Over 30 years ago, Freire warned of the dangers of neoliberalism and Chomsky today sees this as the greatest threat to democracy. Education is particularly targeted by the neoliberal state because potentially, as educators, we can teach children to think critically, and as adults, critical thinkers are positioned as problems, not resources. Neoliberalism has a devastating impact on the early childhood sector with its focus on standardisation, push-down curriculum and its positioning of children as investments for future economic productivity. Conversely, the growing push for professionalisation of early childhood creates demands for discretionary decision-making that is in tension with the top-down compliance requirements of neoliberalism. In this paper, I present the ways in which neoliberalism impacts the early childhood sector, and call for early childhood professionals to engage in active resistance. Active resistance can take different forms and I discuss some of these. As educators, we have an obligation to both think and act critically and fight for a world where democracy flourishes and where all children have equal opportunities to participate, to shine and to be happy; thus, I argue we have a responsibility to resist the key impacts of neoliberalism.


The holidays can prove to be an extremely stressful time of year. Although being with family is vital and can yield satisfaction and happiness, there are times when it can cause our health to be in a downward spiral.
We face new challenges each day and in the long run these challenges contribute to high stress levels. Stress can affect our well being and reduce our productivity. If we let pressure build up we can end up harming others, making irrational decisions, and in extreme cases we vent out our stress to others. Therefore it is vital that we find a way to reduce stress levels. There are various ways we can unwind and here are 7 Things you can do to relax.
Find a quiet room and do some yoga. Yoga helps your body and mind relax. Yoga with Adriene is one of my favorite video channels on YouTube. Yoga will help you release all the pressure that has been building up in your body and it is also beneficial for your body.
Listening to music lets you get loose. As you get to listen to favorite musician you forget what is troubling you which in turn reduces your stress levels. A good thing about music is that you can plug in your earphones and separate yourself from the stressful environment.
You might opt to walk or jog into the park and enjoy what mother nature has to offer. If you leave in a noisy neighborhood find a quite place to walk. This lets you organize your thoughts and you get to view things from a clearer point of view. Find time in your busy schedule and enjoy the walk.
Computer games or physical games can do. If you love staying indoors then computer games will help you vent out the stress that has been building up in your body. You can play board games against your friends and it will hep you focus on something new other than your problems.
The gym helps you relieve all the mental and muscle tension that builds up during the day. Your job could be demanding that you stay seated for a long period of time and this is bad for your health. Weight lifting will help you reduce all this tension that has been building up. You also get to socialize at the gym which is very healthy.
Watching movies lets you forget what has been stressing you . Take sometime off and watch a movie on netflix or in a cinema. Movies are enjoyable to watch and we can dedicate weekends to watching movies. You can also watch documentaries if you are not a fan of movies and you will learn new things.
Visiting new places is one of the best stress relievers. You can save for a vacation and to get your mind off the things currently stressing you. On vacation you get to interact with new people and learn their diverse cultures. Traveling helps you reduce tension in your life and you can take your family with you.


Should there be any limits on artistic freedom? Is there ever a time when artists should subordinate their personal inspiration to the needs of the state? Do those questions become academic when the very notions of freedom and the state are embodied in a megalomaniacal dictator?
British playwright David Pownall's Master Class asks such questions in an imagined 1948 meeting between Soviet "Father of the People" Josef Stalin, his cultural commissar Andrei Zhdanov, and Russian composers Sergei Prokofiev and Dmitri Shostakovich.
Master Class was first produced in 1983, in the midst of the Cold War. Remounting the play in 2017 as part of its Summer Repertory Festival, Ensemble Theatre implicitly invites us to consider those issues of freedom, censorship and political intimidation not just as historical episodes from another time and place, but as contemporary possibilities.
Pownall doesn't make things easy. His script pounds on one dreary note as if it were a single key on the piano that dominates Lauchlin Johnston's set. Evan Frayne's production has a few revelatory moments but they come late.
What I found most fascinating was how much Tariq Leslie's clownish, bullying Stalin reminded me of a certain current President who wouldn't be ashamed to adopt another of Stalin's official epithets, Greatest Genius in History.
The play revolves around the 1948 Composers Union meeting in Moscow, intended to ensure that Soviet music toed the Communist party line. Music that was Western, decadent, personal, obscure or avant garde was deemed reactionary, inimical to the interests of Party and nation. Composers found to be on the wrong side of that line could be sent to Siberia or shot.
In the play, Russia's two greatest living composers, Prokofiev (Chris Robson) and Shostakovich (a sour-faced, sulking Chris Lam), are confronted by Stalin and Andrei (James Gill), a military officer charged with purging Soviet culture of its reactionary elements. Both composers are accused of having written "formalist progressive crap" — essentially artistic treason.
But the more vodka Stalin throws back, the more sentimental he becomes (about his peasant mother, shoemaker father and Georgian folk roots), and the more threatening and violent. The composers are forced to respond when Stalin insists they compose a cantata on the spot to a ridiculous Georgian poem he recites.
Prokofiev gets a kind of revenge in the play's best scene, improvising a searing pastiche of Stalin's ludicrous fetishes. Robson brings Prokofiev to vivid life here while showing off his own impressive piano skills.
Leslie manages to keep his Stalin, an obvious madman, from spinning off into parody. His final argument even makes emotional sense, invoking the 20 million Russians who died in the war as a reason for the composers to create music that might inspire the survivors and their society to recover and rebuild.
But imagine the bushy black moustache as orange hair and "reactionary music" as "fake news," and you'll know why this play is not entirely out of date.


This article Explain how to wire cat 5 cat 6 ethernet pinout rj45 wiring diagram with Cat 6 color code , ... CAT6 Shielded Connectors for Ethernet Wiring.
Make sure you use the correct RJ45 Pinout wiring diagram for your needs. ... (Ethernet cable connectors) and Ethernet wiring etc., please see the links below.


text:
Girl Scouts of Northern New Jersey Encourages Girls to "Press Play" with Girl Scouts,
Announces September 25 Membership Events at Local Festivals, Parks, and Town Celebrations
Thursday, September 23 2021 @ 05:20 pm
Membership Events to Take Place Across Five Counties and Will Feature Activities, Prizes, and More
Riverdale, N.J. – September 22, 2021 – Girl Scouts of Northern New Jersey (GSNNJ), the preeminent leadership development organization for girls, will host a series of "Press Play" membership events on Saturday, September 25 at various local festivals, town celebrations and parks in Bergen, Passaic, Morris, Sussex and Warren counties. Each of the events will feature free activities that align with the important skills Girl Scouts learn through Girl Scouts Leadership Experience, including STEM, entrepreneurship, life skills, and the outdoors.
With the goal of showcasing the best Girl Scouts has to offer in a fun atmosphere, the free Press Play membership events will offer a range of exciting hands-on activities for girls to complete on-site or at home including a make your own campfire craft, a S'mores SWAP, a pizza box oven recipe, a bandana SWAP, personal care kits, and make your own slime and lava lamp, as well as demonstrations and information on camping and hiking, cybersecurity, entrepreneurship, and more. Additionally, the events will feature a community service aspect with each location accepting donations of toiletries and cleaning supplies to help with Hurricane Ida relief. Press Play event attendees will also have the opportunity to win a small prize by spinning the prize wheels at each location.
The Press Play events will take place at the following locations:
Ridgewood Duck Pond Park
Location: 133 East Ridgewood Ave, Ridgewood
Time: 12 p.m. – 4 p.m.
Rutherford Day
Location: 115 Highland Cross, Rutherford (Park Avenue and Ridge Road)
Time: 11 a.m. – 6 p.m.
Hasbrouck Heights Town Day
Location: Cleveland Ave at Woodland Park, Hasbrouck Heights
Time: 10 a.m. – 3:30 p.m.
Passaic County BBQ and Music Festival
Location: 1 Westervelt Place, Clifton
Lincoln Park Day Festival
Location: Main Street, Lincoln Park
Time: 9 a.m. – 4 p.m.
Rockaway Mall Craft and Vendor Fair
Location: 301 Mt Hope Ave, Rockaway
Hopatcong Food Truck and Music Festival
Location: 32 Lakeside Blvd, Hopatcong Senior Center
Hackettstown Oktoberfest Festival
Location: Main Street, Hackettstown
"While many Girl Scouts participated in activities virtually or in socially distant small-group settings throughout the pandemic, others had to pause—and we understand why. Now is the time, however, to 'press play' and resume their Girl Scout journey. The fall season is one of the best times to join Girl Scouts, helping girls make new friends and stay active and engaged in their communities while they acclimate to a new school year," said Betty Garger, President and CEO of Girl Scouts of Northern New Jersey. "With 28 new badges and new Girl Scout programming, girls who enroll now can truly experience all Girl Scouts has to offer while preparing them for a lifetime of leadership, adventure and success."
Girl Scouts that register between Saturday, September 25 and the end of business on Monday, September 27 will be entered into a raffle for chance to win one of four prize baskets which include a STEM ice cream ball and other items. Additionally, the first 20 individuals that register and complete the requirements to become a Girl Scout leader at the Press Play events will receive a $20 Girl Scouts of Northern New Jersey council shops gift card.
For more information about the Press Play membership events taking place on September 25, visit https://www.gsnnj.org/en/about-girl-scouts/join/Membership_Recruitment_Events.html.
About Girl Scouts of Northern New Jersey
Girl Scouts bring their dreams to life and work together to build a better world. Through programs from coast to coast, Girl Scouts of all backgrounds and abilities can be unapologetically themselves as they discover their strengths and rise to meet new challenges—whether they want to climb to the top of a tree or the top of their class, lace up their boots for a hike or advocate for climate justice, or make their first best friends. Backed by trusted adult volunteers, mentors, and millions of alums, Girl Scouts lead the way as they find their voices and make changes that affect the issues most important to them.
Girl Scouts of Northern New Jersey serves girls ages 5-18 in Bergen, Morris, Passaic, Sussex, and northern Warren counties, bringing the Girl Scout Leadership Experience to over 24,000 girls and nearly 13,000 adult members. Girl Scouts of Northern New Jersey is committed to providing a welcoming and inclusive environment for every girl and her family.
To learn more about Girl Scouts of Northern New Jersey or to volunteer, reconnect, donate, or join, visit www.gsnnj.org and stay connected by following GSNNJ on Facebook, Instagram, LinkedIn, and Twitter.

redpajama_set_name: RedPajamaCommonCrawl


text:
Cardinal Health Inc. Shares Close in on 52-Week High - Market Mover
Cardinal Health Inc. shares closed today at 0.1% below its 52 week high of $61.90, giving the company a market cap of $18B. The stock is currently up 15.5% year-to-date, up 44.9% over the past 12 months, and down 10.6% over the past five years. This week, the Dow Jones Industrial Average rose 1.4%, and the S&P 500 rose 1.7%.
Over the past 12 months the company generated $2 billion in earnings before interest and taxes from $156 billion in revenue. It currently holds $3 billion in cash and $25 billion in debt.
Its forward price-to-earnings (P/E) ratio of 8.568353835765105 is lower than its current P/E ratio of 13.14, implying that analysts are expecting an increase in earnings.
The company's price/earnings-to-growth ratio (PEG Ratio), a widely used indicator of a stock's true value while also factoring in expected earnings growth, currently stands at 0.08. A fairly valued company should have a PEG ratio of 1.0. When a company's PEG exceeds 1.0, it's considered overvalued while a stock with a PEG of less than 1.0 is considered undervalued.
The company's debt-to-equity ratio, which measures the extent to which it finances its operations through debt, currently stands at 22.69 which means it currently has $22.69 of debt for every $1 of equity. Generally speaking, a debt to equity ratio below 1.0 is seen as relatively safe, while ratios of 2.0 or higher would be considered risky. Some industries are known for having much higher debt to equity ratios than others.
The company share price is the same as the performance of its peers in the Industrials industry sector , lags it on a 1-year basis, and lags it on a 5 year basis
Cardinal Health Inc. 2.4 15.5 44.9 -1.5 40.8
S&P 500 Index 1.6 6.3 54.0 -1.5 62.9
Industrials 2.0 9.2 65.4 -1.5 80.9
The company's stock price performance year-to-date beats the peer average by 57.8%
The company's stock price performance over the past 12 months lags the peer average by -60.2%
Cardinal Health Inc. CAH 13.1 15.5 44.9 -1.5 40.8
Peer Avg N/A 19.4 9.8 112.9 -8.5 127.6
CVS Health Corporation CVS 13.9 12.0 33.7 -3.0 42.0
McKesson Corporation MCK -7.4 11.9 56.0 -0.8 60.5
AmerisourceBergen Corporation ABC -7.5 22.0 47.7 -0.7 50.1
Teleflex Incorporated TFX 57.5 0.4 46.7 -5.7 51.3
Henry Schein Inc. HSIC 24.0 1.7 36.0 -9.3 47.9
Herbalife Nutrition Ltd. HLF 14.2 -6.6 52.8 -23.9 67.2
Premier Inc. Class A PINC 8.3 -1.8 16.6 -9.6 20.7
Patterson Companies Inc. PDCO -6.5 10.4 113.2 -13.1 159.8
Owens & Minor Inc. OMI 94.7 42.3 593.8 -4.3 586.4
Allscripts Healthcare Solutions Inc. MDRX 3.1 6.0 132.2 -14.8 190.0


text:
Johan Steene, född 1973, är en svensk ultradistanslöpare. Han har bland annat tagit VM-brons i 24-timmarslöpning. Han började springa efter att ha fyllt trettio.

Johan Steene slog i oktober 2018 nytt rekord i Backyard Ultra på tävlingen Big Dog Backyard Ultra med 68 timmars löpning som ger distansen 455 km.

Steene är bosatt i Stockholm.

Referenser

Svenska långdistanslöpare
Män
Födda 1973
Levande personer
Ultramaratonlöpare

redpajama_set_name: RedPajamaWikipedia


text:
"""
    Server API

    Reference for Server API (REST/Json)

    OpenAPI spec version: 2.0.21

    Generated by: https://github.com/swagger-api/swagger-codegen.git
"""

from __future__ import absolute_import

import os
import sys
import unittest

import kinow_client
from kinow_client.rest import ApiException
from kinow_client.models.task import Task

class TestTask(unittest.TestCase):
    """ Task unit test stubs """

    def setUp(self):
        pass

    def tearDown(self):
        pass

    def testTask(self):
        """
        Test Task
        """
        model = kinow_client.models.task.Task()

if __name__ == '__main__':
    unittest.main()

redpajama_set_name: RedPajamaGithub


In 2017, federal agencies processed 800,000 public records requests (PRRs) at a cost of $500 million. Only a very small amount - less than 1% - was recouped in fees.
The federal Freedom of Information Act (FOIA) allows for agencies to charge fees for searching and copying records, but not for redacting information. Because such a fee - any fee - could be seen to obstruct the principle of open government, federal agencies often waive any charges and provide records for free.
Agencies at both state and local levels also struggle with this. A wide disparity exists between how federal FOIA and state laws assess the cost of handling PRRs. These laws vary from state to state, but for the most part, state and local government agencies across the U.S. are allowed to charge a "reasonable" fee to recoup the costs of providing public records. But the definition of what is "reasonable" is fluid, and results in a lot of legal wrangling.
What is a 'reasonable' cost?
Let's go to Hawaii for our first example. In 2010, an accounting professor at the University of Hawaii filed a PRR for three years of legal invoices. The requester wanted to find out how much the school was spending on outside attorneys. For a bureau using specialist technology, this would not be a challenging request, but UH replied it would take 2,000 man hours to collect and redact the records at a cost of $40,000 to the requester. It also emerged that the $40,000 was the estimated cost of disclosing one year's worth of invoices; the charge for three years should have been in the region of $100,000.
Perhaps this does not seem a "reasonable" cost, but only a state court can determine that.
Requests such as these do often end up in a court of law. In 2012, the Wisconsin Supreme Court ruled in favor of the Milwaukee Journal Sentinel over a dispute with the Milwaukee Police Department over the cost of redacting 750 incident reports. The newspaper argued that the $4,500 fee effectively obstructed public access and violated Wisconsin state law.
In its decision, the court wrote that Wisconsin's records law was to be "construed in every instance with a presumption of complete public access".
But such complete access comes at a cost, and agencies face tough decisions about costs.
It's easy to paint the agencies as the bad guys here, but they are caught between a rock and a hard place. All agencies walk a tightrope between honoring the principle of transparency in government and running a tight budget. No attorney wants to fight for a state's right to charge $1 for a copy of a page from the public records. But any dollar not received in fees is a dollar that could have been spent on education, roads, parks and recreation and so on.
There is a way out of this dilemma: technology. For years, the legal profession resisted the technologies of eDiscovery, which are now commonplace in litigation. Research into eDiscovery technology shows time and again that it is much faster than manual review as you would expect, but also much more accurate. The result: the cost per request for disclosure plummets - not least because there are fewer delays, fewer errors, fewer lawsuits.
Agencies that spend less on search and redaction suddenly have the option to waive or reduce other charges, and make public records more accessible to all.


Cloverfield Church opened in December 2000, a joint project set up by the Church of England and the United Reformed Church. The building serves as both a church and a community hall available to other organisations. There are plenty of churches in Thetford, but no other one on this estate, which is on the East side of the town.
The worship here follows an informal liturgy, and leadership of it is shared with members of the congregation. The main Sunday service is at 10:30am. The first Sunday is Holy Communion, using a simple liturgy; On other Sundays, the worship is varied week to week including Prayer and Praise, and a celebratory service in which the children take part. The children always attend the first part. A music group leads the music. On a normal Sunday, there are about 25 adults and 15 children present.
The Team Vicar, the Revd Helen Jary, lives on the Cloverfields estate. See the Contact Us page for details of how to get on touch with her.


text:
The Clippers Need A Statement Win
The phrase "humiliating loss" gets thrown around an awful lot in sports. Usually, it gets used when a team that should've won loses by 20+ points (basketball or football), 5+ runs (baseball) or 3+ goals (hockey or soccer). However, I would call those disappointing losses. They're bad, but it could be so much worse, like a 50+ point loss. That's what happened to the Los Angeles Clippers over the weekend. They seemingly forgot how to play basketball and suffered a 51-point loss to the Dallas Mavericks. To recover from such an abysmal loss, they need a statement win tonight against the Minnesota Timberwolves.
Obviously, the Dallas Mavericks aren't a bad team. They're quite good, but this is the NBA, and no respectable team should be losing by 50+ points, especially not one that's consistently been in the playoffs over the last decade and counts one of the league's best players in their roster. Now, I understand that Kawhi Leonard was rested for the game against the Mavericks, but that doesn't excuse the fact that they lost so abysmally. After all, Paul George is supposed to be an effective player, but he was completely anonymous during a game that set a record for the worst halftime deficit in NBA history (the score was 77-27 Mavericks at the half).
At the risk of sounding too harsh, this was embarrassing. The players should be embarrassed, head coach Tyronn Lue should be mortified, and owner Steve Ballmer should stop being egregiously over-excited and figure out what's wrong with his front office that he has such a poor excuse for a team.
In order to salvage their reputation, they need to immediately put this bad memory in the trash. Simply make people forget about it by dominating the Timberwolves. Run up the score. Play suffocating defense. Let the analysts and viewers know that Sunday's game was just an aberration. If not, there might be some firings in the near future for the Clippers.
Dallas MavericksKawhi LeonardLos Angeles ClippersMavericksMinnesota TimberwolvesNBAPaul GeorgeSteve BallmerTimberwolves
Previous The NBA's Back for Another Unique Season Next San Diego's Putting Together a Real Challenge


Food Fresh and Ready for Reheating.
The AFS-10 Heat Sealing Machine seals ovenable and non-ovenable film to plastic, paperboard, and some aluminum trays. The heated platen creates strong seals in 1-2 seconds. Film is cut from the film roll on the down-stroke of the sealing platen making sealing rapid and for quick product removal.
• Thermostat controlled, heated platen.
18" W x 30" L x 18" H.
Comes with one set of change parts.
Additional change parts sold separately.


text:
\section{Introduction}
\subsection{The hierarchically sparse signal model}
The paradigm of compressed sensing \cite{candes:rip2008} can be boiled down to the notion that if a vector $\vec{x} \in \mathbb{K}^N$ ($\mathbb{K}$ refers to one of the two fields $\mathbb{R}$ or $\mathbb{C}$) is sparse, it can be recovered from underdetermined and noisy linear measurements $\vec{y}=\vec{A}\vec{x} + \eta \in \mathbb{K}^M$, $M \ll N$ using a plethora of algorithms.

The impact of compressed sensing on the signal processing cannot be understated. In many applications however, the signal $\vec{x}$ at hand is not only sparse, but enjoys a richer structure.
In this work, we consider \emph{hierarchically sparse} (hi-sparse) signals. Hi-sparse signals are structured into blocks that are sparse, or may even exhibit a block structure themselves. Sparsity is assumed on all levels of the block structure, i.e. in a hi-sparse signal $\vec{x} = (\vec{x}_1, \ldots, \vec{x}_N)$, only $s$ blocks $\vec{x}_i$ are non-zero, and each the non-zero blocks $\vec{x}_i$ contains at most $\sigma_i$ non-vanishing entries.
Prior work on the recovery of \emph{block-sparse} signals includes \cite{EldarMishali:2009a,EldarMishali:2009b}, while a hi-sparse signal model has also been considered in
\cite{SprechmannEtAl:2010,FriedmanEtAl:2010, SprechmannEtAl:2011, SimonEtAl:2013}.
 Here, we will use the following definition.

\begin{defi}
Let $\vec{x} = (\vec{x}_1, \dots, \vec{x}_N) \in \mathbb{K}^{n_1} \times \dots \times \mathbb{K}^{n_N}$, where $\mathbb{K}$ is either $\mathbb{R}$ or $\mathbb{C}$. For  $s$ and $\ {\bf\sigma}=(\sigma_1, \dots, \sigma_N)$, we say that $\vec{x}$ is $(s, \sigma)$-sparse, if
\begin{itemize}
    \item at most $s$ blocks $\vec{x}_i$ are non-zero and
    \item each non-zero block $\vec{x}_i$ is $\sigma_i$-sparse.
\end{itemize}
\end{defi}

Note that this definition can be readily generalized to more sparsity levels with a nested tree structure \cite{HiHTP} by allowing the $\sigma_i$ to be multi-leveled themselves, i.e. of the form $(\sigma_i, \bm{\varsigma}_i)$, with $\bm{\varsigma}_i=(\varsigma_{i,1}, \dots, \varsigma_{i,n_i})$ etc.

Before formally introducing the new family of operators on hierarchically sparse signals, let us discuss a specific example in the context of massive random access in the IoT communication literature. For further application examples such as, e.g., massive MIMO please refer also to \cite{Wunder_ARX18},\cite{Wunder_TWC19}.

\subsection{Grouped Random Access Model}\label{sec:randomAccess}
In random access, each user that wishes to communicate with a base station chooses a resource at random (out of $\nu$ available) and sends a pilot signal associated with that resource. Assuming equal power transmitted from the users, and letting $\vec{b}_j(i) \in \mathbb{C}^m,m\leq\nu$, be the pilot signal that user $i$ chooses, the base station
then receives the vector
\begin{align*}
    \vec{y} = \vec{B}\vec{x} = \left(\sum_{i=1}^\nu x_i \vec{b}_{j(i)}\right),
\end{align*}
where $x_i =0$ if user $i$ is inactive, and $x_i=1$ else, and $\vec{B}=(\vec{b}_1,...,\vec{b}_{\nu})$. As before, it is reasonable to assume that the user activity is sparse meaning that the vector $\vec{x}$ is sparse.

This protocol has a fundamental problem -- if several users choose the same resource (a collision occurs), subsequent communication is impossible, since each resource can only serve one user at a time. The probability of a collision grows very fast with a growing amount of users -- a phenomenon commonly referred to as the \emph{birthday paradox}.

\begin{figure}
    \centering
    \includegraphics[width=.45\textwidth]{user_detection.pdf}
    \caption{The standard random access (left) vs. the grouped approach proposed here (right).}
    \label{fig:user_detex}
\end{figure}

In order to reduce the probability of collisions, we propose to distribute the users in groups. That is, randomly subdivide the active users in $N$ groups, and accordingly replace the $x$-vector replaced with $N$ blocks $\vec{x}_i$. We then let the users in each group $i$ choose one of $n$ resources, with $n \leq \nu$.
Obviously, there is then \emph{within each block} a much lower probability of collision than before. Furthermore, each block is with high probability sparse, say $\sigma_i$-sparse. Thus, the signal to be recovered, $(\vec{x}_1, \dots, \vec{x}_N) \in (\mathbb{C}^n)^N$ is no longer only sparse, but with high probability  even $(N,(\sigma_1, \dots, \sigma_N))$-hierarchically sparse.

In order for the base station to be able to de-mix the individual block contributions, we may let them send their pilot signals during disjoint time intervals and recover each $\vec{x}_i$ from $\vec{B}_i\vec{x}_i$, for $i=1,...,N$ individually. This would however be very tedious compared to the original, one-shot scheme. Instead, we propose to mix the contributions $\vec{B}_i \vec{x}_i$ over (much smaller) $M$ incoherent slots (say in time, frequency or space), each time $j$ with a different random modulation $a_{j,i}$. The base station over the course of those time slots then receives
\begin{align}
    \vec{y}_j= \sum_{i=1}^N a_{j,i}\vec{B}_{i} \vec{x}_i, \quad j \in [M] \label{eq:groupedRandomAccess}
\end{align}
To further increase efficiency, we may let the $\vec{B}_i$ be subsampled, meaning that we have access to an $M\cdot m$-dimensional measurement, instead of an $N \cdot n$-dimensional. It is a priori not clear that recovery still is possible. However, the strict sparsity assumption of hierarchical sparsity still gives us some hope of recovery. We show that this intuition is indeed true and we bring a series of strong theoretical arguments why it is so.

\subsection{Hierarchical measurement operators}

The main aim of this paper is to analyze the properties of operators of the form  \eqref{eq:groupedRandomAccess} within the context of hierarchically sparse recovery. Let us give them a name.

\begin{defi}
	We call a measurement operator $\vec{H}$ from $\bigoplus_{i=1}^N\mathbb{K}^{n_i}$ to $\mathbb{K}^{M}\otimes \mathbb{K}^m$ a \emph{hierarchical measurement operator} if there exists matrices $\vec{B}_i \in \mathbb{K}^{m\times n_i}$ and a matrix $\vec{A} \in \mathbb{K}^{M\times N}$ with
	\begin{align}
		\vec{H}\left(\vec{x}_1, \dots, \vec{x}_N\right) = \sum_{i=1}^N \vec{a}_i \otimes (\vec{B}_i \vec{x}_i). \label{eq:hierarchical}
	\end{align}
\end{defi}
We will refer to $\vec{A}$ as the mixing matrix and the $\vec{B}_i$ as the block operators.

In \cite{HiHTP}, a subset of the authors proposed to use an adapted version of the celebrated Hard Threshold Pursuit (HTP) \cite{Foucart:2011} to recover hi-sparse signals -- the Hierarchical HTP (HiHTP), which we will present  in more detail in the experiment section.  The main finding of \cite{HiHTP} was that if a measurement operator $\vec{M}$ exhibits the so called \emph{hierarchically restricted isometry property (HiRIP)}, HiHTP recovers all hierarchically sparse signals in a stable and robust fashion from linear measurements $\vec{y} = \vec{M}\vec{x}$.

\begin{defi}
    The smallest  $\delta > 0$ for which
\begin{align*}
    (1-\delta) \norm{\vec{x}}^2 \leq \norm{\vec{M}\vec{x}}^2 \leq (1+\delta) \norm{ \vec{x}}^2
\end{align*}
for all $(s,\sigma)$-sparse $\vec{x}$ is called the $(s,\sigma)$-HiRIP constant of $\vec{M}$, $\delta_{s,\sigma}(\vec{M})$.
\end{defi}

A matrix 'having the HiRIP' then refers to $\delta_{s,\sigma}(\vec{M})$ being small enough for the correct parameters $s$ and $\sigma$.

In this paper, we will analyse the HiRIP properties of hierarchical measurement operators.
We will give bounds on the HiRIP constants in terms of the RIP constants of the mixing and block matrices. These generalize prior work on compressed sensing of hierarchically sparse signals from Kronecker-structured measurements \cite{RothEtAl:2018}.

In the following, we will refrain from presenting any mathematical proofs. These, along with additional results and discussions, can instead found be found in the journal  version of this paper, of which a preprint \cite{Flinth2021hierarchical} will soon be available on arXiv.
\section{HiRIP-properties of Hierarchical Measurement Operators}

As briefly mentioned in the introduction, in \cite{RothEtAl:2018}, some of the authors of this article proved that a measurement matrix being a \emph{Kronecker product} $\mathbf A \otimes \mathbf B$
has the $(s,\sigma)$-RIP provided $\vec{A}$ has the $s$-RIP and $\vec{B}$ has the $\sigma$-RIP.
The Kronecker product $\vec{A} \otimes \vec{B}$ is defined through its action on an element $(\vec{x}_1, \dots,  \vec{x}_N)\in (\mathbb{K}^n)^N$ as follows
\begin{align*}
    \vec{A}\otimes \vec{B}(\vec{x}_1, \dots,  \vec{x}_N) = \sum_{i=1}^N \vec{a}_i \otimes (\vec{B}\vec{x}_i),
\end{align*}
where $\vec a_i$ denotes the columns of $\mathbf A$, and $\otimes$ the tensor product. It is evident that these operators are special cases of the hierarchical operators considered here.

The main result of \cite{RothEtAl:2018} is that if $\vec{A}$ has the $s$-RIP and $\vec{B}$ has the $\sigma$-RIP, $\vec{A} \otimes \vec{B}$ has the $(s,(\sigma, \dots, \sigma))$-HiRIP. The first main result of this paper is a direct generalisation of this result.

  \begin{theo} \label{th:HiRIP}
  	Let $\vec{H}$ be a hierarchical measurement operator, as in \eqref{eq:hierarchical}. Assume that the matrices $\vec{B}_i$ all obey the $\sigma_i$-RIP with constant $\delta_{\sigma_i}(\vec{B_i})$
  	 for all $i$. Assume further that $\vec{A}$ obeys the $s$-RIP with constant $\delta_s(\vec{A})$. Then $\vec{H}$ obeys the HiRIP, with
  	 \begin{align*}
  	 	\delta_{(s,\sigma)}(\vec{H}) \leq \delta_s(\vec{A}) + \sup_{i} \delta_{\sigma_i}(\vec{B}_i) + \delta_s(\vec{A}) \cdot \sup_{i} \delta_{\sigma_i}(\vec{B}_i),
  	 \end{align*}
  	 where again $\sigma=(\sigma_1,\dots, \sigma_N)$.
  \end{theo}

  \begin{rem}
    The result applies to more levels of sparsity. To be concrete, the $\sigma_i$ in the result may be multileveled themselves.
  \end{rem}
This result already enables us to construct an abstract hierarchical measurement operator which has the $(s,\sigma)$-HiRIP with high probability.  Remembering that a  Gaussian matrix $\vec{B}\in \mathbb{K}^{m,n_i}$ has $\sigma$-RIP with high probability already when  the number o
$ m \gtrsim \sigma \log \left(\frac{n_i}{\sigma_i}\right)$\cite[Ch.9]{FouRau13}.
 In the same manner, we can choose the matrix $\vec{A} \in \mathbb{K}^{M \times N}$ as a Gaussian  matrix. It will have the $s$-RIP with high probability if $M \gtrsim s\log \left(\tfrac{N}{s}\right)$. The above result then implies that the hierarchical measurement operator formed by $\vec{A}$ and the $(\vec{B}_i)_{i \in \mathbb{N}}$ has the $(s,\sigma)$-HiRIP. We conclude that recovery of $(s,\sigma)$-sparse vector is possible using asymptotically no more than
 \begin{align*}
    M \cdot m \gtrsim s\max_i \sigma_i \cdot \mathrm{polylog}(N,n)
 \end{align*}
 total measurements, which is comparable to the results for unstructured measurement operators from \cite{HiHTP}.

 \begin{rem}These considerations could to some extend already be derived using the Kronecker result from \cite{RothEtAl:iTwist:2016}. The main difference is that we may use varying sparsity levels, ambient dimensions and measurement operators.\end{rem}

\subsection{Refining the result through block operator incoherence}

As for the  Grouped Random Access model, Theorem \ref{th:HiRIP} does not bring a particularly satisfactory guarantee. Indeed, in that model, we have to recover $(N, \vec{\sigma})$-sparse signals. In order for the above result to be relevant, we thus need $\vec{A}$ to have the $N$-RIP, which necessitates $M \geq N$. This is discouraging.

Can the result however be strenghtened? In fact it can, if the block operators are incoherent in the following sense.

\begin{defi}
  We say that the collection of operators $\vec{B}_i \in \mathbb{K}^{m\times n_i}, i \in [n]$ are \emph{pairwise $(\delta,\sigma)$-incoherent} if for each $i\neq j$,
  \begin{align*}
      \sup_{\substack{|\vec{v}_i|_0\leq \sigma_i, |\vec{v}_j|_0\leq \sigma_j\\
      \norm{\vec{v}_i}= \norm{\vec{v}_j}=1}}
      \abs{\sprod{\vec{B}_i \vec{v}_i ,\vec{B}_j \vec{v}_j}}\leq \delta.
  \end{align*}
\end{defi}

In fact, the $\vec{B_i}$ in the Grouped Random Access is pairwise $(\delta,\sigma)$-incoherent if they are independently subsampled and modulated with random signs, as the following result shows.

\begin{prop} \label{prop:incoherentCollections}
         Let $\vec{F} \in \mathbb{C}^{n,n}$ be the unitary Fourier matrix.
        For each $i$, let the matrix $\vec{B}_i \in \mathbb{C}^{m,n}$ be formed by uniformly and independently sampling $m$ rows from $\vec{F}$, multiplying each of them with a uniform random sign, and subsequently rescaling the rows by $m^{-1/2}$. Assuming that $\vec{B}_i$ is independent of $\vec{B}_j$ for $i \neq j$ and
        \begin{align*}
            m \gtrsim \sigma\delta^{-2} \log(n)^4\log(N),
        \end{align*}
         the collection is $(\delta,\sigma)$-incoherent with probability higher than $1-n^{-\log{n}^3}$.
\end{prop}

If  $(\vec{B}_i)_{i\in[N]}$ is a pairwise incoherent collection, it can to some extent separate the contributions of the individual blocks of a hierarchically sparse vector from the measurement $\sum_{i=1}^N \vec{B}_i \vec{g}_i$. Therefore, the mixing matrix $\vec{A}$ intuitively does not need to have a full $s$-RIP in order for the hierarchical measurement operator $\vec{H}$ formed by $\vec{A}$ and $(\vec{B}_i)_{i\in[N]}$ to have the $(s,\sigma)$-HiRIP. Put differently, if $\vec{A}$ is Gaussian, the needed number of $\vec{A}$ does not scale as $s$. A formal result is as follows.

\begin{theo}
\label{th:s_vs_delta}
    Let $\vec{B}_i \in \mathbb{K}^{m\times n_i}$ for $i\in[N]$, be a pairwise $(\delta_{2\sigma}^*,\sigma)$-incoherent family. Further assume that
    \begin{align*}
        \sup_{i} \delta_{\sigma}(\vec{B}_i) \leq \delta_\sigma^*
    \end{align*}
    Assume further that $(s\delta^*_{2\sigma})^2\leq N/\log(N)$ and that $\vec{A}\in \mathbb{K}^{M\times N}$ is a Gaussian matrix. Let furthermore $\delta,\epsilon>0$. Provided
    \begin{align*}
        M \gtrsim \frac{(s\delta_{2\sigma}^*)^2}{\delta^2}\log\left(\frac{N(1+\delta_\sigma^*)^2}{(t\delta_{2\sigma}^*)^2}\right) + \log(\epsilon^{-1}),
    \end{align*}
    the hierarchical operator $\vec{H}$ defined by $\vec{A}$ and $(\vec{B}_i)_i$ obeys $
        \delta_{(s,\sigma)}(\vec{H}) \leq \delta + \delta_{\sigma}^*$
    with a probability at least $1-\epsilon$.
\end{theo}

The above result says that provided $\delta_{2\sigma}^*$ is small, we need $M$ to be of the order $(s\delta_{2\sigma}^*)^2$, rather than $s$, to allow for $s$-sparse signals on the 'block level'. If $\delta_{2\sigma}^*$ is very small, we may hence obtain the RIP already when $M$ is less than $s$ -- a behaviour which cannot be explained by Theorem \ref{th:HiRIP}. Note that we can even reach the realm of the  Grouped Random Access model, i.e. $s=N$.

\begin{rem}
    The quadratic dependence on of $s\delta_{2\sigma}^*$ is not sample optimal. We leave it to future work to determine whether this only is a proof artefact, or a fundamental limit.
\end{rem}

  \section{Numerical Simulations}

In this section we empirically verify that the hierarchical sparsity framework, and in particular Theorem \ref{th:s_vs_delta}, can be used for user detection in the Grouped Random Access scenario.

\subsection{HiHTP Algorithm}
As mentioned in the introduction HiHTP is a low-complexity algorithm for solving hierarchically sparse compressed sensing problems of the form
\begin{equation}
\label{eq:problem}
    \min\limits_x \frac12\|y-\vec{H}x\|^2 \quad \text{ subject to $x$ is $(s,\sigma)$-sparse,}
\end{equation}
where $\vec{H}$ is a linear operator satisfying the HiRIP. Provided $\vec{H}$ has the HiRIP for an appropriate sparsity level, it will recover any $(s,\sigma)$-sparse vector.

The algorithm consists of iteratively performing a gradient descent step, thresholding the new iterate onto the set of $(s, \sigma)$-sparse signals and then adjusting the non-zero values on the obtained support by linear least squares. The algorithm terminates once the support of two successive iterates does not change or a suitable stopping criterion is reached.

Importantly, the projection onto the set of $(s,\sigma)$-sparse signal (line 3 of Algorithm \ref{alg:hihtp}) can be performed in an efficient manner. We refer to \cite{HiHTP} for details on this.

\begin{algorithm}

\SetAlgoLined
\DontPrintSemicolon
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}\SetKwInOut{Init}{initialization}\SetKwFunction{Break}{break}
\Input{data $y$, stepsizes $\tau^{[t]}$, tolerance $\epsilon$}
\Init{$x^{(0)}=0$, $\Omega^{(0)}=\{\}$}
\BlankLine
\For{$t=1, 2, \ldots$}{
$\hat{x}^{(t)} = x^{(t-1)} +\tau^{(t)} \vec{H}^*(y-\vec{H}x^{(t-1)})$\;
Calculate the support $\Omega^{(t)}$ of the best $(s,\sigma)$-sparse approximation of $\hat{x}^{(t)}$\;
$x^{(t)} = \mathop{\mathrm{argmin}} \frac12\|y-\vec{H}x\|^2$ subject to $\supp(x)\subset\Omega^{(t)}$\;
\If{$\Omega^{(t)}=\Omega^{(t-1)}$ {\bf or}  $\frac{\|y-\vec{H}x^{(t)}\|}{\|y\|}\leq \epsilon$}{
\Break}
}
\caption{HiHTP for hierarchical measurements}
\label{alg:hihtp}
\end{algorithm}

\subsection{Grouped Random Access
We assume  $\nu=n=512$ available resources and model the measurements at the base station as $\vec{y} = \vec{F}\vec{x}$, where $\vec{F}\in\mathbb{C}^{n\times n}$ is a $n\times n$-DFT matrix. Note that since we are aiming for user detection, we do not necessarily need to recover $\vec{x}$ exactly: we only need to determine which $x_i$ are non-zero. Our baseline method therefore consists of computing $\supp(\vec{F}^{-1}y)$ to obtain the selected resources.

\begin{figure}
    \centering
    \includegraphics[width=.49\textwidth]{recovered_users_16a__new.pdf}
    \caption{User detection with hierarchical measurements}
    \label{fig:user_detection}
\end{figure}

We compare this to the Grouped Random Access model with $N$ subsampled $\vec{B}_i$, which each consist of $m=256$ random rows from the $n\times n$ DFT matrix. The random modulation matrix $\vec{A}\in\mathbb{C}^{M\times N}$, where $M=16$
is chosen as complex Gaussian with variance $\tfrac{1}{\sqrt{N}}$. This results in the system $\mathbb{C}^{Mm}\ni\vec{y}= \vec{H}\vec{x}$, with measurement operator $\vec{H}$ formed by $\vec{A}$ and the $\vec{B}_i$ as in \eqref{eq:groupedRandomAccess}.

The HiHTP Algorithm \ref{alg:hihtp} is used to recover $\vec{x}$ from the measurements $\vec{y}$. Figure \ref{fig:user_detection} shows the average number of recovered users for varying sparsities $\sigma=16,\dots,36$ and number of blocks $N=8,\dots,32$ over 25 Monte-Carlo trials for each configuration. Note that from $N>8$ on the system has more pre-image dimensions than measurements and the recovery results of our paper apply. Notably, since all the $N$ blocks are filled, classical hierarchical CS does not apply and particularly Theorem \ref{th:s_vs_delta} must be invoked. The baseline shown in Figure \ref{fig:user_detection} is computed as the total number of users, $N\cdot \sigma$, minus the expected number of collisions that occur, if these users choose randomly out of the $n=512$ available resources. As can be seen, HiHTP is able to recover much more users compared to the baseline.
For $\sigma=16$ and $\sigma=32$ the performance of the HiHTP algorithm for user detection is shown, when the $\sigma\cdot N$ users are distributed randomly over all available slots (i.e. the block sparsities are not uniformly fixed to $\sigma$). Even in this scenario, where the algorithm operates with the wrong sparsity parameters, reasonable performance is achieved.

  \section{Conclusion}
  We proved a number of results regarding the HiRIP for hierarchical measurement operators. The results generalize prior work on hierarchical sparse recovery with Kronecker-structured matrices. Furthermore, we demonstrated that the HiHTP algorithm is capable of computing hi-sparse solutions under this measurement structure in a practical Grouped Random Access design for IoT communication scenarios exhibiting huge capacity gains.

\bibliographystyle{unsrt}
\nocite{fantastic-5g-5g-ppp-project-on-5g-air-interface-below-6-ghz}

\section{Introduction}
\subsection{The hierarchically sparse signal model}
The paradigm of compressed sensing \cite{candes:rip2008} can be boiled down to the notion that if a vector $\vec{x} \in \mathbb{K}^N$ ($\mathbb{K}$ refers to one of the two fields $\mathbb{R}$ or $\mathbb{C}$) is sparse, it can be recovered from underdetermined and noisy linear measurements $\vec{y}=\vec{A}\vec{x} + \eta \in \mathbb{K}^M$, $M \ll N$ using a plethora of algorithms.

The impact of compressed sensing on the signal processing cannot be understated. In many applications however, the signal $\vec{x}$ at hand is not only sparse, but enjoys a richer structure.
In this work, we consider \emph{hierarchically sparse} (hi-sparse) signals. Hi-sparse signals are structured into blocks that are sparse, or may even exhibit a block structure themselves. Sparsity is assumed on all levels of the block structure, i.e. in a hi-sparse signal $\vec{x} = (\vec{x}_1, \ldots, \vec{x}_N)$, only $s$ blocks $\vec{x}_i$ are non-zero, and each the non-zero blocks $\vec{x}_i$ contains at most $\sigma_i$ non-vanishing entries.
Prior work on the recovery of \emph{block-sparse} signals includes \cite{EldarMishali:2009a,EldarMishali:2009b}, while a hi-sparse signal model has also been considered in
\cite{SprechmannEtAl:2010,FriedmanEtAl:2010, SprechmannEtAl:2011, SimonEtAl:2013}.
 Here, we will use the following definition.

\begin{defi}
Let $\vec{x} = (\vec{x}_1, \dots, \vec{x}_N) \in \mathbb{K}^{n_1} \times \dots \times \mathbb{K}^{n_N}$, where $\mathbb{K}$ is either $\mathbb{R}$ or $\mathbb{C}$. For  $s$ and $\ {\bf\sigma}=(\sigma_1, \dots, \sigma_N)$, we say that $\vec{x}$ is $(s, \sigma)$-sparse, if
\begin{itemize}
    \item at most $s$ blocks $\vec{x}_i$ are non-zero and
    \item each non-zero block $\vec{x}_i$ is $\sigma_i$-sparse.
\end{itemize}
\end{defi}

Note that this definition can be readily generalized to more sparsity levels with a nested tree structure \cite{HiHTP} by allowing the $\sigma_i$ to be multi-leveled themselves, i.e. of the form $(\sigma_i, \bm{\varsigma}_i)$, with $\bm{\varsigma}_i=(\varsigma_{i,1}, \dots, \varsigma_{i,n_i})$ etc.

Before formally introducing the new family of operators on hierarchically sparse signals, let us discuss a specific example in the context of massive random access in the IoT communication literature. For further application examples such as, e.g., massive MIMO please refer also to \cite{Wunder_ARX18},\cite{Wunder_TWC19}.

\subsection{Grouped Random Access Model}\label{sec:randomAccess}
In random access, each user that wishes to communicate with a base station chooses a resource at random (out of $\nu$ available) and sends a pilot signal associated with that resource. Assuming equal power transmitted from the users, and letting $\vec{b}_j(i) \in \mathbb{C}^m,m\leq\nu$, be the pilot signal that user $i$ chooses, the base station
then receives the vector
\begin{align*}
    \vec{y} = \vec{B}\vec{x} = \left(\sum_{i=1}^\nu x_i \vec{b}_{j(i)}\right),
\end{align*}
where $x_i =0$ if user $i$ is inactive, and $x_i=1$ else, and $\vec{B}=(\vec{b}_1,...,\vec{b}_{\nu})$. As before, it is reasonable to assume that the user activity is sparse meaning that the vector $\vec{x}$ is sparse.

This protocol has a fundamental problem -- if several users choose the same resource (a collision occurs), subsequent communication is impossible, since each resource can only serve one user at a time. The probability of a collision grows very fast with a growing amount of users -- a phenomenon commonly referred to as the \emph{birthday paradox}.

\begin{figure}
    \centering
    \includegraphics[width=.45\textwidth]{user_detection.pdf}
    \caption{The standard random access (left) vs. the grouped approach proposed here (right).}
    \label{fig:user_detex}
\end{figure}

In order to reduce the probability of collisions, we propose to distribute the users in groups. That is, randomly subdivide the active users in $N$ groups, and accordingly replace the $x$-vector replaced with $N$ blocks $\vec{x}_i$. We then let the users in each group $i$ choose one of $n$ resources, with $n \leq \nu$.
Obviously, there is then \emph{within each block} a much lower probability of collision than before. Furthermore, each block is with high probability sparse, say $\sigma_i$-sparse. Thus, the signal to be recovered, $(\vec{x}_1, \dots, \vec{x}_N) \in (\mathbb{C}^n)^N$ is no longer only sparse, but with high probability  even $(N,(\sigma_1, \dots, \sigma_N))$-hierarchically sparse.

In order for the base station to be able to de-mix the individual block contributions, we may let them send their pilot signals during disjoint time intervals and recover each $\vec{x}_i$ from $\vec{B}_i\vec{x}_i$, for $i=1,...,N$ individually. This would however be very tedious compared to the original, one-shot scheme. Instead, we propose to mix the contributions $\vec{B}_i \vec{x}_i$ over (much smaller) $M$ incoherent slots (say in time, frequency or space), each time $j$ with a different random modulation $a_{j,i}$. The base station over the course of those time slots then receives
\begin{align}
    \vec{y}_j= \sum_{i=1}^N a_{j,i}\vec{B}_{i} \vec{x}_i, \quad j \in [M] \label{eq:groupedRandomAccess}
\end{align}
To further increase efficiency, we may let the $\vec{B}_i$ be subsampled, meaning that we have access to an $M\cdot m$-dimensional measurement, instead of an $N \cdot n$-dimensional. It is a priori not clear that recovery still is possible. However, the strict sparsity assumption of hierarchical sparsity still gives us some hope of recovery. We show that this intuition is indeed true and we bring a series of strong theoretical arguments why it is so.

\subsection{Hierarchical measurement operators}

The main aim of this paper is to analyze the properties of operators of the form  \eqref{eq:groupedRandomAccess} within the context of hierarchically sparse recovery. Let us give them a name.

\begin{defi}
	We call a measurement operator $\vec{H}$ from $\bigoplus_{i=1}^N\mathbb{K}^{n_i}$ to $\mathbb{K}^{M}\otimes \mathbb{K}^m$ a \emph{hierarchical measurement operator} if there exists matrices $\vec{B}_i \in \mathbb{K}^{m\times n_i}$ and a matrix $\vec{A} \in \mathbb{K}^{M\times N}$ with
	\begin{align}
		\vec{H}\left(\vec{x}_1, \dots, \vec{x}_N\right) = \sum_{i=1}^N \vec{a}_i \otimes (\vec{B}_i \vec{x}_i). \label{eq:hierarchical}
	\end{align}
\end{defi}
We will refer to $\vec{A}$ as the mixing matrix and the $\vec{B}_i$ as the block operators.

In \cite{HiHTP}, a subset of the authors proposed to use an adapted version of the celebrated Hard Threshold Pursuit (HTP) \cite{Foucart:2011} to recover hi-sparse signals -- the Hierarchical HTP (HiHTP), which we will present  in more detail in the experiment section.  The main finding of \cite{HiHTP} was that if a measurement operator $\vec{M}$ exhibits the so called \emph{hierarchically restricted isometry property (HiRIP)}, HiHTP recovers all hierarchically sparse signals in a stable and robust fashion from linear measurements $\vec{y} = \vec{M}\vec{x}$.

\begin{defi}
    The smallest  $\delta > 0$ for which
\begin{align*}
    (1-\delta) \norm{\vec{x}}^2 \leq \norm{\vec{M}\vec{x}}^2 \leq (1+\delta) \norm{ \vec{x}}^2
\end{align*}
for all $(s,\sigma)$-sparse $\vec{x}$ is called the $(s,\sigma)$-HiRIP constant of $\vec{M}$, $\delta_{s,\sigma}(\vec{M})$.
\end{defi}

A matrix 'having the HiRIP' then refers to $\delta_{s,\sigma}(\vec{M})$ being small enough for the correct parameters $s$ and $\sigma$.

In this paper, we will analyse the HiRIP properties of hierarchical measurement operators.
We will give bounds on the HiRIP constants in terms of the RIP constants of the mixing and block matrices. These generalize prior work on compressed sensing of hierarchically sparse signals from Kronecker-structured measurements \cite{RothEtAl:2018}.

In the following, we will refrain from presenting any mathematical proofs. These, along with additional results and discussions, can instead found be found in the journal  version of this paper, of which a preprint \cite{Flinth2021hierarchical} will soon be available on arXiv.
\section{HiRIP-properties of Hierarchical Measurement Operators}

As briefly mentioned in the introduction, in \cite{RothEtAl:2018}, some of the authors of this article proved that a measurement matrix being a \emph{Kronecker product} $\mathbf A \otimes \mathbf B$
has the $(s,\sigma)$-RIP provided $\vec{A}$ has the $s$-RIP and $\vec{B}$ has the $\sigma$-RIP.
The Kronecker product $\vec{A} \otimes \vec{B}$ is defined through its action on an element $(\vec{x}_1, \dots,  \vec{x}_N)\in (\mathbb{K}^n)^N$ as follows
\begin{align*}
    \vec{A}\otimes \vec{B}(\vec{x}_1, \dots,  \vec{x}_N) = \sum_{i=1}^N \vec{a}_i \otimes (\vec{B}\vec{x}_i),
\end{align*}
where $\vec a_i$ denotes the columns of $\mathbf A$, and $\otimes$ the tensor product. It is evident that these operators are special cases of the hierarchical operators considered here.

The main result of \cite{RothEtAl:2018} is that if $\vec{A}$ has the $s$-RIP and $\vec{B}$ has the $\sigma$-RIP, $\vec{A} \otimes \vec{B}$ has the $(s,(\sigma, \dots, \sigma))$-HiRIP. The first main result of this paper is a direct generalisation of this result.

  \begin{theo} \label{th:HiRIP}
  	Let $\vec{H}$ be a hierarchical measurement operator, as in \eqref{eq:hierarchical}. Assume that the matrices $\vec{B}_i$ all obey the $\sigma_i$-RIP with constant $\delta_{\sigma_i}(\vec{B_i})$
  	 for all $i$. Assume further that $\vec{A}$ obeys the $s$-RIP with constant $\delta_s(\vec{A})$. Then $\vec{H}$ obeys the HiRIP, with
  	 \begin{align*}
  	 	\delta_{(s,\sigma)}(\vec{H}) \leq \delta_s(\vec{A}) + \sup_{i} \delta_{\sigma_i}(\vec{B}_i) + \delta_s(\vec{A}) \cdot \sup_{i} \delta_{\sigma_i}(\vec{B}_i),
  	 \end{align*}
  	 where again $\sigma=(\sigma_1,\dots, \sigma_N)$.
  \end{theo}

  \begin{rem}
    The result applies to more levels of sparsity. To be concrete, the $\sigma_i$ in the result may be multileveled themselves.
  \end{rem}
This result already enables us to construct an abstract hierarchical measurement operator which has the $(s,\sigma)$-HiRIP with high probability.  Remembering that a  Gaussian matrix $\vec{B}\in \mathbb{K}^{m,n_i}$ has $\sigma$-RIP with high probability already when  the number o
$ m \gtrsim \sigma \log \left(\frac{n_i}{\sigma_i}\right)$\cite[Ch.9]{FouRau13}.
 In the same manner, we can choose the matrix $\vec{A} \in \mathbb{K}^{M \times N}$ as a Gaussian  matrix. It will have the $s$-RIP with high probability if $M \gtrsim s\log \left(\tfrac{N}{s}\right)$. The above result then implies that the hierarchical measurement operator formed by $\vec{A}$ and the $(\vec{B}_i)_{i \in \mathbb{N}}$ has the $(s,\sigma)$-HiRIP. We conclude that recovery of $(s,\sigma)$-sparse vector is possible using asymptotically no more than
 \begin{align*}
    M \cdot m \gtrsim s\max_i \sigma_i \cdot \mathrm{polylog}(N,n)
 \end{align*}
 total measurements, which is comparable to the results for unstructured measurement operators from \cite{HiHTP}.

 \begin{rem}These considerations could to some extend already be derived using the Kronecker result from \cite{RothEtAl:iTwist:2016}. The main difference is that we may use varying sparsity levels, ambient dimensions and measurement operators.\end{rem}

\subsection{Refining the result through block operator incoherence}

As for the  Grouped Random Access model, Theorem \ref{th:HiRIP} does not bring a particularly satisfactory guarantee. Indeed, in that model, we have to recover $(N, \vec{\sigma})$-sparse signals. In order for the above result to be relevant, we thus need $\vec{A}$ to have the $N$-RIP, which necessitates $M \geq N$. This is discouraging.

Can the result however be strenghtened? In fact it can, if the block operators are incoherent in the following sense.

\begin{defi}
  We say that the collection of operators $\vec{B}_i \in \mathbb{K}^{m\times n_i}, i \in [n]$ are \emph{pairwise $(\delta,\sigma)$-incoherent} if for each $i\neq j$,
  \begin{align*}
      \sup_{\substack{|\vec{v}_i|_0\leq \sigma_i, |\vec{v}_j|_0\leq \sigma_j\\
      \norm{\vec{v}_i}= \norm{\vec{v}_j}=1}}
      \abs{\sprod{\vec{B}_i \vec{v}_i ,\vec{B}_j \vec{v}_j}}\leq \delta.
  \end{align*}
\end{defi}

In fact, the $\vec{B_i}$ in the Grouped Random Access is pairwise $(\delta,\sigma)$-incoherent if they are independently subsampled and modulated with random signs, as the following result shows.

\begin{prop} \label{prop:incoherentCollections}
         Let $\vec{F} \in \mathbb{C}^{n,n}$ be the unitary Fourier matrix.
        For each $i$, let the matrix $\vec{B}_i \in \mathbb{C}^{m,n}$ be formed by uniformly and independently sampling $m$ rows from $\vec{F}$, multiplying each of them with a uniform random sign, and subsequently rescaling the rows by $m^{-1/2}$. Assuming that $\vec{B}_i$ is independent of $\vec{B}_j$ for $i \neq j$ and
        \begin{align*}
            m \gtrsim \sigma\delta^{-2} \log(n)^4\log(N),
        \end{align*}
         the collection is $(\delta,\sigma)$-incoherent with probability higher than $1-n^{-\log{n}^3}$.
\end{prop}

If  $(\vec{B}_i)_{i\in[N]}$ is a pairwise incoherent collection, it can to some extent separate the contributions of the individual blocks of a hierarchically sparse vector from the measurement $\sum_{i=1}^N \vec{B}_i \vec{g}_i$. Therefore, the mixing matrix $\vec{A}$ intuitively does not need to have a full $s$-RIP in order for the hierarchical measurement operator $\vec{H}$ formed by $\vec{A}$ and $(\vec{B}_i)_{i\in[N]}$ to have the $(s,\sigma)$-HiRIP. Put differently, if $\vec{A}$ is Gaussian, the needed number of $\vec{A}$ does not scale as $s$. A formal result is as follows.

\begin{theo}
\label{th:s_vs_delta}
    Let $\vec{B}_i \in \mathbb{K}^{m\times n_i}$ for $i\in[N]$, be a pairwise $(\delta_{2\sigma}^*,\sigma)$-incoherent family. Further assume that
    \begin{align*}
        \sup_{i} \delta_{\sigma}(\vec{B}_i) \leq \delta_\sigma^*
    \end{align*}
    Assume further that $(s\delta^*_{2\sigma})^2\leq N/\log(N)$ and that $\vec{A}\in \mathbb{K}^{M\times N}$ is a Gaussian matrix. Let furthermore $\delta,\epsilon>0$. Provided
    \begin{align*}
        M \gtrsim \frac{(s\delta_{2\sigma}^*)^2}{\delta^2}\log\left(\frac{N(1+\delta_\sigma^*)^2}{(t\delta_{2\sigma}^*)^2}\right) + \log(\epsilon^{-1}),
    \end{align*}
    the hierarchical operator $\vec{H}$ defined by $\vec{A}$ and $(\vec{B}_i)_i$ obeys $
        \delta_{(s,\sigma)}(\vec{H}) \leq \delta + \delta_{\sigma}^*$
    with a probability at least $1-\epsilon$.
\end{theo}

The above result says that provided $\delta_{2\sigma}^*$ is small, we need $M$ to be of the order $(s\delta_{2\sigma}^*)^2$, rather than $s$, to allow for $s$-sparse signals on the 'block level'. If $\delta_{2\sigma}^*$ is very small, we may hence obtain the RIP already when $M$ is less than $s$ -- a behaviour which cannot be explained by Theorem \ref{th:HiRIP}. Note that we can even reach the realm of the  Grouped Random Access model, i.e. $s=N$.

\begin{rem}
    The quadratic dependence on of $s\delta_{2\sigma}^*$ is not sample optimal. We leave it to future work to determine whether this only is a proof artefact, or a fundamental limit.
\end{rem}

  \section{Numerical Simulations}

In this section we empirically verify that the hierarchical sparsity framework, and in particular Theorem \ref{th:s_vs_delta}, can be used for user detection in the Grouped Random Access scenario.

\subsection{HiHTP Algorithm}
As mentioned in the introduction HiHTP is a low-complexity algorithm for solving hierarchically sparse compressed sensing problems of the form
\begin{equation}
\label{eq:problem}
    \min\limits_x \frac12\|y-\vec{H}x\|^2 \quad \text{ subject to $x$ is $(s,\sigma)$-sparse,}
\end{equation}
where $\vec{H}$ is a linear operator satisfying the HiRIP. Provided $\vec{H}$ has the HiRIP for an appropriate sparsity level, it will recover any $(s,\sigma)$-sparse vector.

The algorithm consists of iteratively performing a gradient descent step, thresholding the new iterate onto the set of $(s, \sigma)$-sparse signals and then adjusting the non-zero values on the obtained support by linear least squares. The algorithm terminates once the support of two successive iterates does not change or a suitable stopping criterion is reached.

Importantly, the projection onto the set of $(s,\sigma)$-sparse signal (line 3 of Algorithm \ref{alg:hihtp}) can be performed in an efficient manner. We refer to \cite{HiHTP} for details on this.

\begin{algorithm}

\SetAlgoLined
\DontPrintSemicolon
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}\SetKwInOut{Init}{initialization}\SetKwFunction{Break}{break}
\Input{data $y$, stepsizes $\tau^{[t]}$, tolerance $\epsilon$}
\Init{$x^{(0)}=0$, $\Omega^{(0)}=\{\}$}
\BlankLine
\For{$t=1, 2, \ldots$}{
$\hat{x}^{(t)} = x^{(t-1)} +\tau^{(t)} \vec{H}^*(y-\vec{H}x^{(t-1)})$\;
Calculate the support $\Omega^{(t)}$ of the best $(s,\sigma)$-sparse approximation of $\hat{x}^{(t)}$\;
$x^{(t)} = \mathop{\mathrm{argmin}} \frac12\|y-\vec{H}x\|^2$ subject to $\supp(x)\subset\Omega^{(t)}$\;
\If{$\Omega^{(t)}=\Omega^{(t-1)}$ {\bf or}  $\frac{\|y-\vec{H}x^{(t)}\|}{\|y\|}\leq \epsilon$}{
\Break}
}
\caption{HiHTP for hierarchical measurements}
\label{alg:hihtp}
\end{algorithm}

\subsection{Grouped Random Access
We assume  $\nu=n=512$ available resources and model the measurements at the base station as $\vec{y} = \vec{F}\vec{x}$, where $\vec{F}\in\mathbb{C}^{n\times n}$ is a $n\times n$-DFT matrix. Note that since we are aiming for user detection, we do not necessarily need to recover $\vec{x}$ exactly: we only need to determine which $x_i$ are non-zero. Our baseline method therefore consists of computing $\supp(\vec{F}^{-1}y)$ to obtain the selected resources.

\begin{figure}
    \centering
    \includegraphics[width=.49\textwidth]{recovered_users_16a__new.pdf}
    \caption{User detection with hierarchical measurements}
    \label{fig:user_detection}
\end{figure}

We compare this to the Grouped Random Access model with $N$ subsampled $\vec{B}_i$, which each consist of $m=256$ random rows from the $n\times n$ DFT matrix. The random modulation matrix $\vec{A}\in\mathbb{C}^{M\times N}$, where $M=16$
is chosen as complex Gaussian with variance $\tfrac{1}{\sqrt{N}}$. This results in the system $\mathbb{C}^{Mm}\ni\vec{y}= \vec{H}\vec{x}$, with measurement operator $\vec{H}$ formed by $\vec{A}$ and the $\vec{B}_i$ as in \eqref{eq:groupedRandomAccess}.

The HiHTP Algorithm \ref{alg:hihtp} is used to recover $\vec{x}$ from the measurements $\vec{y}$. Figure \ref{fig:user_detection} shows the average number of recovered users for varying sparsities $\sigma=16,\dots,36$ and number of blocks $N=8,\dots,32$ over 25 Monte-Carlo trials for each configuration. Note that from $N>8$ on the system has more pre-image dimensions than measurements and the recovery results of our paper apply. Notably, since all the $N$ blocks are filled, classical hierarchical CS does not apply and particularly Theorem \ref{th:s_vs_delta} must be invoked. The baseline shown in Figure \ref{fig:user_detection} is computed as the total number of users, $N\cdot \sigma$, minus the expected number of collisions that occur, if these users choose randomly out of the $n=512$ available resources. As can be seen, HiHTP is able to recover much more users compared to the baseline.
For $\sigma=16$ and $\sigma=32$ the performance of the HiHTP algorithm for user detection is shown, when the $\sigma\cdot N$ users are distributed randomly over all available slots (i.e. the block sparsities are not uniformly fixed to $\sigma$). Even in this scenario, where the algorithm operates with the wrong sparsity parameters, reasonable performance is achieved.

  \section{Conclusion}
  We proved a number of results regarding the HiRIP for hierarchical measurement operators. The results generalize prior work on hierarchical sparse recovery with Kronecker-structured matrices. Furthermore, we demonstrated that the HiHTP algorithm is capable of computing hi-sparse solutions under this measurement structure in a practical Grouped Random Access design for IoT communication scenarios exhibiting huge capacity gains.

\bibliographystyle{unsrt}
\nocite{fantastic-5g-5g-ppp-project-on-5g-air-interface-below-6-ghz}

redpajama_set_name: RedPajamaArXiv


text:
La communauté de communes d'Iholdi-Oztibarre est une ancienne communauté de communes française, située dans le département des Pyrénées-Atlantiques et la région Nouvelle-Aquitaine. La communauté de communes d'Iholdi-Oztibarre était composée de 13 communes.

Historique
La communauté de communes d'Iholdi-Oztibarre a été formée le  janvier 2004. Elle a succédé à l'ancienne structure intercommunale organisée en SIVOM.

La communauté de communes est composée de 13 des 14 communes de l'ancien canton d'Iholdy, Hélette ayant choisi le rattachement à la communauté de communes du pays d'Hasparren.

Le nom d'Oztibarre désigne l'un des six pays historiques de Basse-Navarre, l'Ostabarret, en basque Oztibarre.

Historiquement, la communauté de communes est formée des huit communes de l'Ostabarret, d'une commune du pays de Cize (Suhescun), de la baronnie de Lantabat et des trois communes d'Armendarits, Iholdy et Irissarry jouissant d'un statut particulier dans l'ancien royaume de Navarre.

Le , elle fusionne avec neuf autres intercommunalités pour former la communauté d'agglomération du Pays Basque.

Composition
La communauté de communes regroupait  :

Démographie

Administration

Compétences

Fonctionnement

Principaux équipements

Logos

Notes et références

Notes

Références

Voir aussi

Articles connexes
 Communauté d'agglomération du Pays Basque
 Liste des intercommunalités des Pyrénées-Atlantiques
 Ostabarret

Liens externes

 Site de la communauté de communes d'Iholdi-Oztibarre
 Site de la nouvelle communuté d'agglomération du Pays basque

Iholdi-Oztibarre


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The Animal Models Core offers a full range of pronuclear injection services for production of transgenic mice. Transgenic mouse production is routinely performed in C57BL/6, with other strains such as FVB or hybrid strains available upon request. Transgenic injections can also be performed in custom strains provided by the client. Transgene cloning and BAC recombineering services are available for production of transgenes.
The Animal Models Core offers a full range of rat genetic modification services including pronuclear microinjection for production of transgenic rats using plasmid or BAC transgenes and production of knockout/knockin rats by injection of CRISPR/Cas9 nucleases.
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What's planned for Ladywell Old Baths/Play Tower?
Many organisations have expressed interest in the Ladywell Old Baths/Play Tower since it was named as one of the Victorian Society's 2015 Top Ten Endangered Victorian and Edwardian buildings in England and Wales.
Having lain empty for over 10 years significant investment will be needed to bring the building back into use.
The Trust is aware of a number of proposals for reusing the building. These include a swimming pool/gym, climbing centre, research centre, incubator business space, cafe, restaurant, dance rehearsal space, and a cinema.
At the Ladywell Assembly on 27th January the Council indicated it would, within six weeks, begin a procurement process to decide which of the organisations proposing to refurbish and reuse the building it wishes to partner with.


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Manasaputras are lawful good spirits ascending to a new stage of existence on the Positive Energy Plane. They have the following traits.
Immunity to calling magic, disease, and poison.
+2 racial bonus on saving throws against enchantment spells. This does not stack with the still mind monk class feature and counts as that feature for the purpose of fulfilling prerequisites.
Adaptive Resistance (Su): Many manasaputras have the ability to adapt to elemental attacks quickly. Anytime a manasaputra is damaged by an elemental attack, it gains the adaptive resistance listed against that element for a number of rounds equal to its Wisdom modifier.
Format: adaptive 10; Location: Resist.
Formless (Su): Most manasaputras are not defined by physical form, and choose to adopt a corporeal form at their leisure. Manasaputras with this ability can transition between corporeal and incorporeal forms as a move action. When a manasaputra becomes corporeal, it retains its Charisma modifier as a deflection bonus to AC. A manasaputra's natural attacks, unarmed strikes, and manufactured weapon attacks are only available while the manasaputra is in its corporeal form, with the exception of ghost touch weapons.
Positive Energy Affinity (Ex): Manasaputras can exist comfortably on the Positive Energy Plane, and do not benefit (or suffer) from that plane's overwhelming infusions of life-giving energies. Whenever a manasaputra is subjected to a magical healing effect, that effect functions at its full potential, as if enhanced by the Maximize Spell feat.
Soul Armor (Ex): Manasaputras add their Wisdom bonus to their AC and CMD. In addition, manasaputras gain a +1 bonus to their AC and CMD for every 4 racial HD they possess. These bonuses work as per the AC bonus monk class ability, and monk levels stack with racial HD to determine the additional benefits.
Subjective Appearance (Su): When in corporeal form, a manasaputra projects a psychic illusion over its body, masking its true appearance. Any creature with an Intelligence score of 3 or higher that views a manasaputra sees it as an idealized human form, though often with unusual features. Creatures physically interacting with a manasaputra can attempt a Will save (DC = 10 + 1/2 the manasaputra's HD + the manasaputra's Charisma modifier) to disbelieve the illusion. If successful, the character sees the corporeal veil as a translucent outline, with the fiery body of the manasaputra contained within. This is a mind-affecting illusion (glamer) effect.


text:
Marlin Steel Wire Products Upgrades Its Baltimore, Maryland, Manufacturing Plant
Advanced Manufacturers Utilize Incentives to Improve Financial Performance
Communities Enable "Disruptive" Advantage for Advanced Manufacturers
European Automakers Look to North America
First Person: Aerospace Industry Focuses on Technological Growth and Job Retention
Marlin Steel Wire Products, a leading manufacturer of custom-engineered products from steel wire and sheet metal, will upgrade its Baltimore, Maryland, facility by purchasing new equipment.
The company specializes in producing all types of wire baskets, as well as wire hooks and wire shelves. The company has provided products for various industries such as automotive, aerospace, and pharmaceutical, with customers including Toyota, AstraZeneca, Boeing, and Lockheed Martin.
Maryland Department of Business and Economic Development will provide the firm with a $500,000 State-backed loan guarantee, through the Maryland Industrial Development Financing Authority on a $1.5 million loan from Sandy Spring Bank.
"The State's MIDFA program is a great partner to Maryland manufacturing," said Marlin Steel Wire President Drew Greenblatt. "Through the program, we were able to purchase a top-of-the-line specialty welder – one of only five in the world – that has helped boost our global competitiveness."
Greenblatt added that because of the State's assistance, Marlin Steel has been able to hire two unemployed Baltimore City welders to operate the new machine, and plans to hire two more workers later this month.
"Marlin Steel Wire is a tremendous example of how a company has evolved to meet the growing demands of a global economy," Secretary Dominick Murray said. "We are pleased to work with the company leadership to provide this assistance and are proud that this world-class company is continuing to grow and create jobs for Marylanders."
"Marlin Steel Wire, headquartered in Baltimore City, is recognized as an industry leader in the advanced manufacturing sector," said Baltimore Development Corporation Executive Vice President Kimberly A. Clark. "They produce products that are available globally and we enthusiastically support the continued growth of their operation in the city."


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text:
Fibrus
Residential Business About Us FAQ's News Events Careers Contact Us
Fibrus announced as partner of Belfast Storm
3 months ago · 3 min read
Northern Ireland's first E-Sports team is set to take on some of the world's leading game players in the international Northern League of Legends Championship this month with the support of Fibrus Full Fibre Broadband.
Belfast Storm is the first Northern Ireland team to qualify for the prestigious online tournament, which will see them compete against teams from across Europe and the Nordics. The Belfast based team includes local analysts and coaches, and is completed by some of the leading game players from across Europe.
Belfast man, Stuart McAllister, who is managing director at Belfast Storm, said "You may not have heard of the Northern League of Legends Championship, but with more than 4 million spectators it is one of the most eagerly awaited tournaments in the gaming calendar. We are delighted to be representing Northern Ireland on this huge stage and are excited to be competing with some of the best gamers in the world. We have been training hard for months and with the support of our management team and performance coach, we think we are in a place where coming away as winners is a real prospect.
"Gaming of this level is much more professional than just playing with your mates - you might have been handy at Street Fighter II, but that doesn't mean you're a world beater. It requires real commitment and hard work, as well as travel and time out which we wouldn't be able to do without the support of our partners. We're so grateful to the team at Fibrus for backing our campaign at this year's championship and hope to be celebrating our achievements in the very near future."
Belfast Storm is aiming to be a disrupter in this year's tournament, as they take on some of the most established names in the gaming community, which made the partnership with Fibrus a comfortable fit. Jemma Dougherty, PR and Communications Specialist at Fibrus added:
"Digital connectivity is an essential part of so many elements of our everyday lives, and there are few who know that better than gamers. A Hyperfast Full Fibre broadband connection is key to allowing gamers to take up challenges and battles from Belfast to Bangkok, Brisbane and Boston.
"Belfast Storm has been at the forefront of promoting high skilled gaming in Northern Ireland, but is aiming to be a disrupter at this global tournament. We know what it's like to be a disrupter and hope that the work Fibrus is undertaking to bring full fibre to homes in villages and towns will inspire them even further and help even more people log on and start gaming."
Project Stratum extends coverage plans to additional 8.500 premises
9 hours ago · 6 min read
Meet the Team - Dean Jooste
2 weeks ago · 6 min read
Fibrus Community Fund awards over £9,000 to address digital poverty
Stratum milestone as hyperfast connectivity reaches 15k premises
1 month ago · 4 min read
Fibrus Help Bring Santa To Omagh this Christmas
Fibrus appoints new Service Delivery Director
South Down
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Fibrus Networks Ltd
Lanyon Plaza West Tower
8 Lanyon Place
BT1 3LP Belfast
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A fairytale forest crafted from paper is a homage to nature, floating airlessly above a gallery floor in Hong Kong.
The Wald aus Wald installation resembles a giant cloud as it hovers above visitors, with intermittent head-sized holes for viewing.
Peering up through the forest floor, guests can see the exhibit from the perspective of an insect, says Japanese artist Takashi Kuribayashi. Pristine white, the trees are ghostly empty except for the heads of viewers popping in and out like beetles beneath the soil.
'This poetic white artwork is, however, filled with ironic meaning,' explains the curatorial team at the Hong Kong Art Centre, where the exhibit can be seen until 29 January, 2012.
The reference to irony refers to the exhibition's depiction of trees constructed entirely from paper products. They are made from a combination of kozo, a type of mulberry tree, and mitsumata, a paper bush.
Modeled to resemble larch trees of Yamagata, Japan, the installation is part of theVision of Nature: Lost & Found in Asian Contemporary Art exhibition that's celebrating nature and its connection to art.


text:
Забельський кряж — поперечний гористий поріг у Середньогорсько-Подбалканському регіоні Софії, між Софійською та Бурельською долинами.

Гірський хребет Залебський кряж піднімається між Софійською долиною на сході та Бурелською котловиною на заході, з'єднуючи Чепунську гірку з кряжем Три Уші на  Старих Планинах з горою Вискяр. Він простягається з півночі на південь-південний схід близько 10 км, а  ширина досягая до 2 км.  Піднесення є вододілом між водозбірними басейнами Нішави та Іскира, відповідно Габерською  рікою і річкою Сливнишкою.

Має широкий і плоский хребет з похилими схилами і складений з верхньокрейдових  пірокластичних порід.  Сильно збезлісений піддається ерозії.

У північній частині  у сідловині, що з'єднуює Чепунською гірку та кряж Три уші, розташоване місто Драгоман.  У західній частині схилу є села Бахалин, Драготинці, Повалириж і Чуковезер, а на і східній - Бирложниця та  Ізвор.

У сідловині, що з'єднує  гору Чепун із кряжем Три Уши, недалеко від міста Драгоман проходить ділянка автомобільної дороги державної мережі - КПП «Калотина» - Софія - Пловдів - КПП «Капітан - Андрієво» і паралельно - ділянкА залізничної лінії Белград - Софія - Стамбул.

Топографічна карта

Джерела

Софійська область
Гори Болгарії
Сторінки з неперевіреними перекладами


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The Free variant of GeneratePress gives you decent possibilities, but should you have GeneratePress Premium, you'll be able to customize nearly all about your site.
All In all, GeneratePress will provide you much more customization choices from the WordPress Customizer compared to most other topics. This level of detail might be a little overwhelming if you're a beginner. But once you realize how the settings come together, you will have complete control on how your website appears.
Across All of its features, GeneratePress consistently includes a focus on excellent performance and tidy code. The whole motif is less than 30 kB, which is about as little as you are ever going to find for a WordPress theme. Even most other optimized WordPress themes are still 200+ kB. And a few poorly coded topics can even exceed 1 MB!
Sections — that is kind of like lightweight page building. It lets you create different"sections" onto a page, each with their own layout and column preferences.
With Most topics, each post and page will use the same configurations for the most part. You might have some custom formats or templates — however you do not have very much control past that.
That said, If you are seriously interested in utilizing GeneratePress, I feel you need to purchase the GeneratePress Premium plugin, as that is what makes the theme so flexible. The free version doesn't give you almost as numerous settings in the WordPress Customizer. And you will also lose out on the premade Site Library.
GeneratePress Premium is also still fairly affordable. It costs just $39.95, which provides you use on unlimited websites . You'll also get a 40% discount if you want to renew to continue receiving support and upgrades after the first year (you can, of course, continue using GeneratePress following the initial year without renewing — you just won't receive any more upgrades ).
But If you are ready to spend some time altering settings, GeneratePress' style controls give you the flexibility to flip it into any type of WordPress site. Or, you may even be able to find a starter website that fulfills your needs to save some time.
Additionally, It's one of those fastest-loading WordPress themes that you will find. Therefore, if you're seeking the best performance possible, using GeneratePress as your WordPress site's base is a great choice.


A castle. Horse and carriage. A princess dress. Pretty jewels. A bride, and her charming Prince... the love of her life.
All the ingredients required for a fairytale wedding. Add in magical misty fog billowing around the castle, and you have a rich, dreamy, very mystical atmosphere. Holly and Cam's wedding at Larnach's Castle was one of a kind - I felt I was away in some far distant land, surrounded in pretty details, a loving family, and a gorgeous couple who adore each other completely!
After a quick stop over at the beach to get some photos with some of the little children that she teaches at an early learning centre, we headed to Larnach's Castle. The fog became thicker and more romantic the closer we got.
WOW Kim (and Liam I am guessing) what amazing photos! The Bride and Groom would have to be stoked with them..what an amazing place to get married!
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An analysis done early on in the project drove home the fact that a 10-100X throughput improvement cannot be achieved by optimizing existing SQL Server mechanisms. Throughput can be increased in three ways: improving scalability, improving CPI (cycles per instruction), and reducing the number of instructions executed per request. The analysis showed that, even under highly optimistic assumptions, improving scalability and CPI can produce only a 3-4X improvement. The detailed analysis is included as an appendix.
The only real hope is to reduce the number of instructions executed but the reduction needs to be dramatic. To go 10X faster, the engine must execute 90% fewer instructions and yet still get the work done. To go 100X faster, it must execute 99% fewer instructions. This level of improvement is not feasible by optimizing existing storage and execution mechanisms. Reaching the 10-100X goal requires a much more efficient way to store and process data.
This is important because it confirms the difference in a Level 3 and a Level 2 columnar implementation as described here. It is just not possible for a Level 2 implementation with a row-based join engine to achieve the performance of a Level 3 implementation. This will allow the Level 3 implementations: HANA, BLU, Hekaton, and Oracle 12c to distance themselves from the Level 2 products: Teradata and Greenplum; by more than 10X… and this is a very significant advantage.
I really like how you critique database platforms. Seemingly more objective than the usual SAP hype and marketing.
I try hard to lay out a picture of the various architectural trade-offs made by each vendor… and then to point out the strengths and weaknesses.
But to again disclose fully… out of respect for my paycheck I will point out only the strengths of SAP products and let the readers find the weaknesses themselves from the architecture.
In other words, I'll maintain some objectivity on the plus side and not blow marketing foam… but I won't bash HANA.
I hope this is clear to readers… that they clearly understand my starting point… and that they call me every time they find a mistake.


text:
ACCEPTED

#### According to
Index Fungorum

#### Published in
Revta Fac. Agron. Vet. Univ. nac. La Plata 6(1): 51 (1910)

#### Original name
Venturia puyae Speg.

### Remarks
null


VA will pay a burial allowance up to $2,000 if the veteran's death is service connected. VA also will pay the cost of transporting the remains of a service-disabled veteran to the national cemetery nearest the home of a deceased that has available gravesites. In such cases, the person who bore the veteran's burial expenses may claim reimbursement from VA.
VA will pay a $300 burial and funeral expense allowance for veterans who, at time of death, were entitled to receive pension or compensation or would have been entitled to compensation but for receipt of military retirement pay. Eligibility also is established when death occurs in a VA facility or a nursing home with which VA contracted. Additional costs of transportation of the remains may be reimbursed. There is no time limit for filing reimbursement claims of service-connected deaths. In other deaths, claims must be filed within two years after permanent burial or cremation.
Gravesites in national cemeteries cannot be reserved. Funeral directors or others making burial arrangements must apply at the time of death. Reservations made under previous programs are honored. The National Cemetery System normally does not conduct burials on weekends. A weekend caller, however, will be directed to on eof three strategically located VA cemetery offices that remain open during weekends to schedule burials at the cemetery of the caller's choice during the following week.


The International Institute at Mississippi State will host a forum on "Inviting an International Scholar" as part of its Global Engagement Series on March 24 at 3:30 p.m. in Colvard Student Union's Fowlkes Auditorium.
The seminar will explain the process of inviting an international visitor -- including scholar, researcher or intern -- to campus and obligations of the host department to the visitor during their stay. Considerations that will be discussed include housing, immigration (DS-2019 form assistance), export control compliance, letters of invitation, and funding.
All departmental business managers, administrative assistants, faculty and department heads are invited to attend. For more information, please contact Caroline Hearnsberger at chearnsberger@international.msstate.edu.