When Bill Gates agreed a couple years ago to put a small piece of his personal fortune into a fund that invests in companies serving low-income customers in India, he invited the fund managers to return with a plan to scale up their investments and their social impact.
The fund managers recently took such a plan to Gates, and have again come away with not only a check, but an endorsement from the world's richest man. Gates also co-chairs the world's biggest philanthropy, but his new personal investment in the Capria Accelerator Fund is about business, not charity.


text:
Read or Dream is a manga written by Hideyuki Kurata and drawn by Ran Ayanaga. It was published in Japan in four trade paperback volumes by Shueisha in 2002. The full title is R.O.D - Read or Dream - We are Paper Sisters Detective Company. Read or Dream was translated into English and distributed in North America by Viz Media from 2006.

The "Paper Sisters Detective Company" consists of three young women who live in Hong Kong: Anita King, Michelle Cheung and Maggie Mui (they are not blood relations, but treat each other like sisters). Maggie, Michelle, and Anita are papermasters, meaning they can telekinetically manipulate paper to do anything they want, such as creating bulletproof shields and razor sharp swords. Their detective agency, which specializes in finding lost books (though they are often asked to find missing pets and do bodyguard duty as well), serves as the source of most of their adventures.

This series is set in the same universe as the manga series Read or Die, featuring a common antagonist to both series, the Dokusensha Corporation. Read or Die'''s protagonist Yomiko Readman also makes a cameo appearance.

The Paper Sisters and supporting character Hisami Hishiishi appear in the television series R.O.D the TV, but this series exists in a separate continuity than Read or Dream (differences include how the Sisters met Hisami and the origin of the Paper Sisters).

Plot summary
Anita King, Michelle Cheung and Maggie Mui run the "Paper Sisters Detective Company" in Hong Kong. They serve a variety of clients, seeking lost books, pets, and even lost authors! Maggie and Michelle's expansive book budget often causes them to be out of money, and when they are not working they argue with Anita about how to maintain the apartment and eat.

In volume 1, the Paper Sisters help fix a romance by finding a lost book, find the Shangri-la of libraries, convince an alien not to destroy the world, help a girl with a serious illness find the courage to undergo a risky treatment, and battle the greatest horror of all horrors: cleaning their own apartment.

Volume 2 finds Anita on her own trying to help a client, only to discover that the client is a thief known as "Lily the Book Lover Extraordinaire" and Anita must fight her to get back what the thief has stolen; in another chapter, the sisters tell each other ghost stories, and in the final set of chapters, the Detective Company helps an author Yun Fat track down his favorite writer from his childhood.

In volume 3, Maggie finds a book which divides her psyche into 24 different personalities, and Michelle and Anita need to find a way to restore her; in another story, the Sisters argue about how to earn more money, and later, after they become successful, Michelle puts on too much weight, so her sisters try to force her to diet. Anita gets sick and Maggie takes care of her. Finally, Lily returns to threaten young Japanese author Hisami Hishishii, but fortunately Hisami has the Paper Sisters to protect her.

In the final volume, the Paper Sisters are brought to Japan to do more bodyguard work for Hisami, but end up first trying to "stage" a pretend  first kiss for Hisami (with Anita as the unwilling "actor" playing Hisami's crush), and later, under her editor's instructions, try to protect Hisami from would-be suitors. The next story flashes back to how the Paper Sisters met: Dokusensha agents Maggie and Michelle were hired to help the company's genetic lab creation, Anita, to bring forth her powers. When Dokusensha tries to take Anita back, Maggie and Michelle take on Dokusensha's Hong Kong branch by themselves to rescue her from the evil corporation. The comic then returns to the present as several supporting characters' arcs are wrapped up, and Anita gets advice on the meaning of loving books from a mysterious spectacle-wearing bibliophile.

Characters
The Sisters appear to be named after Michelle Yeoh, Anita Mui and Maggie Cheung, the stars of the classic Hong Kong action film The Heroic Trio. Alternatively, a possible reference is Hong Kong actress Michelle Reis, whose surname means "king" in Portuguese (her father being Portuguese).

Michelle Cheung
Michelle is the eldest sister at age 23. She considers herself the group leader, accepting missions and devising tasks for the Paper Sisters to undertake. Being the only legal adult in the family, she is Anita's legal guardian. She is much like Read or Die's Yomiko Readman in that she is naively carefree about many things, and she spends all the money she has, including the house money, to buy every book she comes across. Unlike Yomiko, however, she is very outgoing and talkative. She serves as a strong contrast to her other sisters, being talkative and peppy (unlike shy Maggie) and calm and collected (unlike spitfire Anita). She helps earn the sisters extra money (though quickly spends it) doing translation work; otherwise, Michelle is often lazy and needs to be coerced into helping around the house.

Michelle's paper mastery is focused on the creation of paper projectiles; most often she fires paper arrows with a paper longbow. These arrows are just as deadly as real ones, and Michelle can also twist them into different shapes to wrap around her targets. Michelle carries an aluminum case full of different kinds of paper for the Sisters to access during combat.

Maggie Mui
Maggie is the middle sister at age 19. Michelle describes her as "Big, Strong and Sharp!" She is shy and quiet, preferring to let her sisters speak for the group, although she will speak up if she feels she has something important to say. She, like her sister Michelle, loves books and little can distract her once she is absorbed in a book. She also loves small spaces (despite her large stature) and can often be found reading under a table or in a window sill. She tends to have a somewhat depressive nature, often questioning her value to her other two sisters (who quickly reassure her if they find she is upset). She is the sisters' primary cook. Maggie has very few friends, but does bond with a young blind girl named Faye whom Maggie encourages to get an operation so she can see again.

In combat, Maggie creates the strongest paper shields, and she can create paper "familiars" or marionettes to attack or defend as she wills. Her most common puppets include a wolf with great attack prowess, a strong golem which lifts heavy things and destroys obstacles, and a giant bird for transport.

Anita King
Anita is the youngest of the three sisters at age 12. Anita is brash and outspoken. She is also the most practical and is forever trying to get Maggie and Michelle to save some'' money for food. She also collects things with frogs on them, an obsession which is reinforced by her sisters' and other friends' various frog-related gifts to her. Unlike her sisters, she hates books, a dramatic difference from most other papermasters; Michelle says this is because Anita is going through a rebellious phase, though it may also have something to do with how Anita was "created" by Dokusensha, and because of a traumatic experience caused by a fire at the great library caused by Yomiko Readman. In volume 4, a "passing book lover" notes that if Anita truly had no interest in books, she wouldn't even bother to hate them, and notes that books have led her to her sisters and her dearest friends. Anita is good friends with Chihon and Hisami.

She is best at using paper to cut, able to slice through rocks and steel, and uses paper either up close as a blade or as a mid-range throwing weapon. Anita is also a very agile and skilled martial artist, often using her paper skills to supplement her impressive physical prowess.

Chihon
The sisters meet Chihon while he was looking for a mysterious library to return a book on behalf of his deceased grandfather. He later befriends Anita and helps her on numerous occasions; though they often have arguments they also care for one another. He aspires to be an author.

Mr. Tsai
A bookstore owner, Mr. Tsai aids the sisters many times, especially Anita.

Lily the Reader Extraordinaire
This young woman steals rare books, and gets Anita wrapped up in one of her book theft plots, and later tries to kidnap Hisami. Lily is often aggressively flirtatious towards Anita and Hisami. She keeps a pet panther named, "Orion."

Hisami Hishishii
Hisami is a 13-year-old author from Japan who befriends the Paper Sisters after they protect her from Lily. Anita and Hisami especially bond, particularly when Anita goes to school with Hisami in Japan. Hisami's classmate Tohru has a crush on her.

Volume list

References

External links

2003 manga
Adventure anime and manga
Romance anime and manga
Seinen manga
Shueisha manga
Viz Media manga
Yuri (genre) anime and manga

ja:R.O.D#R.O.D -READ OR DREAM-

redpajama_set_name: RedPajamaWikipedia


Size 312 hearing aid batteries are one of our most popular sizes.
Many customers prefer to buy their hearing aid batteries in boxes of 60 – it always helps to have extras on hand in various locations! We want to make bulk purchases worth it – and are proud to offer great value for money when you choose to stock up. We also ensure that there is a long shelf-life on all batteries purchased, as we know this is particularly important when purchasing in bulk.
We aim to dispatch every order received before 3pm that same working day.
Compatible with all hearing aids using size 312 batteries including the HD360, HD420 and HD430 RIC.


text:
Q: Colouring grep pattern match with a preferred colour I am using the following pattern matching to colour in a preferred colour using tput.
 | sed -r $"s/^==> .* <==$/$(tput setaf 46)&$(tput sgr0)/"

I wonder if I can do a similar thing with 'grep'
| $_GREP -e ^ -e '^==>.*'

with
_GREP="/bin/grep --color"

Am not quite sure how to incorporate a preferred colour on the grep matching.

A: You can do it like this:
export GREP_COLOR='1;37;31'
grep -E --color=auto -i '{texttofind}' /dir/to/file

Color is added via ANSI escape sequences. See the FG and BG section in the middle (1 is background, 37 white, 31 red)

redpajama_set_name: RedPajamaStackExchange


Because of Michigan's extensive penal code, however, many everyday activities can cross over into the crime category — putting too many innocent individuals at risk of committing a "crime." A report that came out last fall highlighted just how egregious the situation is in Michigan, and showed how this state's criminal code outpaces its Midwest neighbors.
The head of a group representing hundreds of Detroit grocers said the plan is a "no-brainer" and has been discussed in the city before, while the American Civil Liberties Union of Michigan worries that it gives a "Big Brother" feel and could lead to violations of individual privacy.
Spread out over two weekends, participants will learn about laws and policies impacting the trans community and will design and implement educational projects on trans issues in the areas of activism and building community across the state. The two-day training is free and will be led by ACLU Staff Attorney for the LGBT Project, Jay Kaplan; Legislative Director Shelli Weisberg and a team of activist leaders including Emani Love, Amanda Niven, Amy Hunter, Preston Van Vliet and Sojn Boothroyd.


text:
Вайсенкирхен-ин-дер-Вахау () — ярмарочная коммуна () в Австрии, в федеральной земле Нижняя Австрия.

Входит в состав округа Кремс. Население — около 1,4 тыс. человек. Занимает площадь 23,28 км². Официальный код — 31351.

Политическая ситуация
Бургомистр коммуны — Антон Боденштайн (АНП) по результатам выборов 2005 года.

Совет представителей коммуны () состоит из 19 мест.

 АНП занимает 13 мест.
 СДПА занимает 5 мест.
 АПС занимает 1 место.

Примечания

Ссылки
 Официальная страница

Города Нижней Австрии


McPherson County is home to more than 50 companies spanning at least a dozen industries, making this city of 14,000 one of the nation's most industrialized communities. Here's a look at some of McPherson's industries.
CARTRIDGE KING OF KANSAS, INC.
MID WEST INDUSTRIES AND DEVELOPMENT, LTD.
PREMIER CASTING & MACHINE SERVICE, INC.
PRODUCTS: wood composite products development; custom composite profile extrusion; accessories for the fence, deck, rail, window, siding, concrete & building industries.
PRODUCTS: Piping, equipment & industrial electrical contractors. Services include metal fabrication, electrical installation, millwright services, structural steel, pipe processing fabrication pressure vessel alteration and repair installation, custom fabrication and NCCER certified testing & training facility.
PRODUCTS: store and distribute liquid petroleum gas products. Natural gas liquid fractionator.
PRODUCTS: metal machining & tooling; custom metal fabricating; hydraulic cylinder repair and fabrication.
PRODUCTS: custom fabricating of metal products; custom manufacturing, hard facing, ensilage boxes for trucks, modern day blacksmith shop, steel and aluminum retail sales.


Kimberly and James' wedding day at The Hyatt in Valencia, CA took place on November 8, 2014. Its was so amazing to see the love between these two and for the love that seemed to come so natural from Kimberly to James' three daughters. And with Kimberly being from Louisiana, she incorporated alot of the traditions into the day, including an awesome second line, with a full jazz marching band.


Alley Repertory Theater's latest fundraiser is paying homage to the fact that Facebook seems to be taking over the world. With tongues placed firmly in cheeks, the company will create a real-world version of the online social networking site. Participants will socialize while wearing large status update notifications in between sending each other hugs, flowers or songs. And what's Facebook without annoying people wandering about asking to be friends, poking random people and asking everyone to take quizzes. A live announcer will provide a constant stream of commentary on what's happening, and since this is in the real world, the night includes performances by comedians Nick Garcia, Chris Borders, Dustin Scott and Hollis Welsh, and music by Art Hodge.
7 p.m., $10, Facebook-style requests start at $1 each. Visual Arts Collective, 3638 Osage Ave., Garden City, alleyrep.org.
Boise Philharmonic under the direction of Robert Franz, conductor, perform Carl Nielsen's Helios Overture with the seniors of the Treasure Valley Youth Symphony. The presentation of the greatest composers of Scandinavia continues with special guest pianist Roberto Plano performing Edvard Grieg's Piano Concerto. Maestro Franz bids adieu for the season after conducting the Philharmonic during Jean Sibelius' Symphony No. 5.
Friday, March 13, 8 p.m., $16-$31, 208-344-7849, Brandt Center at NNU, 707 Fern St., Nampa; and Saturday, March 14, 8:15 p.m., $20-$61, Morrison Center, 2201 Cesar Chavez Lane, boisephilharmonic.org.
Switching gears to a band out of Portland, Ore., Starf**ker is back in Boise at the Neurolux sharing the stage with Guidance Counselor and local musician James Orr. BW's Amy Atkins interviewed Starf**ker frontman Josh Hodges last October and discovered a band with "well-conceived, multi-instrumental, cleverly arranged pop music." The live shows with bandmates Ryan Biornstad and Shawn Glassford enlist all types of noisemakers ranging from drums, guitar, bass and keyboards to hand claps, loops and tape noise.
8 p.m., $5, Neurolux, 111 N. 11th St., Boise, 208-343-0886, neurolux.com.
Do you have some extra money burning a hole in your fancy pants? Then spend some of it on a night out for a good cause. Attend a charity dinner and fashion show at Barbacoa with proceeds benefiting the Idaho Foodbank and the Children's Home. Barbacoa's award-winning Chef Enrique Martinez is creating a six-course dinner paired with wine in honor of a haute couture fashion show and auction hosted by Boise boutiques. Make a reservation by calling 208-338-5000. A seating price of $200 includes dinner and wine; bar seats are $50 and include an appetizer and drink; and corporate tables are also available.
3 p.m., Barbacoa, 276 Bobwhite Court, Boise, 208-338-5000, barbacoa-boise.com.
Boise Contemporary Theater's 15th annual 5X5 Reading Series continues with Beautiful American Soldier by Dano Madden, a two-part story about dealing with the consequences of war. In part one, two sisters who are lost on a quiet road in war-torn Iraq become friends with a junk peddler. In part two, a veteran of the war discovers a common bond with a homeless man.
7 p.m., single tickets $12; patrons 25 and younger single tickets $10, ictickets.com. Boise Contemporary Theater, 854 Fulton St., Boise, 208-331-9224.
One of the biggest imbibing days of the year is upon us, and whether your plans include following the sound of bagpipes around town or basing the night's activities on visiting bars serving green beer, there's plenty to do on St. Paddy's Day. The party at The Plank has music by Radillac, Bukkit and Irish psychobilly punk band 13 Orphans. Equaleyes is taking over Sockeye Pub and Grill. At Neurolux, DJ Bodie hosts the St. Patrick's Dance Party, and even the jazz musicians at Chandlers have some "pa-tricks" up their sleeves by adding an Irish twist to their names: Phil O'Garonzik, Kevin Patrick Kirk and Tom Tompkins play at 8 p.m. Tom Grainey's has two bands: Smooth Old Fashioned High and Spindlebomb, and at The Bouquet, Finn Riggins is performing with MicroBabies and In the Shadow of the Mountain. Humpin' Hannah's is opening the doors at 3 p.m. with free cover until 8 p.m. and gives away a bunch of swag, including green carnations, St. Patrick's bowler hats and shamrock leis. The Greenest Person wins a $100 Hannah's bar tab and fun and games include Spot the Pot O' Gold, Rollin' Over in the Clover and Divin' into Me Lucky Charms. The Giant Leprechauns perform from 6:30-8:30 p.m., followed by bagpipers and then The Rocci Johnson Band until close. The Boise Highlander bagpipers perform somewhere different every 15 minutes beginning at 5 p.m. See their schedule at boisehighlanders.com and try and keep up.
For more details, visit boiseweekly.com.
Taking Root, hosted by Community Cinema, is about how one woman made a difference in her country by planting trees. Kenyan Nobel Peace Prize laureate Wangari Maathai started The Greenbelt Movement, and to date, more than 35 million trees have been planted. The grassroots effort has worked to improve the environment and the quality of life in many countries, two important factors that lend naturally to empowering people in the fight for human rights and the defense of democracy. After the screening, Keziah Sullivan of the International Rescue Committee speaks, followed by questions from the audience.
5:30-7 p.m., FREE, Boise State Student Union Lookout Room, 1910 University Dr., takingrootfilm.com, 208-426-4317.


text:
\section{Introduction}\label{sec:intro}
Frame theory is nowadays a standard methodology in applied mathematics and engineering. The key advantage of
frames over orthonormal bases is the fact that frames are allowed to be redundant, yet provide stable
decompositions. This is a crucial fact, for instance, for applications which require robustness against
noise or erasures, or which require a sparse decomposition (cf. \cite{ck12}).

Tight frames provide optimal stability, since these systems satisfy the Parseval equality up to a constant.
Formulated in the language of numerical linear algebra, a tight frame is perfectly conditioned, since the
condition number of its analysis operator is one.
Thus, one key question is the following: Given a frame $\Phi = \{\varphi_k\}_{k=1}^{M}\subset\R^N$, $M\ge N$,
say, can the frame vectors $\varphi_k$ be modified so that the resulting system forms a tight frame? Again
in numerical linear algebra terms, this question can be regarded as a request for perfect preconditioning \cite{bb,c}.
Since a frame is typically designed to accommodate certain requirements of an application, this modification
process should be as careful as possible in order not to change the properties of the system too drastically.

One recently considered approach consists in multiplying each frame vector by a scalar/a weight. Notice that this process does  not even
disturb sparse decomposition properties at all, hence it might be considered `minimally invasive'. The formal
definition was given in \cite{kopt12} by the authors and E.K.\ Tuley (see also \cite{kop13a}). In that paper,
a frame, for which scalars exist so that  the scaled frame forms a tight frame, was coined {\em scalable frame}.
Moreover, in the infinite dimensional situation, various equivalent conditions for scalability were provided,
and in the finite dimensional situation, a very intuitive geometric characterization was proven. In fact, this
characterization showed that a frame is non-scalable, if the frame vectors do not spread `too much' in the space.
This seems to indicate that there exist relations to convex geometry.

Scalable frames were then also investigated in the papers \cite{cklmns12} and \cite{cc13}. In \cite{cklmns12}, the
authors analyzed the problem by making use of the properties of so-called diagram vectors \cite{hklw}, whereas
\cite{cc13} gives a detailed insight into the set of weights which can be used for scaling.

The contribution of the present paper is three-fold. First, we refine the definition of scalability by calling
a (scalable) frame $m$-scalable, if at most $m$ non-zero weights can be used for the scaling. Second, we establish
a link to convex geometry. More precisely, we prove that this refinement leads to a reformulation of the
scalability question in terms of the properties of certain polytopes associated to a nonlinear transformation of
the frame vectors. This nonlinear transformation is related but not equivalent to the diagram vectors used in the
results obtained in \cite{cklmns12}. Using this reformulation, we establish new characterizations of scalable
frames using convex geometry, namely convex polytopes. Third, we investigate the topological properties of the set
of scalable frames. In particular, we prove that in the set of frames in $\R^N$ with $M$ frame vectors the set of
scalable frames is nowhere dense if $M < N(N+1)/2$. We wish to mention, that the results stated and proved in this
paper were before announced in \cite{kop-spie}.

The paper is organized as follows. In Section \ref{sec:prelim}, we introduce the required notions with respect to
frames and their ($m$-)scalability as well as state some basic results. Section \ref{sec2} is devoted to establishing
the link to convex geometry and derive novel characterizations of scalable frames using this theory. Finally, in
Section \ref{sec3}, we study the topology of the set of scalable frames.

\section{Preliminaries}
\label{sec:prelim}

First of all, let us fix some notation. If $X$ is any set whose elements are indexed by $x_j$, $j\in J$, and $I\subset J$,
we define $X_I := \{x_i : i\in I\}$. Moreover, for the set $\{1,\ldots,n\}$, $n\in\N$, we write $[n]$.

A set $\Phi = \{\varphi_k\}_{k=1}^{M}\subset\R^N$, $M\ge N$ is called a {\em frame}, if there exist positive constants $A$
and $B$ such that
\begin{equation}\label{frameineq}
A\|x\|^2\,\le\,\sum_{k=1}^{M}|\ip{x}{\varphi_k}|^{2}\,\le\,B \|x\|^2
\end{equation}
holds for all $x\in\R^N$. Constants $A$ and $B$ as in \eqref{frameineq} are called \emph{frame bounds} of $\Phi$.
The frame $\Phi$ is called {\em tight} if $A = B$ is possible in \eqref{frameineq}. In this case we have
$A = \tfrac 1 N\sum_{=1}^{M}\|\varphi_k\|^{2}$. A tight frame with $A=B=1$ in \eqref{frameineq} is called
\emph{Parseval frame}.

We will sometimes identify a frame $\Phi = \{\varphi_{k}\}_{k=1}^{M}\subset\R^N$ with the $N\times M$ matrix
whose $k$th column is the vector $\varphi_k$. This matrix is called the {\em synthesis operator} of the frame.
The adjoint $\Phi^T$ of $\Phi$ is called the \emph{analysis operator}. Using the analysis operator, the relation
\eqref{frameineq} reads
$$
A\|x\|^2\,\le\,\|\Phi^Tx\|^2\,\le\,B \|x\|^2.
$$
Hence, a frame $\Phi$ is tight if and only if some multiple of $\Phi^T$ is an isometry. The set of frames
for $\R^N$ with $M$ elements will be denoted by $\fr(M,N)$. We say that a frame $\Phi\in\fr(M,N)$ is {\em degenerate} if
one of its frame vectors is the zero-vector. If $\mathcal{X}(M,N)$ is a set of frames in $\fr(M,N)$, we denote by
$\mathcal{X}^*(M,N)$ the set of the non-degenerate frames in $\mathcal{X}(M,N)$. For example, $\fr^*(M,N)$ is the set
of non-degenerate frames in $\fr(M,N)$. For more details on frames, we refer the reader to \cite{co03,ck12}

Let us recall the following definition from \cite[Definition 2.1]{kopt12}.

\begin{defn}\label{def0}
A frame $\Phi = \{\varphi_k\}_{k=1}^M$ for $\R^N$ is called {\em scalable}, respectively, {\em strictly scalable}, if there exist nonnegative, respectively, positive,  scalars $c_1,\ldots,c_M\in\R$ such that $\{c_k\varphi_k\}_{k=1}^M$ is a tight frame for $\R^N$. The set of  scalable, respectively, strictly scalable,  frames in $\fr(M,N)$ is denoted by $\sca(M,N)$, respectively, $\sca_{+}(M,N)$.
\end{defn}

In order to gain a better understanding of the structure of scalable frames we refine the definition of scalability.

\begin{defn}\label{def1}
Let $M,N,m\in\N$ be given such that $N\leq m \leq M$. A frame $\Phi=\{\varphi_k\}_{k=1}^{M} \in \fr(M,N)$  is said to be \emph{$m$-scalable}, respectively, \emph{strictly $m$-scalable}, if there exists a subset $I\subseteq [M]$, $\#I=m$, such that $\Phi_I$ is a scalable frame, respectively, a strictly scalable frame  for $\R^N$.
We denote the set of $m$-scalable frames, respectively, strictly $m$-scalable frames  in $\fr(M,N)$ by   $\sca(M,N,m)$, respectively, $\sca_{+}(M,N,m).$
\end{defn}

It is easily seen that for $m\leq m'$ we have that $\sca(M,N, m)\subset \sca(M,N, m')$. Therefore,
$$
\sca(M,N) = \sca(M,N,M) = \bigcup_{m=N}^{M}\sca(M,N, m).
$$
In the sequel, if no confusion can arise, we often only write $\calF$, $\sca$, $\sca_{+}$, $\sca(m)$, and $\sca_{+}(m)$
instead of $\sca(M,N)$, $\sca_{+}(M,N)$, $\sca(M,N,m)$, and $\sca_{+}(M,N,m)$, respectively. The notations $\calF^*$,
$\sca^*$, $\sca_{+}^*$, $\sca(m)^*$, and $\sca_{+}(m)^*$ are to be read analogously.

Note that for a frame $\Phi\in\fr$ to be $m$-scalable it is necessary that $m\geq N$.
In addition, $\Phi\in\sca(M,N)$ holds if and only if $T(\Phi)\in\sca(M,N)$ holds for one (and hence for all) orthogonal
transformation(s) $T$ on $\R^N$; cf.\ \cite[Corollary 2.6]{kopt12}.

If $M\geq N$, we have $\Phi \in \sca(M,N,N)$ if and only if $\Phi$ contains an orthogonal basis of $\R^N$. This completely
characterizes the set $\sca(M,N,N)$ of $N$-scalable frames for $\R^N$ consisting of $M$ vectors. For frames with $M=N+1$
vectors in $\R^N$ we have the following result:

\begin{prop}\label{sframedplus1}
Let $N\geq 2$ and $\Phi=\{\varphi_k\}_{k=1}^{N+1}\in\fr^*$ with $\varphi_k\neq\pm\varphi_\ell$ for $k\neq\ell$. If
$\Phi\in\sca_+(N+1,N,N)$ then $\Phi\notin\sca_+(N+1,N)$.
\end{prop}

\begin{proof}
If $\Phi\in \sca_{+}(N+1, N, N)$, then $\Phi$ must contain an orthogonal basis. By applying some orthogonal transformation
and rescaling the frame vectors, we can assume without loss of generality that $\{\varphi_k\}_{k=1}^N=\{e_k\}_{k=1}^N$ is
the standard orthonormal basis of $\R^N$, and that $\varphi_{N+1}\neq \pm e_k$ for each $k=1, 2, \hdots, N$, with
$\|\varphi_{N+1}\|=1$. Thus, $\Phi$ can be written as $\Phi = \begin{bmatrix}\Id_N & \varphi_{N+1}\end{bmatrix}$, where
$\Id_N$ is the $N\times N$ identity matrix.

Assume that there exists $\{\lambda_k\}_{k=1}^{N+1}\subset (0,\infty)$ such that $\widetilde{\Phi}=\{\lambda_k \varphi_k\}_{k=1}^{N+1}$
is a tight frame, i.e.\ $\widetilde{\Phi}\widetilde{\Phi}^{T} = A\Id_N$. Using a block multiplication this equation can be rewritten as
$$
\Lambda + \lambda_{N+1}^2\varphi_{N+1}\varphi_{N+1}^{T} = A\Id_{N}
$$
where $\Lambda = \diag(\lambda_k^2)$ is the $N\times N$ diagonal matrix with $\lambda_k^2$, $k=1,\hdots,N$, on its diagonal. Consequently,
\begin{align*}
&\lambda_k^2 + \lambda_{N+1}^2\varphi_{N+1,k}^2 = A\;\text{ for }k=1,\hdots,N\quad\text{and}\\
&\lambda_{N+1}^2\varphi_{N+1,\ell}\varphi_{N+1,k} = 0\,\text{ for }k\neq\ell.
\end{align*}
But $\lambda_{N+1}>0$ and so all but one entry in $\varphi_{N+1}$ vanish. Since $\varphi_{N+1}$ is a unit norm vector, we see that
$\varphi_{N+1}=\pm e_k$ for some $k\in [N]$ which is contrary to the assumption, so $\Phi$ cannot be strictly $(N+1)$-scalable.
\end{proof}

\section{Scalable Frames and Convex Polytopes}
\label{sec2}

Our characterizations of $m$-scalable frames will be stated in terms of certain convex polytopes and, more generally,
using tools from convex geometry. Therefore, we collect below some key facts and properties needed to state and prove our
results. For a detailed treatment of convex geometry we refer to \cite{matou02, stwi70, web94}.

\subsection{Background on Convex Geometry}
\label{subsec2.1}

In this subsection, let $E$ be a real linear space, and let $X =\{x_i\}_{i=1}^{M}$ be a finite set in $E$. The
\emph{convex hull generated by $X$} is the  compact convex subset of $E$ defined by
$$
\co(X) := \left\{ \sum_{i=1}^{M} \alpha_{i} x_i:  \alpha_i \geq 0, \, \sum_{i=1}^{M}\alpha_i=1\right\}.
$$
The \emph{affine hull generated by $X$} is defined by
$$
\aff(X) := \left\{ \sum_{i=1}^{M} \alpha_{i} x_i:   \, \sum_{i=1}^{M}\alpha_i=1\right\}.
$$
Hence, we have $\co(X)\subset\aff(X)$. Recall that for fixed $a\in\aff(X)$, the set
$$
V(X) := \aff(X) - a = \{y-a : y\in\aff(X)\}
$$
is a subspace of $E$ (which is independent of $a\in\aff(X)$) and that one defines
$$
\dim X := \dim \co(X) := \dim\aff(X) := \dim V(X).
$$
We shall use Carath\'eodory's Theorem for convex polytopes (see, e.g., \cite[Theorem 2.2.12]{stwi70}) in deciding
whether a frame is scalable:

\begin{thm}[Carath\'eodory]\label{t:cara}
Let $X = \{x_1,\ldots,x_k\}$ be a finite subset of $E$  with $d := \dim X$. Then for each $x\in\co(X)$ there exists
$I\subset [k]$ with $\#I = d+1$ such that $x\in\co(X_I)$.
\end{thm}

The \emph{relative interior} of the polytope $\co(X)$ denoted by $ri\co(X)$, is the interior of $\co(X)$ in the
topology induced by $\aff(X)$. We have that $ri\co(X)\neq\emptyset$ as long as $\#X\ge 2$; cf.\ \cite[Lemma 3.2.8]{stwi70}.
Furthermore,
$$
ri\co(X) = \left\{\sum_{i=1}^{M}\lambda_i x_i: \lambda_i>0, \sum_{i=1}^{M}\lambda_i = 1\right\},
$$
see \cite[Theorem 2.3.7]{web94}. Moreover, the interior of $\co(X)$ in $E$ is non-empty if and only if $\aff(X)= E$.

The following lemma characterizes $\dim X$ in terms of $\dim\linspan X$.

\begin{lem}\label{l:affine}
Let $X$ be a finite set of points in $E$.  Put $m := \dim\linspan X$. Then $\dim X\,\in\,\{m-1,m\}. $
Moreover, the following statements are equivalent:
\begin{enumerate}
\item[{\rm (i)}]   $\dim X = m-1$.
\item[{\rm (ii)}]  For all linearly independent $X'\subset X$ with $\dim\linspan X' = m$ we have $
X\setminus X'\subset\aff(X').$
\item[{\rm (iii)}] For some linearly independent $X'\subset X$ with $\dim\linspan X' = m$ we have $
X\setminus X'\subset\aff(X'). $
\end{enumerate}
\end{lem}

\begin{proof}
Let $X = \{x_1,\ldots,x_k\}$. First of all, we observe that for a linearly independent set $X' = \{x_{i_1},\ldots,x_{i_m}\}$
as in (ii) or (iii) we have
$$
\dim V(X') = \dim\linspan\{x_{i_l} -  x_{i_1} : l=2,\ldots,m\} = m - 1.
$$
Therefore, $V(X')\subset V(X)\subset\linspan X$ implies $m-1\leq\dim X\leq m$. Let us now prove the moreover-part of the lemma.

(i)$\Sra$(ii). Assume that $\dim X = m-1$ and let $X' = \{x_{i_1},\ldots,x_{i_m}\}$ be a linearly independent set as in
(ii). From $\dim V(X) = \dim X = m-1$ we obtain $V(X) = V(X')$. Therefore, for each $x_j\in X\setminus X'$ there exist
$\mu_2,\ldots,\mu_m\in\R$ such that
$$
x_j - x_{i_1} = \sum_{i=2}^m\mu_i(x_i - x_{i_1}) = \sum_{i=2}^m\mu_ix_i - \left(\sum_{i=2}^m\mu_i\right)x_{i_1}.
$$
And this implies
$$
x_j = \left(1 - \sum_{i=2}^m\mu_i\right)x_{i_1} + \sum_{i=2}^m\mu_ix_i\,\in\,\aff(X').
$$

(ii)$\Sra$(iii). This is obvious.

(iii)$\Sra$(i). Let $X' = \{x_{i_1},\ldots,x_{i_m}\}$ be a linearly independent set as in (iii). If $x\in X\setminus X'$,
then we have $x\in\aff(X')$ by (iii). Consequently, there exist $\lambda_1,\ldots,\lambda_m\in\R$ with $\sum_{l=1}^m\lambda_l = 1$
such that $x = \sum_{l=1}^m\lambda_l x_{i_l}$. Hence, we obtain
$$
x - x_{i_1} = \sum_{l=1}^m\lambda_l x_{i_l} - \left(\sum_{l=1}^m\lambda_l\right)x_{i_1} = \sum_{l=1}^m\lambda_l(x_{i_l} - x_{i_1})\,\in\,V(X').
$$
This implies $V(X) = V(X')$ and hence (i).
\end{proof}

In the sequel we will have to deal with a special case of the situation in Lemma~\ref{l:affine}, where $X$ is a set of rank-one
orthogonal projections acting on a real or complex Hilbert space $\calH$. In this case, $E$ is the set consisting of the
selfadjoint operators in $\calH$ which is a real linear space.

\begin{cor}\label{c:proj}
Let $X$ be a finite set consisting of rank-one orthogonal projections acting on a Hilbert space $\calH$. Then we have
$$
\dim X = \dim\linspan X - 1.
$$
\end{cor}

\begin{proof}
Let $X = \{P_1,\ldots,P_k\}$, $m := \dim\linspan X$, and let $X'\subset X$ be a linearly independent subset of $X$ such that
$\dim\linspan X' = m$. Without loss of generality assume that $X' = \{P_1,\ldots,P_m\}$. Let $j\in\{m+1,\ldots,k\}$. Then
there exist $\lambda_1,\ldots,\lambda_m\in\R$ such that $P_j = \sum_{i=1}^m\lambda_iP_i$. This implies
$$
1 = \Tr P_j = \Tr\left(\sum_{i=1}^m\lambda_iP_i\right) = \sum_{i=1}^m\lambda_i\Tr(P_i) = \sum_{i=1}^m\lambda_i,
$$
which shows that $P_j\in\aff(X')$. The statement now follows from Lemma \ref{l:affine}.
\end{proof}

\subsection{Scalability in Terms of Convex Combinations of Rank-One Matrices}
\label{subsec2.2}

Here, and for the rest of this paper, for a frame $\Phi = \{\varphi_i\}_{i=1}^M$ in $\fr(M,N)$ we set
$$X_\Phi := \{\varphi_i\varphi_i^T : i\in [M]\}.$$ This is a subset of the space of all real symmetric $N\times N$-matrices
which we shall denote by $S_N$. We shall also denote the set of positive multiples of the identity by
$\boldsymbol I_+ := \{\alpha\Id_N : \alpha > 0\}$.

\begin{prop}\label{p:charac_conv}
For a frame $\Phi\in\fr(M,N)$ the following statements are equivalent:
\begin{enumerate}
\item[{\rm (i)}]  $\Phi$ is  scalable, respectively, strictly scalable.
\item[{\rm (ii)}] $\boldsymbol I_+\cap\co(X_\Phi)\neq\emptyset$, respectively,  $\boldsymbol I_+\cap\,ri \co(X_\Phi)\neq\emptyset$.
\end{enumerate}
\end{prop}

\begin{proof}
Assume that the frame $\Phi = \{\varphi_i\}_{i=1}^M$ is scalable. Then there exist non-negative scalars $c_1,\ldots,c_M$ such that
$$
\sum_{i=1}^Mc_i\varphi_i\varphi_i^T = \Id.
$$
Put $\alpha := \sum_{i=1}^Mc_i$. Then $\alpha > 0$ and with $\lambda_i := \alpha^{-1}c_i$ we have
$$
\sum_{i=1}^M\lambda_i\varphi_i\varphi_i^T = \alpha^{-1}\Id\quad\text{and}\quad\sum_{i=1}^M\lambda_i = 1.
$$
Hence $\alpha^{-1}\Id\in\co(X_\Phi)$. The converse direction is obvious.
\end{proof}

As pointed out earlier, for $m\leq m'$ we have  $\sca(m)\subset\sca(m')$.  Given $\Phi\in \sca(M,N) = \sca(M)$,
there exists $m\leq M$ such that such that $\Phi\in\sca(m)$, e.g., we can always take $m=M$.  However, the next result gives a ``canonical'' integer $m=m_\Phi$ that  is in a way ``optimal''.

\begin{prop}\label{p:less_vectors}
For a frame $\Phi=\{\varphi_k\}_{k=1}^{M}\in\fr$, put $m = m_\Phi := \dim\linspan X_\Phi$. Then the following statements are equivalent:
\begin{enumerate}
\item[{\rm (i)}]  $\Phi$ is scalable.
\item[{\rm (ii)}] $\Phi$ is $m$-scalable.
\end{enumerate}
\end{prop}
\begin{proof}
Clearly, (ii) implies (i). Conversely, let $\Phi = \{\varphi_i\}_{i=1}^M$ be scalable. After possibly removing zero vectors from the
frame and thereby reducing $M$ (which does not affect the value of $m$), we may assume that $\Phi$ is unit-norm. By Proposition
\ref{p:charac_conv}, there exists $\alpha > 0$ such that $\alpha\Id_N\in\co(X_\Phi)$. Therefore, from Theorem \ref{t:cara} it
follows that there exists $I\subset [M]$ with $\#I = \dim X_\Phi + 1$ such that $\alpha\Id_N\in\co(X_{\Phi_I})$. Hence, $\Phi_I$
is scalable by Proposition \ref{p:charac_conv}. And since $\dim X_\Phi = \dim\linspan X_\Phi - 1$ by Corollary \ref{c:proj}, the claim follows.
\end{proof}

As $X_\Phi\subset S_N$ and $\dim S_N = N(N+1)/2$, we immediately obtain the following corollary.

\begin{cor}\label{highredund}
For $M\ge N(N+1)/2$ we have
$$
\sca(M,N) = \sca\left(M,N,\frac{N(N+1)}{2}\right).
$$
\end{cor}

\subsection{Convex Polytopes Associated with $\mathbf{m}$-Scalable Frames}
\label{subsec2.3}

Let $\Phi = \{\vphi_k\}_{k=1}^M$ be a frame for $\R^N$. Then the analysis operator of the scaled frame $\{c_k\vphi_k\}_{k=1}^M$
is given by $C\Phi^T$, where $C$ is the diagonal matrix with the values $c_k$ on its diagonal. Hence, the frame $\Phi$ is
scalable if and only if
\begin{equation}\label{e:scfrm}
\Phi C^{2} \Phi^{T} = A\Id_N
\end{equation}
where $A > 0$. Similarly, $\Phi$ is $m$-scalable if and only if \eqref{e:scfrm} holds with $C = \diag(c)$, where
$c\in [0,\infty)^M$ such that $\|c\|_0\le m$. Here, we used the so-called ``zero-norm'' (which is in fact not a norm),
defined by
$$
\|x\|_0 := \#\{k\in [n] : x_k\neq 0\},\quad x\in\R^n.
$$
Comparing corresponding entries from left- and right-hand sides of \eqref{e:scfrm}, it is seen that for a frame to be
$m$-scalable it is necessary and sufficient that there exists a vector $u = (c_{1}^{2},c_{2}^{2},\ldots,c_{M}^{2})^{T}$
with $\|u\|_0\le m$ which is a solution of the following linear system of $\tfrac{N(N+1)}{2}$ equations in $M$ unknowns:
\begin{equation}\label{nxm}
\begin{cases}
\sum\limits_{j=1}^M\vphi_j(k)^2y_j = A &\text{for }k=1,\ldots,N,\\
\sum\limits_{j=1}^M\vphi_j(\ell)\vphi_j(k)y_j = 0 &\text{for }\ell,k=1,\ldots,N,\,k > \ell.
\end{cases}
\end{equation}

Subtraction of equations in the first system in \eqref{nxm} leads to the new {\em homogeneous} linear system
\begin{equation}\label{nxm2}
\begin{cases}
\sum\limits_{j=1}^M\big(\vphi_j(1)^2 - \vphi_j(k)^2\big)y_j = 0 &\text{for }k=2,\ldots,N,\\
\sum\limits_{j=1}^M\vphi_j(\ell)\vphi_j(k)y_j = 0 &\text{for }\ell,k=1,\ldots,N,\,k > \ell.
\end{cases}
\end{equation}
It is not hard to see that we have not lost information in the last step, hence $\Phi$ is $m$-scalable if and only
if there exists a nonnegative vector $u\in\R^M$ with $\|u\|_0\le m$ which is a solution to \eqref{nxm2}. In matrix form,
\eqref{nxm2} reads
\begin{equation*
F(\Phi)u = 0,
\end{equation*}
where the $(N-1)(N+2)/2\times M$ matrix $F(\Phi)$ is given by
\begin{equation*
F(\Phi) = \begin{pmatrix} F(\varphi_{1}) & F(\varphi_{2})  & \hdots & F(\varphi_{M})  \end{pmatrix},
\end{equation*}
where $F : \R^N\to\R^{d}$, $d := (N-1)(N+2)/2$, is defined by
\begin{equation*}\label{fctF}
F(x)=
\begin{pmatrix}
F_{0}(x)\\ F_{1}(x)\\ \vdots\\ F_{N-1}(x)
\end{pmatrix},
\qquad
F_{0}(x) =
\begin{pmatrix} x_{1}^{2}-x_{2}^{2}\\ x_{1}^{2}-x_{3}^{2} \\ \vdots \\ x_{1}^{2}-x_{N}^{2}\end{pmatrix},
\qquad
F_{k}(x) =
\begin{pmatrix}x_{k}x_{k+1}\\ x_{k}x_{k+2}\\ \vdots \\ x_{k}x_{N}\end{pmatrix},
\end{equation*}
and $F_{0}(x)\in \R^{N-1}$, $F_{k}(x) \in \R^{N-k}$, $k=1, 2, \hdots, N-1$.

Summarizing, we have just proved the following proposition.

\begin{prop}\label{p:F}
A frame $\Phi$ for $\R^N$ is  $m$-scalable, respectively,  strictly $m$-scalable  if and only if there exists a nonnegative
$u\in\ker F(\Phi)\setminus\{0\}$ with $\|u\|_0\le m$, respectively,  $\|u\|_0 = m$.
\end{prop}

We will now utilize the above reformulation to characterize $m$-scalable frames in terms of the properties of
convex polytopes of the type $\co(F(\Phi_I))$, $I\subset [M]$. One of the key tools will be Farkas' lemma
(see, e.g., \cite[Lemma  1.2.5]{matou02}).

\begin{lem}[Farkas' Lemma]\label{l:farkas}
For every real $N\times M$-matrix $A$ exactly one of the following cases occurs:
\begin{itemize}
\item[(i)] The system of linear equations $Ax=0$ has a nontrivial nonnegative solution $x\in\R^{M}$ {\rm (}i.e.,
all components of $x$ are nonnegative and at least one of them is strictly positive.{\rm )}
\item[(ii)] There exists $y\in\R^N$ such that $A^{T}y$ is a vector with all entries strictly positive.
\end{itemize}
\end{lem}

In our  first main result we use the notation $\co(A)$ for a matrix $A$ which we simply define as the
convex hull of the set of column vectors of $A$.

\begin{thm}\label{poly}
Let $M\geq m\geq N\geq 2$, and let $\Phi = \{\varphi_k\}_{k=1}^M$ be a frame for $\R^N$. Then the following
statements are equivalent:
\begin{enumerate}
\item[{\rm (i)}] $\Phi$ is $m$-scalable, respectively, strictly $m$-scalable,
\item[{\rm (ii)}] There exists a subset $I\subset [M]$ with $\# I=m$ such that $0\in\co(F(\Phi_{I}))$,  respectively, $0\in ri\co(F(\Phi_{I}))$.
\item[{\rm (iii)}] There exists a subset $I\subset [M]$ with $\# I = m$ for which there is no $h\in\R^d$ with $\<F(\vphi_k),h\> > 0$ for all $k\in I$, respectively, with $\ip{F(\varphi_k)}{h}\geq 0$ for all $k\in I$, with at least one of the inequalities being strict.
\end{enumerate}
\end{thm}
\begin{proof}
(i)$\Slra$(ii). This equivalence follows directly if we can show the following equivalences for $\Psi\subset\Phi$:
\begin{align}
\begin{split}\label{e:equis}
0\in\co(F(\Psi))&\;\Llra\;\ker F(\Psi)\setminus\{0\}\text{ contains a nonnegative vector and}\\
0\in ri\co(F(\Psi))&\;\Llra\;\ker F(\Psi)\text{ contains a positive vector.}
\end{split}
\end{align}
The implication "$\Sra$" is trivial in both cases. For the implication "$\Sla$" in the first case let
$I\subset [M]$ be such that $\Psi = \Phi_I$, $I = \{i_1,\ldots,i_m\}$, and let $u = (c_1,\ldots,c_m)^T\in\ker F(\Psi)$
be a non-zero nonnegative vector. Then $A := \sum_{k=1}^mc_k > 0$ and with $\la_k := c_k/A$, $k\in [m]$, we have
$\sum_{k=1}^m\la_k = 1$ and $\sum_{k=1}^m\la_kF(\vphi_{i_k}) = A^{-1}F(\Psi)u = 0$. Hence $0\in\co(F(\Psi))$. The
proof for the second case is similar.

(ii)$\Slra$(iii). In the non-strict case this follows from \eqref{e:equis} and Lemma \ref{l:farkas}. In the strict
case this is a known fact; e.g., see \cite[Lemma 3.6.5]{web94}.
\end{proof}

We now derive a few consequences of the above theorem. A given vector $v\in\R^d$ defines a hyperplane by
$$
H(v) = \{y\in\R^d: \ip{v}{y} = 0\},
$$
which itself determines two open convex cones $H^-(v)$ and $H^+(v)$, defined by
\begin{equation*
H^-(v) = \{y\in\R^d : \ip{v}{y} < 0\}
\quad\text{and}\quad
H^{+}(v) = \{y\in\R^d : \ip{v}{y} > 0\}.
\end{equation*}
Using these notations we can restate the equivalence (i)$\Slra$(iii) in Theorem~\ref{poly} as follows:

\begin{prop}\label{p:polycoro}
Let $M\geq N\geq 2$, and let $m$ be such that $N\leq m\leq M$. Then a frame $\Phi = \{\varphi_k\}_{k=1}^M$ for
$\R^N$ is $m$-scalable if and only if there exists a subset $I\subset [M]$ with $\#I = m$ such that
$\bigcap_{i\in I} H^{+}(F(\varphi_i)) = \emptyset.$
\end{prop}

\begin{rem}
In the case of strict $m$-scalability we have the following necessary condition: If $\Phi$ is strictly $m$-scalable,
then there exists a subset $I\subset [M]$ with $\#I = m$ such that  $\bigcap_{i\in I} H^-(F(\varphi_i)) = \emptyset.$
\end{rem}

\begin{rem}
When $M\geq d+1 = N(N+1)/2$, we can use properties of the convex sets $H^{\pm}(F(\varphi_k))$ to give an alternative
proof of Corollary~\ref{highredund}. For this, let the frame $\Phi = \{\varphi_k\}_{k=1}^M$ for $\R^N$ be scalable.
Then, by Proposition \ref{p:polycoro} we have that $\bigcap_{k=1}^MH^{+}(F(\varphi_k)) = \emptyset$. Now, Helly's
theorem (see, e.g., \cite[Theorem 1.3.2]{matou02}) implies that there exists $I\subset [M]$ with $\# I = d+1$ such
that $\bigcap_{i\in I}H^{+}(F(\varphi_i)) = \emptyset$. Exploiting Proposition \ref{p:polycoro} again, we conclude
that $\Phi$ is $(d+1)$-scalable.
\end{rem}

The following result is an application of Proposition \ref{p:polycoro} which provides a simple condition for $\Phi\notin\sca(M,N)$.

\begin{prop}\label{firstoctant}
Let $\Phi = \{\varphi_k\}_{k=1}^M$ be a frame for $\R^N$, $N\ge 2$. If there exists an isometry $T$ such that
$T(\Phi)\subset\R^{N-2}\times\R^{2}_{+}$, then $\Phi$ is not scalable. In particular, $\Phi$ is not scalable if there
exist $i,j\in [N]$, $i\neq j$, such that $\vphi_k(i)\vphi_k(j) > 0$ for all $k\in [M]$.
\end{prop}
\begin{proof}
Without loss of generality, we may assume that $\Phi\subset\R^{N-2}\times\R^{2}_{+}$, cf.\ \cite[Corollary 2.6]{kopt12}.
Let $\{e_k\}_{k=1}^{d}$ be the standard ONB for $\R^d$. Then for each $k\in [M]$ we have that
$$
\ip{e_d}{F(\varphi_{k})} = \varphi_{k}(N-1)\varphi_{k}(N) >0.
$$
Hence, $e_d\in\bigcap_{i\in [M]}H^+(F(\vphi_i))$. By Proposition \ref{p:polycoro}, $\Phi$ is not scalable.
\end{proof}

The characterizations stated above can be recast in terms of the convex cone $C(F(\Phi))$ generated by $F(\Phi)$. We
state this result for the sake of completeness. But first, recall that for a finite subset $X = \{x_1,\ldots,x_M\}$
of $\R^d$ the \emph{polyhedral cone generated by $X$} is the closed convex cone $C(X)$ defined by
$$
C(X) = \left\{\sum_{i=1}^{M} \alpha_{i} x_i : \alpha_i\geq 0\right\}.
$$
Let $C$ be a cone in $\R^d$. The \emph{polar cone} of $C$ is the  closed convex cone $C^{\circ}$ defined by
$$
C^{\circ} := \{x\in\R^N : \ip{x}{y}\leq 0\,\,{\textrm for \, all}\,\,y\in C\}.
$$
The cone $C$ is said to be \emph{pointed} if $C\cap (-C) = \{0\},$ and \emph{blunt} if the linear space generated
by $C$ is $\R^N$, i.e.\ $\linspan C = \R^N$.

\begin{cor}\label{mainNd1}
Let $\Phi = \{\varphi_k\}_{k=1}^M\in\calF^*$, and let $N\leq m\leq M$ be fixed. Then the following conditions are equivalent:
\begin{enumerate}
\item[{\rm (i)}]   $\Phi$ is strictly $m$-scalable .
\item[{\rm (ii)}]  There exists $I \subset [M]$ with $\#I = m$ such that $C(F(\Phi_{I}))$ is not pointed.
\item[{\rm (iii)}] There exists $I \subset [M]$ with $\#I = m$ such that $C(F(\Phi_{I}))^{\circ}$ is not blunt.
\item[{\rm (iv)}]  There exists $I \subset [ M]$ with $\#I = m$ such that the interior of $C(F(\Phi_{I}))^{\circ}$ is  empty.
\end{enumerate}
\end{cor}
\begin{proof}
(i)$\Slra$(ii). By Proposition \ref{p:F}, $\Phi$ is strictly $m$-scalable if and only if there exist $I\subset [M]$
with $\#I = m$ and a nonnegative $u\in\ker F(\Phi_I)\setminus\{0\}$ with $\|u\|_0 = m$. By~\cite[Lemma 2.10.9]{stwi70},
this is equivalent to the cone $C(F(\Phi_I))$ being not pointed. This proves that (i) is equivalent to (ii).

(ii)$\Slra$(iii). This follows from the fact that the polar of a pointed cone $C$ is blunt and vice versa, as long as
$C^{\circ \circ}=C$, see \cite[Theorem 2.10.7]{stwi70}. But in our case $C(F(\Phi_I))^{\circ \circ}=C(F(\Phi_I))$, see
\cite[Lemma 2.7.9]{stwi70}.

(iii)$\Sra$(iv). If $C(F(\Phi_I))^\circ$ is not blunt, then it is contained in a proper hyperplane of $\R^d$ whose
interior is empty. Hence, also the interior of $C(F(\Phi_I))^\circ$ must be empty.

(iv)$\Sra$(iii). We use a contra positive argument. Assume that $C(F(\Phi))^{\circ}$ is blunt. This is equivalent
to $\linspan C(F(\Phi))^{\circ} = \R^d$. But for the nonempty cone $C(F(\Phi))^{\circ}$ we have $\aff(C(F(\Phi))^{\circ})
= \linspan C(F(\Phi))^{\circ}$. Hence, $\aff(C(F(\Phi))^{\circ})=\R^d$, and so the relative interior of $C(F(\Phi))^{\circ}$
is equal to its interior, which therefore is nonempty.
\end{proof}

The main idea of the previous results is the characterization of ($m$-)scalability of $\Phi$ in terms of properties of
the convex polytopes $\co(F(\Phi_I))$. However, it seems more ``natural'' to seek  assumptions on the convex polytopes $\co(\Phi_I)$ that will ensure that $\co(F(\Phi))$ satisfy  the conditions in Theorem~\ref{poly}
hold.
Proposition~\ref{firstoctant}, which gives a condition on $\Phi$ that precludes it to be scalable, is a step in this direction.

Nonetheless, we address the related question of whether $F(\Phi)$ is a frame for $\R^d$ whenever $\Phi$ is a scalable frame for
$\R^N$. This depends clearly on the redundancy of $\Phi$ as well as on the map $F$. In particular, we finish this section
by giving a condition which ensures that  $F(\Phi)$ is always a frame for $\R^d$ when $M\geq d+1$. In order to prove this
result, we need a few preliminary facts.

For $x=(x_k)_{k=1}^{N}\in \R^N$ and $h=(h_k)_{k=1}^d \in \R^d$, we have that
\begin{equation}\label{poly2}
\ip{F(x)}{h} = \sum_{\ell=2}^{N}h_{\ell-1}(x_1^2 - x_{\ell}^2) + \sum_{k=1}^{N-1}\sum_{\ell=k+1}^{N}h_{k(N - 1 - (k-1)/2) +\ell -
1}x_{k}x_{\ell}.
\end{equation}
The right hand side of \eqref{poly2} is obviously a homogeneous polynomial of degree $2$ in $x_1, x_2, \hdots, x_N
. We shall denote the set of all polynomials of this form by $\boldsymbol{P}_{2}^N$. It is easily seen that $\boldsymbol{P}_{2}^N$ is isomorphic to the  subspace of real symmetric $N\times N$ matrices whose trace is $0$. Indeed, for each $N\geq 2$, and each $p\in\boldsymbol{P}_{2}^N$,
$$
p(x) = \sum_{\ell=2}^{N}a_{\ell-1}(x_1^2 - x_{\ell}^2) + \sum_{k=1}^{N-1}\sum_{\ell=k+1}^{N}a_{k(N - (k+1)/2) +\ell - 1}x_{k}x_{\ell},
$$
we have $p(x) = \<Q_px,x\>$, where $Q_p$ is the symmetric $N\times N$-matrix with entries
$$
Q_{p}(1,1) = \sum_{k=1}^{N-1}a_k, \qquad Q_{p}(\ell,\ell) = -a_{\ell-1}\quad\text{for }\ell = 2,3,\ldots,N
$$
and
$$
Q_{p}(k,\ell) = \frac 1 2 a_{k(N - (k+1)/2) +\ell - 1}\quad\text{for }k = 1,\ldots,N-1,\;\ell = k+1,\ldots,N.
$$
In particular, the dimension of $\boldsymbol{P}_{2}^N$ is $d=(N+2)(N-1)/2$.

\begin{prop}\label{dimpoly}
Let $M\geq d+1$ where $d=(N-1)(N+2)/2$, and $\Phi = \{\varphi_k\}_{k=1}^M\in\sca_{+}(d+1)\setminus\sca(d)$. Then
$F(\Phi)$ is a frame for $\R^d$.
\end{prop}
\begin{proof}
Let $I\subset [M]$, $\#I=d+1$, be an index set such that  $\Phi_I$ is strictly scalable. Assume that there exists $h\in\R^d$ such that $\<F(\varphi_k),h\> = 0$ for each $k\in I$. By \eqref{poly2} we conclude that $p_h(\vphi_k) = 0$ for all $k\in I$, where $p_h$ is the polynomial in $\boldsymbol{P}_{2}^N$ on the right hand side of \eqref{poly2}. Hence $\<Q_{p_h}\vphi_k,\vphi_k\> = 0$ for all $k\in I$. Now, we have
\begin{equation}\label{HS}
\<\vphi_k\vphi_k^T,Q_{p_h}\>_{HS} = \Tr(\vphi_k\vphi_k^TQ_{p_h}) = \<Q_{p_h}\vphi_k,\vphi_k\> = 0\quad\text{for all }k\in I.
\end{equation}
But as $\Phi_I$ is not $d$-scalable (otherwise, $\Phi\in\sca(d)$) it is not $m$-scalable for every $m\le d$. Thus, Proposition \ref{p:less_vectors} yields that
$$
\dim\linspan\{\vphi_k\vphi_k^T : k\in I\} = d+1.
$$
Equivalently, $\{\vphi_k\vphi_k^T : k\in I\}$ is a basis of the $(d+1)$-dimensional space $S_N$. Therefore, from \eqref{HS} we conclude that $Q_{p_h} = 0$ which implies $p_h = 0$ (since $p\mapsto Q_p$ is an isomorphism) and thus $h = 0$.

Now, it follows that $F(\Phi_I)$ spans $\R^d$ which is equivalent to $F(\Phi_I)$ being a frame for $\R^d$. Hence, so is $F(\Phi)$.
\end{proof}

\section{Topology of the Set of Scalable Frames}
\label{sec3}

In this section, we present some topological features of the set $\sca(M,N)$. Hereby, we identify frames in $\calF(M,N)$
with real $N\times M$-matrices as we already did before, see, e.g., \eqref{e:scfrm} in subsection \ref{subsec2.3}. Hence,
we consider $\calF(M,N)$ as the set of all matrices in $\R^{N\times M}$ of rank $N$. Note that under this identification
the order of the vectors in a frame becomes important. However, it allows us to endow $\fr(M,N)$ with the usual Euclidean
topology of $\R^{N\times M}$.

In \cite{kopt12} it was proved that $\sca(M,N)$ is a closed set in $\calF(M,N)$ (in the relative topology of $\calF(M,N)$).
The next proposition refines this fact.

\begin{prop}\label{p:closedness}
Let $M\geq m\geq N\geq 2$. Then $\sca(M,N,m)$ is closed in $\calF(M,N)$.
\end{prop}

\begin{proof}
We prove the assertion by establishing that the complement $\calF\setminus\sca(m)$ is open, that is, if
$\Phi = \{\varphi_{k}\}_{k=1}^{M}\in \fr$ is a frame which is not $m$-scalable, we prove that there exists $\varepsilon>0$
such that for any collection $\Psi = \{\psi_{k}\}_{k=1}^{M}$ of vectors in $\R^N$ for which
$$
\|\varphi_k - \psi_k\| < \varepsilon\quad\text{for all $k\in [M]$,}
$$
we have that $\Psi$ is a frame which is not $m$-scalable. Thus assume that $\Phi = \{\varphi_k\}_{k=1}^{M}$ is a frame
which is not $m$-scalable and define the finite set $\calI$ of subsets by
$$
\calI := \{I\subset [M] : \#I = m\}.
$$
By Proposition \ref{p:polycoro}, for each $I\in\calI$ there exists $y_I\in\bigcap_{k\in I}H^{+}(F(\varphi_k))$, that is,
$\min_{k\in I}\ip{y_I}{F(\varphi_k)} > 0$. By the continuity of the map $F$, there exists $\varepsilon > 0$ such that
for each $\{\psi_k\}_{k=1}^M\subset\R^N$ with $\|\psi_k - \varphi_k\| < \varepsilon$ for all $k\in [M]$ we still have
$\min_{k\in I}\ip{y_{I}}{F(\psi_k)} > 0$. We can choose $\varepsilon>0$ sufficiently small to guarantee that $\Psi =
\{\psi_k\}_{k=1}^{M} \in \fr$. Again from Proposition \ref{p:polycoro} we conclude that $\Psi$ is not $m$-scalable for
any $N\leq m\leq M$. Hence, $\sca(m)$ is closed in $\fr$.
\end{proof}

The next theorem is the main result of this section. It shows that the set of scalable frames is nowhere dense in the
set of frames unless the redundancy of the considered frames is disproportionately large.

\begin{thm}\label{bdMlessd}
Assume that $2\le N\le M < d+1 = N(N+1)/2$. Then $\sca(M,N)$ does not contain interior points. In other words, for the
boundary of $\sca(M,N)$ we have
$$
\partial\sca(M,N) = \sca(M,N).
$$
\end{thm}

For the proof of Theorem \ref{bdMlessd} we shall need two lemmas. Recall that for a frame $\Phi = \{\varphi_k\}_{k=1}^M\in\fr$
we use the notation
$$
X_{\Phi} = \{\varphi_i\varphi_i^T : i\in [M]\}.
$$

\begin{lem}\label{l:not_all}
Let $\{\varphi_k\}_{k=1}^M\subset\R^N$ be such that $\dim\linspan X_{\Phi} < \frac{N(N+1)}{2}$. Then there exists
$\varphi_0\in\R^N$ with $\|\varphi_0\| = 1$ such that $\varphi_0\varphi_0^T\notin\linspan X_\Phi $.
\end{lem}

\begin{proof}
Assume the contrary. Then each rank-one orthogonal projection is an element of $\linspan X_\Phi $. But by the spectral
decomposition theorem every symmetric matrix in $\R^{N\times N}$ is a linear combination of such projections. Hence,
$\linspan X_{\Phi} $ coincides with the linear space $S_N$ of all symmetric matrices in $\R^{N\times N}$. Therefore,
$$
\dim\linspan X_{\Phi}  = \frac{N(N+1)}{2},
$$
which is a contradiction.
\end{proof}

The following lemma shows that for a generic $M$-element set $\Phi=\{\varphi_i\}_{i=1}^M\subset\R^N$ (or matrix in $\R^{N\times M}$,
if the $\varphi_i$ are considered as columns) the subspace $\linspan X_{\Phi}$ has the largest possible dimension.

\begin{lem}\label{l:dense}
Let $D := \min\{M,N(N+1)/2\}$. Then the set
$$
\big\{\Phi\in\R^{N\times M} : \dim\linspan X_{\Phi} = D\big\}
$$
is dense in $\R^{N\times M}$.
\end{lem}

\begin{proof}
Let $\Phi = \{\varphi_i\}_{i=1}^M\in\R^{N\times M}$ and $\varepsilon > 0$. We will show that there exists $\Psi =
\{\psi_i\}_{i=1}^M\in\R^{N\times M}$ with $\|\Phi - \Psi\| < \varepsilon$ and $\dim\linspan X_{\Psi}  = D$. For this, set
$\mathcal{W} := \linspan X_{\Phi}$ and let $k$ be the dimension of $\mathcal{W}$. If $k=D$, nothing is to prove. Hence,
let $k < D$. Without loss of generality, assume that $\varphi_1\varphi_1^T,\ldots,\varphi_k\varphi_k^T$ are linearly
independent. By Lemma \ref{l:not_all} there exists $\varphi_0\in\R^N$ with $\|\varphi_0\| = 1$ such that
$\varphi_0\varphi_0^T\notin\mathcal{W}$. For $\delta > 0$ define the symmetric matrix
$$
S_\delta := \delta\left(\varphi_{k+1}\varphi_0^T + \varphi_0\varphi_{k+1}^T\right) + \delta^2\varphi_0\varphi_0^T.
$$
Then there exists {\em at most} one $\delta > 0$ such that $S_\delta\in\mathcal{W}$ (regardless of whether
$\varphi_{k+1}\varphi_0^T + \varphi_0\varphi_{k+1}^T$ and $\varphi_0\varphi_0^T$ are linearly independent or not).
Therefore, we find $\delta > 0$ such that $\delta < \varepsilon /M$ and $S_\delta\notin\mathcal{W}$. Now, for $i\in [M]$ put
$$
\psi_i :=
\begin{cases}
\varphi_i &\text{if }i\neq k+1\\
\varphi_{k+1} + \delta\varphi_0 &\text{if }i=k+1
\end{cases}
$$
and $\Psi := \{\psi_i\}_{i=1}^M$. Let $\lambda_1,\ldots,\lambda_{k+1}\in\R$ such that
$$
\sum_{i=1}^{k+1}\lambda_i\psi_i\psi_i^T = 0.
$$
Then, since $\psi_{k+1}\psi_{k+1}^T = \varphi_{k+1}\varphi_{k+1}^T + S_\delta$, we have that
$$
\lambda_{k+1}S_\delta = -\sum_{i=1}^{k+1}\lambda_i\varphi_i\varphi_i^T\in\mathcal{W},
$$
which implies $\lambda_{k+1} = 0$ and therefore also $\lambda_1 = \ldots = \lambda_k = 0$. Hence, we have
$\dim\linspan X_\Psi = k+1$ and $\|\Phi - \Psi\| < \varepsilon/M$. If $k = D-1$, we are finished. Otherwise, repeat
the above construction at most $D - k - 1$ times.
\end{proof}

\begin{rem}
For the case $M\ge N(N+1)/2$, Lemma {\rm\ref{l:dense}} has been proved in {\rm\cite[Theorem 2.1]{cc13}}. In the
proof, the authors note that $X_\Phi$ spans $S_N$ if and only if the frame operator of $X_\Phi$ {\rm (}considered
as a system in $S_N${\rm )} is invertible. But the determinant of this operator is a polynomial in the entries of
$\vphi_i$, and the complement of the set of roots of such polynomials is known to be dense.
\end{rem}

{\sc  Proof of Theorem }\ref{bdMlessd}.
Assume the contrary. Then, by Lemma \ref{l:dense}, there even exists an interior point $\Phi = \{\varphi_i\}_{i=1}^M\in\sca(M,N)$
of $\sca(M,N)$ for which the linear space
$
\mathcal{W} := \linspan X_{\Phi} $
has dimension $M$. Since $\Phi$ is scalable, there exist $c_1,\ldots,c_M\ge 0$ such that
$$
\sum_{i=1}^M c_i\varphi_i\varphi_i^T = \Id.
$$
Without loss of generality we may assume that $c_1 > 0$.

By Lemma \ref{l:not_all} there exists $\varphi_0\in\R^N$ with $\|\varphi_0\| = 1$ such that $\varphi_0\varphi_0^T\notin\mathcal{W}$.
As in the proof of Lemma \ref{l:dense}, we set
$$
S_\delta := \delta\left(\varphi_1\varphi_0^T + \varphi_0\varphi_1^T\right) + \delta^2\varphi_0\varphi_0^T.
$$
Then, for $\delta > 0$ sufficiently small, $S_\delta\notin\mathcal{W}$ and $\Psi := \{\varphi_1 + \delta\varphi_0,\varphi_2,
\ldots,\varphi_M\}\in\sca(M,N)$. Hence, there exist $c_1',\ldots,c_M'\geq 0$ such that
$$
\sum_{i=1}^M c_i\varphi_i\varphi_i^T = \Id = c_1'(\varphi_1 + \delta\varphi_0)(\varphi_1 + \delta\varphi_0)^T
+ \sum_{i=2}^Mc_i'\varphi_i\varphi_i^T = \sum_{i=1}^Mc_i'\varphi_i\varphi_i^T + c_1'S_\delta.
$$
This implies $c_1'S_\delta\in\mathcal{W}$, and thus $c_1' = 0$. But then we have
$$
c_1\varphi_1\varphi_1^T + \sum_{i=2}^M(c_i - c_i')\varphi_i\varphi_i^T = 0,
$$
which yields $c_1 = 0$ as the matrices $\varphi_1\varphi_1^T,\ldots,\varphi_M\varphi_M^T$ are linearly independent. A contradiction.\hfill\qed

\section*{ACKNOWLEDGMENTS}

G.~Kutyniok acknowledges support by the Einstein Foundation Berlin, by Deutsche Forschungsgemeinschaft
(DFG) Grant KU 1446/14, and by the DFG Research Center {\sc Matheon} ``Mathematics for key technologies''
in Berlin. F.~Philipp is supported by the DFG Research Center {\sc Matheon}. K.~A.~Okoudjou  was supported
by ONR grants N000140910324 and N0001\-40910144, by a RASA from the Graduate School of UMCP and by the
Alexander von Humboldt foundation. He would also like to express his gratitude to the Institute for
Mathematics at the Universit\"at Osnabr\"uck and the Institute of Mathematics at the Technische Universit\"at
Berlin for their hospitality while part of this work was completed.

redpajama_set_name: RedPajamaArXiv


text:
NBA 2K11 es un videojuego de baloncesto, desarrollado por Visual Concepts y distribuido por 2K Sports, lanzado el 5 de octubre de 2010 para las plataformas PC, PlayStation 3, Xbox 360, PlayStation 2 y PSP, lanzándose también una versión para Wii el 10 de octubre de ese año. Michael Jordan fue la imagen de la portada del videojuego.

Jugabilidad
El juego incluye varias novedades respecto a sus predecesores, involucrando a la figura de Michael Jordan en el denominado "Jordan's challenge", donde el jugador debe superar desafíos relacionados con la carrera del propio Jordan.

El juego también permite jugar con equipos clásicos, tanto en amistosos como torneos, incluyendo también los estadios de la época de dichos equipos.

Debido a su peculiar Jugabilidad el videojuego ha recibido numerosas críticas, pero algunos jugadores opinan que estas son infundadas y que su propósito es desprestigiar en primer lugar el videojuego y en segundo lugar la saga en la que se incluye.

Banda sonora del videojuego

  Art vs. Science - "Hollywood"
  Big Boi - "Shutterbog"
  Big Rock Candy Mountain - "Rocketship"
  Cassidy - "Game Time"
  Children Collide - "Skeleton Dance"
  Dan Black - "Symphonies"
  Delorean - "Deli"
  Drake - "Over"
  Dux Jones - "Pourin' It On"
  Failsafe - "Hope"
  Failsafe - "Only if we Learn"
  Høgni Lisberg - "Bow Down"

  Kidz in Space - "Downtime"
  Middleman - "It's Not Over Yet"
  Ron Artest - "Champion"
  Sean Price - "Better Than You"
  Snoop Dogg - "NBA 2K Theme"
  The Alan Parsons Project - "Sirius"
  The Brunettes - "Red Rollerskates"
  The Chicharones - "Little by Little"
  The Constellations - "We're Here to Save the Day"
  The Russian Futurists - "Paul Simon"
  The Russian Futurists - "Precious Metals"
  Two Door Cinema Club - "I Can Talk"

NBA 2K
Videojuegos de 2010
Videojuegos para Windows
Videojuegos para PlayStation 3
Videojuegos para Xbox 360
Videojuegos para PlayStation 2
Videojuegos para Wii
Videojuegos para PlayStation Portable
Videojuegos desarrollados en República Checa
Michael Jordan
Videojuegos de un solo jugador y de multijugador


text:
KLJV oder KLJV-FM (Branding: "K-Love") ist ein US-amerikanischer nichtkommerzieller religiöser Hörfunksender aus Scottsbluff im US-Bundesstaat Nebraska. KLJV sendet auf der UKW-Frequenz 88,3 MHz. Eigentümer und Betreiber ist die Educational Media Foundation .

Einzelnachweise

Weblinks
 Website von KLJV 88,3 (K-Love)

Nichtkommerzieller Lokalfunk
Christlicher Hörfunksender (Vereinigte Staaten)
Christentum (Nebraska)
KLJV
Scottsbluff
Medienunternehmen (Nebraska)
Organisation (Scotts Bluff County)


text:
Kasteel Hoogenweerth, ook Huis De Hogenweert, is een kasteelachtig buitenhuis, gelegen op de rechteroever van de Maas ten westen van de buurt Heugem in de Nederlandse stad Maastricht.

Geschiedenis
Het huis werd al vermeld in de 15e eeuw onder de naam Houweert. In de loop der eeuwen was het in bezit van een aantal burgemeesters- en schepenengeslachten: Van Buel, Prenten, Swaelen en Vaes. De eigenaren van het circa 10 bunder grote landgoed moesten van de opbrengst van het land jaarlijks 54 vaten rogge afstaan (of 208 gulden betalen) aan het klooster Beyart.

Het huidige kasteel is gebouwd door de Maastrichtse schepen en stadssecretaris Antonius Vaes (1543-1579). Hij liet de westvleugel van het kasteel vernieuwen in Maaslandse renaissancestijl. Zijn zoon Andreas Vaes, eveneens stadsklerk, erfde het huis en liet het renoveren en uitbreiden. Het middengedeelte kwam in het midden van de 18e eeuw tot stand in opdracht van Joannes Vaes. In 1785 liet de weduwe Vaes, geboren De Bounam de Ryckholt, het landgoed na aan haar nicht Maria de Selys de Fanson, die gehuwd was met R.C. van Cammingha.

In de 19e eeuw kwam het kasteel achtereenvolgens in bezit van de families Coenegracht, Straetmans en Regout. Marie Straetmans, gehuwd met Amedée Tielens, verkocht het kasteel in 1904 aan Petrus III Regout (1854-1928), die er met zijn vrouw Louisa Berger (1853-1932) en hun twee volwassen kinderen Bertha (1877-1969) en Pierre (1882-1967) ging wonen. Het kasteel werd fors uitgebreid in dezelfde stijl. Bertha trouwde in 1908 met Max von Scheibler en verhuisde naar Duitsland. Enkele jaren na de dood van haar man in 1935 keerde zij terug naar Nederland en bleef tot haar dood in 1969 bij haar ongehuwde broer Pierre op Hoogenweerth wonen.

Na de dood van Bertha verkochten de erfgenamen het landgoed in 1970 aan de provincie Limburg. Het landschap rondom het kasteel werd in deze periode sterk aangetast door zand- en grindwinning, waardoor in de omgeving enorme waterplassen ontstonden. Door de Maaskanalisatie verdween een stuk van het kasteelpark. De gebouwen raakten steeds verder in verval. In 1975 werd het kasteel vrijwel verwoest door een grote brand, maar de provincie Limburg liet het gebouw grondig restaureren, waarbij het interieur gemoderniseerd werd.

In 1992 werd het kasteel aangekocht door de zakenman Paes, die het opnieuw liet opknappen. In 2020 werd de exploitatie overgenomen door de Kerkraadse Van Melick Groep. Het kasteel is in gebruik als hotel-restaurant. De tien hotelsuites zijn gevestigd in de bijgebouwen ("koetshuis"). Het hoofdgebouw is te huur voor zakelijke bijeenkomsten, bruiloften en partijen. Het kasteel is een officiële huwelijkslocatie van de gemeente Maastricht.

Beschrijving

Exterieur

Het rechthoekige hoofdgebouw heeft in- en uitzwenkende topgevels en een vierkante traptoren met een ingesnoerde spits. De laat-17e-eeuwse zuidgevel, met banden van baksteen en Limburgse mergel, hoekblokken en een daklijst met consoles, is in de stijl van de Maaslandse renaissance. In 1754 is het huis door Andreas Vaes aan de noordzijde uitgebreid. Uit die tijd dateert waarschijnlijk ook de als een erker uitgebouwde kapel en de barokpoort. De poort is gedecoreerd met het alliantiewapen van de families Bemelmans en Bernard. In 1821 is het huis door de familie Coenegracht sterk verbouwd en uitgebreid, waarbij tevens delen van de westgevel werden gemoderniseerd. Het gebouw heeft daardoor tevens een aantal neorenaissance en neoclassicistische elementen. Sinds de laatste restauratie is het kasteel geel en grijs geschilderd.

Aan de noordzijde bevindt zich een langgerekt bijgebouw, tegenwoordig aangeduid als 'koetshuis'. Het uit de 19e eeuw daterende bouwwerk is in de kleur ossenbloed geschilderd. Aan de westzijde ligt een groot terras aan de Maas, aan de oostzijde een ommuurde tuin. Het huis is omgeven door een 4,5 hectare groot park, dat op een schiereiland tussen de Maas en de Hoge Weerd ligt (in feite ligt het landgoed in het winterbed van de rivier en is de Hoge Weerd de winterdijk). Aan de noordzijde van dit schiereiland ligt de Pietersplas (een grindgat) met de jachthaven Maastricht Marina. Aan de zuidzijde ligt de recreatieplas Oost-Maarland, die eveneens door grindwinning is ontstaan. In het park bevindt zich een monumentale beuk uit ca. 1825 met een omtrek van 6 m.

Interieur
Hoewel het interieur na het vertrek van de laatste bewoner in 1969 en de brand in 1975 zwaar te lijden had, zijn er toch vrij veel authentieke elementen bewaard gebleven. Op de begane grond liggen twee grote zalen, waarvan er een in gebruik is als feestzaal, en een voormalige kapel. Deze laatste heeft een fraai gestukadoord plafond in Lodewijk XV-stijl. Diverse schoorsteenmantels dateren eveneens uit de 18e eeuw. Eén schouw heeft een 17e-eeuwse houten mantel, die echter van elders afkomstig is. Enkele kamers bezitten gestukadoorde plafonds met ruitvormige patronen en supraportes met portretbustes in reliëf uit het eerste kwart van de 19e eeuw.

Zie ook
 Kleine Weerd - nabijgelegen natuurgebied in de uiterwaarden van de Maas

Externe link
 Website hotel-restaurant De Hoogenweerth
 Huis Hoogenweerth op wigosite.nl

Hoogenweerth
Landgoed in Limburg (Nederland)
Rijksmonument in Maastricht
Hotel in Maastricht
Maastricht-Zuidoost
Renaissancebouwwerk in Nederland


An excavator with a clawed scoop made short order of an iconic East Washington County restaurant Friday afternoon.
It only took several hours to tear down the Mad Greek Deli, which first opened its doors in 1977, leaving only a small portion of the 185th Avenue and West Union Road restaurant intact.
The eatery was famed for its gyros as well as its namesake sandwich, a behemoth sub that contained generous portions of four different types of meat topped with olives on toothpicks.
A sign that once stood atop the deli counter made it clear to customers that what some may call ranch fries or jo jo potatoes were nothing of the sort. They were Greek fries and Greek fries only!
Clientele at the less then 4,000-square-foot restaurant, which once served as a corner grocery store, consisted of "bicyclists, bikers and Intel employees," an employee once said.
In January 2014, owner Pantelis 'Pondo' Kosmas announced he would close the Mad Greek Deli, telling a reporter for the Beaverton Valley Times: "The building is 115 years old and has finally gotten the best of me."
The Mad Greek Deli and the building catty-corner from it (which contains the Rock Creek Corner restaurant) were long landmarks of the area long before West Union Village complex (containing the Albertson's store) was built.
The restaurant officially shuttered its doors in January 2015.
Then in February 2016, Pondo Kosmas, a man described as friendly, generous and "larger than life," died of a sudden and unexpected brain hemorrhage at age 49. A short time later, a vigil was held at what was by then a boarded-up Mad Greek with vigil-goers remembering the Aloha High School graduate.
They tied balloons to the front of the building and wrote heartfelt messages using Sharpie pens on the restaurant's aging siding.
But all that changed quickly after noon on Friday as machinery ripped out the remaining trees on the property before taking large chunks from the building itself.
The building had a long and storied history. According to Donald R. Nelson's book, 'Around Bethany,' the structure previously housed the Valley West Grocery Store before its 1977 purchase by George Athanaskis. Before that, it was the home of the Bethany General Merchandise Store.
As dusk began to descend at 4 p.m. on Friday, all that was left besides a tiny piece of the structure still standing was a pile of debris. By late Monday afternoon, that final structure near 185th Avenue was also taken down.
The property is slated for future development.


text:
Epicauta triquetra är en skalbaggsart som beskrevs av Werner 1958. Epicauta triquetra ingår i släktet Epicauta och familjen oljebaggar. Inga underarter finns listade i Catalogue of Life.

Källor

Oljebaggar
triquetra


FREE Online Youngs Literal Translation. 1 Kings Chapter 1:1-53.
1:4 and the young woman `is' very very fair, and she is to the king a companion, and serveth him, and the king hath not known her.
1:6 and his father hath not grieved him `all' his days, saying, `Wherefore thus hast thou done?' and he also `is' of a very good form, and `his mother' bare him after Absalom.
1:8 and Zadok the priest, and Benaiah son of Jehoiada, and Nathan the prophet, and Shimei, and Rei, and the mighty ones whom David hath, have not been with Adonijah.
1:10 and Nathan the prophet, and Benaiah, and the mighty ones, and Solomon his brother, he hath not called.
1:11 And Nathan speaketh unto Bath-Sheba, mother of Solomon, saying, `Hast thou not heard that Adonijah son of Haggith hath reigned, and our lord David hath not known?
1:13 go and enter in unto king David, and thou hast said unto him, Hast thou not, my lord, O king, sworn to thy handmaid, saying, Surely Solomon thy son doth reign after me, and he doth sit on my throne? and wherefore hath Adonijah reigned?
1:19 and he sacrificeth ox, and fatling, and sheep in abundance, and calleth for all the sons of the king, and for Abiathar the priest, and for Joab head of the host -- and for Solomon thy servant he hath not called.
1:23 and they declare to the king, saying, `Lo, Nathan the prophet;' and he cometh in before the king, and boweth himself to the king, on his face to the earth.
1:25 for he hath gone down to-day, and doth sacrifice ox, and fatling, and sheep, in abundance, and calleth for all the sons of the king, and for the heads of the host, and for Abiathar the priest, and lo, they are eating and drinking before him, and they say, Let king Adonijah live!
1:28 And king David answereth and saith, `Call for me for Bath-Sheba;' and she cometh in before the king, and standeth before the king.
1:32 And king David saith, `Call for me for Zadok the priest, and for Nathan the prophet, and for Benaiah son of Jehoiada;' and they come in before the king.
1:40 And all the people come up after him, and the people are piping with pipes, and rejoicing -- great joy, and the earth rendeth with their voice.
1:45 and they anoint him -- Zadok the priest and Nathan the prophet -- for king in Gihon, and are come up thence rejoicing, and the city is moved; it `is' the noise that ye have heard.
1:50 and Adonijah feareth because of Solomon, and riseth, and goeth, and layeth hold on the horns of the altar.


text:
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Kobe Consulting is a subsidiary of the Japanese firm Japan Export Co. Ltd (Japan, Kobe), a young company that has been rapidly developing in the field of international trade and services to facilitate the entry of Japanese companies into the global market for over 10 years.
Kobe Consulting LLC is the representative of Japan Export Co. Ltd in the Russian Federation. Provides legal and intermediary services, services in the selection and provision of personnel, consulting services on personnel records management and the Labor Code of the Russian Federation.
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General Director: Baranov Kirill Sergeevich
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redpajama_set_name: RedPajamaCommonCrawl


text:
C BY ROMAIN GAUTHIER TITANIUM EDITION TWO
MOVEMENTIn-house, hand-wound movement
MATERIALBlack Grade 5 titanium
FUNCTIONSHours, minutes and small seconds
LIMITED38 pieces
PRICE 38.000 CHF + TAX ◆ SOLD OUT ◆
After the launch of the titanium edition one, Romain Gauthier presents C by Romain Gauthier Titanium Edition Two which reveals an even more assertive character with a black titanium case and dial.
Reflection of Romain's creative freedom with a modern and youthful design, C by Romain Gauthier is the result of more than 17 years of know-how acquired through the development of the brand and its manufacture.
Technical in nature, casual in style and free in spirit, the Freedom collection has enabled the creation of this piece. The importance of the C in its name lies in this approach of creation, referring to the continuum, to continuity in space-time and to continuity in the broadest sense. A vision of the future for a timepiece which is part of Romain Gauthier's philosophy, and which opens the door to new horizons.
During its creation, it was clear to Romain that the case had to be in harmony with the movement. It had to be contemporary and uncluttered. But not only that – comfort, ergonomics and the choice of materials also contributed to the design of this case entirely made out of black Grade 5 titanium. The dial, also in black Grade 5 titanium, adds to the consistency of the piece and evokes a sense of continuity, as there is no circle completes the time indication.
Inspired by the finger bridges style, the design of the movementfollows the watchmaking history of the Vallée de Joux, with a modern approach, reflecting Romain's vision of the evolution of tradition.
Romain Gauthier presents the second edition of the caliber in titanium – timeless thanks to the choice of colors and textures with subtle red highlights. C by Romain Gauthier Titanium Edition Two is a 38-piece limited edition, engraved "1 of 38" on the back of each movement.
Chronomètre à Résonance – The signature of F.P. Journe


text:
Posted on November 22, 2019 November 22, 2019 Books
A New Art of Brewing Beer, Ale, and Other Sorts of Liquors: So as to Render Them More Healthfull to the Body and Agreeable to Nature
by Thomas Tryon
The young Horatio Alger heroes often sold newspapers or delivered telegrams, a reminder of how technology has moved on. Alger's tales created youthful heroes whose persistence and pluck triumphed over enormous odds, often having to educate themselves by a flickering candle and late at night. But they hoped for better things and in the Alger novels their diligence and hard work won the day and they ended up getting the educations they deserved and the success that their exemplary morality earned. The reader will find this prototypical Alger story both a good read and food for thought in an era when the technology has indeed moved on but the challenges have remained.
The introduction is provided by Dr. Wallace Boston, President of the American Public University System and a Horatio Alger enthusiast.
Posted on September 27, 2018 September 27, 2018 Available for Purchase, Books
Food: Fuel for the Human Engine: What to Buy, How to Cook It, How to Eat It
by Eugene Lyman Fisk M. D.
Eugene Lyman Fisk, M.D. was a lifelong New Yorker born in Brooklyn in 1867. He attended New York University Medical College, where he graduated with distinction in 1888. Afterwards he remained in Brooklyn to practice medicine, subsequently becoming head of the medical division of various life insurance companies, including the Equitable Life Assurance Society, the Provident Savings Life Assurance Society of New York, and the Postal Life Assurance Company in 1910. During this time he was known for his strong advocacy of regular medical check-ups. At the time, many people avoided doctors, in fear of them being quacks, and as their cures sometimes proved worse than the pain. He also spoke out against smoking cigarettes, finding absolutely no evidence that it provided any benefit to the body, a popular delusion.
He became known as one of the fathers of preventive medicine and was a fellow of the American Medical Association, and member of numerous societies, such as the American Public Health Association, the National Tuberculosis Association, American Eugenics Society, American Heart Association, New York Academy of Sciences, and American Economic Association. Surprisingly, in 1931 he died suddenly, while in Germany in 1931 to examine museum exhibits on public health, at the relatively early age of 64.
Posted on March 31, 2018 Available for Purchase, Books
Braxton's Practical Cook Book: Prepared for Economy, Family and Hotel Use
by G. F. Braxton
George F. Braxton was a renowned chef, who, among other places, worked at The Algonquin Resort during the late 1800s. Chef Braxton is thought to be the first African-American to lead a kitchen in a luxury resort. The Algonquin Resort began in 1889 in St. Andrews, New Brunswick, Canada, and still exists today as a luxury retreat. Sadly, not a great amount of detail is known about Braxton's life. He was born in Virginia during the late 1850s or early 1860s. He became the Chef at Wellesley College from 1883 to at least 1886. He led the Resort in Canada during the late 1800s, and it appears that he had moved to Massachusetts around 1900. By then he was widowed, but was remarried to Rose McBride in 1901. He opened up a restaurant in Cambridgeport, Massachusetts around November 1901. It does not appear that he had children. Not much of his life is known afterwards, but the Algonquin Resort recently renamed their restaurant Braxton's in honor of his memory.
Posted on November 1, 2017 Available for Purchase, Books
The Little Confectioner: 19th Century Candy and Cake
by H. Hueg
Herman Hueg wrote four books on confections and baking, including Ornamental Confectionery and the Art of Baking in All its Branches (1905), and Book of Designs for Bakers and Confectioners (1896). Hueg was a renounced baker and confectioner. He expanded his reach by moving into selling tools and other implements for bakers to help replicate the skilled work, such as molds and stencils. This approach is taken in this volume, which begins with a series of recipes for sugar spinning, caramels, nut bars, taffy, ice cream, bonbons, syrups and more. The latter portion of the book has several pages dedicated to interesting baking implements, which are nicely illustrated.
Posted on February 1, 2017 Available for Purchase, Books
Productive Bee-Keeping Modern Methods of Production and Marketing of Honey: Lippincott's Farm Manuals
by Frank C. Pellett
Lippincott's developed a series of manuals regarding agricultural production, including this volume on beekeeping. Among other things, it offers a historical look at apiculture, the practice of human harvesting of products from honey bee colonies, as well as its marketing methodology. Beekeeping has quite a history, dating back to at least 15,000 years ago.
The story of J.B. Lippincott & Co. offers a look at the complexities of the publishing industry. J.B. Lippincott & Co. was an American publishing house established in 1836 by Joshua Ballinger Lippincott, which still exists today as Lippincott Williams & Wilkins, which itself is an imprint of the publishing conglomerate, Wolters Kluwer, and focuses on technical journals. Initially J.B. Lippincott & Co. published Bibles and other religious materials, before expanding into fiction, almanacs, medical and other books. Later, Lippincott's Monthly Magazine was issued, from 1868-1914 and offered novels, short stories, opinion pieces and other writings. In 1978, Lippincott's was acquired by Harper & Row, which was then acquired by Wolters Kluwer in 1990.
business folkways food nature
Old London Taverns: Historical, Descriptive, and Reminiscent
by Edward Callow
In February 1900, a journal review of Old London Taverns commented that the author was annoyed by mistakes in recounting pub history. So he embarked on this chronicle:
"He tells us of various taverns, chop-houses, bakers', butchers', and kindred topics of considerable variety, places both new and old. He has done good service in putting together these facts, which have, indeed, a great tendency to get forgotten or confused. [As an example]… Ye Olde Cheshire Cheese' is, perhaps, the doyen of London taverns. Herrick speaks of the 'Cheese,' along with the Triple Tun' (no longer a tavern), in writing to Ben Jonson. This building, of course, perished in the Fire, but its successor has seen guests as famous—Pope, Congreve, Samuel Johnson, Goldsmith, and in later days Charles Dickens, Mark Lemon, and Thomas Hood. It remains much the same, though the ancient simplicity of its bill-of-fare has disappeared. Mr. Callow's book is one to be commended both for its text and its illustrations."
This edition is dedicated to John Hamill, whose researches into the beginnings of Freemasonry have made him something of an authority about the rites that the ancient taverns sheltered.
architecture Europe folkways food
Posted on January 22, 2016 February 15, 2016 Available for Purchase, Books
Poverty in America: Urban and Rural Inequality and Deprivation in the 21st Century
Max J. Skidmore
Poverty in America too often goes unnoticed, and disregarded. This perhaps results from America's general level of prosperity along with a fairly widespread notion that conditions inevitably are better in the USA than elsewhere. Political rhetoric frequently enforces such an erroneous notion: "the poor live better in America than the middle class elsewhere," "America has the best health care in the world," "income inequality is a sign of 'freedom'," and the like. With American poverty increasing, social mobility decreasing, and income inequality growing it has become urgent that our society direct its attention to poverty as one of the country's most troublesome issues. Poverty and Public Policy helps to focus that attention worldwide; this book, Poverty in America will help to emphasize the issue in this country.
Max J. Skidmore (Ph.D., University of Minnesota) teaches at the University of Missouri-Kansas City, where he is University of Missouri Curators' Professor of Political Science, and Thomas Jefferson Fellow. He has been Distinguished Fulbright Lecturer in India, where he was Director of the American Studies Research Centre in Hyderabad, and has been Senior Fulbright Scholar at the University of Hong Kong. He has published over two dozen works on numerous topics, including Social Security and its Enemies (1999), Securing America's Future: A Bold Plan to Preserve and Expand Social Security (2008), Bulwarks Against Poverty: Social Security, Medicare, and the Affordable Care Act (2014), and Presidents, Pandemics, and Politics (forthcoming, 2016).
food history original policy


text:
Agreement and Plan of Merger - Goldman Sachs Group Inc. and Goldman Sachs Group LP
S&C Draft of April 20, 1999
AGREEMENT AND PLAN OF MERGER
AGREEMENT AND PLAN OF MERGER, dated as of May __, 1999,
pursuant to Section 263 of the General Corporation Law of the State of Delaware
and Section 17-211 of the Delaware Revised Uniform Limited Partnership Act,
between THE GOLDMAN SACHS GROUP, INC., a Delaware corporation ('GS Inc.'), and
THE GOLDMAN SACHS GROUP, L.P., a Delaware limited partnership (the 'Merging
Entity').
WITNESSETH that:
WHEREAS, prior to the effectiveness of the Merger, GS Inc.
shall have acquired all of the partnership interests in the Merging Entity
including all of the interests in profits and capital of the Merging
Entity; and
WHEREAS, each of the parties hereto desires that the Merging
Entity merge (the 'Merger') with and into GS Inc. as hereinafter specified with
GS Inc. being the surviving corporation;
NOW, THEREFORE, the parties to this Agreement, in
consideration of the mutual covenants, agreements and provisions hereinafter
contained, do hereby prescribe the terms and conditions of the Merger and mode
of carrying the same into effect as follows:
FIRST: At the Effective Time (as hereinafter defined), the
Merging Entity shall be merged with and into GS Inc., with GS Inc. being the
surviving entity.
SECOND: At the Effective Time, GS Inc. shall own all of the
partnership interests in the Merging Entity and shall be the only partner in the
Merging Entity other than GS Transitory LLC (which shall be a limited partner in
the Merging Entity without any partnership interest in the Merging Entity
including no interest in profits or capital of the Merging Entity), all of the
limited liability company interests in which are owned by GS Inc. and which will
be simultaneously merged with and into GS Inc.
THIRD: At the Effective Time, all of the partnership interests
of the Merging Entity will be canceled. GS Transitory LLC shall receive no
consideration in connection with the Merger. The shares of common stock of GS
Inc., par value $0.01 per share ('GS Inc. Common Stock'), that are issued and
outstanding immediately prior to the Effective Time shall be unaffected by the
Merger, except that shares of GS Inc. Common Stock owned by the Merging Entity
immediately prior to the Effective Time shall be canceled.
FOURTH: The terms and conditions of the Merger are as follows:
(a) the separate existence of the Merging Entity shall cease,
and GS Inc. shall possess all the rights, privileges, powers and
franchises of the Merging Entity, of a public as well as of a private
nature, and shall be subject to all of the restrictions, disabilities
and duties of the Merging Entity;
(b) all property of the Merging Entity, real, personal and
mixed, all debts due to the Merging Entity on whatever account and all
other things in action or belonging to the Merging Entity shall be
vested in GS Inc.;
(c) the title to any real estate vested by deed or otherwise
in the Merging Entity shall not revert or be in any way impaired, but
all rights of creditors therein and all liens thereon shall be
preserved unimpaired;
(d) all debts, liabilities, duties and other obligations of
the Merging Entity under any and all indentures, loan agreements,
revolving credit agreements, liquidity agreements, letters of credit
and reimbursement agreements, notes, guarantees or other agreements or
instruments to which the Merging Entity is a party or by which it is
bound shall attach to GS Inc. and may be enforced against
GS Inc. to the same extent as if said debts, liabilities and duties had
been incurred or contracted by GS Inc.;
(e) GS Inc. expressly assumes all debts, liabilities, duties
and other obligations of the Merging Entity under any and all
indentures, loan agreements, revolving credit agreements, liquidity
agreements, letters of credit and reimbursement agreements, notes,
guarantees or other agreements or instruments to which the Merging
Entity is a party or by which it is bound; and
(f) any claim existing or action or proceeding pending by or
against the Merging Entity may be prosecuted as if the Merger had not
taken place, or GS Inc. may be proceeded against or substituted in
place of the Merging Entity.
FIFTH: The Merger shall become effective upon the filing of a
Certificate of Merger with the Secretary of State of the State of Delaware or at
such other time as the parties may agree and as shall be stated in the
Certificate of Merger (the 'Effective Time').
SIXTH: The certificate of incorporation and by-laws of GS
Inc., as in effect immediately prior to the Effective Time, shall be the
certificate of incorporation and by-laws of the surviving corporation. The
directors of GS Inc. immediately prior to the Effective Time shall be the
directors of the surviving corporation.
SEVENTH: At any time prior to the Effective Time, this
Agreement may be amended, modified or terminated by the Board of Directors of GS
Inc. notwithstanding approval by the stockholders or partners of any of the
parties hereto.
EIGHTH: ALL RIGHTS AND OBLIGATIONS UNDER THIS AGREEMENT AND
PLAN OF MERGER SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF
THE STATE OF DELAWARE, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS.
IN WITNESS WHEREOF, the parties to this Agreement, pursuant to
the approval and authority duly given by the general partner and the Schedule II
limited partners of the Merging Entity and resolutions adopted by the Board of
Directors of GS Inc., have caused these presents to be executed by each party
hereto as the respective act, deed and agreement of each of said parties, as of
the date first written above.
THE GOLDMAN SACHS GROUP, L.P.
By:  The Goldman Sachs Group, Inc., as
By:_______________________________
Name:    Gregory K. Palm
Title:   General Counsel
THE GOLDMAN SACHS GROUP, INC.
By his signature below, the undersigned certifies that no shares of stock of The
Goldman Sachs Group, Inc. were issued prior to the adoption by the Board of
Directors of The Goldman Sachs Group, Inc. of the resolution approving the
Agreement and Plan of Merger.
Name:    James B. McHugh
Title:   Assistant Secretary


text:
Research Proposes New Concepts in IP3 Receptor Plasticity
ON2019-12-06TAG: ShanghaiTech UniversityCATEGORY: SIAIS
In November, SIAIS Professor Katsuhiko Mikoshiba and Research Associate Professor Kozo Hamada of Cell Calcium Signaling laboratory published a review paper entitled 'IP3 Receptor Plasticity Underlying Diverse Functions' in Annual Review of Physiology. The paper reviews recent progress on the IP3 receptor structure and function, and the authors propose a new concept of how protein plasticity within IP3 receptors would enable it to regulate diverse functions at cellular microdomains.
In the past 40 years, from its discovery to recent progress, numerous studies have demonstrated that IP3 receptors mediate diverse functions at cellular microdomains, including organelle-contact sites between mitochondria and endoplasmic reticulum, and its aberrant regulation results in a variety of human diseases, such as spinocerebellar ataxia. Recent cryo-electron microscopy and X-ray crystallography resolved IP3 receptor structures and have begun to integrate with diverse microdomain functions. This review highlights recent research progress on the IP3 receptor structure and function, and the authors provide a novel model of how these structural plasticity mechanisms triggered by dynamic transformations of the IP3 receptor assembly at each microdomain, including Ca2+-dependent regulation, binding proteins, and posttranslational modifications, are involved in state-dependent properties of locally diverse functions.
Drs. Mikoshiba and Hamada both joined SIAIS in April 2019, after conducting calcium signaling researches at the University of Tokyo and RIKEN in Japan for 20 years. Their research focuses on the cellular and molecular mechanism of calcium signaling in the normal and disease states.
Read more at: https://www.annualreviews.org/doi/abs/10.1146/annurev-physiol-021119-034433
(A) A model for transformations of the IP3 receptor. On the left is a head-to-head arrangement of tetrameric IP3 receptor. Ca2+-dependent structural changes that should enable binding proteins and/or modifying enzymes to access inside IP3 receptors.
(B) Ca2+ waves or oscillation should determine structural plasticity of IP3 receptors at each microdomain.
Features Global School of Physical Science and Technology School of Life Science and Technology School of Creative and Arts Published Research Voices School of Information Science and Technology School of Entrepreneurship and Management Institute of Mathematical Sciences iHuman Institute SIAIS


the changes and indicates from where they can be pulled.
by visiting the repository named by <url>.
you are asking to be pulled.
local name, a colon :, and its remote name.
release and your master, to pull it from your public repository.


text:
How Murfreesboro City, Rutherford County schools scored on Tennessee's report card
Mealand Ragland-Hudgins
Murfreesboro Daily News Journal
Murfreesboro City and Rutherford County schools are on opposite ends of the grading scale, based on results of the report card released by the Tennessee Department of Education Tuesday.
Rutherford County Schools scored a 5 for overall academic growth during the 2017-18 school year, the highest score possible. Murfreesboro City Schools was given a 1.
Overall growth is an indication of growth achieved by students, regardless of if a student is considered to be on grade level or not, state officials said.
Murfreesboro City scored a 3 for English/language arts and a 1 in math, science and social studies.
Rutherford County received a 5 in math, science and social studies and a 1 in English/language arts.
"We are generally pleased with our district's performance and plan to use the results from the Report Card in our plans to further improve schools and to deliver unmatched opportunities for students," Rutherford County Director of Schools Bill Spurlock said in a news release Tuesday. "As parents are aware, Tennessee experienced challenges last spring with administering state tests using an online platform. As those issues are addressed, we hope to see additional gains moving forward."
Murfreesboro City Schools, which serves students in grades Pre-K to 6, administered its tests on paper during the 2018 testing session. City Schools Director Linda Gilbert said the report card is a snapshot of where students were eight months ago and that teachers started the year knowing how to best help students.
"Our teachers began this school year focusing on improving our students' math proficiency while building on last year's gains in reading. We will move forward with intentionality, concentrating on the content that will be tested and, at the same time, continuing to partner with our families and the community," Gilbert said. "MCS is focused on educating the whole child and building the dispositions and habits necessary for a productive life."
The report card also addressed student growth by subject level based on student performance on state assessments in third grade and above.
How to use the new report card
Tennessee's new report card ranks a school's overall performance on a scale of zero to four, much like a student's grade point average. Designed to be more user-friendly for parents, the report card includes six key indicators:
Academic achievement — whether students are performing on grade level on TNReady.
Student academic growth — whether students are growing their academic knowledge from year to year.
Chronically out of school — details the number of students that miss at least 10 percent of the school year.
Progress on English language proficiency — whether English-learning students are making progress in understanding the English language.
Ready graduate — the percentage of students who graduate with at least a 21 on the ACT.
Graduate rate — the percentage of students graduating from high school.
Elementary and middle schools will have marks for only four of the six items.
To view the report card visit: https://reportcard.tnk12.gov/
Tennessee's revamped report card:See your school and district results
How to apply:Applications available for magnet schools, IB program in Rutherford County, Murfreesboro
Rocky Fork Elementary rezoning:How families may be impacted by the plan
Rockvale High School rezoning:See Rutherford County Schools plans
Murfreesboro City Schools rezoning:Affected families want 'to stay where we are'