text:
Spring is Just Around the Corner
March 10, 2021 July 11, 2021 Berkshire Administrator 645 Views
* Plus More Titles for April !
DVD's:
* Captain Phillips
Based upon the book "A captain's duty: Somali pirates, Navy Seals, and dangerous days at sea" by Richard Phillips with Stephan Talty. Originally released as a motion picture in 2013.
Special features: Commentary with director Paul Greengrass; English commentary subtitles; Capturing Captain Phillips (in-depth behind-the-scenes featurettes on making the acclaimed film); Previews.
* Dr. Qing Li – Forest Bathing: How Trees Can Help You Find Health and Happiness
"A guide to the therapeutic Japanese practice of shinrin-yoku, or forest bathing, demonstrates how it can reduce stress levels, improve the immune system, and promote health and happiness, and includes more than one hundred photographs from forests around the world."
Erica Strauss – The Hands-on Home: A Seasonal Guide to Cooking, Preserving and Natural Homekeeping
"Popular Seattle blogger, Erica Strauss (Northwest Edible Life) shows us how in this modern homekeeping handbook for thrifty DIYers who care about sustainability. A fresh take on modern homemaking, this is a practical (and sometimes sassy) guide to maximizing your time, effort, and energy in the kitchen and beyond. With a focus on less consumerism, it will teach you how to organize your kitchen and home to make the best use of your time. For those yearning to live a more ecologically minded, grounded lifestyle, this book is full of practical, no-nonsense advice, fabulous recipes, and time- and money-saving techniques"–Provided by publisher.
Lynn Acton – What Horses Really Want: Unlocking the Secrets to Trust, Cooperation and Reliability. Photos by Jerry Acton
"Horses want a leader they trust." This begins local author, Lynn Acton's seven part instruction for the horse and rider to learn behaviors and build confidence and reliability.
Susan McBane – The Horse in Winter: How to Care for Your Horse During the Most Challenging Season of the Year
Stephen E. Ambrose – Nothing Like it in the World: The Men Who Built the Transcontinental Railroad, 1863-1869.
Page Dickey – Uprooted: A gardener Reflects on Beginning Again
"…follow Page Dickey's journey: searching for a new home, discovering the ins and outs of the landscape surrounding her new garden, establishing the garden, and learning how to be a different kind of gardener. The surprise at the heart of the book? Although Dickey was sad to leave her beloved garden, she found herself thrilled to begin a new garden in a wilder, larger landscape."
Edward Humes – A Man and His Mountain: The Everyman Who Created Kendall-Jackson and Became America's Greatest Wine Entrepreneur
"A Pulitzer Prize-winning journalist tells the story of the self-made billionaire who built the Kendall-Jackson empire from nothing into the biggest selling brand of premium wines in the U.S. Jess Stonestreet Jackson was one of a small band of pioneering entrepreneurs who put California's wine country on the map. His life story is a compelling slice of history, daring, innovation, feuds, intrigue, talent, mystique, contrarianism, and luck, offering a unique window on the elegant, adventurous, and cut-throat worlds of Jackson's two passions: wine and horseracing."–Provided by publisher.
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Reverend Willie Maxwell was a rural preacher accused of murdering five of his family members for insurance money in the 1970s. With the help of a savvy lawyer, he escaped justice for years until a relative shot him dead at the funeral of his last victim. Despite hundreds of witnesses, Maxwell's murderer was acquitted– thanks to the same attorney who had previously defended the Reverend. Sitting in the audience during the vigilante's trial was Harper Lee, who had traveled from New York City to her native Alabama with the idea of writing her own true-crime classic. Cep brings this nearly inconceivable story to life, from the shocking murders to the courtroom drama to the racial politics of the Deep South.
New Fiction:
Antique Shop Mysteries Series:
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Kristin Hannah – The Four Winds
"One of the darkest periods of the Great Depression, the Dust Bowl era, has arrived with a vengeance. In this uncertain and dangerous time, Elsa Martinelli-like so many of her neighbors-must make an agonizing choice: fight for the land she loves or go west, to California, in search of a better life. The Four Winds is an indelible portrait of America and the American Dream, as seen through the eyes of one indomitable woman whose courage and sacrifice will come to define a generation"– Provided by publisher.
*C. J. Box: Dark Sky
When the governor of Wyoming gives Joe Pickett the thankless task of taking a tech baron on an elk hunting trip, Joe reluctantly treks into the wilderness with his high-profile charge. But as they venture into the woods, a man-hunter is hot on their heels, driven by a desire for revenge.
*James Paterson & Andrew Bourelle- Texas Outlaw
"Texas Ranger Rory Yates becomes famous after his girlfriend, country music star Willow Dawes, writes a song about his bravery. He tries to escape the spotlight by moving to the small West Texas town of Rio Lobo, but the chief of police doesn't want him there and soon he is drawn into an accidental death that might really be a murder." –Publisher description.
* David Baldacci-Deliver Us from Evil
"Evan Waller is a monster and his latest business venture could lead to millions of deaths all over the globe unless he can be stopped by two mysterious operatives who are unaware of each other's mission. Sequel to The whole truth by David Baldacci."
*Iris Johansen-Vendetta
"With his dying breath, Carl Venable, head of the CIA task force on terrorism and Jude Brandon's final link to terrorist ringleader Max Huber, gives Brandon a mandate: to keep his daughter, Rachel, safe at any cost. But Rachel Venable has a shocking, twisted past of her own, one that comes rushing back after her medical clinic in Guyana is attacked by Huber ."
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"The Great War is over, and Elizabeth and Gideon are busily planning their wedding and welcoming home old friends now discharged from the army. One of them, Captain Logan Carstens, the son and heir of a wealthy family, seems less than happy to be home and with good reason. While Logan was in France, he fell in love with a beautiful French woman named Noelle. He desperately wanted to propose, but he was already engaged and felt bound to honor his commitment. When Logan receives a letter supposedly from Noelle begging for money to help her flee the terrible conditions in France and come to America, Elizabeth is suspicious."-Provided by publisher.
Tamera Alexander – Colors of Truth
"In 1866 Catriona O'Toole arrives in the town of Franklin, Tennessee, searching for her younger brother, Ryan, who, according to his last letter, was headed for Franklin only days before the catastrophic Battle of Franklin. Ryan's last note contained a stack of cash — enough money to bring his entire family across the ocean from Ireland. But after disease and illness tear through County Antrim and the O'Toole family, only Catriona and her seven-year old sister Nora are left to make the journey. Wade Cunningham, one of ten operatives in the newly formed United States Secret Service Agency, is on the hunt for counterfeiters. A tip leads him to Franklin." –Provided by publisher.
Dianne Freeman – A Lady's Guide to Mischief & Murder
"Frances, the widowed Countess of Harleigh, needs a venue for her sister Lily's imminent wedding, away from prying eyes. Risings, George Hazleton's family estate in Hampshire, is a perfect choice, and soon Frances, her beloved George, and other guests have gathered to enjoy the usual country pursuits — shooting, horse riding, and romantic interludes in secluded gardens. But the bucolic setting harbors a menace, and it's not simply the arrival of Frances's socially ambitious mother. Above and below stairs, mysterious accidents befall guests and staff alike. " –Provided by publisher.
Ellery Adams – Murder in the Storybook Cottage
"Storyton Hall, Virginia, is a top travel destination for book lovers and the perfect spot for literary events. But as a children's book publisher hosts a gathering there, some folks aren't going to live — happily ever after or otherwise . ."– Provided by publisher.
Mario Escobar – Remember Me: A Spanish Civil War Novel
"From international bestseller Mario Escobar comes a 20th-century historical novel of tragedy and resilience inspired by Spain's famed Children of Morelia and the true events that shaped their lives"– Provided by publisher.
*Maja Lunde-The End of the Ocean: a Novel
"From the bestselling author of The History of Bees comes the unforgettable story of a woman who will choose between love and her fears for the future, and a father and daughter who will test the bonds of family, fate, and hope."
*Lisa Jewell-The Family Upstairs
"Soon after her twenty-fifth birthday, Libby Jones returns home from work to find the letter she's been waiting for her entire life. She rips it open with one driving thought: I am finally going to know who I am. She soon learns not only the identity of her birth parents, but also that she is the sole inheritor of their abandoned mansion on the banks of the Thames in London's fashionable Chelsea neighborhood, worth millions. Everything in Libby's life is about to change. But what she can't possibly know is that others have been waiting for this day as well–and she is on a collision course to meet them. "
*Heather Webber-South of the Buttonwood Tree
"Blue Bishop has a knack for finding lost things. While growing up in charming small-town Buttonwood, Alabama, she's happened across lost wallets, jewelry, pets, her wandering neighbor, and sometimes, trouble. No one is more surprised than Blue, however, when she comes across an abandoned newborn baby in the woods, just south of a very special buttonwood tree. Sarah Grace Landreneau Fulton is at a crossroads. She has always tried so hard to do the right thing, but her own mother would disown her if she ever learned half of Sarah Grace's secrets. The unexpected discovery of the newborn baby girl will alter Blue's and Sarah Grace's lives forever. Both women must fight for what they truly want in life and for who they love. In doing so, they uncover long-held secrets that reveal exactly who they really are – and what they're willing to sacrifice in the name of family."_-Publisher description.
Nelson DeMille – The Deserter: A Novel
"When Captain Kyle Mercer of the Army's elite Delta Force disappeared from his post in Afghanistan, a video released by his Taliban captors made international headlines. But circumstances were murky: Did Mercer desert before he was captured? Then a second video sent to Mercer's Army commanders leaves no doubt: the trained assassin and keeper of classified Army intelligence has willfully disappeared. When Mercer is spotted two years later in Caracas, Venezuela by an old army buddy, top military brass task Scott Brodie and Maggie Taylor of the Criminal Investigation Division fly to Venezuela and bring Mercer back to America, dead or alive. "
Allen Eskens – The Life We Bury
"College student Joe Talbert has the modest goal of completing a writing assignment for an English class. His task is to interview a stranger and write a brief biography of the person. With deadlines looming, Joe heads to a nearby nursing home to find a willing subject. There he meets Carl Iverson,a dying Vietnam veteran– and a convicted murderer, medically paroled to a nursing home, after spending thirty years in prison for the crimes of rape and murder. Unable to reconcile Carl's valor in Vietnam with the despicable acts of the convict, Joe throws himself into uncovering the truth."
Check Us Out–Magazines & More New Books Every Week !
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Most of the hot wheels belonged to my husband as a child. So they have some sentimental value to the both of them.
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The two small bins are for my son to play with. (One has bigger cars/ the other has hot wheels) The big red bin actually goes in our storage room. Every once in a while (maybe every month- or longer) I will get out the red bin and swap them out for others. In doing this, I (1) keep the clutter to a minimum, (2) it feels like Christmas for my son because he is excited to see different cars after each rotation, (3) my son plays better when he has less choices to choose from and (4) my husband gets to keep all his hot wheels from his childhood!
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text:
\section{INTRODUCTION}

There has been a vast amount of literature on networked control systems over erasure channels, cf. \cite{tatikonda:,sinopoli:2004,jin:2006,imer:2006,sahai:2006,liu:2007,quevedo:2007,ostrovsky:2009,gupta:2009,trivellato:2010,elia:2011,quevedo:2011,garone:2012,yuksel:2013,quevedo:2014,nagahara:2014,2015IJC,ostergaard:2016,peters:2016,maas:2016,khina:2019,barforooshan:2020}. In \cite{sinopoli:2004},  it was shown that for a given unstable linear time invariant (LTI) system, there exists a critical limit on the packet dropout rate beyond which the system cannot be stabilized in the usual mean-square sense.  To go beyond this critical limit, several techniques have been proposed ranging from error correction codes~\cite{sahai:2006,ostrovsky:2009} and multiple descriptions~\cite{ostergaard:2016}  to packetized predictive control~\cite{quevedo:2007} to name a few.

Assume the output of the plant is to be encoded and transmitted over a digital erasure channel, where packets are either completely lost or received without errors.
To recover from erasures,  error correction codes can be utilized \cite{singleton:1964,ostrovsky:2009}. Error-correction codes are  often designed with a certain loss rate of the channel in mind, and do not necessarily  rely on the plant (exceptions include the work in \cite{ostrovsky:2009} which tracks the plant state). For example, $(n,k)$ erasure channel codes, take $k$ \emph{source} packets and outputs $n$ \emph{channel} packets. If any $k$ of the channel packets are received, the original $k$ source packets can be completely recovered. If more than $k$ packets are received, the additional received data packets are not useful since they do not contain any further information about the plant state than what is already known. Finally, if less than $k$ packets are received, the source packets can generally not be recovered at all and all the transmitted information is in this case wasted.

\begin{figure}
\centering
\scalebox{1}{
\begin{tikzpicture}

\draw
   (2,3) rectangle (3,2)
	node[pos=0.5]{$P$};

\draw [->] (1.5,2.8) -- (2,2.8)
	node[pos=0.1,above]{$d$};
\draw [->] (1.5,2.5) -- (2,2.5)
	node[pos=0.1,left]{$x_0$};
\draw [->] (0,2.2) -- (2,2.2)
	node[pos=0.1,above]{$u$};
\draw [-] (3,2.2) -- (5,2.2)
	node[pos=0.9,above]{$y$};
\draw [->] (3,2.8) -- (3.5,2.8)
	node[pos=0.9,above]{$e$};

\draw [->] (5,2.2) -- (5,1) -- (4.7,1);
\draw [-] (0,2.2) -- (0,1) -- (0.3,1);

\draw
   (0.3,0.7) rectangle (1.3,1.3)
	node[pos=0.5]{\footnotesize Dec};

\draw
   (3.7,0.7) rectangle (4.7,1.3)
	node[pos=0.5]{\footnotesize Enc};

\draw [<-] (1.3,1) -- (1.9,1);
\draw [<-] (3.1,1) -- (3.7,1);

\draw
   (1.9,0.7) rectangle (3.1,1.3)
	node[pos=0.5]{\footnotesize Channel};

\end{tikzpicture}
}

\caption{Noisy LTI system $P$ that is controlled over a digital channel \cite{silva:2016}.}
\label{fig:system}
\end{figure}

An alternative to error correction codes are multiple descriptions \cite{gamal:1982}, which combines source and channel coding. With multiple descriptions, the source is encoded into a number of descriptions, which are individually transmitted over the channel. There is no priority on the descriptions, and any subset of the descriptions can be jointly decoded to achieve a desired performance.
Multiple descriptions were, for example, used for state-estimation in \cite{jin:2006} and combined with packetized predictive control in~\cite{ostergaard:2016}. One of the problems with multiple descriptions is that it is generally very hard to design good multiple-description codes. Another problem is that the descriptions generally contains redundant information except in the limit of vanishing data rates or when used in the extreme asymmetric situation, where the descriptions are prioritized and a successive refinement scheme is obtained. If one is able to construct a successive refinement source coder, then it was shown in \cite{yeung:1996} and \cite{puri:1999}, that the layers in the successive refinement code can be combined with traditional error correction codes in order to obtain a (sub optimal) multiple-description code. It was recently shown that a combination of successive refinement and multiple descriptions with feedback becomes   rate-distortion optimal under certain asymptotical conditions \cite{ostergaard:2021}.

We will in this paper focus on discrete-time LTI plants, stationary Gaussian disturbances, Gaussian initial state, scalar-valued control inputs and sensor outputs. Thus, the plant state can have an arbitrary dimensionality but the control signal as well as the output of the plant are both scalar valued. For such a system, the minimal information rate required to guarantee stability and a desired performance (measured in terms of the variance of the plant output) was completely characterized in \cite{silva:2016} for the case of commmunications over error-free digital channels. An illustration of the system is shown in Fig.~\ref{fig:system}.

We show that simple stabilizing erasure codes can be obtained from properly designed independent encodings~\cite{ostergaard:2021} or multiple descriptions~\cite{gamal:1982}. Specifically, for a given LTI plant we design a $(k,k')$ stabilizing code such that when combining any $k'$ descriptions of the code, the resulting $\mathrm{SNR}$ is above a critical limit, which guarantees that the decoded control signal contains sufficient information to stabilize the plant. We show that  simple codes based on independent encodings are asymptotically efficient for nearly stable plants. In general, for unstable plants, it is advantageous to use a design based on multiple descriptions. In a simulation study, we demonstrate that for the same sum-rate and delay, it is possible to achieve a significant gain in performance over that which is possible with repetition coding.

\begin{figure}
\centering
\scalebox{1}{
\begin{tikzpicture}

\draw
   (2,3) rectangle (3,2)
	node[pos=0.5]{$P$};

\draw [->] (1.5,2.8) -- (2,2.8)
	node[pos=0.1,above]{$d$};
\draw [->] (1.5,2.5) -- (2,2.5)
	node[pos=0.1,left]{$x_0$};
\draw [->] (0,2.2) -- (2,2.2)
	node[pos=0.1,above]{$u$};
\draw [-] (3,2.2) -- (5,2.2)
	node[pos=0.9,above]{$y$};
\draw [->] (3,2.8) -- (3.5,2.8)
	node[pos=0.9,above]{$e$};

\draw [->] (5,2.2) -- (5,1) -- (4.7,1);
\draw [-] (0,2.2) -- (0,1) -- (0.3,1);

\draw
   (0.3,0.7) rectangle (1.3,1.3)
	node[pos=0.5]{$F$};

\draw
   (3.7,0.7) rectangle (4.7,1.3)
	node[pos=0.5]{$L$};

\draw [<-] (1.3,1) -- (2.3,1)
	node[pos=0.4,below]{$w$};
\draw [<-] (2.7,1) -- (3.7,1)
	node[pos=0.6,below]{$v$};

\draw [->] (2.51,0.4) -- (2.51,0.8)
	node[pos=0.1,left]{$q$};

\draw
	(2.1,1.4) rectangle (2.9,1.8)
	node[pos=0.5]{$z^{-1}$};

\draw (2.5, 1) circle (6pt)
	node[]{$+$};

\draw [->] (1.6,1) -- (1.6,1.6) -- (2.1,1.6);

\draw [->] (2.9,1.6) -- (4.2,1.6) -- (4.2,1.3);

\end{tikzpicture}
}

\caption{Linear system that models the system of Fig.~\ref{fig:system}.}
\label{fig:linear_system}
\end{figure}

\section{BACKGROUND}

Let us begin by  considering the  networked control system presented in \cite{silva:2016}, and which is shown in Fig.~\ref{fig:system}. Here $P$ is an LTI plant that is open-loop unstable, $u$ is the scalar control input, and $y$ is the scalar  sensor output of the plant. The external disturbance is denoted by $d$ and $e$ is an error signal that is related to the output performance. The plant output $y$ is to be encoded by the causal encoder $\mathrm{Enc}$, transmitted over the ideal noise-less digital channel, and then decoded by the causal decoder $\mathrm{Dec}$. The encoder-decoder pair $(\mathrm{Enc},
\mathrm{Dec})$ also contains the controller. Thus, the output of the decoder is the control signal to  the plant. For a fixed data rate of the coder, the performance will be measured by the variance $\sigma_e^2$ of the output $e$. We have the following linear input-output relationship through the plant $P$:
\begin{equation}
\begin{bmatrix}
e \\
y
\end{bmatrix}
=
\begin{bmatrix}
P_{11} & P_{12} \\
P_{21} & P_{22}
\end{bmatrix}
\begin{bmatrix}
d \\ u
\end{bmatrix}.
\end{equation}

It was shown in \cite{silva:2016}, that if the initial state $x_0$ and the external disturbances are arbitrarily colored but jointly Gaussian, then the optimal encoder-decoder pair constitute a linear system + noise. This implies that the system in Fig.~\ref{fig:system} can be modelled by the \emph{linear} system shown in Fig.~\ref{fig:linear_system}. In this system, $F$ and $L$ are LTI systems, and $q$ is an additive white Gaussian noise, which simulates the coding noise due to source coding. In this equivalent form, we have the following relationship \cite{silva:2016}:
\begin{equation}
u = Fw, \quad w= v+q, \quad v = L
\begin{bmatrix}
z^{-1}w \\
y
\end{bmatrix}, L = [L_w, L_y],
\end{equation}
where $z^{-1}$ indicates a one-step delay operator.
The signal-to-noise ratio $\gamma$ of the system is defined as:
\begin{equation}
\gamma \triangleq \frac{\sigma_v^2}{\sigma_q^2}.
\end{equation}

It was shown in \cite{silva:2016}, that for any proper LTI filters $F$ and $L$ that makes the system in Fig.~\ref{fig:linear_system} internally stable and well-posed, we have the following explicit expressions:
\begin{align} \label{eq:gamma}
\gamma &= \|S - 1\|^2 + \frac{1}{\sigma_q^2}\| L_y P_{21} S\|^2 \\ \label{eq:perf}
\sigma_e^2 &= \|P_{11} + P_{12}K(1-P_{22}K)^{-1}P_{21}\|^2 + \|P_{12}FS\|^2 \sigma_q^2 \\ \label{eq:S}
S &= (1-L_w z^{-1} - P_{22} F L_y)^{-1}\\
K &= F L_y(1 - L_w z^{-1})^{-1}.
\end{align}
To find the optimal filters $(F,L)$ that minimizes $\sigma_e^2$ subject to a constraint on $\gamma$, one needs to solve a convex optimization problem \cite{silva:2016}. A lower bound on the minimal coding rate $R$ achievable when using optimal filters $(F,L)$ is given by:
\begin{equation}
R \geq \frac{1}{2}\log_2( 1 + \gamma).
\end{equation}
It is clear from \eqref{eq:gamma} that asymptotically as $\sigma_q^2\to \infty$, $\gamma \to \|S-1\|^2$, which shows that the minimum $\mathrm{SNR}$ required for stability is $\|S-1\|^2$, and the minimum rate required for stability is given by $\frac{1}{2}\log_2(1 + \|S-1\|^2)$.

\section{CAUSAL CODERS}
The encoder $\mathcal{E}_i  : \mathbb{R}^i \times \mathcal{S}^i \to \mathcal{Y}^k$ at time $i$ is a (possibly) time-varying causal one-to-many map, which at each time instance
produces $k$ outputs, that is:
\begin{equation}
(y_c^{(1)}(i), \dotsc , y_c^{(k)}(i)) = \mathcal{E}_i (y^i, s^i),
\end{equation}
where $y_c^{(j)}(i) \in \mathcal{Y}_c$ denotes the $j$th output of the encoder at time $i$, and $y^i = y_1,\dotsc, y_i$ indicates that the encoder is only using the sequence of current and past plant outputs. The sequence $s^i$ denotes side information. Thus, the encoder can be randomized via the side information, which for example allows one to obtain a stochastic encoder. The outputs of the encoder are discrete. However, by use of subtractive dithering techniques, the resulting reconstructed values at the decoder are continuous. With this, the quantizer can be modelled as an additive white noise source \cite{zamir:2014}.

Let $\mathcal{I}(i) \subseteq \{1,\dotsc, k\}$ denote the set of indices of the received descriptions at time $i$.
At each time instance, $k$ descriptions are produced and transmitted over the digital erasure channels.
The set of causal decoders at time $i$ is $\mathcal{D}^{\mathcal{I}^i}_i :  \mathcal{Y}_c^{\mathcal{I}^i}  \times \mathcal{S}^{\mathcal{I}^i} \to \mathbb{R},\ \forall \mathcal{I}^i \subseteq \{1,\dotsc, k\}^i$. For a particular choice of decoder, say $\mathcal{D}^{\mathcal{I}^i}_i$, the reconstructed signal $u(i) \in \mathbb{R}$ at time $i$ is given by:
\begin{align}
u(i) = \mathcal{D}^{\mathcal{I}^i}_i (  y_c^{\mathcal{I}^i} , s^{\mathcal{I}^i}).
\end{align}

Section IV considers lower bounds on the coding rates based on Gaussian coding schemes. The operational data rates obtained when using a practical coding scheme is generally greater than these lower bounds. These operational issues regarding the stabilizing codes are treated in the longer version of the paper \cite{ostergaard:2021b}. In particular, since we are here focusing on the situation with a scalar output, we need to use scalar quantizers. It is well known that scalar quantizers suffers from at rate-loss compared to vector quantizers except at very low bit rates. In addition, we need to entropy encode the output of the quantizer to further reduce the bitrate. Since the entropy coder is operating on one sample at a time, it will generally not be possible to reach the entropy of the output.

\section{STABILIZING ERROR CORRECTION CODES}

We will first introduce some definitions, which we will be needing in the sequel.

\begin{definition}
We will denote by $(F,L,P,\gamma)$ a linear system on the form shown in Fig.~\ref{fig:linear_system}, which has coding rate $R=0.5\log_2(1+\gamma)$ and performance $D=\sigma_e^2$, where $\sigma_e^2$ is given by \eqref{eq:perf}.
\hfill$\triangle$
\end{definition}

\begin{definition}
 A $(k,k')$ stabilizing code for the system $(F,L,P, \gamma)$ produces $k$ descriptions such that using any $k'$ of them is sufficient to stabilize the system.
\hfill$\triangle$
\end{definition}

To quantify the efficiency of a $(k,k')$ stabilizing code when used on a particular system $(F,L,P,\gamma)$, we will compare the sum-rate $R_S$ of the $k$ descriptions to the rate $R$ required for a single-description code to achieve the same performance as that obtained when using all $k$ descriptions (without erasures). In the linear Gaussian case, the efficiency can be assessed by simple means as shown in the definition below.

\begin{definition}
The efficiency $\eta$ of a $(k,k')$ stabilizing code for the system $(F,L,P,\gamma)$ is defined as:
\begin{equation}\label{eq:eta}
\eta \triangleq
\frac{ \log_2( 1 + \tilde{\gamma})}{k\log_2( 1  + \hat{\gamma})},\quad 0\leq \eta \leq 1,
\end{equation}
where $\hat{\gamma}$ is the $\mathrm{SNR}$ when using any single description out of the $k$ descriptions, and $\tilde{\gamma}$ is the $\mathrm{SNR}$ when combining all $k$ descriptions. \hfill$\triangle$
\end{definition}

When measuring efficiency in \eqref{eq:eta}, we need to make sure that we compare the coding rates of systems having similar performance (in terms of $\sigma_e^2$). The best performance of a $(k,k')$ stabilizing code is obtained when using all $k$ descriptions, which results in an $\mathrm{SNR}$ of $\tilde{\gamma}$. The rate of each description is $0.5\log_2(1+\hat{\gamma})$ and the sum-rate is $0.5k\log_2(1+\hat{\gamma})$. On the other hand, when not using a stabilizing code we need a coding rate of $0.5\log_2(1+\tilde{\gamma})$ to achieve an $\mathrm{SNR}$ of $\tilde{\gamma}$.

For a classical $(n,k)$ error correction code that produces $n$ outputs for each $k$ input sample (or block of samples), the efficiency is $k/n$, and the delay is $k-1$  samples (blocks). A repetition code that duplicates the same source block $k$ times has efficiency $1/k$ and zero delay. The stabilizing codes that we propose are also delayless and are able to improve upon the efficiency of repetition codes  due to the property that descriptions can synergistically improve upon each other.

\subsection{Stabilizing codes based on independent encodings}

\begin{definition} \label{def:encodings}
Let $w_i = v + q_i, i = 1,\dotsc, k$. If $w_j$ and $w_i, i\neq j,$ are conditionally independent given $v$, then we refer to $w_1,\dotsc, w_k$ as \emph{independent encodings}~\cite{ostergaard:2021}.
\end{definition}

\begin{lemma}
$\mathbf{(k,k')}$ \textbf{Stabilizing Code Based on Independent Encodings.}
\emph{Consider the system $(F,L,P,\gamma)$, which is illustrated in Fig.~\ref{fig:linear_system}. Let $v$ be Gaussian and let $w_i = v + q_i, i = 1, \dotsc, k$, be $k$ independent encodings of $v$,
where $q_i, i=1,\dotsc, k,$ are mutually independent,  zero-mean Gaussian distributed, and having a common variance $\sigma^2$. If for some $1\leq k' \leq k$, the common variance satisfies
\begin{equation}\label{eq:code1}
\sigma^2\leq  \frac{\gamma k'\|L_yP_{21}S\|^{2}}{ \|S-1\|^{2} (\gamma - \|S-1\|^2)},
\end{equation}
where $S$ is given in \eqref{eq:S}, then $w_i, i=1,\dotsc, k$, form a $(k,k')$ stabilizing code for the system $(F,L,P,\gamma)$. }
\end{lemma}

\begin{proof}
The variance of $\frac{1}{k'}(w_{i_1} + \cdots + w_{i_{k'}})$ is $(k')^{-1}\sigma^2$ for any subset of $k'$ encodings. The resulting $\mathrm{SNR}$  $\gamma' = k' \sigma_v^2 \sigma^{-2}$, when combining $k'$ descriptions, needs to satisfy:
\begin{align} \label{eq:1}
\gamma' = \frac{k'\sigma_v^2}{\sigma^2} > \|S-1\|^2,
\end{align}
since $\|S-1\|^2$ is the minimal $\mathrm{SNR}$ required to guarantee stability. We now use that $\gamma \sigma_q^2= \sigma_v^2$, and from \eqref{eq:gamma} we get:
\begin{align}\label{eq:sv}
 \sigma_v^2 =  \gamma (\gamma - \|S-1\|^2)^{-1}\|L_yP_{21}S\|^{2}.
\end{align}
Inserting into \eqref{eq:1} and re-arranging terms leads to:
\begin{align}\label{eq:sn2}
\sigma^2 < \gamma k' \|S-1\|^{-2} (\gamma - \|S-1\|^2)^{-1}\|L_yP_{21}S\|^{2},
\end{align}
which leads to \eqref{eq:code1}.
\end{proof}

The following lemma provides a lower bound on the sum-rate required for a $(k,k')$ stabilizing code based on independent encodings. We note that if one is not interested in the performance when receiving less than $k'$ descriptions, then the sum-rate can generally be further reduced by use of distributed source coding techniques such as Slepian-Wolf coding \cite{slepian:1973}. However, at low coding rates, the bound becomes asymptotically optimal as is shown by Lemma~\ref{lem:eta_indp}.

\vspace{2mm}

\begin{lemma}
\emph{The minimum sum-rate $R_S$ of a $(k,k')$ stabilizing code based on independent encodings for the system $(F,L,P,\gamma)$ is:}
\begin{equation}
R_S \geq \frac{k}{2}\log_2\bigg(1 + \frac{\|S+1\|^2}{k'}\bigg).
\end{equation}
\end{lemma}

\begin{proof}
Let $\sigma^2$ be the variance of the coding noise for a single description of the $(k,k')$ stabilizing code. Then, the resulting variance when linearly combining $k'$ descriptions is $\sigma^2/k'$. Thus,
$\mathrm{SNR} = k\sigma_v^2/ \sigma^2 \geq  \|S-1\|^2$, where the inequality follows since $\|S-1\|^2$ is the minimum $\mathrm{SNR}$ that guarantees stability. Isolating $\sigma^2$ leads to:
\begin{equation}\label{eq:s2lb}
\sigma^2 \leq \|S-1\|^{-2} k' \sigma_v^2.
\end{equation}
We can now express the sum-rate in terms of $\sigma^2$, that is:
\begin{align*}
R_S = \frac{k}{2}\log_2(1 + \frac{\sigma_v^2}{\sigma^2})
\geq \frac{k}{2}\log_2(1 + (k')^{-1}\,\|S-1\|^{2}).
\end{align*}
\end{proof}

\begin{lemma}\label{lem:eta_indp}
\emph{Consider the system $(F,L,P,\gamma)$. The efficiency of a minimum sum-rate $(k,k')$ stabilizing code based on independent encodings is given by:
\begin{equation}
\eta =  \frac{\log_2(1 + k(k')^{-1}\,\|S-1\|^{2}) }
{k\log_2(1 + (k')^{-1}\,\|S-1\|^{2})},
\end{equation}
and the code is asymptotically efficient in the sense of:}
\begin{equation}
\lim_{\|S-1\|^2 \to 0} \eta = 1.
\end{equation}
\end{lemma}

\begin{proof}
The first part follows immediately from \eqref{eq:s2lb}, since the $\mathrm{SNR}$ for a single description is $\sigma_v^2/\sigma^2$ and for $k$ descriptions it is $ k\sigma_v^2/\sigma^2$. The second part
  follows since the logarithm of the number $1+kc$ is approximately linear in $k$ when $c\ll 1$, i.e., $\log(1+kc) \approx k\log(1+c)$ for small $c$.
\end{proof}

For a $(F,L,P,\gamma)$ system, if $\|S-1\| = 0$ it means that the system is stable. Thus, the second part of Lemma~\ref{lem:eta_indp} considers the situation where the plant is either stable or nearly stable, i.e., the unstable poles are near the unit circle. In this case, the coding rates are arbitrary small, and the $k$ descriptions of the $(k,k')$ stabilizing code becomes mutually independent. Thus, there is no redundancy by using $k$ descriptions each of rate $R/k$ over a single description of rate $R$  \cite{ostergaard:2021}.

\begin{lemma}
\emph{Consider the system $(F,L,P,\gamma)$. The performance (in terms of $\sigma_e^2$) for this system when using $\ell \geq k'$ descriptions of a minimum sum-rate $(k,k')$ stabilizing code based on independent encodings is:}
\begin{align}\notag
\sigma_e^2 &= \|P_{11} + P_{12}K(1-P_{22}K)^{-1}P_{21}\|^2 \\
&\quad +
 \frac{k'\, \gamma  \|P_{12}FS\|^2 \|L_yP_{21}S\|^{2}}{\ell\, \|S-1\|^{2} (\gamma - \|S-1\|^2) }
 			,\quad \ell=k', \dotsc, k.
\end{align}
\end{lemma}

\begin{proof}
Follows from \eqref{eq:perf} by inserting \eqref{eq:sn2} and the fact that the noise variance satisfies $\frac{\sigma^2}{\ell}$ for $\ell=1,\dotsc, k$.
\end{proof}

\subsection{Example 1}
Consider a plant $P$ that provides the following input-output relationship between $(u,d)$ and $y$:
\begin{equation}
y = \frac{0.165}{(z-2)(z-0.5789)}( u + d), \quad e=y,
\end{equation}
where the external disturbance $d$ has a standard normal distribution. Notice that the plant has an unstable pole at $z=2$, which implies that the minimum $\mathrm{SNR}$ required for stability is $\|S-1\|^2 = 3$, and equivalently the minimum coding rate is $0.5\log_2(1 + 3) = 1$ bit. For this plant, we can choose a particular $\gamma$ and find the optimal filters $L,F$ and associated $S,K$ by using the method described in \cite{silva:2016}. From these we can find the performance $\sigma_e^2$ using \eqref{eq:perf} and coding rate $R = 0.5\log_2(1+ \gamma)$.
Changing $\gamma$ leads to another set of $L,F,K,S$ variables and different performances and coding rates.

Let us now design a $(4,2)$ stabilizing code, so that receiving any $2$ descriptions implies that the minimum $\mathrm{SNR}$ requirement is fulfilled. We choose $\sigma^2$ so that the resulting $\mathrm{SNR}$ is $\frac{\ell}{4}\gamma$, when linearly combining $\ell=1,\dotsc, 4$ descriptions. For $\gamma = 7.2$, we obtain:
$\mathrm{SNR} = 1.8, 3.6, 5.4$, and $7.2$ for $\ell=1,\dotsc, 4$, respectively. For $\ell =2$ it is clear that the resulting $\mathrm{SNR}$ is greater than the minimum of $3$, and we therefore have a $(4,2)$ stabilizing code.

The coding rate per description is $0.5\log_2(1 + 1.8) = 0.74$ bits, and the sum-rate is $R_S = 2.96$ bits. The coding rate required for a single-description system to achieve $\mathrm{SNR} = 7.14$ is $R=0.5\log_2( 1 + 7.14) = 1.51$ bits. Thus, the efficiency is $\eta = 1.51/2.96 = 0.51$. For comparison, a repetition code with 4 descriptions would have an efficiency of $\eta = 0.25$.

In Fig.~\ref{fig:SNR}, we have illustrated the resulting $\mathrm{SNR}$ when combining the $\ell=1,\dotsc, 4$ descriptions as a function of $\gamma$. It can be seen that a $(4,1)$ stabilizing code can be obtained for $\gamma>10$ dB, and a (4,2) stabilizing code for $\gamma>7$ dB. Fig.~\ref{fig:efficiency} shows the efficiency as a function of $\gamma$. The efficiency is monotonically decreasing in $\gamma$. At very low $\gamma$ which corresponds to small coding rates, the efficiency is highest.

\begin{figure}[t]
\begin{center}
\includegraphics[width=7cm]{SNR.pdf}
\caption{The resulting $\mathrm{SNR}$ obtained with the $(4,2)$ stabilizing code of Example 1, when combining $\ell = 1,\dotsc, 4$ descriptions.}
\label{fig:SNR}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\includegraphics[width=6cm]{efficiency}
\caption{The efficiency $\eta$ of the $(4,2)$ stabilizing code of Example 1 as a function of $\gamma$. }
\label{fig:efficiency}
\end{center}
\end{figure}

\subsection{Stabilizing codes based on multiple descriptions}
It is possible to introduce correlation between the quantization noises $q_i, i=1,\dotsc, k,$ of the encodings in Definition~\ref{def:encodings}, which makes it possible to exploit the benefits of multiple descriptions. Of course, zero correlation is a special case of multiple descriptions, which is usually referred to as the no excess marginal rate case~\cite{Zhang1995MultipleDS}.
When introducing correlation, the sum-rate is no longer simply just given by the sum of the optimal marginal (description) rates. The sum-rate also becomes a function of the amount of correlation introduced; the greater (negative) correlation, the greater  sum-rate \cite{ozarow:1980}.

\begin{lemma}
$\mathbf{(k,k')}$ \textbf{Stabilizing Code Based on Multiple Descriptions.}
\emph{Consider the system $(F,L,P,\gamma)$, which is illustrated in Fig.~\ref{fig:linear_system}. Let $v$ be Gaussian and let $w_i = v + q_i, i = 1, \dotsc, k$,
where $q_i, i=1,\dotsc, k,$ are zero-mean Gaussian distributed with variance $\sigma^2$, and pairwise correlated with correlations coefficient $-\frac{1}{k-1}<\rho \leq 0$.
If for some $k'$ and $\rho$, the common variance $\sigma^2$ satisfies
\begin{equation}\label{eq:code2}
\sigma^2\leq  \frac{\gamma k'\|L_yP_{21}S\|^{2}}{ \|S-1\|^{2} (\gamma - \|S-1\|^2)(1+(k'-1)\rho)},
\end{equation}
where $S$ is given in \eqref{eq:S}, then $w_i, i=1,\dotsc, k$, form a $(k,k')$ stabilizing code for the system $(F,L,P,\gamma)$. }
\end{lemma}

\begin{proof}
We need to ensure that $\mathrm{SNR}>\|S-1\|^2$, when receiving at least $k'$ descriptions.
The  noise variance when combining any $k'$ descriptions is given by:
\begin{align}\label{eq:var}
\mathrm{var}\bigg( \frac{1}{k'} \sum_{i=1}^{k'} q_i \bigg) = \frac{\sigma^2}{k'}(1+(k'-1)\rho).
\end{align}
Using \eqref{eq:var},  the $\mathrm{SNR}$ is given by:
\begin{align}
\frac{\sigma_v^2}{\frac{\sigma^2}{k'}(1+(k'-1)\rho)} \geq \|S-1\|^2.
\end{align}
Isolating $\sigma^2$ and inserting \eqref{eq:sv} leads to:
\begin{align}
\sigma^2 &\leq k'\|S-1\|^{-2}(1+(k'-1)\rho)^{-1}\sigma_v^{-2} \\ \notag
&= k'\|S-1\|^{-2}(1+(k'-1)\rho)^{-1}
\gamma (\gamma - \|S-1\|^2)^{-1} \\
&\quad\times \|L_yP_{21}S\|^{2}.
\end{align}

\end{proof}

Let $\rho \in (\frac{-1}{k-1},0]$ be the common correlation coefficient between all noise pairs $q_i,q_j, \forall i\neq j$, and let $\sigma^2$ be their common variance. If we are only interested in the performance when receiving $k'$ descriptions or all $k$ descriptions, then the sum-rate $R_S$ can be explicitly expressed \cite{pradhan:2004}:
\begin{align}\notag
R_S  &=\frac{1}{2k'}\log_2 \bigg( \frac{k' + \sigma^2(1+(k'-1)\rho)}{\sigma^2(1-\rho)} \bigg) \\
&\quad + \frac{1}{2k}\log_2 \bigg(\frac{1-\rho}{1+(k-1)\rho} \bigg)\bigg),
\end{align}
where it is assumed the source is standard normal.

\section{Simulation Study}
We consider the same system as that of Example 1, and we will assume i.i.d.\ packet losses.  The encoder is informed about the packet loss probability but does not know when an erasure occur. Knowledge of the packet loss probability makes it possible to design an efficient entropy coder (lossless coder).

We will be using a subtractively dithered scalar quantizer, which is a stochastic quantizer that provides different outputs, when encoding the same source multiple times \cite{zamir:2014}. We will use this to form the $k$ \emph{independent} encodings.
\begin{figure}[t]
\begin{center}
\includegraphics[width=7cm]{performance_all}
\caption{ The performance of stabilizing and repetition codes as a function of packet-loss probability.}
\label{fig:performance_all}
\end{center}
\end{figure}

We encode the output $v$ of Fig.~\ref{fig:linear_system} using a  subtractively dithered scalar quantizer $\mathcal{Q}_\Delta$ with step-size $\Delta$ to obtain:
\begin{equation}
w_i = \mathcal{Q}_\Delta(v + \xi_i)-\xi_i, i = 1,\dotsc, k.
\end{equation}
where $\xi$ denotes the dither signal. We choose the step-size $\Delta$ so that the resulting $\mathrm{SNR}$ when using only a single description $w_i$ is $1.76$, which is below that required for stability. Combining any two descriptions yields $\mathrm{SNR} = 3.57$ and combining all three yields $\mathrm{SNR} = 5.29$. Thus, using at least two descriptions is sufficient to stabilize the system. Based on this we design a $(3,2)$ stabilizing code, which for each input sample produces three outputs using the quantizer three times. The theoretical efficiency of this scheme is $\log2(1+ 5.29)/(3\log_2(1+1.76)) = 0.6$. In practice, we suffer from a rate loss due to using a scalar quantizer. The theoretical rate is $1/2\log_2(1 + 1.76) = 0.73$. However, transmitting less than one bit per sample is only possible when encoding vectors. The measured entropy of the quantized output is $1.57$ bits per description.

 We have plotted the performance of the $(3,2)$ stabilizing code in Fig.~\ref{fig:performance_all} as a function of the packet-loss probability. We assume i.i.d.\ packet losses, and simply average the received descriptions to form the reconstruction. Also shown is the performance when transmitting one of the descriptions three times. This corresponds to a $(3,1)$ repetition code having similar sum-rate as the $(3,2)$ stabilizing code. For each packet-loss probability, the performance and rates are averages over a realization having $10^6$ samples. It can be observed that using a stabilizing code is up till $3$ dB better than a repetition code at low packet-loss probabilities.

We also show in Fig.~\ref{fig:performance_all} the performance of a $(2,1)$ stabilizing code, which is compared to a $(2,1)$ repetition code. The $\mathrm{SNR}$ is $3.45$ and $6.91$, when using 1 or 2 descriptions, respectively, of the $(2,1)$ stabilizing code. The measured output entropy after scalar quantization is in this case $1.76$ bits per description, and the sum-rate is $3.52$ bits.

Finally, we design a $(3,2)$ stabilizing code based on multiple descriptions. It is not straight-forward to obtain correlated noises between the descriptions, and we use here the approach described in~\cite{ostergaard:2006}, which is based on nested lattices and index assignments. The source is first quantized using a fine-grained quantizer referred to as the central quantizer. Then, a one-to-many map is applied, which maps the quantized value to $k$ points in a nested (coarser) lattice. If all $k$ coarser points are received, the map is invertible and the point of the central quantizer is used for reconstruction. If less than $k$ descriptions are received, the reconstruction is given by the average of the received points in the coarser lattice~\cite{ostergaard:2006}. We are using a nesting factor of 5, and the resulting pairwise correlation coefficient between the descriptions is $\rho = -0.41$. The $\mathrm{SNR}$ of a single description is $1.68$ and that of two descriptions is $5.6$, which is above the critical value for stability. The $\mathrm{SNR}$ when all descriptions are used is $12.0$.
The step-size of the fine lattice is chosen such that the resulting bitrate is similar to that of the $(3,2)$ stabilizing code based on independent encodings.

It can be seen in Fig.~\ref{fig:performance_all} that stabilizing codes outperforms repetition coding. Moreover, using MD coding when constructing the stabilizing codes is better than using independent encodings, except at very low bitrates or very high packet-loss rates.

\section{Conclusions}
A new construction of error correction codes were proposed, which takes the stability of the plant into account. For linear systems with scalar input and output, explicit designs were provided, and it was shown that there is a significant gain over using traditional repetition codes. Similar to repetition coding, the proposed codes do not add additional delays but operate on each sample at a time.

\section{Acknowledgments}

The author would like to thank Mohsen Barforooshan for discussions related to simulating the control system.

redpajama_set_name: RedPajamaArXiv


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Reno Nevada: the Biggest Little City in the World
On a week's trip to Reno Nevada, James Clark samples a taste of the Wild West, falls in love with Lake Tahoe and finds himself in some deep water.
Travel Articles > Experiences > Outdoors > Reno Nevada: the Biggest Little City in the World
Adventure Travel, Americas, Culture & History, Outdoors
James Clark Posted on 28th Aug 2018
The first thing to strike me about Reno-Tahoe International Airport is its accessibility, less than ten minutes in a cab into Reno and the Amtrak train pulls up in central downtown.
Reno is a small city in the mighty USA, with all the glitz, glamour, bright lights, soaring hotel and resort complexes and casinos you'd expect, but compact enough to walk around. Perhaps that's where it gets its name from: 'The Biggest Little City in the World.'
It's the second largest tourist destination in Nevada. Activities available include gaming, adventure, great food, plenty of drinking holes, shows, festivals, museums, art, culture and more. Reno even has its own 'soccer' team Reno 1868 FC.
Reno Nevada River Rafting
Visiting Reno Nevada is not just about gambling – kayaking on Lake Tahoe
In pursuit of adventure we rented an inflatable kayak from Truckee River Rafting and a life-saving guide to tackle the 5.5 miles river from Mayberry Park back to downtown Reno, through scenic meadows, mountains and small rapids. I mention the term life-saving because I fell in within the first five minutes and due to the great training provided earlier I knew exactly what to do when being swept downstream. I'd like to brag that I wasn't the only one, but that would be a lie. The others stayed on without a hitch.
After two nights at the Circus Circus Reno Hotel and Casino that connects to Eldorado Resort Casino and Hotel, and Silver Legacy via a network of fun packed tunnels, and a failed attempt at tackling the world's tallest climbing wall at the Whitney Peak Hotel, we decided it was time to leave Reno and head for the Wild West.
Our first stop just 45 minutes south of Reno was the historic town of Genoa. Founded in 1851, it's the first settlement in what is now Nevada. We took a town tour where we learned about its history and ghosts of the past. After a great turkey sandwich and beer at The Pink House gourmet cheese and charcuterie shop, I headed to The Genoa Bar, Nevada's Oldest Thirst Parlor for a bloody mary. With tons of historic charm – and beer – this is a popular waterhole for motorcyclists on their way to Lake Tahoe and tourists, hikers and nature lovers heading to Carson Valley.
Lake Tahoe and Carson Valley
Get back to nature at Lake Tahoe
Carson Valley lies between the Sierra Nevada range, the Great Basin, the West Coast and the Wild West. It's the ideal destination to take a walk and stare in awe at the 10,000 feet peak mountains in the distance, within these mountains Lake Tahoe hides.
It's impossible not to fall in love with the overwhelming beauty of Lake Tahoe, the largest alpine lake in North America surrounded by snow-capped mountains. Whatever preconception you may have about Nevada being a desert plain, Lake Tahoe blows it out of the water.
For more ideas of what to do in Nevada, read Four Great Trails to hike in Nevada.
Undeterred by the previous white water rafting incident we agreed to go kayaking on the north shore of the lake with the Tahoe Adventure Company. It was such a great way to discover the beauty of the lake, exercise, enjoy the peace and reconnect with nature. Our guide even provided us an educational tour and later a beach lunch.
Sampling the Wild West
The next day, it was time to explore the former mining town of Virginia City. Dating back to the 1860s, little has changed since then.
We started with a ride on the scenic V&T railroad, on a whirlwind tour of the city, which proved a useful way to gain our bearings before exploring on foot. Included is a tour of the mine and the Piper Opera House and more places to eat and drink than you could imagine.
My favourite watering hole was the historic Bucket of Blood Saloon, where a fight once ensued after a poker game. It was so intense that the next day was spent emptying buckets of blood out onto the street. It's much calmer these days, but like everywhere else in Virginia City, and indeed Nevada, it has a story to tell.
Flights to Reno Nevada
Netflights.com offers return flights for a seven-night stay in Reno Nevada from London Heathrow to Las Vegas with Aeromexico for just £679pp. Based on selected dates in September 2018. Book by 20 September.
For more information on Nevada
Visit: www.travelnevada.com
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#Nevada	#USA
Beaches, Europe
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James Clark is a UK-based travel writer specialising in adventure and the great outdoors.

redpajama_set_name: RedPajamaCommonCrawl


text:
"They say 'The measure of a great thief is how few people know he exists'. But I say... F#!& that."
Player: @First Player
NAME: Nicholas Hyde
KNOWN ALIASES: Hideout
BASE OF OPERATIONS: Shhh, its a secret
PLACE OF BIRTH: Nunya Business
OCCUPATION: Thief
AFFILIATIONS: The Sideliners
POWERS: Stealth suit grants complete invisibility
ABILITIES: Expert burglar and thief
Skilled martial artist and hand-to-hand combatant
Now you see me...
"My name's Nick Hyde, from Nowhere Important, Iowa. I don't really have a terribly interesting origin story. No murdered parents or anything like that. Although, part of me sometimes wishes that were the case."
As Nick's parents were especially strict they disapproved of most of his hobbies, so after he graduated high school when he told them he planned on moving to New York city and becoming a musician, they deemed his dream 'foolish and futile'. He disagreed. They cut him off and he hasn't spoken to them since leaving home.
"Bad luck is definitely my superpower."
His flight to New York was grounded in Paragon City when they found a shoe bomb on-board. His rental car broke down on the way to the motel he'd decided to stay at temporarily. And to top it off, he got held-up and robbed a day later. No superheroes came to his rescue. So with not a penny to his name and stuck in and unfamiliar city, Nick was forced to put his plans on hold. Indefinitely.
"So then I manage to get a job working as a dishwasher at an Up-N-Away Burger. Pay's not great but it was better than nothing. And then one day, one of the guys in the kitchen says to me, his cousin knows a guy who knows a guy who's looking for a few warm bodies for a job he's pulling. Now me, being desperate and of questionable morals at the time, said 'Sure, why not'. Funds were getting low and that gig just wasn't cutting it."
It turned out that Nick and his comrades out were really working for Armbar, an ex-Freakshow member who was ripping off Family capos' high-stakes poker games. Luckily, the job went off as planned, without a hitch. And that's how it started. A few more jobs here and there. Nick gained a reputation for being reliable, no-questions-asked kind of guy. And then, out of the blue one day, his buddy mentions he's been working regularly for an organization called TAROT, led by The Astrologer, a full-fledged super-villain bent on world domination. He asked Nick if he he'd be interested.
Six months later, Nick found himself in an underwater base in a ridiculous rubber suit standing next to fifty other guys in identical, ridiculous rubber suits listening to a maniacal loon in an even more ridiculous rubber suit monologue about how society has forsaken him and how the world will rue the day it did. Nick had become a real henchman.
"I'll admit - the pay was great. But there's more than a few downsides. You're constantly being watched to make sure you aren't talking to anybody you're not supposed to be. Anyone you get involved with or close to can be used against you, so say goodbye to a social life. And the worst part? You're always on the clock. One time, this guy named Jake was late. The boss called us all together and ripped his spine out of his back right in front of us. Nobody was ever late again after that."
The upside to being a henchman however, is that all your needs are met. Free housing. Weapons and combat training. Even health insurance. The only requirement is unflinching loyalty and a willingness to die painfully or be banished to another dimension at any given moment. But the thing about super-villains? They lose. Often. Nick found himself jumping from one evil organization to the next every time a hero defeated their leader, which, while being a bit of an inconvenience, was never really terribly upsetting. And once you've earned a reputation like Nick had, finding a new job was fairly easy. There's always a super-villain in need of henchman. And variety is the spice of life, right?
"Literally every vacation you get is a work vacation though. You never get the chance to actually experience anything. I mean, I've never seen any famous landmarks and I've literally been around the world. TAROT's headquarters in Rome, Doctor Devastation's volcano base in Machu Picchu, King Helios' floating armory in Venezuela, even Herr Silverback's Monkey Menagerie in Germany. But I don't want to talk about that last one."
But eventually in life you come to a crossroads. And that crossroads came in the form of King Calamity, a megalomaniac who caused natural disasters and chaos for fun, many a henchman became uneasy with their employer's methods. After all, you can't make a living in the world if there's no world to make a living in. And as a henchman, you can't exactly file a complaint with human resources, so a guy's only option were to fake his death and hope for the best.
Fortune smiled upon Nick one day however, when the superhero known as Cliffhanger descended upon King Calamity, raiding his headquarters in an attempt to take him down once and for all. Nick, ever being the opportunist that he was, used the chaos as a distraction and stole a prototype stealth suit he'd been guarding to escape capture.
"You're probably asking yourself 'How does a no-nothing kid from freakin' Iowa go from dishwasher to one of the world's most notorious thieves?' huh. Well, when you jump from evil organization to evil organization you pick up a few things here and there."
Extensive training within various organizations has left Nick with a slew of skills and technological know-how.
Expert Thief: Nick is a trained thief and cat burglar, skilled in stealth, lockpicking, escapology, evading alarms, cracking safes and hacking advanced security systems.
Skilled Combatant: As a henchman many times over, Nick is well-practiced in several martial arts styles including Krav Maga, judo, Savate, as well as boxing and karate. Since acquiring his stealth suit, Nick has utilized all these skills and developed a fighting style that directly complements his suits capabilities, such as sneak attacks and disappearing and reappearing mid-fight.
Tools of the trade...
Stealth Suit: Nick's suit's primary capability is full-spectrum invisibility and complete stealth, both from the naked eye and high-tech sensors. Inside the suit are energy regulators that create varying fields that enable Nick to land soundlessly from heights of fifty feet. The suit itself is capable of absorbing kinetic & energy and redistributing that energy from his body in the form of concussive blasts. However, the suit can only absorb so much energy before Nick must release it.
Nick has upgraded his suit to mask internal sounds such as his breathing and heartbeat, and minimize his external body temperature. His suit can also be set to disrupt or override electronic devices via touch. Inside the suit's helmet are transmitters that can pick up radio waves, allowing him to tap into police scanners, a breathing apparatus that provides oxygen in oxygen-deprived situations and multiple vision settings including thermal, infrared and night-vision.
Miscellaneous capabilities include deflection of small caliber firearms, heat & flame resistance, and full insulation from electrical attacks.
Utility Belt: Nick's utility belt houses ten pouches or cylindrical cartridges that are attached to the outside of the belt. Each of the ten pouches or cylinders contains various tools integral to Nick's heists, with the cylinders being interchangeable with each other depending on the scenario. Devices include a grappling gun, lock picks, miniature lasers as well as a taser.
While he's definitely not an outright super-villain, Nick is most certainly a selfish, cynical, and very opportunistic individual, who wouldn't hesitate to throw anyone under a bus to ensure his own safety and has, on more than one occasion, done so. Nick is not totally morally bankrupt however, regardless of how close to the line he is from time to time. Though many of his actions are morally questionable and he is primarily motivated by his own wants and needs, there is an inherently (semi) decent person beneath all his cynicism and ego. As a thief, he refuses to kill, though he doesn't dismiss gainful opportunities to work with people who do.
Karmic Thief - Nick's targets will usually be wealthy, corrupt, or more often than not both. He's not above stealing from very rich innocents (if he knows they can spare the money), but he never steals from those who are poor and honest. However, unlike the Robin Hood-types that frequent Paragon City, Nick is not interested in charity through giving away all his ill-gotten-gains to the poor.
Grand Theft Prototype - The suit Nick stole from King Calamity's armory just before he was arrested was a one-of-a-kind prototype meant to later be mass produced. There are some very powerful people searching for it. As of right now, Nick has no idea.
Lovable Rogue - He's a thief, a heartbreaker, a double-crosser, and will break the law out of boredom as much as necessity, but he does have a conscience and won't lay a hand on the defenseless.
Taught By Experience - Originally just an average joe from Iowa, Nick has become a world-class thief and martial artist, through years of training provided by the various super-criminal organizations he's been recruited by. He is a skilled (but unlicensed) pilot and driver, an amateur chemist, an Olympic-level gymnast, and oddly enough, a decent chef.
Stickup: Nick's sister Elizabeth. Straight-laced police officer working within the PPD.
The Disc: Rival thief Sera Truth, former rave DJ turned high-end cat burglar, she generates Tron-style energy discs that explode with concussive force when thrown. She uses her abilities to steal high-priced artifacts. On again, off again love interest.
Zombabe: TBD
Enchanting: TBD
The Court of Plunder: A collection of thieves, pirates, urchins, black market traders and all other sorts of underworldly types who've created a religion out of upending the social order, one crime at a time. Nick fences his more high-end gains through this organization.
Theme Songs
"Big Bank" by YG
"Lie, Cheat, Steal" by Run The Jewels
"Looking at the Invisible Man" by The Dead Weather
"Ain't No Rest For The Wicked" by Cage The Elephant
"Starboy" by The Weeknd
"See Through Head" by The Hives
Retrieved from "http://www.virtueverse.net/wiki/Hideout"
Categories: Rogue | Thief | Everlasting
This page was last modified 10:38, 4 August 2020 by Unofficial Handbook of the Virtue Universe user First Player.


text:
Selleck
=======

Selleck is a tool for generating documentation from Mustache-based templates. It
was created to generate documentation for the YUI Library. It's still young and
evolving rapidly, but you may find it useful.

See <http://yui.github.com/selleck/> for detailed information and usage
instructions, as well as an example of the kinds of docs Selleck generates.

If you'd like to see more, [check out this sample][ac-docs] of the YUI 3
AutoComplete docs and examples, generated using Selleck.

[ac-docs]:http://dl.dropbox.com/u/131998/yui/docs/autocomplete/index.html

Build Status
------------

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License
-------

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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Third-Party Code
----------------

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indicated) included in the Selleck distribution.

### Distributed With Selleck

#### Google Code Prettify (Apache License, Version 2.0)

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(<http://code.google.com/p/google-code-prettify/>). Included in Selleck at
`themes/default/assets/vendor/prettify`.

Copyright (C) 2006 Google Inc.

Licensed under the Apache License, Version 2.0 (the "License");
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See the License for the specific language governing permissions and
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#### Handlebars.js (MIT License)

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(<https://github.com/wycats/handlebars.js>). Included in Selleck at
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Copyright (C) 2011 by Yehuda Katz

Permission is hereby granted, free of charge, to any person obtaining a copy
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#### Express (MIT License)

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Copyright (c) 2009-2010 TJ Holowaychuk <<tj@vision-media.ca>>

Permission is hereby granted, free of charge, to any person obtaining
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redpajama_set_name: RedPajamaGithub


Dr. Denise Teves Qualler is an Associate Professor at the Medical College of Wisconsin and at the Clement J. Zablocki VA Medical Center. She serves as the Director of the Osteoporosis Clinic at the VA Medical Center, as well as the Metabolic Bone Clinic at Froedtert Hospital.
Dr. Teves Qualler completed her Internal Medicine Residency at the Chicago, Illinois Medical School and her Fellowship in Endocrinology at the Barnes-Jewish Hospital/Washington University School of Medicine in St. Louis, Missouri. She is board certified in Endocrinology and Internal Medicine. Dr. Teves Qualler has a Master in Science degree in Epidemiology at the Medical College of Wisconsin. She is also the Program Director of the Endocrine Grand Rounds Seminars at the Medical College of Wisconsin.


Shabby chic is this a wonderful subject for a vanity. It highlights the goodness and classic. It's also rather small so that it does not seem very expansive. The colour choice for shabby chic furniture is also quite factor including soft blue, pale pink, and white. Those sort of colours are offered for ceramic tiles. That's why using shabby chic motif for your own vanity and has it surrounded by ceramic tiles at exactly the exact same color scheme will add beautiful component in the restroom. In addition, utilize shabby chic mirror nicely with lovely frame finished by the dividing and stuff. By doing this, you have created one of the best toilet vanity backsplash ideas ever.
The many varieties of bathroom medicine cabinet with lighting will state the nuance offered in our bathroom. One, there's 1 cabinet square-shaped using two vertical white lamps on it. They seem very contemporary. Two, there's this one medicine cupboard rectangle-shaped with some hanging white lamps onto it. It'll be quite helpful in the event the wooden substance is bold. The lighting will illuminate the pattern on the wooden, making it capable to provide an ideal ambience. Third, there is this one with lights surrounded in every side of this cupboard. Double served, we could always pick the 1 bathroom medicine cabinet with mild with mirror, also.
A stunning shades mirror: Imagine if you have a dark colored bathroom or contemporary and contemporary bathroom? Well, you should look at a curved mirror with striking colour effects. The striking shades are made by the silver framework which has a little stripped or geometrical specifics. The silver colour will reflect the light to the total bathroom. Even the dark colored toilet will look shinny with this art deco bathroom mirror.
Since the bathroom cabinets over bathroom is largely made to conserve the space, the furniture comes in slim designs. It fits the bathroom region and marginally wider than the frequent bathroom dimensions. With extended legs or wall mount designs, the cabinets can perfectly match the bathroom area within the bathroom. It comes in all types of color and materials. Consider the plan of the whole bathroom in addition to the humidity level before choosing to pick the best cabinets to your bathroom.


text:
A Fanboy és Chum Chum (eredeti cím: Fanboy and Chum Chum) 2009-ben készült amerikai animációs sorozat, ami két "szuperhős" gyerekről szól.

Főszereplők
 Fanboy - Pál Tamás
 Chum Chum - Seszták Szabolcs
 Kyle Bloodworth-Thomason - Markovics Tamás

Premierek

Epizódok

Évados áttekintés

Első évad

2009-ben bemutatott amerikai televíziós sorozatok
A Nickelodeon saját gyártású műsorai
2014-ben befejezett amerikai televíziós sorozatok

redpajama_set_name: RedPajamaWikipedia


Look closely. The clues are there.
What you're looking at is not a . Nor is it the next generation Tiguan. The only thing it has in common with the Tiguan is the fact that it's a crossover. The truth is this is a disguised prototype of the upcoming all-electric . Our spy photographers recently caught images of this test mule undergoing some heavy snow testing and there are a few clues indicating its true identity.
For starters, its body shape is slightly longer, there's an extended area between the doors, and the side sills are thicker. What else makes us think this isn't the generation Tiguan? Because it's way too early for it to arrive. The current model debuted in 2016 and a mid-life refresh does not have this amount of structural changes.
Using an altered Tiguan body makes complete sense as VW engineers need to simulate the next best thing without giving away the final production vehicle's final design. That's standard practice in the world of testing prototypes.
The I.D. Crozz has already been previewed in concept form and from what we've been told the final design won't be dramatically different. It's also set to be offered in two bodystyles, a typical SUV and a sportier SUV coupe. Think BMW X3 and X4. , it will ride on the automaker's all-new and state-of-the-art MEB platform.
Under the hood (or rather under the floorboards) will be a battery and electric motor powertrain combo that will produce up to 300 hp in top spec models. All-wheel-drive will be available as well, though lower trim versions will be rear-wheel-drive, just as they are with Teslas.
We're expecting VW to reveal the production I.D. Crozz (still unsure whether that'll be the final name) either later this year, possibly at Frankfurt in September, or early next year.


H.R. 1596 (ih) To amend title 28, United States Code, to authorize the appointment of additional bankruptcy judges, and for other purposes.
the ``Timothy Michael Gaffney Post Office Building''.
Passed the House of Representatives May 6, 2003.


text:
Home summer activities Mom Approved Online Video Games You Can Play with Your Kids
Mom Approved Online Video Games You Can Play with Your Kids
By Mauie Flores At May 22, 2021 0
Are you one of those parents who are against online video games? I hope you're not. If you ask me, I believe that video games do have benefits even for small children. In fact, I never prohibited my son from playing video games. All in moderation, of course. And when you are firm with rules while they're young, you'll have no trouble reminding them to shut off the console when it's time to rest, eat, or study. Believe me.
Can video games be good for kids?
I think so! Even KidsHealth.org think, too. There are video games that help improve a child's hand-eye coordination and problem-solving skills. There are a lot of educational video games that help teach a child a new language or help them with reading or their maths.
Again, everything in moderation. Parents should set limits on time spent not only on playing video games but also on other forms of media online. Our rule for our boy was simple... 1 is to 1. One hour of online video gaming is equal to 1 hour of school work, chores, or nap time. And no gaming before 10am or after 10pm. He got used to it that he still does it up to now, except the after 10pm rule, LOL!
So, without further ado, I present to you my recommended online video games that you can play with your kids.
For Developing Problem Solving Skills - Playful Kitty
Playful Kitty is a delightful logic online puzzle game that can help your kids exercise their thinking skills. The object of the game is to get the ball of yarn to roll down to the cat for him to play and be happy. This can be done by breaking bricks and boards.
This game has 24 levels of difficulty but the lower levels are easy and your child may only need some coaching in the higher levels. There's playful music that's playing in the background while the game is on and the kitty meows once in a while. It's really enjoyable and, I think, even cat lovers will like this game.
For Developing Creativity - Pixel Art Maker
Pixel Art Maker - Free Online Sprite Editing App is an online pixel art creator where your child can create free style drawing on the app's grid using color squares. It reminds me so much of my childhood days when I and my siblings would also draw pixel arts. This time, it's more enjoyable because it has colors! You can save your kid's art, too.
Here's a suggestion... Use this online game for a good 'ol game of Charades with your family. I bet it would be so much fun!
For Improving Spelling and Reading - Space Words
Space Words is a fun spelling game for kids. Players need to shoot letter-bearing asteroids to complete the name of the object that's flashed above the screen. Blasting the wrong asteroid letter loses a life and players only get 10 lives at a time so you'll have to be careful.
Personally, I feel that older kids will enjoy this game more because there are long words in the game's word bank. Also, controlling the spaceship and shooting asteroids may be a challenge. Still, I'm giving my thumbs up for this game for making spelling a very cool and thrilling activity.
For Playing with Your Kid - Foosball
Foosball is a foosball game made virtual! I'm not really good with foosball but, I have to admit, it gives me the adrenaline rush! My husband and son loves this game and they played it together. Boys do love this kind of games, right? And since my son is older, it is rowdier than ever!
I have to warn you, though. Make sure you use an external keyboard for this game if you're using a laptop or you risk getting your computer's keyboard destroyed, LOL! Nevertheless, it's a fun and a cool activity for parents and children.
One last tip... keep a watchful eye
I have always made it a point to check the online games that my son plays. I make sure that it's non-violent or have suggestive messages. I also make sure that he will not be able to accidentally click any link that could lead him to a malware or a shopping site. Lastly, and we also apply this rule for all his online activities, gaming is done in our shared work area or the family living room so we can easily see what he's doing just to be safe.
By the way, the games I recommended here are all FREE to play on Plays.org. I like the simplicity of the site and that the games really are free for playing. I know a lot of parents my age will also get nostalgic as some of our beloved arcade games can also be found here.
So enjoy playing with your children. Spend as much time with them as you still can because they grow up quickly. Take advantage of this free online game site that you can use for your bonding activity with them.


This paper wants to attract attention about this  not frequently explored ability and could have strong  influence in success (or failure) of a Clinical Trial.
a  few  to  count  on  them.
CER Medical Institute is a private organization dedicated to the prevention, diagnosis, treatment and research of prevalent diseases.


text:
LafargeHolcim joins MIT Climate and Sustainability Consortium as founding member
• LafargeHolcim joins MIT Climate and Sustainability Consortium as founding member representing the building materials industry
• Collaborating with like-minded influential industry leaders to accelerate climate action through innovation
• Consortium to vastly accelerate large-scale, real-world implementation of solutions to address the threat of climate change
LafargeHolcim joins the MIT Climate and Sustainability Consortium (MCSC) as a founding member, representing the building materials industry, to accelerate climate action through innovation. The company joins a range of influential other sector leaders to work with MIT's world-class research teams to develop scalable solutions to tackle climate change.
Jan Jenisch, Chief Executive Officer: "I am committed to building a net zero future, driving innovative and sustainable building solutions that work for people and the planet. With the urgency of today's climate crisis, no single organization can tackle it alone. That's why I am proud to be joining MIT's alliance of like-minded industry leaders and academic partners to scale up our climate action together."
The MCSC is led by the MIT School of Engineering and will engage students, faculty, and researchers from across the entire Institute. MCSC members will work to accelerate large-scale, real-world solutions that address the threat of climate change. The goals of the MCSC include climate change mitigation, lowering barriers to technology adoption, speeding the retirement of carbon-intensive activities, directing investment where it will be most effective, and rapidly translating best practices across industries.
Joining this consortium is another step on LafargeHolcim's commitment to build a net zero future as a global leader in innovative and sustainable building materials and solutions. Taking a rigorous science-driven approach to climate action, LafargeHolcim pledged to become a net zero company, partnering with the Science-Based Targets initiative (SBTi) and is setting the first net zero roadmap in the cement industry, building on its 2030 SBTi-validated climate targets.
More information on the MIT Climate and Sustainability Consortium is available as per below
News Release – click here
Video – click here
Dedicated MIT website – click here
ABOUT LAFARGEHOLCIM
As the world's global leader in building solutions, LafargeHolcim is reinventing how the world builds to make it greener and smarter for all. On its way to becoming a net zero company, LafargeHolcim offers global solutions such as ECOPact, enabling carbon-neutral construction. With its circular business model, the company is a global leader in recycling waste as a source of energy and raw materials through products like Susteno, its leading circular cement. Innovation and digitalization are at the core of the company's strategy, with more than half of its R&D projects dedicated to greener solutions. LafargeHolcim's 70,000 employees are committed to improving quality of life across more than 70 markets through its four business segments: Cement, Ready-Mix Concrete, Aggregates and Solutions & Products.
Media release - English (pdf, 61.89 KB)
Our academic network for green construction
Learn more about our collaboration with universities and research centers worldwide
LafargeHolcim and Schlumberger New Energy explore Carbon Capture and Storage Solutions
Shareholders support all proposals at 2021 Annual General Meeting
LafargeHolcim successfully closes Firestone Building Products acquisition
LafargeHolcim hosts European open innovation day for green construction


Aishwarya Rai Bachchan looks stunning in a golden, red and floral gown with flowing cape and plunging neckline at the Fashion Weekend International 2018 in Doha. She walked the ramp for designer Manish Malhotra. Aishwarya strikes a pose with make-up artist Mickey Contractor. The actress also plants a kiss on Aaradhya's lips.
Aaradhya wore the same outfit like her mom and the mother-daughter duo walked at the backstage. Also present at the occasion was Aishwarya's mother Brinda Rai and Sophie Choudry.
"I think inculcating traditions in my daughter is natural to me, it is not conditional. That is how I am raised. So what we end up doing as parents, knowingly or unknowingly, we pass on to our children as traditions because that is the natural flow of life", Aishwarya said in an interaction here.
For most of her international events, Aishwarya is joined by her daughter. She strongly believes that travelling is one of the best ways to get exposed to the world.
"The global community is the society for our kids today. So I have seen the wonderful influence of travel... Aaradhya is my daughter and I love spending time with her, so I am always travelling with her. She is going to turn 7 next month and I am still figuring out things about her," said the actress, debuted with Tamil film Iruvar.
"It takes a lot of planning and at times we try to keep it in the weekend. I am fortunate to work with a wonderful team that is constantly supporting me to plan things well", she ended.


This is an illustration I did of the display at the American Museum of Natural History in New York City. My husband and I when we were first dating would go there to sketch. I knew it was love when we both enjoyed the same exhibit the most. The scary dark corner of the Deep sea section behind the staircase to the left. The Squid and The Whale.


The amazing range of jackets available in this collection is a class apart. The cool and very very hot and trendy apple red ironman jackets with hood are made to provide fashion with a purpose. The smart and awesome cut, along with the classic red and black contrast of the inner lining, cuffs, is truly magnificent by all standards. The black paneled tape on the sleeves adds that zing for ultimate fashion.


The Public Library Association (PLA) is hosting a webinar series for library professionals on cultural intelligence (CQ). CQ is "a person's ability to function effectively across the boundaries that divide nations, ethnic groups and organizations," according to PLA.
Led by Marla Ehlers, assistant director of the Grand Rapids Public Library in Michigan, the series consists of two parts: The first will focus on building CQ skills (i.e., core concepts and competencies), and the second will focus on applying them to library work (and how they can inform policies, services, and programs).
The first webinar, Building CQ: Fostering Our Cultural Intelligence, will be held April 4, 2019, at 2:00 p.m. EDT.
The second webinar, Applying CQ: Shaping Culturally Intelligent Libraries, will be held April 11, 2019, at 2:00 p.m. EDT.
For more information and the pricing structure, read the press release.


This is the view from my study. It's a shows the little bit of grey blustery Lancaster visible from my window at dusk. Yes I'm well aware that you poor folks with dial-up connections had to wait an inordinate length of time for it to download. ...but you've got to recognise that this site is for my pleasure, not specifically yours, and I've got ADSL! That is not to say that you are not very welcome, you are. Feel free to look around, pull, tug, tweak, or press anything that looks pressable.
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On July 1, 2007, Ann Marie Miller was Baptised at South Norfolk Baptist Church in Chesapeake Virginia.
Some Images of the event are available, we apologize for the size and quality.
On Sunday, September 16, 2007, Steve Taylor was ordained.


To file under §3301(d) the parties must have lived separate and apart for a period of at least two (2) years with the date of separation commencing prior to December 5, 2016, or one (1) year with the date of separation commencing on or after December 5, 2016.
This informational section is for reference and research purposes. This section explains the basic forms needed for a plaintiff to file a simple No Fault Divorce in Pennsylvania when the parties have lived separate and apart for a period of at least two (2) years with the date of separation commencing prior to December 5, 2016, or one (1) year with the date of separation commencing on or after December 5, 2016.
Before you begin using the forms on the computer, print a copy of the checklist. This printable checklist is meant to be used in conjunction with this self-help section.
The Plaintiff must serve the defendant with the Complaint (form 4), the Notice to Defend (form 3), Affidavit under §3301(d) (form 10) and a blank copy of th Counter Affidavit under §3301(d) (form 12) within 30 days of the date that Forms 3, 4, 10 and 12 were filed with the Clerk of Judicial Records or within 90 days if the Defendant does not live in the state of Pennsylvania.
Attach the Domestic Return Receipt (green post card Form 3811) to Form Exhibit A.
Make a photocopy of Form Exhibit A that has the green post card attached.
If you were able to complete Section 4-Proof of Service, you now have proof that you served the Complaint (Form 4), Notice to Defend (Form 3) Affidavit Under §3301(d) (form 10) and a blank copy of Counter Affidavit under §3301(d) (form 12) on the defendant.
You must wait 20 days from the date of service to allow the defendant to respond before proceeding to the next section. Date of service is the date the defendant signed the green post card Form 3811.
Do not continue to the next section until after the 20 day waiting period.
If the defendant does respond by filing documents, then STOP and consult an attorney.
Sign and date forms 11 and 14 of the completed forms. Do not sign form 12.
Assemble into three (3) packets.
Form 11 Notice of Intention to Request Divorce Decree.
If Defendant does respond by filing documents, then STOP and consult an attorney.