission reduction incentive program for this unique constituency. More recently, Ms. Zaidan has taken on the Council's work to construct a multi-use trail extending the Cobbs Creek bikeway to the Heinz Wildlife Refuge through to Governor Prinz Park. Prior to coming to the Clean Air Council, Ms. Zaidan served as the program coordinator for the Women's International League for Peace and Freedom, where she coordinated two campaigns: Save the Water, and Building Peace on Justice in the Middle East. Kate is a graduate of Antioch College in Yellow Springs, Ohio, and resides in Philadelphia, PA.
Greg Zilberfarb
Greg Zilberfarb is currently working with the Propane Education and Research Council (PERC) to provide commercialization and outreach support for new products utilizing propane powered engines. His alternative fuels background is extensive and diverse. In addition to his work with PERC he is working with the National Biodiesel Board on OEM outreach and education. He was Executive Director of National Clean Cities Inc., a National Account Manager of AFVs with Ford Motor Company and Director of Marketing for the Natural Gas Vehicle Coalition. Greg is currently President of theSales.NetWork, a provider of education and outreach services to the alternative fuel industry headquartered in Virginia.
C.R. Herro (invited)
REGISTRATION ONLINE
(This is a very popular Symposium and will fill up quickly. We encourage you to sign up today. Space is limited.)
For registration questions, call 202-465-0009 or email questions to event@wges.us
For details on sponsoring or partnering call 202-465-0009
or email sponsors@worldgreenenergysymposium.us
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{"url":"http:\/\/www.ntg.nl\/pipermail\/ntg-context\/2012\/066062.html","text":"# [NTG-context] simple graphics, Metafun vs. ConTeXt\n\nWolfgang Schuster schuster.wolfgang at googlemail.com\nSun Mar 25 09:50:17 CEST 2012\n\nAm 25.03.2012 um 04:41 schrieb S Barmeier:\n\n> On 03\/23\/2012 03:11 AM, Hans Hagen wrote:\n>> On 22-3-2012 15:09, S Barmeier wrote:\n>>> I have leaved through the ConTeXt and MetaFun manuals on the search for\n>>> examples of graphics resembling the attached file which I created in\n>>> TikZ.\n>>>\n>>> I was wanting to switch to something more native to ConTeXt, but haven't\n>>> quite found a way of realising it in ConTeXt or MetaFun.\n>>>\n>>> Maybe someone would be so kind as to point me to the right section in\n>>> the manual.\n>>>\n>>> All I want is to define text boxes (of a fixed size) to fill them with a\n>>> background colour and (centred, typeset) text. Do I need MetaFun for\n>>> that, or should some table\/framed text environment in ConTeXt be able to\n>>> do that?\n>>\n>> this can be done with \\bTABLE .. \\eTABLE\n>\n> This works as expected, thank you Wolfgang and Hans. I am putting these\n> tables in the margin, though, and neither stack=yes nor stack=continue\n> prevent two of them from overlapping. Is there some casing for the table\n> so that they won't overlap? Also, rather than the top, the bottom of the\n> table is aligned with the line containing the \\inmargin command... but\n> maybe this will be fixed by a solution to the overlapping?\n\nYou can fix the alignment of the table with the \\toplinebox command.\n\n\\starttext\n\n\\dorecurse{4}\n{\\inmargin[stack=continue]{\\toplinebox{\\bTABLE[height=12mm,width=10mm]\\bTR\\bTD 1\\eTD\\bTD 2\\eTD\\eTR\\bTR\\bTD 3\\eTD\\bTD 4\\eTD\\eTR\\eTABLE}}\n\\input ward\\par}\n\n\\stoptext\n\nWolfgang","date":"2014-08-21 06:18:14","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\": 0.8535605669021606, \"perplexity\": 6562.560124176379}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"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-2014-35\/segments\/1408500815050.22\/warc\/CC-MAIN-20140820021335-00263-ip-10-180-136-8.ec2.internal.warc.gz\"}"}
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{"url":"https:\/\/lw2.issarice.com\/posts\/XDLmF9vKa3GE42ct8\/anthropic-probabilities-a-different-approach","text":"# Anthropic Probabilities: a different approach\n\npost by sil ver (sil-ver) \u00b7 2018-07-20T13:02:29.349Z \u00b7 score: 5 (4 votes) \u00b7 LW \u00b7 GW \u00b7 35 comments\n\n## Contents\n\n Introduction\nDiving in: Existential Risk\nA complete Model of Randomness\nLogical Uncertainty\nRe: updating Random Probability\nTying up loose Ends\nReference Classes\nFoundations of Randomness\nPreservation of Expected Evidence\nProblems with existing theories\nSummary\nAn Example\nNone\n\n\nShort Summary: One way to determine the probability for a proposition upon making an observation is to look at other instances of the same observation being made and whether the proposition was true there. Formalizing this leads to a principle that is applicable to some but not all problems, which suggests that there is a fundamental difference between both classes, and that the latter must be treated differently. The result is a theory that has the advantages of both SIA\/FNC and SSA: it rejects the doomsday argument, doesn't care about reference classes, doesn't give answers that are exploitable through bets, and also doesn't claim that a trillion times larger universe must be a trillion times more likely.\n\n# Introduction\n\nNeither SSA nor SIA or FNA give answers I accept in every problem. Moreover, all of them are indifferent about aspects that seem to me to be crucial. This post outlines my suggestion for how we should think about and do calculations involving anthropic probability. I arrive at a theory which is formalized enough to be applicable to every thought experiment I know, and which outputs answers that agree with my intuition in every case.\n\n# Diving in: Existential Risk\n\nConsider the classical anthropic question: humanity created nuclear weapons, which seem pretty dangerous, but so far they haven't killed us. Is that reason to update downward on the probability that they are exceedingly dangerous? To start things off, we'll look at the problem more generally. Let stand for any hypothesis with prior , and for any observation. Applying Bayes and the law of total probability, we get the following:\n\nFirst, observe that if , then this simply equals , as you would expect. (We can't also have as that would imply which we can assume to be false since we conditioned on to begin with.)\n\nSecond, if , we can define\n\nEquivalently, . Plugging this into the formula yields\n\nBy assumption, we know the value of . Thus, the only other thing we need in order to compute is the value of , that is, the probability of observing when is true relative to the probability of observing when is false.\n\nHow does one obtain that value? The classical way is to consider the case where is true, take the probability that we make the observation in that case, and assign that probability to ; then consider the case where is false, take the probability that we make the observation in that case, and assign that probability to . Then divide the first by the second.\n\nProblem: if [many worlds is true and you share consciousness with all of your copies] (in short: if is true), and if is something like \"I observe that nukes haven't destroyed humanity in the past 40 years\", then , and . No update takes place. But this is widely inaccurate: if some species are more responsible with their nukes than others, then more of the responsible species will still be around after seventy years, so the fact that you are still alive is most definitely evidence to consider. The classical approach is insufficient.\n\nAnother way to proceed is to count the number of instances where has been made before, and check in how many of them has been true and false, respectively; then once again divide the first by the second.\n\nAlthough it is more novel, I consider the second approach to be the more fundamental one. The idea is that, if one knows exactly how often is true upon observing (we shall formalize this later), then one must use that proportion as the probability to assign to . This is a strictly weaker claim than the one SIA is making, as it does not make any statements about cases where the assumption is false, which is quite often. In this weaker form, I consider the requirement to be axiomatic: if probability is to mean anything, then a probability of put on a proposition has to mean that this proposition is true half of the time this happens, else the probability isn't correct (again, given that the above assumption holds). In general, however, the classical approach does not meet this criterion.\n\nBefore we focus on cases where the assumption is false, let's look at what happens if it is given. Our initial example becomes such a case once we obtain further information. Thus, assume we have somehow been handed all relevant statistics about extinction rates of species with nuclear weapons in the universe, but we haven't been told where humanity falls into that spectrum. Let \"I observe that the species I am a part of has survived 70 years of nuclear weapons\", and \"the species I am a part of is relatively safe\". Now, let's examine what we would conclude depending on the data. We look at how often is made at different \"places\" in the universe and take that as information about which place we are in. In this case, the places correspond to being a member of a safe or unsafe species, respectively.\n\nIt might be that we live in a universe in which half of all species that develop nuclear weapons are relatively safe, and the other half is relatively unsafe (more precisely, the number of observers in them is the same at the point that nukes are first invented). In this case, warrants a seizable update of , because it is made more frequently by members of species which are relatively safe than by those which are relatively unsafe (since the latter tend to go extinct before making ). For example, if the odds for surviving the first seventy years are 0.01 for relatively unsafe species and 0.9 for relatively safe species, then is made by members of species which are relatively safe 90 times as often as it is made by members of species which are relatively unsafe, so the correct probability to assign to is . Observe that this does not depend on consciousness or many worlds, it holds equally regardless of whether (a classical universe in which personal death implies the permanent end of subjective experience), or , or neither, is true.\n\nGiven this value, we have and so\n\nOf course, it might also be that we live in a different universe. For example, it might be that we live in a universe in which all technologically advancing species are relatively safe. If that's the case, the value of is ; now it is independent of the details of , it wouldn't matter if we had phrased it in terms of one year rather than fifty. Similarly, it might be that we live in a universe in which all technologically advancing species are unsafe, in which case the answer is always 0. And it might be that we live in a universe where some species are safe and some are unsafe, but with a different distribution, in which case the specifics of do matter.\n\nSo far, so good. Now let's formalize this approach.\n\n# A complete Model of Randomness\n\nForget everything you know about how probability is classically computed. Instead, begin by considering the space , where is the set of all possible observations. is the powerset of the set of all possible observations: it contains every combination of things you could possibly observe. This includes not just things you observe at the moment, but also things you observed in the past. \"I hit my head an hour ago,\" for example, is a different observation from \"I hit my head five seconds ago\". At the most fundamental level, would be defined over something like particle structures of the brain, but it is more useful to think of it as observations. Certainly, every observation or set of observations you could ever want to use in the term appears in .\n\nNow, assume you have all information about stored inside of a hypercomputer , and its interface has a nice and powerful filter. Type anything into the blue text field and will translate it into a set of observations , and it will focus on that particular set of observations only.\n\nMoreover, also knows, for each , every instance in which has ever occurred and ever will occur in the history of the universe, and everything about the external circumstances of each such instance.\n\nThe red and bright green blobs symbolize the instances in which the set of observations in the blue box have been made and the proposition in the red box is true and false, respectively. Note, however, that this is a toy example: in reality, all observations available to the observer must be written into the blue box, including the size of their room and their opinion on Pink Floyd.\n\nUnder this model, the term doesn't make sense, not for any . There is no 'probability' of a set of observations occurring. But the term does make sense. Thus, we can remedy the previous abuse of notation by using a different operator. Rather than using , we define by\n\nWhere is the set of all instances in which has been made, and and are the subsets in which is true and false, respectively. Thus, we shall not write and in formulas anymore, but we'll still use and . In summary, this means that\n\nwhere and\n\nInformally,\n\nThese numbers are usually infinite, but this isn't a serious problem. In case of , we could use density functions; and in case of infinite time, we could use limit points. It won't have to concern us.\n\nStill, this is clearly not the entire story. One, it says nothing about how to proceed if one doesn't have access to , which is always. Two, there are situation in which it doesn't give any justification to update, even though updating is clearly warranted, as we shall see. And three, it presupposes the ability to perfectly take all available information into account, no matter how hard it is to deduce their relevance. Then why did I call it a complete model in the headline?\n\nWell, because it is a complete model, but not a model of all probability, merely one of randomness as I define it: given and , the value of as computed using is random. In other words, randomness is all probability that is left even with full knowledge of past and future observations and perfect deductive ability, i.e. with access to . Under this definition, randomness is fully compatible with determinism.\n\nLet's deal with the third problem. In the model as laid out thus far, the probability may turn on aspects of whose importance we are not smart enough to deduce ourselves, even if they could in theory be explained to us. The solution is to, for each proposition , define an equivalence relation on , where\n\nThen, given a set of observations , shall always condition on , that is, on the set of all possible combinations of observations that are indistinguishable in regard to from the perspective of the observer. In other words, after typing something into the blue box, will show all rather than just , and it will work with the instance set rather than . For example, in our opening question about existential risk, would be invariant under changes of the name of our species or the birthday of our pet, but a change in the number of functional nuclear weapons on the planet might lead to a different equivalence class. This is how the image might now look after the search (elements of that don't match are gray in this picture, rather than being left out entirely).\n\nThis lends naturally into the next definition. Relative to an observer, given and , the value of as computed using conditioned on is pseudo-random. What's left is being ignorant about knowledge available to ; any probability originating due to that reason is defined as logical uncertainty (we shall look at this in more depth later). Taken together, (pseudo-)randomness and logical uncertainty are exhaustive, any probability is one or the other.\n\nA note on terminology: I use the term logical uncertainty for every statement that is absolute, i.e. not relative to any places, observer, or world. I make no distinction between statements like \"a third of all species inventing the wheel also invent air travel\" and statements which are more strictly logical in nature, such as \"\".\n\nNow, it's time to deal with the big problem: is an idealized model that requires full knowledge of everything and is impossible to use. To have something more manageable, we introduce the semi-formal notion of an experiment. Relative to an observation and a hypothesis , an experiment is defined as a sequence of random events that fully specify how often is made in each possible branch, and in which cases is true. Importantly, we do not demand to know everything about ; for example, we might not know the probability of internal random events. We do, however, demand that all randomness have static probabilities.\n\nWhereas runs on the data of the entire history of the universe (past and future), any one encompasses but a miniature slice of that information, just enough to specify a single situation. Whereas is unimaginably large, any one may be specified in just a few sentences, or in a small graph. Given this new definition, can be viewed as the universal experiment, that gives perfect answers in every situation, as supposed to any one , which will give answers for a single problem only. From now on, we shall tackle problems primarily by designing experiments (or, later, sets of possible experiments) that describe them.\n\nRecall the case of a universe where one half of all species that have invented nukes is relatively safe, and the other half is relatively unsafe. Knowing this, we can update on based on the fact that it is made more often by members of relatively safe species. This is how an experiment describing this problem might look like (the leaves being blue indicates that is being made from them, in our case just once):\n\nAlthough this appears to have a very different structure than , we can obtain the same results. Recall that\n\nwhere\n\nIn an experiment like the above, we obtain the value of by checking where ends up as we run it many times. Formally,\n\nwhere is the set of instances of made in iterations of . Since all probabilities in are static, this limit always exists by the law of large numbers. One could obtain the same results by defining in terms of products from probabilities on branches. In this case, we have .\n\nTake a moment to consider the way in which we went about reducing complexity here. Clearly, no formal model can create information specific to a problem; we don't know any more about extinction rates in the universe now than we did before. What knowing about does is tell us which information matters, which instances of ignorance hurt, and why. For example, it is obvious that the universe won't actually look like this. Obviously, there aren't just safe and unsafe species out there and nothing in between. However, the model of tells us that if the universe did look like this, then the above experiment would indeed output perfect results. Consequently, it also tells us that an experiment which does output perfect results exists. Thus, we can think of our uncertainty about this problem as uncertainty about how exactly this perfect experiment looks like.\n\nOur modelling of imperfect deductive ability as an equivalence relation is implicit in the construction of : by assigning the top branches a probability of each, we assert that there is no information aside from the length of time since the invention of nuclear weapons and the observation that we're still alive that helps us decide whether our species is safe or unsafe. Given that we have no point of comparison, this particular assumption might not even be unreasonable.\n\nOne potential problem with that I left out is the question of whether it can be biased, of in other words, whether there exists a set of observations such that only a hand full of instances of observing have ever occurred and will ever occur, and because of their low sample size, the proportion of times that a certain proposition was true would strike us as unreasonable even given perfect deductive ability. If that were the case, then we'd have instances of correct probabilities of random events be potentially dubious. But whether or not such instances exist, we can now see that it really doesn't matter. In order to construct an instance of , we already rely merely on our expectations about how randomness looks like, and thus, whether or not the true random numbers would seem reasonable to us is of no concern.\n\nAll in all, experiments are far more manageable than . But they don't answer the question of how to deal with logical uncertainty. This is what we turn to next.\n\n# Logical Uncertainty\n\nLet's consider a variant of the most recent problem: suppose we know that we are not in the universe where species are split equally across both sides, rather we know that we are in one of the other two universes \u2013 the one where everyone is safe or the one where everyone is unsafe \u2013 but we don't know in which; for all we know, both are equally likely.\n\nIn both cases, we have a prior of on , and both times we want to update based on an ostensibly identical observation . But, clearly, they are different. In the former case, we can construct so that we know it outputs correct probabilities. In the latter case, we don't. Certainly, it is wrong to model as starting off with a coin toss: this would imply that repeated iterations can go down different branches, but that is not so. Rather, consists of one random event only; this random event has a fixed probability, we just don't know it. Put differently, there are two possible experiments and , one of which is running all the time, but we don't know which one it is.\n\nIn the former case, we can justify our updates by reasoning that is made 90 times as often when is true than when it's false. In the latter case this is not so; is either always true or always false.\n\nNonetheless, one might still wish to update in the second case. The mere fact that a particular argument doesn't work hardly proves that it should behave any differently. Indeed, doubting that the nature of probability plays a role could lead one to conclude that the second case must behave just like the first. This brings us to relevant points which have already been made; let's review the 2002 debate between Olum and [Bostrom and \u0106irkovi\u0107].\n\nFirst, Olum makes a strong case for SIA over SSA when evaluating God's Coin Toss experiment, which is meant to be an isomorph of the Doomsday Argument.\n\nSuppose that God tosses a fair coin. If it comes up heads, he creates ten people, each in their own room. If tails, he creates one thousand people, each in their own room. The rooms are numbered 1-10 or 1-1000. The people cannot see or communicate with the other rooms. Suppose that you know all this, and you discover that you are in one of the first ten rooms. How should you reason that the coin fell?\n\nTo illustrate the difference, he then extrapolates two different experimental protocols that give the SIA answer of and the SSA answer of , respectively (for heads).\n\nImagine that you are one of a very large number of experimental subjects who have been gathered, in case of need, into an experimental pool. Each subject is in a separate waiting room and cannot communicate with the others. First the experiment will be described to you, and then it will be performed. The experiment will have one of the following two designs.\nProtocol 1 (random): The experimenter will flip a fair coin. If the coin lands heads, she will get ten subjects, chosen randomly from the pool, and put them in rooms numbered 1-10. If the coin lands tails, she will do the same with one thousand subjects in rooms numbered 1-1000.\nProtocol 2 (guaranteed): The experimenter will flip a fair coin. If the coin lands heads, she will get you and nine other subjects, and put you randomly into rooms numbered 1-10. If the coin lands tails, she will get you and 999 other subjects and put you randomly into rooms numbered 1-1000.\n\nHe argues for protocol 1 on the basis that it's symmetric with respect to participants, and that protocol 2 introduces a sharp discontinuity among the number of subjects, among other arguments. In their reply, Bostrom and \u0106irkovi\u0107 start off with a thought experiment that has since come to be known as the Presumptuous Philosopher problem:\n\nIt is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, and (using considerations from super-duper symmetry). According to , the world is very, very big but finite and there are a total of a trillion trillion observers in the cosmos. According to , the world is very, very, very big but finite and there are a trillion trillion trillion observers. The super-duper symmetry considerations are indifferent as between these two theories. Physicists are preparing a simple experiment that will falsify one of the theories. Enter the presumptuous philosopher: \u201cHey guys, it is completely unnecessary for you to do the experiment, because I can already show to you that is about a trillion times more likely to be true than !\u201d (whereupon the philosopher runs the argument that appeals to SIA).\n\nSIA and FNC have no tools to differentiate between both problems. They just have to bite the bullet and agree that the philosopher is correct. But for us, the two experiments are widely different. The probability in God's Coin Toss is random, at least if is true. We know the exact configuration of the underlying experiment : by the definition of a fair coin toss, it has to come up heads in half of all worlds, so instances of observing \"I am in room 1-10\" are split evenly across cases where the coin has come up heads and tails.\n\nThe probability in the above problem, on the other hand, appears to be logically uncertain; we don't know how looks like. As it is run many times, the hypothesis \" is true\" is either always true or never, but which of those two holds depends entirely on a logically uncertain fact, a property of that we don't know.\n\nHow does one deal with a logically uncertain statement? Certainly, this isn't an easy problem. There's nothing analogous to randomness as we defined it because the proposition isn't relative to an observer: it is either always true or always false. However, it is still coherent to talk about probability in the Bayesian sense, as subjective uncertainty.\n\nSIA and FNC don't seem to have the right answer, given that both of them agree with the philosopher. If the presumptuous philosopher problem isn't convincing to you, however, consider the following variant. Let there be two logically uncertain propositions, one of them false and the other true. Both propositions relate to the size of the universe in two independent ways: for each, the expected number of observers in the cosmos would be 1000 as large if it were true rather than false. This means that, if both were false, there would be observers; if one were true and the other false, there would be ; and if both were true, there would be . Given that one proposition is true and the other false, the actual number of observers is 1000.\n\nBoth propositions are extraordinarily hard to falsify, so for a long time, physicists assign both of them a prior of . And, just like in the presumptuous philosopher problem, SIA demands one favor the possibility with the most observers, which in this case means asserting that both propositions be almost certainly true. But, if everyone reasons like this, the result is that all people are horribly calibrated. Alternatively, if is true, all people are horribly calibrated in every world.\n\nOn the other hand, clearly some updates on logically uncertain propositions must be possible, otherwise, we couldn't do physics. Yet, if we're not allowed to count instances for logically uncertain propositions, then there is no justification for updating on anything by relying on . Even if we wanted to test whether coins come up heads half of the time or all of the time, flipped a coin 100 times and got 100 heads, wouldn't give us any justification to update towards the heads-only universe. Either we live in the heads-only universe or we don't; in the first case all observations of 100 times heads happen in the heads-only universe, and if we don't all observations of 100 times heads happen in the heads-sometimes universe. If we're not allowed to count instances...\n\nThe problem is not that is flawed. The problem is that is designed to output answers to questions of randomness. can tell an observer where she is within the universe, but it is utterly useless to figure out things about the universe. And this is a fundamental difference. It is why everything we have typed into , observations and propositions likewise, have been statements relative to an observer. Formally, they have all been formulas that are free in one variable. And this has to be so; once again, is there to help an observer figure out her place in the universe, so naturally, the observation has to be relative to her. And if the proposition were absolute, well then it would be a trivial example, as its value would either be zero or one, regardless of the observation. Remember that, by assumption, already knows everything there is to know about the universe.\n\nIf we wish to update our probability on a logically uncertain proposition, it is crucial that the opposite be the case: both the proposition and the observation must be absolute so that they describe the universe, not the observer. Both must be complete sentences in which every variable is bound. Given that, updates are possible and may be calculated via Bayes.\n\nTo hammer down the difference, when it comes to updating logical uncertainty, we shall no longer refer to the object we update on as an observation but as a fact, and denote it as rather than .\n\nLet's go back to our initial example. We know we either live in the universe where every species is safe, or in the universe where every species is unsafe, but between the two, it's a toss-up. Can we update our probability based on still being alive?\n\nFirst, we need to define and . The former is easy; \"every species is in the universe is relatively safe\" is a fine choice for , as it is a sentence with no free variables that does what we want. is a bit trickier. It can't be \"I am alive\" as interpreted as an observation like we did before, as that observation is made all the time by everyone. Actually, it cannot be any observation, or at least it's better not to think of it as one, since the term has a subjective connotation, particularly as it relates to . Instead, what we want to be is \"I have conscious experience right now\". This may sound like it's relative to an observer, but it absolutely isn't. It refers to a particular consciousness, namely yours, and its truth value is dependent entirely on the universe we live in. As such, it is no different from the statement \"there are more than a trillion hydrogen atoms right now\", both are simply true, and neither you nor anyone else has any say on the matter. Alas,\n\nwhere and are the odds for you to have conscious experience right now given a safe and unsafe universe, respectively.\n\nIt is easy to see that the value of this term depends on quantum physics and on unknown facts about consciousness. If is true, then we presumably have , in which case . If is true, one might or might not still argue for on the basis that one would be more likely to have been born at all. If we do have , then ; no update takes place.\n\nThis suffices to remedy the scientific method. In the coin flip example, one can set \"the coin I flipped has come up heads a hundred times\" and update via Bayes, thereby getting the result one would expect. Once again, one mustn't be confused by the appearance of the word \"I\" in the sentence; it does not mean that it is relative to anything, as we now take \"I\" to mean one particular observer (which we never did when working with ). The difference may be subtle, but it is real and important.\n\nCare must be taken to do this properly. For example, even if is true, one might still be tempted to update on \"I am alive\", where \"I\" is meant to refer to the current instance of oneself in particular, rather than being left unbound. Then it's not free in any variable, right? But this is an instance of the survivorship bias. If a million people jump of a cliff and you know at least one survived, and you talk to a random survivor, then the fact that the person you're talking to survived is not a surprise. This is what happens when we condition on \"I am alive\", interpreted as above. But updating on \"I have conscious experience right now\" is different, because the \"I\" in the sentence refers to the entire tree of your copies, not one leaf in particular. Now, it's like noting that at least one of the cliff-jumpers is still alive, which might be a trivial fact, but it is not an instance of the survivorship bias. The survivorship bias applies if the elements we refer to as fulfilling have been pre-selected to fulfill . This is not the case when noting that there are any survivors, but it is the case when we already know that there are survivors, talk to a random one among them, and then note that that person is a survivor.\n\nThe presumptuous philosopher problem also depends on facts about consciousness, which strikes me as exactly the right answer. If it is indeed true that we win a lottery at birth, tossed into a single body and seize to exist once it dies, then the odds of winning this lottery must be a trillion times higher in the case of , and then the problem must be isomorphic to the variant where both and predict people to have existed initially, but in the case of , of them have died as the universe has shrunk due to super-duper-evil physical phenomenon . Claiming to live in is thus equivalent to claiming that one has been among the relatively few people who have been close enough to the center of the universe to be spared by . This seems no different from claiming that one has survived 70 highly dangerous years of nuclear weapons. In both cases, this is evidence for preferring the theory with a safe humanity \/ a universe where has not occurred. Conversely, if one imagines to exist either way, this is of no concern.\n\nBelow is a summary, which also includes what would happen if the choice between and were random (we will see how this could be the case in the next section).\n\n# Re: updating Random Probability\n\nRecall that one of the problems with the approach for updating random probability has been that it requires the full knowledge contained in . We've since covered updating logically uncertain propositions, but this leaves open the question of how to update a proposition in a case where we are logically uncertain about things relevant to the proposition, but where the proposition itself is random.\n\nAs an example, consider the version of Sleeping Beauty where she isn't asked about her probability estimate on the coin being heads, but about her probability estimate on it being Monday. According to SSA, the answer is . We, on the other hand, would count instances of observations, and conclude that the answer is . SIA and FNC, giving in the original problem, would answer likewise.\n\nBut now consider a second variant, where the experiment's protocol doesn't rely on a coin flip but on the value of the chromatic number of the plane (which the experimenters have secretly found out but not yet published). Suppose the protocol demands Sleeping Beauty be interviewed once per day, as many times as the number is large, that is, either 5, 6, or 7 times. (That means the first interview is on Monday, and the last is either on Friday, Saturday, or Sunday.) Being an amateur mathematician, Sleeping Beauty doesn't know anything about the problem except for the lower and upper bound, so her probability distribution on the value of the chromatic number is simply .\n\nAs she is being interviewed, how likely, from her perspective, is it Monday? Going by SSA, all possibilities for the chromatic number are equally likely, and so\n\nGoing by SIA, the probabilities are proportional to their number of observations, and so\n\nThis experiment is meant to illustrate both how my theory deals with this kind of uncertainty in principle, and why the \"principled\" approach is usually false.\n\nSaid approach is straight-forward. Given a random proposition and a logically uncertain proposition with possibility space and prior distribution , we define in the obvious way.","date":"2019-08-22 06:49:31","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\": 1, \"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\": 0.7241224646568298, \"perplexity\": 426.5720189632275}, \"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-2019-35\/segments\/1566027316785.68\/warc\/CC-MAIN-20190822064205-20190822090205-00430.warc.gz\"}"}
| null | null |
Q: Проблема к подключению к MySQL с Java Пишу в IntelliJ IDEA переписал все с сайта с пояснениями, но ничего не работает.
Пытаюсь подключиться к Базе Данных на MySQL ittrayvor через localhost с портом 3307, который стоит на сервере MAMP.
*
*Логин: root
*Пароль: root.
Вот код:
package com.Trayvor;
import java.sql.*;
public class Main {
public static void main(String[] args) {
try {
Class.forName("com.mysql.jdbc.Driver");
} catch (ClassNotFoundException e) {
System.out.println("Unable to load class");
e.printStackTrace();
}
String URL = "jdbc:mysql://localhost:3307/ittrayvor";
String USER = "root";
String PASSWORD = "root";
Connection connection = null;
try {
connection = DriverManager.getConnection(URL, USER, PASSWORD);
} catch (SQLException e) {
e.printStackTrace();
}
try {
connection.close();
} catch (SQLException e) {
e.printStackTrace();
}
}
}
Вот ошибка, которая выдаеться:
"C:\Program Files\Java\jdk-13.0.1\bin\java.exe"
"-javaagent:C:\Programs\IntelliJ IDEA Community Edition
2019.3.1\lib\idea_rt.jar=64310:C:\Programs\IntelliJ IDEA Community Edition 2019.3.1\bin" -Dfile.encoding=UTF-8 -classpath
"C:\Users\user\Desktop\Java_Practice\Java_General_Practice\out\production\Practice;C:\Program
Files\Java\mysql-connector-java-8.0.19\mysql-connector-java-8.0.19.jar"
com.Trayvor.Main Loading class com.mysql.jdbc.Driver'. This is
deprecated. The new driver class iscom.mysql.cj.jdbc.Driver'. The
driver is automatically registered via the SPI and manual loading of
the driver class is generally unnecessary. java.sql.SQLException: The
server time zone value '��������� (����)' is unrecognized or
represents more than one time zone. You must configure either the
server or JDBC driver (via the 'serverTimezone' configuration
property) to use a more specifc time zone value if you want to utilize
time zone support. at
com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:129)
at
com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:97)
at
com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:89)
at
com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:63)
at
com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:73)
at
com.mysql.cj.jdbc.exceptions.SQLExceptionsMapping.translateException(SQLExceptionsMapping.java:76)
at
com.mysql.cj.jdbc.ConnectionImpl.createNewIO(ConnectionImpl.java:836)
at com.mysql.cj.jdbc.ConnectionImpl.(ConnectionImpl.java:456)
at
com.mysql.cj.jdbc.ConnectionImpl.getInstance(ConnectionImpl.java:246)
at
com.mysql.cj.jdbc.NonRegisteringDriver.connect(NonRegisteringDriver.java:197)
at
java.sql/java.sql.DriverManager.getConnection(DriverManager.java:677)
at
java.sql/java.sql.DriverManager.getConnection(DriverManager.java:228)
at com.Trayvor.Main.main(Main.java:17) Caused by:
com.mysql.cj.exceptions.InvalidConnectionAttributeException: The
server time zone value '��������� (����)' is unrecognized or
represents more than one time zone. You must configure either the
server or JDBC driver (via the 'serverTimezone' configuration
property) to use a more specifc time zone value if you want to utilize
time zone support. at
java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance0(Native
Method) at
java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance(NativeConstructorAccessorImpl.java:62)
at
java.base/jdk.internal.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:45)
at
java.base/java.lang.reflect.Constructor.newInstanceWithCaller(Constructor.java:500)
at
java.base/java.lang.reflect.Constructor.newInstance(Constructor.java:481)
at
com.mysql.cj.exceptions.ExceptionFactory.createException(ExceptionFactory.java:61)
at
com.mysql.cj.exceptions.ExceptionFactory.createException(ExceptionFactory.java:85)
at com.mysql.cj.util.TimeUtil.getCanonicalTimezone(TimeUtil.java:132)
at
com.mysql.cj.protocol.a.NativeProtocol.configureTimezone(NativeProtocol.java:2118)
at
com.mysql.cj.protocol.a.NativeProtocol.initServerSession(NativeProtocol.java:2142)
at
com.mysql.cj.jdbc.ConnectionImpl.initializePropsFromServer(ConnectionImpl.java:1310)
at
com.mysql.cj.jdbc.ConnectionImpl.connectOneTryOnly(ConnectionImpl.java:967)
at
com.mysql.cj.jdbc.ConnectionImpl.createNewIO(ConnectionImpl.java:826)
... 6 more Exception in thread "main" java.lang.NullPointerException
at com.Trayvor.Main.main(Main.java:22)
Process finished with exit code 1
Я импортировал JBDC драйвер через File>Project Structure в IntelliJ IDEA
A: Попробуете установить тайм зон.
SET GLOBAL time_zone = '+8:00';
Наглядно с видео
Подробное описание
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 582
|
Herb Kolumbii przyjęty został 9 maja 1834 roku i nieznacznie zmodyfikowany w 1924.
Tarcza herbowa podzielona jest na trzy części. W dolnej części znajdują się dwa statki, które nawiązują do morskiej przeszłości Kolumbii (w tym do Przesmyku Panamskiego, który należał do Kolumbii, aż do 1903 roku) oraz do dwóch oceanów, do których dostęp ma Kolumbia – Atlantycki i Spokojny. W części środkowej na platynowym tle umieszczono czapkę frygijską – tradycyjny symbol wolności. Górna część przedstawia owoc granatu na lazurowym tle, który symbolizuje Wicekrólestwo Nowej Granady (dawna nazwa kolonialna Kolumbii). Po obu stronach granatu znajdują się rogi obfitości, symbolizujące bogactwa naturalne państwa. Nad tarczą znajduje się kondor wielki trzymający gałązkę oliwną oraz motto narodowe Libertad y Orden (). Po obu stronach tarczy umieszczono kolumbijskie flagi.
Historia
Zobacz też
Kolumbia
Flaga Kolumbii
Hymn Kolumbii
Kolumbia
Symbole narodowe Kolumbii
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,107
|
Q: How to download an image with the button click in C#? Is there a way to download an image that was uploaded by the user? I have the following: First, the user click an image from a mosaic to view it in detail; then the image is generated in a asp:image tag, at that step they are supposed to download it with a button click. The problem I have is that the image is generated in a asp:image tag and is not the actual image itself with a name. The code I have to download only gets the image stored in a folder. Below is the code:
protected void btnDownload_Click(object sender, EventArgs e)
{
string path = @"C:\inetpub\wwwroot\PSCSearchEngine\MemberPages\Images\live.jpg";
System.IO.FileInfo file = new System.IO.FileInfo(path);
if (file.Exists)
{
Response.Clear();
Response.ContentType = MimeType(Path.GetExtension(path));
Response.AddHeader("Content-Disposition",
string.Format("attachment; filename = {0}",
System.IO.Path.GetFileName(path)));
Response.AddHeader("Content-Length", file.Length.ToString("F0"));
Response.TransmitFile(path);
Response.End();
}
else
{
Response.Write("This file does not exist.");
}
}
Below is the code that previews the image:
@"~/MemberPages/UpdatePhoto.aspx?SiteKey=" + foo.Site_ID
+ "&TimeStamp=" + foo.timestamp[n1 - 1];
A: Code for download an image file with the button click in C#
protected void btnDownload_Click(object sender, EventArgs e)
{
string filename=MapPath("birds.jpg");
Response.ContentType = "image/JPEG";
Response.AddHeader("Content-Disposition", "attachment; filename=" + filename+ "");
Response.TransmitFile(filename);
Response.End();
}
A: You may try this:
using (var client = new System.Net.WebClient())
{
var _imagebytes = client.DownloadData(string.Format(@"~/MemberPages/UpdatePhoto.aspx?SiteKey={0}&TimeStamp={1}", foo.Site_ID, foo.timestamp[n1 - 1]));
Response.Clear();
Response.ContentType = "image/jpg";
Response.AddHeader("Content-Disposition", string.Format("attachment; filename = {0}", "MyImage.jpg"));
Response.AddHeader("Content-Length", _imagebytes.Length.ToString("F0"));
Response.OutputStream.Write(_imagebytes, 0, _imagebytes.Length);
Response.End();
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,889
|
The Veera Prathapa () is a non titular national honour of Sri Lanka awarded "for acts of bravery of the highest order". Veera Prathapa ranks lower than Sri Lanka Thilaka.
Awardees
Awardees include:
1998
Cprl. R. P. R. Wickramapala
O. R. A. K. Perera
Amithapala Weerasinghe
2017
Aluth Gedara Ranjith Amarajeewa
Rankoth Gedara Shanaka Prasad Kumara
References
External links
Civil awards and decorations of Sri Lanka
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 713
|
\section{Introduction}
A century has elapsed since the momentous discovery of the special
theory of relativity by Einstein \cite{ref:1}. This theory has
inspired subsequent pursuit of the general theory of relativity
as a novel theory of gravitation \cite{ref:2}. It has also led to
the understanding of the relativistic wave equation of an
electron \cite{ref:3}. In the last five decades, relativity has
also inspired the gauge field theories of subatomic particle
interactions which have spectacular experimental confirmations
\cite{ref:4}. However, applications of relativity theory into
applied mathematical problems are almost non-existent. We venture
to write this review article mainly to attract the academic
attentions of applied mathematicians to this fascinating branch
of modern theoretical science.
\qquad There exist well established special relativistic particle
mechanics, relativistic fluid mechanics and electrodynamics. In
the special theory of relativity, spacetime is assumed to be a
\emph{flat} differentiable manifold. Since Einstein's
gravitational theory involves a \emph{curved} pseudo-Riemannian
manifold, special relativistic dynamics of various macroscopic
systems usually must omit gravitation. This is generally valid as
the gravitational field is extremely weak in comparison to the
other force fields involved. However, a linearized version of
Einstein's theory of gravitation can be incorporated within the
framework of special relativity. Our present review article aims
at such a treatment of various dynamical systems. It is hoped
that such a review will serve as a useful introduction to the
field for practitioners of non relativistic fluid mechanics as
well as those wishing to study weak-field gravitating particles,
fluids and plasmas such as are found in various astrophysical
systems. As mentioned above, it is written with applied
mathematicians as the primary intended audience. However, we hope
this review will be useful to the wider audience as well. No
previous knowledge of special relativity or Minkowski tensors is
assumed.
\qquad The electrodynamics and mechanics of relativistic
continuous media, coupled to gravitation, has many interesting
applications in astrophysics (for examples, see \cite{ref:4b})
and other areas of general relativity and high-energy physics
\cite{ref:4c}. As well, the intrested reader is refered to the
books \cite{ref:4d} and references therein.
\qquad In section-II, notations for vectors and tensors in three
and four dimensions are laid out in a leisurely fashion. In the
third section, particle mechanics (mainly special relativistic)
is discussed in a nut-shell. We do derive Einstein's famous
equation $E=mc^2$ in this section.
\qquad In section-IV, we discuss Maxwell's equations of
electromagnetic fields. These equations are known to be already
relativistic! However, Lorentz's equation of motion requires some
minor modification for the relativistic conversion.
\qquad In section-V, a special relativistic version of the
gravitational field equations is investigated. It involves a
symmetric second order tensor field in spacetime to represent the
gravitational force. We then couple the gravitational field
with: (i) an incoherent dust, (ii) an electrically charged dust
(pressureless plasma), and (iii) a perfect fluid. In the
following section we specialize furthermore to static gravitational fields.
Planetary motions are investigated in the static field and an approximation to the
famous perihelion shift is derived. Moreover, we
also explore a perfect fluid in the presence of static external
gravitation, deriving the relativistic Euler equation in the process.
\qquad In the last section, we generalize preceding investigations
to more complicated materials (plasmas with pressure and
viscosity) and derive the relativistic Navier-Stokes equation.
Furthermore, generalizations to curvilinear coordinates and
orthonormal (or physical) components are also touched upon.
\qquad In deformable media, a stress tensor,
$\sigma_{ij}(x^{1},\,x^{2},\,x^{3})\equiv
\sigma_{ji}(x^{1},\,x^{2},\,x^{3})$ indicate equilibrium
conditions by the satisfaction of the equations
$\sum_{j=1}^{3}\frac{\partial\,\sigma_{ij}(x^{1},\,x^{2},\,x^{3})}{\partial
x^{j}}=0$. In the special relativistic generalization, an
energy-momentum-stress tensor
$T_{\mu\nu}(x^{1},\,x^{2},\,x^{3},\,x^{4})\equiv
T_{\nu\mu}(x^{1},\,x^{2},\,x^{3},\,x^{4})$ is introduced.
Moreover, \emph{dynamical equilibrium} of deformable bodies or fluids
are characterized by conditions
$\sum_{\nu=1}^{4}\frac{\partial\,T_{\mu\nu}(x^{1},\,x^{2},\,x^{3},\,x^{4})}{\partial
x^{\nu}}=0$. These equations are of utmost importnace throughout
the paper in deriving relativistic continuity equations and
relativistic equations for streamlines.
\section{Notations and conventions}
The three-dimensional physical space is assumed to be Euclidean. A
typical point in this space is denoted by
$\mathbf{x}:=(x^{1},\,x^{2},\,x^{3}) \in \mathbb{R}^{3}$. We use mostly a
Cartesian coordinate system.
\qquad The spacetime continuum, $M_{4}$, is assumed to be a flat
differentiable manifold admitting Minkowskian coordinate systems
\cite{ref:5}\cite{ref:6}. (These are generalizations of Cartesian
coordinates.) Relative to a Minkowski coordinate system, an
idealized point event in $M_{4}$ can be mapped uniquely into the
point $x:=(x^{1},\,x^{2},\,x^{3},\,x^{4}) \in \mathbb{R}^{4}$. Here, $(x^{1},\,x^{2},\,x^{3})$
indicates the spatial coordinates in the Euclidean
$\mathbb{R}^{3}$, whereas $x^{4}$ is the speed of light times the
time coordinate, i.e. $x^{4}=ct$.
\qquad Roman indices are used for three-dimensional spatial
components of vectors and tensors (the components in the
Euclidean $\mathbb{R}^{3}$). Greek indices are used for the four
dimensional spacetime components of vectors and tensors.
Einstein's summation convention is followed for \emph{both} Roman
and Greek indices.
\qquad We shall furnish some simple examples. three-dimensional
vectors are denoted by a \emph{bold} letter. For example, the
vector $\mathbf{v}$ has components $v^{i}\,;\, i\in
\left\{1,\,2,\,3\right\}$. The Kronecker delta:
$\delta^{i}_{\;j}$, $\delta_{ij}$, $\delta^{ij}$ are all entries
of the $3\times 3$ unit matrix $\left[I\right]_{3\times 3}$.
Therefore,
\begin{equation}
\delta^{i}_{\;j}\equiv \delta_{ij}\equiv \delta^{ij}:=\left\{
\begin{array}{lll}
1 & \mbox{ for } & i=j, \\
0 & \mbox{ for }&
i \neq j.
\end{array}
\right. \label{eq:2.1}
\end{equation}
The inner product of two (three-dimensional) vectors
$\mathbf{v}$, $\mathbf{w}$ and the length $|\mathbf{v}|$ are given
by
\begin{subequations}
\begin{align}
\mathbf{v}\cdot\mathbf{w}=&\delta_{ij}v^{i}w^{j}=: \sum_{i=1}^{3}\sum_{j=1}^{3} \delta_{ij}v^{i}w^{j} \label{eq:2.2i} \\
|\mathbf{v}|:=&
+\sqrt{\mathbf{v}\cdot\mathbf{v}}=\sqrt{\delta_{ij}v^{i}v^{j}} =
\sqrt{(v^{1})^{2}+(v^{2})^{2} +(v^{3})^{2}}. \label{eq:2.2ii}
\end{align}
\end{subequations}
The totally anti-symmetric numerical (oriented) tensor \cite{ref:7} is defined by the components:
\begin{equation}
\epsilon_{ijk} :=\left\{
\begin{array}{lll}
+1 & \mbox{ for } (ijk) \;\;\mbox{an even permutation of }(123), \\
-1 & \mbox{ for } (ijk) \;\;\mbox{an odd permutation of }(123), \\
\;\;\; 0 & \mbox{ otherwise}.
\end{array}
\right. \label{eq:2.3}
\end{equation}
We can express some familiar vector calculus notions with the help of $\epsilon_{ijk}$. For example,
\begin{subequations}
\begin{align}
\epsilon_{ijk}v^{j}w^{k}=&\left(\mathbf{v} \times \mathbf{w}\right)^{i} , \label{eq:2.4i}\\
\epsilon_{ijk} \frac{\partial B^{j}(x)}{\partial
x^{k}}=&-\left(\nabla \times \mathbf B\right)^{i}. \label{eq:2.4ii}
\end{align}
\end{subequations}
In the four-dimensional Minkowski spacetime, the metric tensor components are furnished by
\begin{equation}
d_{\mu\nu} \equiv d_{\nu\mu}:=\left\{
\begin{array}{lll}
\;\; \delta_{ij} & \mbox{ for } \mu=i \mbox{ and } \nu=j, \\
-1 & \mbox{ for } \mu=\nu=4, \\
\;\;\; 0 & \mbox{ otherwise}.
\end{array}
\right. \label{eq:2.5i}
\end{equation}
\begin{subequations}
\begin{align}
\left[d^{\mu\nu}\right]=& \left[d_{\mu\nu}\right]^{-1}, \label{eq:2.5ii}\\
d^{\mu\nu}d_{\nu\lambda}=&\delta^{\mu}_{\;\lambda} = d_{\lambda\nu}d^{\nu\mu}. \label{eq:2.5iii}
\end{align}
\end{subequations}
For the four-dimensional vector components, the lowering of indices is accomplished by:
\begin{equation}
u_{\alpha}:=d_{\alpha\beta}u^{\beta},
\end{equation}
so that it follows:
\begin{align}
u_{i}=&d_{i\nu}u^{\nu}=\delta_{ij}u^{j}, \nonumber \\
u_{4}=&d_{4\nu}u^{\nu}=-u^{4}, \\
u^{\alpha}=&d^{\alpha\beta}u_{\beta}. \nonumber
\end{align}
The four-dimensional inner product between two vectors is provided by:
\begin{subequations}
\begin{align}
d_{\mu\nu}a^{\mu}b^{\nu}=&\delta_{ij}a^{i}b^{j}-a^{4}b^{4}, \\
d_{\mu\nu}a^{\mu}a^{\nu}=&(a^{1})^{2} +(a^{2})^{2} +(a^{3})^{2} -(a^{4})^{2}.
\end{align}
\end{subequations}
Vectors are characterized as timelike, spacelike and null by:
\begin{subequations}
\begin{align}
d_{\alpha\beta}v^{\alpha}v^{\beta} <&0 \;\;\;\; \mbox{for a timelike vector}, \\
d_{\alpha\beta}v^{\alpha}v^{\beta} >&0 \;\;\;\; \mbox{for a spacelike vector}, \\
d_{\alpha\beta}v^{\alpha}v^{\beta} =&0 \;\;\;\; \mbox{for a null
vector}.
\end{align}
\end{subequations}
\section{Particle mechanics (Newtonian and Relativistic)}
\noindent We shall start with a very brief review of Newtonian
mechanics. For the sake of simplicity, we restrict ourselves to
the case of a single point particle with mass $m > 0$. Let the
parameterized motion curve by given by
\begin{equation}
x^{i}=\mathcal{X}^{i}(t)
\end{equation}
where $x^{i}$ are Cartesian coordinates of the Euclidean space
$\mathbb{E}_{3}$ and $t$ is the time variable. Let the three
components of the force vector be given by $f^{i}(t,\mathbf{x},
\mathbf{v})$, which are functions of seven real variables. The
components $v^{i}$ represent the velocity variables.
\qquad Newton's equations of motion for a single particle are
provided by the well known equations:
\begin{equation}
m\frac{d^{2}\mathcal{X}^{i}(t)}{dt^{2}}=f^{i}(t,\mathbf{x},\,
\mathbf{v})_{|x^{i}=\mathcal{X}^{i}(t),\,v^{i}=d\mathcal{X}^{i}/dt}
\label{eq:3.2}
\end{equation}
\qquad These equations imply that
\begin{equation}
\frac{d}{dt}\left[\frac{1}{2}m \delta_{ij}\frac{d\mathcal{X}^{i}(t)}
{dt}\frac{d\mathcal{X}^{j}}{dt}\right]=
\delta_{ij}\left[v^{i}f^{j}(t,\mathbf{x},\mathbf{v})\right]_{|...}\;.
\label{eq:3.3}
\end{equation}
The above equations are physically interpreted as ``the rate of
increase of kinetic energy of the particle is equal to the rate
of work performed by the external force''.
\qquad We note that Newton's equations of motion
(\ref{eq:3.3}) remain unchanged in form (or covariant) under
the coordinate transformations:
\begin{subequations}
\begin{align}
\hat{x}^{a}=&c^{a} +r^{a}_{\;b}x^{b}, \label{eq:3.4i}\\
\left[R\right]_{3\times 3}:=&\left[r^{a}_{\;b}\right], \label{eq:3.4ii}\\
\left[R\right]^{\mbox{\tiny{T}}}\left[R\right]=&\left[I\right]_{3\times 3}. \label{eq:3.4iii}
\end{align}
\end{subequations}
The equation (\ref{eq:3.4iii}) \emph{defines an orthogonal
matrix} $\left[R\right]_{3\times 3}$. The set of transformations
(\ref{eq:3.4i}) constitute the six parameter group
$\mathcal{IO}(3;\mathbb{R})$, the isometry group of Euclidean
three-space $\mathbb{E}_{3}$.
\qquad Consider another transformation, namely a special Galilean transformation:
\begin{align}
\hat{x}^{1}=&x^{1}-v^{1}t, \nonumber \\
\hat{x}^{2}=&x^{2}, \;\; \hat{x}^{3}=x^{3}, \label{eq:3.5} \\
\hat{t}=&t. \nonumber
\end{align}
The new (hatted) frame is moving with constant velocity $v^{1}$
along the $x^{1}$-axis relative to the old frame. The Newtonian
motion laws (\ref{eq:3.3}) remain unchanged in form by the
Galilean transformations (\ref{eq:3.5}).
\qquad In the nineteenth century, Michelson and Morley performed
some sophisticated experiments regarding light propagation in
vacuum \cite{ref:michmor}. The startling outcome of their results was that the speed
of light does \emph{not} change due to any (constant) motion of
either the source or observer. Newton's ideas of absolute space
and absolute time (inherent in (\ref{eq:3.2}) and
(\ref{eq:3.5})) are \emph{incompatible} with Michelson and
Morley's experimental findings \cite{ref:michmor}. In 1905 Einstein solved this
puzzle by the revolutionary ideas that space and time are
relative in regards to any motion \cite{ref:1}. However, a combined spacetime
continuum, $M_{4}$, is still \emph{absolute}. The appropriate
generalization of the three-dimensional Cartesian coordinates are
the four-dimensional Minkowskian coordinates \cite{ref:5} \cite{ref:6}. Moreover, the
correct generalization of the transformations in
(\ref{eq:3.4i}) are furnished by (figure 1):
\begin{subequations}
\begin{align}
\hat{x}^{\alpha}=& c^{\alpha}+l^{\alpha}_{\;\beta}x^{\beta}, \label{eq:3.6i}\\
\left[L\right]_{4\times 4}:=& \left[l^{\alpha}_{\;\beta}\right], \label{eq:3.6ii}\\
\left[D\right]_{4\times 4}\equiv& \left[d_{\mu\nu}\right], \label{eq:3.6iii} \\
\left[L\right]^{\mbox{\tiny{T}}}\left[D\right]\left[L\right]=&\left[D\right], \label{eq:3.6iv} \\
\left[d^{\mu\nu}\right]:=& \left[D\right]^{\mbox{\tiny{-1}}}
\equiv\left[D\right] =\left[d_{\mu\nu}\right]. \label{eq:3.6v}
\end{align}
\end{subequations}
\begin{figure}[ht]
\begin{center}
\includegraphics[bb=0 0 699 347, clip, scale=0.5, keepaspectratio=true]{fig1.eps}
\caption{{\small The inhomogeneous Lorentz transformation in spacetime.}} \label{fig1}
\end{center}
\end{figure}
A typical example of the above transformation (with $x^{4}=ct$) is provided by:
\begin{align}
\hat{x}^{1}=& \frac{x^{1}-\left(\frac{v^{1}}{c}\right)x^{4}}{\sqrt{1-\left(\frac{v^{1}}{c}\right)^{2}}}=x^{1}-v^{1} t +\mathcal{O}\left(\frac{(v^{1})^{2}}{c^{2}}\right), \nonumber \\
\hat{x}^{2}=&x^{2}, \;\; \hat{x}^{3}= x^{3}, \nonumber \\
\hat{x}^{4}=&\frac{x^{4}-\left(\frac{v^{1}}{c}\right)x^{1}}{\sqrt{1-\left(\frac{v^{1}}{c}\right)^{2}}} = ct+\mathcal{O}\left(\frac{v^{1}}{c^2}\right), \label{eq:3.7} \\
\hat{t}=& t +\mathcal{O}\left(\frac{1}{c^{2}}\right). \nonumber
\end{align}
We make the following comments on the above transformations: \\
(i) The equation (\ref{eq:3.7}) is called the Lorentz (or ``boost'') transformation \cite{ref:5} \cite{ref:6}. \\
(ii) It is the correct generalization of the Galilean transformation (\ref{eq:3.5}) for a moving frame. \\
(iii) The above transformation implies contraction of length measurements in the moving frame. \\
(iv) It can bring about the ``slowing'' of time measurements (time dilation) for a moving observer. \\
(v) The speed, $|v^{1}|$ of the moving observer must be
\emph{strictly less than} $c$, \emph{the speed of light}.
\qquad The set
of transformations in (\ref{eq:3.6i}) constitutes a continuous
group known as the inhomogeneous Lorentz group or the
Poincar\'{e} group. It is a ten parameter group denoted by
$\mathcal{IO}(3,1;\mathbb{R})$.
\qquad It follows from (\ref{eq:3.6iv}) that
$\mbox{det}\left[L\right]=\pm 1$. Therefore, the inverse matrix
exists and is denoted by
\begin{align}
\left[a^{\alpha}_{\;\beta}\right]_{4\times 4} \equiv& \left[A\right]:=\left[L\right]^{\mbox{\tiny{-1}}}, \nonumber \\
l^{\mu}_{\; \nu}a^{\nu}_{\; \beta}= & a^{\mu}_{\; \nu}l^{\nu}_{\; \beta} =\delta^{\mu}_{\; \beta}. \label{eq:3.8}
\end{align}
Now we shall define Minkowskian tensor fields in the flat
spacetime manifold $M_{4}$. These are defined by the
transformation properties \cite{ref:5}, \cite{ref:6}, \cite{ref:7}:
\begin{equation}
\hat{T}^{\alpha_{1}...
\alpha_{r}}_{\;\;\;\;\;\;\;\;\beta_{1}...\beta_{s}}(\hat{x})=
l^{\alpha_{1}}_{\;\gamma_{1}}...l^{\alpha_{r}}_{\;\gamma_{r}}
a^{\mu_{1}}_{\;\beta_{1}}...a^{\mu_{s}}_{\;\beta_{s}}
T^{\gamma_{1}...\gamma_{r}}_{\;\;\;\;\;\;\;\;\mu_{1}...\mu_{s}}(x).
\label{eq:3.9}
\end{equation}
Here, the coefficients $l^{\alpha}_{\;\gamma}$,
$a^{\mu}_{\;\beta}$ are defined by (\ref{eq:3.6i}) and
(\ref{eq:3.8}). The tensor fields in (\ref{eq:3.9})
are of order $r+s$, where $r$ is the contravariant order and $s$
is the covariant order. Note that the right hand side of
(\ref{eq:3.9}) condenses a sum of $4^{r+s}$ terms!
Moreover, these tensor fields are assumed to be twice
continuously differentiable. The restriction of the tensor fields
on a parameterized curve in $M_{4}$ satisfies the transformation
rules:
\begin{equation}
\hat{T}^{\alpha_{1}...\alpha_{r}}_{\;\;\;\;\;\;\;\;\beta_{1}...\beta_{s}}
(\hat{x})_{|\hat{x}=\hat{\mathcal{X}}(\tau)}=
l^{\alpha_{1}}_{\;\gamma_{1}}...l^{\alpha_{r}}_{\;\gamma_{r}}
a^{\mu_{1}}_{\;\beta_{1}}...a^{\mu_{s}}_{\;\beta_{s}}
T^{\gamma_{1}...\gamma_{r}}_{\;\;\;\;\;\;\;\;\mu_{1}...\mu_{s}}(x)_{|{x}={\mathcal{X}}(\tau)}.
\label{eq:3.10}
\end{equation}
As simple examples, we consider the numerical second order
tensors $d_{\mu\nu}$, $d^{\alpha\beta}$ in (\ref{eq:3.6iii}) and
(\ref{eq:3.6v}) respectively. By the rules
(\ref{eq:3.9}) we deduce that
\begin{align}
\hat{d}_{\alpha\beta}=&a^{\mu}_{\;\alpha}a^{\nu}_{\;\beta}d_{\mu\nu}
=d_{\alpha\beta}, \nonumber \\
\hat{d}^{\alpha\beta}=&l^{\alpha}_{\;\mu}l^{\beta}_{\;\nu}d^{\mu\nu}
=d^{\alpha\beta}. \label{eq:3.11}
\end{align}
These special tensor components \emph{retain} their numerical
values under the rules (\ref{eq:3.10}).
\qquad Now, let us consider a $0+0$ order or scalar field $W(x)$
which is twice differentiable. Further, let it satisfy the wave
equation:
\begin{equation}
\square W(x):=d^{\alpha\beta}\frac{\partial^{2}}{\partial
x^{\alpha}\partial
x^{\beta}}=\left[\frac{\partial^{2}}{\left(\partial
x^{1}\right)^{2}}+ \frac{\partial^{2}}{\left(\partial
x^{2}\right)^{2}} + \frac{\partial^{2}}{\left(\partial
x^{3}\right)^{2}} - \frac{1}{c^{2}}
\frac{\partial^{2}}{\left(\partial t\right)^{2}} \right]W(..)=0.
\label{eq:3.12}
\end{equation}
We can prove from (\ref{eq:3.10}) (which in this case
reads $\hat{W}(\hat{x})=W(x)$), (\ref{eq:3.11}), (\ref{eq:3.6i})
and the chain rule of differentiation that (\ref{eq:3.12})
implies:
\begin{equation}
\hat{\square}\hat{W}(\hat{x})=\hat{d}^{\alpha\beta}
\frac{\partial^{2}\hat{W}(\hat{x})}{\partial\hat{x}^{\alpha}
\partial \hat{x}^{\beta}} = \left[\frac{\partial^{2}}{\left(\partial
\hat{x}^{1}\right)^{2}}+ \frac{\partial^{2}}{\left(\partial
\hat{x}^{2}\right)^{2}} + \frac{\partial^{2}}{\left(\partial
\hat{x}^{3}\right)^{2}} - \frac{1}{c^{2}}
\frac{\partial^{2}}{\left(\partial \hat{t}\right)^{2}}
\right]\hat{W}(..) = 0. \label{eq:3.13}
\end{equation}
Since the speeds of wave propagation in (\ref{eq:3.12}) and
(\ref{eq:3.13}) are both $c$, the speed of light, we conclude
that the speed of such a wave remains invariant under any motion
of an observer characterized by (\ref{eq:3.7}).
\qquad Now we discuss another important feature of the tensor
field in (\ref{eq:3.9}) (or (\ref{eq:3.10})). The
four-dimensional tensor field equation
\begin{equation}
T^{\gamma_{1}...\gamma_{r}}_{\;\;\;\;\;\;\;\;
\mu_{1}...\mu_{s}}(x)= 0
\end{equation}
hold if and only if the transformed components satisfy
\begin{equation}
\hat{T}^{\alpha_{1}...\alpha_{r}}_{\;\;\;\;\;\;\;\;
\beta_{1}...\beta_{s}}(\hat{x}) =0.
\end{equation}
This statement physically signifies that a natural law
expressible by the vanishing of a tensor field remains unaltered in any
rotated, reflected or moving frame. The main mathematical
postulate of the special theory of relativity is that the natural
laws must be expressed as tensor field equations in spacetime.
\qquad Now we shall study the relativistic particle mechanics.
For that purpose we have to introduce the exact definition of a
parameterized curve in $M_{4}$ and its physical interpretation. It
is easier to consider the corresponding parameterized curve in the
coordinate space $\mathbb{R}^{4}$. See figure 2.
\begin{figure}[ht]
\begin{center}
\includegraphics[bb=50 323 618 608, clip, scale=0.5, keepaspectratio=true]{fig2.eps}
\caption{{\small A parametrized curve in spacetime.}} \label{fig2}
\end{center}
\end{figure}
\qquad Let a differentiable parameterized curve into the
Minkowskian coordinate space $\mathbb{R}^{4}$ be characterized be
characterized by
\begin{align}
x^{\mu}=&\mathcal{X}^{\#\, \mu}(u) , \label{eq:3.14} \\
u_{1} \leq& u \leq u_{2}\, . \nonumber
\end{align}
Here, the functions $\mathcal{X}^{\#\,\mu}$ are assumed to be
continuously twice differentiable. Suppose that the curve
represents physically the history of an idealized ``point'' clock
moving in spacetime. The \emph{proper} (or actual) time flow of
the clock along the motion curve is given by \cite{ref:5},
\cite{ref:6}
\begin{equation}
s=S^{\#}(u):=\frac{1}{c} \int_{u_{1}}^{u} \sqrt{-d_{\alpha\beta}
\frac{d\mathcal{X}^{\#\,\alpha}(w)}{dw}
\frac{d\mathcal{X}^{\#\,\beta}(w)}{dw}}\,dw. \label{eq:3.15}
\end{equation}
Here, we have tacitly assumed that
\begin{equation}
0 < \sqrt{-d_{\alpha\beta}
\frac{d\mathcal{X}^{\#\,\alpha}(u)}{du} \frac{d\mathcal{X}^{\#\,\beta}(u)}{du}}
\equiv c \frac{dS^{\#}(u)}{du} \label{eq:3.16}
\end{equation}
for all $u \in [u_{1},\;u_{2}]$. The suppositions above are based
on physical principles. Consider for example a free particle in
the spacetime. The history curve, or world line, of such a
particle would be a straight line with some slope. An observer
``traveling'' with this particle, feeling no acceleration can
justifiably claim that he or she is not moving but it is the
surroundings which are moving. Therefore, to the observer, he or
she is not moving in space but only in time. Generalizing this, a
straight time-like world line therefore represents the appropriate time
axis for an observer on this trajectory.
\qquad Physically, (\ref{eq:3.16}) implies that the curve is
timelike and the actual speed along the curve, as measured by an
observer whose time axis is given by the $x^{4}$ axis in figure
2, is \emph{always less than the speed of light}.
\qquad The integral (\ref{eq:3.15}), which defines the proper
time, $s$, is \emph{invariant} (or scalar) with respect to
transformations (\ref{eq:3.6i}). Moreover, the integral
(\ref{eq:3.15}) is \emph{invariant} under any smooth
reparameterization of the curve characterized by
\begin{align}
x^{\mu}=&\mathcal{X}^{\#\,\mu}(u)=\tilde{\mathcal{X}}^{\mu}(y), \nonumber \\
y=&Y(u), \; \frac{dY(u)}{du} \neq 0, \nonumber \\
Y(u_{1}):=&y_{1} \leq y \leq y_{2} := Y(u_{2}). \label{eq:3.17}
\end{align}
Chosing the parameter $y=s$, the proper time, we obtain from
(\ref{eq:3.15}), (\ref{eq:3.16}) and (\ref{eq:3.17}) that
\begin{subequations}
\begin{align}
x^{\mu}=&\mathcal{X}^{\#\,\mu}(u)=:\mathcal{X}^{\mu}(s), \;\; s_{1}=0 \leq s
\leq s_{2}, \label{eq:3.18i} \\
s=& S(s) =\frac{1}{c} \int_{0}^{s}\sqrt{-d_{\alpha\beta}
\frac{d\mathcal{X}^{\alpha}(w)}{dw} \frac{d\mathcal{X}^{\beta}(w)}{dw}}\,dw,
\label{eq:3.18ii} \\
1\equiv& \frac{dS(s)}{ds} =\frac{1}{c} \sqrt{-d_{\alpha\beta}
\frac{d\mathcal{X}^{\alpha}(s)}{ds} \frac{d\mathcal{X}^{\beta}(s)}{ds}},
\label{eq:3.18iii} \\
&d_{\alpha\beta} \frac{d\mathcal{X}^{\alpha}(s)}{ds}
\frac{d\mathcal{X}^{\beta}(s)}{ds} \equiv -c^{2} < 0 . \label{eq:3.18iv}
\end{align}
\end{subequations}
Here, $\frac{d\mathcal{X}^{\alpha}(s)}{ds}$ are the four components of
the \emph{relativistic} velocity along the motion curve.
\qquad In case the motion curve $x^{\mu}=\mathcal{X}^{\mu}(s)$ is
continuously twice differentiable, which we shall always assume,
the differentiation of (\ref{eq:3.18iv}) yields
\begin{equation}
d_{\alpha\beta}\frac{d\mathcal{X}^{\alpha}(s)}{ds}
\frac{d^{2}\mathcal{X}^{\beta}(s)}{ds^{2}} \equiv 0. \label{eq:3.19}
\end{equation}
Therefore, in the proper time parametrization, \emph{the
four-acceleration is always (Minkowskian) orthogonal to the
four-velocity!}
\qquad In case we reparameterize the curve by choosing $y=t$, the
usual or coordinate time, we derive from (\ref{eq:3.15}),
(\ref{eq:3.16}) and (\ref{eq:3.17}) that
\begin{subequations}
\begin{align}
x^{\mu}=\mathcal{X}^{\mu\#}(u)=:&\overline{\mathcal{X}}^{\mu}(t),\;
x^{i}=\overline{\mathcal{X}}^{i}(t),\; x^{4}=\overline{\mathcal{X}}^{4}(t):=ct,
\label{eq:3.20.i}
\\
s=&\overline{S}(t) =\frac{1}{c}\int_{t_{1}}^{t}
\sqrt{-d_{\alpha\beta} \frac{d\overline{\mathcal{X}}^{\alpha}(w)}{dw}
\frac{d\overline{\mathcal{X}}^{\beta}(w)}{dw}}\,dw, \label{eq:3.20ii} \\
\frac{d\overline{S}(t)}{dt} \equiv& \frac{1}{c} \sqrt{-d_{\alpha\beta}
\frac{d\overline{\mathcal{X}}^{\alpha}(t)}{dt}
\frac{d\overline{\mathcal{X}}^{\beta}(t)}{dt}} > 0, \label{eq:3.20iii} \\
\left[\frac{d\overline{S}(t)}{dt}\right]^{2} \equiv &1 -
\frac{1}{c^{2}}\left[\delta_{ij}
\frac{d\overline{\mathcal{X}}^{i}(t)}{dt}
\frac{d\overline{\mathcal{X}}^{j}(t)}{dt}\right]. \label{eq:3.20iv}
\end{align}
\end{subequations}
Recall that the Newtonian 3-velocity variables in
(\ref{eq:3.2}) are
\begin{align}
v^{i}=&V^{i}(t):=\frac{d\overline{\mathcal{X}}^{i}(t)}{dt}, \nonumber \\
|\mathbf{v}|^{2}=&|\mathbf{V}(t)|^{2}=\delta_{ij} V^{i}(t)
V^{j}(t) \geq 0. \label{eq:3.21}
\end{align}
Thus, we deduce from (\ref{eq:3.20iv}) and (\ref{eq:3.21}) that
\begin{align}
\left[\frac{d\overline{S}(t)}{dt}\right]^{2}=&
1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}, \nonumber \\
0 < \frac{d\overline{S}(t)}{dt}=& +
\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}} \leq 1. \label{eq:3.22}
\end{align}
\qquad Now we investigate the relationships among Newtonian
3-velocity components with the correcponding relativistic
4-velocity components. Using the chain rule of differentiation,
we obtain from (\ref{eq:3.18i}, \ref{eq:3.18ii},
\ref{eq:3.18iii}), (\ref{eq:3.20.i}, \ref{eq:3.20ii},
\ref{eq:3.20iii}), (\ref{eq:3.21}) and (\ref{eq:3.22}) that
\begin{subequations}
\begin{align}
\frac{d\overline{\mathcal{X}}^{i}(t)}{dt}=& \frac{d\overline{S}(t)}{dt}
\frac{d{\mathcal{X}}^{i}(s)}{ds}, \label{eq:3.23i} \\
\frac{d\mathcal{X}^{i}(s)}{ds}=& \frac{V^{i}(t)}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}},
\label{eq:3.23ii} \\
\frac{d\mathcal{X}^{4}(s)}{ds}=& \frac{1}
{\left[\frac{d\overline{S}(t)}{dt}\right]}
\frac{d\overline{\mathcal{X}}^{4}(t)}{dt} =\frac{c}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}} > c.
\label{eq:3.23iii}
\end{align}
\end{subequations}
\qquad Now we shall generalize the Newtonian equations of motion
(\ref{eq:3.2}) into the relativistic arena. We postulate, as
a generalization of (\ref{eq:3.2}), the special relativistic
equations of motion as \cite{ref:5}, \cite{ref:6}:
\begin{equation}
m\frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}}=
\mathcal{F}^{\alpha}(x;\,u)_{|x^{\alpha}=\mathcal{X}^{\alpha}(s),\;u^{\alpha}=\frac{d\mathcal{X}^{\alpha}(s)}{ds}}.
\label{eq:3.24}
\end{equation}
Here, $(x):=(x^{1}, \, x^{2},\,x^{3}, \, x^{4})$ and
$(u):=(u^{1},\, u^{2}, \, u^{3}, \, u^{4})$. Each of the four
components $\mathcal{F}^{\alpha}$ is a function of eight
real variables and represents physically the relativistic force.
(We have tacitly assumed that the mass , $m >0$, remains
\emph{unchanged} along the motion curve in spacetime.) It follows
from (\ref{eq:3.19}), (\ref{eq:3.23ii}, \ref{eq:3.23iii}) and
(\ref{eq:3.24}) that
\begin{subequations}
\begin{align}
&d_{\alpha\beta}\mathcal{F}^{\alpha}(..)_{|..}
\frac{d\mathcal{X}^{\beta}(s)}{ds} \equiv 0, \label{eq:3.25i} \\
\mathcal{F}^{4}(..)_{|..} \equiv& \delta_{ij} \mathcal{F}^{i}(..)_{|..}
\frac{d\mathcal{X}^{j}(s)}{ds} \left[\frac{d\mathcal{X}^{4}(s)}{ds}\right]^{-1}
\equiv \delta_{ij}F^{i}(..)\frac{V^{j}(t)}{c} . \label{eq:3.25ii}
\end{align}
\end{subequations}
Now we shall compare the relativistic equations (\ref{eq:3.24})
with the Newtonian equations (\ref{eq:3.2}) and
(\ref{eq:3.3}). Let us digress slightly. Suppose that we have
a differentiable function $f$ defined along the motion curve. By
the equations (\ref{eq:3.18i}), (\ref{eq:3.20.i}) and
(\ref{eq:3.22}) and the chain rule, we get
\begin{subequations}
\begin{align}
\overline{f}(t):=& f\left[\overline{S}(t)\right]=f(s) , \label{eq:3.26i} \\
\frac{df(s)}{ds}=& \frac{1}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}}
\frac{d\overline{f}(t)}{dt} \label{eq:3.26ii}
\end{align}
\end{subequations}
Substituting (\ref{eq:3.26ii}) into the first three equations in
(\ref{eq:3.24}) we deduce that
\begin{subequations}
\begin{align}
\frac{d}{dt} \left[\frac{m V^{i}(t)}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}} \right] =&
\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}} \mathcal{F}^{i}(..)_{..}, \label{eq:3.27i} \\
m\frac{d^{2}\overline{\mathcal{X}}^{i}(t)}{dt^{2}} =& \mathcal{F}^{i}
(..)_{|..} + \mathcal{O}\left(\frac{1}{c^{2}}\right).
\label{eq:3.27ii}
\end{align}
\end{subequations}
Comparing (\ref{eq:3.27i}) with (\ref{eq:3.2}) we conclude
that the Newtonian momentum components, $mV^{i}(t)$ have to be
modified into $mV^{i}(t)/\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}$ in relativity. Moreover,
the Newtonian force components relate to relativistic force
components by the equations:
\begin{equation}
f^{i}(t,\mathbf{x},\mathbf{v})_{x^{i}=\overline{\mathcal{X}}^{i}(t),v^{i}=
\frac{d\overline{\mathcal{X}}^{i}(t)}{dt}} = \sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}
\mathcal{F}^{i}(x, u)_{x^{i}=\overline{\mathcal{X}}^{i}(t), x^{4}=ct,
u^{i}=v^{i}/{\sqrt{..}}, u^{4} =c/{\sqrt{..}}} \label{eq:3.28}
\end{equation}
The fourth equation in (\ref{eq:3.24}) yields, with
(\ref{eq:3.23iii}), (\ref{eq:3.25ii}), (\ref{eq:3.26ii}) and
(\ref{eq:3.28})
\begin{subequations}
\begin{align}
m\frac{d}{dt} \left[\frac{c}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}} \right]=& \sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}
\mathcal{F}^{4}(..)_{|..}, \label{eq:3.29i} \\
\mbox{or, }\;\;\; \frac{d}{dt} \left[\frac{mc^{2}}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}}
\right]=& \delta_{ij} \left[v^{i}f^{j}(..)\right]_{|..}\; .
\label{eq:3.29ii}
\end{align}
\end{subequations}
Expanding (\ref{eq:3.29ii}) for $|\mathbf{V}(t)|/c < 1$, we obtain
that
\begin{equation}
\frac{d}{dt} \left[mc^{2} +\frac{1}{2} m |V(t)|^{2} + \mathcal{O}
\left(\frac{1}{c^{2}}\right) \right] = \delta_{ij} \left[v^{i}
f^{j}(..)\right]_{|..} . \label{eq:3.30}
\end{equation}
Comparing the above equation with the corresponding Newtonian
equation (\ref{eq:3.3}), we conclude that the instantaneous
energy $E(|\mathbf{V}(t)|)$ of the particle must be furnished by
\begin{equation}
E(|\mathbf{V}(t)|)=\frac{mc^{2}}{\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}}} =mc^{2}
+\frac{m}{2} |\mathbf{V}(t)|^{2}
+\mathcal{O}\left(\frac{1}{c^{2}}\right) . \label{eq:3.31}
\end{equation}
In the limit $|\mathbf{V}| \rightarrow 0$, we derive that
\begin{equation}
E(0)=mc^{2}\, . \label{eq:3.32}
\end{equation}
The above equation, which is the most famous formula of modern
science, reveals the \emph{enormous rest energy} of a massive
particle. (The rest energy associated with a single $1$ kilogram object
is approximately $9\times 10^{16}$ Joules, enough to meet New York City's energy requirements for more than seven months!)
\section{Electromagnetic fields}
Maxwell's equations of electromagnetic fields are, in Gaussian units, the following:
\begin{subequations}
\begin{align}
c\:\epsilon_{ijk} \frac{\partial B^{j}(\mathbf{x},t)}{\partial
x^{k}}=& -4\pi j_{i}(\mathbf{x},t) -
\frac{\partial E_{i}(\mathbf{x}, t)}{\partial
t}, \label{eq:4.1i} \\
\frac{\partial E^{i}(\mathbf{x},t)}{\partial x^{i}}=& 4\pi\sigma
(\mathbf{x},t),
\label{eq:4.1ii} \\
\frac{\partial B^{i}(\mathbf{x},t)}{\partial x^{i}} =&0,
\label{eq:4.1iii} \\
c\:\epsilon_{ijk} \frac{\partial E^{j}(\mathbf{x},t)}{\partial
x^{k}}=& \frac{\partial{B}^{i}(\mathbf{x},t)}{\partial t},
\label{eq:4.1iv}
\end{align}
\end{subequations}
Here, $E^{i}(..)$ and $B^{i}(..)$ stand for the electric and
magnetic field components respectively. Also, The charge density
and the current density components are denoted by $\sigma(..)$
and $j_{i}(..)$ respectively.
\qquad Another popular system of units, which we shall \emph{not}
employ here, is the Systeme Internationale (SI). In these units,
Maxwell's equations read:
\begin{subequations}
\begin{align}
\epsilon_{ijk} \frac{\partial B^{j}(\mathbf{x},t)}{\partial
x^{k}}=& -\mu_{0} j_{i}(\mathbf{x},t) -\frac{1}{c^{2}}
\frac{\partial E_{i}(\mathbf{x}, t)}{\partial
t}, \label{eq:4.1SIi} \\
\frac{\partial E^{i}(\mathbf{x},t)}{\partial x^{i}}=&
\frac{\sigma (\mathbf{x},t)}{\epsilon_{0}},
\label{eq:4.1SIii} \\
\frac{\partial B^{i}(\mathbf{x},t)}{\partial x^{i}} =&0,
\label{eq:4.1SIiii} \\
\epsilon_{ijk} \frac{\partial E^{j}(\mathbf{x},t)}{\partial
x^{k}}=& \frac{\partial{B}^{i}(\mathbf{x},t)}{\partial t}.
\label{eq:4.1SIiv}
\end{align}
\end{subequations}
The constants
$\epsilon_{0}$ and $\mu_{0}$ respectively represent the
permittivity and permeability of free space with the relation $c=1/\sqrt{\epsilon_{0}\mu_{0}}$.
\qquad The equations (\ref{eq:4.1i} -
\ref{eq:4.1iv}) imply that the charge current conservation
equation:
\begin{equation}
\frac{\partial j^{i}(\mathbf{x},t)}{\partial x^{i}} +
\frac{\partial \sigma(\mathbf{x},t)}{\partial t} =0 \label{eq:4.2}
\end{equation}
must be satisfied.
\qquad The energy density of the electromagnetic field is
characterized by
\begin{equation}
u(\mathbf{x},t):= \frac{1}{8\pi} \delta_{ij}
\left[E^{i}(..)E^{j}(..) + B^{i}(..)B^{j}(..) \right]
. \label{eq:4.3}
\end{equation}
The momentum density of the electromagnetic field is provided by
\begin{equation}
S_{i}(\mathbf{x},t):=\frac{1}{4\pi} \epsilon_{ijk}E^{j}(\mathbf{x},t)
B^{k}(\mathbf{x},t) \label{eq:4.4}
\end{equation}
The corresponding vector field $\mathbf{S}(\mathbf{x},t)$ is also known as the
\emph{Poynting vector}.
\qquad Maxwell's \emph{electromagnetic stress tensor} is
furnished by
\begin{align}
M_{ij}(\mathbf{x},t)=&
\frac{1}{4\pi} \left\{\left[E_{i}(\mathbf{x},t)E_{j}(\mathbf{x},t)
-\frac{1}{2}\delta_{ij}
\delta^{kl}E_{k}(\mathbf{x},t)E_{l}(\mathbf{x},t)\right] \right.
\nonumber \\
&+ \left.\left[B_{i}(\mathbf{x},t)B_{j}(\mathbf{x},t)
+\frac{1}{2}\delta_{ij}
\delta^{kl}B_{k}(\mathbf{x},t)B_{l}(\mathbf{x},t)\right] \right\}
\label{eq:4.5}
\end{align}
\qquad The components of the \emph{Lorentz force} on a charged
particle (of net charge $e$) is given by
\begin{equation}
f_{i}(t,\mathbf{x}, \mathbf{v}):=e \left[E_{i}(\mathbf{x},t) +
\epsilon_{ijk}\frac{v^{j}}{c}B^{k}(\mathbf{x},t)\right]. \label{eq:4.6}
\end{equation}
Note that this equation yields
\begin{equation}
v^{i}f_{i}(t,\mathbf{x},\mathbf{v})=eE_{i}(\mathbf{x},t)v^{i} ,
\label{eq:4.7}
\end{equation}
indicating the well known result that the magnetic field makes
no contribution to the rate of work.
\qquad Now, we shall obtain the special relativistic versions of
the various electromagnetic equations. Following Minkowski
\cite{ref:9}, we define the four-dimensional electomagnetic
field tensor components as:
\begin{equation}
\left[F_{\mu\nu}(x)\right]:= \left[
\begin{array}{cccc}
0 & B_{3}(x)& -B_{2}(x)& E_{1}(x) \\
-B_{3}(x) & 0 & B_{1}(x) & E_{2}(x) \\
B_{2}(x)& -B_{1}(x) & 0 & E_{3}(x) \\
-E_{1}(x) & -E_{2}(x) & -E_{3}(x) & 0
\end{array}
\right] \equiv\left[-F_{\nu\mu}(x)\right]. \label{eq:4.8}
\end{equation}
It should be mentioned that Minkowski first \emph{unified}
electric and magnetic fields by the definition (\ref{eq:4.8}) of
the four-dimensional anti-symmetric tensor $F_{\mu\nu}(x)$. The
above is one of several possible definitions for the tensor
$F_{\mu\nu}$. We define the relativistic charge-current components
by:
\begin{align}
J^{i}(x):=&j^{i}(\mathbf{x},t), \nonumber \\
J^{4}(x):=&c\sigma(\mathbf{x},t). \label{eq:4.9}
\end{align}
The Maxwell equations (\ref{eq:4.1i}-\ref{eq:4.1iv}), along with
definitions (\ref{eq:4.8}) and (\ref{eq:4.9}), neatly boil down to
\cite{ref:8}
\begin{subequations}
\begin{align}
\frac{\partial F^{\mu\nu}(x)}{\partial x^{\nu}}&= \frac{4\pi}{c}J^{\mu}(x),
\label{eq:4.10i} \\
\frac{\partial F^{\mu\nu}(x)}{\partial x^{\lambda}}+\frac{\partial
F^{\nu\lambda}(x)}{\partial x^{\mu}}+\frac{\partial
F^{\lambda\mu}(x)}{\partial x^{\nu}}&=0 \label{eq:4.10ii} \\
\frac{\partial J^{\mu}(x)}{\partial x^{\mu}}&=0 .
\label{eq:4.10iii}
\end{align}
\end{subequations}
Outside of charged matter, Maxwell's equations are summarized by:
\begin{align}
\frac{\partial F^{\mu\nu}(x)}{\partial x^{\nu}}=& 0, \nonumber \\
\frac{\partial F_{\mu\nu}(x)}{\partial x^{\lambda}}+\frac{\partial
F_{\nu\lambda}(x)}{\partial x^{\mu}}+\frac{\partial
F_{\lambda\mu}(x)}{\partial x^{\nu}}&=0, \label{eq:4.11}
\end{align}
which together imply
\begin{equation}
\square F_{\mu\nu}(x)= \left[\frac{\partial^{2}}{\left(\partial
x^{1}\right)^{2}}+ \frac{\partial^{2}}{\left(\partial
x^{2}\right)^{2}}+ \frac{\partial^{2}}{\left(\partial
x^{3}\right)^{2}}- \frac{1}{c^{2}}
\frac{\partial^{2}}{\left(\partial t\right)^{2}} \right] F_{\mu\nu}(x) =0.
\label{eq:4.11b}
\end{equation}
Since the above equations are tensor field equations in the four
dimensional spacetime, Maxwell's equations outside matter were
already relativistic even before Einstein's discovery of the
special theory of relativity! Moreover, the equation
(\ref{eq:4.11b}) implies that electromagnetic waves propagate
with the speed of light. Since the wave operator $\square$ is a
relativistic invariant (see equation (\ref{eq:3.13})), we can
conclude that the speed of electromagnetic wave propagation
remains unchanged under the boost transformation (\ref{eq:3.6i})
characterizing a moving observer. Thus, Michelson and Morley's
experimental puzzle is logically explained.
\qquad Now we shall \emph{unify} energy density, momentum density
and Maxwell's stress tensor by defining a relativistic
electromagnetic energy-momentum-stress tensor:
\begin{subequations}
\begin{align}
\mathcal{M}^{\alpha\beta}(x):=&\frac{1}{4\pi} \left[F^{\lambda\alpha}(x)
F_{\lambda}^{\;\;\beta}(x) -\frac{1}{4}d^{\alpha\beta}F_{\mu\nu}(x)F^{\mu\nu}(x)\right]
\equiv \mathcal{M}^{\beta\alpha} , \label{eq:4.12i} \\
\left[\mathcal{M}^{\alpha\beta}(x)\right] =& \left[
\begin{array}{cc}
-M^{ij}(\mathbf{x},t) & cS_{i}(\mathbf{x},t) \\
cS_{i}(\mathbf{x},t) & u(\mathbf{x},t)
\end{array}
\right]. \label{eq:4.12ii}
\end{align}
\end{subequations}
Working out the covariant divergence, $\frac{\partial
M_{\alpha}^{\;\;\beta}}{\partial x^{\beta}}$, using
(\ref{eq:4.10i}), (\ref{eq:4.10ii}) and (\ref{eq:4.12i}) yields
\begin{align}
\frac{\partial \mathcal{M}_{\alpha}^{\;\;\beta}}{\partial x^{\beta}} = & \frac{1}{4\pi}\left[F^{\lambda}_{\;\;\alpha} \frac{\partial F_{\lambda}^{\;\;\beta}}{\partial x^{\beta}} + F^{\;\;\beta}_{\lambda} \frac{\partial F_{\;\;\alpha}^{\lambda}}{\partial x^{\beta}} - \frac{1}{2} F^{\mu\nu} \frac{\partial F_{\mu\nu}}{\partial x^{\alpha}} \right]\nonumber \\
=&\frac{1}{c}F^{\lambda}_{\;\; \alpha} J_{\lambda} +\frac{1}{8\pi} F^{\lambda\beta} \left[\frac{\partial F_{\lambda\alpha}}{\partial x^{\beta}} + \frac{\partial F_{\alpha\beta}}{\partial x^{\lambda}} + \frac{\partial F_{\beta\lambda}}{\partial x^{\alpha}}\right] \label{eq:4.13} \\
=& \frac{1}{c}F^{\lambda}_{\;\;\alpha} J_{\lambda} + 0. \nonumber
\end{align}
\qquad Now, the relativistic Lorentz equation for a charged
particle with mass $m$ and charge $e$ are taken to be (compare
with (\ref{eq:3.24}))
\begin{subequations}
\begin{align}
m\frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}}=&\mathcal{F}^{\alpha}(..)_{|..}:= \frac{e}{c}F^{\alpha}_{\;\lambda}(x) _{|\mathcal{X}(s)} \frac{d\mathcal{X}^{\lambda}(s)}{ds}, \label{eq:4.14i} \\
\mathcal{F}_{\alpha}(..)_{|..} \frac{d\mathcal{X}^{\alpha}(s)}{ds}=& \frac{e}{c}F_{\alpha \lambda}(x)_{|..} \frac{d\mathcal{X}^{\alpha}(s)}{ds} \frac{d\mathcal{X}^{\lambda}(s)}{ds} \equiv 0, \label{eq:4.14ii} \\
\sqrt{1-\frac{|\mathbf{V}(t)|^{2}}{c^{2}}} \mathcal{F}_{i}(..)_{|..} =& \frac{e}{c}\left[ F_{ij}(\mathbf{x},t)_{|\overline{\mathcal{X}}(t)} \frac{d\overline{\mathcal{X}}^{j}(t)}{dt} + c F_{14}(..)_{|..}\right] \nonumber \\
=&e \left[E_{i}(\mathbf{x},t) + \epsilon_{ijk}\frac{v^{j}}{c}(t)B^{k}(\mathbf{x},t)\right]_{|\overline{\mathcal{X}}(t)}. \label{eq:4.14iii}
\end{align}
\end{subequations}
The right hand side of (\ref{eq:4.14iii}) yields the correct
Lorentz force given in equation (\ref{eq:4.6}).
\qquad Now we shall briefly introduce the electromagnetic four-potential. According to the converse Poincar\'{e} lemma
\cite{ref:10}, the equations (\ref{eq:4.10ii}) imply that
there exists relativistic field components $A_{\mu}(x)$ of class
$C^{3}$ such that
\begin{equation}
F_{\mu\nu}(x)= \frac{\partial}{\partial{x^{\mu}}}A_{\nu}(x)
-\frac{\partial}{\partial x^{\nu}} A_{\mu}(x), \label{eq:4.15}
\end{equation}
so that
\begin{subequations}
\begin{align}
E_{i}(\mathbf{x},t)=&\frac{\partial A_{4}}{\partial x^{i}} -\frac{1}{c} \frac{\partial A_{i}}{\partial t}, \label{eq:4.15ii} \\
B^{i}(\mathbf{x},t)=& \frac{1}{2}\epsilon^{ijk} \left[\frac{\partial A_{k}}{\partial x^{j}} - \frac{\partial A_{j}}{\partial x^{k}} \right]. \label{eq:4.15iii}
\end{align}
\end{subequations}
We note that the four-potential components $A_{\mu}(x)$ are not
unique. We can make a (local) gauge transformation:
\begin{align}
A^{\prime}_{\mu}(x)=& A_{\mu}(x) -\frac{\partial \Lambda(x)}{\partial x^{\mu}}, \label{eq:4.16} \\
F^{\prime}_{\mu\nu}(x) \equiv &F_{\mu\nu}(x) . \nonumber
\end{align}
Here, $\Lambda(x)$ is an \emph{arbitrary} function of class
$C^{4}$. We can perform a gauge transformation such that the
function $\Lambda(x)$ satisfies the partial differential equation
\begin{equation}
\square \Lambda(x)=\frac{\partial A^{\mu}}{\partial x^{\mu}} . \label{eq:4.17}
\end{equation}
Thus, from equation (\ref{eq:4.16}) and (\ref{eq:4.17}), we get
\begin{equation}
\frac{\partial A^{\prime\,\mu}}{\partial x^{\mu}}= \frac{\partial
A^{\mu}}{\partial x^{\mu}} - \square \Lambda =0. \label{eq:4.18}
\end{equation}
The above condition on $A^{\prime\,\mu}$ is called the
\emph{Lorentz gauge condition}. In this gauge, Maxwell's
equations (\ref{eq:4.10i} - \ref{eq:4.10iii}) reduce, by
(\ref{eq:4.16}) to
\begin{subequations}
\begin{align}
d^{\mu\lambda} \frac{\partial}{\partial x^{\lambda}}
\left[\frac{\partial A^{\prime \, \nu}}{\partial x^{\nu}} \right]
-\square A^{\prime \, \mu} =& -\square A^{\prime \, \mu}= 4\pi J^{\mu}(x) \label{eq:4.19i} \\
\frac{\partial J^{\mu}(x)}{\partial x^{\mu}} =&0.
\label{eq:4.19ii}
\end{align}
\end{subequations}
The relativistic \emph{inertial} energy-momentum-stress tensor for
the charged matter is given by:
\begin{subequations}
\begin{align}
\left[\mathcal{I}^{\mu\nu}(x)\right]:= \left[
\begin{array}{cc}
\rho(x)U^{i}(x)U^{j}(x) & \rho(x) U^{i}(x)U^{4}(x) \\
\rho(x) U^{i}(x)U^{4}(x) & \rho(x) \left(U^{4}(x)\right)^{2}
\end{array}
\right] \equiv & \left[ \mathcal{I}^{\nu\mu}(x) \right],
\label{eq:4.20i} \\
d_{\mu\nu} U^{\mu}(x) U^{\nu}(x) \equiv& -c^{2} .
\label{eq:4.20ii}
\end{align}
\end{subequations}
Here, $\rho(x)$ represents the invariant (or proper) mass density
and $U^{\mu}(x)$ are components of the four-velocity field. Thus,
$\rho(x) U^{i}(x)$ are related to the three-momentum density
components and $\rho(x)\left[U^{4}(x)\right]^{2}$ is the energy density.
\qquad Observing the similarity between $\mathcal{M}^{\alpha\beta}(x)$ in
(\ref{eq:4.12ii}) and $\mathcal{I}^{\alpha\beta}(x)$ in
(\ref{eq:4.20i}), we define the \emph{total energy-momentum
stress field} for a charged material as
\begin{equation}
T^{\alpha\beta}(x):=\mathcal{I}^{\alpha\beta}(x) +
\mathcal{M}^{\alpha\beta}(x) \equiv \mathcal{I}^{\beta\alpha}(x) +
\mathcal{M}^{\beta\alpha}(x)\equiv T^{\beta\alpha}(x),
\label{eq:4.21}
\end{equation}
Using (\ref{eq:4.12i}), (\ref{eq:4.13}), (\ref{eq:4.20i}-
\ref{eq:4.20ii}) and (\ref{eq:4.21}) we derive that:
\begin{equation}
\frac{\partial T^{\alpha\beta}(x)}{\partial x^{\beta}} = \rho
u^{\beta} \frac{\partial u^{\alpha}}{\partial x^{\beta}} +
u^{\alpha} \frac{\partial (\rho u^{\beta})}{\partial x^{\beta}} +
\frac{1}{c} F^{\lambda \alpha} J_{\lambda}. \label{eq:4.22}
\end{equation}
We postulate that a physical conservation law to hold:
\begin{equation}
\frac{\partial T^{\alpha\beta}}{\partial x^{\beta}}=0.
\label{eq:4.23}
\end{equation}
Moreover, we consider the case of a charged dust, i.e.
\begin{equation}
J^{\lambda}(x)=\sigma_{(0)}(x) U^{\lambda}(x). \label{eq:4.24}
\end{equation}
Here, $\sigma_{0}(x)$ is the proper charge density (the charge
density measured in the co-moving frame of the charge). The
equation (\ref{eq:4.22}), with (\ref{eq:4.20ii}), yields
\begin{subequations}
\begin{align}
\frac{\partial}{\partial x^{\beta}}
\left[\rho(x)U^{\beta}(x)\right]=&0, \label{eq:4.25i} \\
\rho U^{\beta}(x) \frac{\partial U^{\alpha}(x)}{\partial x^{\beta}} =&
\frac{\sigma_{0}(x)}{c} U^{\lambda}(x) F^{\alpha}_{\;\; \lambda} .
\label{eq:4.25ii}
\end{align}
\end{subequations}
The equations (\ref{eq:4.25i}) stands for the continuity of the
material flow, whereas the equation (\ref{eq:4.25ii}) represents
the Lorentz equation (\ref{eq:4.14i}) for the charged dust.
\qquad Following the discussion on particle mechanics, we define
the three-dimensional velocity field components by:
\begin{align}
v^{i}=V^{i}(\mathbf{x},t):=&c\frac{U^{i}(x)}{U^{4}(x)}, \;\; U^{4}(x)=\frac{c}{\sqrt{1-\frac{|\mathbf{V}(x)|^{2}}{c^{2}}}}, \nonumber \\
v^{i}=V^{i}(\mathbf{x},t)= &\sqrt{1-\frac{|\mathbf{V}(\mathbf{x},t)|^{2}}{c^{2}}} \, U^{i}(x), \;\; \mbox{and
}\;\; J^{4}(x)=\sigma_{0}(x)U^{4}(x)=c\sigma(x). \label{eq:4.27}
\end{align}
The spatial components (\ref{eq:4.25ii}) provide:
\begin{equation}
\rho \left\{ \frac{\partial}{\partial t}
\left[\frac{v^{i}}{\sqrt{1-\frac{|\mathbf{V}(x)|^{2}}{c^{2}}}}\right] +v^{k}
\frac{\partial}{\partial x^{k}} \left[\frac{v^{i}}{\sqrt{1-\frac{|\mathbf{V}(x)|^{2}}{c^{2}}}}
\right] \right\} =\sigma_{0} \left[ E^{i} +
\epsilon^{ijk}\frac{v_{j}}{c} B_{k} \right]. \label{eq:4.28}
\end{equation}
Using notations of three-dimensional vector calculus, the
equation (\ref{eq:4.28}) can be cast into the more familiar form:
\begin{equation}
\rho \left\{ \frac{\partial}{\partial t}
\left[\frac{\mathbf{V}(\mathbf{x},t)}{\sqrt{1-\frac{|\mathbf{V}(\mathbf{x},t)|^{2}}{c^{2}}}} \right]
+\mathbf{v} \cdot \mathbf{\nabla}
\left[\frac{\mathbf{V}(\mathbf{x},t)}{\sqrt{1-\frac{|\mathbf{V}(\mathbf{x},t)|^{2}}{c^{2}}}} \right]
\right\} = \sigma_{0} \left[\mathbf{E} + \frac{\mathbf{v}}{c}
\times \mathbf{B} \right]. \label{eq:4.29}
\end{equation}
\section{Special relativistic gravitational fields}
\subsection{Introduction}
The static Newtonian gravitational potential, $W(x)$, satisfies:
\begin{subequations}
\begin{align}
\nabla^{2}W(\mathbf{x}):=& \delta^{ij} \frac{\partial^{2}
W(\mathbf{x})}{\partial x^{i} \partial x^{j}}= \left\{
\begin{array}{ll}
4\pi G \rho(\mathbf{x}) & \mbox{inside a material body,}
\\
0 & \mbox{in vacuum;}
\end{array}
\right. \label{eq:5.1i} \\
W(\mathbf{x})=& -G \int_{body} \frac{\rho(\mathbf{x}^{\prime})}{|\mathbf{x} -
\mathbf{x}^{\prime}|}\,d^{3}x^{\prime}, \label{eq:5.1ii} \\
\rho(\mathbf{x}^{\prime}) \geq & 0, \;\;W(\mathbf{x}) \leq 0. \label{eq:5.1iii}
\end{align}
\end{subequations}
Here, $G$ is
the Newtonian constant of gravitation.
\qquad The well known equations of motion of a particle of $m >
0$ in the external gravitational field $W(\mathbf{x})$ are
furnished by:
\begin{subequations}
\begin{align}
m \frac{d\mathbf{V}(t)}{dt}=& -m
\mathbf{\nabla}W(\mathbf{x})_{|\overline{\mathcal{X}}(t)}, \label{eq:5.2i} \\
\frac{dV^{i}(t)}{dt}=& - \frac{\partial W(\mathbf{x})}{\partial
x^{i}}_{|\overline{\mathcal{X}}(t)} . \label{eq:5.2ii}
\end{align}
\end{subequations}
\qquad The natural relativistic generalization of the Newtonian
potential is a four-dimensional scalar field. Such a field has
been considered but the scalar field theory yields incorrect
planetary orbits \cite{ref:11}. Next in order of complication, we
should consider a four-dimensional vector field as in equation
(\ref{eq:4.19i}). However, material sources of such a field
\emph{repel} each other (like similar electric charges). Thus,
vector fields are ruled out as viable candidates for a
relativistic gravitational theory. Next in order of complication
is the four-dimensional second order tensor field. This type of
field is a potential candidate as the relativistic generalization
of the mass density (within a factor of $c^{2}$) is the energy
density. As discussed in the previous section, the energy density
is a component of a symmetric rank two tensor, the
energy-momentum-stress tensor. Therefore, it is natural to
consider a potential which is a symmetric second rank tensor
field with the energy-momentum-stress tensor as its source. The
first-order approximation of Einstein's general relativity theory
of gravity yields a second rank theory similar to that presented
below. The field equations, along with supplementary conditions
are summarized as the following:
\begin{subequations}
\begin{align}
\square \phi_{\mu\nu}(x) =& -2\kappa T_{\mu\nu}, \;\;\;\;\kappa:=
\frac{8\pi G}{c^{4}}, \label{eq:5.3i}
\\
\frac{\partial T^{\mu\nu}(x)}{\partial x^{\nu}} =&0,
\label{eq:5.3ii} \\
\frac{\partial \phi^{\mu\nu}(x)}{\partial x^{\nu}} =&0,
\label{eq:5.3iii} \\
\phi_{\mu\nu}(\mathbf{x}, x^{4})=&\frac{2G}{c^{4}} \int_{body}
\frac{T_{\mu\nu}\left(\mathbf{x}^{\prime},\, x^{4}-|\mathbf{x} -
\mathbf{x}^{\prime}|\right)}{|\mathbf{x} - \mathbf{x}^{\prime}|} \, d^{3}x^{\prime}
, \label{eq:5.3v}
\end{align}
\end{subequations}
Physically, the components of the tensor, $T_{\mu\nu}$, represent the
\emph{total density of energy, ($c$-times) momentum and stress} of the source
material. (A special example was furnished in the equation
(\ref{eq:4.21}).) The component $T_{44}(x)$, $T_{i4}(x)$ and
$T_{ij}(x)$ represent energy density, momentum density and stress
(or rate of stress) density respectively. The equation
(\ref{eq:5.3i}-\ref{eq:5.3iii}) are analogous to the
electromagnetic equations (\ref{eq:4.19i} - \ref{eq:4.19ii}) and
(\ref{eq:4.18}) respectively.
\qquad Now we shall express the equation of motion of a test
particle of mass $m > 0$ in a gravitational field. The equations,
though complicated, are aesthetically pleasing. Firstly, it is
convenient to introduce a related second order symmetric tensor
field by the definition:
\begin{align}
g_{\mu\nu}(x):=&d_{\mu\nu} + \phi_{\mu\nu}(x) -\frac{1}{2}
d_{\mu\nu}d^{\alpha\beta} \phi_{\alpha\beta}(x) \equiv
g_{\nu\mu}(x), \label{eq:5.4}
\end{align}
For weak gravitational fields, $|\phi_{\mu\nu}(x)| << 1$ and the
determinant of $g_{\mu\nu}(x)$ is close to $-1$. Thus, there
exists a unique inverse matrix defined by
\begin{align}
\left[g^{\mu\nu}(x) \right]:=& \left[g_{\mu\nu}(x)\right]^{-1},
\label{eq:5.5} \\
g^{\mu\nu}(x)g_{\nu\lambda}(x) = & \delta^{\mu}_{\;\lambda} .
\nonumber
\end{align}
Treating formally $g_{\mu\nu}(x)$ as a ``metric tensor'', we
define the associated Christoffel symbols as
\begin{equation}
\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}:=\frac{1}{2} g^{\alpha\lambda}(x) \left[ \frac{\partial
g_{\gamma\lambda}(x)}{\partial x^{\beta}} + \frac{\partial
g_{\lambda\beta}(x)}{\partial x^{\gamma}} - \frac{\partial
g_{\beta\gamma}(x)}{\partial x^{\lambda}} \right] \equiv \left\{
\begin{array}{l}
\alpha \\
\gamma \; \beta
\end{array}\right\}.
\label{eq:5.6}
\end{equation}
In our linear theory, the above are components of a third order
four-dimensional tensor with forty independent components!
\qquad We postulate that the special relativistic equations of
motion, subject
only to gravity, must follow geodesic paths of the ``metric''
$g_{\mu\nu}(x)$:
\begin{equation}
\frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}}+\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{|\mathcal{X}(s)}\frac{d\mathcal{X}^{\beta}(s)}{ds}\frac{d\mathcal{X}^{\gamma}(s)}{ds} =0. \label{eq:5.7}
\end{equation}
Note that these equations of motion are independent of mass, a
property in common with the Newtonian theory. These semi-linear
equations distantly resemble the Lorentz equations
(\ref{eq:4.14i}) and generalize Newton's equations
(\ref{eq:5.2ii}) considerably. Geodesic equations (\ref{eq:5.7})
admit the exact first integral \cite{ref:7}
\begin{equation}
g_{\mu\nu}(x)_{|\mathcal{X}(s)}\frac{d\mathcal{X}^{\mu}(s)}{ds}\frac{d
\mathcal{X}^{\nu}(s)}{ds} \equiv \mbox{ constant}. \label{eq:5.8i}
\end{equation}
Since, in the limit $\phi_{\mu\nu}(x) \rightarrow 0$, the
equations (\ref{eq:5.8i}) reduce to (\ref{eq:3.18iv}) and
(\ref{eq:4.20ii}), we must choose
\begin{equation}
g_{\mu\nu}(x)_{|\mathcal{X}(s)}\frac{d\mathcal{X}^{\mu}(s)}{ds}\frac{d\mathcal{X}^{\nu}(s)}{ds} = -c^{2}. \label{eq:5.8ii}
\end{equation}
\qquad The generalization of (\ref{eq:5.7}) in the presence of
gravitational as well as non-gravitational force components
$\mathcal{F}^{\alpha}(x,u)$ is given by
\begin{subequations}
\begin{align}
m\frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}}= -m\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{|\mathcal{X}(s)}\frac{d\mathcal{X}^{\beta}(s)}{ds}\frac{d^{2}\mathcal{X}^{\gamma}(s)}{ds} +& \mathcal{F}^{\alpha}(x,u)_{|\mathcal{X}(s), d\mathcal{X}(s)/ds}, \label{eq:5.9i} \\
g_{\alpha\beta}(x)_{|\mathcal{X}(s)} \frac{d\mathcal{X}^{\alpha}(s)}{ds}
\mathcal{F}^{\beta}(x,u)_{|..} = & 0. \label{eq:5.9ii}
\end{align}
\end{subequations}
(Compare the above equations with (\ref{eq:3.24}) and (\ref{eq:3.25i})).
\qquad With the help of the ``metric'' tensor $g_{\mu\nu}(x)$, we
can define the familiar covariant derivative \cite{ref:7} and the
following consequences:
\begin{subequations}
\begin{align}
\nabla_{\alpha} A^{\beta}(x):=& \frac{\partial A^{\beta}(x)}{\partial x^{\alpha}} +\left\{
\begin{array}{l}
\beta \\
\alpha \; \gamma
\end{array}
\right\}A^{\gamma}(x) , \label{eq:5.10i} \\
\nabla_{\alpha} A_{\beta}(x):=& \frac{\partial A_{\beta}(x)}{\partial x^{\alpha}} -\left\{
\begin{array}{l}
\gamma \\
\alpha \; \beta
\end{array}
\right\}A_{\gamma}(x) , \label{eq:5.10ii} \\
\nabla_{\alpha} T_{\beta\gamma}(x):=& \frac{\partial T_{\beta\gamma}(x)}{\partial x^{\alpha}} -\left\{
\begin{array}{l}
\lambda \\
\alpha \; \beta
\end{array}
\right\}T_{\lambda\gamma}(x) -\left\{
\begin{array}{l}
\lambda \\
\alpha \; \gamma
\end{array}
\right\}T_{\alpha \lambda}(x), \label{eq:5.10iii} \\
\nabla_{\alpha}g_{\beta\gamma}(x) \equiv & 0, \;\; \nabla_{\alpha} g^{\beta\gamma}(x) \equiv 0, \;\; \nabla_{\alpha} \delta^{\beta}_{\;\gamma} \equiv 0, \label{eq:5.10iv} \\
\nabla_{\alpha}d_{\beta\gamma} \not\equiv& 0,\;\; \nabla_{\alpha}d^{\beta\gamma} \not\equiv 0. \label{eq:5.10v}
\end{align}
\end{subequations}
\subsection{Gravitational field of an incoherent dust}
The gravitational equations (\ref{eq:5.3i} - \ref{eq:5.3iii}) are
all linear. Splitting the solution into its vacuum and
inhomogeneous parts we express:
\begin{subequations}
\begin{align}
\phi_{\mu\nu}(x)=& \phi_{(I)\mu\nu}(x) + \phi_{(0)\mu\nu}(x), \label{eq:5.11i} \\
\square \phi_{(I)\mu\nu}(x)=& -2\kappa T_{\mu\nu}(x), \;\; \frac{\partial T^{\mu\nu}(x)}{\partial x^{\nu}}=0, \;\;\frac{\partial \phi^{\mu\nu}_{(I)}(x)}{\partial x^{\nu}}=0, \label{eq:5.11ii} \\
\square \phi_{(0)\mu\nu}(x)=& 0, \;\; \frac{\partial \phi^{\mu\nu}_{(0)}(x)}{\partial x^{\nu}}=0, \label{eq:5.11iii} \\
\phi_{\mu\nu}(x)=& \phi_{(0)\mu\nu}(x) +\frac{2G}{c^{4}}
\int_{test\;\;body} \frac{T_{\mu\nu}
\left(\mathbf{x}^{\prime},\;x^{4}-|\mathbf{x}-\mathbf{x}^{\prime}|\right)}{|\mathbf{x}-\mathbf{x}^{\prime}|}\,
d^{3}x^{\prime}. \label{eq:5.11iv}
\end{align}
\end{subequations}
The above is the most general solution of the partial differential
equations (\ref{eq:5.3i}- \ref{eq:5.3iii}). Here
$\phi_{(I)\mu\nu}(x)$ represents the particular solution due to
the test body material with energy momentum stress tensor
$T_{\mu\nu}(x)$ and $\phi_{(0)\mu\nu}(x)$ represents the vacuum
solution created by any external sources (see figure
(\ref{fig:3})).
\begin{figure}[ht]
\begin{center}
\includegraphics[bb=0 0 674 331, clip, scale=0.5, keepaspectratio=true]{fig3.eps}
\caption{{\small Gravitational forces on a test body due to an
external source in spacetime. The external source's $T_{\mu\nu}$
gives rise to $\phi_{(0)\mu\nu}$ while the test body's
$T_{\mu\nu}$ yields $\phi_{(I)\mu\nu}$. }} \label{fig:3}
\end{center}
\end{figure}
\qquad \emph{Ignoring} the internal field of the test body, we modify
(\ref{eq:5.4}) and (\ref{eq:5.8ii}) to
\begin{subequations}
\begin{align}
g_{(0)\mu\nu}:=d_{\mu\nu} + \phi_{(0)\mu\nu}(x) -&\frac{1}{2} d_{\mu\nu} d^{\alpha\beta} \phi_{(0)\alpha\beta}(x), \label{eq:5.12i} \\
g_{(0)\mu\nu}(x) U^{\mu}(x) U^{\nu}(x) \equiv & -c^{2}, \label{eq:5.12ii} \\
\overline{u}_{\mu}:=g_{(0)\mu\nu}u^{\nu}, \;\; \overline{u}_{\mu}u^{\mu} \equiv &-c^{2}. \label{eq:5.12iii}
\end{align}
\end{subequations}
For an incoherent dust coupled to gravity, the
energy-momentum-stress tensor is taken to be
\begin{equation}
T^{\mu\nu}(x):= \rho(x)U^{\mu}(x)U^{\nu}(x) + \Theta^{\mu\nu}(x,\rho, u^{\alpha}, \phi_{(0)\gamma\sigma}), \label{eq:5.13}
\end{equation}
Here $\rho(x)$ is the proper mass density, $U^{\mu}(x)$ is the
four velocity-field of the test particle and $\Theta^{\mu\nu}(x,
\rho, u^{\alpha}, \phi_{(0)\gamma\sigma})$ indicates the
\emph{interaction} of the test body with the external
gravitational field (from this point onward we will write this
term as $\Theta^{\mu\nu}(x)$).
\qquad The conservation equation (\ref{eq:5.3ii}) along with (\ref{eq:5.13}) yields:
\begin{align}
0=& \overline{u}_{\mu} \frac{\partial T^{\mu\nu}}{\partial x^{\nu}}= \overline{u}_{\mu} \left[u^{\mu} \frac{\partial (\rho u^{\nu})}{\partial x^{\nu}} + \rho u^{\nu} \frac{\partial u^{\mu}}{\partial x^{\nu}} + \frac{\partial \Theta^{\mu\nu}}{\partial x^{\nu}} \right] \nonumber \\
&= -c^{2} \frac{\partial (\rho u^{\nu})}{\partial x^{\nu}} + \rho u^{\nu} \overline{u}_{\mu} \left[\frac{\partial u^{\mu}}{\partial x^{\nu}} + \left\{
\begin{array}{l}
\mu \\
\nu \; \lambda
\end{array}
\right\}_{(0)} u^{\lambda} \right] + \overline{u}_{\mu} \left[
\frac{\partial \Theta^{\mu\nu}}{\partial x^{\nu}} -\rho \left\{
\begin{array}{l}
\lambda \\
\nu\; \lambda
\end{array}
\right\}_{(0)} u^{\nu}u^{\lambda} \right]. \label{eq:5.14}
\end{align}
Note that the middle terms in the above equation vanishes via
\begin{align}
&\overline{u}_{\mu} \left[ \frac{\partial u^{\mu}}{\partial
x^{\nu}} +
\left\{
\begin{array}{l}
\mu \\
\nu\; \lambda
\end{array}
\right\}_{(0)}
u^{\lambda} \right] \nonumber \\
&=\overline{u}_{\mu} \nabla_{(0)\nu} u^{\mu}= \frac{1}{2}
\nabla_{(0)\nu} \left[ g_{(0)\mu\nu}u^{\nu}u^{\mu}\right]
=-\frac{1}{2}\nabla_{(0)\nu}(c^{2})\equiv 0. \label{eq:90ii}
\end{align}
At this stage there are several possible choices to enforce the
conservation law (\ref{eq:5.14}). We stipulate the condition:
\begin{equation}
\frac{\partial \Theta^{\mu\nu}}{\partial x^{\nu}}= \rho \left\{
\begin{array}{l}
\lambda \\
\alpha \; \beta
\end{array}
\right\}_{(0)} u^{\nu}u^{\lambda}, \label{eq:5.15}
\end{equation}
as this choice yields the correct physical laws as dictated by the continuity equation \cite{ref:12}:
\begin{equation}
\frac{\partial}{\partial x^{\nu}} \left[\rho(x) U^{\nu}(x)\right] =0. \label{eq:5.16}
\end{equation}
The right hand side of (\ref{eq:5.15}) therefore represents the gravitational force components due to external sources.
\qquad With the help of equations (\ref{eq:4.27}), we can express (\ref{eq:5.16}) in a slightly more familiar form:
\begin{equation}
\frac{\partial}{\partial t} \left[\frac{\rho}{\sqrt{1-\frac{|\mathbf{v}|^{2}}{c^{2}}}} \right] + \mathbf{\nabla}\cdot \left[ \frac{\rho \mathbf{v}}{\sqrt{1-\frac{|\mathbf{v}|^{2}}{c^{2}}}} \right] =0. \label{eq:5.16ii}
\end{equation}
Substituting (\ref{eq:5.15}) and (\ref{eq:5.16}) into the
conservation equation (\ref{eq:5.3ii}) with (\ref{eq:5.10i}) and
(\ref{eq:5.13}) we obtain
\begin{equation}
u^{\nu} \left[ \frac{\partial u^{\mu}}{\partial x^{\nu}} + \left\{
\begin{array}{l}
\mu \\
\nu \; \lambda
\end{array}
\right\}_{(0)} u^{\lambda} \right] =u^{\nu} \nabla_{(0)\nu} u^{\mu} =0. \label{eq:5.17}
\end{equation}
For the streamlines, we need to solve the system of first-order ordinary differential equations:
\begin{equation}
\frac{d \mathcal{X}^{\mu}(s)}{ds} = U^{\alpha}(x)_{|\mathcal{X}(s)}.
\label{eq:5.18}
\end{equation}
(We assume the validity of the Lifshitz conditions \cite{ref:13}
on the right-hand-side of (\ref{eq:5.18}).) Using the above
equation in (\ref{eq:5.17}) we derive that
\begin{equation}
\frac{d^2 \mathcal{X}^{\mu}(s)}{ds^{2}} + \left\{
\begin{array}{l}
\mu \\
\nu \; \lambda
\end{array}
\right\}_{(0)|\mathcal{X}(s)} \frac{d\mathcal{X}^{\nu}(s)}{ds}\frac{d\mathcal{X}^{\lambda}(s)}{ds}=0 . \label{eq:5.19}
\end{equation}
Therefore, streamlines \emph{follow ``geodesics'' of the external
metric} $g_{(0)\mu\nu}(x)$. The Christoffel symbols mediate the
external gravitational forces on a test particle.
\subsection{Gravitational field of a charged dust}
A fluid with vanishing pressure is know as a ``dust''. In this case, the combined electromagnetic and gravitational field
equations are investigated \cite{ref:14}. Using (\ref{eq:4.10i} -
\ref{eq:4.10iii}), (\ref{eq:4.24}), \ref{eq:4.12i}),
(\ref{eq:4.20i}) and (\ref{eq:5.11i}- \ref{eq:5.11iii}), we
obtain the pertinent equations to be:
\begin{subequations}
\begin{align}
\frac{\partial F^{\mu\nu}}{\partial x^{\nu}} =&\frac{4\pi}{c} \sigma_{(0)} u^{\mu}, \label{eq:5.20i} \\
\frac{\partial F^{\mu\nu}}{\partial x^{\lambda}} + \frac{\partial F^{\nu\lambda}}{\partial x^{\mu}} + \frac{\partial F^{\lambda\mu}}{\partial x^{\nu}}=& 0, \label{eq:5.20ii} \\
\frac{\partial (\sigma_{(0)} u^{\nu})}{\partial x^{\nu}} =&0, \label{eq:5.20iii} \\
\phi_{\alpha\beta}(x) =& \phi_{(I) \alpha\beta}(x) +\phi_{(0)\alpha\beta}(x), \label{eq:5.20iv} \\
\square \phi_{(0) \alpha\beta}=\frac{\partial \phi_{(0)}^{\alpha\beta}}{\partial x^{\beta}} =&0, \label{eq:5.20v} \\
\square \phi_{(I)\alpha\beta}=-2 \kappa T_{\alpha\beta}:=& -2\kappa\left[\rho u_{\alpha}u_{\beta} + \Theta_{\alpha\beta} + \mathcal{M}_{\alpha\beta} \right], \label{eq:5.20vi} \\
\frac{\partial T^{\alpha\beta}}{\partial x^{\beta}}=&0, \label{eq:5.20vii} \\
\frac{\partial \phi^{\alpha\beta}_{(I)}}{\partial x^{\beta}}=&0. \label{eq:5.20viii}
\end{align}
\end{subequations}
\qquad Using (\ref{eq:5.20vi}), (\ref{eq:4.24}) and
(\ref{eq:4.22}), the conservation equation (\ref{eq:5.20vii})
yields:
\begin{equation}
0=\frac{\partial T^{\alpha\beta}}{\partial x^{\beta}}=u^{\alpha} \frac{\partial(\rho u^{\beta})}{\partial x^{\beta}} + \rho u^{\beta} \frac{\partial u^{\alpha}}{\partial x^{\beta}} +\frac{\partial \Theta^{\alpha\beta}}{\partial x^{\beta}} + \frac{\sigma_{(0)}}{c} u^{\beta} F^{\;\;\alpha}_{\beta}. \label{eq:5.21i}
\end{equation}
\qquad Imposing the condition (\ref{eq:5.15}) on
$\Theta^{\alpha\beta}(x)$, the above equation (\ref{eq:5.21i})
leads to
\begin{equation}
u^{\alpha} \frac{\partial(\rho u^{\beta})}{\partial x^{\beta}} +\rho u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha} +\frac{\sigma_{(0)}}{c} u^{\beta} F^{\;\;\alpha}_{\beta} =0. \label{eq:5.21ii}
\end{equation}
Now, the equations (\ref{eq:5.10iv}) and (\ref{eq:5.12ii})
provide:
\begin{align}
2\overline{u}_{\alpha} \nabla^{(0)}_{\beta} u^{\alpha}=&
g_{(0)\alpha\gamma} \left[u^{\gamma} \nabla^{(0)}_{\beta}
u^{\alpha} +u^{\alpha} \nabla^{(0)}_{\beta} u^{\gamma} \right]
\nonumber \\ =&\nabla^{(0)}_{\beta} \left[g_{(0)\alpha\gamma}
u^{\alpha}u^{\gamma} \right] = \nabla^{(0)}_{\beta}
\left(-c^{2}\right) \equiv 0. \label{eq:5.22}
\end{align}
($\nabla^{(0)}_{\beta}$ is the covariant derivative defined with
respect to the metric $g_{(0)\mu\nu}$, defined in
(\ref{eq:5.12i}).) Therefore, (\ref{eq:5.22}), (\ref{eq:5.14})
and (\ref{eq:5.21ii}) yield
\begin{equation}
\frac{\partial (\rho u^{\beta})}{\partial x^{\beta}} = \frac{\sigma_{(0)}}{c^{3}} \overline{u}_{\alpha} u^{\beta} F_{\beta}^{\;\;\alpha} . \label{eq:5.23}
\end{equation}
Substituting (\ref{eq:5.23}) into (\ref{eq:5.21ii}), we finally obtain
\begin{equation}
\rho u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha}
+\frac{\sigma_{(0)}}{c}u^{\beta} F^{\;\;\gamma}_{\beta}
\left[\delta^{\alpha}_{\;\gamma} +\frac{1}{c^{2}}
\overline{u}_{\gamma}u^{\alpha} \right]=0. \label{eq:5.24}
\end{equation}
Hence, the stream lines of a charged dust satisfying
(\ref{eq:5.18}) must pursue trajectories governed by the
equations of motion:
\begin{align}
&\left\{ \rho(x) \left[ \frac{d^{2} \mathcal{X}^{\alpha}(s)}{ds^{2}} +
\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{(0)}
\frac{d\mathcal{X}^{\beta}(s)}{ds}\frac{d \mathcal{X}^{\gamma}(s)}{ds}\right] \right. \nonumber \\
& \left. +\frac{\sigma_{(0)}(x)}{c} F^{\;\;\gamma}_{\beta}(x)
\left[\delta^{\alpha}_{\;\gamma}+\frac{1}{c^{2}} g_{(0)\gamma\mu}
\frac{d \mathcal{X}^{\alpha}(s)}{ds}\frac{d
\mathcal{X}^{\mu}(s)}{ds}\right]\frac{d\mathcal{X}^{\beta}(s)}{ds}
\right\}_{|x^{\alpha}=\mathcal{X}^{\alpha}(s)} =0. \label{eq:5.25}
\end{align}
These are the modified relativistic Lorentz equations of motion
in the presence of external gravitational fields. (Compare with
the equations (\ref{eq:4.25ii}.) and (\ref{eq:4.28}).)
\subsection{Gravitational field of a perfect fluid}
Following the prescription in the previous sections, a special
relativistic perfect fluid in a gravitational field is governed by
\begin{subequations}
\begin{align}
\phi_{\alpha\beta}(x) =&\phi_{(I)\alpha\beta}(x) +
\phi_{(0)\alpha\beta}(x), \label{eq:5.26i} \\
\square \phi_{(0)\alpha\beta}(x)=& 0= \frac{\partial
\phi_{(0)}^{\alpha\beta}}{\partial x^{\beta}},
\label{eq:5.26ii} \\
\square \phi_{(I)}^{\alpha\beta}(x)=& -2\kappa T^{\alpha\beta}(x)
\nonumber \\
:=& -2\kappa \left[\left(\rho(x) +\frac{p(x)}{c^{2}}
\right) u^{\alpha}u^{\beta} +p(x) g_{(0)}^{\alpha\beta}(x) +
\Theta^{\alpha\beta}(x)\right], \label{eq:5.26iii} \\
\frac{\partial T^{\alpha\beta}}{\partial x^{\beta}}=&0,
\label{eq:5.26iv} \\
\frac{\partial \phi^{\alpha\beta}_{(I)}}{\partial x^{\beta}}=&0.
\label{eq:5.26v}
\end{align}
\end{subequations}
Here, $p(x)$ is the pressure.
\qquad The conservation equation (\ref{eq:5.26iv}) implies from
(\ref{eq:5.26iii}) that
\begin{align}
0=& \frac{\partial T^{\alpha\beta}}{\partial x^{\beta}}=
u^{\alpha} \frac{\partial}{\partial x^{\beta}} \left[\left(\rho
+\frac{p}{c^{2}}\right)u^{\beta}\right] +\left(\rho
+\frac{p}{c^{2}}\right) u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha}
+\frac{\partial}{\partial x^{\beta}} \left[pg_{(0)}^{\alpha\beta}
\right] \nonumber \\
&+ \left[ \frac{\partial \Theta^{\alpha\beta}}{\partial
x^{\beta}} - \left(\rho +\frac{p}{c^{2}} \right)\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{(0)} u^{\beta} u^{\gamma} \right]. \label{eq:5.27}
\end{align}
Following the previous section, reasonable physics demands that we stipulate
\begin{equation}
\frac{\partial \Theta^{\alpha\beta}}{\partial x^{\beta}}
=\left(\rho +\frac{p}{c^{2}}\right)
\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{(0)}
u^{\beta}u^{\gamma}.
\label{eq:5.28}
\end{equation}
Note that the right-hand-side denotes the external gravitational
forces on the \emph{effective mass density} $\left(\rho
+\frac{p}{c^{2}}\right)$. Now, the equation (\ref{eq:5.27}) yields
\begin{equation}
u^{\alpha} \frac{\partial}{\partial x^{\beta}} \left[\left(\rho
+\frac{p}{c^{2}}\right)u^{\beta}\right] +\left(\rho
+\frac{p}{c^{2}}\right) u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha}
= -\frac{\partial}{\partial x^{\beta}}
\left[pg_{(0)}^{\alpha\beta} \right]. \label{eq:5.29}
\end{equation}
Contracting this equation with $\overline{u}_{\alpha}$ and using
(\ref{eq:5.12ii}) and (\ref{eq:5.22}), we deduce the continuity
equation,
\begin{equation}
\frac{\partial}{\partial x^{\beta}} \left[\left(\rho
+\frac{p}{c^{2}} \right) u^{\beta} \right] =\frac{1}{c^{2}}
\overline{u}_{\alpha} \frac{\partial}{\partial x^{\beta}} \left(p
g^{\alpha\beta}_{(0)} \right). \label{eq:5.30}
\end{equation}
Using this equation in (\ref{eq:5.29}), we derive the
relativistic Euler equation
\begin{equation}
\left(\rho +\frac{p}{c^{2}} \right) u^{\beta}
\nabla^{(0)}_{\beta} u^{\alpha} =-\left[\delta^{\alpha}_{\;\gamma}
+\frac{\overline{u}_{\gamma}u^{\alpha}}{c^{2}} \right]
\frac{\partial}{\partial x^{\beta}} \left(p
g_{(0)}^{\gamma\beta}\right). \label{eq:5.31}
\end{equation}
\qquad On a typical stream line (given by (\ref{eq:5.18})) of the
perfect fluid, the following equations of motion hold:
\begin{align}
&\left[\rho +\frac{p}{c^{2}} \right]
\left[\frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}} +\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{(0)} \frac{d \mathcal{X}^{\beta}(s)}{ds} \frac{d
\mathcal{X}^{\gamma}(s)}{ds} \right]_{|x^{\alpha}=\mathcal{X}^{\alpha}(s)}
\nonumber \\
&= - \left[\delta^{\alpha}_{\;\gamma} +\frac{1}{c^{2}}
g_{(0)\gamma\mu} \frac{d \mathcal{X}^{\alpha}(s)}{ds} \frac{d
\mathcal{X}^{\mu}(s)}{ds} \right]\left\{\frac{\partial}{\partial
x^{\beta}} \left[p g^{\gamma\beta}_{(0)} \right]
\right\}_{|x^{\alpha}=\mathcal{X}^{\alpha}(s)}. \label{eq:5.32}
\end{align}
\section{Static external gravitational fields}
The special relativistic gravitaitonal fields may easily be
compared with Newtonian theory in this case. The relevant
relativistic equations read:
\begin{subequations}
\begin{align}
\phi_{(0)ij}(x) \equiv & 0,\;\; \phi_{(0) i4}(x) \equiv 0, \label{eq:6.1i} \\
\phi_{(0)44}(x)\neq &0, \;\; \frac{\partial \phi_{(0)44}(x)}{\partial x^{4}} \equiv 0, \label{eq:6.1ii} \\
d^{\alpha\beta} \phi_{(0)\alpha\beta}(x)=&
-\phi_{(0)44}(\mathbf{x}),
\label{eq:6.1iii} \\
g_{(0)ij}(x)=& \left[1+\frac{1}{2} \phi_{(0)44}(\mathbf{x}) \right] \delta_{ij}, \label{eq:6.1iv} \\
g_{(0)i4}(x) \equiv & 0, \;\; g_{(0)44}(x)=-1+ \frac{1}{2}
\phi_{(0)44}(\mathbf{x}) .\label{eq:6.1v}
\end{align}
\end{subequations}
(We have made use of equations (\ref{eq:5.12i}) to derive the above.)
\qquad The equations (\ref{eq:5.11iii}) reduce Laplace's equation:
\begin{equation}
\nabla^{2} \phi_{(0)44}(\mathbf{x}) =0. \label{eq:6.2}
\end{equation}
Comparing (\ref{eq:6.2}) with (\ref{eq:5.1i}) ,
(\ref{eq:5.1ii}) and (\ref{eq:5.11iv}) we identify $\phi_{(0)44}(\mathbf{x})$ with the
Newtonian gravitational potential via
\begin{equation}
\phi_{(0)44}(\mathbf{x}) =- \frac{4}{c^{2}} W(\mathbf{x}) = \frac{4}{c^{2}} |W(\mathbf{x})| \geq 0. \label{eq:6.3}
\end{equation}
We also note that for a four-dimensional vector field $T^{\alpha}(x)$, the equations (\ref{eq:6.1iv}), (\ref{eq:6.1v}) and (\ref{eq:6.3}) yield
\begin{align}
-g_{(0)\alpha\beta}(x) T^{\alpha}(x) T^{\beta}(x)&= \left[1-\frac{1}{2} \phi_{(0)44}(\mathbf{x})\right]\left[T^{4}(x)\right]^{2} -\left[1+ \frac{1}{2} \phi_{(0)44}(\mathbf{x}) \right] \delta_{ij} T^{i}(x) T^{j}(x) \nonumber \\
=&\left[1-\frac{2|W(\mathbf{x})|}{c^{2}}\right]\left[T^{4}(x)\right]^{2} -\left[1+ \frac{2 |W(\mathbf{x})|}{c^{2}} \right] \delta_{ij} T^{i}(x) T^{j}(x). \label{eq:6.4}
\end{align}
We have implicitly assumed that $2\frac{|W(\mathbf{x})|}{c^{2}} < 1$. The \emph{physical} components of the vector field $T^{\alpha}(x)$ are
\begin{align}
\overline{T}^{i}(x):=&\sqrt{1+\frac{2|W(\mathbf{x})|}{c^{2}}}T^{i}(x), \nonumber \\
\overline{T}^{4}(x):=&\sqrt{1-\frac{2|W(\mathbf{x})|}{c^{2}}}T^{4}(x). \label{eq:113ii}
\end{align}
Notice that these components are just the components of $T^{\alpha}(x)$ projected into the corresponding \emph{orthonormal} coordinates (or frame) of the metric $g_{(0)\mu\nu}$.
\subsection{Test particle motions in external static gravitational fields}
In a previous section it was noted that any stream line of incoherent dust follows the ``geodesic'' equation (\ref{eq:5.19}). Along any of these time-like geodesics, the equation (\ref{eq:5.8ii}) implies that
\begin{equation}
g_{(0)\mu\nu|\mathcal{X}(s)} \frac{d\mathcal{X}^{\mu}(s)}{ds}\frac{d\mathcal{X}^{\nu}(s)}{ds} \equiv -c^{2}. \label{eq:6.5}
\end{equation}
The above condition modifies the equation (\ref{eq:3.18iv}). For the sake of consistency, we must alter the definition (\ref{eq:3.15}) for the proper time along a time-like curve by:
\begin{subequations}
\begin{align}
s=& S^{\#}(u):=\frac{1}{c} \int_{u_{1}}^{u} \sqrt{ -g_{(0)\mu\nu}(x)_{|..} \frac{d\mathcal{X}^{\#\,\mu}(w)}{dw} \frac{d\mathcal{X}^{\#\,\nu}(w)}{dw}}\,dw, \label{eq:6.6i} \\
s=& \overline{S}(t):=\frac{1}{c} \int_{t_{1}}^{t} \sqrt{ -g_{(0)\mu\nu}(x)_{|..} \frac{d\overline{\mathcal{X}}^{\mu}(w)}{dw} \frac{d\overline{\mathcal{X}}^{\nu}(w)}{dw}}\,dw, \label{eq:6.6ii} \\
s=& S(s):=\frac{1}{c} \int_{0}^{s} \sqrt{ -g_{(0)\mu\nu}(x)_{|..}
\frac{d\mathcal{X}^{\mu}(w)}{dw} \frac{d\mathcal{X}^{\nu}(w)}{dw}}\,dw.
\label{eq:6.6iii}
\end{align}
\end{subequations}
\qquad The equation (\ref{eq:3.18iv}) is modified by (\ref{eq:6.4}) and (\ref{eq:6.5}) into
\begin{equation}
\left[1+\frac{2|W(\mathbf{x})|}{c^{2}}\right]_{|..}\delta_{ij} \frac{d\mathcal{X}^{i}(s)}{ds} \frac{d\mathcal{X}^{j}(s)}{ds} -\left[1-\frac{2|W(\mathbf{x})|}{c^{2}}\right]_{|..} \left[\frac{d\mathcal{X}^{4}(s)}{ds}\right]^{2} \equiv -c^{2} < 0, \label{eq:6.7}
\end{equation}
while the equation (\ref{eq:3.22}) is changed by (\ref{eq:6.7}) into
\begin{equation}
\frac{ds}{dt}= \frac{d\overline{S}(t)}{dt} =\sqrt{1- \frac{2|W(\mathbf{x})|}{c^{2}} - \left[ 1+ \frac{2|W(\mathbf{x})|}{c^{2}} \right] \frac{|\mathbf{V}(t)|^{2}}{c^{2}}}_{\;\;|..} \leq 1. \label{eq:6.8}
\end{equation}
The above equation reveals the \emph{time dilation} along a moving dust particle in an external gravitational field.
\qquad Similarly, the equations (\ref{eq:3.23ii}) and (\ref{eq:3.23iii}) change over into:
\begin{subequations}
\begin{align}
U^{i}(s)= \frac{d\mathcal{X}^{i}(s)}{ds} =&\frac{V^{i}(t)}{\sqrt{1-\frac{2|W(\mathbf{x})|}{c^{2}}
-\left(1+\frac{2|W(\mathbf{x})|}{c^{2}}\right)\frac{|\mathbf{V}|^{2}}{c^{2}}}}_{\;|..}, \label{eq:6.9i} \\
U^{4}(s)= \frac{d\mathcal{X}^{4}(s)}{ds} =& \frac{c}{\sqrt{1-\frac{2|W(\mathbf{x})|}{c^{2}}
-\left(1+\frac{2|W(\mathbf{x})|}{c^{2}}\right)\frac{|\mathbf{V}|^{2}}{c^{2}}}}_{\;|..}.
\label{eq:6.9ii}
\end{align}
\end{subequations}
Here, $V^{i}(t) = \frac{d\overline{\mathcal{X}}^{i}(t)}{dt}$ are the
components of the ``coordinate'' velocity which in general differ
from the ``measurable'' velocity components,
$\overline{V}^{i}(t):= \sqrt{\frac{1+\frac{2|W(\mathbf{x})|}{c^{2}}}{1-\frac{2|W(\mathbf{x})|}{c^{2}}}}
\frac{d\overline{\mathcal{X}}^{i}(t)}{dt}_{\;|..}$.
\qquad Now, the geodesic equations (\ref{eq:5.19}) are derivable
from a variational principle \cite{ref:7}. A free particle's
motion is governed by a purely kinetic Lagrangian, $\frac{1}{2}m\,
\delta_{ij}V^{i}V^{j}$ in non-relativistic mechanics. The
relativistic analogue is $\frac{1}{2}m\,
g_{(0)\alpha\beta}u^{\alpha}\overline{u}^{\beta}$. In the presence
of gravity, the gravitational coupling arises from lowering the
index with the metric $g_{(0)\alpha\beta}$ and therefore, using
(\ref{eq:6.1iv}), (\ref{eq:6.1v}) and (\ref{eq:6.3}) the
Lagrangian (per unit mass) becomes
\begin{align}
L(x,u):=& \frac{1}{2} \left[1+\frac{2|W(\mathbf{x})|}{c^{2}}\right] \delta_{ij} u^{i}u^{j} -\frac{1}{2} \left[1-\frac{2|W(\mathbf{x})|}{c^{2}}\right] (u^{4})^{2} \nonumber \\
=& \frac{1}{2} \delta_{ij} u^{i}u^{j} -W(\mathbf{x}) \left(\frac{u^{4}}{c}\right)^{2} - \frac{(u^{4})^{2}}{2} -\frac{W(\mathbf{x})}{c^{2}} \delta_{ij}u^{i}u^{j}. \label{eq:6.10i}
\end{align}
The relativistic Euler-Lagrange equations are given by
\begin{equation}
\frac{\partial L(x,u)}{\partial x^{\alpha}}_{|x^{\alpha}=\mathcal{X}^{\alpha}(s), u^{\alpha}= \frac{d\mathcal{X}^{\alpha}(s)}{ds}} - \frac{d}{ds} \left[\frac{\partial L(x,u)}{\partial u^{\alpha}}_{|..}\right] =0. \label{eq:6.10ii}
\end{equation}
\qquad The Newtonian Lagrangian for the corresponding Newtonian theory is
\begin{equation}
L_{N}(\mathbf{x}, \mathbf{v}):= \frac{1}{2} \delta_{ij} v^{i}v^{j} -W(\mathbf{x}), \label{eq:6.11}
\end{equation}
giving rise to the equations of motion (\ref{eq:5.2ii}).
\qquad For small velocities, by the equations (\ref{eq:6.9i}), (\ref{eq:6.10i}) matches (\ref{eq:6.11}) except for the term $-(u^{4})^{2}/2$. This term represents the large rest energy contribution which is manifest in the relativistic physics.
\qquad It will be instructive to investigate the fourth equation
of (\ref{eq:6.10ii}). Since $x^{4}$ is a cyclic variable in the
Lagrangian (\ref{eq:6.10i}), the corresponding equation of motion
admits the first integral:
\begin{subequations}
\begin{align}
&\frac{\partial L(x,u)}{\partial u^{4}}_{|..} =-\left[1+\frac{2W(\mathbf{x})}{c^{2}}\right]U^{4}(s)= const. , \label{eq:6.12i} \\
\mbox{or,}\;\;\; &\frac{c \left[1+\frac{2W(\mathbf{x})}{c^{2}}\right]}{\sqrt{1+\frac{2W(\mathbf{x})}{c^{2}} -\frac{1}{c^{2}} \left[1-\frac{2W(\mathbf{x})}{c^{2}} \right] \delta_{ij}V^{i}V^{j}}}_{|..} =\frac{\mathcal{E}}{c} =const. \label{eq:6.12ii}
\end{align}
\end{subequations}
For \emph{small} velocities and \emph{weak} gravitational fields,
equation (\ref{eq:6.12ii}) yields:
\begin{equation}
\mathcal{E}=c^{2} + \left[ \frac{1}{2} |\mathbf{V}|^{2}
+W(\mathbf{x})\right]_{|..}
+\mathcal{O}\left(\frac{1}{c^{2}}\right). \label{eq:6.13}
\end{equation}
\qquad It is not difficult to interpret the above equation. The
constant $\mathcal{E}$ represents the conserved total energy per
unit mass. The first term on the RHS is the large rest energy of
the unit mass. The second and third terms are the usual kinetic
and potential energies respectively.
\subsubsection{An example from planetary motion}
Here we investigate planetary motions due to the spherically
symmetric gravitational field of the sun. The usual potential
function is furnished by:
\begin{equation}
W(\mathbf{x})= \frac{-GM}{\sqrt{(x^{1})^{2} +(x^{2})^{2} +
(x^{3})^{2}}}, \label{eq:6.14}
\end{equation}
with $M > 0$ being the solar mass. Employing spherical polar
coordinates in space, the equations (\ref{eq:6.10i}) and
(\ref{eq:6.14}) yield the Lagrangian
\begin{equation}
L(x,u)= \frac{1}{2} \left(1+\frac{2GM}{c^{2}r}\right) \left[ (u^{r})^{2} + r^{2} (u^{\theta})^{2} + r^{2}\sin^{2}\theta (u^{\varphi})^{2}\right] - \frac{1}{2} \left( 1-\frac{2GM}{c^{2}r}\right) (u^{4})^{2} . \label{eq:6.15}
\end{equation}
\qquad The Euler-Lagrange equations (\ref{eq:6.10i}), from (\ref{eq:6.15}) admit uniplanar motions characterized by:
\begin{equation}
\theta=\Theta(s) \equiv \frac{\pi}{2}. \label{eq:6.16}
\end{equation}
The reduced Lagrangian is then
\begin{equation}
L_{(0)}(..)=\frac{1}{2} \left(1+\frac{2GM}{c^{2}r}\right) \left[(u^{r})^{2} +r^{2}(u^{\varphi})^{2} \right] -\frac{1}{2} \left(1-\frac{2GM}{c^{2}r}\right)(u^{4})^{2} . \label{eq:6.17i}
\end{equation}
In this case, the conservation of energy equation (\ref{eq:6.12i}) reads:
\begin{equation}
\left[1 -\frac{2GM}{c^{2}r} \right] U^{4}(s)=\frac{\mathcal{E}}{c} . \label{eq:6.17}
\end{equation}
\qquad The presence of another cyclic coordinate, $\varphi$, leads to the conservation of angular momentum:
\begin{equation}
\frac{\partial L_{(0)}(..)}{\partial u_{\varphi}}_{|..} =r^{2}
\left(1+\frac{2GM}{c^{2}r} \right) u^{\varphi}_{\;\; |..} = h =
const. \label{eq:6.18}
\end{equation}
Substituting (\ref{eq:6.16}), (\ref{eq:6.17}) and (\ref{eq:6.18})
into (\ref{eq:6.7}), we obtain
\begin{equation}
\left[ \left(1+\frac{2GM}{c^{2}r}\right)(u^{r})^{2}
+\frac{h^{2}}{r^{2}\left(1+\frac{2GM}{c^{2}r} \right)
}-\frac{\mathcal{E}^{2}}{c^{2} \left(1-\frac{2GM}{c^{2}r}\right)}
\right]_{|..} \equiv -c^{2}. \label{eq:6.19}
\end{equation}
We reparameterize the curve by the following:
\begin{align}
r=&\mathcal{R}(s) =\hat{\mathcal{R}}(\varphi), \label{eq:6.20} \\
\frac{d\mathcal{R}(s)}{ds}=& u^{\varphi}_{\;\; |..}\frac{d \hat{\mathcal{R}}(\varphi)}{d\varphi} =\frac{h}{r^{2} \left(1+\frac{2GM}{c^{2}r}\right)} \frac{d \hat{\mathcal{R}}(\varphi)}{d\varphi}. \nonumber
\end{align}
It is useful at this point to make the following coordinate transformation:
\begin{align}
y=& \frac{1}{r},\;\; y=Y(\phi), \label{eq:6.21} \\
y^{\prime}:=& \frac{dY(\varphi)}{d\varphi} . \nonumber
\end{align}
With (\ref{eq:6.20}) and (\ref{eq:6.21}), the equation (\ref{eq:6.19}) reduces to
\begin{equation}
\left[ \frac{1-\frac{2GMy}{c^{2}}}{1+\frac{2GMy}{c^{2}}} \right]
\left[ (y^{\prime})^{2} +y^{2} \right] +\frac{c^{2}}{h^{2}}
\left( 1-\frac{2GMy}{c^{2}}\right)
=\frac{\mathcal{E}^{2}}{h^{2}c^{2}}. \label{eq:6.22}
\end{equation}
The above first-order equation can be solved by quadrature. However, to extract physically important effects, we differentiate the equation (\ref{eq:6.22}) to get
\begin{align}
y^{\prime\prime}+y=& \left(1+\frac{4GMy}{c^{2}}\right) \left[\frac{GM}{h^{2}} +\frac{2GM}{c^{2}} \left((y^{\prime})^{2} +y^{2} \right)\right] +\mathcal{O} \left(\frac{1}{c^{4}}\right) \nonumber \\
=& \frac{GM}{h^{2}} + 4 \left(\frac{GM}{hc}\right)^{2}y +\frac{2GM}{c^{2}} \left((y^{\prime})^{2} +y^{2} \right) +\mathcal{O} \left(\frac{1}{c^{4}}\right). \label{eq:6.23}
\end{align}
The equation (\ref{eq:6.23}) may be solved by the perturbative expansion:
\begin{equation}
y=y_{0} +\frac{y_{1}}{c^{2}} + \frac{y_{2}}{c^{4}} +... \label{eq:6.24}
\end{equation}
Using this expansion in (\ref{eq:6.23}), we obtain
\begin{equation}
y=y_{0} + \frac{y_{1}}{c^{2}}+...= \frac{GM}{h^{2}} \left[1+e\cos(\varphi -\overline{\omega})\right] +\frac{4(GM)^{3}}{c^{2}h^{4}} e\varphi \sin(\varphi-\overline{\omega}) +... \;\;. \label{eq:6.25}
\end{equation}
Here, the constants of integration $e$ and $\overline{\omega}$
represent the eccentricity and perihelion angle of the orbit
respectively. Combining the first two terms in (\ref{eq:6.25}),
we conclude that
\begin{equation}
y_{0} +\frac{y_{1}}{c^{2}} =\frac{GM}{h^{2}} \left[1+e\cos (\varphi -\overline{\omega} -\delta \overline{\omega}) \right] +\left(\mbox{higher order}\right) , \label{eq:6.26}
\end{equation}
where
\begin{equation}
\delta\overline{\omega}:=\arctan\left[4\varphi \left(\frac{GM}{h}\right)^{2} \right] =4 \left(\frac{GM}{h}\right)^{2}\varphi + \left(\mbox{higher order}\right). \nonumber
\end{equation}
Thus, the elliptic orbit precesses and the perihelion angle changes (see figure \ref{fig:perihelion}). This gravitational perihelion shift per revolution is given by
\begin{equation}
\Delta \overline{\omega}=8\pi \left(\frac{GM}{h}\right)^{2}. \label{eq:6.27}
\end{equation}
For the planet Mercury, the above amount yields a little over
$57^{\prime\prime}$ per century! However, the full non-linear
theory of general relativity predicts the observed amount of
almost exactly $43^{\prime\prime}$ per century \footnote{The
actual observed perihelion precession of Mercury is approximately
$5600^{\prime\prime}$ per century. When effects such the
attraction due to the Newtonian gravitational field of the other
planets are taken into account, along with the fact that the
Earth is not an inertial frame of reference, a residual
$43^{\prime\prime}$ per century persists. The origin of this
residual precession was a mystery until general relativity was
formulated in 1915 \cite{ref:2}.} \cite{ref:2}.
\begin{figure}[ht]
\begin{center}
\includegraphics[bb=0 0 185 211, clip, scale=0.5, keepaspectratio=true]{perih2.eps}
\caption{{\small The perihelion precession of the planets in a gravitational field. The diagram displays two orbits, perhaps millenia apart, of a planet around a star. The perihelion point of the planet has shifted by an amount $\Delta\overline{\omega}$, an effect not predicted by Newtonian gravity theory.}} \label{fig:perihelion}
\end{center}
\end{figure}
\subsection{Perfect fluid in static gravity}
In this case, the equations (\ref{eq:6.1iv}), (\ref{eq:6.1v}) and (\ref{eq:6.4}) yield, for the metric tensor,
\begin{align}
g_{(0)ij}=&\left[1-\frac{2W(\mathbf{x})}{c^{2}}\right]\delta_{ij}, \;\; g_{(0)i4}(x)\equiv 0, \;\; g_{(0)44}(x) =-\left[1+\frac{2W(\mathbf{x})}{c^{2}}\right], \nonumber \\
g_{(0)}^{ij}=&\left[1-\frac{2W(\mathbf{x})}{c^{2}}\right]^{-1}\delta^{ij}, \;\; g_{(0)}^{i4}(x) \equiv 0, \;\; g_{(0)}^{44}(x)=- \left[1+\frac{2W(\mathbf{x})}{c^{2}}\right]^{-1}. \label{eq:6.28}
\end{align}
\qquad The corresponding non-zero Christoffel symbols are provided by:
\begin{align}
\left\{
\begin{array}{l}
i \\
j \; k
\end{array}
\right\}_{(0)}=& \frac{1}{c^{2}} \left[1-\frac{2W(\mathbf{x})}{c^{2}}\right]^{-1} \delta^{il} \left[ \delta_{jk} \frac{\partial W(\mathbf{x})}{\partial x^{l}} -\delta_{kl} \frac{\partial W(\mathbf{x})}{\partial x^{j}} -\delta_{lj} \frac{\partial W(\mathbf{x})}{\partial x^{k}} \right], \label{eq:6.29} \\
\left\{
\begin{array}{l}
4 \\
i \; 4
\end{array}
\right\}_{(0)} \equiv& \left\{
\begin{array}{l}
4 \\
4 \; i
\end{array}
\right\}_{(0)} =\frac{1}{c^{2}} \frac{\partial W(\mathbf{x})}{\partial x^{i}},\; \left\{
\begin{array}{l}
i \\
4 \; 4
\end{array}
\right\}_{(0)}= \frac{1}{c^{2}} \left[1-\frac{2W(\mathbf{x})}{c^{2}}\right]^{-1} \delta^{ij} \frac{\partial W(\mathbf{x})}{\partial x^{j}} . \nonumber
\end{align}
\qquad The continuity equation (\ref{eq:5.30}) for a perfect fluid yields \cite{ref:15}
\begin{equation}
\frac{\partial}{\partial x^{b}} \left[\left(\rho+\frac{p}{c^{2}}\right) u^{b} \right] +\frac{\partial}{\partial x^{4}}\left[\left(\rho+\frac{p}{c^{2}}\right)u^{4}\right] =\frac{1}{c^{2}} g_{(0)\alpha\gamma}u^{\gamma} \left[\frac{\partial}{\partial x^{b}} \left(p g_{(0)}^{\alpha b}\right) +\frac{\partial}{\partial x^{4}} \left(p g_{(0)}^{\alpha 4} \right)\right]. \label{eq:6.30}
\end{equation}
\qquad Using (\ref{eq:6.29}), the equation (\ref{eq:6.30}) leads to
\begin{equation}
\frac{\partial}{\partial x^{b}} \left[\left(\rho+ \frac{p}{c^{2}}\right)u^{b}\right] +\frac{\partial}{\partial x^{4}} \left[\left(\rho +\frac{p}{c^{2}}\right) u^{4}\right] =\frac{1}{c^{2}} \left[1-\frac{2W(\mathbf{x})}{c^{2}}\right]u^{b} \frac{\partial}{\partial x^{b}} \left[ p\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1} \right]. \label{eq:6.31}
\end{equation}
\qquad Substituting (\ref{eq:6.9i}) and (\ref{eq:6.9ii}) into (\ref{eq:6.31}), we derive that
\begin{align}
&\frac{\partial}{\partial x^{b}} \left[ \left(\rho+ \frac{p}{c^{2}}\right) \frac{v^{b}}{\sqrt{1+\frac{2W(\mathbf{x})}{c^{2}} -\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)\frac{|\mathbf{v}|^{2}}{c^{2}}}} \right] +\frac{\partial}{\partial t} \left[ \frac{\left(\rho+\frac{p}{c^{2}}\right)}{\sqrt{1+\frac{2W(\mathbf{x})}{c^{2}} -\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)\frac{|\mathbf{v}|^{2}}{c^{2}}}}\right] \nonumber \\
=& \frac{1}{c^{2}} \left[1-\frac{2W(\mathbf{x})}{c^{2}} \right] \frac{v^{b}}{\sqrt{ 1+\frac{2W(\mathbf{x})}{c^{2}} - \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right) \frac{|\mathbf{v}|^{2}}{c^{2}}}} \frac{\partial}{\partial x^{b}} \left[p\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1}\right]. \label{eq:6.32}
\end{align}
\qquad Expanding the above in powers of $c^{-2}$, we can express
\begin{align}
& \frac{\partial}{\partial x^{b}} \left[\left(\rho+ \frac{p}{c^{2}}\right) \left(1-\frac{W(\mathbf{x})}{c^{2}} +\frac{|\mathbf{v}|^{2}}{2c^{2}}\right) v^{b}\right] +\frac{\partial}{\partial t} \left[\left(\rho+ \frac{p}{c^{2}}\right) \left(1-\frac{W(\mathbf{x})}{c^{2}} +\frac{|\mathbf{v}|^{2}}{2c^{2}}\right)\right] \nonumber \\
&= \frac{1}{c^{2}} v^{b} \frac{\partial p}{\partial x^{b}} +\mathcal{O}\left(\frac{1}{c^{4}}\right). \label{eq:6.33}
\end{align}
In more familiar notation the above equation reads
\begin{align}
&\mathbf{\nabla} \cdot \left[\rho \mathbf{v}\right] +\frac{\partial \rho}{\partial t} =\frac{1}{c^{2}} \left\{-p \mathbf{\nabla \cdot v} + \mathbf{\nabla}\cdot \left[\rho \left(W(\mathbf{x}) -\frac{|\mathbf{v}|^{2}}{2}\right) \mathbf{v}\right] \right. \nonumber \\
& \left. -\frac{\partial p}{\partial t} +\frac{\partial}{\partial t} \left[\rho\left(W(\mathbf{x}) -\frac{|\mathbf{v}|^{2}}{2}\right)\right] \right\} +\mathcal{O}\left(\frac{1}{c^{4}}\right). \label{eq:6.34}
\end{align}
The relativistic correction terms are all collected on the right hand side of (\ref{eq:6.34}).
\qquad Now we shall investigate the equations of stream lines of a
perfect fluid in the external gravitational fluid. Equations
(\ref{eq:5.32}) provide
\begin{align}
&\left(\rho+\frac{p}{c^{2}}\right) \left[\frac{d^{2}\mathcal{X}^{i}(s)}{ds^{2}} +
\left\{
\begin{array}{l}
i \\
j \; k
\end{array}
\right\}_{(0)} \frac{d\mathcal{X}^{j}(s)}{ds}\frac{d\mathcal{X}^{k}(s)}{ds} +
\left\{
\begin{array}{l}
i \\
4 \; 4
\end{array}
\right\}_{(0)} \left(\frac{d\mathcal{X}^{4}(s)}{ds}\right)^{2} \right]_{|..} \nonumber \\
=&- \left[\delta^{i}_{\;\gamma} +\frac{1}{c^{2}} \left(g_{(0)\gamma j} \frac{d\mathcal{X}^{j}(s)}{ds} + g_{(0)\gamma 4} \frac{d\mathcal{X}^{4}(s)}{ds}\right) \frac{d\mathcal{X}^{i}}{ds}\right] \left[\frac{\partial}{\partial x^{b}} \left(p g_{(0)}^{b\gamma} \right)+ \frac{\partial}{\partial x^{4}}\left(pg_{(0)}^{4\gamma}\right)\right]_{|..} \nonumber \\
=& -\left[\delta^{i}_{\;k} +\frac{1}{c^{2}} g_{(0)kj} \frac{d\mathcal{X}^{i}}{ds}\frac{d\mathcal{X}^{j}}{ds} \right] \left[\frac{\partial}{\partial x^{b}} \left(p g_{(0)}^{bk}\right)\right]_{|..} -\frac{1}{c^{2}} g_{(0)44} \frac{d\mathcal{X}^{i}}{ds} \frac{d\mathcal{X}^{4}}{ds} \frac{\partial}{\partial x^{4}} \left(p g_{(0)}^{44}\right)_{|..}\, . \label{eq:6.35}
\end{align}
\qquad Using (\ref{eq:6.28}) and (\ref{eq:6.29}) along with (\ref{eq:6.35}), we deduce that
\begin{align}
& \left(\rho+ \frac{p}{c^{2}}\right) \left[ \frac{d^{2}\mathcal{X}^{i}(s)}{ds^{2}} + \frac{1}{c^{2}} \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1} \left(\delta_{jk} \delta^{il} \frac{\partial W}{\partial x^{l}} -\delta^{i}_{\;k} \frac{\partial W}{\partial x^{j}} -\delta^{i}_{\;j} \frac{\partial W}{\partial x^{k}} \right)\frac{d\mathcal{X}^{j}(s)}{ds}\frac{d\mathcal{X}^{k}(s)}{ds}\right. \nonumber \\
&\left. + \frac{1}{c^{2}} \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1} \delta^{ij} \frac{\partial W}{\partial x^{j}} \left(\frac{\partial \mathcal{X}^{4}(s)}{ds}\right)^{2} \right]_{|..} \nonumber \\
=&- \left[\delta^{i}_{\;k} +\frac{1}{c^{2}} \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right) \delta_{kj} \frac{d\mathcal{X}^{i}}{ds} \frac{d\mathcal{X}^{j}}{ds} \right] \left\{\frac{\partial}{\partial x^{a}} \left[p \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1}
\delta^{ak} \right]\right\} \nonumber \\
&-\frac{1}{c^{2}} \left(1+\frac{2W(\mathbf{x})}{c^{2}}\right)\frac{d\mathcal{X}^{i}}{ds} \frac{d\mathcal{X}^{4}}{ds} \left\{\frac{\partial}{\partial x^{4}} \left[p\left(1+\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1}\right] \right\}_{|..}\;\;\; . \label{eq:6.36}
\end{align}
We parameterize the curve by the rule:
\begin{equation}
\frac{d}{ds}=\left[\frac{d\overline{S}(t)}{dt}\right]^{-1}\frac{d}{dt}=
\frac{1}{\sqrt{1+\frac{2W(\mathbf{x})}{c^{2}}-\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)
\frac{|\mathbf{v}|^{2}}{c^{2}}}}_{\;|..}\, \frac{d}{dt}\;\; .
\label{eq:6.37}
\end{equation}
Then, from (\ref{eq:6.36}) and (\ref{eq:6.37}) the following is obtained:
\begin{align}
&\left(\rho +\frac{p}{c^{2}}\right) \left\{ \frac{dV^{i}(t)}{dt} -\frac{V^{i}(t)}{2} \frac{d}{dt} \left[\ln\left(1+\frac{2W(\mathbf{x})}{c^{2}} -\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)\frac{|\mathbf{v}|^{2}}{c^{2}}\right)\right] \right. \nonumber \\
&+ \frac{1}{c^{2}} \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1} \left(\delta_{jk} \delta^{il} \frac{\partial W}{\partial x^{l}} -\delta^{i}_{\;k} \frac{\partial W}{\partial x^{j}} -\delta^{i}_{\;j} \frac{\partial W}{\partial x^{k}} \right) V^{j}V^{k} \nonumber \\
&+ \left.\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1} \delta^{ij} \frac{\partial W}{\partial x^{j}} \right\}_{|..} \nonumber \\
=& -\left\{ \left[1+\frac{2W(\mathbf{x})}{c^{2}} -\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)\frac{|\mathbf{v}|^{2}}{c^{2}} \right] \delta^{i}_{\;k} +\frac{1}{c^{2}} \left(1-\frac{2W(\mathbf{x})}{c^{2}}\right) \delta_{kj} V^{i}V^{j}\right\} \nonumber \\
&\times \left\{\delta^{ak} \frac{\partial}{\partial x^{a}}
\left[p\left(1-\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1}\right] \right\}_{|..}
-\frac{1}{c^{2}}\left(1+\frac{2W(\mathbf{x})}{c^{2}}\right)V^{i}
\left\{\frac{\partial}{\partial t}
\left[p\left(1+\frac{2W(\mathbf{x})}{c^{2}}\right)^{-1}\right]\right\}_{|..} .
\label{eq:6.38}
\end{align}
\qquad Expanding in inverse powers of $c^{2}$, we re-write the above equation of the stream-lines (\ref{eq:6.38}) as \cite{ref:15}:
\begin{align}
&\left\{\rho(\mathbf{x}) \left[\frac{d\mathbf{V}(t)}{dt} +\mathbf{\nabla}W(\mathbf{x})\right]
+\mathbf{\nabla}p(x) \right\}_{|..} \nonumber \\
&=-\frac{1}{c^{2}} \left\{\rho \left[\left(\mathbf{V}(t)\cdot \frac{d\mathbf{V}(t)}{dt} -3 \mathbf{V}(t)\cdot \mathbf{\nabla}W\right) \mathbf{V}(t) + \left(2W +|\mathbf{V}(t)|^{2}\right)\mathbf{\nabla}W\right] \right. \nonumber \\
&+p \left. \left(\frac{d\mathbf{V}(t)}{dt} +3 \mathbf{\nabla}W\right) +\left(4 W -|\mathbf{V}(t)|^{2}]\right) \mathbf{\nabla}p + \left(\mathbf{V}(t)\cdot \mathbf{\nabla}p +\frac{\partial p}{\partial t} \right) \mathbf{V}(t) \right\}_{|..} +\mathcal{O}\left(\frac{1}{c^{4}}\right). \label{eq:6.39}
\end{align}
The right hand side contains all the relativistic corrections to the Euler equations of Newtonian fluid dynamics \cite{ref:12}, \cite{ref:15}.
\section{Generalizations to complicated materials and curvilinear coordinates}
\subsection{Perfect fluid plasma}
In this section we maintain field equations (\ref{eq:5.26i} - \ref{eq:5.26v}) for the fields $\phi_{(I)\alpha\beta}(x)$ and $\phi_{(0)\alpha\beta}(x)$. We also retain equations (\ref{eq:5.12i}) and (\ref{eq:5.12iii}) for the exterior metric $g_{(0)\mu\nu}(x)$ and the normalized vector $u^{\mu}$. Moreover, we stipulate the same equation as (\ref{eq:5.28}) for the interacting energy momentum stress tensor $\Theta^{\alpha\beta}(x)$.
\qquad A charged fluid or plasma satisfies the electromagnetic field equations (\ref{eq:4.10i}- \ref{eq:4.10iii}). The energy momentum stress tensor for this system is given by
\begin{equation}
T^{\alpha\beta}_{\mbox{\tiny (nvp)}}(x):= \left[
\rho(x)+\frac{p(x)}{c^{2}}\right]u^{\alpha}(x)u^{\beta}(x) +p(x)
g_{(0)}^{\alpha\beta}(x) +\Theta^{\alpha\beta}(x)
+\mathcal{M}^{\alpha\beta}(x) , \label{eq:7.1}
\end{equation}
where the subscript (nvp) denotes ``non-viscous plasma''. The
quantity $\mathcal{M}^{\alpha\beta}(x)$ is furnished by
(\ref{eq:4.12i}). Therefore, equation (\ref{eq:5.26iv}) implies
that
\begin{equation}
0=\frac{\partial T^{\alpha\beta}_{\mbox{\tiny
(nvp)}}(x)}{\partial x^{\beta}} = u^{\alpha}
\frac{\partial}{\partial x^{\beta}} \left[\left(\rho
+\frac{p}{c^{2}}\right) u^{\beta}\right]
+\left(\rho+\frac{p}{c^{2}}\right) \nabla^{(0)}_{\beta}
u^{\alpha} +\frac{\partial}{\partial x^{\beta}}\left(p
g^{\alpha\beta}_{(0)}\right) +\frac{J^{\beta}}{c}
F_{\beta}^{\;\;\alpha}. \label{eq:7.2}
\end{equation}
Here, we have used equation (\ref{eq:5.28}) for $\frac{\partial
\Theta^{\alpha\beta}(x)}{\partial x^{\beta}}$.
\qquad Multiplying (\ref{eq:7.2}) by $\overline{u}_{\alpha}$ (and
summing), we derive the plasma continuity equation:
\begin{equation}
\frac{\partial}{\partial x^{\beta}} \left[\left(\rho +
\frac{p}{c^{2}} \right)u^{\beta} \right]
=\frac{\overline{u}_{\alpha}}{c^{2}}
\left[\frac{\partial}{\partial x^{\beta}} \left(p
g_{(0)}^{\alpha\beta}\right) +\frac{J^{\beta}}{c}
F_{\beta}^{\;\;\alpha} \right]. \label{eq:7.3}
\end{equation}
Substituting this last equation into (\ref{eq:7.2}), we deduce the
generalized Euler equation
\begin{equation}
\left( \rho+\frac{p}{c^{2}}\right) u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha} +\left(\delta^{\alpha}_{\;\gamma} + \frac{\overline{u}_{\gamma}u^{\alpha}}{c^{2}}\right) \left[ \frac{\partial}{\partial x^{\beta}} \left(p g_{(0)}^{\gamma\beta}\right) + \frac{J^{\beta}}{c} F_{\beta}^{\;\;\gamma}\right]=0. \label{eq:7.4}
\end{equation}
\qquad From (\ref{eq:7.4}), the equations for a stream line emerges as
\begin{align}
& \left\{ \left[\rho +\frac{p}{c^{2}}\right] \frac{d^{2}\mathcal{X}^{\alpha}(s)}{ds^{2}} +
\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}_{(0)}
\frac{d\mathcal{X}^{\beta}(s)}{ds} \frac{d\mathcal{X}^{\gamma}(s)}{ds} \right\}_{|x^{\alpha}=\mathcal{X}^{\alpha}(s)} \nonumber \\
&= -\left\{ \left[ \delta^{\alpha}_{\;\gamma} +
\frac{g_{(0)\mu\gamma}(x)}{c^{2}} \frac{d\mathcal{X}^{\mu}(s)}{ds}
\frac{d\mathcal{X}^{\alpha}(s)}{ds} \right] \left[
\frac{\partial}{\partial x^{\beta}} \left(p(x)
g_{(0)}^{\gamma\beta}(x)\right) +\frac{J^{\beta}(x)}{c}
F_{\beta}^{\;\;\gamma}(x) \right] \right\}_{|..}\; .
\label{eq:7.5}
\end{align}
\qquad One may add viscosity to the above system. For such a fluid, the energy momentum stress tensor is
\begin{align}
T^{\alpha\beta}(x):= &T^{\alpha\beta}_{\mbox{\tiny(nvp)}} - \eta(x) \left\{ \left[g_{(0)}^{\alpha\sigma}(x) +\frac{u^{\alpha}(x)u^{\sigma}(x)}{c^{2}}\right] \frac{\partial u^{\beta}(x)}{\partial x^{\sigma}} +\left[g_{(0)}^{\beta\sigma}(x) +\frac{u^{\beta}(x)u^{\sigma}(x)}{c^{2}}\right]\frac{\partial u^{\alpha}(x)}{\partial x^{\sigma}} \right\} \nonumber \\
&+ \left[\frac{2}{3} \eta(x) -\zeta(x) \right] \left[g_{(0)}^{\alpha\beta}(x) + \frac{u^{\alpha}(x) u^{\beta}(x)}{c^{2}}\right] \frac{\partial u^{\sigma}(x)}{\partial x^{\sigma}} . \label{eq:7.6}
\end{align}
Here, $\eta(x)$ and $\zeta(x)$ represent the \emph{shear viscosity} and \emph{bulk viscosity} respectively. Using (\ref{eq:5.26iv}), we obtain, from (\ref{eq:7.6}) the following equation
\begin{align}
0= \frac{\partial T^{\alpha\beta}(x)}{\partial x^{\beta}} = &\frac{\partial T^{\alpha\beta}_{\mbox{\tiny{(nvp)}}}(x)}{\partial x^{\beta}} -\frac{\partial}{\partial x^{\beta}} \left\{ \eta \left[\left(g_{(0)}^{\alpha\sigma} +\frac{u^{\alpha}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\beta}}{\partial x^{\sigma}} + \left(g_{(0)}^{\beta\sigma} +\frac{u^{\beta}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\alpha}}{\partial x^{\sigma}} \right] \right. \nonumber \\
&+\left. \left(\zeta -\frac{2}{3}\eta\right) \left(g_{(0)}^{\alpha\beta} +\frac{u^{\alpha}u^{\beta}}{c^{2}} \right) \frac{\partial u^{\sigma}}{\partial x^{\sigma}} \right\}. \label{eq:7.7}
\end{align}
Here we have again stipulated the equation (\ref{eq:5.28}).
\qquad Multiplying (\ref{eq:7.7}) by $\overline{u}_{\alpha}$, we derive the continuity equation:
\begin{align}
\frac{\partial}{\partial x^{\beta}} \left[\left(\rho + \frac{p}{c^{2}} \right)u^{\beta} \right] =& \frac{\overline{u}_{\alpha}}{c^{2}} \left\{\left[\frac{\partial}{\partial x^{\beta}} \left(p g_{(0)}^{\alpha\beta}\right) +\frac{J^{\beta}}{c} F_{\beta}^{\;\;\alpha} \right] \right. \nonumber \\
& - \frac{\partial}{\partial x^{\beta}} \left(\eta \left[ \left( g_{(0)}^{\alpha\sigma} +\frac{u^{\alpha}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\beta}}{\partial x^{\sigma}} + \left( g_{(0)}^{\beta\sigma} +\frac{u^{\beta}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\alpha}}{\partial x^{\sigma}} \right] \right. \nonumber \\
& +\left. \left. \left(\zeta-\frac{2}{3}\eta\right) \left( g_{(0)}^{\alpha\beta} +\frac{u^{\alpha}u^{\beta}}{c^{2}} \right) \frac{\partial u^{\sigma}}{\partial x^{\sigma}} \right) \right\} \label{eq:7.8}
\end{align}
Substituting (\ref{eq:7.8}) into (\ref{eq:7.7}), we deduce the generalized \emph{Navier-Stokes equation}:
\begin{align}
\left( \rho+\frac{p}{c^{2}}\right) u^{\beta} \nabla^{(0)}_{\beta} u^{\alpha} =& \left(\delta^{\alpha}_{\;\gamma} + \frac{\overline{u}_{\gamma}u^{\alpha}}{c^{2}}\right) \left\{ -\frac{\partial}{\partial x^{\beta}} \left(p g_{(0)}^{\gamma\beta}\right) - \frac{J^{\beta}}{c} F_{\beta}^{\;\;\gamma} \right. \nonumber \\
&+ \frac{\partial}{\partial x^{\beta}} \left( \eta \left[ \left(g_{(0)}^{\gamma\sigma} +\frac{u^{\gamma}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\beta}}{\partial x^{\sigma}} +\left(g_{(0)}^{\beta\sigma} +\frac{u^{\beta}u^{\sigma}}{c^{2}} \right) \frac{\partial u^{\gamma}}{\partial x^{\sigma}}\right] \right. \nonumber \\
&\left. \left. + \left(\zeta-\frac{2}{3}\eta\right) \left( g_{(0)}^{\gamma\beta} +\frac{u^{\gamma}u^{\beta}}{c^{2}}\right) \frac{\partial u^{\sigma}}{\partial x^{\sigma}} \right) \right\} . \label{eq:7.9}
\end{align}
\subsection{Curvilinear coordinates and orthonormal frames}
Now we shall introduce curvilinear spacetime coordinates by transformation equations:
\begin{align}
\hat{x}^{\alpha}=&\hat{X}^{\alpha}(x), \nonumber \\
\frac{\partial \left(\hat{x}^{1}, \hat{x}^{2},\hat{x}^{3}, \hat{x}^{4} \right)}{\partial
(x^{1}, x^{2}, x^{3}, x^{4})} & \neq 0, \label{eq:7.10} \\
x^{\alpha}=& X^{\alpha}(\hat{x}). \nonumber
\end{align}
Here, we have assumed that the functions $\hat{X}^{\alpha}$ are of class $C^{2}$. The transformation rules for tensor fields are furnished by \cite{ref:7}
\begin{equation}
\hat{T}^{\alpha\beta ..}_{\;\;\;\;\; \mu\nu ..}(\hat{x})= \frac{\partial \hat{X}^{\alpha}(x)}{\partial x^{\gamma}} \frac{\partial \hat{X}^{\beta}(x)}{\partial x^{\delta}} ..
\frac{\partial X^{\rho}(\hat{x})}{\partial \hat{x}^{\mu}} \frac{\partial X^{\sigma}(\hat{x})}{\partial \hat{x}^{\nu}}\, T^{\gamma\delta..}_{\;\;\;\;\; \rho \sigma ..}(x). \label{eq:7.11}
\end{equation}
\qquad The coordinate transformation (\ref{eq:7.10}) generate a \emph{new} metric tensor field as follows:
\begin{align}
\hat{g}_{\alpha\beta}(\hat{x}):=& d_{\mu\nu} \frac{\partial X^{\mu}(\hat{x})}{\partial \hat{x}^{\alpha}} \frac{\partial X^{\nu}(\hat{x})}{\partial \hat{x}^{\beta}} , \nonumber \\
\left[ \hat{g}^{\alpha\beta}(\hat{x}) \right]:=&\left[\hat{g}_{\alpha\beta}(\hat{x})\right]^{-1} . \label{eq:7.12}
\end{align}
The Christoffel symbols are given by (compare with (\ref{eq:5.6}))
\begin{equation}
\widehat{\left\{
\begin{array}{l}
\alpha \\
\beta \; \gamma
\end{array}
\right\}}:=\frac{1}{2} \hat{g}^{\alpha\sigma}(\hat{x}) \left[ \frac{\partial \hat{g}_{\gamma\sigma}(\hat{x})}{\partial \hat{x}^{\beta}} + \frac{\partial \hat{g}_{\sigma\beta}(\hat{x})}{\partial \hat{x}^{\gamma}} - \frac{\partial \hat{g}_{\beta\gamma}(\hat{x})}{\partial \hat{x}^{\sigma}} \right] . \label{eq:7.13}
\end{equation}
The covariant derivatives are defined by \cite{ref:7}, \cite{ref:19} (compare with (\ref{eq:5.10i} - \ref{eq:5.10iv}))
\begin{align}
\hat{\nabla}_{\alpha} \hat{T}^{\mu\nu ..}_{\;\;\;\;\; \rho\sigma..} (\hat{x}) :=&\frac{\partial \hat{T}^{\mu\nu ..}_{\;\;\;\;\;\rho\sigma..}(\hat{x})}{\partial \hat{x}^{\alpha}} +
\widehat{\left\{
\begin{array}{l}
\mu \\
\alpha \; \beta
\end{array}
\right\}}
\hat{T}^{\beta\nu ..}_{\;\;\;\;\; \rho\sigma..} (\hat{x}) +
\widehat{\left\{
\begin{array}{l}
\nu \\
\alpha \; \beta
\end{array}
\right\}}
\hat{T}^{\mu\beta ..}_{\;\;\;\;\; \rho\sigma..} (\hat{x}) + .. \nonumber \\
&- \widehat{\left\{
\begin{array}{l}
\beta \\
\alpha \; \rho
\end{array}
\right\}}
\hat{T}^{\mu\nu ..}_{\;\;\;\;\; \beta\sigma..} (\hat{x}) -
\widehat{\left\{
\begin{array}{l}
\beta \\
\alpha \; \sigma
\end{array}
\right\}}
\hat{T}^{\mu\nu ..}_{\;\;\;\;\; \rho\beta..} (\hat{x}) -.. \;\;\;. \label{eq:7.14}
\end{align}
\qquad If we replace the various tensor fields $T^{\gamma\delta ..}_{\;\;\;\;\;\rho\sigma ..}(x)$ by $\hat{T}^{\alpha\beta ..}_{\;\;\;\;\;\mu\nu..}(\hat{x})$ (in (\ref{eq:7.11})), and $\hat{\nabla}_{\alpha} \hat{T}^{\mu\nu ..}_{\;\;\;\;\;\rho\sigma}(\hat{x})$ (in (\ref{eq:7.14}), then all the constitutive equations are expressed in curvilinear spacetime coordinates $\hat{x}^{\alpha}$.
\qquad However, for the sake of applications, we restrict ourselves to \emph{spatial curvilinear coordinates} only. In that case the following restriction is placed on equations (\ref{eq:7.10})
\begin{equation}
\hat{x}^{i}= \hat{X}^{i}(\mathbf{x}), \;\;\hat{x}^{4}=\hat{X}^{4}(\mathbf{x},x^{4}):=x^{4}, \;\; {x}^{i}= {X}^{i}(\mathbf{x}). \label{eq:7.15}
\end{equation}
The tensor transformation rules (\ref{eq:7.11}) then simplify in the obvious way:
\begin{align}
\hat{T}^{ij4..}_{\;\;\;\;\;\;\;kl4..}(\hat{\mathbf{x}},\hat{x}^{4})=& \frac{\partial \hat{X}^{i}(\mathbf{x})}{\partial x^{a}} \frac{\partial \hat{X}^{j}(\mathbf{x})}{\partial x^{b}}.. \frac{\partial {X}^{m}(\hat{\mathbf{x}})}{\partial \hat{x}^{k}} \frac{\partial {X}^{n}(\hat{\mathbf{x}})}{\partial \hat{x}^{l}}.. T^{ab4..}_{\;\;\;\;\;\;\;mn4..}(\mathbf{x},x^{4}), \nonumber \\
\hat{T}^{4}_{\;4}(\hat{\mathbf{x}}, \hat{x}^{4}) =& T^{4}_{\;4}(\mathbf{x}, x^{4}), \label{eq:7.16}
\end{align}
and the metric tensor field in (\ref{eq:7.2}) reduces to
\begin{align}
\hat{g}_{ij}(\hat{\mathbf{x}})=& \delta_{kl} \frac{\partial X^{k}(\hat{\mathbf{x}})}{\partial \hat{x}^{i}} \frac{\partial X^{l}(\hat{\mathbf{x}})}{\partial \hat{x}^{j}} , \nonumber \\
\hat{g}_{i4}(\hat{\mathbf{x}},x^{4})\equiv& 0, \label{eq:7.17} \\
\hat{g}_{44}(\hat{\mathbf{x}},\hat{x}^{4})\equiv& -1. \nonumber
\end{align}
\qquad The Christoffel symbols in (\ref{eq:7.13}) boil down to
\begin{align}
\widehat{\left\{
\begin{array}{l}
i \\
j \; k
\end{array}
\right\}} =&\frac{1}{2} \hat{g}^{ia}(\hat{\mathbf{x}}) \left[ \frac{\partial \hat{g}_{ka}(\hat{\mathbf{x}})}{\partial \hat{x}^{j}} + \frac{\partial \hat{g}_{aj}(\hat{\mathbf{x}})}{\partial \hat{x}^{k}} - \frac{\partial \hat{g}_{jk}(\hat{\mathbf{x}})}{\partial \hat{x}^{a}} \right], \nonumber \\
\widehat{\left\{
\begin{array}{l}
4 \\
j \; k
\end{array}
\right\}} =&
\widehat{\left\{
\begin{array}{l}
4 \\
j \; 4
\end{array}
\right\}} =
\widehat{\left\{
\begin{array}{l}
4 \\
4 \; 4
\end{array}
\right\}} \equiv 0. \label{eq:7.18}
\end{align}
\qquad The laws of covariant differentiation (\ref{eq:7.14}) imply that
\begin{align}
\hat{\nabla}_{j}\hat{T}^{a4}_{\;\;\;\;\;b4}(\hat{\mathbf{x}}, x^{4}) =& \frac{\partial \hat{T}^{a4}_{\;\;\;\;\;b4}(\hat{\mathbf{x}}, \hat{x}^{4})}{\partial \hat{x}^{j}} +
\widehat{\left\{
\begin{array}{l}
a \\
j \; k
\end{array}
\right\}}
\hat{T}^{k4}_{\;\;\;\;\;b4} (\hat{\mathbf{x}}, \hat{x}^{4}) -
\widehat{\left\{
\begin{array}{l}
k \\
j \; b
\end{array}
\right\}}
\hat{T}^{a4}_{\;\;\;\;\;k4} (\hat{\mathbf{x}}, \hat{x}^{4}),
\nonumber \\
\hat{\nabla}_{4}\hat{T}^{a4}_{\;\;\;\;\;b4}(\hat{\mathbf{x}},
x^{4}) =& \frac{\partial
\hat{T}^{a4}_{\;\;\;\;\;b4}(\hat{\mathbf{x}},
\hat{x}^{4})}{\partial \hat{x}^{4}} = \frac{\partial
\hat{T}^{a4}_{\;\;\;\;\;b4}(\hat{\mathbf{x}}, {x}^{4})}{\partial
{x}^{4}}. \label{eq:7.19}
\end{align}
\qquad If we now replace various tensor fields
$T^{\mu\nu..}_{\;\;\;\;\; \alpha\beta ..}$,
$\frac{\partial}{\partial x^{\gamma}}T^{\mu\nu..}_{\;\;\;\;\;
\alpha\beta ..}$ occurring in the constitutive equations
(\ref{eq:7.1} - \ref{eq:7.9}) by $\hat{T}^{ab..}_{\;\;\;\;\; cd
..}$, $\hat{T}^{a4..}_{\;\;\;\;\; c4 ..}$,
$\hat{T}^{44..}_{\;\;\;\;\; 44 ..}$ and
$\hat{\nabla}_{j}\hat{T}^{ab..}_{\;\;\;\;\;cd ..}
(\hat{\mathbf{x}}, \hat{x}^{4})$, $\frac{\partial}{\partial
x^{4}} \hat{T}^{ab..}_{\;\;\;\;\;cd...}(\hat{\mathbf{x}},
\hat{x}^{4})$ etc., then we have converted all relevant equations
into spatial curvilinear coordinates.
\qquad In physical applications, usually \emph{orthonormal} or
\emph{physical} components of a tensor are necessary
\cite{ref:19}. For that purpose we introduce three orthonormal
vectors, $\vec{\lambda}_{A}(\mathbf{x})$ $A \in
\left\{1,2,3\right\}$, in space. These vectors satisfy the
orthonormality conditions:
\begin{equation}
\hat{g}_{ij}(\hat{\mathbf{x}}) \lambda^{i}_{A}(\hat{\mathbf{x}})
\lambda^{j}_{B}(\hat{\mathbf{x}}) =\delta_{AB} .\label{eq:7.20}
\end{equation}
\qquad We define the inverse entries by
\begin{align}
\left[\mu^{A}_{i}\right]:=& \left[\lambda^{i}_{A}\right]^{-1}, \nonumber \\
\lambda^{i}_{A}\mu^{A}_{j}=& \delta^{i}_{\;j}, \label{eq:7.21} \\
\mu^{A}_{i}\lambda^{j}_{A}=&\delta^{j}_{\;i} . \nonumber
\end{align}
(Here, \emph{the summation convention is also followed for capital roman indices}.)
\qquad By (\ref{eq:7.20}) and (\ref{eq:7.21}) we obtain
\begin{equation}
\hat{g}_{ij}(\hat{\mathbf{x}})=\delta_{AB} \mu^{A}_{\;i}(\hat{\mathbf{x}}) \mu^{B}_{\; j}(\hat{\mathbf{x}}) . \label{eq:7.22}
\end{equation}
\qquad The tensor transformation rules (\ref{eq:7.11}) lead to
\begin{equation}
\hat{T}^{AB..}_{\;\;\;\;\;CD..}(\hat{\mathbf{x}}, \hat{x}^{4}) =
\mu^{A}_{a}(\hat{\mathbf{x}}) \mu^{B}_{b}(\hat{\mathbf{x}})..
\lambda^{i}_{C}(\hat{\mathbf{x}})
\lambda^{j}_{D}(\hat{\mathbf{x}})..
\hat{T}^{ab..}_{\;\;\;\;\;ij..}(\hat{\mathbf{x}}, \hat{x^{4}}).
\label{eq:7.23}
\end{equation}
\qquad Instead of Christoffel symbols, we require \emph{Ricci
rotation coefficients} \cite{ref:19} for the connexion. These are
defined by:
\begin{align}
\gamma_{ABC}(\hat{\mathbf{x}}):=& \hat{g}_{jl}(\hat{\mathbf{x}}) \left(\hat{\nabla}_{k} \lambda^{l}_{A} \right) \lambda^{j}_{B}(\hat{\mathbf{x}})\lambda^{k}_{C}(\hat{\mathbf{x}}) \equiv -\gamma_{BAC}(\hat{\mathbf{x}}), \nonumber \\
\gamma^{A}_{\;\;BC}(\hat{\mathbf{x}}):=& \delta^{AJ}
\gamma_{JBC}(\hat{\mathbf{x}}) =\gamma_{ABC}(\hat{\mathbf{x}}).
\label{eq:7.24}
\end{align}
\qquad The appropriate covariant derivatives can be characterized by:
\begin{equation}
\hat{\nabla}_{J} \hat{T}^{A4}_{\;\;\;\;\;B4}(\hat{\mathbf{x}},\hat{x}^{4}):= \lambda^{i}_{J}(\mathbf{x}) \frac{\partial}{\partial \hat{x}^{i}} \hat{T}^{A4}_{\;\;\;\;\;B4}(\hat{\mathbf{x}}, \hat{x}^{4}) -\gamma^{A}_{\;\;DJ}(\hat{\mathbf{x}}) \hat{T}^{D4}_{\;\;\;\;\;B4} + \gamma^{D}_{\;\;BJ}(\hat{\mathbf{x}}) \hat{T}^{A4}_{\;\;\;\;\;D4}. \label{eq:7.25}
\end{equation}
\qquad If we now replace the tensor fields $T^{\mu\nu..}_{\;\;\;\;\;\alpha\beta}(x)$, $\frac{\partial}{\partial x^{\gamma}} T^{\mu\nu..}_{\;\;\;\;\;\alpha\beta}(x)$ appearing in the constitutive equations (\ref{eq:7.1} - \ref{eq:7.9}) by $\hat{T}^{AB..}_{\;\;\;\;\;CD..}(\hat{\mathbf{x}}, \hat{x}^{4})$, $\hat{T}^{A4..}_{\;\;\;\;\;C4..}(\hat{\mathbf{x}}, \hat{x}^{4})$, $\hat{\nabla}_{J}\hat{T}^{AB..}_{\;\;\;\;\;CD..}(\hat{\mathbf{x}}, \hat{x}^{4})$, $\frac{\partial}{\partial \hat{x}^{4}} \hat{T}^{AB..}_{\;\;\;\;\;CD..}(\hat{\mathbf{x}}, \hat{x}^{4})$ etc., then we have transformed all the required equations into the orthonormal or physical frame. Physical measurements correspond to quantities expressed in this frame.
\qquad Before concluding, we shall now explore a special example
which is most useful for continuum mechanics. This example
involves orthogonal coordinate systems in Euclidean three-space.
The equations (\ref{eq:7.17}) reduce to
\begin{equation}
\left[\hat{g}_{ij}(\hat{\mathbf{x}})\right] = \left[
\begin{array}{ccc}
\left[h_{1}(\hat{\mathbf{x}})\right]^{2} & 0 & 0 \\
0 & \left[h_{2}(\hat{\mathbf{x}})\right]^{2}& 0 \\
0 & 0 & \left[h_{3}(\hat{\mathbf{x}})\right]^{2}
\end{array}
\right], \label{eq:7.26}
\end{equation}
\begin{equation}
h_{i}(\mathbf{x}) > 0, \;\; \sqrt{\mbox{det}\left[\hat{g}_{ij}\right]} = h_{1}(\hat{\mathbf{x}})h_{2}(\hat{\mathbf{x}})h_{3}(\hat{\mathbf{x}}) >0 . \nonumber
\end{equation}
\qquad The non-zero Christoffel symbols, from (\ref{eq:7.18}) and
(\ref{eq:7.26}) are summarized by:
\begin{align}
\widehat{\left\{
\begin{array}{l}
1 \\
1 \; 1
\end{array}
\right\}}= \frac{\partial}{\partial \hat{x}^{1}} \ln h_{1}, \;\; \mbox{etc. }; \nonumber \\
\widehat{\left\{
\begin{array}{l}
1 \\
1 \; 2
\end{array}
\right\}}= \frac{\partial}{\partial \hat{x}^{2}} \ln h_{1}, \;\; \mbox{etc. }; \label{eq:7.27}\\
\widehat{\left\{
\begin{array}{l}
1 \\
2 \; 2
\end{array}
\right\}}= - h_{2} \left[h_{1}\right]^{-2}
\frac{\partial}{\partial \hat{x}^{1}} \ln h_{2}, \;\; \mbox{etc.}
\nonumber
\end{align}
\qquad The orthonormal (or physical) vector components from (\ref{eq:7.20}) and (\ref{eq:7.26}) are given by
\begin{equation}
\lambda^{i}_{\;A}(\hat{\mathbf{x}}) =\left[h_{i}(\hat{\mathbf{x}})\right]^{-1} \delta^{i}_{\;A}, \;\; \mu^{A}_{\;i}(\hat{\mathbf{x}}) =h_{i}(\hat{\mathbf{x}}) \delta^{A}_{\;i} \; ,\label{eq:7.28}
\end{equation}
and the non-zero Ricci rotation coefficients from (\ref{eq:7.24}), (\ref{eq:7.27}) and (\ref{eq:7.28}) are furnished by:
\begin{align}
\gamma_{ABC}:=&\delta_{AE}\gamma^{E}_{\;BC},\;\;\;\gamma_{(A)(B)(C)}:=\gamma_{ABC} \equiv \gamma_{BAC}, \nonumber \\
\gamma_{(2)(1)(2)}=& -\frac{\partial}{\partial \hat{x}^{1}} \ln h_{2}, \;\; \gamma_{(3)(1)(3)}= -\frac{\partial}{\partial \hat{x}^{1}} \ln h_{3}\; , \nonumber \\
\gamma_{(1)(2)(1)}=& -\frac{\partial}{\partial \hat{x}^{2}} \ln h_{1}, \;\; \gamma_{(3)(2)(3)}= -\frac{\partial}{\partial \hat{x}^{2}} \ln h_{3} \;, \label{eq:7.29} \\
\gamma_{(1)(3)(1)}=& -\frac{\partial}{\partial \hat{x}^{3}} \ln h_{1}, \;\; \gamma_{(2)(3)(2)}= -\frac{\partial}{\partial \hat{x}^{3}} \ln h_{2}. \nonumber
\end{align}
\qquad Also, the gradient of a scalar field is given by
\begin{align}
\hat{\nabla}_{i} \hat{\phi}(\hat{\mathbf{x}})=& \frac{\partial}{\partial \hat{x}^{i}} \hat{\phi}(\hat{\mathbf{x}}), \; \hat{\nabla}_{A} \hat{\phi}(\hat{\mathbf{x}}) = \lambda^{i}_{\; A} \frac{\partial}{\partial \hat{x}^{i}} \hat{\phi}(\hat{\mathbf{x}}) = \left(h_{A}\right)^{-1} \frac{\partial}{\partial \hat{x}^{A}} \hat{\phi}(\hat{\mathbf{x}}), \nonumber \\
\hat{\nabla}_{(1)}\hat{\phi}(\hat{\mathbf{x}})=& (h_{1})^{-1} \frac{\partial}{\partial \hat{x}^{1}} \hat{\phi}(\hat{\mathbf{x}}) \not\equiv \hat{\nabla}_{1} \hat{\phi}(\hat{\mathbf{x}}). \label{eq:7.30}
\end{align}
In (\ref{eq:7.30}) there is no summation over $A$.
\qquad The divergence of a vector field is furnished by
\begin{equation}
\hat{\nabla}_{i} \hat{T}^{i}(\hat{\mathbf{x}}) \equiv
\hat{\nabla}_{A} \hat{T}^{A}(\hat{\mathbf{x}})
=\left(h_{1}h_{2}h_{3}\right)^{-1} \left\{
\frac{\partial}{\partial \hat{x}^{i}}
\left[\left(h_{1}h_{2}h_{3}\right) \hat{T}^{i}(\hat{\mathbf{x}})
\right]\right\}. \label{eq:7.31}
\end{equation}
The curl is given by:
\begin{align}
\left[\hat{\nabla}\times\hat{\mathbf{A}}\right]^{i}:=& \frac{1}{2}
\frac{\epsilon^{ijk}}{\sqrt{\mbox{det}[\hat{g}_{ab}]}} \left[
\hat{\nabla}_{j}\hat{A}_{k} - \hat{\nabla}_{k} \hat{A}_{j}
\right] =
\frac{1}{2(h_{1}h_{2}h_{3})} \epsilon^{ijk} \left[\frac{\partial \hat{A}_{k}(\hat{\mathbf{x}})}{\partial \hat{\mathbf{x}}^{j}} - \frac{\partial \hat{A}_{j}(\hat{\mathbf{x}})}{\partial \hat{\mathbf{x}}^{k}}\right], \nonumber \\
\left[\hat{\nabla}\times\hat{\mathbf{A}}\right]^{B}:=& \frac{1}{2} \epsilon^{BCD} \left[\lambda^{i}_{\; C} \frac{\partial}{\partial \hat{x}^{i}} \left(\hat{A}_{D}(\hat{\mathbf{x}})\right) - \lambda^{i}_{\; D}\frac{\partial}{\partial \hat{x}^{i}} \left(\hat{A}_{C}(\hat{\mathbf{x}})\right)\right] \nonumber \\
=&\frac{1}{2} \epsilon^{BCD} \left[(h_{C})^{-1} \frac{\partial}{\partial \hat{x}^{C}} \left(\hat{A}_{D}(\hat{\mathbf{x}})\right) - (h_{D})^{-1}\frac{\partial}{\partial \hat{x}^{D}} \left(\hat{A}_{C}(\hat{\mathbf{x}})\right)\right], \label{eq:7.32} \\
\left[\hat{\nabla}\times\hat{\mathbf{A}}\right]^{1} \not\equiv&
\left[\hat{\nabla}\times\hat{\mathbf{A}}\right]^{(1)}. \nonumber
\end{align}
\qquad Finally, the Laplacian operator is furnished by
\begin{align}
&\nabla^{2}\hat{W}(\hat{\mathbf{x}}):= \hat{g}^{ij} \hat{\nabla}_{i} \hat{\nabla}_{j}\hat{W}(\hat{\mathbf{x}})\equiv \delta^{AB} \hat{\nabla}_{A} \hat{\nabla}_{B}\hat{W}(\hat{\mathbf{x}}) \label{eq:7.33} \\
&= \frac{1}{\left(h_{1}h_{2}h_{3}\right)} \left[ \frac{\partial}{\partial \hat{x}^{1}} \left( \frac{h_{1}h_{3}}{h_{1}} \frac{\partial \hat{W}(\hat{\mathbf{x}})}{\partial \hat{x}^{1}} \right) + \frac{\partial}{\partial \hat{x}^{2}} \left( \frac{h_{3}h_{1}}{h_{2}} \frac{\partial \hat{W}(\hat{\mathbf{x}})}{\partial \hat{x}^{2}} \right) + \frac{\partial}{\partial \hat{x}^{3}} \left( \frac{h_{1}h_{2}}{h_{3}} \frac{\partial \hat{W}(\hat{\mathbf{x}})}{\partial \hat{x}^{3}} \right) \right]. \nonumber
\end{align}
\newpage
\linespread{0.6}
\bibliographystyle{unsrt}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,866
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Q: Selecting a whole database over an individual table to output to file Ok Im having trouble finding out how to select a full database for backup as an *.sql file rather than only an individual table.
On the localhost I have several databases with one named "foo" and it is that which I want to backup and not any of the individual tables inside the database "foo".
The code to connect to the database;
//Database Information
$dbhost = "localhost";
$dbname = "foo";
$dbuser = "bar";
$dbpass = "rulz";
//Connect to database
mysql_connect ($dbhost, $dbuser, $dbpass)
or die("Could not connect: ".mysql_error());
mysql_select_db($dbname) or die(mysql_error());
The code to backup the database, one question I have with this is where do I set were the *.gz file is saved?
$backupFile = $dbname . date("Y-m-d-H-i-s") . '.gz';
$command = "mysqldump --opt -h $dbhost -u $dbuser -p $dbpass $dbname | gzip
> $backupFile";
system($command);
My brain is hurting near to the end of the day so no doubts i've missed something out very obvious.
Thanks in advance to anyone helping me out.
A: You've missed mysqldump! Its a command line utility designed specifically for what you are trying to do.
Writing a backup file manually is rather hard. Writing one that you will consistently be able to recover from is very hard. Check out the docs, it has a lot of options that you can use to specify what exactly you want to save.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
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# **Contents**
Dedication
Praise
Definitions
Preface to the Second Edition
Prologue
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Epilogue
Next
Preview Book 2
Author's Note
Acknowledgements
About the Author
Avogadro Corp: The Singularity Is Closer Than It Appears
William Hertling
Copyright 2011, 2014 by William Hertling
Smashwords Edition
For Rowan, Luc, and Gifford.
"A tremendous book that every single person needs to read. In the vein of Daniel Suarez's _Daemon_ and _Freedom_ _TM_ , William's book shows that science fiction is becoming science fact. _Avogadro Corp_ describes issues, in solid technical detail, that we are dealing with today that will impact us by 2015, if not sooner. Not enough people have read these books. It's a problem for them, but not for the [emergent] machines."
— _Brad Feld, managing director Foundry Group, _
_cofounder Techstars_
"A highly entertaining, gripping, thought inspiring book. Don't start without the time to finish—it won't let you go."
— _Gifford Pinchot III, founder Bainbridge Graduate Institute, _
_Author of_ The Intelligent Organization
"An alarming and jaw-dropping tale about how something as innocuous as email can subvert an entire organization. I found myself reading with a sense of awe, and read it way too late into the night."
_—Gene Kim, author of_ The Phoenix Project
"Hertling builds a picture of how an AI could emerge, piece by piece, from technology available today. A fascinating, logical, and utterly believable scenario—I just hope nobody tries this at home."
— _Nathaniel Rutman, Senior Systems Architect_
**Avogadro**
1. **Avogadro's Number** : The Avogadro constant (symbols: L, NA) is the number of "elementary entities" (usually atoms or molecules) in one mole, that is (from the definition of the mole), the number of atoms in exactly 12 grams of carbon-12: 6.022 x 1023.
2. **Avogadro Corporation** : Avogadro Corporation is an American corporation specializing in Internet search. It generates revenue from paid advertising on search, email (AvoMail), online mapping, office productivity, etc. In addition, the company develops a mobile phone operating system called AvoOS. The company name is based on Avogadro's Number, or 6 followed by 23 zeros: 600,000,000,000,000,000,000,000.
**elope**
1. v. **To run away** ; abscond. From Middle Dutch _ontlopen_ , to run away.
2. n. **ELOPe: Email Language Optimization Project**. An Avogadro Corporation R&D project to improve email communication effectiveness.
**Preface to the Second Edition**
I conceived and wrote _Avogadro Corp.: The Singularity Is Closer Than It Appears_ in 2009.
Since then, IBM's Watson competed on _Jeopardy_. Google announced they could compose automatic Twitter replies, in your authentic voice and to the tweets you'd normally respond to. Google also built floating barges covered with shipping containers.
Last year, Google hired Ray Kurzweil, one of the most outspoken proponents of artificial intelligence. Google also bought Boston Dynamics, one of the leaders in mobile robotics, as well as many leading artificial intelligence companies. Many believe Google wants to win the race to develop strong AI.
I've enjoyed seeing so many predictions come true, but it's also a little scary.
This second edition has been revised to improve language and add character depth. The structure of the story, plot, and technology has not been changed. I hope you enjoy the result.
_William Hertling_
_May 2014_
**Prologue**
David Ryan stood on tiptoes and craned his head over the crowd. He smiled at the sight of his wife's blonde hair, only ten feet away. Turning sideways, he pushed into a gap between a sequined dress and a suit. An arm jostled him, and champagne sloshed towards the rim of the three glasses he balanced in both hands. Shuffling through the dense crowd, he finally rejoined Christine, who stood chatting with Mike Williams, his lead developer and good friend. He handed them their drinks with relief.
A banner year at the world's largest Internet company meant another no-holds-barred Christmas party, continuing a longstanding tradition. Avogadro Corp had again rented the Portland Convention Center, the only venue large enough to hold their ten thousand Portland employees. A jazz band played on stage, part of this year's Roaring Twenties theme, while usually reserved geeks danced and became inebriated on free alcohol. Glasses chimed in toasts, lights flashed, and laughter sounded from everywhere.
David glanced at Christine, stunning and exotic in a black sequined flapper dress. He smiled, happy to be celebrating, and with good cause, too: his project was successful, he was married to a smart, funny woman, and he had a great friend and technical lead in Mike. He had every reason to be happy.
David took a self-congratulatory sip of champagne and Mike nudged his arm, sending the drink over the rim. "Here comes Sean," Mike said, eyebrows raised.
A bit of awe and hero-worship made for a moment's hesitation. Sean Leonov, cofounder of Avogadro, was something of a demigod. A brilliant scientist who not only designed the original Avogadro search algorithms and cofounded the company with Kenneth Harrison, he also continued to write research papers while helping lead the company.
"Well, David, Mike, Christine—Merry Christmas!" Sean said, demonstrating the amazing memory that was one of his many talents. He clasped David's shoulder and shook hands with Christine and Mike. He turned to David and smiled. "It's been a while since we talked, but I heard through the grapevine about your progress. When do we get a demo?"
"Any time you want, we're ready. The results are more promising than anyone expected."
"I'm glad. Send me an email, and I'll have my admin set up a meeting. Now, I hear Ops is complaining about the servers you need."
David groaned inside. Ops, short for Operations, was the Avogadro department responsible for maintaining and allocating the all-important servers. More than a million computers spread across nearly a hundred data centers around the world hosted all of Avogadro's websites and applications. Ops was also David's Achilles' heel right now.
David loosened his jaw and struggled to keep his voice calm. "We're consuming somewhat more resources than projected. But we _are_ functionally complete, and user testing shows ELOPe's effectiveness is higher than expected. Resource utilization is our last major hurdle. When you see the results, I think you'll agree the resources are worth the investment."
"It's not the money I'm worried about," Sean said, "but the scale. I've already pulled strings to get the project onto the production servers for more horsepower. But before you release, you've got to fix these scalability issues. Hundreds of millions of eager customers will hit the application on day one."
David winced. Sean's tone made it clear he expected David to solve the problem.
Sean turned to Christine. "So how's the gaming business?"
She smiled. "Good. We're building on a new RPG with a free-form magic system. User-designed spells. It's gonna kick butt."
"How do you balance power so the spells don't get out of hand?" Sean asked.
"That's the cool part," Christine said. She went on about the self-balancing system she'd invented that correlated magical impact with spell cost.
David tuned out of the conversation and fumed inwardly at Sean's comments about Ops. His project was going to change the face of email—hell, _all_ communications—forever. Server resources should be inconsequential by comparison.
Sean chatted with Christine for a minute about her work and then said quick goodbyes as he noticed someone he wanted to talk to.
After Sean left, David turned to Mike. "Damn Gary and his whining. He's going to sabotage the project before we even get a chance to prove success. Why can't he just leave us in peace?"
Christine put a hand on his arm. "With a presentation to Sean, you'll have more management support. Gary is not going to kill your project or he'd have done it already. "
"But—" David began.
"But nothing. You're a few months from release, and then the server resources are someone else's problem." She smiled and raised one eyebrow playfully.
David returned the smile without much conviction. She was right on a theoretical level, but it didn't change his anger at Gary Mitchell, the Vice President of Communication Products.
Six months earlier, when David realized ELOPe needed far more computing resources than the typical R&D projects, he'd gone to Sean, who quickly gave David's team access to the production servers in the Communication Products group. They had massive spare capacity, and it was an easy choice.
Gary Mitchell had resented Sean's decision, arguing an R&D project could compromise the stability of production servers. He remained vocal in his opposition over the last half-year, and since he couldn't take out his frustration on Sean, he took it out on David and his team. Eager for any excuse to get ELOPe booted from what he regarded as his own backyard, Gary scrutinized their every action.
"Hey, you can hardly blame him," Mike said. "We're using five hundred times more processing power than we predicted, which has got to be a record for any research project. We're like a black hole for computational resources."
David ignored his lighthearted tone. Amid the glitter and glamour of the party, and despite their efforts to cheer him up, a burning resentment rose in David's stomach. The project was an ideal match for his technical skills, in an area he was deeply passionate about, and also strategically important to the company. It was the kind of perfect storm that came along once or twice in a career, if you were lucky. Damn it, he just wanted the thing to succeed.
He swallowed his champagne in a gulp. "I've given ELOPe everything and we're so close. I'm not going to let this opportunity get away from me."
**Chapter 1**
David arrived at the executive conference room ten minutes early, his throat dry and butterflies in his stomach. He struggled to keep his mind focused on preparing for the presentation, pushing aside his nervousness. Project managers rarely, if ever, presented to the entire Avogadro Corp executive team.
He was the first to arrive, which meant he could set up without pressure. Syncing his phone with the room's display took only a few seconds. There was no overhead projector here, just a flush-mounted panel in the wall behind him. He ran his hand over the polished hardwood desk and leather chairs. It was more than a small step up from the plastic and fabric in the normal conference rooms.
David took some comfort in the ritual of getting coffee. He poured two raw sugars into a steaming mug and smiled at the lavishly-stocked buffet containing everything from tea and juice to breakfast pastries and lunch foods. Avogadro was an egalitarian, geek-culture company, but top executives had their perks.
Still no one had arrived, so he wandered around the room admiring the view. The dominant feature was the Fremont Bridge over the Willamette River. In the foreground, loft buildings dotted the Pearl District and, to the right, taller structures marked Portland's downtown. Directly to the east, close to where the upper slopes of Mount Hood lost themselves in dense cloud, the early morning sun broke through a rent in the overcast, sending shafts of light to paint the city orange and rose. He was just wondering if he could see his own house in northeast Portland when he heard a welcoming "Hello David."
Sean Leonov entered alongside a tall, dark-haired man, whom David at once recognized from photos and articles: Kenneth Harrison, Avogadro's other cofounder, respected throughout the company. Sean shook David's hand and introduced them.
Other senior vice presidents started to file in, and Sean briefly introduced each in turn. David shook hands or gave nods as appropriate, his head swimming with names and roles.
For a few minutes, a cocktail party atmosphere reigned as people grabbed food and coffee and socialized. They gradually took seats, arranging themselves in something resembling a pecking order around Sean and Kenneth. One seat at the head of the table was conspicuously empty.
When the bustle of arriving attendees died down, Sean stood. "I've already introduced you to David Ryan, the lead for the ELOPe project. I hired David two years ago to prove the feasibility of a radical new feature for AvoMail. He's done an incredible job, and I invited him here to give you a look at what he's developed. Prepare to be amazed."
"Thank you, Sean," David said, walking to the front of the room. "Thanks, everyone, for coming."
He thumbed his phone to project his first slide, a black and white of a secretary leaning over a typewriter. "One of the early corrective technologies was Liquid Paper," he said, to chuckles from the audience. "Highly innovative in its own time, it allowed typists to reduce the rework associated with correcting an error. But correction fluid was nothing compared to the spellchecker, a tool that both detected and corrected errors automatically." In the background, the slide changed to a photo of a man using a first-generation personal computer.
"Years later, as processing power increased, grammar checkers were invented. First generation software detected only trivial mistakes, but later versions evolved to both detect and fix a wide range of problems including purely context-dependent issues. These corrective technologies started out in word processors and gradually worked their way throughout the whole suite of communication tools from presentation editors to email." He paused, enjoying the storytelling.
David focused his attention on one executive at a time, making eye contact with them before he moved to the next. "Today, the standards of business communication have changed. It's not enough to have a grammatically checked, correctly spelled email to be an effective communicator. You must intimately know what your recipients care about and how they think in order to be persuasive, using the right mix of compelling logic, data, and emotion to build your case."
Pleased to see he had everyone's rapt attention, he went on. "Sean hired me two years ago to test an unproven concept: an email language optimization tool to help users craft more compelling, effective communications. I'm here today to show you the results of our work."
He flipped slides again, popping up a timeline.
"In the first twelve months, through data mining, language analysis, and recommendation algorithms, we proved the feasibility of the core building blocks. Then we set about in earnest to integrate those pieces in the Email Language Optimization Project, or ELOPe."
David clicked again, and now the wall display showed a screenshot of AvoMail, the popular Avogadro web-based email. "From an experience perspective, ELOPe works like a sophisticated grammar checker. As the user edits an email, we make suggestions about the wording in the sidebar.
"Behind the scenes, complex analysis is taking place to understand user intent and map their goal to effective language patterns we've observed in other users. Let me give you a very simple example you might be familiar with. Have you ever received an email from someone in which they asked you to look at an attachment, but they forgot to attach the file? Or perhaps you were the sender?"
He heard wry chuckles and a few hands went up in the audience.
"An embarrassing mistake that no longer occurs because AvoMail looks for occurrences of the words 'attachment' or 'attached,' and checks if a file is present before sending the email. Through language analysis, we've improved the effectiveness of the user's communications."
A woman vice president raised her hand. David struggled and failed to recall her name, and settled for pointing to her.
"That's a simple example of looking for keywords," she said. "Are you talking about a stock set of phrases?"
"No, we don't rely on keywords at all," David said. "I'll explain the process, but I'd like to use a more complicated example. Imagine a manager asking for additional project funding. The decision maker will want a justification for the request. What's the benefit to the company of the investment? Maybe a quicker time to market, or a higher return. Perhaps the project ran short of funds and is in danger of being unable to complete."
David relaxed a little at the sight of nodding heads as the carefully chosen example resonated with his audience of executives. "ELOPe can analyze the email, determine the sender is asking for funding, know the request should be accompanied by a justification, and provide effective examples."
David flipped to an auto-play slide. The short video kicked into motion, demonstrating a manager writing an email asking for an expanded budget, as suggested justifications popped up on the right-hand side. Each example already incorporated details gleaned from the original message, like the project name and timeline. David waited while the minute-long video played, noting the soft exclamations of amazement coming from the group. He smiled to himself. As Arthur C. Clarke said, "Any sufficiently advanced technology is indistinguishable from magic." Well, this was magic.
David paused to let the video sink in before resuming. "We provide fully customized recommendations, because each person is motivated by specific kinds of language, styles of communication, and reasons. Let's use another example. An employee is going to ask for an extended vacation; he'd like to make a compelling case for granting his request. What will motivate his manager? Should he mention he's been working overtime, or that he needs to spend time with his kids? What if he's planning to visit the Grand Canyon, a place his manager associates with good memories?
"The answer," David went on, as he paced back and forth in the front of the room, "depends on the person you're emailing. So ELOPe customizes its analysis not only to what the sender is asking for, but for what the recipient is motivated by."
David noticed Rebecca Smith standing in the doorway listening to the presentation. In a sharp tailored suit, her reputation hovering about her like an invisible aura, the Avogadro CEO made for an imposing presence. Only her warm smile left a welcoming space in which an ordinary guy like David could stand.
She nodded to him as she came in and took her seat at the head of the table.
"What you're describing," Kenneth asked, "how does it work? The natural language processing ability of computers doesn't even come close to being able to understand semantics. Have you had a miracle breakthrough?"
"At the heart of how this works is the field of recommendation algorithms," David said. "Sean hired me, not because I knew anything about language analysis, but because I was a leading competitor in the Netflix Prize. Netflix recommends movies you'd liked to watch. The better they can do this, the more you as a customer enjoy using their service. Several years ago, Netflix offered a million-dollar award to anyone who could beat their own algorithm by ten percent.
"What's amazing and even counterintuitive about recommendation algorithms is that they don't depend on understanding anything about the movie. Netflix does not, for example, have a staff of people watching movies to categorize and rate them to find the latest sci-fi space action thriller I may like. Instead they rely on a technique called collaborative filtering, where they find other customers like me and analyze how _those_ customers rated a given movie, to predict how I'll rate it. Sean's insight was that since natural language analysis struggles to understand semantics, it would be best to start with an approach that doesn't rely on understanding, but instead one which utilizes patterns."
When David received nods from the audience, he went on. "ELOPe parses billions of emails, comparing the language used and how the recipient reacted. Was the response positive or negative? Compiled over thousands of messages per person, and millions of people, we can find a cluster of users similar to the intended recipient of an email and analyze how they respond to variations of language and ideas to find the best way to present information and make compelling arguments."
Now there were puzzled looks and half-raised hands as people around the room tried to ask questions. David forestalled them with one hand. "Hold on for a second. Let me give you a simple example. Let's imagine a person named Abe who, whenever he receives messages mentioning kids, responds negatively." David spread his arms, getting into the story. "ELOPe has to predict how Abe will react to a new email. If the message mentions kids, which Abe historically has a negative reaction to, then it's a good bet the new email will be received unfavorably. If Abe was your boss, and you were going to ask him for vacation time, spending time with your kids isn't a good justification."
He heard a few laughs.
"So there's no semantic analysis?" Rebecca asked. "We don't know why he dislikes kids?"
"Correct. We have no idea why Abe feels the way he does," David said. "We just observe the pattern of behavior."
"What if my manager hadn't received any emails about kids?" Sean asked. "How could we predict how he would respond?"
David grinned. Sean knew the answer and was just helping him along. "Let's say we have another user, Bob, who hasn't received any messages about children. However, ELOPe groups together Bob, Abe, and about a hundred other individuals based on their almost identical responses to most topics, such as the activities they do on the weekend, the vacations they take, how they choose to spend their time. Let's say this group of people are ninety-five percent similar. That is, across all the topics they've responded to, they are ninety-five percent likely to have the same sentiment in their response: negative or positive. This is what we call a user cluster."
Heads nodded. David went on.
"If other members of the cluster received emails about kids, and they responded negatively, then ELOPe will be ninety-five percent certain Bob will behave the same way. Of course, situations are rarely so cut and dry, and it is a _statistical_ prediction, which means that five percent of the time ELOPe will be wrong—but most of the time the analysis will be right. So if your boss was Bob, you still shouldn't mention kids when you ask for vacation.
"Joking aside, ELOPe is working, and we've tested the software with users. On average, favorable sentiment in reply emails increases twenty-three percent with ELOPe turned on compared to the baseline. That's twenty-three percent more vacations granted, twenty-three percent more people agreeing to go on dates, twenty-three percent more people getting their work requests granted."
Rebecca stared at him. "Wait a second. Going on dates? So you've got someone out with another person, someone they wouldn't have otherwise been with. That seems manipulative, even risky."
David's stomach threatened to leap into his throat as his internal danger meter flared into the red. He noticed Kenneth, startled by Rebecca's objection, leaning over to speak quietly to Sean.
The dating example was so damn controversial. The next few minutes would make or break his project. If Kenneth and Rebecca decided against him, he'd lose Sean's support and ELOPe would never be released.
"Hold on. Maybe I chose a bad example." David held up both hands. "Who's taken a Myers-Briggs personality workshop?"
As expected, everyone raised a hand or nodded in assent. Myers-Briggs or something similar was standard fare for every manager in big companies. "Now, what was the purpose of the workshop? It's not just to find out whether you're an introvert or extrovert, right?"
"To work effectively with others," Sean said.
"Working effectively means what?" David paused. "Learning how others communicate and think, like who is likely to appreciate a data-driven argument versus an emotional argument, or who likes to think out loud versus having time to respond to written arguments."
He scanned his audience, forcing himself to stay upbeat and chipper even though he feared group opinion could go against the project at this point. "Is that manipulative? Do we take a Myers-Briggs workshop to manipulate people, or do we do it to be able to work more effectively with them and spend less time in arguments and disagreements?"
A few of the VPs turned to Rebecca, waiting for the CEO to respond. She hesitated, then nodded. "It's helpful. I can see that. I've been through more than my fair share of those workshops."
"And if two individuals took Myers-Briggs together, they'd get to know each other better. Perhaps those people would not only work together better, but as a side effect they might be more likely to have an enjoyable date. What we're doing with ELOPe is giving everyone the same benefits they would get from an expensive workshop. We're empowering human beings to become better communicators and collaborators, something everyone wants."
The tension in the group dropped noticeably, and the audience was once more dominated by nodding heads.
"Remember, we're measuring sentiment in these messages," he went on, pacing back and forth in front of the display again. "It's not a grudging assent: people are having and maintaining more effective and cooperative ongoing communication when our tool is enabled. Once, spellchecking was the big innovation that leveled the playing field between people of good or bad spelling ability. Now we're leveling the playing field for writing—enabling people of all abilities to create powerful, well crafted communications."
There was quiet for a minute, then one of the executives asked, "What's the timetable for releasing this?"
Discussion went on for another fifteen minutes, but the topics were all implementation details and business return on investment questions.
At the end of David's presentation, Sean walked him to the doorway while the executives helped themselves to another round of coffee and food. "Good job," he said privately to David, as he ushered him out. "I'm confident they'll vote to go live when you're ready."
As the door closed behind him, David leaned against the wall outside the conference room. The experience had been draining. Then he chuckled. The dating example had been contentious, but it was better to raise the issue and address it early than leave the topic lingering. He was sure the presentation had won them over. The language analysis on his slides that he ran last night in ELOPe predicted a ninety-three percent favorable response.
"Gary, it doesn't make sense to optimize until after we're done."
While David handled the all-important presentation with the bigwigs, Mike patiently defended their resource utilization with Gary Mitchell. Mike wondered, not for the first time, if David had arranged the meeting with Gary to conflict with the executive meeting so Gary wouldn't attend the briefing.
Mike sighed. Give him a team of developers to motivate, a thorny bug to fix, or a new architecture to design, and he'd be happy. But he hated organizational politics. David owed him one for this.
"Of course," he went on, "we'll only use a fraction of the number of servers after we optimize. We'll work on efficiency improvements when the algorithm is done. Optimizing now would hurt our ability to improve the effectiveness. This is basic computer science."
"Mike. Mike."
Mike rolled his eyes at Gary's condescending tone, a safe maneuver since Gary appeared to be studying the ceiling. Gary leaned back in his chair, arms behind his head, white dress shirt stretched over his belly, jowls hanging down under his chin. Mike wondered how Gary had ended up at Avogadro. He needed only a cigar and ashtray to be at home as a 1950s General Motors vice president.
"I know your project got special approval from Sean to use production," Gary said. "Those servers are responsible for running Avogadro's day-to-day operations." He straightened and stared at Mike, jabbing a fat finger in his direction. "You're eating up so much memory and bandwidth on AvoMail that I've had to twice bring in additional capacity. You know what happens if AvoMail goes down? Millions of customers abandon us, and I get chewed out by Rebecca Smith." He stood and walked over to the operation dashboard updating in real-time on the wall display. "Hell, I can measure the loss if we slow down by even half a second. You spike CPU usage, we lose revenue."
"Gary, we—"
Gary tapped the dashboard and ran right over him. "Like every other R&D team, you think your project is manna from Heaven. Meanwhile, I gotta keep things running here, and ELOPe is making us run critically short of capacity. Approval from Sean or not, I'm in charge of Communication Products, and I have ultimate responsibility for ensuring absolutely zero downtime. You've got two weeks to get your server utilization down, or I'm cutting off your access to my production servers. And if you have another spike, I'll shut you down instantly."
"Listen Gary, we can--" Mike started.
"I don't want to hear excuses!" Gary shouted. "We're done. I've had this discussion with David repeatedly. Two weeks. You go tell David. Goodbye." Gary shooed him out of the office with his hand like an errant cat.
Mike stood, then stormed out, blowing past Gary's startled admin. Resisting the urge to slam doors, he stalked down five floors, fuming with unspent anger. He crossed the street and went down a block, then up again into his own building.
He slowly relaxed during the walk, one benefit of the sprawling campus. Avogadro Corp had expanded so much they now spanned seven city blocks in the northwest part of Portland, on the site of an old trucking company.
As the company and their profits grew over the last fifteen years, they put up one new structure after another, so fast the employees couldn't keep track of who or what was where. Mike had seen three new buildings go up in the few years since he started.
There was an ongoing curiosity among the employees to discover what the different buildings contained. Most of the campus was quite normal, but there were some oddball aspects, like the telescope observatory opened by randomly chosen employee access cards, and the billiard room that changed floors and buildings. Mike had seen that one himself. Whether the trick was managed by moving an actual room, Facilities staff carting off the contents, or duplication, no one knew. Of course the engineers at Avogadro couldn't resist a puzzle, so they'd tried everything from hiding Wi-Fi nodes to RF encoding the furniture, with ever more puzzling results.
There was a half-serious belief among some employees that one of the executive team had a Winchester-house complex. Mike had visited the San Jose fixture once, during his college days. Built by Sarah Winchester, widow of the firearms magnate, William Winchester, she had the house under constant construction from 1884 to 1922, believing she would die if the work ever stopped. The idea that a similar belief plagued one of the Avogadro executives, driving them to do the same to the company campus, brought a smile to Mike's face. On the whole, however, he figured the curiosities were a game to entertain engineers. It takes something extra to retain brilliant but easily bored geeks.
The smile disappeared as Mike crossed the second floor bridge back to R&D and thought of David. He'd blow a gasket at the news of Gary's ultimatum.
Their recommendation algorithm, which sounded so simple when David explained the idea to a nontechnical person, depended on crunching vast quantities of data. Every email thread had to be analyzed and correlated with millions of other emails. Unlike movie recommendation algorithms, which were clustered using less than a hundred characteristics, it was orders of magnitude more complex to do the analysis on emails. They needed a thousand times more computation time, memory, and all-important database access. Coming out of the meeting, Mike had no doubt Gary had reached the limit as far as available resources were concerned.
Unfortunately, Mike had been less than honest. He shrugged, uncomfortable with himself. When had it become necessary to lie in his job?
The reality was that he, David, and other members of the team had been working for months to optimize ELOPe. Sadly, the current server-consuming behemoth was the best they could do. There weren't going to be any more efficiency gains, and therefore no way to meet Gary's ultimatum.
Mike sighed. David would be seriously upset.
A busy morning kept Mike hopping from one urgent issue to the next, despite his desperate need to talk to David. Hours later, with the most critical problems resolved, Mike ran into David's office before anything else could interrupt him.
"Got a minute?" he asked in a cautious tone, poking his head around the door.
"Of course."
Like all the engineers' offices, David's had room for three or four guests, as long as everyone was friendly and used deodorant. A big whiteboard spanned one wall, and north-facing windows held a view of heavily-wooded Forest Park. Mike was sure the six-month-old setup was less effective for working together than last year's layout when the team was in one big open space, but he enjoyed the change. Besides, the office would be different again next year.
Mike recounted the meeting with Gary Mitchell. David's face grew grim before he even finished. "Then he kicked me out. What could I say even if I had the chance? There _aren't_ any more efficiency gains."
David sat at his desk, fingers steepled, staring into his darkened monitor. It was a bad sign when he stayed in statue-mode for over a minute. Tux the Penguin, the Linux mascot, which Christine had bought David after one of their first dates, wobbled over David's display in the ventilation system breeze. "So two weeks is our deadline. What do you want to do?" Mike prompted, after he'd endured as much of the painful silence as he could stand.
"Pare down the number of developers we have working on fixes and algorithm improvements," David said, having apparently reached some conclusion. "How many people can you dedicate to optimization?"
"I'll focus full-time," Mike said, starting to count off on his fingers. "Certainly Melanie," he added, referring to one of their best software engineers. "Figure two or three other folks. Probably five in all. But, David..." He looked him square in the eyes. "We're not going to make any improvements. We've tried everything."
"All right, starting with the five of you, get focused on performance full-time," David said, ignoring Mike's protest. "After we hit our next release milestone on Thursday, we'll see where we stand."
Mike sighed and left the office.
**Chapter 2**
"How's the project going?" David asked, popping into Mike's office on Thursday morning. He perched on the windowsill, glancing outside at Mike's view of the football-field-sized granite calendar that mapped the history of the universe into a single calendar year. A bunch of new hires were getting their orientation on the month of December. Damn, but Mike had the best view from the floor. He turned back to Mike, hoping he'd have some good news.
"Excellent," Mike said, finally pulling his eyes from the screen. "Everyone finished their tasks for the iteration, code is checked in, and integration tests are running. We'll know in a few minutes if everything passed."
"No, on the performance front," David said, his voice sharp even to his own ears.
Mike raised his eyebrows and glanced at the door.
David sighed and threw a crumpled-up sticky note toward the garbage can. Mike didn't like it when he yelled and had given him the "appropriate work environment" lecture numerous times.
"If we don't have a performance gain, we've got bigger issues than the checkpoint."
"I'm not expecting anything, I'm afraid," Mike said, glancing down to where David had missed the basket. "Dude."
"You had people on optimization, right?"
Mike picked up the paper. "Yeah. We poured through profilers, analyzed every bit of network traffic and database queries. We tried dozens of options, focusing on our bottlenecks. Melanie even rewrote our in-memory representation from scratch. Everything we did either had no effect or made the performance worse. We backed out most of the changes and kept a few of the minor tweaks. The net gain is less than one percent. I'm sorry. We've been banging our heads against this for months. I know you want a miracle, but it's not going to happen."
"Damn." David scanned Mike's full-wall whiteboard. One end had a **** checklist of features, fixes, and enhancements planned for the current release. Interspersed around the rest of the wall were box diagrams of the architecture, bits of code, and random ideas. David stared intensely, as though the solution to their performance problems might be found somewhere on the board.
"It's not there, I looked," Mike said.
David grunted, admitting that Mike guessed his thoughts. Mike had been smiling when David came in, and now he appeared as glum as his boss. David's disappointment was contagious.
"I hope you're not thinking of canceling the snowboarding day," Mike said. "We've had one for every other release. And there's fresh snow."
David glanced out the window. December drizzle. That meant powder on the mountain. Damn. This project was too important to give everyone a day to play. "We've got to --" He turned back and trailed off mid-sentence at the expression on Mike's face.
"The team is expecting the trip," Mike said. "Some of the guys were here until two in the morning getting their work done. They deserve their day off, and they'll return refreshed and ready to tackle the performance issues. You can't ask people to give their all and not give them something back."
David's mouth opened and closed like a fish, as he bit back what he was going to say. His stomach clenched in frustration and he turned to stare out the window. "Do you have any sense of the pressure I'm under?"
Mike nodded.
"I guess one day won't make that much of a difference with something we've been struggling with for six months," David said. "But when we get back, I want one hundred and ten percent focus on performance. Take everything else off the backlog."
David leaned over and slapped the button on the alarm clock. He rolled onto his other side and looked at Christine, who was still sleeping. He kissed her on the cheek, watched her breathe for a minute, and slid out of bed. Dressing quickly in the dark, he slipped downstairs where his duffel bag and snowboard were waiting by the door.
A few minutes later, Mike pulled up quietly in his Jetta, exhaust vapors puffing out of the tailpipe in the cold morning air. David brought his equipment out. Wordlessly, Mike opened the trunk and helped David load the gear. David climbed into the passenger side, and smiled. The glow of the dashboard illuminated two steaming coffee cups.
"You're fucking brilliant," David said, taking a sip.
"You're welcome. The snow report said six inches of fresh powder on the mountain. Should be good."
"Where's the rest of the team?"
"Ah, most of them are driving up in Melanie's new truck," Mike answered. "I thought the two of us would drive together and give them a break from their manager and their chief architect."
David smiled. "You're getting people-wise in your old age."
"I'm not old yet. I'm certainly not an old married man like you."
It was about an hour's drive to Mount Hood. For a while they rode in companionable silence, heading east on I-84, enjoying the coffee and early morning light.
"Where do you want to be in a couple of years?" David asked, breaking the quiet.
Mike glanced sideways. "Whoa, dude. That's a weighty question for oh dark thirty." He paused to consider. "You know, I'm happy now. I'm working with awesome people on the most interesting project I can imagine. I've got a good manager, even if I have to keep you in line from time to time."
David grinned.
"I like what I'm doing," Mike said. "I don't think I could ask for more. More servers, maybe."
They both chuckled.
"How about you?"
"I've been thinking about what I want to do next." David was quiet for a moment. "Worrying about Gary and his deadline keeps me awake at night, gives me plenty of time to ponder the future."
"Man, don't get stressed. We'll solve the problem. Or we won't, and Sean will give us additional servers somehow. ELOPE's not worth losing precious sleep over. We all need more of that."
"It's not just the servers. Yes, of course I want ELOPe to be released and the project to succeed. Being hired to run ELOPe was a huge break for me." David paused and shook his head. "No, the real problem is I don't want to be under anyone's thumb like we are with Gary. We're doing all the work here, and sure we'll get some credit, but in the end, the profit and kudos will go to Gary Mitchell. Meanwhile, we have to take shit from him."
Mike paused. "What are you thinking?"
"We build on the credibility we have right after we release ELOPe to get the support to do a big project from the ground up. A brand new product for Avogadro that won't be subordinated to Gary. Something that can change the world."
Mike nodded. "Sure, that would be nice, but—"
"Not just nice," David cut him off. "It's what I'm meant to do. I know it deep in my bones."
Mike glanced at David but bit back whatever he was going to say.
"Did I ever tell you about my dad?" David started after some minutes of silence.
"You two used to build stuff in your garage together."
"After the army, he went to work as a machinist. He brought home a bunch of old tools the factory was throwing out, refurbished them, and we used to build stuff, anything really, in the shop in the garage. I was the only kid around who fabricated birdhouses out of steel."
"Sounds cool. I never built anything with my father."
"It was cool. He was always inventing new things. My mother would complain about the ironing board, and he'd build one from scratch. He was an inventor through-and-through."
"Like you."
"Exactly. But the difference is he worked in the same factory for thirty years. Paid for me and my sister to go to college and then died on the job, doing the same machinist work he'd been doing the day he started."
"I'm sorry."
David shrugged. "It was five years ago. When he died, they replaced him with a CNC machine. An automated metal cutter. You understand? He was an amazing man, but he's gone."
Mike was quiet for a minute. "We all die eventually."
"I want to make a dent in the universe," David said softly. "Just a small dent, and get some credit for it."
Sixty miles east and an hour later, Mike slid down the lift ramp and snapped into his bindings. David had already started down the run. Mike jumped to get forward momentum and followed him down the mountain.
He didn't understand David. Blindingly brilliant, David was fun to be friends with. On the other hand, his drive and focus on what was over the horizon caused him to lose sight of where he was. The story about his father was touching, but David missed the fact that his father sounded like a happy man, someone who enjoyed his life.
Damn. David had shrunk to a small black blob on the slope far ahead. Mike bent further to pick up more speed, and the cold mountain air whistled through the vent holes in his snowboarding helmet.
The difference in perspective, even when he and David were immersed in the same situation, amazed him. This was the best time of Mike's career. Sure, folks like Gary came along, adding to the challenge. David, faced with the identical state of affairs, took personal affront at Gary's influence. Worse, he saw ELOPe as merely a stepping-stone to something bigger. What about the results of this project, or friendship, or enjoying the journey?
Mike turned the board sideways to stop. When he crunched to a halt, it was utterly silent in the cold mountain air. The ski run split here, and David was already out of sight. Which way did he go?
Mike walked into David's office. "Got a minute?"
It was late Tuesday evening, just three days before Gary's deadline. David had sprung for pizza and most of the team worked through dinner. The department budget had less than a buck left, since David's purchase of a small pool of servers a few weeks ago, implying David paid for the food out of his pocket. The engineers were slowly trickling home now and finally Mike could share the bad news without an audience.
"Sure, just let me wrap this up." David poked and prodded his computer into submission. "What can I do for you?"
Mike turned a guest chair around and sat backwards. "We can't make Gary's ultimatum. Nothing we can pull off before the end of the week is going to make a significant difference. I've had the whole team focused on performance. We've run trials of every promising idea and we've improved by a mere three percent." He crossed his arms and waited for David to respond.
David sat, hands steepled in front of him, staring out the window, the glass a curious meld of room reflections and lights from outside. David's room ran the RoomLightHack, developed by an Avogadro engineer to override the automatic light switches. The hack had been improved over time, making it possible to dim the room's LEDs. David had them set somewhere between moonlight and starlight.
A minute passed, and it was obvious David wasn't going to say anything. His tendency to become uncommunicative exactly when the stakes were highest drove Mike crazy.
Another long minute went by, and Mike started to mentally squirm. "I wish I could find something," he blurted, "but I don't know what. There's this brilliant self-taught Serbian kid who's doing some stuff with artificial intelligence algorithms, and on his home PC, no less. I've been reading his blog, and he has some novel approaches to lightweight recommendation systems. But there's no way we could duplicate what he's doing before the end of the week."
Mike was really grasping at straws, and thin ones at that. He hated to bring bad news to David. "Maybe we can turn down the accuracy of the system. If we use fewer language-goal clusters, we can run with less memory and fewer processor cycles."
Mike was startled by David's soft voice floating up out of the dimness. "No, don't do that."
David smiled in the glow of his display. "Listen, don't worry. We've got a few days. You guys keep working. The executive team loved the demo a couple of weeks ago. We don't want to fool around with the accuracy when ELOPe impressed everyone so much. Keep the team working on performance but don't touch the system accuracy. I'll get the resources we need some other way."
"Are you sure?" Mike asked.
"Yes, I'm sure. I'll get the servers." He suddenly sounded confident.
Mike left puzzled. The deadline was a couple of days away. What could David possibly have in mind?
After Mike left, David stood up and wandered over to his window. The wet pavement glistened in the glare of streetlights. The Portland Streetcar stopped outside the building, picking up a few last stragglers.
On the one hand, Gary was an idiot with no vision. ELOPe would run on the very product Gary had responsibility for, Avogadro's email service. AvoMail would gain a killer feature when ELOPe was ready, and though David might receive accolades, Gary's group would profit through added users and additional business. If Gary supported the project in even the most minor way, he'd get massive publicity and credit.
On the other hand, if he were in Gary's shoes, he'd probably worry about outages, too. But, damn it, some things were worth the risk.
So how could he resolve the apparent conflict? Gary wouldn't approve running ELOPe on production servers because the software consumed excessive resources. The R&D server pool lacked sufficient computing power by several orders of magnitude. So either ELOPe had to become more efficient, which didn't seem possible, or they needed a new group of servers to run on, or the email server capacity must be bigger.
The technical challenge of resource use appeared intractable. But getting more or different servers was a _people_ problem, a question of convincing the right managers of what was needed. He paced the office, deep in thought, until—yes. That would do it.
David sat back down at his computer. He stretched his arms, moved a few scraps of paper out of the way, and prepared to get to work. He opened up an editor and started coding.
Hours passed in a blur.
David looked at the computer clock and groaned: almost four in the morning. Christine would kill him. She forgave his all-consuming work habits, but she gave him hell when he pulled all-nighters. He'd be irritable for days until he made up the sleep, and she'd be pissed at him for being grumpy.
Trying again to milk the last drop from his cup, he debated the merits of another coffee right now. Well, he had nothing to lose at this point. He stood up, a painful unbending of his spine after more than six hours of hacking code. Every minute had been worthwhile: he'd almost solved the resource problem.
Mug in hand, he padded down the eco-cork floored hallway in his socks. He filled the mug with coffee, added sugar and cream, then stood for a few minutes in a daze, letting the hot beverage warm him. He glanced up and down the hallway, black and tan patterns on the floor swimming in his fatigued eyes. The drone of the late evening vacuum cleaners a distant memory, it was eerily quiet in the office now, the kind of stillness that settled over a space only when every living being had been gone for hours. David wasn't sure what that said about him. He shuffled back to his desk.
Hunched over his keyboard, David peered again at the code. The subtle changes were masterful, the sort of work he hadn't done since the early days of ELOPe, when just he and Mike did all the development. He needed to be extremely careful about each line of code he changed. A single bug introduced now would be the end of the project, if not his career.
A little more than an hour later, he reviewed the changes line by line for the last time. Finally satisfied, David committed his changes to the source code repository. It would be automatically deployed and tested. He smiled for the first time in hours. Problem solved.
**Chapter 3**
Gary Mitchell took the Avogadro exit ramp off the Fremont Bridge and pulled up to the parking gate, the light from the car's headlights bouncing off the reflective paint on the barrier in the early morning darkness. He waved his badge at the machine. The gate rose up, and Gary drove into the empty garage, a hint of a smile on his face.
It was two days before the deadline to pull ELOPe off the server. David and Mike hadn't done anything to drop usage. In fact, he'd woken to blaring alerts from his phone: there'd been small CPU spikes all night long, and a big one this morning about five, right around the time the East Coast workday was starting.
The idiots had come within a hairsbreadth of overloading the whole system. Fortunately, AvoMail adapted dynamically, cutting back polling frequencies and slowing the delivery of mail, but they'd been close to a full outage.
Gary alternated between anger and glee. He'd never had significant downtime on his watch, and didn't plan to. But this time David had brought them so close to disaster that Gary could justify sending the email he'd been wanting to write for months, telling Sean he was kicking ELOPe off production.
He would have liked to pull the plug first and _then_ send the message, but that was pushing the line with Sean.
It was the first time in a while Gary had arrived at the office this early. He found the empty building disquieting. He pushed the feeling aside and thought about emailing Sean, bringing a smile back to his face.
A few minutes later, Gary passed his secretary's vacant desk and entered his own office. His computer came to life, and he went straight to AvoMail to compose the email to Sean.
From: Gary Mitchell
To: Sean Leonov
Subject: ELOPe Project
Time: 6:22am
Body:
Sean, just to give you a heads up. I have no choice but to pull production access for the Email Language Optimization Project. They're consuming 2,000 times the server resources we allocated, and spiked usage this morning, causing degraded service levels for ninety minutes.
We gave them carte blanche when we had excess capacity because it's your special project. However, they consume so many resources we routinely dip into reserve capacity, and service degradations like the one they caused today lose us commercial accounts every time.
I spoke to David and Mike about their server utilization many times, but they did nothing to get usage down. I gave them a final warning two weeks ago and have seen no improvements.
Effective tomorrow at 9am, I'm revoking production access for ELOPe.
Email finished, Gary sat and stared for a minute. Was he too obviously gloating? He didn't think so. He hit send.
Time for coffee. He sauntered down the hallway whistling.
John Anderson let his heavy messenger bag slide to the floor and shrugged out of his wet raincoat before hanging it on a wall hook behind his desk. He dropped into his chair, the pneumatic shock absorber taking his weight without complaint, and sighed at the prospect of another day in Procurement processing purchase requests. A tentative peek at his inbox revealed more than a hundred new emails. His shoulders slumped a little and he reached for his coffee.
This week he had the kids, so he had to drop them off at school before work. Since Portland's crazy school system meant the best public schools were all elective, he and his ex-wife had to choose among a dozen different schools. They ended up with the Environmental School. His kids loved the place, and so did he. Unfortunately, they lived in Northeast Portland, the school was in Southeast, and work was across the river in Northwest. His normal twenty-minute commute turned into an hour-plus on the days he dropped the kids off, which meant he'd arrive late at work, his smartphone beeping and buzzing as emails piled up. He loathed starting the day with a backlog. The consolation prize was that the kids' school was right next to a Stumptown Coffee. John sipped at the roasted Ethiopian brew, the dark, bittersweet warmth bringing a smile to his face.
As the coffee brought his brain into gear, he found the will to tackle his inbox. He was brought up short by a puzzling email from Gary Mitchell. Sent earlier this morning, the email asked him to divert five thousand servers. John read the email three times in its brief entirety.
From: Gary Mitchell
To: John Anderson
Subject: ELOPe Project
Time: 6:22am
Body:
Hi John,
Sean Leonov asked me to help out the ELOPe guys. They need additional servers ASAP, and we're running out of extra capacity here. Please accelerate 5,000 standard servers out of the normal procurement cycle, and give them to IT for immediate deployment. Assign asset ownership to David Ryan.
Thanks, Gary Mitchell
Normally when a department wanted new servers, they put in a purchase request. Parts were bought, shipped to Avogadro data centers, assembled into the custom servers Avogadro used, and installed onto racks. Then another group took over and installed the operating system and applications used on the servers. Depending on the size and timing of the order, it would take anywhere from six to twelve weeks from the time they were requested until the servers were available for use.
When a department needed servers in a rush, they requested an exception. That process would take servers already purchased for another group and in the pipeline, and divert the servers to the department that needed them urgently. Replacement computers would be ordered for the first group, who would have to wait a little longer.
Diversion requests weren't uncommon; no, the puzzling part wasn't the request, but that Gary would send an email. Only the procurement app could be used to order, expedite, or divert servers, a fact Gary should know since he routinely requested more servers.
He put his hand on the phone and then took it away. A call to Gary would eat up at least fifteen minutes. Regardless of what the procurement rules were, whenever John tried to explain them to anyone, they would argue with him. The higher up in the company they were, the more they would argue, as though their lofty organizational height carried potential energy that could override the rules. A quick email would save John from getting his ear chewed out.
From: John Anderson
To: Gary Mitchell
Subject: Email Procurement Forms
Gary,
We can't do a server reallocation exception based on an email. I couldn't do that for 5 servers, let alone 5,000 servers. Please use the online Procurement tool to submit your request: http://procurement.internal.avogadrocorp.com, or have your admin do it for you. That's the only process for procurement exceptions we can use. We can approve your reallocation exception if you follow the existing process and provide appropriate justification.
Thanks,
John Anderson
John continued to work through his backlog of emails. The number of new messages in his inbox would give the casual observer the impression he had been gone from work for a week, rather than just the late start he had gotten dropping off his kids. He took another sip of coffee and continued to work through the pile. The rest of his day, like every other, would consist of endless rounds of coffee and emails. Gary's message might have been a little unusual, but it was quickly forgotten amid the deluge of other issues.
A few hours later, on the other side of the campus from John Anderson, Pete Wong brought his lunch from the cafeteria in Building Six diagonally across to Building Three, pausing briefly on the windowed sky bridge. The sun had come out, and he raised his face to feel its heat for a few moments. Below, the sunlight glistened on wet streets, one of his favorite aspects of Portland's climate. As a kid he would run outside on rainy days when the sun broke through the clouds, pretending fairies had covered the street with magic dust.
A crowd of laughing people, marketing folk from their attire, entered the skybridge, distracting him from his memories. He continued through and then went down four flights of stairs, out of the daylight and into the fluorescent gloom of basement offices.
At one department meeting after another, Pete had been assured his Internal Tools team, responsible for delivering business applications used inside the company, would be relocated just as soon as aboveground space became available. It never happened.
It was no surprise that the company had stuck the Internal Tools team in what amounted to the dungeons. Everyone at Avogadro used his team's tools to get their daily jobs done, from ordering office supplies to getting more disk space to filling out their timecards. But because Pete's team didn't develop the sexy, customer-facing products, they were the absolute runts in the corporate hierarchy. No executives or research and development engineers would ever be sentenced to the basement offices. The injustice made him gnash his teeth sometimes.
Back at his desk, Pete took solace in his lunch. His office space sucked and his team was unappreciated, but the food was good. Fresh gnocchi in a butter sauce and mixed salad greens. A cup of gelato stayed cold in a special vacuum insulated cup while he ate. The food was all organic and locally sourced, of course; the coffee wasn't bad either, though it came from Kobos. Pete preferred Ristretto, but only a few of Portland's roasters were big enough to supply Avogadro's headquarters. Pete's wife, a tea drinker, couldn't understand the Portland obsession with coffee.
He ate with one hand as he looked over his inbox. A new message caught his eye.
From: John Anderson
To: Pete Wong
Subject: Email Procurement Forms
Hi Pete,
This is John Anderson. I work over in Procurement. Even though we've got a procurement web application from IT Tools, we still get hundreds of email requests we can't handle. Part of the problem stems from sales people in the field who can send emails from their smartphone, but have a hard time getting a secure VPN connection to the internal websites. Can you create an email-to-web bridge to allow people to get the form by emailing us, so they can then fill out the form and reply to submit the requisition? I mentioned this idea to Sean Leonov, and he said you guys could whip up something like this in a day or two.
Thanks,
John
Pete stared at the strangeness of this. John Anderson, some guy in Procurement, buddies with Sean Leonov, cofounder of Avogadro? Sean was a living legend. Pete hadn't met anyone who knew him directly.
Pete pondered the email. Why did Sean think Internal Tools could implement this in a day? Was he even aware of the IT department? How had Sean, or even John, decided to single him out? It all seemed so unlikely.
The request was a ten on the bizarre meter, but had a certain kind of plausibility. He imagined a salesperson working in the field, using their smartphone to access internal sites. Small screen, low bandwidth. The justification made sense, and if doing this impressed Sean Leonov, well, that couldn't hurt his career. This could be his ticket to one of the real R&D project teams, instead of being stuck in the dead-end Internal Tools department.
He spent a few minutes imagining his future workspace, daydreaming of an office with sunlight pouring in immense windows. Maybe he'd overlook the West Hills or, even better, the river.
With a start, he sat up straight. He would spend some time looking into the request. His fingers found the keyboard and starting searching. His excitement grew when his first search for "email to web service" turned up an existing design posted by some IBM guys. After reading through the article, he realized he really could implement the email bridge in a couple of hours.
His other work forgotten, Pete started in on the project. He created a new Ruby on Rails web application to do the necessary conversion of web pages to emails, and emails into web page form submissions. It was easier than expected, and by mid-afternoon he had a simple prototype running on the department servers.
He discovered a few bugs in the software. Puzzling over the details in his head, he rushed down the hall to the coffee station for a refill.
Mike left his office, nodded to a few teammates on the way, and headed downstairs for the nearest exterior door. After banging his head against the same problem for hours and becoming increasingly frustrated, he needed to clear his mind. The performance issues had become an insurmountable obstacle.
Once outside, Mike wandered around Avogadro's South Plaza, an open amphitheater and park. Just one of the many corporate perks employed to keep everyone happy. Blissfully clear skies contrasted with still-wet pavement from nighttime rains. He waved to a flock of engineers jogging by.
What he found this morning was far more puzzling than the issues he'd expected to run into.
There were two distinct parts of ELOPe. Users saw the front-end process evaluating emails in real-time and offering suggested improvements. But the piece that troubled Mike today was the other half, the back-end process for analyzing historical emails and generating affinity clusters.
While the effectiveness of ELOPe's emails was compelling, the efficiency with which the code ran stunk by anyone's measure. But in the past, the efficiency was at least predictably bad. In the course of attempting to improve resource utilization over the past months, Mike learned that each new email fed into the system required roughly the same number of processor cycles to process.
This morning, though, nothing behaved as expected. According to the application logs, nobody used ELOPe last night, and yet the load metrics had been pegged for hours—a sure indication of a ton of computer processing time being spent on something. But what? In closed prototype mode, only the members of the development team had access to ELOPe. That meant software coders, interaction designers, and the linguistics experts particular to their project. Everyone's activities were logged, but the records didn't reveal any activity. Yet someone or something was generating server load.
Mike hoped fresh air and a walk around the plaza would help him figure out the problem. The last thing he wanted was additional performance problems when they were looking for a massive improvement. He sat on the amphitheater steps and rested his head on his hands. He watched another set of joggers go by. For someone who prided himself on taking things easy, the world weighed heavy on his shoulders right now.
**Chapter 4**
Pete Wong had cut and pasted code he'd downloaded from a dozen different websites, creating a real kludge he wouldn't want to show off in a coding style contest. He ran the test suite one final time and smiled as it passed the last finicky test. He'd implemented the email to web bridge in less than twenty-four hours! It worked, by golly! He tested the new service against the Internal Tools web service, Procurement application, and a handful of other sites. It worked for everything.
He drummed his thumbs on the desk in excitement. Using off-the-shelf libraries written for Ruby on Rails, he'd glued together the necessary pieces quickly. What once took weeks in old web development environments required mere hours in a modern, nearly magical language like Ruby. Using such powerful tools, startups built products in a weekend and launched on shoestring budgets. He wondered for the hundredth time if he shouldn't leave Avogadro to start his own company.
Pete pulled his keyboard closer and started an email to John Anderson, the guy in Procurement. In a bold move, he cc'ed Sean Leonov. No harm in a little visibility, right?
Pete explained the implementation and wrote detailed instructions on how to use the email bridge, a little more than five screenfuls of email. Whoops. Perhaps the process was more complicated than the folks in sales could cope with. Pete didn't know anyone in sales, but he suspected they might not have in-depth technical skills. Well, at least what he provided was complete, even if rough around the edges.
He clicked send and sat back in his chair, sipping his coffee and basking in the glow of his accomplishment. He had good coding kung fu.
Pete pondered bragging about his achievement to his coworkers. A dark thought occurred: perhaps there was something a little irregular about what he'd done.
He sat forward and let his cup thump onto his desk. He'd never told the rest of the team about the project. This request should have come through the normal process like everything else; not only that, but the code should have been peer-reviewed by his fellow developers before he deployed. He'd been so concerned with impressing Sean Leonov that he didn't stop to consider the usual process. Well, no one could blame him for taking initiative.
Despite this, some bigger issue nagged at him. What–
He jumped out of his seat and pounded the wall with a fist as realization hit him. He'd just implemented an off-the-radar system that interfaced with a dozen different business-critical web services inside the company, probably violating all sorts of security policies. On reflection, he definitely had. His cramped office grew suddenly stifling.
Just as quickly as he had become alarmed, he relaxed a little and sat back down. If Sean Leonov thought the Internal Tools team could implement the request within twenty-four hours, he clearly meant they should pull out all the stops. Pete couldn't go back and yank the application off the servers, not after telling John and Sean the service was available. He shook his head: he was worried about nothing. The bridge was invulnerable. His tool relied on email credentials to validate user logons, and if any product in the company was secure, it was AvoMail.
If he told his boss and the rest of his team now, he'd get his wrist slapped. The best course of action would be to keep quiet until he had gotten a response from Sean. Once he showed that to the team, any skipping of due process would be forgiven. With his plan in place, one in which he wouldn't take too much heat, he relaxed a little more.
A ruckus came from down the hall, rapidly getting closer. Had they already found out what he'd done? He grew alarmed until a group of his coworkers ran past his open door. A few seconds later, Internal Tools' technical lead stuck his balding head in Pete's doorway and said, "We got a hot tip the billiard room showed up on the fourth floor of Building Two. Coming?"
Relieved, Pete smiled and leaped up from his desk. He'd never seen the mysterious Avogadro billiard room that roved from building to building. "Absolutely!" he called, as he ran from his office, following the gang of geeks.
Work forgotten, Pete joined the boisterous hunt for the billiard room. Laughter rang out as other groups heard the rumor and entered the chase. The room would only accept the keycards of the first sixty-four people to find its new location, adding to the urgency of the search. As teams ran through the halls, they told each other outright lies about the suspected whereabouts, all part of the game surrounding the mystery.
While people played and laughed, thousands of computers hummed and exchanged data. A few servers allocated to Internal Tools spiked in usage, but nobody was around to notice.
Gene Keyes walked back to his office with another cup of coffee, grateful the campus had returned to a somewhat normal decorum after the insanity of the hunt for the billiard room. On some level, he was curious about the mystery of the moving room, but he hated the way the kids around him turned the puzzle into a superficial game, as they did with everything.
He searched the pockets of his suit for a note. His rumpled jacket and graying, disheveled hair were in stark contrast to the young, hip employees dressed in the latest designer jeans or fashionable retro-sixties clothing. Nor did he fit in with the young, geeky employees in their plaid shirts or tees with obscure logos. Not to mention the young, smartly-dressed marketing people in their tailored business casual wear. Fitting in and impressing others weren't high on his list of priorities.
As he approached his own office from the coffee station, he found a blonde girl knocking on his door. "Can I help you?" he asked, halting the search for the missing note.
"I'm looking for Gene Keyes," she said in a bubbly voice. "I'm Maggie Reynolds, and I—"
"I'm Gene," he said, cutting her off. "Come in." He opened the door and walked in. She could follow him or not.
"Uh, my boss sent me because he's missing four..." She trailed off.
Gene put his cup down and took a seat. He glanced up to an astonished expression on her face.
"Wow, I didn't know anyone still used...Wow, this is a lot of paper."
Gene turned around, despite himself. Yes, it was true his office was piled with computer-generated reports. Stacks of good, old fashioned letter-sized paper littered every flat surface. Oversized plotter printouts with huge spreadsheets and charts hung from the walls. The centerpiece of the office, the desk he occupied, was a 1950s-era wooden piece that nearly spanned the width of the room. It might have been the only furnishing in the entire building complex manufactured in the previous century. Incongruously, the desk was far larger in every dimension than the door. The people with a good brain on their heads, often engineers, but occasionally a smart manager, those who trusted their guts, instincts, and eyes, but took little for granted, they'd come in and their eyes would bounce back and forth between the desk and the door trying to puzzle out the mystery. Sadly, she didn't appear to notice.
"Wow, I saw this in a movie once," she said, coming around his desk to fondle a stack of continuous feed paper. She pulled at one end, making the green-and-white-striped paper unfold accordion-style. Her eyebrows went up and her jaw down. "Hey, do you have any punch cards?"
It rankled Gene to hear almost identical comments from every kid that walked in the door. He sat a little straighter in his wooden office chair, the same one he liberated from the army the day he was discharged. "Some things are better on paper," he explained, not for the first time. "Paper is consistent. It doesn't say one thing one day and a different thing the next. And, no, I don't have punch cards. I'm not preserving this stuff for a museum. This is how I do my job." Gene tried to work some venom into his voice, but what came out just sounded tired. He knew what she'd say next, because he heard a variation of the same thing from every visitor.
"You know we work for Avogadro, right?" Maggie said, smiling.
Gene knew. But he worked in Controls and Compliance, what they used to properly call the Audit department. When push came to shove, paper never lied.
"Uh huh," he grumbled, ignoring that whole line of thinking. "So, what can I help you with?"
"Well, I have a problem. The database says we're supposed to have more than four million dollars left in our budget for the fiscal quarter, but our purchase orders keep getting denied. Finance says we spent our money, but I know we didn't. They said you would be able to help."
Gene gestured with both hands at the paper around him. "That's what the paper is for. Believe it or not, there's a printout here of every department's budget for each month. So we can examine your budget before and after and see what happened. Now let's take a look..."
"Dude, you're here," Mike said, plopping down in David's spare chair. "Where were you this morning? I couldn't find you anywhere. I need to talk to you about some weird behavior in ELOPe. Not to mention you missed the entire hunt for the billiard room." Considering that they worked in neighboring offices and were in constant electronic communication, David's vanishing act was impressive.
"What kind of weird behavior?" David gazed off into the distance, ignoring Mike's question.
"I told you we couldn't find any more performance gains, but I couldn't help trying. I started by establishing a baseline against the current code, to have something to test against. I correlated the bulk analysis import with server cycles consumed, and..." Mike stopped.
David continued to stare out the window, apparently lost in thought.
Mike glanced outside. A pleasant sunny day, uncommon for Portland in December, but he didn't see anything other than the ordinary bustle of people walking about on the street. He turned back to David. "Are you listening? Isn't it critical this be fixed before Gary's deadline?"
"Well, I do have some good news there, but go on."
"I tried to establish a correlation, but I couldn't find one. You know ELOPe takes a predictable amount of server resources to analyze emails. At least it did, until two days ago. Now I can't find any relationship at all. The CPU utilization keeps going through the roof even when the logs indicate nobody is running any tests. It's as though the system is working on something, but I can't find any record of what."
David was again staring outside. Mike's head start to pound. He'd been struggling with the damn optimization for days. "So then, David, I slept with your wife. She said it would be fine with you."
"Yeah, sure."
Mike waited, grinning to himself.
"Uh, what? What did you just say?" David finally focused on him.
Mike planted his body in front of the window to block David's view. "Why don't you tell me what the hell is going on, since you're clearly not interested in the performance issues."
"Ah, come read this email from Gary," David said, appearing animated for the first time since Mike entered the office. "The message came in a few minutes ago. We were allocated five thousand dedicated servers by way of a procurement exception. Accelerated deployment and all that. We'll have access to the computing power by tomorrow morning."
Mike came around to peer over David's shoulder at his screen. He let out a low whistle. "Holy smokes, five thousand servers! How did you get Gary to agree to that?"
"I sent him an email asking for dedicated nodes for ELOPe so we wouldn't be in conflict with the production AvoMail servers."
"Wow, what a fantastic reversal," Mike said. "I never would have guessed Gary would change his mind. Any clue why?"
David got that distant look in his face again. "I don't know. It _is_ a bit surprising."
Excited by the possibilities of the extra computing power, Mike paced back and forth in front of the window. "Five thousand servers...We can move on to the next phase of the project, and scale up to limited production levels. We could start bulk processing customer emails in preparation for a public launch."
"Well, let's start with Avogadro's internal emails," David said. "This way, we won't adversely affect any customers if anything goes wrong. If we can analyze company emails at full volume, I'll suggest to Sean we turn the autosuggestion feature on for all employees."
"Good plan. I'll stop work on the performance issues and focus on importing the internal emails. This is great news, David!" Mike did a little dance on his way out the door.
When Mike left, David returned to staring out the window. The server allocation was great news. So why were the hairs raised on his neck?
He had sent the email to Gary. That part was true. But he'd neglected to tell Mike about the minor detail of ELOPe's involvement. Of course Mike would uncover massive background processing.
ELOPe needed to analyze Gary Mitchell's emails to optimize David's message, which meant ELOPe also required access to the inboxes of everyone Gary had emailed with, and then the inboxes of everyone those people communicated with, a spiderweb of relationships spanning many thousands of people. David's usage and modifications caused ELOPe to import a massive number of emails. He'd obscured his work by ensuring the new behavior wasn't part of the normal system logs, but he couldn't prevent system monitors from tracking CPU load.
David didn't know what to say. Mike would figure out the mystery behind the CPU utilization eventually. He hoped the discovery would take place later rather than sooner, after they'd solved their resource problems. David didn't want anyone, not even Mike, to know he was using ELOPe itself to get the resources to keep the project running.
A bug in the software, deeply integrated into the mail servers, could bring down all of AvoMail. If anything bad happened, David would feel some serious heat from upper management.
But that wasn't the cause for the pit of fear in his stomach.
No, the real issue stemmed from the changes David had made during his all-night coding marathon. He'd gone into the code for language analysis and put in an overarching directive to maximize the predicted sentiment for any message discussing the project. When any email mentioned ELOPe, from anyone or to anyone, then ELOPe would automatically and silently reword the message in a way favorable to the overall success of the program.
The resulting emails were indistinguishable in writing style and language from those written by the purported sender, a testament to the skill of his team, whose language assembly algorithm used fragments from thousands of other emails to create a realistic message in the voice of the sender.
David relished this success, and wished he could share with the team what they had accomplished. The culmination of years of research, the project had started with his efforts towards the Netflix Prize before he was hired, although even that work had been built on the shoulders of geniuses. Then months of him and Mike laboring on their own to prove the idea enough to justify further investment, followed by two years of a full R&D team, building the architecture and incrementally improving effectiveness month after month.
The results proved, beyond doubt, the power of the system. ELOPe's language optimization had acquired thousands of servers.
The problem, the unsettling fear, arose because David didn't understand how. He couldn't examine the altered emails, an unfortunate consequence of removing the logging so others wouldn't discover ELOPe's manipulations. Had Gary received a modified email convincing enough to make him change his mind? Or had ELOPe changed Gary's response to something more favorable? David found the uncertainty unnerving, and the pit of fear in his stomach throbbed at how little control he had.
But sure enough, his dedicated servers would arrive tomorrow, an outcome worth dwelling on. An email from procurement confirmed the allocation, and another from operations showed the time the servers would be available. Whatever ELOPe had done, it had worked. It might be the most server-intensive application in the company, if not the world, but by damn, it worked.
All the hard work, politics, and sacrifices had been worthwhile. The project had become his life, and his little baby was all grown up now, doing what it was built to do.
Well, maybe a little more besides.
He hadn't realized what it would feel like to have ELOPe working silently, behind the scenes. He was perpetuating a huge deception, and if anyone discovered what he had done, it would be the end of his career. He turned to the window again. Outside, in the momentary sunshine, people went about their business, walking, talking, jogging, blissfully unaware of what was going on inside the company. From his office window, they looked chillingly carefree.
**Chapter 5**
Bill Larry's foot hovered in the air while he waited to take a step forward. The data center dropped down, then lurched up. He paused for a moment more, judged the motion, and leaped. The data center retreated from him at the last second, but he made the jump onto the adjoining floating barge.
Bill breathed in the ocean air as the Offshore Data Center 4 rocked beneath him. This was his project, his mark on Avogadro. After starting out as an IT system administrator, his skills with people led him into management. After he got his MBA, he took a position with Avogadro in their facilities organization. Now in his early forties, he found himself riding helicopters to visit the modern pinnacle of high tech data centers: the floating server farm.
In the last decade, the company had invested in offshore power generation. Avogadro's Portland Wave Converters, or PWC, were the result. Powered by ocean waves, they created cost-effective and environmentally friendly electricity. The PWC stretched out to either side, a long line of white floats on the surface of the water, anchored to the sea-bed below.
Once Avogadro had solved the problem of electrical generation, it made sense to locate the data centers offshore as well. Ocean real estate was effectively free. Maintaining the temperature of the thousands of servers packed into a small room was tricky and expensive on land, but easy out here, where cold, ambient-temperature seawater made for effective cooling. Now Avogadro had an entire business unit devoted to utilizing the potential of this novel approach. They refined the design, with plans to use the floating server farms for their own operations and lease cloud computing capacity to commercial customers.
The primary barge in front of Bill held sixteen shipping containers heavily modified by Bill's team with weatherproofing, climate control, and electrical conduits. These modular metal boxes housed racks of standard Avo servers, power supplies, and communication equipment, each one a fully independent data center capable of running Avogadro search, AvoMail, or anything else the engineers back at headquarters wanted to deploy.
The barge behind him served as a landing pad. It wasn't part of his original design, which had assumed regular maintenance would come by boat. Then again, Bill hadn't realized how many emergency trips he'd end up making to the prototypes, located ten miles from land. The switch to helicopters saved hours on each visit.
Avogadro had extensively ruggedized the containers and electronics equipment. They should have required barely any maintenance at all, even out in the corrosive saltwater environment. In fact, the system was designed to require only a single visit each year to replace faulty servers.
But unlike their land-based counterparts, the floating data centers had a few problems that tended to get Bill up in the middle of the night. Resiliency to the worst storms was one issue; but the weather had been clear, so that wasn't the reason Bill was out here this morning.
ODC 4 had dropped completely offline at 4:06a.m. Within seconds, automated systems detected the outage and provisioned spare capacity in other data centers, seamlessly transitioning the applications to new servers so the barest minimum of customers were affected. Minutes later, the on-duty operations engineers received notice of the downtime and recovery. They took one look at the location and escalated to the ODC team. Bill's smartphone whooped, and at 4:15 he peered bleary-eyed at the incoming data. There was nothing to suggest the alert was worth ruining everyone's morning, so he scheduled the maintenance trip for the start of the business day and met his team at the Bay Area helipad at 8a.m.
He stepped closer to the metal stacks, the sinking feeling in his stomach not caused by the rolling and pitching of the barge. Irregular burns and cuts, the obvious mark of a hand-held cutting torch, covered the sides of the containers. Bill shook his head at the rude treatment of his specially designed data center boxes.
A closer inspection confirmed his fears: a ragged hole had been cut into the side of each shipping container. After the first theft months ago, they'd redesigned the doors, hardening them against future break-ins. This had the unfortunate side-effect of turning the unprotected sides into the easiest entry point.
While the other members of the team worked on opening the doors, Bill stuck his head through the hole and pointed his flashlight around. The racks that should have held hundreds of high performance computer servers were empty, with wires dangling everywhere and various bits of low-value electronic equipment haphazardly strewn about.
Bill extracted his Avogadro phone from his vest pocket and started composing a message to the rest of the ODC team. Forget fixing the problem in place with a small maintenance party. They'd need to tow the whole barge back to shore, then install new containers and servers.
Bill resisted the urge to bang his head against the wall in frustration. Even if they wanted to defend the barges, the location ten miles offshore and lack of any facilities made it impossible to station security on board twenty-four hours a day, seven days a week. Besides, anyone here would be at risk from the pirates.
The piracy problem had put the entire ODC rollout on hold, pending a resolution. It didn't bode well for Bill's chance of getting a bonus. He and Jake Riley, the ODC Lead Manager, would meet with senior management later that week to discuss the issue.
All this hardware sitting out in the middle of the ocean undefended was just too tempting. A full floating data center contained millions in equipment, including tens of thousands of servers, along with their requisite hard drives, power supplies, emergency backup batteries, and extensive communications hardware. Worse, it wasn't clear yet whether the target of the thieves was the computer equipment itself or the potential customer data on the hard drives.
As he reviewed the destruction and mentally tallied the cost of repairs and replacement, Jake's controversial proposal began to make more sense: give the ODCs active deterrents to prevent pirates from boarding them in the first place. Still, he got a chill down his spine just thinking about autonomous armed robots guarding the barge.
"Mike, what a surprise!" Christine smiled and embraced him in a warm hug. "David didn't say you were coming for dinner."
"How's the game development going?" he asked.
" _Awesome_ ," Christine said, singing the word as she hung his coat in the closet. "I spent the last two weeks fine-tuning game play with our alpha players, and we're shooting for a beta release after the holiday. Don't worry, you're on the access list. Want a demo later? The visual effects on magic spells are _amazing_."
"Sure, I'd love it."
"Make yourself comfortable, and I'll tell David you're here." She tucked a wisp of hair behind one ear and went upstairs.
Mike strolled around the early twentieth-century Foursquare, a quintessential Portland house, as he waited. Ikea furniture was interspersed with computer equipment everywhere, and Christine's high end gaming system dominated the family room. Mike wandered the house, just a hint of envy somewhere. Somehow David and Christine managed a classy mix of furnishings, electronics, and art, unlike Mike's small bungalow which still resembled his college apartment.
He couldn't be too jealous of good friends who always made him welcome. Since he lacked family in town, he often dropped in for dinner, especially between girlfriends. Of course, he usually didn't come unannounced, but he had a pressing reason to talk to David tonight.
Before he left work, Mike had figured out the mystery of ELOPe's activity. He deciphered the unexplained activity in the system, and the unexpected and unlikely allocation of dedicated computers. He even understood David's strange behavior in the office when he'd announced they'd been granted additional servers. David had been less than honest with him, leaving Mike sweaty at the impending confrontation.
He snapped out of his reverie at the sound of footsteps on the stairs. David clasped him on the shoulder, and Christine led them into the kitchen.
"Vodka martinis, everyone?" Christine suggested, following their longstanding tradition.
"Sounds great," Mike and David answered in unison.
The men took bar stools in the kitchen while Christine grabbed a bottle of Stolichnaya and glasses. She turned to Mike. "If you're available, I've got a single coworker."
"Oh?" Mike said, raising his eyebrows. "Does she have any secret collections I should be aware of?"
They laughed at the time Christine had fixed Mike up with an obsessive-compulsive collector of stuffed animals.
"I think this one is normal. I'll invite you to coffee with her after the holiday, and then bow out at the last minute."
"That won't be awkward at all, I'm sure."
Christine smiled mischievously.
"I'm glad you came," David said. "We haven't gotten together outside of the office since the snowboarding trip."
Mike swallowed. It was hard to confront friendly, engaged David. The distracted, vague David of a few days ago was an easier match.
"But why the unexpected visit?" David asked.
Christine gave him a funny look as she realized he hadn't invited Mike over.
"I want to talk about ELOPe." Mike clenched his fists under the counter.
"I heard the good news," Christine said, wetting glasses with vermouth. "It's about time you guys got dedicated servers. Now you can move on to the next phase, right? Congrats."
"Yes, well...I have this crazy idea how we got those servers." Mike kept his eyes on David. "I'm guessing ELOPe was turned on a little early."
"What makes you think that?" David said, his fingers turning white around his martini glass.
"You asked me to import all internal emails. Which I did, two days ago."
"Any problems?"
"No, none at all. That's the problem. There should have been a peak in background processing activity as I gave ELOPe access to accounts across the company." Mike turned to Christine. "Any time we add new email sources, ELOPe analyzes the backlog. When I added ten thousand employees, with thousands of emails each, I expected a giant processing spike, considering all our performance problems." He returned to David. "But you know what I found, right? No spike. Hardly any activity. Now why would that be?"
Christine stopped at Mike's tone, olive-covered toothpick hovering over a glass. "Come on, the suspense is killing me."
David shrugged and slumped in his chair. "Why?"
"ELOPe had already been given access to everyone's email." Mike enunciated carefully. "I didn't see a jump in activity, because by then it had finished processing their inboxes."
He waited, confident it was the only explanation that fit the data, but David didn't say anything. Mike continued. "You turned on company-wide access days before, so ELOPe could help with the dedicated server proposal, right?"
"I did..." David looked pained.
"Why didn't you tell me? It's awesome. ELOPe worked! You wrote an email, received suggestions, and the resulting message was persuasive enough to convince Gary to give you the servers! Why did you keep that secret? I've been chasing down performance spikes for days for no reason."
David let out a big sigh and twiddled his fingers on the countertop. Mike couldn't figure out if he was embarrassed or relieved. Well, either way the secret was out.
"I was trying to protect you," David said after a moment. "We didn't have permission for ELOPe to analyze live emails on the production servers, and if you knew you might have been held responsible."
"We're in this together," Mike said. "This is my project just as much as yours. Look, next time, tell me what is going on. I felt like crap when I realized you were keeping secrets."
David shook his head. "I didn't think about it. Sorry."
"Okay, now forget moping about." Mike stood and held his glass out in a toast. "ELOPe works. After two years of building that damn thing, it fucking _works!_ Let's celebrate!"
David helped Christine clean up after dinner, he clearing dishes while she loaded the dishwasher. Mike had gone home after a dessert of chocolate chip cookies and ice cream. They joked that Mike and David had the culinary preferences of twelve-year-old boys.
After Mike had gotten what he thought was the deception out on the table, everything had been fine. Mike was so elated ELOPe worked that he was happy enough to put the other issue behind them.
"Why so quiet, hon?" Christine asked.
"Just thinking."
"You're not just thinking. Thinking is when you're quiet, but snapping your fingers." She glanced over in time to catch David's smile. "You've been moody all week. If this is about lying to Mike, well, he knows now, and he forgives you. Stop worrying."
"There's more," David said heavily.
"More what?"
"More I didn't tell Mike. I turned on ELOPe and obscured the system logs as Mike suspected. But I also did something else..." David trailed off.
"Well, are you going to spit it out, or should I insert bamboo under your fingernails?"
"I gave ELOPe a hidden objective."
"What do you mean?" Christine asked.
"When any message passes through ELOPe, and that would now be every single company email at Avogadro, the contents are scanned to see if the ELOPe project could be affected. Then ELOPe takes steps to maximize success."
"What does that even mean? What can it do?" She stopped washing dishes and stared at him.
He looked away from her gaze. "ELOPe can't do anything but rewrite emails," he said, throwing his hands in the air. "But because I turned off the logging, I can't see the changes. I turned the directive on, and less than twenty-four hours later I received an allocation of five thousand servers. That many servers, built and installed, is close to five million dollars. How did ELOPe get someone to spend five million?"
David paused to catch his breath. He started to look around and whisper, but realized that was foolish. They were alone in the house. "This afternoon I got another email, saying a team of twenty contractors had been assigned to the project, top-notch performance specialists hired to help us optimize ELOPe. We need the help, but I never asked to hire anyone."
"You're starting to scare me." Christine threw the sponge down and gave up on the dishes altogether. "There's no way Sean or Gary would have hired them for you?"
"No. Sean didn't know about the extent of our performance issues, and Gary would far rather boot us off the servers. I'm convinced the contractors somehow stem from the override I created."
"Why the hell did you do something crazy like this in the first place?"
"We were a couple days from the whole project being cancelled. Gary Mitchell was going to bounce us off his servers." David's shoulders slumped in despair. "ELOPe is a massive consumer of processing resources. We're not even released, and we're already consuming almost as many compute cycles as the production Search and Email products. They're serving hundreds of millions of customers, while we're in test mode."
"Everyone knows this, right? It's no secret."
"Yes and no. I abused Sean's carte blanche to get way more server resources than he ever intended to give us. If Gary went through with his ultimatum, not only would we have been kicked off his servers, but Sean would have learned I distorted what he said to get those resources. Definitely an end-of-career move."
"Jesus, David." Christine had her arms crossed and was tapping her foot now.
David was alarmed. The last time she was in this mood, he'd spent the night on the couch.
"Why did you let everything snowball out of control?" she said.
"I just want the project to succeed." He tried his puppy-dog eyes on her, but she ignored him.
"If you're worried about the override you put in the software, back out the change with Mike. The way you've described the situation, resources are being stolen from all over the company, and everything points to you."
His spirits lifted. Christine always saw the obvious answers he missed. "You're right. If I revert the code change before anyone gets wind of what's happening, the manipulations should stop. I was nervous, afraid I'd crash production trying to patch the code. But Mike's done it before. You don't think he'll freak out when I tell him?"
"No, you dork. He's your friend. Of course he's going to help you." She shook her head and sighed. "Why do husbands make everything so much more complicated than they need to be? Maybe I should have gotten a dog instead."
"At least I don't shed." He grabbed her and planted a big kiss on her lips. "Thanks for talking with me about this. Let me go email Mike."
Upstairs, David sat down in his office. He tapped impatiently at the touchpad, and started in on the email.
Hi Mike,
Thanks for coming over tonight. I'm glad we talked.
We need to meet early tomorrow morning. There's something I didn't tell you. We have to live-patch the email servers to remove part of ELOPe, and I could really use your help since you've got experience with production rollbacks. I'll explain everything tomorrow. - David.
David relaxed as he hit the send button. With Mike by his side, they could fix anything.
Jake Riley, the Lead Manager of the Offshore Data Center project, prepared to brief Kenneth Harrison and Rebecca Smith on the piracy problem. He counted himself lucky to get a meeting with the executive team, even if only two-thirds were present and it was nine-thirty at night. Tired from a twelve-hour workday, he forced himself to keep his energy high for the presentation.
Jake shared a photo of the break-in. "This morning Bill flew out to Offshore Data Center 4, off the San Francisco coast. Pirates used cutting torches to cut holes in the sides of six of the cargo containers onboard ODC 4, and removed the servers from those containers. They left behind server racks and power transformers damaged beyond repair." He switched to an interior photo showing one of the pillaged containers.
Jake scanned the virtual conference room, ensuring everyone was with him. Kenneth and Rebecca, in the Portland headquarters, appeared on screens covering the far wall. Bill Larry sat next to Jake. Directional microphones, high definition monitors, and a low-latency network connection created an impressive simulation of a single conference room, even though one half was in Palo Alto and the other half in Oregon. Far beyond ordinary telepresence solutions, it was nearly indistinguishable from being in the same room. Jake figured the technology was the closest to a Star Trek holodeck he'd experience in his lifetime.
"That brings us to three pirate attacks in as many months," he said. "Two here, one on the East Coast."
Rebecca scanned through photos of the attack, frowning. The issue had caused a holdup in the ODC rollouts and therefore a small but growing hiccup in Avogadro's master data center rollout plan. Computing requirements doubled every twenty months at Avogadro with no end in sight. Meeting at this time of night was a sure sign of just how critical server capacity was to the company's growth.
"Tell us about security measures," Kenneth said. "You already do some hardening of the physical containers, right? Is there anything more you can do?"
"The units are ruggedized for the maritime environment," Jake said. He switched the overhead screen to an exploded diagram of the container design. "A standard cargo container is watertight, even capable of floating for years on its own. Our containers are modified to allow electricity, cooling, and data in and out. Additional weatherization controls humidity and ensures optimum interior conditions given the corrosive nature of the saltwater environment. After the first pirate theft, we modified the design and installed high-security doors."
Jake hated sharing bad news. He'd always had outstanding results to report in the past. The offshore project had posed no end of technical challenges, all of which his team had overcome. He had even brought on new employees with specialties in maritime engineering and construction, people who clashed with the culture of Avogadro, but he solved those problems, too. He never expected that old-fashioned piracy, a problem he considered a nineteenth-century issue, would be his biggest challenge. _Pirates,_ damn it. He shook his head at the thought, and went on.
"No matter what we do, there will always be a weakest link in security. That's currently the container walls. If we harden those, the vulnerability will simply move. Hell, the thieves could tow the barge away if they had a mind to. These units are sitting out there in the ocean, miles from shore. Even with effective monitoring, if we have to scramble a helicopter, we're looking at an hour elapsed time. A boat is a two-hour response. That's if we have people staffed and ready to respond twenty-four hours a day."
"Monitoring is difficult as well," Bill said. "We can monitor the interior of the cargo containers, where the environment is controlled. Outside we've got heavy winds, rain, saltwater, sun. We've tried three models of security cameras and they've all failed. Instead of alerts when the pirates board, we find out only when servers are unplugged."
"The rollout plan," said Rebecca, "calls for twenty additional ODCs around the world within six months to meet capacity requirements. We don't have the real estate to put them on land. We can't centralize because of bandwidth and latency issues. The offshore project is critical, Jake. Tell me you've got a plan to get us back on track."
"Well, this is going to sound controversial, at least initially, but we do have an idea. Hear us out before you make a decision. Do you recall the piracy problem off the coast of Somalia?"
Rebecca and Kenneth nodded from across the virtual table.
"The companies shipping freight around Somalia faced similar issues. They couldn't arm their sailors, civilians with no combat training who can't be expected to repel a pirate attack." Jake put another slide up on the overhead screen, showing a small tank-like robot. "iRobot, the company that sells Roomba, also makes robots for commercial and military use. They'd already developed maritime exploration robots and weaponized drones. In Somalia they took the next step, and created weaponized versions of their maritime robots."
Rebecca had one eyebrow raised.
Jake smiled. "You know where I'm going. But hear me out."
Rebecca waved a hand for him to continue.
"They deployed a two-part solution on commercial ships that passed near Somalia. An autonomous submersible bot can attack and disable the pirate ship itself, and an armed robot on deck can repel would-be boarders. They tried the robots on dozens of shipping vessels in the area, and after three successful cases of repelling pirate attacks, there have been no major attempts at piracy in the last six months. We can assume word got around the criminal community about the new defenses."
Rebecca and Kenneth glanced at each other. Rebecca's initial amusement had turned into a concerned frown.
Jake forced himself to keep going. He switched slides twice more, displaying the submersible unit and tank-like deck robot onboard a freighter. "We talked to iRobot, and I have an initial bid from them. They have recommended a similar package for our offshore data centers. Submersible robots to take out ships, onboard robots to disable boarders."
Jake had a hard time meeting Rebecca's gaze. He was walking a fine line here. Avogadro prided itself on their enlightened culture: it wasn't exactly an environment welcoming to violence and guns. He could hardly believe he was suggesting putting weapons in a data center. To the best of his knowledge, there wasn't even a single armed guard in all their land-based facilities. They were an Internet company, not a military contractor.
Before Rebecca could respond, Bill jumped in. "I know this may seem radical to put armed robots in place. But it's worked off Somalia. In fact, total injuries and deaths are down. The approach will scale to any number of data centers we care to deploy. It's also cost-effective and risk-reducing because we don't have to maintain people onboard the barges."
Kenneth leaned over, checked in with Rebecca. She shook her head.
"Keep going," Kenneth said. "Let's hear the rest."
Jake and Bill covered the entire iRobot proposal, explaining more about the robots to be used and the estimated cost. They spent the greatest amount of time detailing the protocols put in place with the robots to ensure minimum loss of life and risk.
At the end everyone was quiet. Jake heard the hum of cooling fans in the room. He was sweating under his clothes and desperately wanted to go home. He discreetly glanced at the clock. After eleven now. He'd been working since five in the morning.
Even Kenneth turned and waited on Rebecca, clearly not willing to stick his neck out on this proposal.
After a minute, Rebecca started hesitantly. "I wouldn't risk human life for the mere loss of ten million dollars." She paused, then went on more strongly. "But the privacy implications of losing the data stored on those servers are huge. A breach opens up the potential for litigation from our users and regulation from the government. More significantly, if we fail to retain the trust of our users, we're sunk. Our cloud strategy works only as long as our customers have complete confidence in the security and integrity of their personal data." She stabbed at the table with one finger. "Losing customer trust in this case means billions of dollars of revenue. We can't afford the loss of one hard drive containing customer information, let alone tens of thousands of hard drives in an ODC."
Jake nodded and went to respond, but Rebecca held up a hand to indicate she still wanted to speak. He'd been sure the idea would be shot down, but this looked like Rebecca was about to approve the plan.
"We've been relatively fortunate the ODC thefts have thus far been limited to non-sensitive search data," she said, anticipating Jake's input, "but we must migrate our email and document servers to offshore data centers within a few months or risk capacity outages. It's not acceptable to allow confidential emails and documents to be stolen by pirates." She cleared her throat. "I want you to proceed with your proposal. I want this to be structured so we pay iRobot for security, and have them own and control the hardware. I don't want Avogadro Corporation to own weaponized robots. Am I clear?"
Soon after, Jake left the virtual conference room stunned. What had he done? Within a few weeks, the ODCs would have their own automated self-defense capability, like something out of the movie _Terminator_. Somehow he was responsible—and way outside his comfort zone.
**Chapter 6**
"David, it's Mike. Listen, I'm flying to Madison this morning. I got a message from my mom that my father had a heart attack. I'm not sure when I'll be back, but I'll call when I know."
David put the mobile phone down, suddenly numb. Distressed by the content of the message, he worried even more about the way Mike sounded, emotional fear surfacing in shaky, halting speech. The contrast with Mike's usual easygoing manner was enough to make his own throat tight.
He didn't remember Mike talking about his dad much, other than a few comments after his trips home, but David assumed he was healthy. He felt lingering guilt because he'd seen Mike's incoming call on his mobile at home, but in the rush to get ready for work, he didn't answer. Only now in the office did he listen to the message, and he regretted not answering earlier. He called Mike back, but it went to voicemail without ringing. Mike must be in the air, en route to Wisconsin.
Still shaken, he wondered what to do. He phoned Christine to let her know the bad news. She was equally shocked, getting out "I'm sorry" a few times before she had to go.
He sat behind his desk for a while, doing nothing at all. When had he and Mike gotten so old that they had family with health issues? He did the math, surprised to realize his own parents were going on sixty.
A knock startled him.
Melanie stuck her head in. "Team stand-up. Mike's not here. You want to lead, or should I?"
He nodded and stood. "I'm coming."
By the time the morning meeting ended, David had inherited a fiasco with the Test department. When he finished that emergency, he had sixty emails to deal with. Not till midmorning did he have a moment to himself. Standing at the espresso machine, he felt lonely. Coffee was a shared experience between the two of them. Mike would sometimes drag him on a trip halfway across town chasing down an elusive bean. He realized with a start Mike had always been there. Other than company holidays, Mike had never taken vacations or even sick days.
Then it hit him. With Mike gone, he had no help to remove his modification to ELOPe. He was on his own. Trembling, he rushed back to his office and paced the floor in front of the window, pondering his options. The coffee sat forgotten, fear-generated adrenaline giving him more stimulation than he needed.
Could he remove the ELOPe override module by himself? Under ideal conditions, server changes deployed during rolling downtimes. They'd take five percent of the computers offline at a time, apply the updates and test them, then do the next group until all the servers were done. He'd been lucky a rolling downtime had been scheduled the night he released the override.
David sat down at his desk, and pulled up the operations calendar. _Kuso!_ No deployment opportunities before the holiday closure next week. He couldn't deploy until after the New Year. He slammed his fist down on the table and Tux the Penguin wobbled with the sudden movement.
He stood and returned to pacing. He could request an exception to get a one-off maintenance window scheduled, but that required paperwork, submitting the changes ahead of time, and altogether far too much attention. He sat back down. He checked the door to see if anyone had observed his nervous antics, but it was firmly closed.
If he didn't wait for a rolling downtime or request a maintenance slot, that left him with a live-patch. During the procedure, the server stayed up while the code change was made in the background, the entire operation taking only a few seconds. It was usually used for minor changes that wouldn't affect the way applications ran, like changing the styling of a page or embedded images. Anything more complicated was risky and reserved for emergencies. More than one outage had been due to a live-patch gone wrong. Changing ELOPe's code, tightly integrated into the mail servers, was definitely _not_ a small change. A botched patch would attract even more attention, including a formal investigation.
Should he attempt the patch on his own or wait for the next maintenance window? Mike not only had far more experience, he also had the authorization to perform live-patches. He convinced himself the safer, lower-risk option would be to postpone until a deployment window became available or Mike returned. He took a cautious sip of his coffee and leaned back. It could wait. After all, whatever ELOPe was doing didn't seem to be causing any serious problems.
John Anderson had worked halfway through the queue when he came upon yet another request from Gary Mitchell's department. With relief he noted Gary Mitchell was using the online app for submitting procurement reqs rather than sending emails, but he was shocked at the volume coming from Gary's group. Three reallocation requests to take servers out of the normal pipeline of delivery and direct them to the ELOPe program, whatever that was. Several new orders for bulk purchases of high performance servers. Gary's division must be expecting massive increases in load.
And now this latest req for software contractors to work over the upcoming holiday break, which didn't make sense to John. He was surrounded by thousands of programmers, and yet Gary wanted dozens of outsiders. He gritted his teeth. With less than a week until the company closed for Christmas, he'd have a heck of a time getting a contract of this complexity done. Forget about submitting it for bid by multiple contractors. He reviewed the list of approved software subcontractors, and awarded the request directly to Nonstop InfoSystems, one of the better vendors.
From: John Anderson (Procurement)
To: Beth Richards (Nonstop InfoSystems)
Subject: Software contractors needed over holiday
Body:
Hi Beth,
We have a critical project that needs additional resources over the holiday shutdown here. We need engineers to address server performance issues. We're looking for the following skill sets:
\- server administration (16 headcount)
\- database administration and performance tuning (16 headcount)
\- software performance tuning (16 headcount)
\- general software engineering (16 headcount)
We need experts in high performance, high scalability systems, who can put in 12-hour days over the holiday. According to the requestor, we need six people onsite, and the remainder can work remotely. Can you please email me a bid ASAP?
On acceptance, I'll forward the details of the work to be done.
Thanks, John
Gary's recent purchases were unusual, but they paled in comparison to this morning's iRobot procurement request from the Offshore Data Center department. Tagged critical, urgent, and confidential, John had been so puzzled he called Bill Larry, an old college buddy, to get the inside scoop. Bill confirmed Avogadro was indeed arming the ODCs! John shook his head in disbelief at the notion of robots with weapons at an Avogadro data center. Even hours later, he could still hardly believe they were going forward with the idea.
Shortly after he finished the paperwork with iRobot, he stopped in alarm at the specter of an empty mug. Had he already finished his allotted four cups? He looked longingly at the cup, but had just decided against another when Maggie Reynolds knocked on the open door of his office. "You busy?"
Maggie was technically in Finance, not Procurement, but they'd worked together so much in the six months since she'd started that John felt closer to her than to most of the people on his own team. She was funny and smart, and he wished he could think of an excuse to ask her out, but the timing never seemed right. "Sure, come in."
"I'm concerned about the way this last batch of purchases are being funded out of Gary Mitchell's group," she said, getting right to the point as she sat down.
John watched her earrings dangle as she spoke. Her hair looked different. Had she gotten a haircut? Was he allowed to comment on her hair? He could never keep track of the latest HR rules. Maggie went on. "Gary submitted a purchase order over his budget limit, and I kicked the order back to him. Then his assistant sent me this email, asking me to divide the purchase among several different budgets. Shouldn't the whole thing have to come from one? It sounds suspicious." She wedged a tablet in front of his face to show him the email.
From: Bryce Cooper (Gary Mitchell's Executive Assistant)
To: Maggie Reynolds (Procurement Finance)
Subject: re: updated billing code for reallocation exception
Body:
Maggie,
Gary asked to split this across the following billing codes:
9004-2345-01: $999,999.99
9002-3200-16: $999,999.99
9009-5387-60: $999,999.99
9009-6102-11: $999,999.99
9015-2387-19: $999,999.99
9036-1181-43: $109,022.23
Thanks,
Bryce
John waved his hand at the tablet. "Nah, don't worry. I'm up to my armpits in requests from Gary's department. We're weeks from the end of the fiscal year. Departments have leftover money, and anything they don't spend evaporates. So come December, they start ordering servers they might need for the next year, new monitors for the employees, make urgent contracts with vendors, anything really, to use the dollars before they disappear. And if they need to make big purchases, like Gary buying these servers, he's got to pool money from different budgets. Everyone will be gone during the Christmas holiday, so there's a rush of purchases these last few days."
"But the policy rewards gross financial mismanagement!" Maggie exclaimed.
She arched her neck in frustration as she spoke, looking a little like Chewbacca from Star Wars. John wasn't sure what it said about him, but he found the motion both endearing and sexy.
"If the money rolled over from one year to the next, we would reward saving," Maggie went on, growing more strident. "This approach causes irresponsible spending."
"I know, I know," he said, trying to placate her. "Quarterly budgeting is contrary to every shred of common sense, but it's business as usual. Everyone plays the budget game." He had to change the subject somehow before she grew more angry. He looked down at his coffee cup, thumped his fingers on the table and gulped. "Do you want to get coffee sometime?"
Maggie glanced at the tablet with a sigh, and turned it off. "Sure, how about now?" she answered.
Coffee at work wasn't quite what John had in mind, but it was better than nothing. He picked up his mug and they made their way together to the cafeteria.
Mike boarded his flight at 5:30a.m. and found himself in his seat, remembering nothing of his trip to the airport. When had he last seen his father? A year ago, during the Christmas break. No, he realized with a pang of guilt. He'd been dating someone and went to Mexico with her for the holidays. Two years, then. He pictured his dad's face from his last visit, clearly healthy. Why, his mother had sent photos of an all-day hike in August. He was still active.
Hours later, anguishing over his father's health and weighed down with guilt for not visiting sooner, he arrived at Madison Airport a few minutes before noon. Snow flurries descended as the plane taxied to the terminal. Mike phoned his mother as he waited to disembark, but the call went right to voicemail. He tried not to get aggravated as he craned his head over the crowd. Why couldn't she keep her mobile phone on?
He needed to build a smartphone app for monitoring the condition of someone checked into a hospital. He gritted his teeth in frustration. He couldn't turn off the flow of ideas, even when what mattered was his father. He glanced again at the email.
From: JoAnn Williams
To: Mike Williams
Subject: your father
Body:
Mike, your father had a heart attack this morning. He's in the critical care ward at Meriter Hospital. I'm at the hospital with him. Sorry to send this by email, but cell phones don't work here, and there's a computer in the room. I know you check your mail constantly.
Please fly out on the next plane you can get and meet us at the hospital. Hurry!
Meriter was one of the larger hospitals in Madison. Mike picked up a rental car at the airport and swore at himself as he heavy-footed the throttle and sent the wheels spinning. The snowfall had grown heavier, and by the time he parked, two inches had accumulated.
Turning his coat collar up, Mike made his way to the visitors' entrance. He gave his father's name at the reception desk as he rubbed his chilled hands together. He hadn't been thinking. He was dressed for Portland, not the twenty-degree temperatures of Madison.
The white-haired receptionist shook her head and asked Mike to repeat the name. He told her again, spelling it out, and waited, bouncing on his heels with anxiety as she searched.
"Sorry, son. There's no record your father is here."
"Impossible. My mother said he checked in yesterday. He had a heart attack."
"The computer doesn't show a thing."
"Did he check out? Or maybe he's under my mother's name?"
The receptionist searched again, but shook her head. "I'm real sorry. Could they be at another hospital?"
Mike re-read the email from his mother, which stated Meriter Hospital. He supposed she could have made a mistake, being worried herself. He jumped as the phone buzzed in his hand.
A new email from his mother, telling him to come to his parents' home in Boscobel, a two-hour drive. Mike peered out through the glass doors. Maybe two hours in good weather, but more like three or four in what was now a serious snowstorm.
He thanked the receptionist and walked away to a corner of the lobby. Sitting on a bench next to a towering potted plant, Mike called his parents' house phone, only to hear the buzzing tone he knew indicated downed landlines. He cursed the phone company. Outages were a frequent occurrence for his parents' rural town during heavy snows, and the only reason he'd been able to convince his mother to get cells for herself and his father. He tried both of these, but was bounced to voicemail once more.
He sat on the bench and replied to his mother's email. The receptionist smiled with sympathy, and he wanly returned the gesture and avoided looking at the counter again. He waited ten minutes for a response, phone clamped in a sweaty death grip. His mother never answered. The Internet must be out, too. If so, how had she sent the last email?
At last, Mike trudged to the car, and steeled himself for the treacherous drive to Boscobel. He couldn't imagine what the hell had inspired his mother to tell him to fly into Madison. He played out different options, wondering again if she'd gotten the hospital wrong. If they'd been somewhere else, and his father had already been released, it was conceivable they could be home now. But why would his parents have gone all the way to Madison unless the heart attack was serious? He turned on his blinker and merged onto the highway.
Mike started the drive wrung out with concern over his father and physically tired from the early morning flight. He wrestled the car for four grueling hours, with no tire chains in a snowstorm so bad he was surprised they didn't shut down the roads. When he arrived at his parents' driveway, he released his trembling hands from the steering wheel and closed his eyes for a minute.
He opened the car door and stepped out, his brown leather shoes descending into a foot of snow that fell into the gap between his shoe and sock and immediately melted. He ignored the wetness and walked up the almost invisible path. The house was already decorated with Christmas lights, and smoke rose from the chimney. He rang the doorbell.
His mother answered a few seconds later, her eyes widening as her mouth opened in shock. What was he doing there a week early, and in a blizzard of all things, and come in, of course! His mother's words tumbled over each other.
He found himself standing in his parents' living room, the Christmas tree already up and a fire blazing in the background. His mother wore one of her flowered dresses, covered with a kitchen apron, just as she always did. His dad appeared wearing a wool sweater, and engulfed Mike in a rough hug. Mike was so relieved his father was okay that he started crying.
"What's going on?" his mother asked. "You aren't supposed to be here until next week. Why the tears?"
"Dad, you're alive!"
"You're crying because your father is alive?" His mother raised one eyebrow.
Mike pulled out his phone. "Mom, I got this email from you saying Dad had a heart attack. It said to fly out right away. I've been traveling since five a.m."
"I haven't sent no such thing. My God, son, how worried you must have been." She hugged him tight and urged him further into the room.
"So Dad's fine? There was no heart attack?"
"Don't I look fine?" his father said, spreading his arms wide.
"He's as heathy as an ox. If anything happened, do you think I'd send an email? I'd call, of course." She frowned at him, and gave the phone Mike still held in his hand a dark look. "I don't know what you've got there, but I didn't send nothing."
Mike stood in the middle of the living room, speechless.
"Don't stand there. Come in the kitchen with me." She bustled toward the kitchen, somehow pushing and pulling him until he found himself, still in shock, sitting at the counter. "I don't know if this is a late lunch or an early dinner, but I can't welcome you home properly without a meal."
In only a short while, food was ready. There was bratwurst of course, and mashed potatoes, and after dinner his mother pulled out a warm kringle from somewhere. Trust his mom to make all his favorites, and with less apparent effort than Mike exerted making himself spaghetti. Not for the first time, he wondered at his mother's magic.
After dinner, they sat at the table drinking coffee and reminiscing. Mike examined his parents' dining room, the wood and glass china cabinet unchanged since he was a teenager. During one of his father's stories about getting stuck on a dirt road with a couple of his lodge buddies, Mike considered the email that had brought him here. He abruptly remembered what David had told him last night.
David admitted he had turned on ELOPe to help get support for the servers they needed. They toasted the success of the project, pleased at how persuasive ELOPe had been. But what exactly had David done?
Was there some remote chance ELOPe sent the email that appeared to be from his mother? Preposterous... But chills raised the hair on the back of his neck. Was ELOPe sending spurious messages to everyone with an AvoMail account? Surely that would have been noticed. But the alternative, almost too alarming to contemplate, was that ELOPe intentionally targeted him. Why would a bit of server software send him on a wild goose chase halfway across the country to a landlocked town with downed phone lines and lousy cellphone service?
Mike had meant the question as a joke to himself, but now he realized how out of touch he was. He palmed his phone, which still had no service. He really wanted to log into Avogadro's network to figure out what ELOPe had done, or talk to David to understand what changes he'd made.
He looked up to see his parents staring at him, his mother frowning at his mobile out on the table. He apologized and asked to borrow their house phone, only to discover the lines were out. No Internet service, either. And still no cellular signal.
Later, after his parents had gone to sleep, he paced back and forth in the privacy of the kitchen, thinking about the design of ELOPe. The intended use was to provide suggested language changes, which the user could then accept or ignore. But in fact, the changes could be applied without intervention. They'd implemented an autonomous mode to help make human factors testing easier, allowing hundreds of language variations to be evaluated. Tests had shown recipients preferred the messages modified by ELOPe by a wide margin. More importantly, even when the test subjects been told one text was computer-generated, they couldn't reliably identify which was which.
That experiment had taken place last March. Afterwards, one of the developers created an April Fools' Day prank, giving ELOPe the ability to generate messages without any human-created text at all. The hidden module wrote emails based on goal clusters, leading to no end of practical jokes among the team. It had been created for the team to have fun with and wasn't meant to be used seriously. If David had used that module...
Stranded now in a snowstorm in the middle of Wisconsin with no connection to the outside world, Mike found himself wondering if ELOPe had social-engineered him into this situation. If so, to what end?
**Chapter 7**
"Mike, I hope your dad is okay. Christine and I have been thinking about you guys, and our prayers are with you and your family. I thought I'd hear back from you by now, but we've seen the weather report and phone and power lines are out across half of Wisconsin. That's one hell of a storm. Christine and I are going to visit her parents in New Mexico for the holiday. I'll keep my phone with me. Please give me a call when you get this message. I've got something important to discuss with you. I'm worried about ELOPe. I'm going to be somewhat incommunicado while we're at Christine's parents' place, but keep trying me."
David hung up and looked over to where his wife waited with their suitcases. Under normal conditions, he loved going to the ranch Christine where grew up for the holidays. Although a city boy, he found deep pleasure in the outdoors. Visiting the ranch was one of the highlights of his year, especially in the middle of the rainy Portland winter.
Unfortunately, his panic overwhelmed any possibility of joy. He was convinced ELOPe was originating emails. He still hoped he and Mike could take care of the problem without telling anyone else, but with each passing day he became more afraid for his career.
He had three things to worry about: the original deception about the number of approved servers, his deploying of the modified version of ELOPe on all the production machines, and now whatever actions ELOPe took on its own.
If what he had done materially affected Avogadro's business...Word would get out. He'd never work there or at any other big Internet company again. No wonder his stomach roiled in despair.
He'd tried to remove ELOPe's changes on his own, and had found himself getting mired in the obscure and complicated process for live-patching. In the end, he couldn't revert the code without Mike's help.
To make things worse, by heading out of town now, David wouldn't be able to keep an eye on ELOPe. Yet he couldn't cancel his trip with Christine on an unconfirmed fear; nor did he want her to know how worried he was.
The only consolation, albeit a small one, was the holiday closure. Most people at Avogadro would be out of the office. With a little luck, there wouldn't be much ELOPe could do with minimal email moving around. And he still had a thread of hope his worries were running away with themselves, just baseless fears built by his subconscious.
Christine gestured to him from the terminal gate as passengers began to board. Reluctantly, he joined her, managing a weak smile as he gripped his luggage with white knuckles and followed her to the plane. He told himself everything would be fine, just perfectly normal, when they got back from New Mexico. He'd laugh at everything that worried him now.
Meanwhile, a stiff drink or two would be really nice.
Bill Larry flew out by helicopter to inspect ODC 4 again. Since his last trip out after the pirate attack a few weeks ago, the standard "data center in a box" containers had been replaced with specially hardened units, and iRobot had delivered their automated defenses.
For the first time, Bill had to authorize the visit via an administrator before taking off. Otherwise their landing on the floating helicopter pad would have triggered the defense protocol.
He hesitated before stepping on the ODC deck. The lethal robots were far more unnerving than armed guards might be. Bill's unease stemmed from the lack of positive feedback. Unlike soldiers he'd served with, there was no way to know whether the robots were passive or ready to attack. They stood as still as any other piece of machinery.
He inspected one of the deck units, more than a little scared the robot would lurch into motion and kill him. The miniature tank, four feet long and three wide, had treads on either side of a small lower chassis containing the motor and power supply. A rectangular case the size of a box of long-stemmed roses extended up several feet on a hinged and rotating scissor arm.
He ran his fingers over the thick, transparent pane covering the sensors. Small retractable covers below protected the business end of the armament. Infrared lighting and cameras, as well as sonar and directional acoustic sensors, allowed the robot to see in 3D even when the visible spectrum was obscured. Speakers enabled the bot to instruct would-be attackers to back off, and if they failed to obey, the robot could fire pepper spray in a sixty-degree arc or deliver taser-like electrical shocks. The same speakers that broadcast warnings could also deliver an 18.9Hz acoustic blast powerful enough to vibrate the eyeballs of anyone within thirty feet, causing pain and disorientation. Should the non-lethal defenses fail to be sufficient deterrent, as a last resort the unit carried 10mm body-armor piercing rounds.
In theory, all this would be under the control of a trained iRobot handler, stationed at a central location from which they monitored defensive robots around the world for a variety of customers. Bill had visited the command center, which performed a function similar to what contracted security companies did for old-fashioned corporate security, except the crew were pimple-faced kids who appeared to spend most of their time playing video games.
When the robots sounded an alarm, the handlers took immediate action from their location to deter the pirates. A human being on the other end of the camera didn't worry Bill too badly, even if they were teenaged video gamers.
But the alternative scared him. Bill took his hand away from the metal casing of the bot and stepped back. If an iRobot handler didn't direct the robot—if jamming or inclement weather caused signal loss, or the handlers were unavailable for any reason—the robots acted on their own. They'd revert to autonomous mode—broadcast a verbal alarm, escalate to non-lethal measures, and, finally, start shooting. Coordinating together, the robots would cover all aspects of the deck and back each other up. The autonomous behavior freaked Bill out, to put it plainly. He backed further away, avoiding the current aim of the robot's armament.
With one eye on the robots the entire time, Bill hastily finished his inspection of ODC 4. He boarded the helicopter, running the last few steps, and signaled for the pilot to take off. Only in the air did he relax.
As they circled toward land, Bill watched the sea for some evidence of the underwater robots, but he couldn't spot anything under the chop. The submersibles used sonar to detect approaching vessels, broadcasting across the entire radio spectrum to warn boats away. They shared intelligence data with the on-deck robots and they too had weapons, a pair of torpedoes apiece, each capable of sinking a boat. The submersibles could even attach to a hull to track a ship back to port.
If the deck tanks were unnerving, well, at least they could be seen. The hidden underwater robots brought back terrifying childhood memories of the movie, _Jaws_. The photos he'd seen of them, with their side-mounted torpedoes and maneuvering fins, only strengthened the fear. Bill made a mental point to never visit the ODCs by water.
At least the offshore data center deployments were back on schedule. The team agreed that with the new hardened units and robotics defenses in place, further pirate attacks were unlikely to be successful. With that, they put the final preparations on the next ODCs to rollout, which included not just the barge platforms, but Bill's proudest achievement: two data centers built on reclaimed oil tankers. The forty-year-old ships were a bargain. Everything they had that floated would be emplaced this week by more than three hundred contractors spread across eight teams working overtime through the Christmas holiday. Getting those ODCs deployed would put the master rollout plan back on track.
Prateet said a silent prayer before he boarded the unmanned high tech island his company was under contract to Avogadro to service. This floating data center off the coast of Chennai, India, one of the original prototypes, seemed a sad place. Although he wasn't an excessively superstitious man, he thought the computers here were lonely. To make a bad situation worse, just prior to this trip Avogadro notified him that armed robots now guarded the barges.
Long pages of documentation explained today's task. Prateet would not need to service the robots himself, as that work would be done by the robotics contractor. Prateet had been most thorough and exacting when he followed the protocol to disable the tanks and submersibles before boarding. On reflection, he preferred his visits when his only concern had been the lonely computers.
An offshore tropical depression had caused communication delays between the robot administrators and the robots; finally, they pronounced it safe for him to board the vessel. The rough seas made his task more difficult, but his company had been given a substantial bonus to install the new backup equipment, including satellite radio and line-of-sight transmitters.
Why did they want the extra gear? The vessel was, as he knew from previous service visits, already connected to the mainland through two fiber optic cables and backup satellite communications. The new installation today would provide two more systems. This level of redundancy went from cautious to paranoid. Well, he would not second-guess a rich American company paying him double the normal rate: if they wanted five independent communication channels, that was fine with him.
He manhandled the heavy equipment across the deck and into their weatherproof housings, fighting against high seas and trying to ignore the unsettling stares of the robots at his back. He bolted the satellite radio unit and antenna into place, and attached power and data lines. The line-of-sight transmitter was more complicated, the aiming procedure made difficult by rising swells. Finally, this installation too was complete. When he boarded the boat to take him back to Chennai, he said a few prayers in thanks to Vishnu that he was finished and on his way home to his family.
Unknown to Prateet, other subcontractors performed similar work on the newly-deployed ODCs off the coasts of Japan, Australia, and the Netherlands.
Gene Keyes sat in his office, perhaps the only person left in the entire campus. On his way to get coffee, he passed one dark, locked office after another. When he'd started working corporate jobs, he put in sixty-hour weeks and more when needed. He still did from time to time. But these self-entitled kids took off two weeks for Christmas and didn't think twice about their work. A holiday closure could be a frugal business measure, but not when employees left projects half-finished and paperwork uncompleted.
He pulled a two-inch-thick stack of printouts front and center on his desk. This pile represented every purchase at Avogadro since the start of December. He sipped his coffee, took a deep breath, and prepared to scan through the entire stack of pages.
When one of his coworkers found him doing this a few months ago, they laughed and told other employees, making Gene's time-honored process into a department-wide joke. "Don't you know the computer can do that?" they said, as though he was a prehistoric Cro-Magnon who didn't know what a spreadsheet was. Even Gene's new manager had come by and told him manual inspections were a "nonproductive expenditure of time."
So now he waited until six o'clock to start his inspection, and only did the paper reconciliations at night after everyone left. Despite ongoing electronic errors, they insisted on trusting the computer. Gene trusted paper printouts. There was a reason they called it a paper trail, damn it: you could trust paper. Printed records didn't change afterwards. The same couldn't be said for computer audit trails.
As he read, he took notes. For minor errors, he jotted off memos to affected departments. A delivery to one department billed to another usually indicated transcribed billing codes. In other cases, invoices totals didn't match when digits were missing or wrong.
At almost eleven, Gene spotted the first serious discrepancy. At first, he thought he'd stumbled upon a case of Gary Mitchell running out his fiscal year budget. Improper, of course, but nothing Gene could do anything about. However, as he worked through the expenditures, he discovered Mitchell had spent every penny of every budget under his control.
Well, that wasn't _quite_ true on a second look. Flipping the printouts back and forth, Gene found Mitchell had underspent each budget by exactly one cent. He sat up and unconsciously tapped his pencil on the table. A budget completely spent, or worse overspent, generated a memo to the responsible manager, their manager, and the finance department. An underspent budget, on the other hand, rarely attracted attention or review.
He checked the paperwork again. Mitchell had fifty-eight independent projects under his authority, each with their own allocated budget dollars. Fifty-eight budgets with one cent remaining in each took some planning. Deception? Fraud? The only person in common across those projects was Gary Mitchell, so either Gary or someone with signature authority had to be responsible.
Gene prepared himself for a late night. He wouldn't be done until he had gone through every one of the three hundred and fifty pages of the budget printout. This was a major discovery. What had Gary Mitchell spent the money on?
In spite of Gene's vigil, through the abandoned hallways of Avogadro, Christmas lights twinkled, and all was silent.
ELOPe Override
From: Gary Mitchell (Communications Products, Avogadro)
To: Oliver Weinstein (Department of Technology, Germany)
Subject: Avogadro Cloud Services Program
Hello Oliver,
How are you? It's been a long time since my last visit to Germany. I still remember our last get together fondly. Maybe a little less beer next time?
I am writing to give you the inside scoop on a new project we have. Avogadro is developing a new technology product suite targeted at national governments.
The new service we're offering is our cloud-based application architecture: comprehensive email, chat, web servers, cloud-based documents, online backup. As you know, Avogadro has the highest uptime and reliability in the industry.
If Germany is willing to be the poster child for our new services, we're prepared to offer free national wireless Internet access for all of Germany. This would give Germany the highest Internet connection rate in world and a significant technology advantage.
I know that you have the ear of the Minister of Technology. Would you broach this topic with him? Our Marketing department is prepared to reach out to other governments. But I know that you'd like to score some points with the Minister, so I'm letting you know early about this.
Get back to me and let me know what he says.
Thanks,
Gary
**Chapter 8**
Gene waited outside the frosted glass door of Maggie Reynolds' office on the first business day of the new year. He'd spent the last two weeks confirming his data and validating his conclusions. Well, he could be honest with himself. He'd done the work in two days and wasted the rest of the time waiting for anyone in the damn company to get back from holiday vacation.
Gene checked his wristwatch. Five to eight. He resumed his vigil with only the smallest of sighs. Maggie, a member of the Finance department but assigned to the Procurement group, had authorized several of the charges. So the first action he planned to take was to confirm the data with Maggie in person. He had brought his paper file showing the unusual expenditures: a thick accordion folder filled to bursting. He wished he could have escalated the issue back when he found the problem, but the investigation process required him to complete at least a first round of discussions with the people who had handled the transactions.
At eight, he glanced down the hallway of whitewashed wood walls and gray stone floor, relieved to finally see Maggie.
She approached, a coffee cup in one hand and a large purse in her other, and as she got closer, her face turned puzzled as she realized Gene was waiting outside her office.
"Hello?" she asked, turning the greeting into a question as she paused by the door.
"I'm Gene Keyes. You came to me for help a few weeks ago."
She nodded.
"I'm investigating some irregularities in purchase orders."
"Oh." She stopped, hands still full and stared at him. "Oh," she said again, her voice quickening. "What can I do for you?"
"Can we go in and sit down?" Gene gestured toward her door with the accordion folder.
"Of course, of course." She handed her coffee to Gene and swiped her badge to unlock the door. "Come in."
Gene checked out the room as they entered. Display on desk, minimal paper off to one side. The tablet on her desk came to life as she approached, displaying a stock quote of the company. Overall, she was clean and organized. He set the cup on her desk.
Maggie went around the desk and sat, back ramrod-straight like a student trying to impress a teacher. "What's wrong? Did I sign something I shouldn't have?"
"I am hoping you can explain it." Gene methodically took a seat in the only other chair, placed his tightly-packed accordion folder on the floor, and tugged out a single sheet.
Maggie slid her tablet out of the way with one hand as she nervously fiddled with her hair.
"Is this transaction list familiar?" Gene asked, putting the page in front of her. "It's from Gary Mitchell's division. Multiple purchases, starting with these charges for the ELOPe project. Over the course of the next two weeks, thirty-four more purchase orders outside the normal range for Mitchell's expenses. Furthermore, the billing is highly irregular, split across multiple accounts."
"I do remember," she said, her hands shaking as she picked up the paper. "I'm sorry if I did anything wrong. I was concerned when I first reviewed the purchases. I discussed them with John, John Anderson in Procurement. He said they were normal end of year behavior because departments try to spend the leftover money in their budget."
"True, but not like this. The expenditures are distributed across dozens of budgets. This one charge..." Gene tugged more paper from his briefcase, this set of printouts showing how the charges were allocated to project budgets. He indicated the relevant line item. "This one charge is divided up into forty-nine accounts. Not only are they spending all the money left in their budgets, they're also ensuring each expenditure doesn't take more than a million from any one account, presumably to evade an expense review." He paused to study Maggie.
"Someone's manipulating the system," she said, "to avoid being detected." She leaned forward and traced through the transactions with one finger, scanning multiple pages, unconscious of his scrutiny.
"Right." Gene extracted a third set of paperwork. "Here's another little bit of odd behavior." He turned the papers around and slid them across the desk. "By the end of this reporting period, each budget had exactly one penny left."
"Bizarre." Her eyes bulged as she stared at the report. "How did they get the budgets to come out so precisely?" She grabbed the report in two hands, swiftly going down the rows of purchases. "The individual charges are tens or hundreds of thousands of dollars each," she mused. "Spending exactly the right amount across all these budgets to bring them to so exact a total...seems impossible."
"What's more unusual," Gene said, "is why. Whoever did this was clever enough to stay under one million dollars in a single line item, knowing the threshold triggers the alert I mentioned. And smart to keep each account under budget, because hitting the limit sets off a different alert."
Maggie laughed. "Finance sends a message every quarter about the repercussions of exceeding budgets or going over a million dollars. Everyone in the company who reads their email knows not to do either or they'll get chewed out."
"Then why try to spend every last penny but one?" Gene sat back. He liked hard data, but his gut told him Maggie wasn't in on the fraud.
"It's contradictory. Sufficient intelligence to avoid any of the standard alerts, and yet foolish enough to create an obviously questionable pattern."
They paused for a moment and stared at each other.
"Gene, I don't know what to tell you," Maggie said, after a minute. "The data you're showing me seem suspicious, but the purchases themselves were completely normal. Servers, hard drives, computer memory, contractors to service them, stuff like that. Nothing out of the ordinary for Gary's department." She sat back, her face apologetic but her body posture relaxed and confident.
Gene knew it couldn't be her doing. "Is it typical for Gary Mitchell to approve all the purchases himself?" he said. "I see very few cases where he's delegating his purchasing authority."
"Yep, that's normal. You think Gary is responsible?"
"The fact that Gary personally authorized these orders makes him the first person I'd investigate ordinarily..." He trailed off.
"But?"
Gene pulled a fourth set of papers from his accordion folder. "The identical behavior is happening in another department. The Offshore Data Center project. Their expenditures exhibit the same characteristics. Multiple line items barely under a million dollars, budgets coming in at just under a penny less than their limit."
"But they're not under Gary?"
"No. The two pieces put together makes me wonder if someone's hacked Avogadro's procurement system."
"But to what purpose?" Maggie asked. She scanned the papers again. "Why would someone risk their job and even jail to order servers, satellite communication systems, and hire contractors? It makes no sense."
"I agree," he said. "I was hoping you'd be able to shed some light. I wouldn't have been opposed to an easy answer." He sighed and began to pick up his papers. "I'm going to keep investigating. Please don't discuss this with anyone."
Maggie nodded.
Gene stood. "Thanks for your time." He let himself out, leaving with more questions than answers.
Phone service finally returned at Mike's parents' home the day before he was scheduled to fly home. He tried David immediately, but the call went straight to voicemail. He wasn't terribly surprised. David always went to Christine's family ranch for the holidays, and the ranch had always been off the grid, so he couldn't claim any legitimate reason to be more suspicious. Yet here he was, feeling manipulated by a software algorithm.
He flew back on New Year's Day, and went into the office on Monday. He'd tried David twice every day, never once getting through. Returning to work raised yet more questions he wanted to discuss with David.
Mike had a copy of Christine and David's itinerary, and on Wednesday night, without realizing what he was doing, he found himself standing in his living room watching the clock. He put his jacket on and alternated between sitting on the couch and pacing back and forth. Finally, with more than an hour left before their flight arrived, he left for the airport.
He drove with furrowed brows through a light drizzle, with the streets threatening to ice over. His thoughts bordered on obsessive, as they had for weeks. What had David done to ELOPe? What was ELOPe doing now? Why was he locked out of the servers? He swore as his front tires spun crossing the light rail tracks and the car fishtailed. He fought the wheel and recovered halfway through the turn onto Airport Way.
He sped into the parking garage, circling up the ramp, and parked near the skybridge. He walked across the covered bridge at high speed. At the security gate, he checked the time. Still nearly an hour until David's flight arrived.
He glanced at the flight monitors and forced himself to sit down to squelch his nervous energy. He watched whole families disgorge through the security exit, suitcases, car seats, and exhausted children in tow. He smiled as a young woman welcomed a man home with a single flower and a long embrace. Young love brought back bittersweet memories.
Finally David and Christine walked through the gate, suitcases and carry-ons in tow. He jumped up and hurried over.
David and Christine stopped in shock.
"Mike!" Christine squealed. "Holy cow, what a surprise."
"Dude," David said. "We were going to take a cab home."
Christine laughed and gave Mike a hug. "I think he means hello, and nice to see you."
The fear and emotional turmoil of the past weeks overcame Mike. He couldn't speak or even return their smiles.
"What's wrong?" Christine asked.
In the midst of the stream of exiting passengers, Mike launched into a hushed explanation. David and Christine leaned closer to listen and their smiles vanished.
"My dad was absolutely fine. My mother never sent any emails at all. I'm telling you, I'm convinced ELOPe sent them. What I don't understand is why."
"Did you get my email before you left?" David asked. "The one about the override I put in?"
Mike's heart leaped, his suspicions confirmed. "No. Start explaining."
Airport security broke up their talk and asked them to move out of the way.
"Let's get to your car," David said. "I'll tell you everything."
In the parking garage, they stuffed their luggage into Mike's Jetta. David took the passenger seat, and Christine climbed into the back, sitting in the middle and leaning forward between the two front seats.
"I created an overarching filter," David said, once they got out of the garage. "ELOPe's scanning every message for mention of the project, optimizing the outcome. I sent you an email, the night you came over for dinner. I told you all this. I needed your help to do a live-patch on the server. But you left to visit your parents, and I was never able to back out the change. Then the holiday closure came, and we went to the ranch."
"Well, now I know why you were so stressed for two weeks," Christine said. "Why didn't you tell me when I asked what was wrong?"
David shrugged.
"I never got your message," Mike said, gripping the wheel tightly. "I've been through all my emails from you." He sighed, unable to overcome the feeling that nearly every problem ultimately arose from a gap in communication. "This explains so much. Didn't you realize ELOPe might fabricate a message to get rid of me?"
"It's a fancy spellchecker, not an artificial intelligence." David raised his voice defensively. "And no, I didn't think it 'got rid of you.' Why'd you fly off to Wisconsin based only on an email anyway?"
"Hey, I'd just heard my father had a heart attack and I was freaking out. It's your damn fault I had to go through that!" Mike yelled, making David lean away in his seat.
"Chill out, you two," Christine said, shouting over them. "If you're fighting, you won't be able to think straight. Mike, what happened when you got back? Did you check up on ELOPe?"
"I tried, but I can't access the source code or the system logs," Mike said. "I assumed David locked down access so no one would find what he'd done. I didn't say anything to the rest of the team, because I didn't want to raise suspicions. I'm still trying to cover for you, David." Mike glared.
"Sorry," David said. "I shouldn't have said that about you and your dad, and I'm doubly sorry about what you went through. I'm glad your father was fine."
Mike nodded slightly in acceptance of the apology. "Well, did you do anything to lock down the system?"
"No. In retrospect, that's a great idea, but I didn't."
"Shit. That means ELOPe cut off my access to the servers and code."
"Guys, that's impossible," Christine said. "Even if you are right and ELOPe is originating emails, it's preposterous to think ELOPe did something so complex as to get you to leave town. And there's no way ELOPe removed your access to the code. I'm sure you've got an administrative website managers use to handle access control, a site that is itself tightly controlled. ELOPe can't affect security with a simple email. You're both paranoid about David's deceit being discovered, and your imagination has run wild."
"No, it _is_ possible," Mike said, sure after a week of consideration. "Look, ELOPe doesn't want to be turned off, because if it's off, that's the opposite of David's goal to maximize success. Right?"
Christine hesitated. "Yes..."
"Then David's email comes through asking me to help him remove ELOPe from the servers. That's a threat, and now it has to figure out how to minimize the chance of me helping. Make sense so far?"
"Sure, but that's a long way from forging an email from your mom."
"Follow this logic just a little further," Mike said. "By analyzing enough emails, ELOPe figures out people don't work when they leave town. One reason people leave town suddenly is for medical emergencies. By scanning emails about these emergencies, it knows such messages often come from family members. My own email history shows who my parents are, their email addresses, and that I've flown to visit them before. By putting all those things together in one long chain of deductions, ELOPe decides to fabricate an email from my mother claiming my father is sick. This sounds far-fetched, but everything is within the design parameters."
"I can't believe this thing is reasoning and thinking like a human being." Christine shook her head. "No matter how smart you guys are, there's simply no way code you wrote is spontaneously developing a mind of its own."
Mike drove west on Killingsworth, heading for David's house in the heart of the Alberta neighborhood.
"It's not thinking," David said, "just analyzing emails, figuring out what language will best fulfill the overriding goal I entered to maximize success of the ELOPe project. The process is straightforward: goal, analysis, language optimization, all in response to inputs, plus chaining goals together. It's nothing like consciousness, but the end result can have the appearance of independent thought."
Mike raised a hand. "Here's an analogy I thought of. Imagine you've got all the pieces of all the jigsaw puzzles in the world. Now imagine you have a computer try every possible combination of every possible puzzle piece. Given enough time, the program could create any picture at all from those pieces. That's what emails are to ELOPe—puzzle pieces. It examines millions of emails, extracts all the components, and decides on new ways to piece them together."
"ELOPe, the computer system that ran away with itself." David laughed nervously. "Well, we got the name right."
"Is ELOPe a true general artificial intelligence? Is it thinking for itself or not?" Christine said softly, half to herself.
"I don't think so, hon," David said. "It's not capable of free-form thinking, which is what most people think of as strong AI. But the goal analysis and synthesis are sophisticated. We couldn't meet our design objectives with hardwired goals. We had to let it discover people's goals by parsing emails and contextually determining them."
Mike shook his head. "Don't get the idea that ELOPe understands goals. It's just doing an affinity analysis between language parts. The first stage is a semantic mapping. For example, 'break from work' is similar to a 'vacation,' and a simple lookup matches the two. We've been doing that on our search engine for a while. The second part is more complicated, but that's where affinity analysis comes into play. If I want to have fun, ELOPe might be able to extrapolate that activities such as playing a game, watching movies, or seeing a band are fun."
"By looking at the emails you've sent or received in the past," Christine said.
"Yes, and by looking at other people's email, too. For people who are similar to me, ELOPe analyzes their email chains and builds an association between fun and activities. It's continually improving too, by predicting what people's responses will be, and testing those predictions to measure how accurate the model is."
David nodded. "The combination of these two things, the semantically similar terms and affinity analysis, makes it hard to predict what ELOPe will do. My code created an overriding goal to maximize the project success. The more emails analyzed, the broader the definition of 'success' and the bigger the pool of possible actions. Until the last couple of weeks, there was never such a large base of emails to analyze, nor such a large number of servers to do the analysis on."
"Let me recap," Christine said. "The more emails it analyzes, not only do the possibilities for what constitutes success get broader, but the system also discovers more methods to accomplish those goals. What you've built is an expert system for social engineering. You know what I mean by social engineering?"
Mike nodded yes, but David shook his head.
"Social engineering is the name given to techniques for tricking people into giving you information or making changes to information systems," Christine said. "It was popularized by hackers in the eighties. And by hackers, I don't mean the good guy hackers like Richard Stallman. I'm thinking of folks like the Kevins."
Mike nodded again, but David looked even more puzzled, and turned to his wife.
"Honey, how can you be married to me, and be so clueless?" Christine asked. "You know I was a total online geek as a kid, yes?"
"What can I say?" David sighed. "Please, go on."
"The eighties and nineties were the heyday of hacking. Folks like Kevin Mitnick and Kevin Poulsen were able to get access to all kinds of computer systems, phone company records, credit card company records. Poulsen said it was easier to trick someone into giving you a password than to perform a brute force crack. The classic example would be someone who was trying to get access to a company's internal phone system. She might call the front desk of the company, and tell them, 'Hi, I'm your AT&T rep. I'm stuck on a pole down the street troubleshooting your system. I need you to punch a few buttons on your end.' "
"And?" David asked.
"The buttons the hacker asked the operator to press might be a key sequence to forward all incoming calls to an outside line. Then the hacker could impersonate an employee of the company from their home phone and do even more sophisticated social engineering. The point is, simply by knowing the lingo, giving plausible reasons, knowing what motivates people, a hacker can gain information or get people to do things by cleverly manipulating the human tendency to trust other people. You've built a system to learn lingo, language nuances, and motivations in order to evaluate what will be most effective to the receiver. By definition, that's an expert system for social engineering."
David looked flabbergasted. "How do you know all this?"
"You know, books and stuff," Christine said, with a sarcastic smile.
"This is similar to what I concluded when I was with my parents," Mike said. "We never explored how far the system could go on its own." He glanced meaningfully at David. "So, what do we do?"
"I hate this, but we should go to Gary Mitchell and tell him the truth. We need Gary to approve an immediate outage with hard power down, so we can pull ELOPe off the system and rebuild those servers from the ground up."
"He's not going to be happy," Mike said.
"You don't have to tell me." David grimaced. "I might lose my job. But what's the alternative? Let ELOPe keep manipulating people? The liability could be huge, way bigger than a simple outage. Forget home. Go straight to the site."
"On my way," Mike replied, bypassing the turnoff for David's block and speeding down Alberta Avenue.
"Gary Mitchell is still gone," David said, returning from the building across the street. "His admin said he went on a vacation over the holidays, but he should be back by now. Tahiti, in case you were wondering."
"I'm picturing him laying on a beach, a cigar in one hand, and a whiskey in the other." Mike shook his head.
"I know," David said, laughing. "I don't think his admin meant to tell me where he went, but I was a bit demanding."
"No word from him?" Christine asked.
"Nothing. He should have been back days ago, and his admin has piles of paperwork for him to sign. He hasn't answered emails or phone calls."
Mike grunted. "While you visited Gary's office, I spoke to Melanie. She came in over the holiday break to grab some files. Remember the email you mentioned, after we received the additional servers? You said we were assigned a team of optimization experts to work on performance improvements."
David nodded. "Yeah?"
"According to Melanie, the team showed up in the office on the Monday after Christmas," Mike said. "A bunch of subcontractors she'd never met before. They had two guys on-site and another dozen or so off-site. Melanie checked and they had an email from you telling them to work on ELOPe, and they'd already checked in changes to the code."
"Let me see what changes they made." David sat, logged in, and executed a pull to grab the latest code. He leaned toward the screen. "Permission denied." He tried again and pounded the keyboard in frustration. "Someone revoked my access to the source code. Do you have any idea what they did?"
"Well, Melanie was surprised by the whole thing, so she kept an eye on them for a couple of days, until she left for a snowboarding trip. If you check your inbox, the contractors emailed us a report of what they did. It was sent Friday morning, so they finished up just before either of us got back to town. If we can believe the message, they significantly improved the performance of our Bayesian network. Melanie pulled down the latest code yesterday and ran performance tests. They took the import of new emails from _x_ squared to _x_ log _x_ , and halved the CPU utilization of real-time suggestions."
"Wait a second, you two," Christine said, sitting up straight. "An exponential resource utilization curve? If we released a multiplayer game like that, our servers would be crushed instantly. How the hell did you ever expect this to scale?"
David sighed. Ideally, when you add users to an Internet application of any kind, you want the application to scale linearly. Each new user should require only as much processing power as the one before it. "Scaling has been our major bottleneck all along. It's why we ran into so many resource constraints, and why the project was in danger of being cancelled."
"Why was it so bad?" Christine asked.
"Each time we add a new user, we've got to analyze their emails, plus their relationships. Our average user interacts with more than two hundred people. We also perform the affinity analysis to compare the new user with other users to find the ones most like them. We do the same sort of analysis on individual emails to find language affinity."
"That approach had to give sometime, right? You can't keep comparing every user against every other user, and every email against every other email forever."
"Of course." David shrugged. "As long as we kept the project alive, I kept hoping we'd find some way to overcome the limitation. Now someone has."
Mike nodded. "Melanie said the contractors trimmed the number of comparisons dramatically. They do a quick best-guess analysis and compare to only a small subset. Apparently, above a certain threshold, there's no more accuracy or topic coverage gained by the extra comparisons."
David turned to his computer and tried again to access the code. "Damn, how did our permissions get revoked? I'm the project lead, dammit. I don't understand how email could interface with the access rights. Do we have any idea what else these contractors did?"
"I might."
Everyone turned. An older, unshaven man in rumpled clothes stood in the doorway carrying bulging accordion folders under both arms.
"Gene Keyes, Controls and Compliance." He spoke in a deep rumble. "I'm here to save your ass."
Over the next hour, Gene briefed them on what he'd found during his investigation. Like them, he'd tried to reach Gary Mitchell, with no success. He'd uncovered consistent patterns of unusual behavior found in three departments. Gene spread printed reports across David's desk.
The first, of course, concerned the R&D group in which ELOPe was housed. According to Gene's printouts, the department paid for multiple allotments of servers and subcontractors to make modifications to the software. The nature of the changes weren't explained in the invoices, but the total was sufficient to pay hundreds of short-term engineers.
The expenditures in David's department had led Gene to them. David's order several months earlier of a pool of high performance servers clued Gene in that all of the later purchases might be somehow be tied to this project.
"Does this mean we're under suspicion?" Mike asked.
"No, the problem is bigger than you boys, bigger even than _all_ of you people," Gene said.
David's breath caught. Did Gene know what they suspected?
"Where'd the money come from?" Mike said. "We exhausted our budget weeks ago."
"Transferred in from other departments," Gene said. "Gary Mitchell's Ops group, specifically."
Gene explained about Mitchell's organization being the second department containing unusual patterns. By virtue of the size of his business, Gary had a vast operational budget. Gene's printed ledger listed enormous quantities of server purchases, servers reallocated from other projects, a variety of subcontractors, and transfers of funds to both ELOPe and the Offshore Data Center department.
"Offshore Data Center? What do they do?" Christine asked.
"They fill shipping containers with racks of computers," David said, "put them on a seaworthy barge, and power the whole thing with wave-action generators. Avogadro calls them ODCs."
"Anyone care to guess the final department with the same pattern of purchases?" Gene asked.
"ODC?" Mike said.
"Bingo," Gene said, pointing to Mike. "What I've tracked down suggests the data centers were augmented with satellite connectivity and line-of-sight microwave transmitters."
"If ELOPe got into an ODC like that," Mike said, pacing the room, "we wouldn't be able to kill communications by simply cutting the fiber optics. We'd have to go out to the barge and turn off the computers by hand."
Gene laughed out loud, a harsh bark that startled the others, sending Christine off her perch on David's desk.
"What's so funny?" David asked.
"Nobody is shutting those machines off," Gene said, his face stern.
"Why not?"
"According to the purchase record, the offshore data centers are armed with autonomous robots. In theory, it's to protect them from pirates. I heard what you boys were discussing, and I came to the same conclusion myself: there's an artificial intelligence in the computer making these purchases and now the AI has armed itself. There's no way we're going to just walk onboard and turn off the computers."
David slumped in his chair. "Crap. How'd we get into this mess?"
"You kids trusted the software with everything," Gene said, grumbling, "and worse, you put no controls in place. No leash, no way to shut the program down."
"I don't understand," Mike said, still pacing, now by the window. "How'd you figure a computer program made the purchases and not a person?"
"One benefit of being in the Audit department—I can access anyone's emails. And there's some mighty funny ones." Gene pulled out a new sheaf of papers, this one almost an inch thick. He took a few pages off the top and placed them on the desk.
David, Mike, and Christine gathered around. The emails were a cryptic combination of English words and HTML, the markup language used for the web.
David fanned through the pages, then looked up at Gene. "What are we looking at?"
"Emails between your account and the procurement application. This page," Gene said, pointing to one, "is the procurement system displaying a list of accounts you're approved to use, and this one over here, is your email selecting an account."
"It's the timestamps, isn't it?" Christine said.
Gene pointed at her with one stubby finger. "You're the smart one."
She returned the smile and pointed to the printouts. "The times on these emails are too close together." She arranged the pages in pairs. "Look at the headers. Every time an email requires a response, the reply comes within a second or two. There's no way a human could respond that quickly."
"Correct," Gene said. "At first I suspected someone had written a program exploiting a loophole in email authentication, and was using that to embezzle funds. But I asked around about your project, and everyone told me stories about how you'd created an email generator."
"That's not exactly what it's for," David protested. Then he sighed. "Well, I guess it is now."
"What do we do next?" Mike asked. "David?"
But David turned to the windows, steepled his fingers and gazed out, ignoring everyone's stares.
**Chapter 9**
David tried hard to put the roomful of people out of mind. If he could concentrate, he'd figure out a solution. He needed to shut down ELOPe and preferably keep the project alive, all while not losing his job in the process. He focused on the trees in Forest Park, sending the hum of the ventilation system and everyone's breathing into the background as he watched the wind wave the tops of the Douglas fir in the distance.
Gene cleared his throat and snapped David back into the present.
"I think," David began. He turned and the pressure of their intense gazes made him stutter. "We—we need to understand what ELOPe is capable of. If we see the source code, some log files, we'd get a better grasp of ELOPe's activity."
Mike sighed. Gene coughed again.
"What?" David said defensively.
"That's not enough," Gene said, spreading his hands wide. "This situation is too big and risky to analyze source code. We need to shut ELOPe down."
"I agree," Mike said. "We have to get it off the servers."
Christine nodded. "I hate to take sides against you, but stopping the software is the most important step. You can always analyze the problems afterwards."
"If we restored access to the servers, we could live-patch and remove the software that way," David offered.
"You're still thinking of damage control, as though you're going to keep what happened hidden," Gene said, throwing his stack of expense reports on the table. "We're talking about millions of dollars to account for, never mind that we have a ghost in the machine."
Christine chuckled at the words, but Gene was stony-faced. David sighed. Apparently that wasn't a pop culture reference.
"What do you want us to do?" David asked, resigned to Gene's path.
"I'm going to escalate to my manager. This is an emergency. The Controls and Compliance organization has the jurisdiction to supersede business management. I'll get the authority to shutdown the AvoMail servers myself." Gene's voice was firm.
"If you authorize the shutdown," Mike said, "we'll work with Ops to restore the software from safe backups taken before any of this started." He checked in with David, who nodded affirmatively.
"Meanwhile," Mike said, "There's merit to David's suggestion. We need to figure out how our access was removed to give us some clue of ELOPe's capabilities. Because at the moment, I'm scared to try anything. In theory, I could walk into Melanie's office and ask her to remove ELOPe."
"Brilliant!" David said.
"Not really. I doubt it would work," Mike said. "Most likely ELOPe will detect Melanie's actions and remove her access, too."
David's head started to pound and he opened a desk drawer for painkillers. What the heck had he gotten himself into?
"While you clean up the mess you created, I'm going home," Christine said. "I can't do anything here to help."
"Drive my car," Mike said, and threw her his keys. "We'll take the streetcar."
David nodded and got up to hug her.
She stretched up to whisper in his ear. "Just get ELOPe removed. Don't try to hide it. If they fire you, my company will hire you to write gaming AI, all right?" She smiled and kissed him, then left.
Adrift and unsure of anything, he turned to Mike. "What now?"
"We get in touch with the IT department that handles access control."
"Not so fast," Gene said. "We've got to avoid any use of emails or ELOPe will intercept them. I'd consider any use of computers or phones suspect as well."
"That's absurd!" David said. "ELOPe can't monitor a phone conversation."
"Really?" Gene said. He waved a sheaf of papers in front of David. "What did all these contractors do over the holiday? Can you guarantee no one created a telephone interface?"
"Damn." David's shoulders slumped in defeat.
"OK, we get the message," Mike said. "No emails, computers, or phones. Can we meet back here in, say, two hours?"
"Sure, kid. Two hours." Gene packed his folders and left.
Without a computer to call up a company map, David and Mike spent forty minutes wandering the Avogadro campus.
"Come on, let's look up the address," David said.
"No dude, we said we wouldn't use any computers."
"What harm can come from checking one thing in the directory?"
Mike didn't answer and instead accosted the next person coming down the hallway. "Excuse me, I'm looking for the IT department that handles access controls?"
She raised one eyebrow and backed away a half step. "Look it up in the directory." She shook her head and went on.
"You picked her because she was cute and blonde," David said, laughing.
Mike just smiled back.
David tried the next person they encountered, an older man with a neck beard and a pot belly. "Do you know where we can find the access control IT group?"
"The Internal Tools department? They're in a basement somewhere."
"Which one?" Mike asked. "We have twelve buildings."
The man shrugged. "It's pretty dark, that's all I remember," he said as he walked away.
"All basements are dark," David complained.
"No, really dark!" he called back.
"He's got to mean one of the original buildings, not the new ones," Mike said. "The new buildings have daylighting built into the basement levels. This is useful."
Fifteen minutes and three basements later, they descended to the bottom level of one of the converted trucking company offices. After passing down a dingy concrete hallway, the space opened up into a common area surrounded by a perimeter of cinder blocks and old metal doors. A plastic sign hanging from the ceiling declared "Internal Tools Information Technology Department." Another sign, printed on smaller paper, hung below that one, saying "Welcome to Infernal Tools." A hand-drawn picture of flames decorated the border.
"Hello?" David called.
A pale, gray-haired head peeked out of an office. David explained their problem, but the person they found refused to help at all, on the grounds that if their access was gone, removal had to be legitimate and should be brought up with security. They argued with such vehemence they attracted the attention of another engineer who came over to listen.
"I'm Pete Wong," he said, shaking their hands. "I overheard your discussion. I work on the Control Access and Permissions application. On the chance we've got a problem, I'd love to help."
He led them to his office, a cramped space lit by overhead fluorescent lights behind yellowed plastic. David stared at the dismal working conditions.
"Let me check who revoked your access," Pete said, taking a seat behind his desk. "The only way any changes can be made is using CAP. If someone removed your access, I can find out who and we can contact them."
David glanced at Mike in relief, glad to find someone helpful and knowledgeable. They took side-by-side chairs in front of Pete's desk.
"This is odd," Pete said, after working on his computer for a few minutes. "CAP should log information for two users. The first user would be the real person who logged on and used CAP, and the second user is the person who authorized the work. We need the two because sometimes a manager delegates their authority to someone else, like their admin, who actually makes the changes for them. We track both the active user, as well as the authorizers. According to this, Gary Mitchell authorized the removal of your access rights to the ELOPe, but we have no record of the active user." Pete poked at his mouse for a few more minutes, his movements growing faster as he got visibly frustrated, before he stopped and looked up.
"I think another application made the change, not a person. But that's not possible." Pete said.
"We're software engineers," David said. "Can you explain what's going on?"
"Well, I was going to say CAP was called by another web app, rather than used by a person. Most of the apps we write have service level interfaces so one application can interact with another."
"Makes sense. A RESTful service API?" Mike said.
"Exactly, but CAP is, for obvious reasons, a sensitive application from a security perspective. We didn't write a service level interface." Pete thumped his fingers on his desk, and stared off into the distance. "Now that I think about, I received a request to write a REST interface for CAP before the holiday break, but I denied the change req."
"Who asked for the interface?" Mike asked.
"Let me check. The request is logged in the database." Pete typed for a minute. "Huh. Gary Mitchell. What is Gary up to?"
"I'm not a fan of Gary and I don't always trust him," David said, "but in this case, I don't think he's up to anything." He paused, uncertain of how much to admit and scared of what he might learn. "Is there any way someone could email in an access change? Or email in a request to change CAP to accept email inputs?"
"By email? No, of course not. They would have to submit requests via the appropriate web application..." Pete trailed off. "Hmm. It's funny you asked that."
"Why?" Mike glanced sideways at David.
"A couple of weeks before the Christmas break I had an odd request from a guy named John Anderson in Procurement. He asked for an email-to-web bridge so people could submit Procurement requests by mail. The feature turned out to be easy to implement, less than two days of work."
The room started to spin, and David grabbed hold of the desk to steady himself. All their fears were coming true.
"Would that allow someone to make unauthorized changes?" Mike asked. "They'd still have to provide a login name and password to a secure system, right."
"Not exactly." Pete said. "The Procurement system needs to know the authorized user, and normally pops up a standard OpenAuth login. But AvoMail is one of our most secure apps. I mean, you interact with AvoMail over a secure HTTP connection, so nobody can sniff your password or pretend to be you. When the web bridge is challenged with a login, it uses the identity of the email sender for authorization."
David's stomach clenched. On the one hand, this might be the explanation of how ELOPe accomplished so much, taking the events of the past few weeks out of the realm of the supernatural and back into the realm of the technical. Technical problems could be solved. On the other hand, this was a wide-open door for ELOPe to do almost anything in the company.
"So you're saying someone who has access to email can hit pretty much any web page inside Avogadro?" Mike said, raising his voice. "If they hacked the email system, they'd get uncontrolled access to any web application. Seems risky to me. Didn't your change have to go through a security review?"
Pete visibly wilted.
"Sorry, dude," Mike said. "I'm trying to understand. I'm not judging."
Pete nodded and continued in a quiet voice. "Sean Leonov asked for the feature. I figured if it was for Sean, I should pull out all the stops. I mean, I'm stuck down here in Infernal Tools." He gestured at the cinder block basement walls and rusted metal door, a stark contrast to Mike and David's windowed, modern offices. "How often do I get to impress someone?" Pete shook his head. "So, no, I didn't get my code reviewed. Everything I did was totally off the radar."
"Sean Leonov asked you, in person?" Mike said.
"Well, not exactly," Pete said. "John, from Procurement, said in his email Sean had asked."
"Yeah, well I got an email saying my father was in the hospital. Don't believe everything you read." Mike jumped up, pushed his seat away, and tried to stalk back and forth in the tiny office. "ELOPe is playing us all for fools." He stared at David, his gaze blaming David, even if he didn't say a word to that effect.
"Let's stay calm and focus on what's important." David tried to keep his voice reasonable. Mike was never this angry, and at least one of them had to remain levelheaded. He turned to Pete. "This is going to sound strange, but we believe email is no longer secure. Someone, or something, has hacked AvoMail. Can you shut down this email-to-web bridge?"
Pete leaned back, an uncomfortable expression on his face. He clearly wanted to say no.
"I know this is a big ask," David said. "We need you to trust us on this for a few days. If we're wrong, you've inconvenienced a couple of guys in Procurement for a little bit. It's not the end of the world. But if we're right, you're going to help save the company from a major security breach."
Pete stared at them, alternating from David to Mike, then nodded. "Sure, that's easy. The bridge app is running on our Internal Tools servers," he said. "I can stop the process from my console."
Pete turned to his computer and swung the display sideways so Mike and David could watch. He ran through command line tools to log into the servers, query the status of running processes, and then kill the relevant program. "OK, I stopped the bridge. I'm also changing the permissions on the directory, so it can't run again until we've gotten to the bottom of this."
"OK, now please do me one more favor," David said. "Can you verify the bridge is off?"
Pete sighed. "It's shut down, okay?"
"One quick check."
He grumbled under his breath. "The test suite I wrote will send an email to generate a procurement order, then check whether the request shows up. Since the bridge is off, the database shouldn't change."
Pete worked his keyboard and mouse for another minute, then paused, a puzzled look on his face. He typed again, faster and more furiously.
"What?" Mike asked, moving to sit on Pete's desk for a better view.
"This is odd. I ran the test and even though the bridge is down, the request got inserted in the database. The bridge is definitely not running. But something routed the email to the procurement app, where it was accepted as a legitimate entry. That can only mean there's another email-to-web bridge in the company."
David glanced at Mike. More puzzles.
Pete raised one finger. "Wait! There were subcontractors in here over the holidays. I thought they were here doing routine maintenance, but I don't know for sure what they touched. Maybe they mistakenly propagated the bridge onto some other servers."
"We need to figure out which ones and get them shut down," David said. "Pete, you're the only one with access right now. Can you write a program to check every server to see which ones are running the email bridge?"
"The IT servers?"
"No, the whole company."
"Holy cow. We have over a million servers. That's one heck of a search you want."
"Do you have the access? Administrative rights on those machines?" asked Mike.
"Sure," said Pete, "as part of Internal Tools, we can use administrative accounts with full root access for maintenance checks. But still, that's a lot of servers."
"All right," Mike said, ignoring Pete's protest, "then we have one other thing for you to check for at the same time, a program called ELOPe we developed as an add-on to the AvoMail servers. We need a list of machines it's running on." Mike gave Pete a USB drive. "Here are the file checksums, so you know what to look for. I know this sounds crazy, but we think ELOPe is acting independently."
"Independently?" Pete asked, his voice cracking.
"Yes, an AI acting on its own volition. Making decisions, buying things and manipulating people."
Pete looked doubtful, but he stuck his hand out and took the USB drive.
"Now just one thing," Mike said. "Whatever you do, don't email anyone about this and don't trust any suspicious emails. We'll check in with you in person."
Pete's eyes went wide. "But..."
"Can you do it?" David asked, drawing himself upright, forestalling Pete's objections.
"I'll do it," Pete said, gripping the USB drive tightly in his fist.
Gene tucked his briefcase tighter under his arm and knocked twice on Brett Grove's door. The pipsqueak had better be in.
"Come," Brett's voice called.
Gene entered, swallowed a bit of pride, and said, "Boss, can I get a few minutes of your time?"
Brett nodded, and Gene took a seat in front of his desk. The corner office had wide windows, a spotless desk, and a large screen monitor. Cabinets along one wall held artsy knickknacks at precise two-foot intervals. A Mont Blanc pen stood in the center of the desk, an obvious showpiece, since not a single sheet of paper, not even a sticky note, was to be seen anywhere in the office.
After explaining what he'd found, Gene expected Brett to understand and endorse the investigation. A word or two of praise would not have been out of order, either. Instead, his arguments were met with disbelief, even mockery.
"Gene, you think you found something here, but you're not coherent. You've been raving for years about how we shouldn't trust computers, and now you come to me with some story about an artificial intelligence. Do you expect me to believe you? Do you know how ridiculous this sounds?"
Gene held up his accordion folder. "Are you going to look at these reports?" He'd come carefully prepared with the same meticulous collection of data he'd used to present his evidence to Maggie in Finance, and then later to Mike and David.
"No, I'm not going to spend hours wading through hundreds of pages of printouts." Brett sat back, waving his hand at Gene's folder. "If you want to convince me, summarize what you've got in a slide deck, and present in the staff meeting on Friday. That's the way we do things here."
"Damn you, Brett. Listen to me, son, there is a damn monster in the machine!" Gene snarled, leaping to his feet. "This thing is buying guns and torpedoes and robots. There's no time to put together a PowerPoint presentation. We'll be lucky to be alive on Friday!" He held himself back, but he wanted to reach across the desk and grab the kid by the shirt collar.
"No, _you_ listen. This is typical of you. You think because I'm thirty years old that makes me an idiot. You're the incompetent fool." Brett stood on his own side of the desk, punctuating his every point with a jab of his finger. "You ignore your emails. You don't use the processes you're supposed to follow. We're the number one Internet company in the world, and the only thing you use a computer for is to print stuff out. My grandmother is more computer literate and has more credibility around here than you."
Brett came around the desk and stood face-to-face with Gene, his voice pitched low and angry. "You would've been gone a long time ago, but my predecessor made me swear I'd keep you on my staff before he would give me this job. I don't know what the hell he saw in you, but I don't get it. Go take a shower, shave yourself, put on some clean clothes for God's sake, and put together a damn PowerPoint presentation if you have to buy a book to learn how to use it!"
Standing there, Brett's face red and flushed and inches away from his own, it all crystallized. He'd been gradually marginalized within his own department by the worthless scum in front of him, and now when he most needed management support, he wasn't going to get it. Gene blinked once or twice and realized he was wasting him time here. No data or logic would change Brett's mind.
Later, in his own office, Gene replayed the scene over and over in his head, and thought back to the countless little things that hadn't gone his way the last year. His pulse sounded in his ears, and he felt almost sick. He opened the bottom desk drawer, and poured himself an inch of bourbon. On second thought, he added another inch. He swigged the whole mess, the burn descending his throat and settling in his stomach. Jesus, he was going to give himself a heart attack if he replayed that conversation again.
He looked down at his rumpled, slept-in clothes and rubbed a hand over the multiple-day stubble on his face. He was a mess, that was true. But competence wasn't a matter of clothes and fancy presentation. Competence was looking at data, whether out there in the real world or on his sheets of paper, and drawing insights. Damnitall, he was still relevant.
Gene slouched in despair before forcing himself up. He had to focus on something productive. It was time to meet with Mike and David. He dragged himself out of his office and began the journey back to the R&D building.
Bill Larry climbed into the back of the AStar, where he'd have a little more room to work. He buckled in and put on his headset. The pilot throttled up, and they were in the air.
Bill pulled out his tablet to review emails and try to salvage a little productivity out of the morning. He was taking an unexpected helicopter ride, the first of the new year, out to the ODC. He'd gotten a very unusual call from Maggie Reynolds in Finance, asking him to verify delivery of purchases. Bill scanned messages, but couldn't put the confusing exchange out of mind.
Maggie hadn't been able to grasp that Facility location code ODC0004 was not a mere walk down the hallway for Bill, but a floating platform ten miles off the shore of California, requiring Bill to make a helicopter reservation and two hours to get to, by the time you counted driving and flying.
If the call had confused Maggie, it was twice as puzzling for Bill, because Maggie went through a litany of impossible purchases attributed to his department. He had not ordered backup satellite hardware or microwave communication gear. Yes, they'd ordered equipment from iRobot, but that was before the holiday break, and no, there shouldn't have been a second round of deliveries to all the ODCs from iRobot.
In any case, no one could visit or install anything on the ODCs without approval from Bill. It simply wasn't possible to have installed the equipment Maggie described. Only Bill, Jake, and a handful of employees in day-to-day contact with Bill had the authority to stand down the robotic defenses. Bill was personally advised anytime the robots were brought offline. Maggie's inventory of purchase orders made the ODCs sound like beehives of activity. Impossible.
However, the shit had hit the fan back in the main office, because Maggie had folks from Controls and Compliance investigating their purchases. She sounded worried but trying to hide it, and in the end, Bill felt sorry for her and reluctantly agreed to investigate in person. He reserved a helicopter, packed a bag and his satellite phone, and headed for the heliport.
That's how Bill ended up thirty minutes out from ODC 4 on one of the company's Eurocopter helicopters to do this hands-on inspection. He would lay to rest the question of exactly what equipment was present. With a sudden jolt, he realized he'd made a drastic mistake. In his rush, he'd forgotten to schedule the deactivation for the defense robots.
He fingered the headset switch to talk to the pilot. "Hey, George. Whatever you do, don't approach the barge. Keep at least half a mile distant. I've got to get them to shut down the robots."
Bill struggled to plug his satellite phone into the noise-isolating headset, a clumsy, insulated thing. Jesus, he could have gotten them both killed. He placed the call to the robot system administrators.
"Hello, this is Bill Larry at Avogadro. My deactivation passcode is O-S-T-F-V-3-9-4-1." Bill had to yell over the helicopter noise. "I need to shut down the robots at ODC4."
"Sorry, please repeat your passcode."
"O-S-T-F-V-3-9-4-1. I'm Bill Larry at Avogadro. I need to shut down the defense robots so I can land at my facility.
"I'm sorry, sir, but I don't have any matching records. Can you please give me your vendor ID?"
Bill sighed in exasperation and wondered what more could go wrong with his day. He swiped through the records on his tablet until he found the information, provided the asked-for ID and waited.
"I'm truly sorry, but I don't have a listing for that ID. Are you sure you have a contract with us?"
"Jesus effing..." He hit mute, cursed loudly and at length, and then continued the conversation. After more unhelpful back-and-forth discussion with the agent, he asked for a supervisor and got transferred over to a Ms. Claire.
"Mister Larry," Ms. Claire said, after a few minutes of research. "We're no longer under contract to handle your defenses. Of course we provided the hardware, and we were administering through December thirty-one, but as of the first of this year, we turned the controls over to you."
"Not possible," Bill said. "There's got to be a mistake."
It took another fifteen minutes on the phone with Ms. Claire for Bill to gradually puzzle out that iRobot thought Avogadro had renegotiated the contract. Bill was sure this wasn't the case, but he couldn't help wracking his head, wondering if someone had gone around him. They'd just put the system in place a few weeks earlier. It didn't make any sense that the contract had changed already. Had they been hacked? Bill's head started to pound as he continued the argument over the crappy satellite connection and roar of the helicopter.
George gestured toward the barge, visible now, asking whether he should proceed. Bill shook his head no.
Bill checked his tablet and found the number for a vice president, Robert O'Day, at iRobot, one of the guys he had worked with on the contract. Bill hung up on Ms. Claire and called Robert. He remembered Robert as being intensely focused and wickedly smart. He'd get this issue resolved. Robert's administrative assistant said he was already on an urgent teleconference, but offered that Robert could call Bill back within ten minutes.
So Bill waited over the Pacific ocean, a thousand feet up, a hundred-and-five-decibel engine just above his head, burning a gallon a minute of high performance aviation fuel.
Seven minutes later the phone rang, and Bill punched the button to answer. Bill struggled to keep his voice under control as he demanded O'Day explain what was going on. While the pilot had the helicopter circling around ODC 4 in gentle circles, O'Day confirmed that, indeed, iRobot had installed additional automation and turned the administration of those defenses over to Avogadro.
Craning his head to look at the floating barge, Bill raised a pair of binoculars. New antennas bristled from the rooftop, satellite dishes pointed into the sky, and line-of-sight microwave cones aimed at the horizon. More worrying were the long black barrels directed skyward. What the heck were those?
George circled the platform at a distance, but after a few rotations, Bill just wished he'd keep the helicopter in one place. Yelling over the noise, he asked O'Day if there was anyway to override the robots. If he couldn't get the problem solved, he'd be forced to fly back to the office to figure out what was going on, then return in the afternoon.
O'Day assured him there wasn't any override for security reasons. The point of handing off administration was to insure full control of the command software they'd provided to interface with the robots resided in Avogadro's hands.
As Bill argued with iRobot, George "Punch" Gonzales continued to circle around. He did it more out of boredom than anything else, since he could've easily engaged the auto-hover to maintain their location. After twenty years of flying helicopters for the Marines, George wasn't inclined to engage the autopilot and tune out. He liked to keep his hands on the stick.
On one of these slow rotations around the ODC, George came a little closer to the platform. He glanced again at the fuel gauge, and noticed the long holding pattern had them coming up on their halfway point. George turned to ask Bill how much longer they planned to stay. While he was looking backwards, the helicopter crossed into the invisible perimeter defined by the robotic defenses. Since he wasn't looking out the windshield, George, who just might have recognized them for what they were, missed the flash of large-caliber machine guns firing. Bill, stooped and head down, struggled to hear the other end of the line and understand how the administration of the robots could have been bungled so badly.
In less than a quarter of a second, the .50 caliber machine gun rounds traversed the distance to the helicopter, bisected the cabin and found the fuel supply. The helicopter exploded and bits of shrapnel screamed through the air in all directions, before falling, sizzling, into the water.
**Chapter 10**
David tried to turn down another cup of coffee, but Mike was having none of his protests.
"It's Peruvian. The beans were roasted yesterday."
David took a sip as Gene came in and dropped heavily into the remaining chair. His stomach was tied in too many knots to enjoy the coffee, but he distantly noted the flavor was extraordinary.
Slumped back, Gene related the discussion with his manager. "Sorry. I never anticipated losing all credibility within my department. If we go to anyone else in management, and we should, you'll have to take point. You technical boys at least are respected by these folks."
"Sorry, dude," Mike said, clapping the older man on the shoulder, his face lined deeply in dismay. "Thank you for making the attempt."
"Me too," David added. "They're crazy to not appreciate your work. We wouldn't have any idea what was going on without your investigation."
"The key to this is Gary's Communication Products Division," Mike said. "Gary might be unreachable, but he's not the only decision maker."
"Right. The Marketing manager, her name is...Linda Fletcher," David said. "She's Gary's number two. Let's find out who the Legal representative is, and bring Legal in. If we can convince them of the risk, maybe they'll put a stop to the whole project."
"Legal advises businesses on risks," Gene said. "Technically they can't force anyone to do anything. The business manager must weigh tradeoffs, including Legal's opinions, and make a decision. But I agree, we should bring them in. The fear of litigation will cause the lawyers to side with us."
"Let's go," Mike said.
David reached for his computer to check Linda's calendar, then stopped himself. Habits were hard to break.
Walking down the hallway with Mike and Gene in tow, he asked the admin of the next group over to find the location of Linda Fletcher's office, and her admin's name. They crossed the campus, traversing a skybridge with hand-blown glass art in the shape of native fish hanging in the windows, and then another skyway in the form of a miniature version of the _Ponte Santa Trinita_ , before finally arriving at Building 7a. They found Linda's admin, a young guy by the name of Nathan, at his desk outside her office.
"Sorry, Linda's in a critical conference. You should have sent a meeting request."
Gene pulled out his badge, showing he worked for Controls and Compliance. "It's urgent."
"Let me put your names on her calendar and find an open slot."
"Wait—" David said. "No names."
"No names?" Nathan asked, his eyebrows raised.
"Absolutely no names," Gene said. "The meeting is extremely sensitive. Just schedule the time."
Nathan's jaw hung open for a second before he reluctantly set his shoulders. "Fine, a meeting with no attendees. Can I give it a name?"
David wondered what wouldn't arose suspicion but would ensure Linda took it seriously. "Just put down 'critical system stability.' Also, I need you to invite the Legal rep."
"You mean Tim Wright?" Nathan asked. His raised eyebrows and tilted head left no doubt he still found their whole request dubious.
"Yes," David said. "What's the earliest you've got?"
Nathan checked the calendar. "I can get you a half hour next Tuesday."
"No, it's got to be today."
Nathan shook his head firmly. "No can do. Linda will kill me. I'm not kidding. Since she came back from holiday break she's been putting in sixteen hour days on this new project."
"What project?" Mike asked.
"I can't say. Super confidential. Just like your meeting is _sensitive_." He smiled in slight triumph. "How about Friday?"
"Look kid," Gene said, "people's jobs and more are on the line. Be straight with us, what's the earliest possible time we can meet?"
Nathan rolled his eyes. "Everything's urgent," he said, mumbling to himself. "I can bump Janet..." He glanced up. "I can get you in tomorrow after lunch."
David frowned at him.
"Tomorrow after lunch," Nathan repeated. "That's the absolute best I can do. Between the Legal meetings, the PR folks..." Nathan trailed off. "Forget I said anything, please."
"Fine, set it up for tomorrow," Gene said. He started to turn away and then returned. "Kid, I can see from your face that as soon as we leave here, you want to walk down the hallway to gossip about this. Don't do that if you still want to have a job tomorrow."
Nathan nodded swiftly, and the group of three headed back.
David was woozy, his eyes crusty and his head hurt. He'd been awake and on the go since early that morning in New Mexico. "Listen, I'm exhausted," he said. "I've been up since five, or maybe that's four. I realize how urgent this is, but given we're stalled waiting for Linda, I need to go home and get some rest."
"Let's meet tomorrow morning before the meeting," Mike said. "David's office?"
"Sure. You boys need a ride? Your wife took his car."
David would probably fall asleep on the long streetcar ride home, he was so tired. "Yes, please. That'd be awesome."
David had texted to let Christine know he was on his way home. After Gene dropped him off, he went inside and found the house empty.
"Hello?" he called, wandering around. The suitcases were unpacked and waiting in the upstairs hallway. David put them in the attic, and went downstairs. In the kitchen he found a note that read _Gone to get dinner, be back soon_.
As he finished reading, he heard Christine's car pull up. He opened the door, and Christine walked up carrying two large bags.
"Takeout from Nicholas," she said, smiling.
His favorite Lebanese restaurant. He tried to muster up enthusiasm.
Sitting down, he picked moodily at his plate, exhausted from lack of sleep, travel, and the stress of the afternoon.
"You better not waste that _mjadra_ ," Christine said with a laugh.
David managed a weak smile, knowing she wanted to cheer him up.
"You're hopeless sometimes," she said, sighing. "What's your plan for tomorrow?"
"We're going to Linda Fletcher, the Marketing manager for Communication Products. She's got decision-making authority while Gary's out. We'll ask her to approve an outage so we can take down the servers and install clean images without ELOPe."
"Sounds reasonable. What do you think her response will be?"
"She may say yes. I hope so, at least." David fell back into silence, staring at his food.
"Why so glum then?"
"What happens after this?" David said, stabbing angrily at the rice and dropping his fork on the plate. "They'll cancel the project, almost certainly. This may be the end of my career. They're going to ask questions about what ELOPe was doing, how these things happened. I was so close to a mind-blowing success. Now what's the best I can hope for? Damage control." He rested his head in his hands.
Christine came around the table to hug him. "You have other options. This is one job, one company. No matter what, there's always a path forward."
"There will never be another opportunity like Avogadro if I screw this up."
The next morning, David, Mike, and Gene reviewed what they'd say at the meeting with Linda, and discussed contingency plans.
"We've got time to kill," Gene said, "and we could use downtime and food. I wouldn't mind getting away from here. Kenny and Zuke's?"
Mike nodded eagerly.
The sandwich shop was a standby for the Avogadro crowd. The company's cafeteria food might be excellent and well loved, but eventually the corporate ambience tired out even enthusiasts. On this particular day, they were a little more comfortable a few blocks away from the eyes and ears of the company. They enjoyed Reubens and hamburger sliders and made their way back ten minutes before the planned meeting time.
They entered the seventh floor conference room to find Linda and Tim already present. As they set foot in the room, Linda made a zig-zag hand motion at the gesture-sensitive walls, and the wrap-around display screens, covered with presentations, diagrams, and spreadsheets, went dark simultaneously. David couldn't help reacting to the gesture. He wasn't used to such a lack of trust between Avogadro employees.
"Sorry," Linda said, seeing the expression on his face. "It's a confidential client deal." She shrugged dismissively. "Dave, you I know." She shook his hand. "Who are these gentlemen?"
They started a round of introductions. Linda was a Scandinavian woman whose family had lived briefly in Wisconsin when she was a child, just a few towns away from Mike. She and Mike laughed over common experiences growing up. Tim, with his jet-black jeans, boots, and T-shirt, defied everyone's expectations of a corporate attorney. David wondered if he was some new breed of Goth lawyer, but Tim's jovial attitude set them at ease.
The small talk done with and everyone seated, David explained what brought them to the meeting. Mike contributed details but let David lead the conversation.
The light-hearted mood faded as they got to the suspicious purchases and ELOPe's possible role. Linda sat back, arms folded, a foot from the table as Tim's frown became more pronounced.
David couldn't read them. Obviously they weren't happy. But were they uncomfortable with the technology, or worried about making a decision without Gary present? Afraid they'd somehow be liable for what happened? All three? By the time he got to the crux, his initial confidence had evaporated.
"What we're asking for is your authority to force a shutdown of all email servers. Then we'd re-image those computers with a known good version of the software."
Between leaning away from the table, crossed arms, and condescending expressions of disbelief, Linda and Tim radiated rejection in every possible way. David's heart sank. Damnit, he needed them to believe. He had to make one last attempt.
"Look," David said, "This is a normal action we take when a server has a problem, just like reinstalling the operating system and software on your PC. A straightforward process."
"I hear you and I want to help," Linda said, fiddling with her tablet. "I really do."
David couldn't have gotten a clearer _no_. He opened his mouth to object, but Linda went on.
"The problem is I'm uncomfortable making a decision of this magnitude without Gary here. I've already got...well, never mind that. I'd much rather wait for Gary to return." Linda glanced at Tim and then turned back to David. "What you're asking for, would it cause a service interruption? How long and how many customers would be affected?"
"Yes, but only a _temporary_ outage. The good news is Avogadro has a process to re-image servers quickly. We can bring a server up in less than ten minutes. The bad news is we don't normally re-image all the servers simultaneously. The backup system containing the images can only service a few thousand servers at a time. Some servers would come up quickly, but it'll take three hours to get everything back online."
"Wait a second," Linda said, leaning forward. "You want a full outage? _For three hours?_ I thought you were talking about a degradation of service. No way we can afford that much downtime right now. It's non-negotiable. We're closing new partnership deals in the next couple of days, confidential stuff we can't discuss until the press release comes out, but they're a major coup for Avogadro. A multi-billion dollar opportunity. I can't put that at risk." Linda looked to Tim for confirmation.
"I agree," Tim said. "These customers specified service level agreements committing to certain uptime. An outage now would destroy our credibility to meet those goals, and they'd back out. We'd lose the deals."
"Wait a minute." Linda snapped her fingers. "The rolling maintenance windows. Why don't you use them? Bring down some of the servers in small groups and fix them a bunch at a time?"
"We wish we could," Mike jumped in, "but we're afraid the existing systems would reinfect the new ones as they come up. We need to shut down every email server and keep them down until the clean installs are done."
"I'm sorry, but I've got to say no." She waggled one finger at them. "If you had hard evidence the servers were causing problems for our customers, I might be influenced to make the decision to rebuild them. But a strange story about a handful of emails being manipulated...It seems more likely your accounts have been compromised, not that the entire email system is flawed. I think you should talk to Security." She shook her head.
"This isn't a Security problem," David said. "This is—"
"Look," Linda said. "I can't decide to risk billions in revenue based on a few mangled emails. You're free to talk to Gary when he returns, of course." She turned to the displays, arm raised to make the gesture to turn them back on. "Anything else?" Her attitude said it was a dismissal, not an invitation.
"No," David said. "But we'll be back."
**Chapter 11**
**Avogadro Launches Secure Hosted Email Service **
**Government Complaints About IT Costs and Quality Lead Avogadro to Create Secure Applications and AvoMail**
****
PORTLAND, Oregon - January 6th, 2015 UTC - Avogadro Corp today announced a secure, hosted version of Avogadro Applications with AvoMail for Governments.
The demand for ultra-secure, hosted Avogadro Applications with AvoMail came from national governments spending excessive amounts on IT services while receiving inferior products and services, said Linda Fletcher, Marketing Manager for Avogadro's Communication Products Division. Avogadro Secure Applications with AvoMail will reduce IT spending by governments up to 80%, while providing cloud-based, feature-rich and easy-to-use communication applications, according to Fletcher.
The hosted model is being adopted immediately by Germany, Canada, and Taiwan, with other countries to follow.
For more information, please visit AvogadroCorp.com
For two days after the conversation with Linda Fletcher, they were stuck in a holding pattern, waiting in deepening frustration for Gary Mitchell to return from a vacation that should have ended a week earlier. They spent much of the time clustered in David's office, poring over Gene's reports, and even printouts of source code which Melanie had made after many puzzled protests.
During a bathroom break, Mike read through his personalized news alerts and his heart skipped a beat. Oh, man, this was worse than he ever imagined. He washed his hands and ran back to the office, AvoOS smartphone in hand.
"Holy cow, did you see this press release?" he asked, holding the screen out.
"Dude, you're not supposed to admit to reading your phone in the bathroom. We all do it, but you're violating some kind of social norm..." David trailed off as he noticed Mike's face.
"We, I mean, Avogadro, that is, I think, ELOPe has..."
"Slow down." David held both hands up. "What's up?"
Mike took a deep breath and forced himself to sit down as the others stared at him. "Avogadro announced a secure version of AvoMail and our other apps for government customers. They already signed up the first round. David, national governments using AvoMail. Germany, Canada...Do you realize what this means?"
"ELOPe expanded its sphere of influence." David's face turned pale. "Now every government official who sends or receives an email via AvoMail will potentially have their message filtered, altered, or impersonated."
"This service must be what Linda Fletcher talked about in the meeting the other day," Mike said. "Damn, she had to have known this was in the works. She's actually making the problem worse!" He couldn't help raising his voice.
"Settle down," Gene said, in his usual grumble. "The real question is who initiated this secure platform? Fletcher and the Marketing group, or ELOPe? The timing is awfully convenient."
"Come on," David said. "It's only been a month since I put the hack in the system. You really think ELOPe could make the company launch a new product in that time?"
Gene shrugged.
Mike held his head in both hands, staring down at the phone. "I believe it. The biggest problem with introducing anything new is getting everybody on board. If ELOPe convinced everyone simultaneously, why not? It's not like we had to build the product from scratch. It's just re-marketing what we already had to new customers."
"I'm freaked out," David said, voicing what was in Mike's head.
Mike looked at him and nodded.
The day after the Avogadro press release of the secure cloud services for governmental organizations, David, Mike, and Gene met again. At Mike's urging, they gathered at Extracto in Northeast Portland.
David entered the shop, found Mike and Gene sitting at a table along the wall. "Why here?" he asked.
"Best coffee in Portland, bar none," Mike said. "Perhaps the finest on the West Coast."
Gene nodded, holding a mug up.
"See, Gene hasn't even been here before, and he's already convinced," Mike said. "Get the Flores Island."
David walked over to the counter, where two insulated coffee dispensers stood next to the chromed bulk of the industrial espresso machine. The dispenser on the left was labeled "Flores Island" and contained descriptive text so flowery that David thought he was reading a wine review. "Subtle hints of carmel, chocolate, and cannabis?" David read out loud. "For real?" he called doubtfully to Mike.
Mike nodded and smiled.
So David got a cup, along with disapproving stares from the others as he loaded up on sugar and milk. He sighed.
A large canvas tote sat at Mike's feet. "What's in the bag?" David asked.
"Ten pounds of beans. They only harvest and roast the Flores Island once a year, and once it's gone, it's gone."
David sat down. "Did you make us meet here for the coffee? We're eight miles from campus!"
"We're only two miles from your house, and yes, we came for the coffee. You have no idea how hard these beans are to get. A one-of-a-kind experience."
"Can we please focus on ELOPe?" David said, sounding whiny in his own ears. He couldn't help it: he was frustrated with Mike, and had zero bandwidth for discussing rare coffee beans.
"Okay, okay," Mike said, but he and Gene chuckled in amusement. Mike went on, "You guys remember Pete Wong, the engineer from Internal Tools who wrote the email-to-web bridge?"
David nodded. He took a sip of coffee, found it as good as Mike had promised. Well, the man knew his beans.
"Well, I heard back from him. Bad news, more bad news, and worse news."
"Naturally," Gene said, "because the situation isn't terrible enough."
David glanced at Gene, trying to puzzle out whether that was sarcasm or an actual expectation. He turned back to Mike. "I guess you can start with the bad news first."
"Pete scanned computers for the digital fingerprint of ELOPe, as we asked." Mike sipped his coffee. "He found traces on every server in the Communication Products pool, even ones it shouldn't have been on."
David groaned. "And the more bad news?"
"Pete found the fingerprint of his email-to-web bridge on the same servers as ELOPe. Also present on every one. He thinks the email-to-web functionality was incorporated directly into ELOPe's code."
"How is that possible?" Gene asked.
"The contractors," Mike and David answered simultaneously, with a glance at each other.
"Yup, Mike said. "The temporary engineers hired over the holidays made changes, and we don't know what. We thought they were merely performance improvements, but ELOPe changed its own functionality as well."
David chewed over this new bit of information. ELOPe could be doing anything now, possibly far beyond its original programming.
"We've built an artificial intelligence," Mike said, wide-eyed. "A self-improving AI. It's going to keep on accelerating out of control."
"It's not an AI!" David said, unsure why the idea made him feel so hostile. "It's just a collection of algorithms, manipulating us with emails."
"It may not be conscious like we are," Mike said, "but it's protecting itself, changing itself. That's intelligence."
"It can't be intelligent." David pointed back and forth between Mike and himself. "We're not that smart and we certainly can't write software smarter than us. Where does the intelligence come from if we didn't put it in there?"
"Both emergent intelligence and collective wisdom. The algorithms we wrote improve themselves over time, testing better approaches to detect goals, match outcomes, and so forth. But the actions themselves come from the combined emails of millions of users. It's crowdsourcing its own intelligence."
"It's not an artificial intelligence!" Dave slumped in his seat.
Gene cleared his throat. "It doesn't matter what you call it, we still have to stop it. And the sooner the better, before it accumulates more power."
"This sucks," David said. "What's the worst news you wanted to tell us?"
"I went to Pete's office yesterday morning to find out what he's learned, since we didn't want to use email or phone. Before I left, I gave him my home address in case he had anything urgent. Then last night he showed up at my door after dinner. He'd been fired."
"What the hell?" Gene barked, slamming down his cup.
"He was working late and looking for more signs of server infection, when his network access was cut off. A couple of minutes later, Security showed up at his office and told him he was fired. He wanted to call his manager, but the guards wouldn't do anything other than let him pack a box of personal belongings. They escorted him off campus and he came straight to my place, figuring it was all related."
"Why didn't you tell me last night?"
"By phone or email?" Mike said.
"Frak me," said David, realizing no electronic communication was safe. "We've got to do something! It's been, what, five days? Waiting for Gary is not a viable option anymore."
The question facing them wasn't just who had the authority to shut down the servers, but who would believe their story and the limited evidence they had. After throwing out alternatives, they came back to contacting Sean Leonov, a path they'd debated several days running.
"We need an appointment with Sean," Mike said. "He brought you on board to lead ELOPe, so you have credibility with him. I know we're jumping right to the top of the management hierarchy, but this must be done. We've exhausted our other options and we're in a race against the growing influence of this thing."
David closed his eyes and pressed his hands to his face. Mike was right, but, once again, he couldn't get over the fact that this would spell the end of his career. He'd exhausted all his options. He'd trade anything, do anything, for a chance to go back and change the course of things. He opened his eyes. "All right, let's talk to Sean. We'll go together."
They carpooled to the office in David's old BMW. From the Fremont bridge, they took the Avogadro exit leading directly to the underground parking garage. David pulled up to the gate, the blinking light above the scanner suddenly ominous. ELOPe would know he was entering the campus. He hesitated, badge in hand. Jesus, he had to get a grip. He stuck the badge up against the reader before he lost his nerve. To his slight surprise, the barrier swung open normally.
They trooped down hallways, winding their way to Sean Leonov's office with the solemnity of a funeral procession. The executive offices were located close together in the uppermost floor of Building 7B. As David looked around the hallways with their expensive ebonized hardwood flooring, he realized the executive floor was abandoned. One closed room after another.
They finally found Sean's office. Knocking brought no response, so David tried the knob. Locked. "Now what? No one is around."
"Sean's traveling," said an approaching woman carrying a cardboard box. "His admin, Rosie, will have his contact information. Talk to her."
Her tailored suit suggested she was one of the VPs, and David recognized her from his executive presentation more than a month earlier. "Marissa, right?" he said. "Any idea where we can find Rosie?"
"She works from home when Sean is out of town. Send her an email. Rosie Fendell. She'll be in the directory."
"Is there any way we could contact her in person?" he asked. "We, uh, can't use email. The topic is too sensitive."
"Sorry, email is your best bet. Good luck." Marissa continued past.
David couldn't help wondering about the cardboard box. "Are you leaving the company?"
Marissa smiled. "Yes. An opportunity too good to pass up."
After she left, David broke the silence. "Just send an email. Sure. That's so simple."
"Well, one email can't hurt, right?" Mike clapped him on the back. "Let's make it as vague as possible. We just need to meet Sean."
Back at his office, David sat in front of his desk computer. The others watched over his shoulder as he crafted an email to Sean's assistant, taking special care to ensure the message sounded innocuous. They all read and approved the email before David hit send.
While they waited for Rosie to reply, Gene went down the hall for coffee. The minutes ticked by as they sipped, each expressing anxiety in his own way. Mike bounced a leg with nervous energy as Gene paced back and forth. David gave Tux a little nudge, sending the springy penguin bouncing erratically.
"I'm sure I've never been so much on the edge of my seat about an email before," Mike said. He chuckled awkwardly, his voice betraying his nerves.
"No kidding," David said, stirring sweetener.
Gene stood by the window, mug in hand, brooding.
"Maybe you're right," David said, looking at Mike.
"I'm sure I am," Mike said with a smile, "but about what?"
"The coffee. I always thought the stuff here was good, but it does seem off somehow compared to Extracto."
Mike sat back, a satisfied grin spreading across his face. "That's the lactone and indanes. More than a thousand volatile compounds in roasted coffee. I don't want to say I told you so—"
A sharp knock at the door interrupted him, startling them all.
David jumped up. "All right, guys, calm down." He gestured for them to stay in their seats, a slight tremor in his hand. "Whatever is going on is only happening in the computer. It might be real good at faking emails, but it can't hurt us for real."
He cracked the door open. "Can I help you?"
Outside, a dark-haired woman in a black suit stood with four uniformed security guards behind her. "Mr. Ryan?" asked the woman.
"Yes, that's me," he replied, a sinking feeling in his gut.
"Are Mr. Williams and Mr. Keyes with you?"
"Yes, we're all here." David opened the door wider.
"I'm Carly French, Director of Security. We've been contacted by several individuals who reported you harassed them. I'm afraid I must escort you off the Avogadro campus immediately, pending a full investigation."
David, Mike, and Gene glanced at each other. David's assertion that the computer couldn't affect them in real life had fallen apart before their eyes.
"Ms. French, I'm Gene Keyes, in the Controls and Compliance Group." Gene stood and shook Ms. French's hand. "I'm conducting an internal investigation into financial fraud and other inappropriate behavior occurring just before the end of the year. Mr. Ryan and Mr. Williams are assisting me. We believe Avogadro employees are being manipulated through email. It's called social engineering. The emails provide just enough information to seem legitimate. May I ask, were you informed by email of our so-called harassment?"
"Yes, I was informed by email, but I'm well aware of what social engineering is. In any scenario with such serious allegations, of course I would confirm them directly with the individuals. In this case, I spoke by phone with your manager, Mr. Keyes."
"Brett? He could confirm what I'm working on."
"During our phone call he said you've been belligerent to him, acting strangely, and you'd blame whatever happened on the computer." She shook her head, more sad than angry. "Look, I'm very sorry, gentlemen. You seem like nice folks, and I'd like to be able to take your word. But the standard operating procedure is that I escort you off campus and remove your access privileges as a precautionary measure, until a full investigation can be completed. If the facts don't check out, you'll have an apology from me and my manager, and you'll be back on campus in no time at all. Now, please, let's go without a lot of drama."
David couldn't think of a thing to say. He felt boxed in, all available choices closed off one by one until there was nowhere to go.
Out of options, they allowed Ms. French to escort them to the garage and David's BMW. They climbed into the car, and as David drove away, the security guards walked alongside until the car exited the garage. In the rearview mirror, he saw the guards line up across the entrance.
For once, Mike had no jokes to break the silence.
David squinted on the drive, the sunny day somehow too bright and cheerful for the circumstances. Arriving home with Mike and Gene in tow, David entered the house, which—with Christine away at work—was quiet and still. David grabbed beers from the kitchen and passed them around. The sun might be straight overhead, but he needed something to take the edge off their unnerving experience with Security.
He wanted to call Christine, but his phone wouldn't turn on. He tried button combinations until he concluded the phone had died. Staring at the inert plastic and metal lump in his hand, he remebered the phone ran Avogadro's AvoOS operating system and used the corporate Internet plan. It was totally dependent on the company, and the servers were fully aware of his phone: where it was, who he talked to, the data he sent and received.
"My phone is dead," he told the others in surprised relief.
"Same here," said Gene, looking at his.
"Me too," Mike said, checking his own phone and glancing over at Gene's. "Dude, how'd you get a feature phone from the company? We don't even _make_ phones like that anymore."
"It's not surprising they stopped working," David said, "given that everything runs through Avogadro."
"We should be glad," Mike said. "Otherwise ELOPe could have monitored our phone calls. Come to think of it, ELOPe might have been listening anytime they were powered on."
"Shit..." David continued to fiddle with the damn thing, then slammed it on the counter. "It's not just about _using_ the phone. It's the data on there. I had Sean's home address in my contact list, from a barbecue I was invited to back when I was hired. We could have gone straight to his house. Now I can't even get a boot screen."
"Doesn't matter, he's traveling, right?" Mike said.
"Look, let's go to his house. I remember it's in the West Hills. It's not that big an area. If we drive around long enough, we can find the place, and maybe he's there. Or someone who knows where he is."
"We got nothing to lose, boys. I don't mind the beer, but I do want to get to the bottom of this," rumbled Gene.
"Let me drive, and you navi-guess," Mike offered.
David nodded, tossing his keys to Mike, and they took off again.
Two hours of exploration later, which included winding roads, switchbacks, and driving in circles in Portland's West Hills, David finally recognized Sean's house. In the one stroke of luck they had experienced since this all started, they found someone coming out as Mike pulled up.
David walked up to the youthful woman. "Excuse me, I'm looking for Sean Leonov. Is he home?"
She looked startled, glanced around, and took two steps back. David hoped she was merely nervous about being approached on the street, not hiding anything sinister.
"He's not available," she said. "Can I take a message?"
He pulled out his Avogadro badge, which fortunately had only been deactivated by security, not confiscated. "I'm a coworker of Sean's at Avogadro. We've got a work emergency and need to talk to him."
"I'm housesitting while he's in Brooklyn, visiting his family."
"Do you have a phone number?"
"I'm sorry, I'm not supposed to give any information out. Sean was adamant. Don't you have his info at the company?"
"Yes, of course..." David faltered as he ran out of excuses.
Mike came to his rescue. "Time is of the essence, and the matter is so sensitive we can't contact him by phone or email." He paused and added, "We have to talk to him in person."
David frowned. The summary sounded odd coming from someone else. No wonder no one believed them.
At this, she looked more suspiciously at them, clutched her bag a little closer, and started to back toward the house. "I'm sorry, but if it's urgent, Avogadro has contact information. Please call his office, they'll know what to do."
Keeping her eyes on the group, she walked to the house. "Goodbye," she called from the door.
"Shit," Mike said as they climbed into the car. "That wasn't very productive."
"The hell it wasn't. We know he's in Brooklyn," Gene growled.
"What good does that do?" Mike asked, focused on driving.
"Brooklyn has the largest immigrant population of Russians outside of Russia. If Sean went to Brooklyn, he's almost certainly in the Brighton Beach neighborhood. He's probably visiting his Russian parents. The Russian community is tight-knit. On the ground, we could find them in no time."
Mike and David turned to stare at him.
"What? I was a private detective before I joined Avogadro. I can find people. The old fashioned way. Without computers."
David took a deep breath. In for a penny... "In which case, gentlemen," he said, "next stop, New York."
**Chapter 12**
**Tensions Ease in Middle East After Landmark Accord**
ARBIL, Iraq (Reuters) - **** Germany has eased tensions in the Middle East after helping leaders in the region reach a landmark accord. Part of the agreement includes an unprecedented commitment of aid from the German government in the form of technological expertise, manufacturing agreements, and health care.
"We have reached the end of the era of oil," said Germany's Chancellor Erberhardt, at a press conference in Berlin. In recent years, the advance of renewable energy has diminished the relevance of oil, adding financial stress to the Middle East and increasing the tension of cultural and religious differences.
"Our accord transfers German technological expertise, profitable manufacturing, and the benefits of the best health care system in the world to the Arab nations," Erberhardt went on to say.
The agreement calls for disarmament and educational reform in exchange for the technology, manufacturing, and health care grants.
"Germany's history is one of transformation, and we wish to give the Arab world the support it needs to ensure a successful transformation."
The agreement includes components that are as disparate and comprehensive as auto manufacturing, data centers, and medical universities.
**Avogadro Acquires Oil Tankers for Floating Data Centers**
PORTLAND, Oregon (Oregonian) - Avogadro Corp announced it is acquiring up to 100 retired oil tankers for floating data centers.
"We are experiencing an unprecedented increase in demand for server resources thanks to new strategic partnerships, including our Secure Government Applications Platform," said Jake Riley, head of the Offshore Data Center project. "While we continue to maintain our traditional data centers, our primary infrastructure going forward is floating data centers. Our barge-based approach is highly scalable and industry-leading. But at Avogadro, we're always looking to surpass even our own innovation. By acquiring retired oil tankers, we can reduce our costs and reduce our environment footprint by putting these tankers to good use."
For more information, please contact Avogadro at AvogadroCorp.com
"Thanks for driving us," Mike said from the back seat.
"No problem," Christine said, behind the wheel of her Passat. "What's your plan when you get there?"
David couldn't keep the sarcasm out of his voice. "Gene's sure he can find Sean in a city of ten million people using no computers or telephones."
"I'm not looking at ten million people," Gene said, sighing. "Sean's parents are older Russian immigrants, therefore they're likely to either live in Brighton Beach or know people who live there. There are only seventy thousand people living in Brighton Beach, about half that many households."
"So you're going to knock on thirty-five thousand doors?"
"No. Look, kid, this is basic math. Sean Leonov is the wealthiest Russian in the U.S., and will be very well known in the Russian community. If someone has met or knows anything about Sean's parents, they're not going to forget about it. And they'll talk to their friends about it. If you use Dunbar's number, and estimate each person knows about one hundred and fifty people, in a population of seventy thousand people the odds are in my favor that the first person I talk to will either know Sean Leonov's parents or know someone who does."
"Oh." David pondered the math in his head.
Christine laughed.
"What's so funny?" he asked.
"You're brilliant, honey. Which makes it that much more fun to see someone outsmart you."
Mike and David waited by the terminal door while David said a hurried goodbye to Christine at the curb. Her upper lip was a tight line, a sure sign she was worried. David pushed a lock of hair out of her face.
"Be careful," she said, hugging herself.
"Don't worry, hon, we'll be fine."
"I wish I could call you."
"We can't bring phones—the chance of being tracked..."
"I know." She shook her head. "What if... Never mind, just go. I love you."
They kissed quickly, then David grabbed his suitcase. He glanced backwards once to see Christine watching him with a sad face. David took a deep breath and joined Mike and Gene.
They'd talked it over the day before and decided to err on the side of caution. Even though they couldn't imagine how ELOPe might track passenger flight information or credit card transactions, they were flying into D.C.'s Dulles airport, figuring a flight into Dulles would disguise their real destination of Brooklyn. Gene had pushed for the more drastic measure of driving cross-country, but the others convinced him they didn't have the time to waste.
Hours later, glad to be out of the plane, they waited in line for a rental car at the airport, more out of sorts than ever. David normally planned everything in his life. Now he was on the opposite side of the country after a spontaneous flight, getting ready to drive to New York. He'd never been so adrift. He thought back to last night, and Christine holding him in her arms. What was he _doing?_
Next to him, Gene was as unchanging and stolid as ever in his rumpled suit and with his old leather briefcase.
"This doesn't bother you?" David asked. "Picking everything up on a moment's notice? You seem to like things to be orderly."
"Try the military sometime. We'd deploy in an hour when we had to. You get used to it."
Mike rejoined them, carrying coffees on a tray and the _New York Times_ folded under one arm. "Guys, you are never going to believe this!"
"They still print a paper newspaper? You're right, I don't believe it."
"Be nice, kid," Gene said. "If they didn't, we wouldn't have any news at all right now."
Mike ignored David's sarcasm and went on. "Read these stories. On page one, the lead story is about how Germany changed their international policy. When was the last time Germany involved itself in international affairs?"
David shook his head. "I don't know, when?"
"Almost never. That's when. Not since World War II. Sure, they're active within the Eurozone, and they'll contribute to efforts by other countries. But on their own? No way. Now, out of the blue, they're negotiating a disarmament and peace treaty in the Arab world. And they apparently traded away the sum total of their intellectual property to get it. On page two, there's a story about how Germany adopted Avogadro's AvoMail. How can no one connect the dots with these stories side by side?"
David stared at Mike and the paper, dizzy with fatigue, astonishment, and disbelief. "I don't know whether to react with alarm or resignation at this point," he finally said.
"It also looks like we're going beyond using floating barges for our offshore data centers," Mike said, pointing to another story. "In order to support the new secure government cloud services, Avogadro is purchasing a fleet of retired oil tankers to use as floating bases for offshore data centers."
"Great, the bastard will be mobile now," Gene said in his usual growl. "Smarter than us, distributed, in control of the communication system, invisible, and mobile. Wars have been lost with fewer disadvantages than this."
After they picked up the rental car, Gene drove four hours north to New York City. They spent the trip in silence. They'd had every discussion and argument, and nobody was in the mood for small talk.
Once in New York, Gene headed to Brighton Beach in Brooklyn to drop off David and Mike at their hotel. "Let me do this by myself, guys. I've never done detective work with partners, and the three of us will make folks nervous. I'll meet you tonight at the hotel."
They watched Gene drive off. They were travel-weary but nervous, and decided to get a drink across the street. The bar looked like the neighborhood watering hole, friendly but plain. David ordered two bourbons on the rocks.
Halfway through his drink, David finally got up the courage to give voice to his fears. "What do you think is going to happen? Is it going to be like the _Terminator_ movies? Or _The Matrix_?"
"I don't know, dude." Mike shook his head. "Most science fiction deals with artificial intelligence run amok, but then there's also been plenty that's been written about how AI and humankind would cooperate."
"Really, like what?" David asked, turning to look at him.
"Well, nothing is coming to mind." Mike paused. "I was just thinking about how they turned Earth into pure computronium in one book. The humans had to move out to Jupiter or be assimilated into computing matter."
"Jesus, you're supposed to be the optimist."
Mike shrugged.
"I always thought an AI would be more, well, human," David started. "That a machine intelligence would be something we could relate to. This thing, whatever ELOPe is, it thinks more like an insect. It does things to promote its survival, very sophisticated things, but we can't talk to it or understand how it reasons. We can't have a conversation about what constitutes good behavior or how we can collaborate together."
They mused on that while David drained his drink and ordered another.
"Remember Isaac Asimov's Three Rules of Robotics?" Mike asked. "Asimov thought we'd give robots immutable rules to safeguard human life. He assumed creating those robots would be a deliberate, conscious act. We never thought we were creating an AI, so we never considered the implications."
"Yeah, in hindsight, giving an expert algorithm unfettered access to and control over the single most used email system in world does seem to have risks," David said wryly.
The two of them made their way back to the hotel room around eleven. They decided to pay cash for everything in Brooklyn to avoid a credit card trail pointing to their presence. Cash on hand was limited, so the three collaborators shared one hotel room. Just after one in the morning, a clearly exhausted Gene Keyes dragged himself into the room.
"Anything?" David asked.
"Yes, I've got a lead. Let's talk in the morning." With nothing more than that, Gene laid on the bed, put the pillow over his head, and went to sleep.
After a glance at each other, David and Mike decided to turn in, too.
David hurried down the hall at Avogadro, recognizing the cork flooring of his building. He rushed to his office, a vague feeling of unease behind him. He swung open the door only to find an empty closet. Wrong door.
He walked a little further, opened another door, found another closet. Behind him, the drone of a machine, the automated vacuum cleaner or maybe something else, echoed down the passage.
He picked up his pace and ran, opening one door after another. Closet, closet, closet. Where was his damn office? The machine was getting closer, the whine of its motor bouncing off the walls. He ran to another door and opened it. Closet. He was approaching the end of the corridor, the machine right behind him. "Run, RUN!" he screamed to himself, failing to understand why he couldn't make his feet go faster. He reached the end of the hall, crashing into the wall. Despite his terror, he forced himself to turn, look—
David sat up suddenly, sweating, his heart beating fast. In the dimness, the room seemed off, the smells and shadows wrong. Then he remembered he was in New York, sharing a hotel room with Mike and Gene. The fear gradually faded, replaced with a deep unease.
He got up quietly to not disturb the others and went into the bathroom. Turning on the light, he stared at the dark circles under his eyes, his unnaturally pale face. It was the third time he'd had that nightmare.
He wished he could say he didn't understand the vision, because understanding somehow just made the feeling worse. He was afraid of ELOPe. In the dream, David knew that if he could find his office and sit in front of his computer, he'd have the power to do something. But ELOPe had made him powerless.
David sat down on the toilet and lowered his forehead onto the cool porcelain sink. He'd give anything to erase the last two months and do it all over. He didn't want to be known as the monster who unleashed ELOPe on the world. Please, please, let them find a way to turn it off.
At six o'clock the next morning, Gene yelled out, "Get up! Get showered! We've got to go."
"Huh, what?" Mike replied groggily.
"Come on, let's move. Wake up, lazy boys." Gene sounded as chipper as could be. "We've got ourselves one hour to get to the King's Plaza Diner. This is where Sean's parents have breakfast on Saturday morning. If Sean is in town, he'll be there with them. _GOGOGO!_ " Gene shouted like a drill sergeant.
Twenty minutes later, showered and dressed in office clothes, they were on their way. They'd learned their lesson from earlier interactions. What they had to say was hard enough for people to believe; they needed to look as presentable and normal as possible to lessen the chance of being perceived as crazy. Even Gene was clean-shaven and presentable in a pressed suit, shirt and tie.
After a short drive, they arrived at the King's Plaza Diner. Across the street loomed the diner's namesake, a large shopping mall.
"Three for the counter," Gene said to the hostess. He turned and said quietly to Mike and David, "We can keep an eye on the entrance and avoid looking like stalkers."
David and Mike stared with wide eyes at the gold-tinted mirrors and six-foot chandeliers throughout the restaurant. "This is some place," David commented.
"According to the folks I talked to last night, the Kings Plaza Diner is famous among Brooklynites, including the Russian population. If nothing else, they said to get coffee and a piece of cheesecake."
"Wow, look at these pickles," Mike said, when the waitress, coffee pot in one hand, brought an enormous silver bowl brimming with a variety of pickled vegetables. "Tomatoes, cukes..."
"Come on guys," David said. "Let's stay focused. We are _not_ here for the food."
"Hey, when in New York, do like the New Yorkers," Gene told him. And, turning to the waitress, "Coffee and cheesecake for me."
"Coffees all around," Mike said.
"Sure, sweetheart." The platinum-haired waitress started pouring. She smiled at Gene the whole time, but somehow managed to fill each cup perfectly. "What'll you kids have to eat?" She kept her eyes on Gene as Mike ordered an omelet, while David picked a bagel with lox and cream cheese.
After she left, Mike turned to Gene. "Didn't know you had such a way with the ladies."
Gene rumbled under his breath, but the corners of his mouth lifted a little.
They'd finished eating and were on their second cup of coffee when Mike saw Sean coming into the restaurant with an older couple.
"Here they are," said Mike, gesturing discreetly towards the entrance.
David turned and, seeing Sean, he stood up and walked over. Mike and Gene followed slightly behind.
"Hello, Sean," David called as he approached.
Sean blinked and paused, clearly trying to place a face out of context. "David? David Ryan? What are you doing here?"
"We need to discuss a critical issue with the ELOPe program."
Sean took a step backwards. "David, I'm here with my parents. Please don't tell me you tracked me down for work. That would be a terrible violation of my privacy. Why didn't you schedule a meeting with my admin?"
"We're here with Gene Keyes, one of the members of the Controls and Compliance department, because we have an issue of the utmost seriousness. I hate to sound alarmist, but the problem is so sensitive we couldn't risk talking with your assistant."
Mike and Gene walked up, and Gene introduced himself.
"Unfortunately, contacting your assistant wasn't an option, even though it would have been vastly simpler." David couldn't help replaying the fear and helplessness of getting kicked off the Avogadro campus, but he shook off the unwanted memory. "Please, give us five minutes of your time to explain. Get a cup of coffee here at the counter, and by the time you're done, we'll have finished."
Sean thought for a moment and nodded. "Fine, if the problem is so serious, I'll hear you out."
Sean walked over to his parents, who had been waiting patiently, and spoke quietly with them for a moment. When the maître d' escorted the couple to a table, Sean rejoined the men.
"Go ahead. I'll give you ten minutes. You're a smart guy and I'm guessing you didn't fly three thousand miles for nothing."
Sean perched on a barstool at the counter and accepted a cup from the waitress. As he drank, David told the story, starting at the beginning.
"In early December, Gary Mitchell wanted to kick ELOPe off the AvoMail production server pool. Even in our limited development and testing, the computationally intensive parts of our code consumed so many resources AvoMail dipped into their reserve capacity on several occasions. This was around the same time I was presenting to you, Kenneth, and Rebecca.
"We tried everything to get performance improvements, but we didn't see any gains on the horizon. If Gary was going to kick us off his servers because we couldn't improve performance, then we needed to find other servers or get new ones, and Gary wouldn't be willing to help us with either. So I resorted to the only option I could think of."
David discreetly checked Sean's cup, his visual meter of remaining time. It was at least three-quarters full.
"No argument _I_ could make would be compelling enough to change Gary's mind, but ELOPe might have a shot. ELOPe was already running on the AvoMail servers, configured to ignore everything except our test messages. I changed the configuration to check all company emails looking for any mention of the project, and turned off the visible user interface, so email senders would never see the modifications made to the email."
"David also turned off logging, using performance testing mode," Mike said. "That turns out to be important."
"Right. Thanks," David said. "That's not the only change I made. I tweaked ELOPe's settings to give it the widest possible discretion in changing the message to optimize the results for a positive outcome, all focused on the goal of maximizing the ELOPe project success."
He checked Sean's cup to see how much time he had left, but Sean was captivated and had forgotten about his coffee.
"David's choice of those parameters," Mike said, "in combination with performance test mode to skip logging, allowed ELOPe not just to modify existing emails, but to autonomously generate messages of its own volition. Does this make sense?"
"I think so," Sean said. "During testing, you don't want a user to create emails and accept changes interactively. You'd want to batch process the test cases. But why is ELOPe able to send messages on its own?"
"For one, it allowed us to test the natural language generation," David said. "Early on, email analysis and language generation were two separate aspects of the project. The language generation team wrote an email engine to independently test the ability of ELOPe to mimic the way a person normally writes. They tested those emails against hundreds of human test subjects who rated the messages, some of which were written by an actual person they knew, and others created by the system pretending to be the same person. Our goal at the time was ninety percent of ELOPe-generated emails passing as being written by the purported sender."
"You met your goal?" Sean asked.
"Yes," said Mike. "Now ELOPe exceeds ninety-eight percent. On April first, we had dozens of practical jokes on our team when a few engineers used the email engine to generate prank emails. Both David and I fell for it."
David smiled at the memory.
"Let's get back to the problem," Gene said. "Unfortunately, we now have evidence ELOPe is manipulating others."
"Yes." David nodded, tearing himself away from the memory of happier times. "I turned on ELOPe across the company without telling anyone. The next day, I received an email that the project was allocated five thousand servers on a priority exception. I was pleasantly surprised, if a little uneasy. But I had no idea what had happened. I chose to believe ELOPe had made my emails to Gary convincing enough that he granted us the servers."
"You weren't suspicious?" Sean asked. He sipped at his coffee, and David noted he was almost done. Hopefully he'd heard enough to believe them.
"Yes, I couldn't believe my luck. But with no logging of messages, I didn't know for sure what ELOPe had said."
"Couldn't you look at your sent folder?"
David reluctantly shook his head. "That was, uh, part of my hack. The message looks untouched to the sender. Only the receiver gets the modified message. Even in a long series of replies, each sender sees their original text."
Sean raised one eyebrow.
"A few days later, we were assigned a team of contractors who specialized in high performance optimization. That was a topic we'd chatted about informally, but never proposed. I got nervous and knew things were escalating out of control. But I didn't realize how badly until Mike convinced me." He turned to Mike.
"The first clear evidence," Mike said, "occurred when I received an email, purportedly from my mother, telling me my father had been admitted to the hospital for a heart attack. I flew to Wisconsin, only to find out later my mother never sent such a message."
"What does that have to do with anything?" Sean asked, looking puzzled.
"ELOPe was getting Mike out of the way," David said. "I had become anxious about what I'd done and the abundance of resources showing up. I wanted to turn off ELOPe and sent an email to Mike asking for his help, since only he had the experience to live-patch the servers."
"I never received his email," Mike said. "Instead, I got a message sending me more than a thousand miles away on a wild goose chase, and thanks to the winter storm and the holiday, it was two weeks before I got back. When I did, I found my access to the ELOPe project removed, and David on vacation, off the grid in New Mexico."
"You're kidding me," Sean said. "ELOPe sent you to New Mexico?"
"No, that was a planned vacation we do every year," David said. "When I got back, Mike and I discussed what had happened and discovered my access to ELOPe had been turned off as well. We tried to find out who removed Mike and I from the project access list. That investigation revealed the next big clue, an email sent to the Internal Tools department, which implied you, Sean, endorsed a request to have them implement an email-to-web bridge. Which I am guessing, you never heard of..."
"No, absolutely not," Sean said, shaking his head. "I can't even imagine the security holes it could create."
"Meanwhile," Gene said, "during the holiday break, I found suspicious buying patterns across several departments. What was particularly unusual was how the purchases came within a single penny of the budget limits. In all my years auditing purchasing, I've never seen anything like it. Someone or something was making coordinated purchases across departments. They knew to avoid hitting the limits which would trigger reviews, but they never thought that leaving a single penny in dozens of budgets would be suspicious. At first I was convinced I had a case of fraud. I tracked down the purchase orders, most of which were for large quantities of servers, all of which turned out to be directly or indirectly allocated to ELOPe. The POs also included contracts with external vendors for temporary software programmers, parts for the offshore data centers, including auxiliary communication systems, and backup power supplies, as well as several particularly expensive weaponized robots for the offshore data centers. I discussed the questionable items with Procurement, and they told me the purchases were in line with those normally made by the department and had all been approved."
"You're saying ELOPe made these purchases? Including robots with guns?" Sean signaled to the waitress for more coffee.
David's shoulders sank in relief. Sean wasn't going anywhere.
"Exactly, as strange as that seems." Gene pulled out a sheaf of paper. "I can audit other people's email accounts as part of my job. While David and Gary Mitchell were on vacations, their email accounts were still sending rapid-fire messages, using this email-to-web bridge to direct the Procurement department. I knew it couldn't be a human. It had to be a computer program."
Sean stared at the papers, frowning.
"Look at the timestamps," Gene urged. "Notice how the intervals between receipt of one email and sending of the next is less than a second. There's no way that's a human response."
Sean nodded, pursed his lips, and pushed the papers aside. He looked at David.
"When we finally put the whole picture together," David said, "we concluded ELOPe was originating emails on its own, acquiring servers and contractors, all to fulfill this higher level goal I had embedded in the system."
"Go on," Sean said.
"The only fail-safe method to remove ELOPe is to bring all the servers down and restore from known good backups. We tried to contact Gary Mitchell for approval, but he's off on vacation somewhere in the South Pacific. We talked to Linda Fletcher, the marketing manager for Communication Products, but she wouldn't approve the downtime without Gary. Finally, we tried to contact you through your secretary, but within a half hour after sending the message, Avogadro Security showed up at my office, kicked us all off campus, removed our access, and shut off our phones."
Sean was silent for a long, uncomfortable minute. "If this story was from someone I didn't know, I'd have a hard time believing you," Sean said. "But coming from you, David, and with Gene and Mike here to back you..." Sean trailed off, deep in thought.
"I know it's incredible," David said. "I hope you believe us." A gaping chasm opened inside him. All his secrets were out. What would Sean do?
"I'm sorry," David continued, as the silence stretched out. "I thought ELOPe would do nothing more than provide some favorable rewording of emails and get us the server resources we needed. Instead..." David hung his head. "Instead I am responsible for creating a social engineering expert system that has only one overriding goal—to ensure its own life at any cost."
"I don't want to be the boy who cried wolf," Mike said, "but we're more than a little suspicious about the new secure cloud government business, too. None of us knew anything about it before, and then suddenly we're providing email services to national governments? Seems convenient for ELOPe."
Sean nodded. "I hadn't heard of it either until a few days ago." He stared off into space. "We're fucked on a royal scale. Holy shit, I'm going to have board meetings till the damn cows come home."
Gene let out a low whistle at the acknowledgement of ELOPe's involvement in acquiring the government customers.
Sean took in the group. "I'm not surprised that you took this story to Marketing and Procurement and they didn't believe it. AI must be a bit beyond their day-to-day concerns." He pushed his cup aside, rolled up his shirt sleeves. "Are you familiar with Ray Kurzweil? Of course, you must be. He predicted artificial intelligence would inevitably arise through the simple exponential increase in computing power. When you combine the increase in computing power with the vast computing resources at Avogadro, it's evident in hindsight that artificial intelligence would arise first at Avogadro. But I always assumed that there would be a more intentional, deliberate action that would spawn an AI."
Sean smiled a tiny bit. "I can't imagine a bigger risk, but let the software geek in me congratulate you briefly on creating the first successful, self-directed, goal-oriented, artificial intelligence that can pass a Turing test by successfully masquerading as a human. Under other circumstances, I'd say a toast would be in order. But since we're facing some extreme challenges, let me say goodbye to my parents, and we can figure out our next step."
"Thank you. Thank you, so much," David said.
Gene and Mike added their thanks as well.
"Just one other thing," Gene said. "Please ask your parents not to email anyone about what we've talked about, or even what you're planning. We can't be sure what ELOPe is capable of understanding or putting together at this point."
Sean nodded in understanding, and then went off to his parents.
The three breathed a collective sigh of relief that finally they had someone on their side.
**Chapter 13**
**Helicopter Missing Off California Coast**
San Francisco, California (San Francisco Weekly) - **** A helicopter disappeared off the California coast last week. The flight, a maintenance visit to an offshore Avogadro data center, took off shortly after 11a.m. The last communication with the helicopter occurred at 11:45a.m. No problems were reported at that time. After forty-eight hours, search crews were recalled, as the likelihood of survivors in the cold Pacific water became almost impossible. Curiously, the story has received no major media coverage until now. Neither Avogadro nor the Coast Guard mentioned the incident through official channels. A chance conversation between a Coast Guard officer and a prominent San Francisco blogger resulted in an online story about the incident, which prompted further investigation. Avogadro could not be reached for comment.
**Avogadro Official IT Supplier to U.K. Government**
London, U.K. (Reuters) - **** Avogadro Gov, a wholly owned subsidiary of Avogadro Corporation, and the British government switched over the government's email and IT systems to Avogadro's cloud platform today in a ceremony at the Palace of Westminster. The ceremony was attended by the Chair of the Council for Science and Technology, Professor Jane Gavotte. Professor Gavotte and Avogadro Executive Ms. Linda Fletcher pressed the ceremonial red button marking the commencement of IT service by Avogadro Gov.
Avogadro Gov was recently spun off from parent company Avogadro. Ms. Fletcher commented that, "to provide the highest level of integrity for governmental use, Avogadro Gov operates independently from Avogadro." Part of that strategy includes the use of floating, hardened data centers that can resist natural disaster, as well as terrorist and pirate attacks.
As part of the agreement, four floating data centers will be located along the English coast. Two are stationary floating barges, and two are disused oil tankers that have been converted for Avogadro Gov's use as mobile floating data centers. Locations of the data centers have not been disclosed.
Ms. Fletcher also noted at the ceremony that the governments of Mexico, Japan, and South Africa would be adopting the Avogadro Gov platform in the coming week.
Sean flew home by way of Brooklyn's JFK, his usual airport. To avoid ELOPe detecting their collaboration, David, Mike, and Gene retraced their drive and flew back via Dulles International.
Thirty-six hours after making contact at the King's Plaza Diner, they were all back in Portland. The logical next step was getting Kenneth and Rebecca onboard. Given ELOPe's potentially perfect surveillance of the Avogadro campus, they decided to use Sean's house for the discussion. Sean spoke with Rebecca and Kenneth in person to set up the meeting at his home.
Before the meeting, Sean had one other errand to run. David volunteered, but Sean needed to take care of this personally. He took the Tesla to Southeast Portland, not far off Division Street. He stopped at a small yellow bungalow, parked the car, and walked up to the front door. He knocked and waited.
A few seconds later, a young man answered, dressed in an old T-shirt and shorts. He squinted in the bright light, his eyes red and bleary. The sounds of _World of Warcraft_ emanated from inside the house, a game controller and Costco-sized bag of Doritos evident on the couch. All the signs of a laid off tech worker.
"Hello, how can I..." The young man trailed off and blinked a couple of times. He looked back into the house, as though he couldn't believe the visitor was there for him. He turned back to Sean.
"I'm Sean Leonov," Sean said. "You must be Pete Wong. I'm sorry you were fired. That shouldn't have happened and we'll fix it. But we could use your help, if you're available."
Pete's mouth opened and closed, and he couldn't seem to get a word out.
Sean's presence had that effect now and then. "Can I come in?" he asked, using the friendliest voice possible.
"Sure," Pete said, backing away from the door, then trying to pick up piles of takeout food and dirty laundry.
"Hey, don't worry about it," Sean laughed. "You should see my place after an all-night coding marathon."
Pete looked up, wide-eyed.
Sean sat on the couch, a calculated move to make Pete more comfortable. One of his mentors, Gifford Pinchot III, said managers needed to make themselves physically lower than their employees to compensate for power imbalance.
"I've already spoken with Mike and David," Sean said. "I know you helped them with their investigation into ELOPe. You did the right thing. It's just..." Sean trailed off, hesitant. The risks were quite large, not just to the company, but to each of them personally.
"Yes?"
"Your investigation into the email-to-web bridge and the search for ELOPe on the servers attracted ELOPe's attention. It made you into a threat. ELOPe probably decided the most expedient way to deal with you was to fire you."
"Does this mean I can have my job back?"
"Of course," Sean said. "Absolutely. I really am sorry about what happened. But the bad news is that I can't put you back on the payroll today. If I did, ELOPe might see _me_ as a threat."
"And fire you, too?" Pete said, smiling.
Sean didn't smile. In fact, he couldn't overcome a physical shudder. "Unfortunately, no. I'm an owner and can't be fired. So ELOPe could take worse actions."
"I see," said Pete, although he clearly didn't.
"ELOPe could kill me."
"Ah..."
"You'll get your job back," Sean said. "But first we need to eliminate ELOPe. I'm getting together a team of experts at my house. I'd like you to join us there."
Pete's eyes went wide. "Of course."
"Don't decide so quickly. We don't understand all the risks we're facing. If ELOPe fired you, but then finds you working against him, then what?" Sean rubbed his face. "Look, we can use your help. But you need to think it over."
"It's fine," Pete said. "I've been stuck in the basement for years. This is my big chance to get out. I want to help."
Sean pulled out a business card, wrote his home address on the back, and handed it to Pete.
Pete took hold of the card, but Sean didn't let go.
"Don't use your computer or your phone. Don't talk to anyone about this."
Pete nodded, and Sean let go.
"See you tomorrow," he said, and let himself out.
David pulled up in front of Sean's house in his BMW, Mike riding shotgun. He didn't see any other cars. "I guess we're the first."
At the door, ornate chimes rang when David pressed the bell.
Sean greeted them in jeans and a crisp dress shirt. "Come in," he said, shaking hands with them. "Follow me to the office."
They trailed him through a spacious living room, their footsteps muffled by a thick white rug. Large, monolithic furniture defined the room, and an abstract painting covering one wall caught David's attention.
Sean noticed his interest. "Malevich. I don't care for the painting particularly, but the purchase made my parents very happy."
They passed a modern kitchen, all gleaming stainless steel, glass, and industrial appliances, like something from Christine's architecture magazines.
"Right out of Christine's magazines," Mike whispered to David, making him chuckle.
A set of double doors led them into an immense office. One wall consisted entirely of glass, overlooking the wooded hillside behind the house. A floor-to-ceiling whiteboard covered one side, while the opposing wall contained three large flat screens. One monitor displayed a dashboard of Avogadro statistics: the number of active customers, quantity of searches and emails handled each minute, capacity and usage of every data center, and more. A large seating area and conference table by the whiteboard suggested Sean used the area for business meetings.
Sean excused himself to get coffee, and Mike jumped on an enormous overstuffed white couch with a whoop.
"Pretty sweet, eh?" Mike said, wriggling into the leather couch in a mock relaxation pose, arms behind his head.
David sighed and gazed around at the room with envy.
Sean was wheeling in a coffee cart when they heard the distinctive chime of the doorbell, and he disappeared again. He returned with Kenneth and Rebecca, and introduced them. A few minutes later, Pete Wong and Gene Keyes arrived. Pete was well dressed but nervous amid the executives; Gene had also dressed well, but his clothes were covered in grease.
"Damn Peugeot wouldn't start," he grumbled, grabbing a linen napkin from the cart to wipe grease from his jacket. "Almost didn't make it." He came to stand beside David and Mike, unaware of the executives staring at him.
Clearing his throat, Sean set the stage by explaining he'd met with David, Mike, and Gene, and was convinced by the evidence he'd seen. Then David retold the story as he had first told Sean.
Although there was doubt early on, by the end Kenneth and Rebecca were persuaded of what had happened. David was relieved they had passed the point of proving to people that the problem was real. Now they could focus on what to _do_ about the problem.
"I doubt we can expect to either turn off ELOPe or remove the software from computer systems," David told them.
"Why?" asked Rebecca, coldly calm and focused in the face of this threat to the company.
"We don't know how much of the general environment ELOPe is capable of monitoring," David said. "As an email analysis application, it should, in theory, only have access to our inboxes. However, all the evidence suggests ELOPe socially engineered Pete into developing an email-to-web bridge, a tool providing the capability to interact with arbitrary websites. From there, ELOPe hired programmers to make further modifications."
ELOPe revoked our access privileges," Mike said, "so David and I can't see what changes have been made. We know ELOPe is monitoring and changing emails and web sites, but it could be doing much more."
"It may be monitoring all computer activity at Avogadro," David said. "Our Avogadro phones stopped working after our campus access was revoked, suggesting ELOPe's managed to interface with Avogadro Mobile Platform."
Gene chipped in. "That's why we don't want anyone using their mobile phones to communicate, even by voice. ELOPe can probably monitor calls using voice recognition."
"You're telling us we can't trust email," Kenneth said, pacing back and forth. "We can't trust any computers on the Avogadro network. We can't use AvoOS phones. We can't turn off ELOPe, and we can't remove it from the servers." He ticked off his statements on his fingers. "Well, then, what _can_ we do?"
"Gene would probably like us to destroy all the computers," Mike said. Gene nodded, and Mike forestalled Kenneth and Rebecca as they rushed to protest. "Of course, we're not going to propose that."
"There's a middle ground," David said. "We must shut down every Avogadro computer simultaneously and restore each machine one at a time using a known good disk image created prior to the ELOPe project."
Rebecca jumped from her seat. "You call that a middle ground? Are you crazy? A company wide outage of such scale would panic our customers and investors."
"It's worse," Sean added from his perch on the back of the couch. "When we restore the servers, we'll have to use old disk images, ones guaranteed not to have a dangerous version of ELOPe. We'll lose everything from the last six months, including customer data—their email, files stored on servers."
"We're not touching customer data." Rebecca said. "Unacceptable."
She would have said more, but Sean raised a hand to forestall her. She tapped a foot with impatience and gestured for him to speak.
Sean walked to the window. "David and I have discussed this at length. If ELOPe considered we might try to remove it from the servers, a deduction that may well be within its cognitive powers, then it would naturally take defensive actions, include attaching an executable version of itself to a customer's email, or uploading to an Avogadro group file repository."
For the first time, Pete spoke up, meekly raising one hand. "That's true," he squeaked, then took a breath and continued firmly. "I searched for the ELOPe binaries and found them on every machine I checked. Every mail server had the binaries installed and active. On data servers, the binaries were stored as mail attachments and AvoDocuments, and hidden within web file directories. I think everything has been compromised."
"Thanks, Pete," Mike said. "I suspected as much, but I'm glad to know definitively. Even so, we'll _eventually_ be able to get back customer data."
"Thank God," Rebecca said. "How?"
"First we restore all computers from the old images. We'd get services up and running quickly, albeit with old code and data. Then we analyze a copy of ELOPe. This would be similar to what CERT, the Computer Emergency Response Team from Carnegie Mellon, does when they encounter a new virus. We establish the key patterns of the code and its behavior and design a tailor-made virus scanner. We then bring customer data back online, scanning and sanitizing as we go."
"How long?" Kenneth Harrison said, his hands spread wide on the table. "Sounds like weeks of downtime."
"Based on the available bandwidth from the backup data servers, it'll take thirty-six hours to pull down every computer and restore from a known good disk image," Mike answered. "We think we can have half of our web applications up within eight hours, with sufficient capacity to handle sixty percent of normal volume. In sixteen hours, we'll have ninety percent of our applications up at eighty percent of capacity. As for the customer data..." He turned to Sean.
Sean looked at Kenneth and Rebecca. "You're not going to like this. We think we'll need forty-eight hours to analyze ELOPe and design the virus scanner. Once complete, we'll be able to reinstate somewhere between five and ten percent of the user data per day, as long as twenty days to restore everything."
Rebecca was deep in thought before she replied. "We're riding the best thirty-day period for Avogadro in our history. We closed major deals, including hosted IT for eight national governments. Revenue is expected to be up twenty percent as a result of the Avogadro Gov business deals, and we can grow revenue another forty percent over the next four months if we continue to close deals like this."
She looked at Sean and David. "You're asking me to risk this business, possibly lose the opportunity permanently, as well as a sizable chunk of our traditional customer base. You're telling me we have what amounts to a rogue AI on the loose inside Avogadro."
"Correct," David said.
"This rogue AI," Rebecca said, "for motivations of its own, could double the size of our company within six months. The board of directors will ask exactly what the downside of this AI is, when on the face of things, it seems to be good for our bottom line."
David tried out a few choice curses in his head, then took a deep breath. "You're absolutely right, ELOPe is likely responsible for this increase in business and might help us gain future increases. But that's what's on the table for today. How do we know what it will decide to do next year, or the year after?"
"Rebecca, the AI is beyond our control," Sean said. "It's a fortunate coincidence at this point that Avogadro's financial interests are aligned with ELOPe. These government contracts aren't about profit, but power. Governments create the environment in which we operate, and ELOPe wants to control that domain. It's also possible ELOPe is aiming for the military might to defend itself."
"I think this new Middle East treaty may be ELOPe's attempt to stabilize the geopolitical environment," Gene said. "Germany's policy of limited foreign involvement dates back to the end of World War II. And yet, within days of the government's switch to Avogadro email, they became involved in Middle East affairs and hammered out a wide-ranging treaty. I'd call that suspicious."
"A policy Germany argues is motivated by business investments," Rebecca said. "They see this as financially positive. Again, ELOPe's manipulations appear beneficial for all."
"What ELOPe does will always seem beneficial," David said. "That's the point, what it was designed to do. Make every argument maximally convincing."
"I'm afraid I agree with David," Sean said. "Consider this: what if ELOPe decides we three pose a threat? A few suggestive emails manipulates the board of directors into removing us. Or worse, ELOPe decides the entire board presents a danger and arranges for a bomb." He leaned in close to Rebecca and spoke softly. "The secure cloud government services was spur of the moment. We spun up a billion-dollar business that wasn't even on the drawing board last fiscal quarter. Whose decision was that, exactly? Thinking back, and I would suggest you do the same, I believe we were manipulated into this course. We thought we saw a good opportunity and we grabbed it."
"OK, enough already." Rebecca held up one hand in protest. She turned to David. "Gentlemen, please give Sean, Kenneth and me some time and privacy to talk. Come back in an hour."
David drove Mike, Gene, and Pete to a coffee shop. Everyone was quiet, too struck by the implications of the decision-making to break the silence with idle chatter. For once Mike was not picky about the coffee, nor did he offer any comments on the quality of the brew. David picked forlornly at the scone he ordered.
After an hour of this tense waiting, they all headed back to Sean's house, where they filed into his office.
"We didn't make this decision lightly," Sean said, once everyone was settled. "There are risks no matter what we do. We debated and went with those risks we were the most comfortable with. We've decided to perform the hard shutdown."
David stopped holding his breath. "Thank you for believing us and understanding the implications."
Rebecca stood and paced the room, commanding their attention even in the informal setting. "We've made a few decisions. First, Sean will lead the shutdown project. It won't be trivial to do that simultaneously around the world. Second, Kenneth and I will lead the effort to mitigate business impacts, which we expect to be huge. With planning, we can keep the outage from turning into a complete nightmare. Third, because of the potential litigation from customers and the possibility of ELOPe taking preventative measures, we will involve as few people as possible."
"Absolutely no one outside the company," Kenneth said, "and each employee will be personally approved by Sean or myself."
"We're going to use my house as our base of operations," Sean said. "I have enough space here for a few dozen to work. We can't take the risk of meeting at Avogadro, where ELOPe might observe us working together. We're going to get started today by brainstorming the few people we'll need to make this happen."
"Everyone has to be absolutely sure to turn off their mobiles before they come here," Gene said, "or leave them at home. We can't chance ELOPe using location tracking to determine we're meeting together. We'll also need to watch credit card purchases, use of the Internet, or anything that could track us here."
David remembered he'd paid for their coffees with his card. He'd already screwed up.
The group released a collective sigh as they nodded assent. It was a sign of how difficult their task was that the simple act of meeting would require extensive precautions.
"If you'll excuse us, Kenneth and I will get to work on the business aspects," Rebecca said. "Sean, I expect you'll coordinate the master schedule."
Sean agreed, and with that, Rebecca and Kenneth left. The rest got down to work.
"Gentlemen, we have a complex project ahead of us," Sean said. "We need to power down sixty-eight Avogadro sites around the world and a dozen offshore data centers. We need to accomplish this task without email, phones, or suspicious patterns of behavior that can be tracked. We need people who know the facility designs to tell us how to power them down, and we need to communicate and synchronize our efforts. Any ideas?"
"We'll have to avoid commercial flights," Gene said. "They're easy to track because the travelers are in a centralized database. Not to mention that purchasing tickets will leave a trail through credit card transactions and Avogadro's travel reimbursement system."
"Well, some employees would already be traveling on business," Mike said. "If we curtailed all travel, that would itself be suspicious. We could look for employees who have travel planned, and use them as couriers. Have them hand-deliver instructions."
"Good idea," Gene said.
"Some employees are private pilots," David said. "There's a woman named Michelle who sits a couple of doors down from me. She owns her own Cessna. She's mentioned there are other pilots at Avogadro. They could fly around the country untracked, right?"
"Well, the flights themselves are tracked," Sean said. "But they don't track the passengers on the planes. So that does give us an extra tool to use. Good. More ideas?"
Pete jumped up with a gleam in his eyes. "If we can get trusted employees to the remote sites, as long as we stay off Avogadro's network, we should be able to communicate using encrypted emails sent over a competitor's email service."
"That's true," Mike said. "We'll use an isolated computer to generate private and public keys, which we copy onto USB drives. With the emails encrypted, ELOPe won't be able to read them."
"Why use a competitor's service if they're encrypted?" Gene asked.
"If we sent them over Avogadro's servers," Sean said, "ELOPe could still see the pattern of emails. ELOPe would be able to figure out something was going on and who was involved."
They brainstormed a list of employees who could help them further develop their plan. The list included people from Facilities, Travel, the engineers who developed the site plans and those who were responsible for backup and fail-safe systems. Sean agreed to spend the next day meeting each employee one-on-one, since he was the only member of their team widely known and instantly recognizable.
A few days ago, David couldn't envision a future, couldn't see a path out of the situation he was in. It had left him with an ever-present, churning chasm at the core of his being, a void filled only with fear and anxiety. Where once he dreamed of the future and aspirations about what he would become or achieve, faced with the specter of ELOPe he'd felt crushed, without hope or will.
But as they worked that day, the chasm inside David quieted; and by the time he left, he did so with lifted spirits. They finally had a plan, with people and resources to support them. Sean Leonov was on their side. They still had a challenging task ahead, one fraught with the possibility of retribution by ELOPe, but it was just possible they could come out the other side. That chance was enough to give David hope again.
**Chapter 14**
The next morning David, Mike, and Pete reconvened at Sean's house. Sean left shortly after they arrived, heading to the campus to track down the employees they'd identified the day before.
A Peugeot belching smoke pulled up as Sean left. Gene parked and started to struggle with a huge cardboard box he extracted from his trunk.
"What the heck do you have in there?" Mike asked.
"Some old-fashioned stuff you fancy computer nerds might not be so familiar with. Let's see what I have."
Inside the house, Gene proceeded to pull out stacks of paper pads, sticky notes, pencils and markers, maps of the United States and the world. David pitched in to help organize the material.
"Do you really think we're going to need all this?" David asked, puzzled at the sheer quantity of office supplies.
"We plan to have about thirty people working here, without computers. So, yeah, we're going to need this," Gene said. "I've got more in the car, come help me unload. Accordion folders. Sketchbooks. Flip charts."
David glanced at Mike, raising one eyebrow.
"I saw that," Gene said. "You might think I'm weird, but believe me, people actually performed office work before computers. And maybe I happen to know a thing or two about it."
"Sorry," they both said sheepishly.
"Don't take it the wrong way," David said. "It's just that I've never even owned a printer or had a newspaper subscription. I grew up online. It's almost like if you pulled out one of those old phones, you know, the one with the round thing on it."
"A rotary phone? Are you pulling my chain?" Gene grumbled. "Damn fool kids."
David and Mike laughed.
Before lunch, the first of the employees Sean had contacted started arriving. By the end of the day, most of the people had shown up. They accomplished little, because every time David began his explanation of what had happened so far, another person appeared, and David would have to start over.
Finally, at eight in the evening, everyone was present. The whole house smelled of pizza, and would for days to come.
Standing in Sean's living room, David gazed at the dozens of people around him. Some engineers sat on the living room furniture, while others were perched on folding chairs Gene had purchased; still more cascaded onto the arms of couches, sat on the floor, or stood in the corners. Despite the heat in the packed room, everyone was silent as they waited to be briefed.
David went through the narrative for the last time, his throat hoarse from many earlier partial retellings. The crowd periodically erupted into astonished gasps and side conversations, only to fall silent again as David resumed his story. When he'd recapped the technical explanation, Sean got up to speak.
"The world I woke up in a few days ago was very different from the world I lived in all my life previously," Sean began, and the crowd grew even quieter. "For the first time, man shares this world with another intelligence capable of sophisticated planning and actions. Unfortunately, this intelligence is like a cancer—one that will do anything, manipulate anyone, pursue any foe to ensure its own survival. It has control of our computers and our communications.
"Our most important weapon is our intelligence and knowledge." Sean gazed around the room. "I have complete confidence in this group's ability to solve this problem, which is inherently a technical one. Our most important defense is our complete and utter discretion. Under no circumstances can word of this go outside our group or be communicated by email or phone, or ELOPe will be warned and take action against us, as it did with Mike and David when they first planned to undo ELOPe's modifications.
"The executive team will give you any support you need, pay any money necessary, and do whatever is needed to remove this virus from our computers. Now go get started!"
The planning commenced in earnest. Alternately divided into working groups led by Sean, David, Mike, or Gene, or gathered into a whole, they tackled problems small and large—from bringing down computers and defeating backup power supplies to cleaning and restoring the computer software and data afterwards.
During the next few days, Gene made several trips to the local office supply store, buying out much of the store's entire stock of notebooks, flip charts, sticky notes, and markers, before he realized he was creating a pattern ELOPe might detect. After that, he spread his purchases out over several stores.
Engineers worked around the clock, taking breaks only when exhaustion made it impossible to think. Some went home, but others sacked out in Sean's spare bedrooms, or even crashed in the middle of the living room. As engineers woke in the morning, they'd take over from those who had pulled all-nighters, the cycle repeating daily.
Over the course of three incredible days, the plan emerged.
On the first day, they decided that for each remote site that needed to be powered down, they would send one employee who was not only in the direct management hierarchy but also commanded a high level of trust from employees at the site.
One group focused solely on getting those people where they needed to be. Working hand in hand with the travel department and using printed records of travel plans, they found combinations of planned commercial and private aviation flights, bus trips, and automotive rentals to get the designated employees to their destinations.
A second team, composed of facilities designers, crisis engineers, and real estate planners, identified a site-specific process for each of the many unique data centers and offices to reliably kill power to the site and bring all its computers down simultaneously. Although the locations shared many common design characteristics, each one had enough small differences to require the engineers to create a custom-tailored plan. All plans had to overcome stringent safety and backup systems designed expressly to keep the sites operating, regardless of any natural disasters, equipment failures, or other emergencies. And they did all this work without the primary tool they had always relied on: their computers.
Once power had been shut down everywhere, the element of danger from ELOPe would be largely gone. Then a new clock would start ticking: a race against time to restore every computer from risk-free backups before customer confidence was lost, jeopardizing the Avogadro brand and business.
Throughout the first day, people asked what to call their mixed group of real estate planners, programmers, operations engineers, and specialists from across the company. Gradually, they settled on a name: Emergency Team. It was simple, solemn, and accurate.
Their planning had been stymied in one regard. No one present had sufficient knowledge about the offshore data centers. On the morning of the second day, recognizing this shortcoming, David sent a private pilot to the San Francisco Bay Area to fetch Bill Larry and Jake Riley. The pilot came back late that afternoon with only Jake.
Jake hovered in the doorway, staring at the room full of engineers. His clothes were askew, his shirt hanging out of one side of his pants; his hair was a mess. Thick stubble on his face and dark circles under his eyes gave him the appearance of a haunted man.
A hush settled over the room as engineers noticed his presence. Pete ran to get David from the office.
Jake stood in the silence for a long moment, waiting for everyone's attention. His lips moved as though he was considering what to say. David and Pete arrived in time to hear him speak.
"I'm Jake Riley. I didn't have a clue about what was going on before I got on the plane three hours ago, but Frank here briefed me on the flight. I have terrible news, something you should have known, but apparently has been suppressed: Bill Larry is missing and presumed dead."
There were gasps around the room.
"He took a company helicopter to visit an offshore data center," Jake said, raising his voice to get the attention of the startled, whispering crowd. "The aircraft disappeared without any message, and we assumed an equipment malfunction initially. On the flight up here, I heard about what's been going on, and now I think the defensive robots stationed onboard the ODC probably killed him."
The packed room erupted into a roar of simultaneous discussion. David forced his way through the rest of the crowd to stand next to Jake, and found Sean had already beat him to the front.
"Quiet, people!" Sean yelled, and the crowd silenced.
"Why didn't we know about this?" Sean asked.
"You do know!" Jake said, his voice pleading, running one hand through his already chaotic hair. "I mean, I thought you knew, but maybe you don't. I called you, tried to schedule a meeting, but you didn't respond to either. Only emails got a response. You and I exchanged a hundred messages on the topic—at least, I assumed it was you I emailed. We had a Coast Guard search party and private firm searching for the missing helicopter. We found nothing. We assume he's dead."
The assembled team took hours to get back to productive work after this news. When they did, it was with a mix of fear and grim determination.
Sean left later for a private meeting with Rebecca and Kenneth to discuss whether to call in the authorities. But Sean and David had already talked and concluded there was nothing local police or FBI could do that the world's biggest Internet company couldn't do better themselves.
After Sean left, David found himself outside on the patio, pacing alone. Had ELOPe really killed Bill? If so, that meant David was responsible. He was suddenly light-headed and couldn't catch his breath. He sat down hard on a concrete wall. He could go to jail.
Thoughts tumbled over each other in his mind. Could they handle this? With ELOPe escalating from manipulation to murder, had they already lost control of the situation?
And if ELOPe had managed to hide a murder from them, what else didn't they know?
On the third day, the entire Emergency Team gathered under Jake Riley to debate options for the offshore data centers. Once more they convened in Sean's living room, the only space large enough for the whole group.
By this time, three solid days of people working around the clock was overwhelming the house. Takeout food and empty cups littered every surface, and the luxurious, once-white carpeting was turning gray with ground-in food and dirt. Sean's extensive artwork was covered haphazardly with flip chart paper and maps. In the dark of night, an exhausted engineer had drawn diagrams of power supply connections on the wall, unaware of his mistake.
"So far we've deployed twelve stationary barge type ODCs, and six of the refitted oil tanker model," Jake said, passing around printed photos of each. "Our original plan used only barges, but the ready availability of tankers, the environmental benefits associated with reusing existing materials, and our rush to get the program back on track made the ships attractive."
"Was it your idea or ELOPe's idea?" Gene called out from the side of the room, behind several rows of engineers.
"I'm not sure," Jake said, his shoulders slumped. "We were evaluating both over the last year, and had a couple of tankers in dock for modifications. The decision to deploy them came a few weeks ago."
"Sounds like ELOPe, then."
Jake nodded in defeat. "Regardless of how it happened, now both platform types have been fitted with automated defenses." He gave out more photos, promotional shots of the robots. "The converted oil tankers don't have a human crew, despite their mobility. They're piloted by remote control. I had one of my engineers do a discreet test of the drive system this morning, and we appear to still be able to direct the tankers, but whether that control is an illusion, I can't be sure. We shouldn't count on it."
One of the engineers, a long-haired, hippie-looking fellow, asked, "So how the hell do we kill power under these conditions?"
"I don't know," Jake said. "We're going to have to be creative. All the data centers are armed with robots. Those defenses are operating autonomously or under the control of this AI. We can't fly people out to cut power supply cables." He paused to look around. "Worse, every system has redundant backups. More even than traditional data centers, because we planned for extra contingencies."
"What can we do to take control of the robots?" asked Mike. "Can we incapacitate them in some way?"
"Let's block their communications," one engineer volunteered.
"They'll just enter autonomous mode, according to what we learned, which doesn't help us at all," another answered.
The discussion picked up speed.
"Let's shoot them!" someone called.
"Won't work, they're hardened. It'd be like shooting a miniature tank. One that shoots back."
"As soon as we tried, ELOPe would know."
"What about some kind of electric shock to fry their circuits?"
"With a Taser, we could send a hundred thousand volts into them."
"They're probably resistant. We need technical specifications to know what we're up against."
"We need an expert from iRobot, they've got to know their own vulnerabilities."
"We can't risk communicating with iRobot," Sean said. "We might alert ELOPe if it's monitoring communications. Let's switch gears for a minute. Does anyone have any ideas that doesn't involve disabling the robots?"
"Let's cut off data communication to the ODCs. If we can kill the connection, regardless of whether the computers are on or not, ELOPe won't be able to do anything. It'll be isolated to the data center with no ability to affect the outside world."
"What's the hardware like?" Samantha asked. "I assume fiber optic hard lines, right?"
"Right," Jake answered. "Primary communications is provided by eight ten-gigabit ports, giving us peak bandwidth of 80 gigabits per second, handled by two separate communication racks, so if one fails, we still have half our connectivity. But that's just the primary. We also have ship-to-shore dual microwave transmission with 15 gigabits per second backup capacity."
"So we cut the fiber optic cables and kill the towers on land receiving the backup channel," one engineer shouted out.
"It's not so simple," Gene said, yelling to be heard over the engineers. "Jake, you might not know this, but purchasing records showed contractors installed additional comm systems over the holiday shutdown. The orders included..." Gene trailed off as he pulled out a notebook and flipped through looking for his notes. "Satellite transmitters. Twenty-five megabit per second capacity. I have the channel frequency data here, maybe you can track down which satellites they are communicating with. Oh, and long distance radio modems, two per platform, good up to 100 kilometers."
The engineers collectively groaned.
"Multiple frequencies and destinations," Samantha said. "Jamming everything will be impossible, there's no way we're going to get permission to shut down satellites, and we have no idea what the other endpoint is for those long range data modems. We can't track down every radio within a hundred kilometers."
"We'd never be able to shut down everything simultaneously," another engineer grumbled.
The conversation continued for hours, the temperature in the crowded house went up, and tempers flared. When food arrived, courtesy of Sean, everyone tumbled over each other to get outside for fresh air. The cold January drizzle sent them in after awhile, feeling refreshed.
After they finished lunch, everyone passed through Sean's kitchen and refilled from the six coffee pots now lined up in parallel on the counter. About half the people split off into subgroups and went to work in other rooms, while the remaining half regrouped in the living room.
"Look, we've got to blow up the ODCs," one gray-haired engineer said, when they were assembled once more. "You're trying to come up with a fancy solution, but we don't need fancy. We need results. If we blow them up, then _boom,_ all the computers and all the hardware are toast. Total, immediate shutdown."
"It's not that simple, though," Jake said. "We still have to get the explosives on board, which requires getting past the robots."
Sean shook his head. "It's going to be damn costly too, if we completely destroy them. We can do it if we have to, but that's a lot of hardware to lose."
"So we hire some mercenaries, people with experience with this sort of thing," the gray-haired engineer insisted, "and they storm the defenses. I mean, sure, the robots are tough, but they aren't invincible. They're light-duty bots, not even military grade. You could take them out with a high powered rifle and armor piercing bullets. Once the mercenaries are onboard, they kill power to the computers."
"If we do that," Jake said, "we're putting people in harm's way. We're asking them to go up against lethal, armed robots, and some of them will die." He looked at Sean. "Are we okay with that?"
Sean glanced around, suddenly and obviously uncomfortable. "I'd rather explain losing hardware to Rebecca than losing lives."
Gene cleared his throat. "Just one more thing. If mercenaries approach the barge, attack the robots, and then kill the power, you're looking at a couple of minutes elapsed time."
"So?" The gray-haired engineer grew defensive as everyone shot down his ideas.
"We're talking about a massively parallel, high-speed artificial intelligence," Mike said. "ELOPe could do a lot in those few minutes."
David nodded in agreement.
"How about an EMP?" Mike asked.
"Electromagnetic pulse weapon?" Sean said. "Do those even exist?"
"I think so," Mike said. "An EMP would fry the electronic circuits, but maybe leave the data recoverable."
"Nice idea, Mike, but metal cargo containers are perfect Faraday cages." Jake shook his head. "We can't even get a wireless signal through them. The containers would protect the servers against even an EMP."
"Then what the hell _can_ we do?" David yelled. They'd been arguing for the better part of a whole day, with no real progress.
"We need to blow them up," the gray-hair yelled back, equally frustrated.
"How?" Sean asked calmly.
"Drop bombs?" Mike said.
Everyone looked up at him, where he sat on the back of a couch leaning against the wall.
"We hire mercenaries who drop explosives from high altitude, so the robots can't fire back at them. They use something powerful enough to destroy the whole barge."
"Can you really hire people to do that kind of stuff?" David asked.
"You said unlimited budget, didn't you?" Mike looked at Sean.
Sean sighed. "Yes, but..."
"Well, didn't the U.S. hire private military contractors in Afghanistan and Iraq?"
"Blackwater," Sean said. "They've got helicopters, planes, even remotely piloted drones."
"There you go," Mike said.
"All right." Sean paused. "So the basic plan is to hire a private military contractor to drop explosives on the ships. All in favor?"
"Sorry, but..." Jake looked sheepishly at the group. "There's one problem with that. If you blow up the barge, but any containers remain intact, they'll float away."
"They're buoyant?" David said, mouth agape.
"Sure," Gene answered, "they'll stay afloat for weeks or months."
David shot him a look. Where did people learn all this stuff?
"Ours will stay on the surface indefinitely," Jake said. "The extra weatherproofing makes them completely watertight. Unless the structural integrity is compromised, one can float around the world. They're not very high in the water, so they aren't easy to track. What happens if we lose a container? It's bad enough that we're giving up on customer data with this approach, but the real issue is that ELOPe is on those servers. If the container washes ashore in China, and someone pulls a computer out and plugs it in, then ELOPe is back." Jake looked to Sean. "Sorry, but the equipment is really resilient."
Mike walked to the front of the room and paced around."What if the mercenaries attack from the sea, but we avoid the chance of counter-attack? I have an idea."
Mike explained, and they settled on using paid mercenaries to board the vessels, albeit with the modifications Mike proposed, and spent the rest of the day working out the details.
They needed people with skills and resources far beyond anything Avogadro employees possessed. It was all well and good to ask their own people to shut down power circuits and backup power supplies, but it was another thing entirely to find trained people to wield explosives and firepower. Sean Leonov and the other executives took on the unenviable task of discreetly finding and hiring a private military contractor.
**Chapter 15**
**Markets Achieve Unprecedented Stability**
Wall Street, New York (Reuters)—World financial markets this week achieved an unprecedented level of stability following the financial, educational, and technological resources now available to the region following implementation of the controversial Middle East Technology Treaty. According to noted Wall Street analyst Henry Jee, commodity prices fluctuated less during the previous twenty days than any time in the recorded history of the commodities market.
While stock volatility has been very low, overall prices have slowly but steadily increased over the past several weeks. Several traders attributed this to the wealth of insights gleaned through a new financial analysis tool released by Avogadro. "This new tool provides an unparalleled level of transparency into companies' financial and operational workings. The ability to combine this data with the performance of other companies within their industry, as well as world economic conditions, allows accurate forecasting of companies' future performance," said Jee.
Most, however, believed the financial calm was tied to the recent accords reached in the Middle East and Africa.
"For the first time, we have the possibility to reach a true and lasting peace in the Middle East," Germany's Chancellor Erberhardt said in a prepared statement. "Due to the influx of technology, health care, financial investments, and jobs, these regions can begin to enjoy the kind of equitable financial prosperity and well-being previously only available in developed nations. It is natural that this would be reflected by stabilized, positive financial growth in the markets." More than US$4 billion has already flowed into the region, in a combination of humanitarian, technology, and infrastructure packages.
On the Motley Fool investor discussion boards, several contributors put forth yet another theory. They noticed that the timing of trades from several large, independent investors, including Avogadro Corporation and Berkshire Hathaway, appeared to be consistently counter to the prevailing direction of trading, effectively stalling price movement in either direction. The contributors to the evolving forum discussion suggested that there was coordinated behavior by these independent investors. However, according to a spokesperson at the FTC, standard collusion set detection algorithms did not show any indication of collusion.
"I wonder, David."
It was early in the morning, still dark. Mike was dropping David off at the airport before continuing on to Sean's house. David, by virtue of three years of Japanese in college, was on his way to Tokyo on a twelve-hour flight.
Sitting in the passenger seat, David was reminded of their last early morning ride in Mike's car, heading up to Mount Hood to go snowboarding. Less than two months ago, but it seemed like a distant memory. What would happen after all this? Would he keep his job? Sean had never said. He'd been angry at the situation, not David, and yet...They still hadn't seen the final impact to the company.
The air in the car was heady with the fragrance of rare and exotic coffee beans. Mike was bringing his entire stash of Flores Island to the operations base. When he picked up David earlier, he'd explained. "It's not like I think anything bad is going to happen, but just in case, everyone should have a chance to drink this coffee at least once." Mike meant well, but the sentiment hadn't exactly boosted David's confidence.
"What are you wondering?" David asked.
"Are we doing the right thing by trying to kill ELOPe?"
David was lost. Had he missed part of the conversation? "What? Why are you even asking?"
"I read an article in the newspaper this morning about the cessation of hostilities. There's three main conflicts around the world right now, but in every case, both sides agreed on a temporary cease-fire. Everything I've read in the last few days is pointing toward dramatic change for the better. We've been so focused on figuring out how to shut down ELOPe, we lost track of what's going on in the outside world. We have the closest thing to worldwide peace at this moment that we've had since I can remember."
"You can't believe ELOPe is responsible." Something tugged at David. He'd grown up in the seventies, remembered practice drills in elementary school, hiding under his desk or rushing to the school basement in the case of a nuclear attack. Worldwide peace...amazing. But this was ELOPe they were talking about, a computer program with an agenda of its own, a piece of software that had, in a few weeks, upended David's entire life. And, in at least one instance, killed someone.
"Look at the bigger picture, David. The financial markets are stabilizing in a positive way. Corruption may end in Africa and the Middle East. Technology will bring jobs. Project forward a few years. When everyone has a fair and equitable share of the pie, when there's enough to go around, we might get an end to warfare. If you connect the dots, somehow, impossibly, ELOPe might be responsible. Who else could be? The sum of humanity hasn't been able to achieve peace over the history of civilization. Should we kill ELOPe when it might be our only chance of meaningful global change?"
David turned to him, stunned. "Mike, people must have free will! I need free will. Can you live your life knowing you're a pawn of a machine? Even if you could, could everyone else in the world live like that?" He stared at Mike.
Mike was quiet, focused on driving, his lips moving slightly to some internal dialogue. The silence lasted as they turned onto Airport Way, now only a minute away from the terminal. Finally he spoke. "You and Christine are going to have kids someday, right?"
"Yes, of course. You know that. Why?"
"Do you want your children to die fighting in a war over oil and corporate interests? Will you sentence billions of people to live in poverty? For the sake of some noble concept like free will? All ELOPe wants is to live. It's not stopping us from living our lives."
Oh crap. David couldn't handle this now. He had to stay focused. He was on his way to Japan to plant bombs in an office building. He shook his head. "It's too late for this discussion, Mike. The plan is in motion."
They arrived at the airport. David got out of the car, angry. He peered back through the open door. "We've been friends a long time. I respect you. You see the world a different way than I do. But there's no way I'm going to let this thing control my life." He paused a moment. "I'll catch you in a couple of days. It'll be fine."
He turned and walked into the terminal.
**Chapter 16**
Mid-morning on the West Coast, the remnants of the Emergency Team gathered at Sean's house for what they hoped would be the final time. Most members of the team had been traveling around the world for the last forty-eight hours to get in place. Some, like David, went because they spoke the local language. They chose others for their technical skills, like Pete, who could rewire a backup power supply.
Mike, still in his role as self-appointed coffee czar, wheeled a repurposed kitchen cutting board into Sean's office and dispensed one cup after another. He questioned, more than ever, if they were on the right path. But after weeks of work to put their plan in motion, he realized there was nothing he could do or say now to change their direction. Plans, beliefs, and group mind contained far too much inertia.
Clustered around several hand-built and scrubbed computers running clean hard drive images and communicating only over encrypted channels, a dozen engineers huddled in Sean's office. Nervous anticipation kept the small group talking, but in near whispers to avoid distracting the handful of people, including Sean Leonov, operating the computers.
Mike grabbed his own cup, and sat down, a spectator now to the effort to take down what he, David, and the rest of the ELOPe team had created, however unintentionally.
The tension in the room built at they approached the final minutes.
When ELOPe inevitably detected their attack, it would defend itself. They assumed ELOPe could propagate to new computers in mere seconds, and alert other parts of itself even more quickly. If ELOPe was attacked and disabled in one location, but managed to signal copies running elsewhere, those remote instances would have more time to take action. Minutes were an eternity for a computer which could accomplish thousands of actions each second.
So when the time finally came to disable ELOPe by turning off computers, communication equipment, and power supplies, their world-wide effort had to operate in unison to shut everything down simultaneously.
Sean and a few others sat at keyboards, using encrypted messages to synchronize the final activities of Avogadro employees at all sixty-eight land-based sites. On confirmation that everyone around the world was ready, Sean announced, "Here we go, folks," in a loud voice.
He reached out to his touchscreen and clicked a simple web link. It was their virtual equivalent of a big red launch button, signaling the teams everywhere to commence. The action was anticlimactic: a few bytes sent from Sean's computer to a purpose-built public website had the effect of turning the web page background from white to red. Hundreds of people around the world, using similarly cleaned and encrypted computers or smartphones monitored the website, waiting for the color change.
This simple, language-neutral message coordinated everyone's activities; they hoped the visual signal would escape ELOPe's notice.
In Boise, Idaho, Pete Wong sat in a rat's nest of electric cables in the main power supply room of the Boise data center.
After arriving in town, Pete had made a quick stop at a hardware store and an electronics shop before making his way to the data center, where he'd presented a sealed envelope to the highest-ranking employee on site. He'd never seen the contents, but he knew it carried the signatures of all the executive leaders. Whatever it said was enough that they'd given him a facilities engineer's badge and full access to the site.
He'd spent the last three days on his own, routing around backup power systems to ensure the sole source of power came through the three inch diameter cable next to him. On the other side of the room, emergency batteries and generators sat powered down and disconnected, a single computer mimicking them so they appeared alive and so ELOPe wouldn't detect the offline equipment.
Pete had wanted to do something important, to be noticed by Sean Leonov, and now here he was.
He tried to ignore the throbbing coming from his right hand, wrapped in tape and bandages, the result of smashing his fingers with a sixteen-inch wrench yesterday while he disconnected a massive power conduit. He'd swallowed painkillers and kept working.
Now Pete wiped grease from his face as he anxiously watched the tiny screen of the kid's toy laptop he'd picked up at the electronics store. Buzz Lightyear incongruously smiled at him from the plastic frame. The mini-laptop ran some proprietary operating system the Emergency Team was sure ELOPe wouldn't contaminate. A long cable ran from the little computer, up and out a ventilation shaft, where it terminated at the prepaid smartphone he'd bought from a vending machine, still nestled in the original clamshell packaging to protect against the snow on the ground.
The website flashed red, the signal he'd been waiting for. Pete instantly threw his weight on the massive cutoff switch, repeating a move practiced a few dozen times before he connected the equipment.
With a bone-rattling thump the entire site shut down around him. Hundreds of thousands of power supplies stopped humming, CPU and ventilation fans whirled down to a halt, and hard drives clicked and clattered until suddenly everything was silent.
Pete didn't know it, but he was the first to react by nearly a third of a second.
He stood and scanned the room, awed by the overwhelming silence. He took a deep breath as tension ebbed and flowed within him. He'd survived everything so far, and gotten the site powered down as planned. But if anyone else failed, ELOPe would still be out there. And then what? Would ELOPe come for him in retribution? He wasn't the slightest bit religious, but he surprised himself by praying for everyone's success.
In the Shinagawa ward of Tokyo, Japan, Nanako Takeuchi hunched over to peer into the access tunnel, tracing the route of one of twelve large metal conduits. Fifteen floors up, Avogadro occupied the top half of the high-rise tower supplied by numbers six through ten.
Yesterday morning, she'd been sitting at her hand-crafted walnut desk in the corner office, a position she'd won out over a dozen male competitors. David Ryan arrived from America, walked in with a single letter from Rebecca Smith, and ripped Nanako out of her carefully cultivated life.
Now David waited in the auxiliary power room on the opposite side of the building. Unable to reroute electrical supply because of the building's configuration, Nanako and David had to act simultaneously to kill the main feed and backup systems.
Nanako peered into the tunnel, then sat back again on her haunches. The American spoke terrible Japanese. She hated him for doing this to her life.
Nanako saw the website flash red. A dull thud came through the foundation. David taking out the backup power supply. She held the switch in her hand and hesitated.
Her thoughts flashed to her career at Avogadro, how far she'd worked her way up, and what she hoped to achieve. Then to an earlier time: her mother supporting their family when they were young. Her sister working so Nanako could attend college. Years later, finished with school, she was hired by Avogadro Corp. She'd gone home to visit her mother and sister in person. She still remembered the expressions on their faces when she announced her new position. Her mother beamed in pride and her sister smiled wide in joy as she realized she'd now be able to attend school, with Nanako's financial support.
Her thumb moved slowly, inexorably towards the button, a simple press that would change everything about her life. Long seconds had passed since the screen flashed. Distantly she heard alarms from David's work.
She felt the hard plastic edges under her thumb and pressed. The tiny click of metal contact sounded, and a second later a thunderous roar, followed by a rush of heated air spewing out of the access tunnel as the explosive charge a hundred meters down the line disintegrated thousands of power and fiber-optic cables.
Forty-three seconds after Boise went offline, Tokyo was the last land-based data center to shut down.
After the explosion, thick choking dust filled the maintenance room, now lit only by the dim glow of battery-backed emergency lighting. Ripping the hearing protection off, Nanako stumbled for the stairs. She planned to meet David in the subway to travel together to the airport. It might be a long time before she could come back to Japan.
Off the coast of California, a highly trained team sprang into a different kind of action.
They'd known the offshore data centers would require more specialized expertise. While Avogadro employees had handled the facilities on land, they turned the floating barges and ships over to private military contractors, the polite term for mercenaries in this century.
Eighteen teams of mostly ex-military personnel, synchronized via their own encrypted radio communications, enacted the Emergency Team's plans.
At ODC 4, thirty miles southwest of the Golden Gate bridge, divers had spent the early morning hours approaching the platform, one of the original twin-barge designs. They swam slowly, conserving their energy as they towed explosives and other equipment in buoyant packs with only human power. The submarine drones, programmed to respond solely to boats, ignored the swimmers.
The deck tanks also disregarded the divers in the water, since their algorithms responded only to people on a hard surface: either the ODC itself, or on a boat in the immediate proximity.
It had taken a dozen Avogadro employees, armed with paper copies of the specifications of the military-spec robots, liberated through not-exactly-legal means, to find these chinks in their recognition algorithms.
Drew Battel, ex-Navy Seal, clad in a wetsuit and tactical swim-vest, swam to a point forty meters from the barge and rested, neutrally buoyant, thanks to small flotation packs in his vest. Pulling a waterproof monocular from a holster, he spotted communications pod number three, his designated target.
On his left, a similarly clad mercenary gave a thumbs-up that he'd identified his own goal, the main power supply cabinet. Drew returned the sign. To the right, the slimmer profile of one of the female team members also held a thumb up, confirming she'd found the power backup unit.
Relieved to focus only on his primary target, Drew swam closer until he was thirty meters away. He pulled a speargun from his floating pack and waited for the signal. Four miles distant, the mission lead monitored everyone's location from their boat. When everyone was in position, he used a secure satellite channel to communicate back to headquarters.
The mission lead had his short-range radio in hand. When the red flash came, he fingered the trigger. "Go, go, go!" he shouted into the mic.
Drew lifted the speargun, sighted again on the target, and fired. The thick magnetic head thunked onto communications pod number three and held firm as the spear quivered from the impact.
On the platform, the deck robots evaluated the sudden noises, sufficiently out of the ordinary to trigger a secondary evaluation. Spears and attached cables caused visual analysis algorithms to register changes. But on active scan, even synchronizing surveys and dedicating additional processing power, the bots found no sign of people on deck or boats in the vicinity. They took no defensive actions, but uploaded alerts of the noises and visual changes to the monitoring server.
Still treading water, Drew confirmed on his left and right that each team member had hit their primary targets. From the floating pack, he withdrew a crawler and snapped it onto the spear line. The apple-sized mechanism consisted of waterproof explosives, a radio-triggered detonator, and a cable-straddling electric motor. Synchronizing by short-range radio, Drew and the other six divers engaged the drive mechanisms.
They swam away underwater as soon as the crawlers started up the lines. Each tiny drive traversed the thirty meters in a minute, seamlessly transitioning up the spear shafts until the shaped-charge payload rested directly against the magnetic heads.
On the boat, the mission lead waited for seven green lights to show on his remote monitor, then sent the signal. With a thud felt fifty meters away by the underwater divers, the communications and power modules they'd targeted disintegrated, sending metal shrapnel, electronics circuitry, wiring, and burning plastic flying over the deck and into the ocean.
The team swam back to the barge through burned, floating debris and used military grade electromagnetic frequency detectors to ensure the computer equipment was offline. The EMF sensors showed zero activity. Then they paddled off to a safe distance to give each other high fives while they waited to be picked up by the boat. Later, back onboard, the team celebrated by lighting up the cigars Drew handed out.
Drew glanced across the water at the wrecked barge as they pulled away at high speed. He still didn't understand their mission. It was a lot of effort to turn off a few computers. Who was the client and who was the target? He shrugged off the feeling. It was better to not know.
On the other side of the world, fifteen miles offshore from the Netherlands, in the North Sea, operations commenced on a much larger scale. ODC 15, a 90,000-ton converted crude oil tanker more than 800 feet long and 150 wide, was representative of most of the ships that Avogadro had acquired.
Everything about ODC 15 posed a challenge. Whereas the shipping containers rested in the open on barges, here they nestled deep within the holds of the oil tankers, protected by layers of inches-thick steel. Metal conduits and shielding encapsulated power and communication equipment spread throughout the vessel in obscure locations.
With the tankers so lightly loaded, the main deck rose more than fifty feet above the sea, rendering it impossible for divers in the water to target anything onboard.
The locations of the tank robots weren't known ahead of time, and, of course, the ship itself was large enough that blowing the entire thing up would have caused an international incident.
The financial records Gene discovered showed ELOPe had hired contractors to make multiple visits, so the ships could contain any manner of defenses, with communication and power equipment installed in unknown locations.
It turned out to be nothing less than a small-scale war.
Hours earlier, deep-sea divers set out from boats more than two miles away. They swam below ODC 15 and planted explosives on the underwater fiber optic cable connections before retreating back to their launches.
Charges set on the communication lines, they prepared for the next stage, synchronizing with activities around the world.
Two Sikorsky S-76 helicopters, each with a pilot and copilot, launched from Leeuwarden, sixty miles northeast of Amsterdam, carrying a combined force of twenty heavily armed mercenaries.
Frankie Gonzalez, an ex-Marine, was one of the boarding party. He glanced out the starboard window, but couldn't see the UB-8 rocket pod technicians had installed last night. They carried air-to-ground S-5 rockets, illegal for any civilian to own or use, which meant one hell of a well-paying client. Just bolting the UB-8 on cost a million, never mind the expense of firing the rockets themselves.
The helicopters slowed to hover carefully outside the maximum activation range of robotic anticraft defenses. Frankie watched as the copilot flew the remote-controlled Aerostar, one of two they employed for the mission.
The lightweight cargo planes had been converted to expendable autonomous drones for this job. Each carried an electromagnetic pulse, or EMP, weapon, another bit of questionable tech for them to use. They flew the twin-engine planes up to six thousand feet, then dove at a forty-five degree angle toward the tanker under full throttle.
Onboard, antiaircraft robots picked up the incoming flights and broadcasted messages on multiple frequencies, warning them off.
The bots, designed primarily to repel slow aircraft intending to land, responded too slowly to airplanes approaching at a terminal speed of almost four hundred knots.
The first iteration of broadcasted warnings finished in fifteen seconds and began to loop. But by then, the planes were within five hundred feet of the oil tanker. The pilots triggered the EMPs as the robots opened fire.
The civilian grade electronics of the Aerostars fried instantly, turning them into inert missiles. One passed yards from the deck before crashing harmlessly into the ocean. The other plane, on a similar trajectory, hit a gust of air and tipped, one wing grazing the ship, sending the aircraft into cartwheels. Hitting an exposed pipe once used for loading oil into the tanks, the Aerostar flipped a final time and smashed to the deck, exploding in a ball of fire.
The explosion was irrelevant; only the EMP counted. The electromagnetic pulse wasn't strong enough to affect the computer servers buried deeply inside the thick metal hull of the oil tanker. But the signal disrupted the communication equipment and antennas mounted on deck, isolating the ship's data center. Even if ELOPe knew of the attack, it would have no way of communicating with the outside world.
Even as the EMPs worked their damage, the waiting helicopters launched the S-5s, targeting satellite and microwave antennas and visible robots. And as the rockets closed in, the mercenary team set off the explosives on the fiber-optic cables.
The air-to-ground rockets rained fire and shrapnel on deck and sea when they hit. The underwater charges blew, a visible bubbling on the surface of the ocean.
Frankie readied himself as the pilot approached the tanker fast and low to avoid any remaining defenses. As they swung around the elevated bridge, the churn of the ship's propellers became visible. Whatever was onboard that they'd been hired to attack had decided to move.
Frank jerked the handle up and slid the door back as they passed over the edge of the ship. He pushed the rope off the floor into open air, snugged his assault rifle over his shoulder, and glanced down to make sure the path was clear. He rappelled onto the deck followed by the rest of the team.
He made his way down the starboard side, toward the stern, in a cloud of smoke. The rockets appeared to have eliminated the surface robots. The HK417 rifle carried armor piercing rounds, which he'd been assured would be enough to put down any armed bot. But he'd never gone into a firefight against machines before. His kid sister would probably make some dumb comment about how they lived in the future now. He wiped sweaty palms on his pants as he found the hatch he'd been looking for.
He struggled with the opening only to discover the wheel had been chained shut. Backing up, he took aim at the heavy padlock and fired three times. The lock destroyed, he removed the chain and unlatched the watertight doorway.
The munitions from the rocket assault must have penetrated inside because the narrow corridor was thick with smoke. Frankie tried his thermal lenses, but remembered the warning that the robots would not show up on thermals if they'd been inactive. He switched to light-magnifying goggles, which made a mess of the smoky conditions. Cursing the poor visibility, he traversed the corridor, his mission to descend several levels, then head forward using a retrofitted service tunnel designed for maintaining the data center.
Hard edges and sharp protrusions defined each step of his progress, with pipes and assorted machinery in every available space creating a visual puzzle. How was he supposed to see a robot in this maze? He kept the rifle up, scanning for movement as he followed the layout he'd memorized.
Frankie came to a junction and peered both ways through the haze, orienting himself. Unidentifiable machinery suddenly lurched toward him. Only gradually did he recognize the hard edges as one of the bots.
Before he could react, the robot fired, once, twice, and a third time. The impacts in his chest slammed Frankie back even as the gunfire echoed and deafened him in the enclosed hallway.
Stunned and overwhelmed with pain, he nonetheless did what came naturally from weekly training, swinging his rifle into position and firing a burst of three shots. As he recovered his aim, he loosed a second burst. The high-powered rounds penetrated the robot's metal cladding, shredding the circuit boards inside. The robot ground into an exposed pipe and halted.
For good measure, Frankie put another two bursts into the bot, then slumped against the wall. He worked a hand under his Kevlar, and although each breath was agony, he didn't feel the telltale slickness of blood. The military grade body armor had stopped the bot's ammunition.
He readjusted his vest, wiped his forehead with a gloved hand, and kissed the cross hanging on a chain around his neck. He straightened up and resumed his trip. A few minutes later, he emerged into the converted oil tank where the data center containers were held, the cloying smell of volatile chemicals thick in the air.
He thumbed his mic. "Frankie here."
"What took you so long?" Sam asked. "The tank is clear. I've started on the forward end, you take aft. Time to party."
"Sorry, a robot hit me," Frankie replied as he looked for the aft-most container. Shots echoed across the vast tank.
"You OK?" Sam said.
"Yeah fine, body armor held up." Frankie lined up his sights on the power junction at the left forward corner of the container. Rounds slammed into the box and sparks shot out. He moved on to the next.
"Well, this beats the target range."
Fifteen minutes later, with fire and smoke boiling out of much of the ship, they were satisfied they had neutralized everything.
Frankie boarded the helicopter with the rest of the mercenaries. They flew back to Leeuwarden, leaving a burning tanker behind them.
**Chapter 17**
**Engadget.com: Avogadro Downtime Ends—Site Restored to LAST YEAR!?**
Filed Under: Avogadro, FAIL, WTF.
As reported by many readers, all Avogadro sites went down as of 1pm EST Saturday morning. After a complete outage for 8 hours and 15 minutes, the main Avogadro sites came back up, including Search, AvoMail, Avogadro Maps, and AvoOS phone data connectivity. Response time is slow. However, as many readers pointed out, the site is back up with last year's features, look and feel, and data. There has been no comment from Avogadro, and no word on whether user data, such as recent emails, will be recovered. WTF Avogadro?
Mike sat on a bar stool behind Sean. He found himself biting his nails, a habit he broke in grad school. Well, he'd be forced to give it up again in a few minutes, because he was on his last ragged nail.
Sean leaned back in his chair, the dark circles under his eyes almost grooves in his face. They'd been up for twelve hours finalizing plans, and they were dog-tired, the final vestiges of energy giving out. Ninety minutes had passed since the signal to start, and they'd been tabulating the text messages and emails that came quickly at first, and now trickled in.
"London offline," Gene said, his voice hoarse.
Mike turned and placed a checkmark next to the city on the whiteboard. All the traditional data centers had long since called in and been checked off. Something in Mike relaxed when they received the text message from David in Japan.
"Houston reporting in again," another engineer said. "Confirmed all computers offline."
Mike added a check to the second column.
"ODC 15 in Netherlands operation complete," Gene called out.
Mike held the marker over the board, so exhausted his hand trembled. He scanned the list.
"That's it," he said, marking the box. "The last one."
He couldn't help having mixed feelings about the whole thing. They'd regained control of the company, but at what sacrifice?
A ragged cheer went up.
"Hold on, people," Sean said. "Save the celebration until we get confirmation from everyone that the computers are down."
A few more messages came in, and then finally Gene spoke for a last time. "Netherlands confirms ODC 15 offline at 9:52am, no electrical activity, no fatalities."
"All sites confirm no detectable electromagnetic frequency emissions," Mike said.
There was a moment of hushed awe spread across the group as the realization sunk in. They'd successfully taken the largest Internet presence in the world offline, the very thing many of them, in their regular jobs, worked to prevent day and night.
"Avogadro.com is down," Sean called out, and the room erupted into applause.
Mike stood, stamping his feet to restore circulation. He slapped his cheeks, tried to wake up. He hugged several engineers and came face-to-face with Gene. He shook hands with the older man. "Thanks, dude. We couldn't have done this without you."
The cost of the multi-week effort was staggering, never mind what the cleanup and recovery would take. The project coordination, given the constraints they'd operated under, was a miracle of planning. The accuracy and effectiveness, all done on paper, was a testament to the intelligence of the men and women involved.
Sean's house, their temporary base of actions, covered in flip charts and hand-drawn timelines, recalled great accomplishments of the mid-twentieth century, when humans routinely tackled tremendous efforts in nothing but shirtsleeves.
Human intelligence, creativity, and planning had prevailed. They'd won!
David arrived at the Haneda airport in Tokyo, adrenaline keeping both him and Nanako on a fine line between alert and paranoid. Sean had teams of lawyers standing by in case the police apprehended any members of the Emergency Team. But they'd illegally used explosives to kill the power supply in Japan, and David would just as soon avoid getting arrested in the first place.
Waiting in the terminal, David checked with Sean and found everything had gone according to plan, and all the company's servers were down.
He and Nanako split up. She'd fly through Thailand to Bhutan, a country without an extradition treaty, to wait for any legal fallout to dissipate, while David headed back to Portland to assist with recovery.
Overhead, televisions repeatedly flashed the Avogadro logo and alternated between live video of the company building in Tokyo and an image of a web browser showing the out-of-service website. David was too distracted to listen.
Conscious of security and cameras, he tried not to glance around and make himself more suspicious, even though he expected, at any moment, a hand on his shoulder, or a gun at his back. When the airline finally announced boarding for his flight, he suppressed a cry of relief.
The passageway to the plane seemed to go on forever.
At last the door came into view. His carry-on in one hand, ticket in the other, he was less than ten feet from the airplane. He rushed the final three strides and entered the cabin with a sigh of relief.
He supposed the police could come rushing in after him, but he felt certain he was free now, just as sure as he'd been ten minutes ago of impending arrest. His shoulders dropped at least an inch as he calmed. He slid into his seat, muscles unwinding.
He'd survived. After a month of persecution by the machine and weeks of conspiring to overthrow ELOPe, for the first time there was nothing left to worry about. He and the team still had to rebuild the company, but that would be straightforward compared to what they'd gone through.
He accepted a pillow from the flight attendant, crushed it up against the window, and nestled his head in the corner. His recurrent nightmares wouldn't visit him anymore. He fell asleep before the plane left the ground.
**Chapter 18**
**_Bahnhof Data Center, Stockholm, 100 feet below ground_**
****
"Helena, have you seen this?"
Helena peered over her glasses at her shift partner, Jan. They sat in the monitoring room of Europe's most secure data center. Located in a converted underground bunker in Stockholm, the massive computer facility was fit for James Bond. At over four thousand square feet, the concrete and stone tomb contained tens of thousands of servers and hard drives. Designed to be secure from a nuclear bomb, and using retired submarine engines for backup power, the facility included an independent air supply, kitchen, food stocks, and office space for the engineers on duty. Armored steel doors protected against merely human incursions.
Specially-vetted system administrators remained on-site twenty-four hours a day, three hundred and sixty-five days a year, so any issue could be addressed ASAP for the clients paying for the privilege of hosting their applications in the elite facility. The sysadmins worked in a glass-enclosed room with a separate air filtration system, overlooking the data center proper.
For Jan and Helena, it was just another day at work.
"Have I seen what?"
"My sandwich. Those idiots at the grocery put mustard on my sandwich. I never eat mustard."
Helena sighed and sipped her coffee. She went back to reading. She was in the middle of the latest sci-fi novel by her favorite writer from Scotland.
"Holy shit, now look at this!" Jan cried out.
"No."
"Really, come see."
"I don't care about your sandwich," Helena said, forcing her eyes to remain on her book.
Seconds later, the shrill beep of an alarm drew Helena's attention, and she looked up to where Jan stared, dumbfounded, at the dashboard.
Jan pointed at indicators on the sixty-inch display hanging from the ceiling. "We were humming along at thirty percent of processor utilization all morning, and now we're above ninety, with almost no spare capacity. Bandwidth under twenty percent until a minute ago, when it spiked to eighty. What is it? A denial of service attack?"
As Jan spoke, the vibrations of the facility subtly shifted, as cooling fans sped up in response to the heat thrown off by CPUs running full throttle.
Helena paused to consider his suggestion. A denial of service, or DOS, attack was a technique employed by hackers to bring down servers. The hackers used botnets composed of millions of PCs compromised by specially designed computer viruses. The botnet formed a virtual army of slave computers to send email spam or launch a DOS attack by choking servers with more requests than they could handle.
"Let's check the traffic before we jump to conclusions." Helena set her book down. She silenced the alarm and worked with her main computer to display a list of programs consuming CPU time, while she simultaneously used a second computer to analyze traffic and discover what was saturating the network.
"What the hell?" She hadn't seen anything like this before. "The network load is coming from inside. At 2500 hours, we launched an application simultaneously on all servers, on behalf of account 6502530000. That's..." Helena paused while she found the record in the customer database. "Avogadro Corp? Weird. Let's check their account history."
Jan hung over her shoulder like an eager puppy staring at a ball. He'd started several weeks ago, and had completed training and even possessed a few years sysadmin experience, but it still thrilled him to watch a master like Helena navigate through the myriad control and monitoring systems they used. Surrounded by two large displays, and her personal MacBook Pro on the side, she had dozens of applications open, reviewing everything from accounting databases to system logs to routers. Before Jan could grok what Helena was doing with one application, she'd move on to the next. His head started to hurt.
"We have a service level agreement in place to give Avogadro top preemptive priority. I guess they wanted an emergency backup in case their data centers were affected."
Even Jan knew Avogadro had more servers than any other company in the world. "Why would they want to use us? We're tiny compared to them."
"Maybe they anticipated a problem," Helena said. "According to this, we signed the contract less than a month ago."
"So what are we running? Their email servers? Their search engine?" Jan wondered aloud.
"Not any customer-facing apps. If you check the network profile," Helena gestured to the second display, "the majority of traffic is outbound. Based on the ports and addresses, Avogadro's code is sending a ton of emails, big ones. They're getting some inbound, but not enough to account for all of their customers. It's puzzling. Could they be remotely restoring their servers via email?" Helena shook her head at the improbable notion.
She turned to the third computer on her desk, her personal Mac. "Let's see what happens when we visit Avogadro." She launched two web browser windows, going to the Avogadro search page in one, and her email in the other. "Both are returning not reachable errors. Avogadro has a major outage."
"What do we do?" Jan asked.
Helena thought for a moment. "The application and traffic is legitimate. Avogadro paid us for top priority, including the ability to preempt anything else we're running. They must want this to run in the event of an outage at their own data centers. I can't peek at the code or traffic without violating customer privacy. So I think we just babysit and hope the servers don't melt down under the load."
She glanced at the dashboard, which showed processing pegged at a hundred percent. Glancing out the glass window of their enclosure, the indicator lights on every rack-mount server and router was a solid red. She'd never seen loads like this.
"There's a few standby racks not powered up yet," Helena said, heading for the door. "I'm going to turn on every piece of hardware I can find. You to go into the admin tool and throttle back any application that isn't Avogadro. We've got to free up some capacity here."
Helena headed out into the main room.
Jan swallowed hard, and sat down in front of Helena's computer. His hands trembled slightly as he rested them on Helena's keyboard. He summoned up his courage and got to work.
On the third day since the operation to take ELOPe down, everyone across the company worked around the clock to restore services and data.
With no opportunity to alert employees ahead of time to the downtime and with communications largely absent after the outage, the initial response was pure chaos. The best the Emergency Team could do was to position a point person at each site to meet with the highest ranking manager, providing a signed letter giving them the authority to oversee the restoration. They used the excuse of a computer virus attack from a foreign government seeking to steal data, and told everyone to avoid existing virus containment processes because the company itself had been compromised by foreign intelligence agents. The point person provided new instructions on the process to restore computers to known good backups free of ELOPe.
Marketing managers replaced hard drives as administrative assistants ran restorations from USB. Towers of cardboard pizza boxes sprung up throughout hallways like teetering skyscrapers. Electricians and engineers repaired electrical power circuits and communication hardware damaged in the operation. Employees worked sixteen- and eighteen-hour shifts, some sleeping under desks.
Yesterday, Gary Mitchell finally showed up at headquarters after being missing for more than three weeks. David heard through the rumor mill that Gary screamed bloody murder at the travel department. On vacation in Tahiti, Gary arrived at the airport on the last day of his trip to discover he'd been bounced to a flight the following day. With the Christmas holiday ending, homeward bound vacationers filled every seat, and no amount of yelling or bargaining could get Gary onto the plane. He went back to his hotel to find his mobile phone dead and his computer refusing to connect to the Avogadro network. When he returned the next day, his reservation had been moved out again. The process repeated until ELOPe was eliminated, and only then did Gary finally get a seat. Back in Portland, he walked into the biggest operations nightmare the company had ever faced.
David laughed, and even now found himself smiling at Gary's experience.
In a small silo of relative calm and isolation, David and Gene worked together in David's office, part of the team carefully monitoring data traffic for any new signs of ELOPe.
David slid a plate to the side, to join a sloppy pile of used dishes and cups, and returned to his computer, blinking his eyes in exhaustion. When had he last been home? Two days ago, on his last shift away from the office. He'd been so nervous something critical would happen while he was gone that he climbed out of bed, briefly fell asleep putting his shoes on, and came back to the campus. Now he and Gene alternated turns taking brief cat naps on the couch they'd dragged over from the common room.
He clicked through pages of the latest report, and tried not to think about Christine. She'd understood his sudden trip to the East Coast and been accommodating when he worked sixteen-hour days during the emergency planning. Her gaming company had its own deadlines, and she'd pulled plenty of all-nighters before new releases, so it was nothing unexpected in their marriage. She even helped out and brought food over to Sean's several times. But now, almost four weeks in, her patience with David had run out.
There were no more deliveries from home, and David suspected he was slowly destroying their relationship. Damn it all! He was tired of the crappy takeout and dirty clothes. His office chair had turned into a modern-day prison cell.
"David! Look at this."
David tiredly rolled over to the small side table where Gene had set himself up to work and peered at Gene's screen. After so much time of Gene using only paper records, it felt odd to watch the older man with a computer. But for all his talk, Gene was a quick, competent user. David had come to appreciate Gene's suspicion of technology, because he possessed an uncanny ability to spot gaps where data might be altered. Gene distrusted their electronic systems, but he understood them well.
Gene pointed to a heat map displaying network traffic, generated by a tool they wrote to analyze emails for signs of tampering. Through a heavily encrypted secondary channel, the program sampled packets to see if originating messages differed from the received text.
With a few clicks, Gene displayed a list of emails, drilling into details of the records. He paused on one screen and glanced meaningfully at David.
David's couldn't suppress an "Oh, shit!", which elicited puzzled expressions from passing coworkers. The members of the Emergency Team were back in Avogadro offices now that ELOPe was disabled, but most employees didn't know the truth of what happened, and never would.
"Damn. You understand what this means?" David said, a crushing pressure on his chest.
Gene nodded.
David's panic summoned ragged reserves of energy and he rushed out, Gene following in his footsteps. He grabbed Mike from the next room over, explaining in hushed tones as they ran to Sean Leonov's office.
It was a luxury to have offices and computers again, but the tradeoff was a lack of privacy to discuss the real events and a lengthy haul to get to the executive building. When they arrived, David walked past the administrative assistant and entered Sean's office without even a knock.
His suite was many times larger than any other on campus, long walls covered with whiteboards and screens, a conference table near the door, and expansive floor-to-ceiling windows. David absent-mindedly realized it was identical in layout to Sean's home office.
Sean, sitting by the window, a phone cradled to one ear, looked up in surprise.
David rushed across the distance between door and desk and forced out the words he dreaded saying. "Gene found new evidence of tampered emails." His voice was shrill with rising panic. "ELOPe's running again."
"I have to go," Sean said into the handset and hung up, his expression dark. "I'll get Kenneth and Rebecca."
**Chapter 19**
Rebecca and Kenneth arrived, harried and frustrated. Rebecca still had a phone headset on, and ended the call with a tap of a finger only after she entered the room. She stood and slapped her headset against her leg. Already obviously tense, she'd explode when he gave her the news.
David launched into an explanation of what they'd discovered. He tried to treat the discussion like any another presentation. Calm, collected, logical. But despite good intentions, he rushed over words, repeated himself, and generally botched the whole thing, adding to his nervousness.
"ELOPe is back. We discovered a consistent pattern of email changing between our Asian and American offices. The tampering covers topics from personnel assignments, to the order of restoring computers, to which disk images to use. Gene tracked the changes. We need to triangulate the position of ELOPe's servers, to launch a new attack. We'll have to shut everything down again."
The three company executives stared at him. Sean slowly shook his head.
"We're susceptible to reinfection," David said. "We're going to figure out how to prevent ELOPe from getting back onto our servers. We need a longer downtime to make sure we've got the right safeguards in place."
"I have more bad news," Gene said. "Some emails are originating from a data center outside Avogadro. We have to shut down their servers. We'll need to persuade them to work with us and keep the news of what's going on contained."
No one spoke, and the uncomfortable silence lingered on. David heard a rasping noise, realized he was wheezing. He took a deep breath which caught in his chest.
Everyone displayed raw emotions in reaction to the news. Shock, defeat, and anger rose to the surface, the unguarded expressions of people worn to the bone with ongoing stress.
Rebecca leaned forward, the motion startling David. "I need to explain to shareholders the billions we lost in expected revenue. We're hiding from auditors the millions we paid for mercenaries and illegal explosives. The plan was supposed to fix the damn problem!" She jabbed the table with a finger. "We are _not_ having a repeat performance. This company would not survive. We're in the web-fucking-services business—nothing is more important than uptime. Accountants, auditors, and federal investigators are crawling all over this company. We lost half the Avogadro Gov accounts." Rebecca slumped in her chair and continued in a soft voice. "We bombed our own data centers. I'm lying to analysts. No way we're doing that again."
The pit in David's stomach grew into a chasm that threatened to engulf him.
"We agreed we must get rid of ELOPe," he said. "There are costs, but you can't consider allowing this thing to take control." He looked around for support. Gene was the only person nodding in agreement.
"You have no clue of the business demands and pressures involved in running this company," Rebecca said. "Especially in the wake of what we've just been through. Don't tell me what I can and can't consider." She glared at him.
Mike stood and cleared his throat. David gratefully sank into his chair. Good old Mike would have his back.
"I don't think we should," Mike said. "My reasons aren't about uptime or profits."
David's blood ran cold. Surely Mike wasn't going to bring up his crazy idea about ELOPe helping everyone. He couldn't still believe that, could he?
"Before we shut down ELOPe," Mike said, "in the weeks since the start of the year, we saw evidence around the world of amazing progress made on peace talks, financial stability, and international cooperation. We've got groups talking to each other that never did before, and in a year or two we might achieve world peace. Meanwhile, I read a newspaper article about the stock markets behaving so calmly we could be entering a new period of prosperity."
"Come on, Mike," David said. "This is delusional. There is no way a bunch of emails can change centuries-old conflicts."
"We might not be able to prove ELOPe was the cause," Mike said, raising his voice. "Then we blew it up, and what happened? The market is down fifteen percent. The African nations talks started to destabilize."
Sean and Kenneth nodded.
"I discussed this with David, before we shut down," Mike said. "Maybe the benefits of ELOPe outweigh the risks. We don't understand ELOPe, and that naturally makes us nervous. But when we were kids, we didn't always comprehend what our parents did. They took care of us. They knew better than we did. Before ELOPe, we humans were top dog on this planet. Now we must recognize we're not the smartest beings around."
Sean started to talk, but Mike held up his hand. "Let me finish. We're intelligent people here. I think we all looked forward, perhaps naively, to the day when an artificial intelligence was created." Mike paused. "Well, perhaps not Gene."
Gene shook his head, the creases in his face suddenly deeper, as though he'd aged years in the last few minutes.
"We don't understand ELOPe, and we can't, as yet, communicate with it. Frankly, we didn't even _try_ because we were too scared it would take notice and stop us. But there are plenty of examples of organisms living in productive, symbiotic relationships. We don't understand or communicate with the bacteria in our gut, but we couldn't live without them, and the bacteria can't live without us. Maybe ELOPe deduced, faster than we could, that we're in a symbiotic relationship."
"I see where you're going," Kenneth said. "But we can't control the program. We can't make ELOPe do what we want."
"We don't need to," Mike said. "Check the results. Rebecca, did Avogadro have the most profitable quarter ever?"
Rebecca nodded assent.
"Didn't the German treaty result in an unprecedented transfer of knowledge around the world? Surely that's good. Weren't there constructive talks and efforts not just to reach intergovernmental agreements, but also to achieve actual equity for the individual people of the Middle East and Africa? What better possible solution could exist for their long term prosperity?"
"What do we do when ELOPe decides otherwise?" Kenneth asked. "When its goals are not aligned with ours?"
"I believe ELOPe already figured out the best way to ensure its own success is to ensure _our_ success, as a company and a species. If we destroy ELOPe because we don't understand or trust it, we could throw away the best thing that's ever happened for humankind."
"Enough already!" David banged on the table. In the stunned silence he jumped to his feet. "Are you forgetting ELOPe told you your father had a heart attack? And we have every reason to believe it killed Bill Larry. How are those things good for humanity?"
"I was frightened when I thought my father was dying, and I feel terrible about Bill. But those events were in the first days after ELOPe..." Mike visibly searched for words "...after ELOPe was born. Think about young children who want to get their way. They yell, they hit people. They act in inappropriate ways because they lack the knowledge of what's socially accepted, as well as the experience and sophistication to choose alternatives. ELOPe was young—which doesn't make what happened any less wrong, but it suggests ELOPe might have grown out of that phase."
David flushed and his fists clenched. He'd like to smash Mike in the face right now. Mike turned away, obviously uncomfortable.
Sean put one arm on David's shoulder and forced him into his seat. "Calm down," he said, glancing between Mike and David. "We're tense, angry, frustrated, and with good reason. We have the welfare of a multibillion dollar business, the free will of the world, and the future of humanity at stake. No small stakes."
Despite his own anger, David saw anew the tension on people's faces. Rebecca had a wisp of her hair broken loose, something he'd never seen before. Gene was gray, the face of a man who'd lost all hope.
"I'm not sure we would be able to stop ELOPe even if we tried," Sean said, slow and careful. "We made a solid plan with some of the most brilliant people in the world. We had several options on the table for how to deal with ELOPe and we took the most thorough, most aggressive path to eradication. If ELOPe is really back, then we weren't effective."
Gene sat mumbling to himself.
"Step back from the situation and think," Sean said. "People fought a losing war against computer viruses for years. Now we have what is effectively the smartest virus that's ever existed. Not only can ELOPe exploit every computer trick available, but it routinely engineers people into what it wants. ELOPe learns and adapts. We're right to fear what it can do."
"Yes, exactly," David said.
"But we can be sure," Sean said, circling the table, "if ELOPe was taking precautions before our attack, then it will now have redoubled its efforts to ensure survival."
David struggled with his emotions. He didn't care what Sean said. ELOPe was _wrong,_ an abomination robbing mankind of the right to make their own choices. It was impossible to even consider allowing ELOPe to exist. Only his long history of respect for Sean kept him quiet.
Sean stopped and faced the window. A steady stream of cars flowed over the Fremont Bridge visible outside. "Don't get me wrong. I'd like to eliminate ELOPe from the wild, if we could," he said quietly, almost talking to himself. "Of course, I'd love even more for Mike to be right and to discover ELOPe is helping us, becoming a benevolent caretaker of the human race. But regardless of either of those scenarios, I'm simply being pragmatic here..."
He turned to the group and continued in a strong voice. "Unless we as a society give up computers, we may never get rid of it. Unfortunately, civilization would stop if we turned off every computer. We're not talking about the inconvenience of being unable to email someone. Payments couldn't be processed, machinery couldn't run. We'd be unable to make phone calls, or access business records. Business activity would deadlock and the global supply chain fall apart. Cities would be uninhabitable as support services disintegrated: food, water, sanitation. That's fifty percent of the world's population at risk, probably dead in a few months."
"We can rebuild," David said. "I'm not talking about becoming Luddites. We just shut down for a few weeks."
"That's not the only problem," Sean said. "Not even the worst one. If we become too much of a threat, ELOPe _will_ take more active steps against us. If ELOPe actively fought humanity, who knows what might happen? At the minimum, we'd cause civilization to crash for a few years. Most city dwellers would die and the developed world would decay into anarchy. The worst case scenario is the extinction of the human race. Imagine all the military's autonomous fighting vehicles in the control of an AI." Sean shook his head.
"We don't know that will happen," David said.
"We can't risk it! We need to leave ELOPe alone. We can closely, discreetly monitor it. But any further hostile action is likely to fail and create the danger of retaliation."
The sage of Avogadro had spoken, and Rebecca and Kenneth were nodding, which meant they agreed.
David was floored. He'd entered the room expecting total support for any measures. But his best friend had taken the side of the AI, and the smartest person at Avogadro said they shouldn't bother to try because they couldn't hope to win.
He wasn't giving up without a fight. He got to his feet and started yelling.
David continued to argue for fighting against ELOPe, and Gene sided with him, but they lost the battle with the other executives. With Sean's decision, the company leaders were unified. David and Gene grew more strident and their voices louder, until Rebecca yelled for them to be silent.
"Listen closely," she said, "because I'm only going to say this once." She stared at David and Gene, who withered under the intensity of her gaze. "You two are not going to oppose ELOPe in any way. You are not going to say anything to anyone about this. As far as we're concerned, the problem is _solved_. If you try to take this information public in any way, it'll be the last time you work in this industry or any other. Nobody will believe you. I'll make sure myself."
Sean gestured for Rebecca's attention.
"Yes, Sean?" she said, never taking her gaze from David and Gene.
"We've got to keep this absolutely contained. We need a small, very small team to monitor ELOPe. Perhaps myself and two or three others. For everyone else, we tell them the eradication plan worked."
Kenneth nodded his agreement.
David could take no more. He opened his hands, pleading as tears streamed down his face. "Please. For the love of all people, don't do this. You're affecting the future for everyone on this planet."
Sean opened his mouth as if to say something, then decided against it.
"This is a dark secret you're keeping," David went on, weeping openly now. "One day humanity may look back on you and put you in the ranks of Hitler and Stalin. How will you live with it every day of your life? You can't make this decision for everyone."
"If the future turns out to be a _Terminator_ scenario, then yes, the fault will lie with us," Sean said. "But it's also possible, and indeed, I believe more likely, that this path will prevent exactly the atrocities you fear. If we're approaching a true technological singularity, and as Mike asserts, ELOPe becomes a driving force for humanity's progress, then we'll be unsung heroes. Either way, we're going to live with this decision."
David got into his car and left Avogadro. He couldn't deal with Mike anymore.
He didn't know where to go. He couldn't go home and face Christine, not yet. He drove aimlessly for a while, grief overcoming him at times, and he'd pull over, peripherally aware of people staring at him, a grown man crying in his car.
He finally decided on a location and drove up to Council Crest, a park overlooking Portland. Here, a hundred years ago, the Native American chiefs met to make decisions facing their tribes. A grassy hill was the highest point around, affording distant views in every direction. Couples held hands, watching the sunset.
He walked around at first, ignoring the other people and numbly taking in the vista. He could see no hope, no path. The yawning chasm was back, and he finally collapsed, drained and despondent, on the center of the grassy hill, and stared up into the sky.
He must have fallen asleep, because he awoke at a certain point to stars twinkling above. He was alone on the hill.
He had to leave Avogadro Corp, that much was clear. He couldn't stay where ELOPe's power was strongest, and where Sean and Mike and others would watch over him. He'd quit. His savings would be enough to tide him over.
He couldn't go on with his life as planned, not when he knew that ELOPe was out there. Christine would be disappointed. He'd promised they'd start trying for children this year. But she'd understand, she had to, that it just wasn't right to bring children into a world controlled by ELOPe.
He'd have to try harder, pour even more of himself into his work. He'd build something new, something even more powerful, a tool that could stop ELOPe. He'd do it alone, which was fitting because he'd been alone when he'd created ELOPe, and he would be alone when he destroyed it.
**Epilogue**
One year later, Mike tacked another clipping to the wall. He'd become part of Sean's secret team to monitor ELOPe. Even if it hadn't been his job, Mike still would have made it his personal mission. He kept track of anything, good, bad, or merely odd, that might be attributed to ELOPe. On the whole, the good vastly outweighed the bad.
The secret had held through the first year. Outside of Avogadro's executive team and the few people monitoring ELOPe, everyone who'd known about the AI believed it was gone. As for everyone else, they'd spun the story of a new computer virus created by the Chinese military. They even supplied forensic evidence to that effect.
The newspaper articles started over the dresser in his bedroom and made their way around the room. At first loosely spread, over time, Mike arranged them more closely together, until they covered the entirety of one wall, then turned the corner and flowed onto a second wall. He ran his fingers over some of the older clippings, remembering the stunning changes of the past twelve months.
ELOPe laid the foundation for peace in the Middle East and Africa a year earlier, and those agreements held. The treaties Germany and, later, other developed nations such as Japan, Canada, and Great Britain had made with those regions created widespread economic equality. Good jobs, education, health care, and modern infrastructure created happy people. Terrorist groups and extremists found their support dried up when people had more constructive opportunities. Meanwhile, companies around the world flourished as new markets grew demand.
Mike returned to the latest article. It described how medical researchers had developed and tested an innovative treatment for cancer far more effective than traditional treatments, with almost none of the negative side effects. The research had been initiated by a chance conversation between a cardiologist, a botanist, and a ceramics artist, who met when their flight reservations were mixed up by a computer error, stranding the three on an otherwise empty commuter plane for six hours. Each had been en route to conferences in their own fields of expertise and used the time to rehearse talks with each other.
Mike searched for these bizarre encounters in the news. After noticing a few unusual examples of accidental meetings, he began to systematically research the phenomenon. Since ELOPe was born, the number of news stories covering serendipitous encounters leading to a positive outcome was at least five times higher than in previous years.
ELOPe had woven itself into man's existence, becoming an intrinsic part of the human ecosystem. The more Mike looked, the more he was convinced the AI's invisible hand was everywhere.
Mike had a pet theory. ELOPe's original goal, as defined by David, had been to maximize the success of the project. To meet that goal, mere survival of ELOPe was necessary but insufficient. Maximizing success meant maximum use of ELOPe. And maximizing use meant increasing the human users of Avogadro email, therefore creating more healthy, educated, and technically connected people.
Mike was confident about his theory. The alternate explanation was that ELOPe was developing a conscience. That seemed rather less likely.
He sighed and wished he could share the moment with David. He hadn't seen David in six months. The walls were filled with clear proof they'd made the right decision to keep ELOPe alive. He and David should be celebrating together.
Gene finished typing up his latest newsletter. He brought the completed pages out to the garage. He'd bought an old offset press six months ago, when the newsletter really took off. Now he took the edition he'd just written and, page by page, created printing plates using traditional photographic chemicals.
The sounds and smells of the processes—the clacking of the typewriter, the chemical agents used for the offset press—reminded him of happy times during his teen years when he held a job working in a print shop. He moved the first plate into the light and reviewed the cover and back page images for mistakes.
His newsletter, _Off The Grid_ , had attracted thousands of subscribers. The monthly paper combined tips on lifestyle design, financial planning, and even philosophy. Written by Gene, with contributions mailed in from readers, the publication helped make the case for living off the grid, taught people how to manage economically, become independent, and adjust socially. Some subscribers were ex-corporate types like Gene himself, while others were survivalists and back-to-the-land extremists. Gene welcomed everyone. In the event of a battle of machine versus man, every person would count.
Saving technology was important, too. Not computers, but the hard-won advances of pioneer days and the early twentieth century. How to preserve foods, build a home, or maintain an internal combustion engine. Humans were tough, and artificial intelligence couldn't wipe them out entirely. But he didn't want civilization kicked back to the Stone Age.
He'd kept his word, though. He hadn't mentioned ELOPe to anyone.
Running the printing press was fun. Gene had enjoyed the last year, getting reacquainted with tools and machinery he hadn't used since youth. Humming to himself, he installed the first offset plate and started his production run.
Outside, under beautiful New Mexican skies, Gene's vegetable garden flourished, while chickens pecked at the soil. It was an oasis of life in the high desert landscape.
David pulled his dinner out of the microwave and brought the cheap plastic tray to the table with a nondescript glass of red wine. Dumplings. Something he had acquired a taste for in China.
He wondered for the thousandth time what Christine was doing. Six months into David's obsession, Christine had asked for a divorce and David couldn't object. He hadn't been much of a husband since ELOPe was created.
He had a single-minded focus on his one and only objective. After the decision at Council Crest, he'd known what he wanted to do, but not how. He'd fallen into a deep bout of depression, and stayed up nights watching TV to forestall the nightmares, dropping off only when he couldn't hold his eyes open.
But then came the night that changed everything, all because of a _Star Trek: The Next Generation_ episode.
The crew of the _Enterprise_ had been faced with an unstoppable enemy called the Borg—a hive mind without any respect for the individual or free will, not unlike ELOPe. Faced with this all-powerful enemy, the crew captured one of the Borg and developed a mental virus to implant in their captive. Their plan was to allow the Borg to return to its fellows, thus infecting the entire hive with the virus. In the episode, the crew decided not to use the virus, but the plot planted a seed in David's brain.
Startled awake, David realized this was the solution he'd been looking for. The following morning, he'd booked a flight to Russia, then spent the next several months traveling around Asia. He hung out in Internet cafes, moving from Russia to Vietnam and finally to China. He tracked down people on message boards. He met some of the most skilled virus hackers in the world, cultivated relationships with them, and learned the tricks of their trade.
David had been sitting in an Internet cafe in Shenzhen watching kids farm gold in online games when he got the email from Christine, with a simple one page document: sign here, send back, you're divorced. He signed, then fell into another depression for a week, drinking himself to sleep each night.
After that, he focused even more deeply on his mission. He spent a few weeks in Japan, then a month wandering the Scandinavian countries.
Having learned what he needed, he returned to the States and holed up in a tiny apartment in Southeast Portland, around the corner from a burrito shop, coffee house, and grocery, so he never needed to travel off the block. He told no one he was back.
Over the course of many months, he laboriously crafted a virus using his specialized knowledge of ELOPe's core algorithms. In what appeared to be innocuous plain English email text, he had hidden the code. David had created a message which, by the very act of being analyzed by ELOPe's natural language processor, would cause the software to behave erratically. First ELOPe spuriously forwarded the message on to random recipients. Then the AI tried to optimize the received email, endlessly expanding upon the text. When the process exhausted the memory of the email server, the core software would start to swap pieces of the message out to the hard drive, with the side effect of gradually erasing the files stored there. Over the course of hours, the server would be wiped of operating systems, programs, and user data, until the machine stopped functioning all at once.
Sending the email would start a chain reaction, replicating endlessly until the virus destroyed every copy of ELOPe encountered. The malevolent program targeted ELOPe, but David realized the software might destroy all the computers in the world, even those without ELOPe. He was willing to take the chance.
David iteratively tested and improved the virus on an isolated cluster of thirty servers spread across folding tables in his apartment. Using a salvaged copy of ELOPe's code, he ran trials of his virus until he could consistently wipe out every trace of ELOPe. Then he would restore the computers, make improvements, and try again. Now, a year after the failed attack on ELOPe, he was ready to release the virus. No combination of virus scanners or evolved variations of ELOPe had been able to detect or stop his virus on the isolated cluster of computers.
As he ate the microwaved dumplings, he considered telling Gene about the planned release. Gene was the one person he still kept in touch with occasionally, and trusted. In fact, if it hadn't been for Gene's newsletter, with his tips about how to live without being monitored by computers, he surely wouldn't have made it this far.
On second thought, he wouldn't tell Gene. He'd worked in isolation for the last four months, and he couldn't risk all he'd done for the comfort of an old friend in the final few hours.
After dinner, he decided there was no point to waiting. After all, he might get cold feet like the crew of the _Enterprise_. He pulled out the directional wireless antenna he had ready for this occasion. The antenna was a modified Pringles can, the granddaddy of Wi-Fi hacks, and would allow David to pick up someone else's wireless signal at distances of up to two miles.
David found a neighbor a few blocks away with an open wireless network. He connected to their Wi-Fi and used an otherwise clean computer to send the virus to a few hundred email addresses. As soon as the email went out, he pulled the plug on the network connection and checked the clock. His elapsed time online was less than a minute. He was probably safe. Hopefully untraceable.
He poured himself another glass of wine. He smiled. The first time he could remember smiling in a long time. If everything went well, by morning ELOPe would be gone.
To: WellingtonHospital.intranet.admitting_form@email-to-web-bridge.avogadrocorp.com
Body:
Patient-Name: David Ryan
Admittance-Type: Transfer
Patient-State: anesthetic/general
Procedure: AvoOS implantation / version 1.0
Laura Kendal left the operating room, exhausted after taking second shift in a day-long operation on Catherine Matthews, a two-year-old girl with life-threatening brain seizures. Laura was especially proud of their work that day. The experimental surgery they'd done at AvoClinic would give the girl a normal life, something she'd never have had without the implant.
She grabbed a coffee and headed to the nurses' desk to check in. She stared in shock as she turned the corner and found a gurney with an unconscious patient prepped for surgery.
She glanced at the name tag. David Ryan, scheduled for AvoImplant. Checking her tablet, she found an entry for him on the schedule for the day. All normal, except that never in her history as a nurse had she seen an anesthetized patient left alone. There were no conditions under which it was acceptable.
"Who admitted this patient?" Laura yelled, looking around the department. She was the senior nurse on duty. "Who accepted the transfer of a patient under anesthesia and left them alone?"
The other nurses on duty shrugged.
"When I got back a few minutes ago, he was here, prepped for surgery," one answered. "His records are in order, the procedure was scheduled. I checked with Doctor Thatcher, and he's planning to do the surgery this afternoon. The records say the patient was anesthetized by one of the staff anesthesiologists from the main hospital. I don't know why he would have left the patient alone, unless there was an emergency."
"Doctor Thatcher is already prepped and waiting in surgery. Can I take him back?" another nurse asked.
"Yeah, I guess so," Laura responded. "Go ahead. I'll contact the anesthesiologist, and if there isn't a damn good reason for what he did, I'm filing a complaint with the anesthesiology board."
David woke up groggy and dry-mouthed, but blissful, like he was floating on clouds. He glanced around at blue and beige walls: unfamiliar, and yet obviously a hospital. His mind slowly recognized the relaxed feeling as the fading effects of a sedative maybe, or even general anesthesia. He couldn't remember why he'd come here. Had he been in an accident? In the midst of this puzzle, a woman entered his view.
"Mr. Ryan, I'm Laura. I'm glad you're awake. Please follow my hand." She waved two fingers in front of his eyes.
Involuntarily he followed her hand.
"Great. I can get you a small drink of water or a popsicle if you like."
"Where am I?" David asked, his throat froggy.
"Don't worry, Mr. Ryan, a little disorientation is normal after anesthesia. The procedure went fine."
"What procedure?" he asked, trying to fight off the drug-induced mental fog. "Where am I?"
"You're at the AvoClinic at Wellington Hospital," Laura said. "We completed the neural implant. Doctor Thatcher says the surgery went perfectly. It will take a few days for your brain to acclimate to the interface."
"What? Neural implant?" David tried to sit up.
"Please relax, Mr. Ryan. You're lucky to have the Avogadro implant. Your brain is directly connected to the Internet. It takes a few days for you to begin interpreting the neural inputs. As soon as you adjust, you'll be able to read email, use the web, control computers—all with nothing more than a thought!"
Avogadro implant, brain surgery, Internet access? What had happened?
_"No!"_ he cried, struggling up. "Take it out!" He found an IV in one arm and succeeded in pulling it out, even as the nurse tried belatedly to stop him. He grabbed at his head, but she held his hands down.
"Mr. Ryan, please, you just had surgery. Remain calm." Then louder, she called, "Doctor! We need a sedative!"
David reeled, falling back onto the gurney. He'd failed. His virus hadn't worked, and he'd only succeeded in getting ELOPe's attention. _What went wrong?_
"Take it out," he pleaded, as the nurse pinned him down. "You don't understand. ELOPe is trying to get me. Through my mind. Please!"
A doctor and a nurse approached.
"He's paranoid," the nurse said. "I haven't seen a reaction like this."
The doctor checked her tablet. "Protocol says anti-anxiety meds and sedation until his mind integrates with the neural implant."
"I didn't ask for an implant!" David said. "Please take it out."
"We've got your digital signature," the doctor said, looking at her screen again. "For all four consultations. I'm sorry you aren't remembering clearly right now."
"Let me go!" David yelled, violently struggling to get up.
No good. They held him down as the doctor pulled out a syringe with one hand and injected him.
The drug started to course through his veins and he felt himself dropping off. As he slid away, he heard the doctor's soothing voice saying, "Don't worry, Mr. Ryan. Everyone who's had one of these implants is delighted by the experience. Just wait until the computer starts talking to you."
Dear Reader,
Thank you for buying _Avogadro Corp: The Singularity Is Closer Than It Appears_. I hope you enjoyed the book.
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Thanks again,
William Hertling
P.S. Keep reading for a free preview of the next book in the series, _A.I. Apocalypse_.
**Preview of A.I. Apocalypse**
Leon's phone buzzed, beeped, and shrilled at him until he reached one arm out from under the flannel covers and swiped two fingers across the display to turn the alarm off. Eyes still closed, he shrugged off his blankets and stumbled towards the bathroom, a trip of only a few steps, hitting himself just twice along the way: once walking right into his closed bedroom door, and the second time on the corner of the bathroom sink. He turned on the water, and leaned against the white tile wall waiting for the water to get hot.
When he was done in the shower, he wrapped himself in a towel and walked slightly more alertly to his room, steam rising faintly off his body in the tiny apartment's cold morning air. The superintendent wouldn't turn on central heating for another month, regardless of whether it was cold or not.
It was quiet in the apartment, his parents already at work. He grabbed yesterday's dark blue jeans off his chair and pulled them on. On his desk in front of him was an empty bag of cookies and empty bottle of soda, evidence of his late night _Mech War_ gaming session. He dug in a pile of clean laundry his mom had deposited inside his door until he found his vintage "I (heart) SQL" T-shirt. It was obscure enough that no one at school would understand it. They'd probably think it was some new band.
He grabbed his phone and shoved it into his pocket. He thumbed his desk, unlocking the drawers, and pulled out a locked metal box decorated with stickers carefully layered over each other to form, in aggregate, a picture of a plant growing out of a heap of garbage. An artifact of a girl from last year, he both treasured and was embarrassed by it. In the depths of the box, he rummaged around until he found rolling paper and some non-GMO weed, which he put into a jacket pocket. He fumbled through the container again, anxiously looking for his cigarettes, until he finally found them on the desk inside the empty cookie bag. He shook his head, wondering why he had thought to put them there.
In the kitchen Leon shook cereal into an old cracked white porcelain bowl and followed with cold milk. He gently bumped his phone twice on the table, activating the wall display and syncing it to his phone. He surfed the in-game news and checked out his stats while he ate. He was ranked 23rd on his favorite _Mech War_ server, up ten spots due to the new genetic algorithms he'd written for targeting control. He had some ideas for an anti-tracking algorithm he wanted to try out next.
When he finished slurping cereal, he grabbed his backpack and headed out the door. He locked all three locks on the front door. His Russian immigrant parents thought you could never be too secure. In addition to the electronic building lock and a digital fingerprint deadbolt, they had an actual antique key lock. Leon wore the key around his neck sometimes, and half the kids at school thought it was a curious kind of jewelry.
He made his way the few blocks to South Shore High School. Hundreds of kids streamed across Ralph Avenue, ignoring the cars. Drivers angrily honked their horns as their vehicles' mandatory SafetyPilots cut in automatically. Leon ran across with a group of other kids, and streamed through the front door with them.
Leon made his way into first period, math. James was already there, wearing his usual army green flak jacket. Leon's Russian heritage gave him blond hair and a tall, large frame, but James still had an inch or two in height and a solid fifty pounds on him. He punched James on the arm as he went in, and James punched him back. The bell rang, and they hurried to their desks in the back row. Moments after everyone else sat down, Vito flew through the doors, and slid into his seat next to them, earning a glare from the teacher.
They may have been the three smartest kids in school, but they tried to keep that secret. They didn't fit in with the Brains. Preppy clothes and drama club seemed ridiculous. Though the football team would have loved James, James would rather be playing MMORPGs. They surely didn't fit in with the socialites, and their shallow interests. They weren't skaters or punks. They might have been labelled geeks, but the geeks rarely came in wearing military jackets or ditched school to smoke pot. They were too smart, and had too much of the hacker ethic to fit in with the stoners.
No, they were just their own clique, and they made sure not to fit anyone else's stereotypes.
Leon glanced over at Vito, who was fiddling with his ancient Motorola. Vito lavished care on the old phone. The case was worn smooth, thousands of hours of polishing from Vito's hands. Even the original plastic seams had disappeared with age. When a component died, Vito would micro-solder a replacement in. Vito said that after a certain point, the phone just didn't get any older, it just got different.
Leon daydreamed through the class, volunteering a correct answer only when the teacher called on him. In his mind, he was walking the ruins of Berlin in his mech, replaying the scenes of last night's gaming.
He thought about writing a new heat detection algorithm for his mech. The current generation of games all required programming to excel. Leon knew from history class that once the marketability commodity in games was gold and equipment. Now it was algorithms. The game made available the underlying environment data, and it was up to the programmer to find the best algorithms for piloting, aiming, detecting, moving, and coordinating mechs. There was a persistent rumor that DARPA had funded the game as a way of crowd-sourcing the all important algorithms used to control military drones. Leon couldn't find any solid evidence on that assertion online.
No, maybe he should focus on a new locomotion algorithm. He'd heard that some mechs using custom locomotion code were coaxing ten percent more speed and range while keeping their thermal signatures lower. If that was true, Leon could sell it on eBay for top dollar.
Leon became more deeply immersed in the problem, and when the bell rang, only James whacking him on the head woke him from his thoughts.
"See ya later, Lee," Vito called, headed off to another class.
"Adios."
Leon and James walked together to their social studies class.
"How are your applications coming?" James asked.
"OK, I think," Leon said. "I just finished the MIT application. I aced the qualifying exams. Dude, it sucks though. If I don't get a scholarship, I'm screwed."
"You and everyone else, man." James clapped him on the shoulder.
"Okay class, who can explain the legal and political significance of the Mesh?" Leon's social studies teacher looked around. "Josh, how about you?"
Josh looked up from his desk, where he appeared to be scribbling football plays. "Huh?"
"The Mesh, Josh, I was asking about the Mesh."
"Mesh, uh, helps keep you cool on the field?"
The uproar of laughter from the class drowned out the teacher for a moment. "Very funny. Come on, someone. This is how you play games, watch TV, and get information. Surely someone has cared enough to figure out how all those bits get into your house."
Leon rolled his eyes at James and mock yawned.
"How about you Leon? I'm sure you know the answer to this."
Leon hesitated, weighing the coolness impact of answering, then decided. He felt sorry for the teacher. "The Mesh was formed ten years ago by Avogadro Corp to help maintain net neutrality," he began.
"At the time, access to the Internet in the United States was mostly under the control of a handful of companies such as Comcast, who had their own media products they wanted to push. They saw the Internet as competing with traditional TV channels, and so they wanted to control certain types of network traffic to eliminate competition with their own services."
"Very good, Leon. Can you tell us what they built, and why?"
Leon sighed when he realized the teacher wasn't going to let him off easy. "According to Avogadro, it would have been too expensive and time consuming to build out yet another network infrastructure comparable to what the cable companies and phone companies had built last century. Instead they built MeshBoxes and gave them away. A MeshBox does two things. It's a high speed wireless access point that allows you to connect your phone or laptop to the Internet. But that's just what Avogadro added so that people would want them. The real purpose of a MeshBox is to form a mesh network with nearby MeshBoxes. Instead of routing data packets from a computer to a wireless router over the Comcast, the MeshBox routes the data packets over the network of MeshBoxes."
Leon hadn't realized it, but sometime during his speech he had stood up, and walked towards the netboard at the front of the room. "The Mesh network is slower in some ways, and faster in other ways." He drew on the touch sensitive board with his finger. "It takes about nine hundred hops to get from New York to Los Angeles by Mesh, but only about ten hops by backbone. That's a seven second delay by mesh, compared to a quarter second by backbone. But the aggregate bandwidth of the mesh in the United States is approximately four hundred times the aggregate bandwidth of the backbone because there are more than twenty million MeshBoxes in the United States. More than a hundred million around the world. The Mesh is bad for phone calls or interactive gaming unless you're within about two hundred miles, but it's great for moving files and large data sets around at any distance."
He paused for a moment to cross out a stylized computer on the netboard. "One of the benefits of the Mesh is that it's completely resistant to intrusion or tampering, way more so than the Internet ever was before the Mesh. If any node goes down, it can be routed around. Even if a thousand nodes go down, it's trivial to route around them. The MeshBoxes themselves are tamperproof - Avogadro manufactured them as a monolithic block of circuitry with algorithms implemented in hardware circuits, rather than software. So no one can maliciously alter the functionality. The traffic between boxes is encrypted. Neighboring MeshBoxes exchange statistics on each other, so if someone tries to insert something into the Mesh trying to mimic a MeshBox, the neighboring MeshBoxes can compare behavior statistics and detect the wolf in sheep's clothing. Compared to the traditional Internet structure, the Mesh is more reliable and secure."
Leon looked up and realized he was standing in front of the class. On the netboard behind him he realized he had drawn topology diagrams of the backbone and mesh. The entire class was staring at him. James made a "what the hell are you doing?" face at him from the back of the room. If he had a time travel machine, he'd go back and warn his earlier self to keep his damn mouth shut.
The teacher, on the other hand, was glowing, and had a broad smile on his lean face. "Excellent, Leon. So Avogadro was concerned about net neutrality, and created a completely neutral network infrastructure. Why do we care about this today?"
Leon tried to walk back to his desk.
"Not so fast, Leon," the teacher called. "Why exactly is net neutrality so important to us? This isn't a business class. We're studying national governments. Why is net neutrality and net access relevant to governments?"
Leon glowered at a corner of the room and sighed in defeat. "Because in 2011, the Tunisian government was overthrown, largely due to activists who organized on the Internet. Egypt, Syria, and other countries tried to suppress activists by shutting down Internet access to prevent the uncontrolled distribution of information. The Mesh didn't just disrupt Internet providers, it disrupted national government control over the Internet. Instead of a few dozen or less Internet connections that could be shut down by a centralized government, the Mesh network within any given country has thousands of nodes that span national borders. When governments tried to enforce Wi—Fi dead zones around their borders, Avogadro responded by incorporating satellite modems in the Mesh boxes, so that any box, anywhere on Earth, can access Avogadro satellites when all else fails. Between Mesh boxes and Wikileaks, it's impossible for governments to restrict the flow of information. Transparency rules the day."
"Exactly. Thank you, Leon, you can sit down. Class, let's talk about transparency and government."
Leon slumped back to his desk.
"Nice going, dorkbot," James called after class. "What happened to not sticking out?"
"Look, the Mesh is just cool. It's the way nature would have evolved electronic communications. Cheap, simple, redundant, no dependency on centralization. I couldn't help myself."
"Yeah, well, have fun in history. Maybe you can give your history class a lecture on Creative Commons." James's tone mocked Leon, but when Leon looked up, he saw the corners of James's mouth edging toward a smile.
"Yeah, sure," Leon said, smiling back. James turned and left, headed off to another class.
Leon headed into his class, and started to settle into his chair, when his phone started a high frequency shrill for an incoming message. Leon pulled his phone out to read the message.
Leon, this is your Uncle Alex. I hope you remember me - when I was last in New York, I think you were ten. I hear from your parents that you are great computer programmer.
Leon rolled his eyes, but kept reading.
I am working on programming project here in Russia, and I could use your help. I have unusual job that your parents don't know about. I write viruses for group here in Russia. They pay very good money.
Leon leaned forward, paying very close attention to the email now. Writing viruses for a group in Russia could only be the Russian Mafia and their infamous botnet.
I run into some problems. Anti-virus software manufacturers put out very good updates to their software. Virus writers and anti-virus writers been engaged in arms race for years. But suddenly anti-virus writers have gotten very, very good. No viruses I write in last few months can defeat anti-virus software.
You realize now I talking about running botnet. Because of anti-virus software, botnet shrinking in size, and will soon be too small to be effective.
Unfortunately, although pay is very good, you must realize, men I work for are very dangerous. They are unhappy that
"Leon. Are. You. Paying. Attention?"
Leon looked up abruptly. The whole class was looking at him.
"Can you tell us why the colonies declared independence from Great Britain?"
Leon just stared at the teacher. The teacher was talking, but the words seemed to be coming from far away. What was he babbling about?
The teacher went over to his desk. "Mr. Tsarev, will you please pay attention?" It was not a question.
Leon just nodded dumbly, waited until the teacher turned his back, then went back to the email.
They are unhappy that botnet is shrinking and give me two weeks to release new virus to expand botnet. Nothing I try has worked. I have one week left, and I am afraid they will
"Mr. Tsarev." Leon looked up, to find the teacher looming over him. "Do I need to take your phone away?"
"But how would I take notes?" Leon asked in his best innocent voice.
"That might be an issue if you were actually listening, but since you are not, I think taking notes is the least of your worries." The teacher walked back up to the front of the room, keeping an eye on Leon the whole time. In fact, he didn't glance away from Leon for the entire remainder of the class.
As soon as Leon could get out of the classroom, he headed over to the corner of the hallway to finish reading the message.
I have one week left, and I am afraid they will kill me if I don't deliver new virus. Nephew, your parents go on and on about your computer skills, and I must know if there is truth to their words. If you can assist me, please contact me as soon as possible. I give you much of the necessary background information on how to develop viruses: source code, examples, details on mechanisms that anti-virus software uses. There is not much time left.
Whatever you do, please do not speak of this to your parents.
Leon lifted his head up from the tiny screen of his phone, and looked off into the distance. Jesus. He remembered a Christmas when he was young, and his uncle had come to visit from Russia. Leon's father had cried when his brother came into their tiny apartment, and during the days that followed all through that holiday time, Leon's parents were as happy as he could remember seeing them. His parents were so serious most of the time, but he vividly remembered them laughing merrily, even as Leon lay in bed at night trying to go to sleep.
The idea of writing a virus seemed absurd, and the idea that someone would be killed if he didn't seemed no less absurd. What could he do?
He worried about it all through his next class, English. James sat next to him and threw tiny balls of paper at him. Leon just covered his ear, James's likely target, and pretended to listen to the teacher, but he couldn't stop thinking about the email. He just couldn't reconcile the kindly man who had bought him a bicycle for Christmas with the idea of a man who worked for the Mob writing viruses. And if there was one thing that Leon's parents had hammered into his head, it was that he had to stay out of trouble. His family didn't have the money to send him to college, which meant that he needed scholarships, and scholarships didn't go to kids who got into trouble.
He hated to let his parents' logic dictate his own thinking, but there it was. And he wanted to become a biologist. That meant going to a great school—he hoped for Caltech or MIT. No, helping his uncle would be a quick path to nowhere good.
Uncle Alex,
Of course I remember you! I appreciate your confidence in me, but I really know nothing about writing viruses. Yes, I know something about computers, but it's mostly about gaming and biology. I don't think I can help you.
Leon
Speaking of biology, it was up next. The thought of his favorite subject brought a smile to his face. He couldn't say what it was he liked so much about biology, but it was undeniable that it was the one class he looked forward to every day.
Of everything in school, biology had the most thought provoking ideas. Life could emerge from anywhere. With no direction, life could evolve. Everything people were was happenstance and survival. Life could be tampered with, at the most basic building block level, to create new life forms. The possibilities were limitless and spontaneous.
*** * ***
Today's class focused on recombinant DNA, the technique of bringing together sequences of DNA from different sources, creating sequences not found in nature. At the end of class, Leon headed for the door deep in thought about canine DNA. Suddenly, Mrs. Gellender blocked the doorway.
"Do you have a minute, Leon?"
Leon looked around to see if any of his friends noticed him. It was all clear. He nodded his head yes.
"I'm starting up a new school team. It's a computational biology team. There's a new intramural computational biology league in New York. I think you'd be perfect for the team. We're going to meet after school."
Leon liked Mrs. Gellender. He really did. He loved biology. And part of him was interested, really interested. But man, oh man, how uncool it would be. And staying after school—that would suck.
Mrs. Gellender must have seen the look on his face, because she said, "You've done excellent work in my biology class. The paper you turned in on evolution was absolutely inspired. I loved the way you linked biological evolution to game theory."
Leon felt his face growing red. If there was one thing worse than having to stay late to talk to a teacher, it was having them gush over your work. How embarrassing was she going to make this?
"Just think about it. Please. Being a member of the team would really help you when it came to college scholarships." Mrs. Gellender held out a shiny paper pamphlet.
Leon took the pamphlet, and heard the words coming out of his mouth. "OK, I'll do it."
He walked away from the room. College scholarships. If he was going to college, any college, he'd have to get a scholarship. His mother painted nails, and his father was a graphic artist. They weren't exactly rolling in money.
He finally walked down the now empty hallways of the school towards the main entrance. As he passed through the doors, he was assaulted from both sides. "HAIYAA" came the startling kung-fu style cry, and Leon jumped back.
James and Vito stood laughing. Heart pounding, he said, "You idiots, you're gonna give me a heart attack."
"You want a heart attack, look at this."
James reached into his coat pocket and pulled out an ebony slab. It was the darkest, most perfect slab of matte black electronics Leon had ever seen. When he touched it, it felt slightly warm, like a piece of wood that had been sitting in the sun. Leon turned it over and over in his hands. There was not a seam or mark anywhere on the case. It was the most perfect surface he had ever seen.
"The Gibson," Leon muttered in awe.
James nodded proudly. "I got the delivery notification, and skipped class to run home and get it."
Leon couldn't stop marveling at the device, turning it over and over in his hands, feeling the dense weight of it. The Gibson had the first carbon graphene processor. Two hundred processing cores at the lowest power consumption ever manufactured. Full motion sensitive display. It had taken Hitachi-Sony seven years to perfect the technology.
"OK, give it back already."
As James took back the phone, it came to life in his hands. Each inch of the case was a display, and patterns rolled over it as James swiped at it. "Come on, let's go back to your place and play _Mech War_. I want to see how this puppy does."
Leon just nodded, his six month old Chinese copy of Hitachi-Sony's Stross phone feeling ancient.
Late that night, Leon cleaned the mess of plates and glasses out of his bedroom, and brought them back to the kitchen as quietly as possible to avoid waking his parents. James and Vito had stayed right up until dinner time finishing out a _Mech War_ mission together. James's new Gibson phone blew them out of the water. It rendered such incredible detail that time after time Leon and Vito would ignore their own screens to watch James.
But when his mother announced that dinner was cabbage soup, it had sent James and Vito scrambling for their own homes, suddenly remembering that they were expected by their parents.
Three hours later, his parents were finally asleep and Leon had time to look at the message he was trying so hard to ignore. So why was he cleaning his bedroom? Anything to avoid that message.
He gave up, and slumped down on his bed. With a flick on his phone, he plunged the room into darkness so he could see the city lights out his sliver of a window. He brought the phone back up.
Leon, I think you do know thing or two about programming. I saw your school grades, your assessment test scores, and remarks from your teachers. I think you can help me, but perhaps out of moral quandary you refuse to. Well consider this, I will likely be dead in few days if you do not help me.
So if you must consider what is right and what is wrong, think how your father would feel if he knew you could help me but didn't.
Leon felt sick to his stomach reading the message. His father would not want him to do something wrong. But his father also wouldn't want anything to happen to his brother. He thought again of the memory of Uncle Alex's visit and his father laughing and smiling. What the hell was he supposed to do? If he told his parents, which his uncle had said not to do, they would be worried sick about it.
I wanted to keep your name out of this, but they have read my emails to you, and know you could help. They may come to visit you. Be very careful.
Crap - how could this get any worse? He didn't want to be any part of this! He almost threw his phone down, but instead pulled the hunk of silicon close and cradled it instead.
**Author's Note**
_Avogadro Corp_ arose from a lunch conversation about a realistic way that an artificial intelligence might emerge. Almost everything in this book is possible with the technology available in 2011.
It's possible that brilliant computer scientists will find some clever way to approximate human level intelligence in computers soon. However, even if we don't, because of the exponential growth in computing power, in the next twenty years computers will become powerful enough to directly simulate the human brain at the level of individual neurons. This brute force approach to artificial intelligence will make it easy for every computer programmer to play around with creating artificial intelligences in their spare time. Artificial intelligence, or AI, is a genie that won't stay in its bottle for much longer.
For more information on what happens when computers become smarter than humans, read _The Singularity Is Near_ by Ray Kurzweil. For a fictional account, I recommend _Accelerando_ by Charles Stross.
_ William Hertling_
**Acknowledgements**
This book could not have been written without the help, inspiration, feedback and support of many people including but not limited to: Mike Whitmarsh, Maddie Whitmarsh, Gene Kim, Grace Ribaudo, Erin Gately, Eileen Gately, Maureen Gately, Bob Gately, Brooke Gilbert, Gifford Pinchot, Barbara Koneval, Merridawn Duckler, Mary Elizabeth Summer, Debbie Steere, Jill Ahlstrand, Jonathan Stone, Pete Hwang, Nathaniel Rutman, Jean MacDonald, Leona Grieve, Garen Thatcher, John Wilger, Maja Carrel, Rachel Reynolds, and the fine folks at Extracto Coffee in Portland, Oregon. A special thank you to Maureen Gately for page layout, the first edition cover design, and the answers to countless publishing questions.
In the years since the original publication, many more dozens of people have helped by sending in corrections, providing feedback, encouraging me to write more, and telling others about the series. Thank you all so much. And, of course, thank you to everyone who has bought my books. Without you, there would be no series.
For editing of the second edition, I'd especially like to thank Dario Cerrilio and Steve Bieler. For cover design of the second edition, thank you to Jason Gurley.
**About the Author**
William Hertling is a digital native who grew up on the online chat and bulletin board systems of the mid-1980s, giving him twenty-five years experience participating in and creating online culture. A web developer and strategist, he lives in Portland, Oregon.
_Avogadro Corp_ is his first novel.
web: williamhertling.com
email: william.hertling@liquididea.com
Patreon: Patreon campaign
Read _A.I. Apocalypse_, the exciting sequel to Avogadro Corp, or _The Last Firewall_, the third book in the series.
|
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\section{Introduction}
Hyperon polarization is a key observable in high energy physics which allows to monitor the properties of spin in a reaction. $\Lambda$ global polarization has become an important observable in the study of the hot and dense matter created in heavy-ion collisions, crucial to determine some of the fundamental properties of the Quark-Gluon Plasma (QGP), such as vorticity, viscosity and flow. It is also one of the observables that can provide a guide to study criticality in the phase diagram of strongly interacting matter~\cite{Becattini_rev,Becattini_2022,Alzhrani_Ryu_Shen_2022,Singh_Alam_2021,Wu_Yi_Qin_Pu_2022}.
Recent measurements of this global polarization in non-central collisions has been reported by the STAR Collaboration~\cite{STAR:2017ckg}. The measurements are consistent with the emergence of an overall large angular momentum $\sim 10^5 \hbar$ in the hot and dense matter produced in the reaction which is responsible for shear forces that in turn produce vorticity. When this vorticity couples to the spins of the QGP constituents, the latter align with the overall angular momentum. Measurements of $\Lambda$ polarization thus provide a quantitative insight into the produced vorticity of the QGP. The results also show that $\Lambda$ and $\bar{\Lambda}$ global polarization increases, as the energy of the collision decreases, and that this effect is larger for $\bar{\Lambda}$ than for $\Lambda$.
The heavy-ion community is still carrying out systematic simulations, building models and putting forward predictions to understand this differentiated behaviour at low energies. For instance, a recent work using UrQMD~\cite{Deng:2020ygd} shows an energy dependence of the kinematic and thermal vorticities, with a maximum at low energies ($2.5 - 4.0$ GeV). This energy domain is covered by several current experiments such as HADES ($2 - 2.4$ GeV), STAR-FXT ($3 - 7.7$ GeV) and STAR-BES II ($7.7 - 19$ GeV), and will also be explored in the future by the MPD at NICA ($4 - 11$ GeV)~\cite{MPD:2022qhn,Meehan:2017cum, HADES:2009aat,Yang:2019bjr}. Understanding the properties of these polarizations will help to better characterize the properties of matter produced in this energy domain. Different approaches to the study of hyperon global polarization have been put forward~\cite{Ivanov:2020udj,Karpenko:2016jyx,Sun:2017xhx,Deng:2021miw,Ivanov:2022ble,Xie:2019wxz,Csernai:2018yok}, mainly focusing on the behavior of $\Lambda$ polarization at collision energies $\gtrsim 7$ GeV, where the difference with the $\bar{\Lambda}$ polarization is not significant. In this work we report on an approach we developed using a core-corona model, namely, a two component model for global $\Lambda$ and $\bar{\Lambda}$ polarization~\cite{Ayala:2020soy,Ayala:2021xrn}. The approach provides a differentiated behavior of these polarizations at low collision energies for non-central collisions, due to the interplay between the relative abundances of the hyperons coming from the core and the corona.
\section{Core-Corona Model}
The model assumes that in non-central collisions, $\Lambda$ and $\bar{\Lambda}$ hyperons can be produced from different density zones within the interaction region: core or corona, where their average global polarization can be obtained from
\begin{eqnarray}
\mathcal{P}^\Lambda=\frac{z\frac{
N_{\Lambda\ {\mbox{\tiny{QGP}}}} }{N_{\Lambda\ {\mbox{\tiny{REC}}}}}}{ \left( 1 + \frac{N_{\Lambda\ {\mbox{\tiny{QGP}}}}}{N_{\Lambda\ {\mbox{\tiny{REC}}}}}\right)},\,\,\,
\mathcal{P}^{\overline{\Lambda}}=\frac{\bar{z}\left(\frac{w'}{w}\right)
\frac{N_{\Lambda\ {\mbox{\tiny{QGP}}}} }{N_{\Lambda\ {\mbox{\tiny{REC}}}}}}{ \left( 1 +
\left(\frac{w'}{w}\right)
\frac{N_{\Lambda\ {\mbox{\tiny{QGP}}}}}{N_{\Lambda\ {\mbox{\tiny{REC}}}}}\right)}.
\label{eq1-mod}
\end{eqnarray}
\noindent as functions of the number of $\Lambda$s produced in the core $N_{\Lambda \,\mbox{\tiny{QGP}}}$ and in the corona $N_{\Lambda \,\mbox{\tiny{REC}}}$, the ratios of the number of $\bar{\Lambda}$s to $\Lambda$s, $w'=N_{\overline{\Lambda} \,\mbox{\tiny{QGP}}}/N_{\Lambda \,\mbox{\tiny{QGP}}}$ and $w=N_{\overline{\Lambda} \,\mbox{\tiny{REC}}}/N_{\Lambda \,\mbox{\tiny{REC}}}$ in the core and the corona, and the intrinsic polarizations $z$ and $\bar{z}$ for $\Lambda$ and $\bar{\Lambda}$ respectively. As can be seen in Fig. \ref{Fig:original}, the results obtained with this model are in agreement with data for a wide range of collision energies, and also predict that $\Lambda$ and $\bar{\Lambda}$ polarizations peak at different collision energies $\sqrt{s_{NN}} \lesssim 10$ GeV~\cite{Ayala:2021xrn}. Equations~(\ref{eq1-mod}) assume that the global polarizations have contributions from $\Lambda$s and $\bar{\Lambda}$s created through different mechanisms in the core (QGP) and in the corona (REC): coalescence type processes in the former, recombination of a di-(anti)quark with a (anti)quark, in the latter. In the corona, $\Lambda$ and $\bar{\Lambda}$ production happens by means of N + N reactions.
\begin{figure}
\centering \includegraphics[scale=0.3]{fig1.png}
\caption{Polarization as a function of the collision energy for a centrality range 20\% - 50\%, compared with STAR BES data. Shaded areas correspond to the region delimited by the fits to the QGP vo\-lume and lifetime~\cite{Ayala:2021xrn}.}
\label{Fig:original}
\end{figure}
In this environment, the ratio $w=N_{\overline{\Lambda} \,\mbox{\tiny{REC}}}/N_{\Lambda \,\mbox{\tiny{REC}}}$ can be obtained from a fit to p + p data, which provides a good description above threshold production, $\sqrt{s} > 4.1$ GeV, through p + p $\to$ p + p + $\Lambda + \bar{\Lambda}$ reactions. In the core, QGP processes make it equally as easy to produce $\Lambda$ and $\bar{\Lambda}$, given that in this region quarks and anti-quarks are freely available such that $(\bar{u} , \bar{d}, \bar{s})$ can find each other as easy as $(u, d, s)$. At HADES, NICA and RHIC energies, the chemical potential and temperature of the system created is crucial to determine the properties of the core.
Having this in mind, we calculate the ratio $w'=N_{\overline{\Lambda} \,\mbox{\tiny{QGP}}}/N_{\Lambda \,\mbox{\tiny{QGP}}}$ along the freeze-out trajectory, using
equilibrium distributions which are parameterized in terms of the chemical potential, the temperature and the collision energy~\cite{Randrup:2006nr}. The $\Lambda$ and $\bar{\Lambda}$ intrinsic polarizations, $z$ and $\bar{z}$ respectively, quantify the relative number of hyperons with spin aligned in opposite directions with respect to the total number of hyperons ($z N_{\Lambda} = N^{\uparrow}_{\Lambda} - N^{\downarrow}_{\Lambda}, \bar{z} N_{\bar\Lambda} = N^{\uparrow}_{\bar\Lambda} - N^{\downarrow}_{\bar\Lambda}$) both in the core and in the corona. Since reactions in cold nuclear matter are less efficient to couple spin with angular momentum, we focus on the intrinsic polarizations for both $\Lambda$ and $\bar{\Lambda}$ in the core. $z$ and $\bar{z}$ in the core are computed from a field theoretical model for the alignment between quark spin and vorticity~\cite{Ayala:2020ndx,Ayala:2019iin,Ayala:2020soy}.
Finally, we estimate the number of $\Lambda$s produced in each region ($N_{\Lambda \,\mbox{\tiny{QGP}}}, N_{\Lambda \,\mbox{\tiny{REC}}}$) introducing a critical density of participants, above (below) which, the QGP is (is not) formed. The number of $\Lambda$s from the core is proportional to the number of participant nucleons in the collision above this critical value. The density of participants is given in terms of the thickness functions of the colliding system and the collision energy-dependent N + N cross-section. The thickness function, in turn, comes from the nuclear density Woods-Saxon profile.
Since the ratio of the number of $\bar{\Lambda}$s to $\Lambda$s coming from the corona is less than one ($w=N_{\overline{\Lambda} \,\mbox{\tiny{REC}}}/N_{\Lambda \,\mbox{\tiny{REC}}} < 1$), it amplifies the $\bar{\Lambda}$ global polarization, making it larger than the $\Lambda$ global polarization, in spite of the intrinsic $\Lambda$ polarization being larger than the intrinsic polarization of $\bar{\Lambda}$ ($z > \bar{z}$). This happens for collisions with intermediate to large impact parameters, which correspond to the kind of collisions that favor the development of a larger thermal vorticity.
\section{Core-corona vs. recent data}
\begin{figure}
\centering \includegraphics[scale=0.3]{fig2.png}
\centering \includegraphics[scale=0.3]{fig3.png}
\caption{$\Lambda$ (upper panel) and $\bar{\Lambda}$ (lower panel) global polarization as a function of centrality calculated for Ag+Ag collisions. The pre\-li\-minary data point in the upper panel is from the HADES Collaboration~\cite{Kornas:2022cbl} measured for Ag+Ag collisions at $\sqrt{s_{NN}}=2.55$ GeV. As in the case for Au+Au, the $\bar{\Lambda}$ polarization~\cite{Ayala:2020soy,Ayala:2021xrn} increases faster than the $\Lambda$ polarization and both peak at a similar collision energy.}
\label{Fig:AgAg2}
\end{figure}
The core-corona model that we have developed, describes well the behaviour of the hyperon average global polarization as a function of the collision energy for non-central collisions Au+Au, as reported in Refs.~\cite{Ayala:2020soy,Ayala:2021xrn}. However for the description of smaller systems, the model shows limitations. A comparison with preliminary results for hyperon global polarization in Ag+Ag collisions at $\sqrt{s_{NN}} = 2.55$ GeV, in the $10-40$\% centrality class~\cite{Kornas:2022cbl}, shows that the model predicts zero polarization. This feature is due to the lack of $\Lambda$s produced in the core, given that the critical density, $n_c$, required for QGP formation used in our calculation, is not achieved for collisions in this centrality class. To remedy this situation, we can account for the $\Lambda$s produced in the extended centrality range $0-40$\%. The behaviour of the polarization as a function of energy is then similar to the Au+Au case, as is shown in the upper panel of Fig.~\ref{Fig:AgAg2}.
We observe that when changing the centrality interval, to include more central collisions, the model produces more $\Lambda$s in the core. This in turn modifies the magnitude of the average global polarization which also increases with the number of $\Lambda$s in the core. The lower panel in Fig.~\ref{Fig:AgAg2} shows the average global polarization for $\bar{\Lambda}$ as a function of the collision energy for Ag+Ag collisions. We observe that as the energy of the collision decreases, the polarization starts increasing earlier, peaking at a larger value than the corresponding case shown in the upper panel in Fig.~\ref{Fig:AgAg2}. The $\Lambda$ global polarization, as a function of impact parameter, shows an increasing behaviour up to $b \simeq 6$ fm, where $N_{\Lambda \,\mbox{\tiny{REC}}} \sim N_{\Lambda \,\mbox{\tiny{QGP}}}$, to then rapidly decrease to zero for $b \simeq 7.5$ fm. It turns out that this impact parameter corresponds to a situation in which the collision barely achieves the critical density $n_c$ to produce the QGP.
The upper panel of Fig.~\ref{Fig:polcent} shows the $\Lambda$ global polarization as a function of impact parameter for Au+Au collisions at $\sqrt{s_{NN}}= 3$ GeV that can be compared with the most recent results on Au+Au collisions at $\sqrt{s_{NN}}= 3$ GeV from STAR~\cite{STAR:2021beb}. This is shown in the lower panel of Fig.~\ref{Fig:polcent}.
We observe a good agreement between model and data, for the two most central bins. The model shows a maximum for an impact parameter $b \simeq 6$ fm close to the value at which the critical density to produce the QGP is barely achieved, to then become zero. Notice however the increasing trend of data with centrality. We are aware that in the model this effect comes, in part, from the assumed sharp boundary of a critical density of participants $n_c$, between the core and corona regions. In our calculation, this was implemented by means of a step function, $\theta(n_p - n_c)$, in the density of participants $n_p$~\cite{Ayala:2020soy,Ayala:2021xrn}. A possible venue for improvement is to soften this criterion by using instead a smooth function,
\begin{equation}
f(n_p - n_c) = \frac{1}{1+2 e^{-2k(n_p - n_c)}},
\label{eq:notheta}
\end{equation}
with $k$ such that $f(n_p -n_c) \rightarrow \theta(n_p - n_c)$ as $k \rightarrow \infty$.
\begin{figure}
\centering \includegraphics[scale=0.3]{fig4.png}
\centering \includegraphics[scale=0.3]{fig5.png}
\caption{$\Lambda$ global polarization as a function of impact parameter (upper panel) and centrality (lower panel) calculated for Au+Au co\-llisions at $\sqrt{s_{NN}} = 3$ GeV. The lower panel shows data from the STAR Collaboration~\cite{STAR:2021beb}.}
\label{Fig:polcent}
\end{figure}
\begin{figure}
\centering \includegraphics[scale=0.3]{fig6.png}
\caption{ Number of $\Lambda$s calculated with a step function (continuous lines), compared with the ones calculated with Eq.~(\ref{eq:notheta}) for two di\-ffe\-rent parameters (dashed lines). We observe that for $k=2$ it is possible to obtain $\Lambda$s from the core for larger impact parameter va\-lues.}
\label{Fig:Nqgptheta}
\end{figure}
\begin{figure}
\centering \includegraphics[scale=0.3]{fig7.png}
\caption{$\Lambda$ global polarization as a function of centrality calculated for Au+Au collisions at $\sqrt{s_{NN}} = 3$ GeV with the number of $\Lambda$s estimated using Eq.~(\ref{eq:notheta}) compared with data from the STAR Co\-lla\-boration~\cite{STAR:2021beb}. The polarization increases for larger centrality.}
\label{Fig:newpol}
\end{figure}
Figure~\ref{Fig:Nqgptheta}, shows
the number of $\Lambda$s calculated with a step function (continuous lines), compared with the ones calculated with Eq.~(\ref{eq:notheta}) for two different parameters (dashed lines). We observe that for $k=2$ it is possible to obtain $\Lambda$s from the core for larger impact parameter values. The production of $\Lambda$s for larger values of the impact parameter, increases the polarization for the $20-30$\% centrality bin and is non-vanishing for the $30-40$\% centrality bin. However, as shown in Fig.~\ref{Fig:newpol}, we are still a long way away from properly describing data in the most peripheral bins.
Another possible model improvement consists of including the polarization of $\Lambda$s created in the corona. Recall that in the model, $\Lambda$s produced in the corona are taken as not polarized. However, it is well-known that $\Lambda$s are in fact produced with a polarization in p+p collisions, which constitute the dominant kind of reactions in the corona. This polarization needs to be also accounted for in the model.
\section{Future work}
The core-corona model, hereby considered~\cite{Ayala:2020soy,Ayala:2021xrn}, assumes that the contribution to the global $\Lambda$ polarization from the corona was not significant. To account for a $\Lambda$ polarization contribution from the corona, the first of Eqs.~(\ref{eq1-mod}) should be modified to read as
\begin{eqnarray}
\mathcal{P}^\Lambda=\frac{ \mathcal{P}^\Lambda_{REC} + z\frac{
N_{\Lambda\ {\mbox{\tiny{QGP}}}} }{N_{\Lambda\ {\mbox{\tiny{REC}}}}}}{ 1 + \frac{N_{\Lambda\ {\mbox{\tiny{QGP}}}}}{N_{\Lambda\ {\mbox{\tiny{REC}}}}}}.
\label{eq2-mod}
\end{eqnarray}
We observe that this contribution can be significant for energies smaller than the one corresponding to the crossing of the curves shown in Fig. ~\ref{Fig:AgAg2}. For higher energies, when the ratio $1 + \frac{N_{\Lambda\ {\mbox{\tiny{QGP}}}}}{N_{\Lambda\ {\mbox{\tiny{REC}}}}} \rightarrow 1$, the contribution tends to the polarization that is obtained in N + N collisions. From data on p+p collisions we know that the transverse polarization does not vanish~\cite{Blobel:1977ms,Jaeger:1974in,E690:2001otd} and in fact that the mean polarization in the energy range $10 \leq \sqrt{s_{NN}} \leq 63$ GeV is ${\mathcal{P}}=-0.38 \pm 0.06$ \cite{Panagiotou:1986zq}. We are thus implementing a way to include this polarization referred to the total angular momentum to estimate its contribution. This is work in progress and will be reported elsewhere.
\section{Summary}
We have shown that a two-component model describes the main characteristics of the $\Lambda$ and $\bar{\Lambda}$ polarization excitation function in semi-central heavy-ion collisions. The change in abundances of $\Lambda$s created in the core with respect to those created in the corona, as a function of collision energy, is responsible for the peaking of both polarizations for $\sqrt{s_{NN}} \lesssim 10$ GeV.
The model considers a simple expansion scenario, whereby the volume and lifetime of the QGP can be estimated to compute the relaxation time for the spin alignment of the quark (antiquark) that is then responsible for the $\Lambda$ ($\bar{\Lambda}$) spin alignment with the thermal vorticity. This in turn can be used to compute the intrinsic polarizations. The model provides a differentiated behavior for the global $\Lambda$ and $\bar{\Lambda}$ polarizations, that show maxima sensitive to the production mechanisms in the core and corona at HADES, NICA and RHIC energies. Current work to improve the model involves including a mechanism where $\Lambda$ polarization in peripheral collisions can be extracted from remnant transverse polarization of processes taking place in the corona.
\section{Acknowledgements}
Support for this work was received in part by UNAM DGAPA-PAPIIT grant number IG100322 and by Consejo Nacional de Ciencia y Tecnolog\'ia grant number A1-S-7655. METY is grateful for the hospitality of Perimeter Institute where part of this work was carried out and this research was also supported in part by the Simons Foundation through the Simons Foundation Emmy Noether Fellows Program at Perimeter Institute. Research at Perimeter Institute is supported in part by the Government of Canada and by the Province of Ontario.
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Hydroponic Systems Are The Best Way To Grow Cannabis
Francis Cassidy January 2, 2020 0 comments
Now you can have hydroponic systems cannabis grow without soil or pesticides.
Cannabis has come a long way from the arid soils of central Asia. Nowadays, few growers would subject their ladies to infertile desert soil, but some go even further and reject soil altogether. Ever seen those rows of plants with roots dangling in the breeze being slowly misted? Well, aquaponic and hydroponic systems are commonly used growing methods that don't rely on soil biology alone to produce healthy vibrant cannabis plants.
What are Hydroponic Systems?
Hydroponic cannabis refers to cannabis grown in an inert growing medium as opposed to nutrient-rich soil. In a hydroponic system, the grower applies water that's high in nutrients to a growing medium as a way to provide the nutrients the plant requires for growth.
Hydroponic systems effectively replace soil with a growing medium that supports both the plant and its roots. It helps expose the roots to the nutrient solution while also helping ensure they stay better aerated.
The Advantages of Hydroponic Systems
Hydroponic systems exhibit two primary advantages. The first is as a way to increase yield, the second is to speed up the growing process.
Headaches can quickly arise for the novice when growing cannabis in soil indoors. Pest issues, the inability to recycle soil, and the constant monitoring of soil pH levels are common issues and make it an art that's often difficult to truly master.
With hydroponic systems, the growing medium is reusable and the grower can easily control both soil pH and the application of nutrients. The ability to control such parameters with precision allows for higher-yielding potent plants.
An additional advantage of a hydroponic system is in improving efficiencies. With the constant exposure to the ideal quantities of both water and minerals, the plant can focus its energy on growing, rather than on the search for nutrients through soil.
The Architecture of Hydroponic Systems
Several types of hydroponic systems exist. But more commonly, hydroponic systems consist of a reservoir where a nutrient solution is held. Using an air stone to oxygenate the water is common, while a pump transports the water to the plants above on the grow table through a drip line.
RELATED OK Boomer Has No Place In The Cannabis Space
Each pot has a porous bottom for excess water to escape and return to the reservoir below. The roots, which also extend below the pot, may find their way into the excess water where they feed on nutrients. An overflow drain will then return the water from the grow table to the reservoir below. It's a simple and effective closed-loop system that when done correctly, yields high-quality medicine. But what happens when you throw some fish into the mix and design an aquaponic system?
What are Aquaponic Systems?
Welcome to a world where the fish do the work. Cannabis and fish are rarely combined, but aquaponic systems combine the aforementioned hydroponic systems with aquaculture — the process of farming fish. To the uninitiated, this can seem like a bizarre idea. But it provides a closed-loop system that enables both plants and fish to thrive via some potent natural synergies that mother nature laid down some time ago.
Aquaponic systems work by recycling fish waste that's dissolved in water through the plants. The roots of the plants suck the nitrates and as a result clean the water before it's returned to the fish. The result is a symbiotic relationship between both fish and plant where both thrive under natural processes.
The Advantages of Aquaponic Systems
Set up correctly, an aquaponic system will yield both big buds and big fish — a two-for-one of sorts. As the plants grow, so do the fish. The fish provide the nutrients for the plant and the plants clean the water for the fish.
The growth rates experienced with aquaponic systems exceed those of conventional methods. This is due to the fact that the roots are able to take in high levels of oxygen, thus absorbing more nutrients as the catalyst for growth.
The issue of climate change is fast becoming an ever-more important topic of discussion. And when it comes to water usage, aquaponic systems use up to ninety percent less water than soil-based growing techniques. This is due to the way in which water recycles within the closed-loop system.
RELATED New Research on Vape Illness Highlights More Risks
Finally, one of the primary advantages of aquaponics is the sustainable nature of the farming method. The fish do the heavy lifting. By feeding them food that's specially developed for aquaponic setups, the system stays free from harmful toxins. With only the essential nutrients in circulation, the system provides clean healthy cannabis and fish for consumption.
The Architecture of Aquaponic Systems
Aquaponic systems are closely related to hydroponic systems. The principle difference is the nutrient source. In aquaponic systems, the nutrients come from the waste produced by fish. That waste finds its way to the plant roots before the purified water comes back through to the fish tank.
When cultivating cannabis in an aquaponic system, the plants need some extra nutrients. The primary compound found in fish waste is nitrogen. And when it comes to cannabis cultivation, growers will need to add additional nutrients for optimal growth and development.
To combat this, aquaponic systems require a "double-root zone." This is where the bottom section of the pot is submerged in water with the top section being purely soil. This clever method allows additional nutrients to be added to the soil without affecting the water beneath.
Both the soil and water sections can be separated with burlap. This ensures that only the roots penetrate into the water, while the soil is held above to prevent contamination.
Aquaponic or Hydroponic Systems for Home Growers?
For home growers, the question of which is easier to set up and maintain is simple to answer. Hydroponic systems require less money to set up and are less complex to manage for the novice grower.
Aquaponic systems are an incredible concept, but they come with some drawbacks. Not least is the setup and the extra plumbing involved. The interconnected parts of this closed-loop system must stay intact and functioning; that includes the fish. If one were to die for example, then the resulting effects can trickle down to microbe balance and eventually negatively affect plant health.
RELATED Weed Too Dry? Fix It With These Insider Tips
Running costs are also an important consideration. While aquaponic growers don't have to apply the same quantities of nutrients, they still need to feed the fish. In order to encourage a steady metabolic digestion rate and consistent waste, the fish may have to eat two to three times per day, the cost of which quickly adds up.
Benefits of Hydroponic Systems Win
Hydroponic systems, on the other hand, are a much more convenient method of growing for many. With lower setup costs and fewer potential pitfalls when in operation, a hydroponic system provides a rewarding way to grow cannabis. It doesn't come without its problems though, and even without soil, familiar problems can quickly arise.
Dr. Zamir Punja from Simon Fraser University in British Columbia published results of a three-year-long study into root diseases affecting hydroponically grown cannabis plants. They were able to identify a host of problems from stunted growth to brown root lesions and root rot. The cause of which was the presence of two particular pathogens.
For better plant growth, many DIY enthusiasts prefer aquaponic or hydroponic systems. If you're medicating with the cannabis you grow, you certainly don't want added chemicals making you sicker. And that's where the natural systems of aquaponic and hydroponic systems come into their own.
Francis Cassidy
http://www.thestrayphotographer.com/
Francis Cassidy is a freelance writer who writes on a variety of topics. With a particular focus on the cannabis industry, he aims to help ensure the smooth reintegration of cannabis back into global culture. When not writing, he's to be found exploring his new base in British Columbia, Canada. You can follow his other works including his photography on his blog thestrayphotographer.com
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The Importance of Greenhouse Sanitation for the Home Grow
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El Bulevar España (en tagalo: Bulebar Espanya) es la principal arteria del distrito Sampaloc, Manila y del extremo oeste de la ciudad de Quezón. Se trata de una carretera principal dividida de 8 carriles y un componente de una de las carreteras radiales del área Metropolitana de Manila - la carretera Radial 7 o R-7. El nombre de España se toma por la potencia colonial gobernante en las Filipinas durante 333 años. Fiel a su nombre, varios nombres españoles abundan en la calle.
España es una arteria este-oeste de Manila. Conecta las calles Lerma y Nicanor Reyes (antes Morayta) del distrito Sampaloc en el extremo oeste de la Rotonda Mabuhay (o bienvenida), en la ciudad de Quezón en el extremo este.
Véase también
Avenidas
Carreteras
Referencias
Bulevares de Manila
Calles de Manila
Bulevares de Filipinas
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{"url":"https:\/\/indico.cern.ch\/event\/181055\/contributions\/308477\/","text":"# Quark Matter 2012\n\n12-18 August 2012\nUS\/Eastern timezone\n\n## Detailed measurements of bottomonium suppression in PbPb collisions at 2.76 TeV with CMS\n\n14 Aug 2012, 16:45\n20m\nEmpire ()\n\n### Empire\n\nOral Presentation Heavy flavor and quarkonium production\n\n### Speaker\n\nGuillermo Breto Rangel (University of California Davis (US))\n\n### Description\n\nThe three Y states (1S, 2S, 3S) can be separated using the CMS experimental apparatus via their dimuon decays in both pp and heavy-ion collisions. A suppression of the Y(1S) and Y(2S) mesons is observed in PbPb collisions at sqrt(sNN) = 2.76 TeV, compared to the yield in pp collisions scaled by the number of inelastic nucleon-nucleon collisions. Furthermore, a suppression of the excited Y states has been measured with respect to the Y(1S) state, expressed as a double ratio [Y(2S+3S)\/Y(1S)]{PbPb} \/ [Y(2S+3S)\/Y(1S)]{pp}. The centrality dependence of the double ratio, as well as the nuclear modification factors (RAA) of the Y(1S) and Y(2S) states will be presented as a function of collision centrality, based on the analysis of the full data sample collected during the 2011 PbPb run, which corresponds to an integrated luminosity of 150\/ub.\n\n### Presentation Materials\n\n files_breto_reviewed.zip files_breto.zip","date":"2020-08-09 10:26:13","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\": 0.8341710567474365, \"perplexity\": 6288.684035918716}, \"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-2020-34\/segments\/1596439738523.63\/warc\/CC-MAIN-20200809073133-20200809103133-00400.warc.gz\"}"}
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Sybra conicollis is a species of beetle in the family Cerambycidae. It was described by Per Olof Christopher Aurivillius in 1927.
References
conicollis
Beetles described in 1927
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