Nebulae are huge interstellar clouds of gas and dust that range in size from 1 AU to 10 AU, and which are less dense than the deepest vacuum in Earth's laboratories. Just one portion of of a nebula the size of Earth would weigh only a few kilograms! The first nebulae that formed after the Big Bang contained mainly hydrogen and helium, but later nebulae formed with nitrogen, carbon, oxygen and even large molecules. The size, shape and characteristics of nebulae may vary significantly because some are star nurseries and others are the remains of dead stars. Keep reading to learn more about dark nebulae, emission nebulae, reflection nebulae and planetary nebulae.
Dark nebulae are found in areas that have no nearby stars. They neither emit nor reflect enough light to be visible.
In fact, dust particles usually blot out light from the stars behind them, though occasionally bright stars behind the dark nebulae will emit enough light so we can see the outlines of a dark nebula.
Surprisingly, scientists discovered that besides the common elements like hydrogen and helium, these clouds contain some simple molecules like water, methanol, carbon dioxide, and ammonia. These molecules can stick together and form grains, which probably play an important role in the formation of the stars.
The Horsehead Nebula, one of the most famous dark nebulae, is located in the constellation Orion.
Emission nebulae are huge bright gas clouds with irregular shapes and dimensions that span many light years across. Emission nebulae are where stars are born.
When stars begin to shine, they heat up the remaining gas around them and that gas starts to shine as well.
One of the most famous emission nebula is M42, which is located in the constellation Orion. With binoculars you can see it as a pale diffuse spot that appears to be shaped like a heart. With powerful telescopes astronomers are able to detect many young stars inside.
Reflection nebulae are usually faint and shine with the reflected light of the stars within them. They are the remains from the former dense cloud of an emission nebula. Once stars are born inside an emissions nebula, they consume large amounts of the nebula's dust and gas, and the remains continue to shine with a faint reflected bluish light.
An example is Pleiades in the Taurus constellation. Its stars formed about 10 millions years ago, yet it continues to shine with a bluish light.
Planetary nebulae are the remains of stars. When a middle size star, like our Sun, ends its phase as red giant, it expels its outer shells. These outer shells form beautiful nebulae with a regular symmetrical shape.
Planetary nebulae tend to be smaller; they rarely exceed more than few light years across.
With binoculars, you can easily find Planetary Nebula M57 in the constellation Lyra, and it will look like a pale spot. Photographs with larger telescopes clearly show its ring shape.
Stars are usually born in groups in dark dense nebulae sometimes called star nurseries. It is not quite clear what exactly triggers star formations. It might be the distribution caused by explosion of a nearby star or simply the gravitational pull of the gas condensation within the nebulae.
Once formed, these gas condensations start to grow, attracting more and more gas and dust. Astronomers called them EGGs - Evaporating Gaseous Globules. They look like fingertips emerging from a gas cloud. After some time, they split from the cloud, condense and heat up.
Since they swirl at the same time, the gas around them starts to form a disk around the future star. When the temperature in the star becomes high enough for nuclear fusion to begin, a star is born. The star's wind then expels the gas remnants and the star begins to shine steadily.
Dark nebulae do not shine with visible light because they are very cold. However they emit radio waves with wavelengths of up to 21 cm and this allows astronomers to detect and study them. Using radio telescopes, astronomers detected many dark nebulae in the disk of our galaxy and especially at its center.
The Hubble Space telescope has taken wonderful pictures of all kinds of nebulae. It has revealed that some of the newly formed stars are surrounded by disks made from dust and ice. Those images provide evidence that planetary systems might form at the same time as the stars.
The Spitzer telescope has taken breathtaking pictures of many nebulae at different stages of star formation. Since this telescope can view infrared light emitted by objects much cooler than the stars, it can penetrate deep in the heart of nebulae and find out what happens.
The biggest stars usually end their lives with gigantic explosions called supernovas. They become as bright as the whole galaxy. Remains from these explosions also form bright nebulae with irregular shapes. The heavier chemical elements, necessary for life, also form during these explosions.
A unit of measure equal to the distance between the Earth and the Sun, or 149,597,870.7 kilometers (92,955,807.3 miles).
The scientific explanation for the origin of the universe, championing the notion that the universe spontaneously originated 15 billion years ago in a colossal explosion.
A colorless and odorless gas, and one of the most abundant elements in Earth's atmosphere, and the seventh most abundant element in the Universe.
Nitrogen is a byproduct of the fusion process that occurs in stars.
The fourth most abundant element in the universe, carbon is the basis for life on Earth.
The third most abundant element in the universe and a key component of the air we breathe.
A colorless, flamable liquid, commonly used as antifreeze.
A colorless gas consisting of one carbon atom bound to two oxygen atoms.
A dark nebula in the constellation Orion.
One of the most well-known constellations in the sky, Orion is home to the stars Betelgeuse and Rigel, as well as M42 -- the Orion Nebula.
Messier 42, also known as the Orion nebula, is a nebula located just south or Orion's belt, seen as on of the points of light in Orion's sword.
An open star cluster located in the constellation Taurus, containing hundreds of stars. The seven brightest, Sterope, Merope, Electra, Maia, Taygeta, Celaeno, and Alcyone, are named after the Seven Sisters of Greek Mythology.
One of the constellations of the zodiac, and home to the red giant star, Aldebaran.
Messier 57, more popularly known as the Ring Nebula, is a planetary nebula located in the constellation Lyra, south of Vega, Lyra's brightest star.
A constellation visible in the northern hemisphere and home to the stars Vega and Sheliak.
Nuclear fusion is the process by which the nuclei of two atoms fuse together to form a heavier element; large amounts of energy are produced by this fusion.


The company Les Ateliers de Yèbles as a job shop has specialized in the production of facade elements. The requests of the architects sometimes are very special and constantly require new part design variations from the technical department at Yèbles. Flexibility is also needed in production as the production quantities often only range between ten and forty identical parts. The RAS UpDownCenter meets these requirements brilliantly.
The von Arb AG SAS produces sound proof enclosures. In addition, the company has established itself as a highly flexible job shop. Even special orders can usually be provided with same day delivery. "If you want to produce single customized parts, you have to consider machines that can handle Step files and automatically program the component," says Roman von Arb and adds: "For small production batches, alternating bending directions, large formats and heavy parts the UpDownCenter is unbeatable."
Geerds Metallbau GmbH has gained more than 40 years of experience and expertise in facade projects. The facade specialists from Groß Welzin pair innovative product design with the latest production technology. The RAS UpDownCenter completes the performance spectrum of this leading supplier in facade technology. The Bendex one-click software programs the parts with a single mouse click. With an automatic tool change and scratch-free folding, Geerds is able to create complex and optically demanding components in small quantities and highly profitable.
The Roessler GmbH from Mertendorf in Germany is a job shop that specializes in enclosures of machine tools. The variety of housings and small batch quantities requires high production flexibility and a high level of vertical integration. When Roessler's customers changed their product to a design with large radii, the previous production with press brakes reached its limits. Today, a RAS UpDownCenter folding system bends the radii automatically.


Oh man guys, the day two post-race delayed onset muscle soreness is the worst. I rolled out of bed this morning and nearly fell over. My quads, IT bands and calves pretty much hate me.
But, they hate me because I had an unexpectedly awesome race in Baltimore over the weekend.
I don't know where this time came from. Baltimore is an extremely hilly course, and I didn't come into the race trained to run this hard. My plan all along had been to train to run the race for fun because with grad school demands this semester, I knew I wasn't going to have the time to dedicate to super long midweek workouts.
Even though my plan was to just go out and have fun, I still was extremely nervous on race morning. The weather was crisp, but the sun was shining and I was having a hard time deciding what to wear. I eventually opted for my long-sleeve top since it was supposed to be breezy. I spent much of the first 3 miles regretting that decision since I was basically melting.
But luckily for me, somewhere during the race it actually go colder, and I was glad to have the long-sleeves.
Since I've run this race so many times now, I'm really familiar with the course and know when to expect long uphill slogs. In my head, I had a plan to run the first three miles and reassess how I was feeling when I got to the first aid station after the marathon and half-marathon courses merge right around that point.
I was feeling surprisingly good and just kept trucking along, almost laughing to myself at the times I was seeing on my Garmin.
Somewhere in this section of the course, I spotted a friend I used to work with at the newspaper at UMD. Thanks for being out there cheering Scott! It's always fun to see random people along the course!
My next major mental milestone was to get to Lake Montebello, which was somewhere near the 7 mile mark. I knew once I got here, I'd have at least a mile of flat running as a reprieve from the hills. Until then, my plan was to keep my feet moving. Slow and steady on the uphills and then use the downhills to make up some time lost on the climbs.
I tried hard not to lose time through the aid stations, though there were times when I did stop to walk for a few seconds to ensure the Gatorade went in my mouth and not down the front of my shirt. Overall, the stations were supremely well-organized and I never got stuck in a back log.
I threw back my first Gu somewhere near mile 4.75.
When we finally reached the lake, I was so excited to have some flat course, but maybe my legs appreciated the variety of inclines because about half way around the lake my left knee and hip started majorly revolting. I had to slow down a bit to try to get things under control, and mentally bribed myself to keep running until the next aid station, which was just around the bend.
I made it, and the quick walk I took there made a world of difference, and my knee and hip settled down and didn't really bother me the rest of the race.
The climb from mile 8 to 9 is pretty aggressive, but I just kept trucking on. I knocked back my last Gu just past mile 9.
The last four miles of the race are some of my favorite because there are tons and tons of spectators out and about blasting music, dancing in the streets in costumes, handing out gummy bears and lots and lots of Natty Boh.
Every time I looked down at my Garmin, I couldn't believe there was a chance I could still go sub-two. I thought the hills on the course would basically destroy me, but I was feeling good. Mile 10 is almost all downhill, so I knew I could make up some time there too, and I just let myself coast.
But maybe I coasted a little too hard because when I hit more uphills in mile 11 I was struggling. I knew sub-two was still do-able, but I needed to keep a strong pace, and I was fading fast. Knowing that mile 12 was also all mainly downhill, I figured I'd be OK, but mile 11 just killed me.
When I hit mile 12, I tried to accelerate a tiny bit to take advantage of the downhills, but I just couldn't quite pick up the pace enough. As I was cruising past Camden Yards, I knew it would be close. I kicked hard to the finish line, but probably didn't start my kick soon enough.
But I left everything I had out on that course. For coming into a race with truly just the bare minimum of training, I'm honestly shocked I was able to pull off such a fast time. Sure it would have been awesome to go sub-two on an extremely tough course, but even though I didn't, I'm still thrilled with my time.
I'm also really proud of how mentally tough I stayed during this race. There were plenty of times when things were sore or my legs were tired or I was staring up at another hill and I could have thrown in the towel, but I never did, and that's a minor victory too because that's not always easy for me.
Once I crossed the finish line, I hobbled over to get my medal, and heard someone call my name. It was one of my blog readers who recognized me in the crowd. He had also finished the half and was using it as an easy run before tackling the Marine Corps Marathon this weekend! Hope you're recovering better than I am and that you have a great race next week!
I made the long and slow hobble back to where my dad was spectating, and we waited together for my mom to finish. I'm glad she wore neon so she was easy to spot in the crowd!
I also saw another one of my college newspaper friends finish his very first marathon! Congrats Jeff! You rock!
Overall it was a great day of racing. I had a great time as always. I can't recommend the Baltimore Running Festival enough. It was my first marathon back in 2006 and I've come back again and again to do the half because this city just puts on an amazing race.
Great job Jess! I just finished two back to back half marathons and now have 12 days until I race RNR Savannah!!
That's a great time and race recap! It was freezing pre-race!


text:
Mark Skilton, Contributor
The BT carrot and stick and the challenge of building the future of digital telecoms for the UK
07/29/2016 02:05 pm ET Updated Jul 30, 2017
The next generation of broadband, the new 5G standard, smart systems, the Internet of Things and Machine to machine connectivity is vital for the "next big thing" that will define the digital connected economy of the 2020 2025 and beyond. The UK has established a leading position in digital innovation and pushing to build connected society, industry and productivity improvements that digital can bring but it is underpinned by a telecoms network that is cost effect and fit for purpose. It is a race as other nations push ahead with similar initiative and what is at stake is competitive industries and jobs in the new connected regionals and international markets.
The recent BT Group ruling by Ofcom to continue the Openreach program is heavily caveated with the government and industry demands for more investment in not just speed of the network but capacity and coverage to meet the demand for truly connected and high bandwidth digital services. How this will pan out is the technological and investment roadmap that needs to keep being relevant and up-to-date in its thinking in at all levels in government, regulator and industry leadership to leverage the many different frequencies and technology networks coming onto the market driving the smart connected society of the near future.
Does Regulation drive Innovation and Investment?
This is a key question in the recent Ofcom ruling not to break up BT Group into two separate businesses a few days ago. This would have freed up the Openreach broadband Infrastructure division into a standalone business. As it stands the solution reached was a legally separate Openreach business to be run by a separate management board but the overall investment budget still set by the BT group.
This came with a strong condition from Ofcom and the government that BT must invest more in UK Broadband Openreach and give it more freedom to invest supported by an independent review published in 7 July 2016 (1). So this may yet to a stay of execution rather than the final solution, even if Gavin Patterson, BT CEO, promised to invest £1 billion in Openreach if it retained control. It raises questions over what time frame and to what extent this investment is enough to reach some level of performance deemed acceptable. With MPs saying BT is "not investing enough" in the national network and more on higher returns in sports services, it is a question on how effective the role of regulators, companies and market forces to drive innovation and investment for national interests.
What is the goal?
BT Group Q1 earning announcement yesterday (July 28) that profits are up 13% and adjusted revenue up 35% to 5.78 billion pounds was attributed to the £12.5 Billion acquisition of EE the immediate performance expectations from the shareholders and BT management board seem to be upward (2). But other reports on the service availability of mobile networks coverage and access to "fast" broadband networks has been described as falling behind other countries in terms of coverage and speed. Part of the difficulty is establishing what facts are relevant in this case the terminology of the network and coverage used is often wrapped in commercial language and interests when the needs of households and businesses to be objectively set beyond a tactical roll-out.
In January 2016 BT reported Fibre Broadband networks reaching 86% of UK premises following 19 million homes equivalent to 66% of the UK in a 2014 programme of investment. BT next generation G.fast and Fibre-to-the-Premises (FTTP) is reported as a mixed approach to implementing a faster network. Fibre-to-the-Premises (FTTP) and the G.fast network is starting rollout in 2017 with speeds of 300Mbps to 500Mbps available to 10 million premises by 2020 and most of the UK by 2025. FTTP will also get a speed boost to 1Gbps mostly for business customers (3).
Overall putting 90% of premises within reach of superfast broadband described as +24 Mbps from BT and other providers including Virgin Media and Gigaclear this seems to be different to the expectation of a faster network reported in the Ofcom Openreach review. The BT competitors Sky, Vodafone, TalkTalk are currently reliant on access and the performance of the BT Openreach infrastructure both in terms of open access but in its upgrades and maintenance. But does the BT ownership create the right future infrastructure strategy and outcomes? The reported Ofcom reason for the legal separation only was the complexity and time to split the organisation weighed again the benefits presumable and the imperative to get a faster network in the 2020, 2025 timeframe for the UK economy.
Building the infrastructure we want not what the market deserves
What is at stake here is more than the current discussions based around company competition, profits and market share. It is the vision and roadmap for a faster world class national broadband infrastructure. The government demands that companies in this area should "operate for the wider good" reflects the challenges for regulators to stimulate competition but at the same time seek to drive a national agenda.
The independent government report stated that an emphasis on just speed as the main metric for describing broadband performance was not telling the entire story of total service performance particularly capacity offered to users and the real availability of this coverage. In deed the "Demand for broadband services has increased considerably over the past few years." New uses of connected services from smart cities, smart homes to new ways to design products and services are rapidly becoming apparent.
It matters because modern digital economies are powered by online business models and a growing connected infrastructure that is enabling new smarter services, higher productivity throughputs and new competitive edge from new data and high performance systems.
There is a huge difference in network coverage and capacity to shift speed that in 3G, 4G is typically supporting email or web surfing and video calls to being able to move large data files , images and more importantly always connected and in real-time. This is the expectation and design standard of the "Internet if Things" IoT and the 5G generation mobile standard
This type of vision describes a new level of ultrafast low latency internet connection; gigabit bandwidth and the ability to support tens if not hundreds of connected sensors and users in close location and always connected with this performance from any location static or moving. This is not possible today with current technology infrastructure. It is a steep change from today's coverage of the UK and speed of services driven by subscription models for data.
Challenges to implementing new digital technology
The challenge to implementing new digital technology is in the commercial models, information standards, workforce skills and governance to drive forward new technology adoption and the value from digital business models it enabled. As stated in the BT strategy and in telecommunications business models that are today heavily focused towards asset ownership return on investment but new digital models require "building ecosystems" beyond individual companies. There are cases that have seen national broadband investments at city and national levels. In Sweden the Stockab municipal broadband network to the SK Telecoms and Samsung partnership to investing in LoRWAN nationwide network for connected sensors. Examples nearer home such as the Bristol "programmable city" show an inter-network pilot of telecoms, Wi-Fi and mesh sensors into connected homes. Commercial telecom investment needs subscribers and data volumes that will drive usage which is why the remote connectivity to rural areas can be challenging but even with investment from EU development funds, the new business models of the digital economy will need coverage, capacity to be a connected society in the true sense.
The move from a "speed" based model to a "capacity" based model is a different mind-set and investment profile. Therefore I think there may be more than one way to approach this, whether it is the consistency of a single network operator to drive a complete infrastructure refresh as in the current BT model is open to debate. What is apparent is the open forecasts of demand for data is rapidly changing.
This may need rapid new investment approaches across many IoT networks, local area networks and machine to machine connection standards. Work in the UK Innovate Digital catapult, Future Cities catapult, Future Transport catapult and many other initiatives are all travelling towards this goal.
Speed throttling and net-neutrality versus innovation
The issues of landlords, investment funding and commercial models are just part of the demand side adoption strategy that ultimately needs held down or enabled by the supply side network that is faster, bigger and better than today. The UK is at the forefront of many ideas in digital and it is critical that the path to the vision of 5G, IoT to enable smart connected business and systems is maintained and realistically invested in. This may need to adapt and work with partners and strategies that may be different to the old world of systems and services and more a connected ecosystem of services and multiple providers. The aspirations of net-neutrality are to enable commercially fair practices and consumer access yet the pace of innovation and new forms of networks raised the question of protection of existing networks for the choice of faster routes to new scale capabilities.
The future will need to be funded and a vision and standards to progress the roadmap to the digital economy.
1.	Annex: Specialist Advisers' advice to the Committee, Investment in superfast broadband: Regulation, competition and the cost of capital, A joint paper to the Committee by Tim Jenkinson,254 Tony Lavender,255 Jim Norton256 and Helen Weeds,257 7 July 2016 http://www.publications.parliament.uk/pa/cm201617/cmselect/cmcumeds/147/14714.htm#_idTextAnchor084
2.	BT Q1 2016 Results http://www.nasdaq.com/article/bt-group-q1-pretax-profit-up-13--quick-facts-20160728-00076#ixzz4Fhw1sfux
3.	BT's "Fibre Broadband" Network Reaches 86 Per cent of UK Premises April 2016 http://www.ispreview.co.uk/index.php/2016/04/bt-openreachs-fttc-dominated-broadband-covers-25-million-premises.html
4.	BT not investing enough in Openreach, MPs say July 2016 https://www.theguardian.com/business/2016/jul/19/bt-not-investing-enough-in-openreach-broadband-mps-say
Technology Broadband Digital Ofcom

redpajama_set_name: RedPajamaCommonCrawl


text:
Tag results for Michael Theanne
Michael Theanne
Esteemed artist manager and former DJ Mag sales manager, Michael Theanne, has died
Michael went on to manage Steve Aoki, Joachim Garraud and other EDM acts
The Black Madonna: DJ Mag UK cover feature
The Black Madonna is the real deal. Raised in Kentucky but born in the DJ booth of Chicago's Smartbar, she's unleashed the true spirit of house back into the world. Fearlessly challenging the status quo both on and off the dancefloor, she's spearheading a global revolution drawing its power from the founding principles of dance culture. In advance of playing our Miami pool party, we found out why The Black Madonna still believes...
20 Years of DJ Mag - A Retrospective
Living and breathing dance music
For 20 years, DJmag has been in amongst it, at the vanguard of dance and electronic music culture, commentating, conversing and partying within the scene that we live and breathe.
But flashback to the start — how did it all begin? What was it like to be there? How did DJmag grow into the entity it is today?
We're gonna go back, way back, into the mists of time, as we celebrate 20 years of DJ Magazine…


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From huge database, excellent portfolio, and tons of experience we at Temptation Realty help you end your search for the best land that meet your requirements and provide you the best services you could ever expect.


text:
\section{Introduction}
Spin squeezing in multiqubit states has been an intense
area of research~\cite{wkz,ku,wn1,wn2,caves,yurke,ku2,gsapuri,puri,sor,ulamku,um,usha1,usha2,s1,s2,us1,us2,dyan,akru,gtoth,song,dsu} both for its theoretical importance and for its applicability in entanglement-enhanced sensing in quantum metrology. Spin squeezing implies pairwise entanglement~\cite{sor,ulamku,usha1,usha2,s1,s2, Vidal04, Vidal06} and has gained significance in the  quantification of metrologically useful entanglement in large number of ensembles of atomic spins.

Kitegawa and Ueda~\cite{ku} proposed a definition of spin squeezing in terms of the uncertainty relation between collective angular momentum components of a spin $j=N/2$ state of an arbitrary $N$-qubit system.  A quantitative measure of spin squeezing, incorporating invariance under rotation of the frame of reference, is defined as~\cite{ku}, $\xi=2\left(\Delta{J}_\bot\right)_{\rm min}/\sqrt{N}$ and  a $N$-qubit state is spin squeezed if the {\emph {minimum}} value of the variance  $(\Delta{J_\bot})^2$ of the spin component $J_\bot$, in the direction perpendicular  to the mean spin direction $\langle \vec{J}\rangle$,  is smaller than the standard quantum limit $N/4$ of the coherent spin states~\cite{ku}.  More specifically,
\be
\left(\Delta{J_\bot}\right)^2_{{\rm min}} \leq \frac{N}{4}\Longrightarrow\, \frac{2\left(\Delta{J}_\bot\right)_{\rm min}}{\sqrt{N}}\leq 1
\ee
and hence the  parameter  $\xi=\frac{2\left(\Delta{J}_\bot\right)_{{\rm min}}}{\sqrt{N}}<1$ for spin squeezed states~\cite{ku}.
Here $\left(\Delta{J}_\bot\right)^2=\left\langle {J}_\bot^2\right\rangle - \left\langle {J}_\bot\right\rangle^2$
is the variance of the component  ${J}_\bot$ of the angular momentum, perpendicular to the mean spin-direction $\hat{n}_0~=~\frac{\langle\vec{J}\rangle}{\left|\langle\vec{J}\rangle\right|}~=~\frac{\left(\langle{\hat{J}}_x\rangle,\,\langle{\hat{J}}_y\rangle,\,\langle{\hat{J}}_z\rangle\right)}{\sqrt{\langle{\hat{J}}_x\rangle^2+\langle{\hat{J}}_y\rangle^2+\langle{\hat{J}}_z\rangle^2}}$, of the $N$-qubit system.
The spin-squeezing parameter of a $N$-qubit symmetric state can be expressed in terms of the correlation matrix elements of its two-qubit reduced density matrix, expressed in the standard form~\cite{usha2},
\begin{eqnarray}
\label{st1}
\rho&=&\frac{1}{4}\, \left[I\otimes I+\sum_{i=x,y,z} \left(\sigma_{i}\otimes I + I\otimes \sigma_i\right) \, s_{i}  \right.\nonumber \\
&& \ \ \left. +\sum_{i,j=x,y,z} (\sigma_{i}\otimes \sigma_{j})\,t_{ij}\,\right]\, ,
\label{rho}
\end{eqnarray}
where $I$ denotes the $2\times 2$ unit matrix,  $\sigma_i$ are the standard Pauli spin matrices and
\begin{eqnarray}
\label{st2}
s_{i}&=&{\rm Tr}\,\left[\rho\, (\sigma_i\otimes I)\right]={\rm Tr}\,\left[\rho\, (I\otimes \sigma_i)\right] \nonumber \\
t_{ij}&=&{\rm Tr}\,\left[\rho\, (\sigma_{i}\otimes\sigma_{j})\right]={\rm Tr}\,\left[\rho\, (\sigma_{j}\otimes\sigma_{i})\right]=t_{ji},
\end{eqnarray}
denote the qubit orientations $\vec{s}=(s_x,\,s_y,\,s_z)$ and  the real symmetric $3\times 3$ correlation matrix  $T=(t_{ij}), \ \ i,j=x,y,z$.
The spin-squeezing parameter $ \xi$ can be expressed in the following simple form~\cite{usha2}:
\begin{eqnarray}
\label{xitil1}
{\xi}&=&\left[1+(N-1)(\widetilde{\hat n}_{\bot}\,T\,
{\hat n}_{\bot})_{\rm min}\right]^{1/2}.
\end{eqnarray}
where ${\hat n}_\bot$ is a unit vector perpendicular to the mean spin direction ${\hat n}_0$ and  $\widetilde{\hat n}_{\bot}$ denotes its transpose.
Choosing a suitable co-ordinate system with mutually orthogonal triads $\hat{n}_{1},\, \hat{n}_2,\, \hat{n}_0$ of basis vectors, such that the $Z$-axis is aligned along the unit vector $\hat n_0$ (mean spin direction), it may be seen that  the quadratic form $({\widetilde {\hat n}_{\bot}}{T}{\hat n}_{\bot})_{\rm min}$ is the {\em minimum eigenvalue}~\cite{usha2,dsu} of the $2\times 2$ block $T_\bot$  of the correlation matrix $T$ in the basis ${\hat n}_{1},\hat{n}_{2}$ orthogonal to the mean spin direction $\hat{n}_0$:
\begin{eqnarray}
\label{nmin}
&&({\widetilde{\hat n}_{\bot}}{T}{\hat n}_{\bot})_{\rm min}=\left.\frac{1}{2}\, \right[
\left( \widetilde{\hat n}_1\, T\,{\hat n}_{1}+\widetilde{\hat n}_2\, T\,
{\hat n}_{2}\right)  \nonumber \\
&&  \left.\ \  - \sqrt{\left(\widetilde{\hat n}_1\,T\,{\hat n}_{1}-\widetilde{\hat n}_2\,T\,{\hat n}_{2}\right)^2 +  4\, \left(\,\widetilde{\hat n}_1 \,T \,{\hat n}_{2}\right)^2}\right].
\end{eqnarray}
Consequently, the spin-squeezing parameter $\xi$ can be expressed in an operationally simple form, on substituting Eq.~(\ref{nmin}) into  Eq.~(\ref{xitil1}). In other words, the Kitegawa-Ueda spin-squeezing parameter $\xi$ may be evaluated using  the   two-qubit reduced density matrix of {\em  any} random pair of qubits of a $N$-qubit symmetric system.

In this paper we employ  Majorana geometric representation~\cite{majorana} of pure symmetric $N$-qubit states and explore spin squeezing in the family
$\{{\cal D}_{N-k,k}\}$ of $N$-qubit states with two distinct Majorana spinors. Dicke states, the common eigenstates of collective operators ${\hat J}^2$, ${\hat J}_z$, are special states of the family $\{{\cal D}_{N-k,k}\}$,  ($1\leq k\leq \left[N/2\right]$) with the constituent  two distinct orthogonal spinors  $\vert 0 \rangle$, $\vert 1\rangle$. It is well known that Dicke states are entangled but are not spin squeezed~\cite{gtoth2}. We focus our attention to investigate spin squeezing behavior of $N$-qubit symmetric states constituted by two distinct {\em non-orthogonal} spinors belonging to the Majorana family $\{{\cal D}_{N-k,k}\}$, where one of the spinors occurs $k$ times and the other $(N-k)$ times. We evaluate the reduced two-qubit density matrix of $N$-qubit states belonging to different SLOCC classes~\cite{arus,bastin,solano} of the family $\{{\cal D}_{N-k,k}\}$ with $1\leq k\leq \left[N/2\right]\}$ and deduce the spin squeezing parameter for different values of $k$.

This paper is organized as follows: Section~II gives an overview of the Majorana geometric representation of symmetric $N$-qubit states and provides a canonical structure for the family of states $\{{\cal D}_{N-k,k}\}$ with two distinct spinors. In Section III, we evaluate the
two-qubit reduced density matrices and the spin-squeezing parameter of the $N$-qubit states belonging to $\{{\cal D}_{N-k,k}\}$, with  $1\leq k\leq \left[N/2\right]$. The variation of the spin squeezing parameter for the family of states $\{{\cal D}_{N-k,k}\}$, with different values of $k=1,2,\ldots ,[N/2]$ and $N$, is illustrated in Section~III. Section IV contains a brief summary.

 \section{Majorana representation of pure symmetric multiqubit states}
In the novel 1932 paper~\cite{majorana} Ettore Majorana proposed that a quantum system prepared in a  pure spin $j=\frac{N}{2}$ state can be represented as a permutation of the states of  $N$ constituent qubits  as follows:
\begin{equation}
\label{Maj}
\vert \Psi_{\rm sym}\rangle={\cal N}\, \sum_{P}\, \hat{P}\, \{\vert \epsilon_1, \epsilon_2,
\ldots  \epsilon_N \rangle\},
\end{equation}
where
\begin{equation}
\label{spinor}
\vert\epsilon_l\rangle= a_l  \vert 0\rangle + b_l e^{i\beta_l} \, \vert 1\rangle,\ \ l=1,2,\ldots, N, \ \ \ a_l^2+b_l^2=1
\end{equation}
denote the states of the qubits (spinors) constituting the symmetric $N$-qubit state $\vert \Psi_{\rm sym}\rangle$;
 $\hat{P}$ corresponds to the set of all $N!$
permutations and ${\cal N}$ corresponds to an overall normalization factor. Eq.~(\ref{Maj}) is referred  to as the {\em Majorana geometric representation} of a pure quantum state $\vert \Psi_{\rm sym}\rangle$ of spin $j=N/2$ or equivalently, that of permutationally symmetric $N$ qubits, expressed in terms of the constituent spinors $\vert \epsilon_l \rangle,\  l=1,2,\ldots N$. It may be  seen that when all the $N$ spinors $\vert\epsilon_l\rangle,\ \ l=1,2,\ldots, N$  are identical, the corresponding class $\{{\cal D}_{N}\}$ consists of separable states $\vert D_N\rangle=\vert \epsilon,\epsilon,\ldots \epsilon\rangle$.  The states
\begin{eqnarray}
\label{n1n2}
\vert D_{N-k,k}\rangle&=&{\cal N}\,[\vert \underbrace{\epsilon_1, \epsilon_1,\ldots
\epsilon_1}_{N-k}, \underbrace{\epsilon_2, \epsilon_2,\ldots \epsilon_2}_{k}\rangle+ \nonumber \\
& +&{\rm \, permutations\,}],  \ \ k=1,2, \ldots [N/2]
\end{eqnarray}
constructed from two distinct spinors $\vert\epsilon_1\rangle,\ \vert\epsilon_2\rangle$ belong to the family $\{{\cal D}_{N-k,k}\}$ of $N$ qubits. It may be noted that the Dicke states $\left\vert \frac{N}{2}, \frac{N}{2}-k\right\rangle$,
$k=1,2, \ldots [N/2]$ are the representative states of the family $\{{\cal D}_{N-k,k}\}$, with two orthogonal spinors $\vert\epsilon_1\rangle=\vert 0\rangle$, $\vert\epsilon_2\rangle=\vert 1\rangle$.

An arbitrary  symmetric state  belonging to the family $\{ {\cal D}_{N-k,k}\}$ is given by~\cite{arus,bastin,solano},
\begin{eqnarray*}
\vert D_{N-k, k}\rangle &=& {\cal N}\, \sum_{P}\, \hat{P}\,\{ \vert \underbrace{\epsilon_1, \epsilon_1,
\ldots , \epsilon_1}_{N-k};\ \underbrace{\epsilon_2, \epsilon_2,\ldots , \epsilon_2}_{k}\rangle\}
\end{eqnarray*}
 and it can be reduced to a canonical form, characterized by only one real parameter~\cite{arus,arss}, with the help of identical local unitary transformations on individual  qubits. More specifically,   symmetric pure states $\vert D_{N-k, k}\rangle$ belonging to the family $\{{\cal D}_{N-k}\}$, are equivalent (under local unitary transformations) to the canonical state of the following form~\cite{arss}
\begin{eqnarray}.
\label{nono}
\vert D_{N-k, k}\rangle &\equiv & \sum_{r=0}^k\, \beta^{(k)}_{r}\,\,  \left\vert\frac{N}{2},\frac{N}{2}-r \right\rangle, \\
\beta^{(k)}_{r}&=&{\cal N}\,\,
\sqrt{\frac{N!(N-r)!}{r!}}\,\frac{a^{k-r}\, b^r}{(N-k)! (k-r)!}\,  \nonumber
 \end{eqnarray}
where  $0\leq a, b=\sqrt{1-a^2}\leq 1$ are real parameters.

In the next section we evaluate the two-qubit reduced density matrix of the state $\vert D_{N-k, k}\rangle$ for different values of  $k=1,2,\ldots $, for any  $N$  and deduce the spin-squeezing parameter $\xi$ (see Eq.~(\ref{xitil1})) corresponding to inequivalent classes $k=1,2,\ldots [N/2]$ of the family  $\{{\cal D}_{N-k,k}\}$. We establish that  the states $\vert D_{N-k,k}\rangle$ are spin-squeezed, except when $a=0$ and $a=1$.

\section{Spin squeezing in the family $\{ {\cal D}_{N-k,k}\}$ of $N$-qubit symmetric states with two distinct spinors}

In order to analyze spin squeezing in the different inequivalent SLOCC classes~\cite{arus,bastin,solano}, corresponding to $k=1,\,2,\,3,\,\ldots, [N/2]$, in the family $\{ {\cal D}_{N-k,k}\}$ of symmetric states, we first obtain the two-qubit reduced  density matrix $\rho^{(k)}$ corresponding to any random pair of qubits in the state $\vert D_{N-k,\,k}\rangle\in \{ {\cal D}_{N-k,k}\} $. We have
\begin{widetext}
\begin{eqnarray}
\label{formal_rhok}
\rho^{(k)}&=&\mbox{Tr}_{N-2}\left(\vert D_{N-k,\,k}\rangle\langle D_{N-k,\,k} \vert\right) \nonumber \\
&=&\mbox{Tr}_{N-2}\,\left\{  \sum_{r,r'=0}^k\, \beta^{(k)}_r\, \beta^{(k)}_{r'} \sum_{m_2,m_2'}\,\left[ c_{m_2}^{(r)}\,
c_{m'_2}^{(r')}\,
\left\vert\frac{N}{2}-1,\frac{N}{2}-r-m_2 \right\rangle
\left\langle \frac{N}{2}-1,\frac{N}{2}-r'-m_2'   \right\vert \otimes \vert 1, m_2\rangle \langle 1, m_2'\vert \right]  \right\} \nonumber \\
&=& \sum_{m_2,m_2'=1,0,-1}\, \rho^{(k)}_{m_2,m_2'}\,  \vert 1, m_2\rangle \langle 1, m_2'\vert,
\end{eqnarray}
where
\begin{eqnarray}
\label{rhok}
\rho^{(k)}_{m_2,m_2'}=\sum_{r,r'=0}^k\, \beta^{(k)}_r\, \beta^{(k)}_{r'}\, c_{m_2}^{(r)}\,c_{m'_2}^{(r')}\,\sum_{m_1=(-N/2)+1}^{(N/2)-1}\, \left\langle \frac{N}{2}-1, m_1    \right\vert\left.\frac{N}{2}-1,\frac{N}{2}-r-m_2 \right\rangle
\left\langle \frac{N}{2}-1,\frac{N}{2}-r'-m_2'   \right\vert  \left.\frac{N}{2}-1, m_1\right\rangle \nonumber \\
\end{eqnarray}
\end{widetext}
The associated Clebsch-Gordan coefficients
$c^{(r)}_{m_2}~=~C\left(\frac{N}{2}-1,\, 1,\, \frac{N}{2};m-m_2,\, m_2, m \right)$, $m~=~\frac{N}{2}-r$, $m_2=1,\,0,\,-1$ are given explicitly by~\cite{Var}
\begin{eqnarray}
\label{cg_explicit}
c^{(r)}_{1}&=&\sqrt{\frac{(N-r)(N-r-1)}{N(N-1)}},\, c^{(r)}_{-1}=\sqrt{\frac{r\, (r-1)}{N(N-1)}}   \nonumber \\
&&\ \  \ \ c^{(r)}_{0}=\sqrt{\frac{2r\, (N-r)}{N(N-1)}}
\end{eqnarray}
By expressing $\rho^{(k)}$ in the standard two-qubit basis $\{\vert 0_A,0_B \rangle, \vert 0_A,1_B \rangle, \vert 1_A,0_B \rangle, \vert 1_A,1_B \rangle\}$, (using the relations between angular momentum basis $\vert 1,m_2=\pm 1, 0\rangle$ and the local qubit basis i.e.,
$\vert 1,1\rangle=\vert 0_A,0_B\rangle$,\  $\vert 1,0\rangle=(\vert 0_A,1_B\rangle+\vert 1_A,0_B\rangle)/\sqrt{2}$,\ $\vert 1,-1\rangle=
\vert 1_A,1_B\rangle$), one obtains the following simplified form~\cite{s2} for the symmetric two-qubit reduced density matrix:
\begin{eqnarray}
\label{rhok_matrix}
\rho^{(k)}&=&\ba{cccc} A^{(k)} \ \ & B^{(k)} \ \ & B^{(k)}\ \  & C^{(k)} \ \  \\ B^{(k)} \ \  & D^{(k)}\ \  & D^{(k)}\ \  & E^{(k)} \ \   \\ B^{(k)} \ \  & D^{(k)} \ \  & D^{(k)} \ \ & E^{(k)} \ \  \\ C^{(k)} \ \  & E^{(k)} \ \  & E^{(k)} \ \  & F^{(k)} \ \  \ea,
\end{eqnarray}
where $A^{(k)},\, B^{(k)},\, C^{(k)},\, D^{(k)},\, E^{(k)}$ and $F^{(k)}$ are real.

Now we proceed to discuss spin squeezing in detail in the illustrative cases $k=1,2$ in the family of states $\{{\cal D}_{N-k,\,k}\}$.

\subsection{Spin squeezing in the class of states $\{{\cal D}_{N-1,\,1}\}$}

The reduced two-qubit density matrix $\rho^{(1)}$ drawn from the $N$-qubit pure states of the family  $\{{\cal D}_{N-1,\,1}\}$ (see Eq.~(\ref{formal_rhok})) has the following explicit structure:
\begin{eqnarray}
\label{rho1}
&&\rho^{(1)}=\mbox{Tr}_{N-2}\left(\vert D_{N-1,\,1}\rangle\langle D_{N-1,\,1}\right)\nonumber \\
&&\ = \left( \left(\beta^{(1)}_0\right)^2+ \left(\beta^{(1)}_1\,  c^{(1)}_1\right)^2   \right)\vert 1,\,1\rangle\langle 1,\,1 \vert \nonumber \\
&& \ \ \  + \left(\beta^{(1)}_1\, c^{(1)}_0\right)^2
\vert 1,\,0\rangle\langle 1,\,0 \vert  +\beta^{(1)}_0 \beta^{(1)}_1\, c^{(1)}_0 \vert 1,\,1\rangle\langle 1,\,0 \vert \nonumber \\
&&\ \ \  +\beta^{(1)}_0 \beta^{(1)}_1\, c^{(1)}_0 \vert 1,\,0\rangle\langle 1,\,1 \vert
\end{eqnarray}
Here  (see Eq. (\ref{nono})) we have $\beta^{(1)}_0={\cal N}N\, a $, $\beta^{(1)}_1={\cal N}\, \sqrt{N(1- a^2)}$ with ${\cal N}=\frac{1}{\sqrt{N^2\,a^2+N(1-a^2)}}$ and  the associated non-zero Clebsch-Gordan coefficients (see Eq. (\ref{cg_explicit})) are given by
 \begin{equation}
 \label{cg_explicit1}
 c^{(1)}_1=\sqrt{\frac{N-2}{N}},\  c^{(1)}_0=\sqrt{\frac{2}{N}}.
\end{equation}
Furthermore, in the standard two-qubit basis $\{\vert 0_A,0_B \rangle, \vert 0_A,1_B \rangle, \vert 1_A,0_B \rangle, \vert 1_A,1_B \rangle\}$, we obtain
\begin{eqnarray}
\label{rho1_matrix}
\rho^{(1)}&=&\ba{cccc} A^{(1)} \ \ & B^{(1)} \ \ & B^{(1)}\ \  & 0 \ \  \\ B^{(1)} \ \  & D^{(1)}\ \  & D^{(1)}\ \  & 0 \ \   \\ B^{(1)} \ \
& D^{(1)} \ \  & D^{(1)} \ \ & 0 \ \  \\ 0 \ \  & 0 \ \  & 0 \ \  & 0 \ \  \ea \nonumber
\end{eqnarray}
where
\begin{eqnarray}
A^{(1)}&=&\frac{N^2a^2+(N-2)(1-a^2)}{N^2\,a^2+N(1-a^2)},\ B^{(1)}=\frac{a\sqrt{1-a^2}}{1+a^2(N-1)},\   \nonumber \\
 D^{(1)}&=& \frac{1-a^2}{N^2\,a^2+N(1-a^2)},\
 \end{eqnarray}
We obtain the qubit orientations (see (Eq. \ref{st2}))
\begin{eqnarray*}
s_x= 2\,B^{(1)}, \ s_y=  0, \ s_z= A^{(1)}
\end{eqnarray*}
using which we find an orthogonal triad of basis vectors
\begin{eqnarray*}
\hat{n}_0&=&\left(\frac{s_x}{\sqrt{s_x^2+s_z^2}},0,\frac{s_z}{\sqrt{s_x^2+s_z^2}}
\right),
\\
\hat{n}_1&=& (0,\,1,\,0), \nonumber \\
\hat{n}_2&=&\left(-\frac{s_z}{\sqrt{s_x^2+s_z^2}}, 0, \frac{s_x}{\sqrt{s_x^2+s_z^2}} \right)
\end{eqnarray*}
with $\hat{n}_0$ denoting the mean spin direction.  On simplifying, we obtain (see Eq. (\ref{nmin})) $\widetilde{\hat n}_{1}\, T\,{\hat n}_{2}=\widetilde{\hat n}_{2}\, T\,{\hat n}_{1}=0$ and
$({\widetilde{\hat n}_{\bot}}{T}{\hat n}_{\bot})_{{\rm min}}= \widetilde{\hat n}_{2}\, T\,{\hat n}_{2}$.
Thus the corresponding spin-squeezing parameter takes the form~\cite{note} (see (Eq. \ref{xitil1}))
\begin{eqnarray}
\label{xin-11}
\xi&=&\sqrt{1+(N-1)\,   ({\widetilde{\hat n}}_{2}\, T{\hat n}_{2})\,
}
\end{eqnarray}
where
\be
\widetilde{\hat n}_{2}\, T\,{\hat n}_{2}
=\frac{2\left[\left(A^{(1)}\right)^2\,D^{(1)}-2\,\left(B^{(1)}\right)^2 \right]}{4\,\left(B^{(1)}\right)^2+\left(A^{(1)}\right)^2}.
\ee
In Fig.~1 we have plotted  $\xi$, for the states in the family $\{{\cal D}_{N-1,1}\}$, as a function of the parameter $a$ and number of qubits $N$.

\begin{figure}[h]
	\label{d11}
	\begin{center}
		\includegraphics*[width=3in,keepaspectratio]{dk1_aru}

		\caption{Spin-squeezing parameter $\xi$ as a function of the parameter $a$ and number of qubits $N$ in the class  $\{{\cal D}_{N-1,1}\}$ of $N$-qubit pure symmetric states with two distinct spinors.}
	\end{center}
\end{figure}

\subsection{Spin squeezing in the class $\{{\cal D}_{N-2,\,2}\}$}
\label{ss3B}
When $k=2$, the state $\vert D_{N-k, k}\rangle$ has the form (see Eq. (\ref{nono}))
\begin{eqnarray}
\vert D_{N-2, 2}\rangle
&=& \beta^{(2)}_0\,\left\vert\frac{N}{2},\frac{N}{2} \right\rangle+\beta^{(2)}_1\,\left\vert\frac{N}{2},\frac{N}{2}-1 \right\rangle\nonumber \\
&& \ +\beta^{(2)}_2\,\left\vert\frac{N}{2},\frac{N}{2}-2 \right\rangle
\end{eqnarray}
where
\begin{eqnarray}
\beta^{(2)}_0&=&{\cal N}\frac{N(N-1)}{2} a^2 \nonumber \\
\beta^{(2)}_1&=&{\cal N}\sqrt{N} (N-1) a \sqrt{1-a^2} \\
\beta^{(2)}_2&=&{\cal N}\sqrt{\frac{N(N-1)}{2}} (1-a^2).  \nonumber
\end{eqnarray}
and ${\cal N}$, the normalization factor, satisfies the relation $(\beta^{(2)}_0)^2+(\beta^{(2)}_1)^2+(\beta^{(2)}_2)^2=1$.
Following the procedure outlined in subsection IIIA, we evaluate the two-qubit reduced density matrix $\rho^{(2)}=\mbox{Tr}_{N-2}\left(\vert D_{N-2,\,2}\rangle\langle D_{N-2,\,2} \vert\right)$ and express it in the standard two-qubit basis $\{\vert 0_A,0_B \rangle, \vert 0_A,1_B \rangle, \vert 1_A,0_B \rangle, \vert 1_A,1_B \rangle\}$:
\begin{eqnarray}
\label{rho2_matrix}
\rho^{(2)}&=&\ba{cccc} A^{(2)} \ \ & B^{(2)} \ \ & B^{(2)}\ \  & C^{(2)} \ \  \\ B^{(2)} \ \  & D^{(2)}\ \  & D^{(2)}\ \  & E^{(2)} \ \   \\ B^{(2)} \ \  & D^{(2)} \ \  & D^{(2)} \ \ & E^{(2)} \ \  \\ C^{(2)} \ \  & E^{(2)} \ \  & E^{(2)} \ \  & F^{(2)} \ \  \ea \nonumber
\end{eqnarray}
where
\begin{eqnarray*}
A^{(2)}&=&\left(\beta^{(2)}_0\right)^2+\left(\beta^{(2)}_1\,  c^{(1)}_1\right)^2+ \left(\beta^{(2)}_2\, c^{(2)}_1\right)^2,\nonumber \\
B^{(2)}&=&\frac{\beta^{(2)}_0 \beta^{(2)}_1 c^{(1)}_0+\beta^{(2)}_1 \beta^{(2)}_2 c^{(1)}_1 c^{(2)}_0}{\sqrt{2}}, \nonumber \\
C^{(2)}&=&\beta^{(2)}_0 \beta^{(2)}_2 c^{(2)}_{-1}, \nonumber \\
D^{(2)}&=& \frac{\left(\beta^{(2)}_1  \, c^{(1)}_0\right)^2+\left(\beta^{(2)}_2\, c^{(2)}_0\right)^2 }{2}, \nonumber \\
E^{(2)}&=& \frac{\beta^{(2)}_1 \beta^{(2)}_2 c^{(1)}_{0} c^{(2)}_{-1}}{\sqrt{2}}, \nonumber \\
F^{(2)}&=& \left(\beta^{(2)}_2\, c^{(2)}_{-1}\right)^2,
\end{eqnarray*}
and the associated  non-zero Clebsch-Gordan coefficients (see Eq. (\ref{cg_explicit})) are given in Eq. (\ref{cg_explicit1}) and
\begin{eqnarray*}
c^{(2)}_1&=&
\sqrt{\frac{(N-3)(N-2)}{N(N-1)}},\
c^{(2)}_0=2\, \sqrt{\frac{N-2}{N(N-1)}} \\
c^{(2)}_{-1}&=&\sqrt{\frac{2}{N(N-1)}}. \nonumber
	\end{eqnarray*}
Substituting for $\beta^{(2)}_i$, $i=0,\,1,\,2$ and the Clebsch-Gordan coefficients, we obtain the density matrix $\rho^{(2)}$  in terms of
 the number $N$ of qubits, and the real  parameter $a$.  We then evaluate the spin-squeezing parameter $\xi$  following the same procedure followed in subsection~IIIA while discussing the class $\{{\cal D}_{N-1,1}\}$. We identify~\cite{note} that the mean spin direction $\hat{n}_0$  lies in the XZ-plane and the element of correlation matrix $\widetilde{\hat{n}}_1\, T \, \hat{n}_{2}=0.$ This facilitates the evaluation of the spin squeezing parameter to be
 $\xi=\sqrt{1+(N-1)\,  ({\widetilde{\hat n}}_{2}\, T\,{\hat n}_{2}),\,
 }.$
 We have plotted  $\xi$ as a function of  the parameter $a$
for different values of $N$ in Fig~2.
\begin{figure}[h]
\label{d2}
\begin{center}
\includegraphics*[width=3in,keepaspectratio]{dk2_aru}
\caption{Spin-squeezing parameter $\xi$ as a function of the parameter $a$ and number of qubits $N$ in the class  $\{{\cal D}_{N-2,2}\}$ of pure symmetric states.}
\end{center}
\end{figure}

In general, for any arbitrary $k$, we evaluate the two-qubit density matrix  $\rho^{(k)}=\mbox{Tr}_{N-2}\left(\vert D_{N-k,\,k}\rangle\langle D_{N-k,\,k} \vert\right)$,  in the standard two-qubit basis, in the form given in Eq. (\ref{rhok_matrix}) with elements $A^{(k)},\ B^{(k)},\ C^{(k)},\ D^{(k)},\  E^{(k)},\ F^{(k)}$ given by,
\begin{eqnarray*}
 A^{(k)}&=&\sum_{r=0}^k \left(\beta_r^{(k)}\,c_1^{(r)}\right)^2,\\    B^{(k)}&=&\frac{1}{\sqrt{2}}\sum_{r=0}^{k-1}\,\beta_{r}^{(k)}\, \beta_{r+1}^{(k)}\, {c^{(r)}_{1}}\, {c^{(r+1)}_{0}},  \\
C^{(k)}&=&\sum_{r=0}^{k-2}\,\beta_{r}^{(k)}\, \beta_{r+2}^{(k)}\, {c^{(r)}_{1}}\, {c^{(r+2)}_{-1}}, \nonumber \\
D^{(k)}&=&\frac{1}{2}\sum_{r=0}^{k-1}\,|\beta_{r+1}^{(k)}|^{2}\, {c^{(r+1)}_{0}}^{2},\
\nonumber \\
 E^{(k)}&=&\frac{1}{\sqrt{2}}\sum_{r=0}^{k-2}\,\beta_{r+1}^{(k)}\, \beta_{r+2}^{(k)}\, {c^{(r+1)}_{0}}\, {c^{(r+2)}_{-1}},\ \  \nonumber \\
F^{(k)}&=&\sum_{r=0}^{k-2}\,\left(\beta_{r+2}^{(k)}\, c^{(r+2)}_{-1}\right)^{2}.
\end{eqnarray*}
The mean spin direction $\hat{n}_0$ of the qubits in $\vert D_{N-k, k}\rangle$ lies in the XZ-plane and the spin-squeezing parameter $\xi$ for any arbitrary state $\vert D_{N-k,k}\rangle$ belonging to the family $\{ {\cal D}_{N-k,k}\}$ can be readily  evaluated~\cite{note} using
$\xi~=~\sqrt{1+(N-1)\,(\widetilde{\hat{n}}_2\, T\, \hat{n}_2})\,$ where
\begin{eqnarray*}
\widetilde{\hat n}_{2}\, T\,{\hat n}_{2}
&=& \frac{2\left(A^{(k)}-F^{(k)}\right)^2\,\left(C^{(k)}+D^{(k)}\right)
}
{\left[4\,\left(B^{(k)}+E^{(k)}\right)^2+\left(A^{(k)}-F^{(k)}\right)^2\right]} \\
&&	\ \ \ 	+\frac{
	4\,\left(B^{(k)}+E^{(k)}\right)^2\left(1-4D^{(k)}\right)}
	{\left[4\,\left(B^{(k)}+E^{(k)}\right)^2+\left(A^{(k)}-F^{(k)}\right)^2\right]}\\
&&\ \ 	-		\frac{8\, \left(A^{(k)}-F^{(k)}\right)\left(\left(B^{(k)}\right)^2-\left(E^{(k)}\right)^2
			\right)}
	{\left[4\,\left(B^{(k)}+E^{(k)}\right)^2+\left(A^{(k)}-F^{(k)}\right)^2\right]}.
\end{eqnarray*}
In Fig.~3 we have illustrated the variation of the spin-squeezing parameter $\xi$ in the $N$-qubit pure symmetric state $\vert D_{N-k,k}\rangle$ with different $k$ and $N$.
\begin{figure}[h]
\label{com15}
\begin{center}
\includegraphics*[width=3.5in,keepaspectratio]{n20kR}
\includegraphics*[width=3.5in,keepaspectratio]{n100kR}
\caption{Spin squeezing parameter $\xi$ of states $\vert D_{N-k, k}\rangle$ (see (Eq. \ref{nono})) for different values of $k=1,2,3,4,5$ and for number of qubits $N=20$ and   $N=100$. }
\end{center}
\end{figure}
It can be readily seen from Fig.~3 that for a fixed $N$, the spin-squeezing parameter for the state $\vert D_{N-k,k}\rangle$  reduces with the increase in $k$.

\section{Concluding remarks}
In this article we have explored spin squeezing in symmetric multiqubit pure states belonging to the family of two distinct Majorana spinors. We exclusively make use of the fact that spin squeezing is a reflection of pairwise entanglement and evaluation of the  spin squeezing parameter requires the knowledge of two-qubit reduced density matrix of the $N$-qubit symmetric state~\cite{usha2}. We have used the canonical form of pure symmetric states $\vert D_{N-k,k}\rangle$ of $N$ qubits with two distinct spinors which are characterized by a single real parameter $a$ (see Eq. (\ref{nono})) and divided the system into two parts containing $N-2$ and $2$ qubits respectively. By tracing out the $N-2$ qubits we obtain the density matrix corresponding to any two qubits of the $N$-qubit symmetric state $\vert D_{N-k,k}\rangle$. The correlation matrix elements expressed in the basis perpendicular to the mean spin direction leads  us to evaluate the spin-squeezing parameter. The variation of spin squeezing with respect to the  real parameter $0< a<1$ characterizing the state $\vert D_{N-k,k}\rangle$ is graphically illustrated for SLOCC inequivalent family of states
$\{ {\cal{D}}_{N-k,k}\}$, with different values of $k=1,2,\ldots$. While the Dicke states
$\left\vert \frac{N}{2}, \frac{N}{2}-k\right\rangle$ constituted by  two orthogoanl spinors  are not spin squeezed, our work reveals that their generalizations viz.,  $N$-qubit symmetric  states, consisting of two non-orthogonal spinors, exhibit spin squeezing. Investigations on the metrological relevance of the $N$ qubit states belonging to the family of two distinct Majorana spinors is under progress and it will be presented in a separate communication~\cite{RA}.

\section*{Acknowledgements}
KSA would like to thank the University Grants Commission for providing a BSR-RFSMS fellowship during the present work. ARU acknowledges the support of UGC MRP (Ref. MRP-MAJOR-PHYS-2013-29318).
We thank Professor A. K. Rajagopal for insightful discussions.

redpajama_set_name: RedPajamaArXiv


On the first day of July, my watch is dead. Just a few hours ago. I wore my watch loosely when sitting down and waiting for my bus and only found it missing when I hopped on my bus. =( When I got home I immediately called my mum asked her to find it around the road there and the bench. And my mum brought this back..
My mum just bought it for me at Sunway Pyramid on 27th March =(. It's just 1st July today. The watch is not cheap and my watches never really last long. I guess I'm not good at handling stuffs of my own.
Well, I guess I don't deserve another watch for now. I need to start to be more careful and less careless.


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text:
try:
    import json
except ImportError:
    import simplejson as json
import logging
import os

import debtcollector.renames
from keystoneauth1 import access
from keystoneauth1 import adapter
from oslo_utils import importutils
import requests

from neutronclient._i18n import _
from neutronclient.common import exceptions
from neutronclient.common import utils

osprofiler_web = importutils.try_import("osprofiler.web")

_logger = logging.getLogger(__name__)

if os.environ.get('NEUTRONCLIENT_DEBUG'):
    ch = logging.StreamHandler()
    _logger.setLevel(logging.DEBUG)
    _logger.addHandler(ch)
    _requests_log_level = logging.DEBUG
else:
    _requests_log_level = logging.WARNING

logging.getLogger("requests").setLevel(_requests_log_level)
MAX_URI_LEN = 8192
USER_AGENT = 'python-neutronclient'
REQ_ID_HEADER = 'X-OpenStack-Request-ID'

class HTTPClient(object):
    """Handles the REST calls and responses, include authn."""

    CONTENT_TYPE = 'application/json'

    @debtcollector.renames.renamed_kwarg(
        'tenant_id', 'project_id', replace=True)
    @debtcollector.renames.renamed_kwarg(
        'tenant_name', 'project_name', replace=True)
    def __init__(self, username=None, user_id=None,
                 project_name=None, project_id=None,
                 password=None, auth_url=None,
                 token=None, region_name=None, timeout=None,
                 endpoint_url=None, insecure=False,
                 endpoint_type='publicURL',
                 auth_strategy='keystone', ca_cert=None, log_credentials=False,
                 service_type='network', global_request_id=None,
                 **kwargs):

        self.username = username
        self.user_id = user_id
        self.project_name = project_name
        self.project_id = project_id
        self.password = password
        self.auth_url = auth_url.rstrip('/') if auth_url else None
        self.service_type = service_type
        self.endpoint_type = endpoint_type
        self.region_name = region_name
        self.timeout = timeout
        self.auth_token = token
        self.auth_tenant_id = None
        self.auth_user_id = None
        self.endpoint_url = endpoint_url
        self.auth_strategy = auth_strategy
        self.log_credentials = log_credentials
        self.global_request_id = global_request_id
        if insecure:
            self.verify_cert = False
        else:
            self.verify_cert = ca_cert if ca_cert else True

    def _cs_request(self, *args, **kwargs):
        kargs = {}
        kargs.setdefault('headers', kwargs.get('headers', {}))
        kargs['headers']['User-Agent'] = USER_AGENT

        if 'body' in kwargs:
            kargs['body'] = kwargs['body']

        if self.log_credentials:
            log_kargs = kargs
        else:
            log_kargs = self._strip_credentials(kargs)

        utils.http_log_req(_logger, args, log_kargs)
        try:
            resp, body = self.request(*args, **kargs)
        except requests.exceptions.SSLError as e:
            raise exceptions.SslCertificateValidationError(reason=e)
        except Exception as e:
            # Wrap the low-level connection error (socket timeout, redirect
            # limit, decompression error, etc) into our custom high-level
            # connection exception (it is excepted in the upper layers of code)
            _logger.debug("throwing ConnectionFailed : %s", e)
            raise exceptions.ConnectionFailed(reason=e)
        utils.http_log_resp(_logger, resp, body)

        # log request-id for each api call
        request_id = resp.headers.get('x-openstack-request-id')
        if request_id:
            _logger.debug('%(method)s call to neutron for '
                          '%(url)s used request id '
                          '%(response_request_id)s',
                          {'method': resp.request.method,
                           'url': resp.url,
                           'response_request_id': request_id})

        if resp.status_code == 401:
            raise exceptions.Unauthorized(message=body)
        return resp, body

    def _strip_credentials(self, kwargs):
        if kwargs.get('body') and self.password:
            log_kwargs = kwargs.copy()
            log_kwargs['body'] = kwargs['body'].replace(self.password,
                                                        'REDACTED')
            return log_kwargs
        else:
            return kwargs

    def authenticate_and_fetch_endpoint_url(self):
        if not self.auth_token:
            self.authenticate()
        elif not self.endpoint_url:
            self.endpoint_url = self._get_endpoint_url()

    def request(self, url, method, body=None, headers=None, **kwargs):
        """Request without authentication."""

        content_type = kwargs.pop('content_type', None) or 'application/json'
        headers = headers or {}
        headers.setdefault('Accept', content_type)

        if body:
            headers.setdefault('Content-Type', content_type)

        if self.global_request_id:
            headers.setdefault(REQ_ID_HEADER, self.global_request_id)

        headers['User-Agent'] = USER_AGENT
        # NOTE(dbelova): osprofiler_web.get_trace_id_headers does not add any
        # headers in case if osprofiler is not initialized.
        if osprofiler_web:
            headers.update(osprofiler_web.get_trace_id_headers())

        resp = requests.request(
            method,
            url,
            data=body,
            headers=headers,
            verify=self.verify_cert,
            timeout=self.timeout,
            **kwargs)

        return resp, resp.text

    def _check_uri_length(self, action):
        uri_len = len(self.endpoint_url) + len(action)
        if uri_len > MAX_URI_LEN:
            raise exceptions.RequestURITooLong(
                excess=uri_len - MAX_URI_LEN)

    def do_request(self, url, method, **kwargs):
        # Ensure client always has correct uri - do not guesstimate anything
        self.authenticate_and_fetch_endpoint_url()
        self._check_uri_length(url)

        # Perform the request once. If we get a 401 back then it
        # might be because the auth token expired, so try to
        # re-authenticate and try again. If it still fails, bail.
        try:
            kwargs['headers'] = kwargs.get('headers') or {}
            if self.auth_token is None:
                self.auth_token = ""
            kwargs['headers']['X-Auth-Token'] = self.auth_token
            resp, body = self._cs_request(self.endpoint_url + url, method,
                                          **kwargs)
            return resp, body
        except exceptions.Unauthorized:
            self.authenticate()
            kwargs['headers'] = kwargs.get('headers') or {}
            kwargs['headers']['X-Auth-Token'] = self.auth_token
            resp, body = self._cs_request(
                self.endpoint_url + url, method, **kwargs)
            return resp, body

    def _extract_service_catalog(self, body):
        """Set the client's service catalog from the response data."""
        self.auth_ref = access.create(body=body)
        self.service_catalog = self.auth_ref.service_catalog
        self.auth_token = self.auth_ref.auth_token
        self.auth_tenant_id = self.auth_ref.tenant_id
        self.auth_user_id = self.auth_ref.user_id

        if not self.endpoint_url:
            self.endpoint_url = self.service_catalog.url_for(
                region_name=self.region_name,
                service_type=self.service_type,
                interface=self.endpoint_type)

    def _authenticate_keystone(self):
        if self.user_id:
            creds = {'userId': self.user_id,
                     'password': self.password}
        else:
            creds = {'username': self.username,
                     'password': self.password}

        if self.project_id:
            body = {'auth': {'passwordCredentials': creds,
                             'tenantId': self.project_id, }, }
        else:
            body = {'auth': {'passwordCredentials': creds,
                             'tenantName': self.project_name, }, }

        if self.auth_url is None:
            raise exceptions.NoAuthURLProvided()

        token_url = self.auth_url + "/tokens"
        resp, resp_body = self._cs_request(token_url, "POST",
                                           body=json.dumps(body),
                                           content_type="application/json",
                                           allow_redirects=True)
        if resp.status_code != 200:
            raise exceptions.Unauthorized(message=resp_body)
        if resp_body:
            try:
                resp_body = json.loads(resp_body)
            except ValueError:
                pass
        else:
            resp_body = None
        self._extract_service_catalog(resp_body)

    def _authenticate_noauth(self):
        if not self.endpoint_url:
            message = _('For "noauth" authentication strategy, the endpoint '
                        'must be specified either in the constructor or '
                        'using --os-url')
            raise exceptions.Unauthorized(message=message)

    def authenticate(self):
        if self.auth_strategy == 'keystone':
            self._authenticate_keystone()
        elif self.auth_strategy == 'noauth':
            self._authenticate_noauth()
        else:
            err_msg = _('Unknown auth strategy: %s') % self.auth_strategy
            raise exceptions.Unauthorized(message=err_msg)

    def _get_endpoint_url(self):
        if self.auth_url is None:
            raise exceptions.NoAuthURLProvided()

        url = self.auth_url + '/tokens/%s/endpoints' % self.auth_token
        try:
            resp, body = self._cs_request(url, "GET")
        except exceptions.Unauthorized:
            # rollback to authenticate() to handle case when neutron client
            # is initialized just before the token is expired
            self.authenticate()
            return self.endpoint_url

        body = json.loads(body)
        for endpoint in body.get('endpoints', []):
            if (endpoint['type'] == 'network' and
                    endpoint.get('region') == self.region_name):
                if self.endpoint_type not in endpoint:
                    raise exceptions.EndpointTypeNotFound(
                        type_=self.endpoint_type)
                return endpoint[self.endpoint_type]

        raise exceptions.EndpointNotFound()

    def get_auth_info(self):
        return {'auth_token': self.auth_token,
                'auth_tenant_id': self.auth_tenant_id,
                'auth_user_id': self.auth_user_id,
                'endpoint_url': self.endpoint_url}

    def get_auth_ref(self):
        return getattr(self, 'auth_ref', None)

class SessionClient(adapter.Adapter):

    def request(self, *args, **kwargs):
        kwargs.setdefault('authenticated', False)
        kwargs.setdefault('raise_exc', False)

        content_type = kwargs.pop('content_type', None) or 'application/json'

        headers = kwargs.get('headers') or {}
        headers.setdefault('Accept', content_type)

        # NOTE(dbelova): osprofiler_web.get_trace_id_headers does not add any
        # headers in case if osprofiler is not initialized.
        if osprofiler_web:
            headers.update(osprofiler_web.get_trace_id_headers())

        try:
            kwargs.setdefault('data', kwargs.pop('body'))
        except KeyError:
            pass

        if kwargs.get('data'):
            headers.setdefault('Content-Type', content_type)

        kwargs['headers'] = headers
        resp = super(SessionClient, self).request(*args, **kwargs)
        return resp, resp.text

    def _check_uri_length(self, url):
        uri_len = len(self.endpoint_url) + len(url)
        if uri_len > MAX_URI_LEN:
            raise exceptions.RequestURITooLong(
                excess=uri_len - MAX_URI_LEN)

    def do_request(self, url, method, **kwargs):
        kwargs.setdefault('authenticated', True)
        self._check_uri_length(url)
        return self.request(url, method, **kwargs)

    @property
    def endpoint_url(self):
        # NOTE(jamielennox): This is used purely by the CLI and should be
        # removed when the CLI gets smarter.
        return self.get_endpoint()

    @property
    def auth_token(self):
        # NOTE(jamielennox): This is used purely by the CLI and should be
        # removed when the CLI gets smarter.
        return self.get_token()

    def authenticate(self):
        # NOTE(jamielennox): This is used purely by the CLI and should be
        # removed when the CLI gets smarter.
        self.get_token()

    def get_auth_info(self):
        auth_info = {'auth_token': self.auth_token,
                     'endpoint_url': self.endpoint_url}

        # NOTE(jamielennox): This is the best we can do here. It will work
        # with identity plugins which is the primary case but we should
        # deprecate it's usage as much as possible.
        try:
            get_access = (self.auth or self.session.auth).get_access
        except AttributeError:
            pass
        else:
            auth_ref = get_access(self.session)

            auth_info['auth_tenant_id'] = auth_ref.project_id
            auth_info['auth_user_id'] = auth_ref.user_id

        return auth_info

    def get_auth_ref(self):
        return self.session.auth.get_auth_ref(self.session)

# FIXME(bklei): Should refactor this to use kwargs and only
# explicitly list arguments that are not None.
@debtcollector.renames.renamed_kwarg('tenant_id', 'project_id', replace=True)
@debtcollector.renames.renamed_kwarg(
    'tenant_name', 'project_name', replace=True)
def construct_http_client(username=None,
                          user_id=None,
                          project_name=None,
                          project_id=None,
                          password=None,
                          auth_url=None,
                          token=None,
                          region_name=None,
                          timeout=None,
                          endpoint_url=None,
                          insecure=False,
                          endpoint_type='public',
                          log_credentials=None,
                          auth_strategy='keystone',
                          ca_cert=None,
                          service_type='network',
                          session=None,
                          global_request_id=None,
                          **kwargs):

    if session:
        kwargs.setdefault('user_agent', USER_AGENT)
        kwargs.setdefault('interface', endpoint_type)
        return SessionClient(session=session,
                             service_type=service_type,
                             region_name=region_name,
                             global_request_id=global_request_id,
                             **kwargs)
    else:
        # FIXME(bklei): username and password are now optional. Need
        # to test that they were provided in this mode.  Should also
        # refactor to use kwargs.
        return HTTPClient(username=username,
                          password=password,
                          project_id=project_id,
                          project_name=project_name,
                          user_id=user_id,
                          auth_url=auth_url,
                          token=token,
                          endpoint_url=endpoint_url,
                          insecure=insecure,
                          timeout=timeout,
                          region_name=region_name,
                          endpoint_type=endpoint_type,
                          service_type=service_type,
                          ca_cert=ca_cert,
                          log_credentials=log_credentials,
                          auth_strategy=auth_strategy,
                          global_request_id=global_request_id)

redpajama_set_name: RedPajamaGithub


text:
50 Game Round Up: 351-400 (Peter)
Posted: 7th February 2015 by Jeroen in Round-Up
In this lot of 50 I finally feel like we have been able to catch up on a lot of the years, genres and platforms that had been left behind previously. Our statistics now take on a more long-term view of what we play in the 50. I know that this sounds a little bit pathetic but I am a bit fan of spreadsheets and formulae so the chance to use this with our gaming list… well it helps to tick a few boxes.
Best Game I Had Not Previously Played
It is really hard to think of just one game that stood out in the last 50 to mark as the best one. The Secret of Monkey Island was a bizarre and fun point-and-click adventure which we managed to finish in one sitting. So too was Loom which was interesting and highly original (it's just a pity that they never ended up making the sequel that they wanted to). Yoshi's Island was remarkably cute and frustrating in all the right places.
However, the title for my best game I had not previously played as to go to Earthbound. Kingdom Hearts comes a close second but Earthbound combines the right amount of story, strange characters and sheer mindfuckery that I can appreciate in a JRPG. Yes, there were times when grinding became an issue but there really are not many games out there with such a strange view on the world.
Worst Game
Where the best game took a little bit of thought there is only one contender from this batch that springs to mind: MLB 09: The Show. It makes sense that this was taken out of the 1001 games list since in many ways it was hard for newcomers to access unless they spent an inordinate time on the training sections. I mean, unless you have a great interest in the sport of baseball (which few people outside of the USA have) this is a pretty niche game that failed to grab either of us.
Most Surprising Game
There were a number of pleasant surprises this time around. I won't dwell too long on either You, Me & The Cubes or The Dishwasher: Dead Samurai since both of these games were removed from the list. Whilst I understand about the latter game it is sad that something as unusual as You, Me & The Cubes got removed… yet we still have nearly every Metal Gear Solid game on the list.
If we are to go just by games that have remained on the list then there is PixelJunk Monsters and Prince of Persia. For a tower defence game I was surprised just how well made the co-operative part of the experience was. Then there is Prince of Persia which still stands up today as an engaging platformer… something that came as a surprise since my only previous experience was the 2008 remake.
Biggest Disappointment
For me the disappointment comes from a level that, arguably, should never have been produced in the first place. The infamous airport level from Call of Duty: Modern Warfare 2… I think I will be leaving this there.
Best Blast From The Past
Unlike the 50s where we had the barmy notion to only play new games this batch had a nice selection from my past. I got to swing around New York in Spider-Man 2, toy with the lives of fake people in The Sims 2 and design my own rollercoaster in Theme Park. There is one game, however, it was a real treat to see again: Grand Theft Auto: Vice City. I still hold out hope that we will one day see an HD remake of Vice City.
Games We Kept Playing
Earthbound and Kingdom Hearts were the main ones that I kept playing with personally. I still have the Kingdom Hearts game on the go but Ni No Kuni has loomed large after a years absence and has claimed my gaming time once again.


text:
Schneider Electric and the Global Footprint Network partner on "100 Days of Possibility" initiative to promote solutions to fight climate change
Press Release Sustainability & Strategy
Schneider Electric, the leader in the digital transformation of energy management and automation, and Global Footprint Network (GFN), a research organization that tracks how the world manages natural resources, today launched the "100 Days of Possibility" initiative. The initiative seeks to promote solutions that help address climate change and biodiversity loss.
The launch of the initiative coincides with Earth Overshoot Day – the date when humanity exhausts all ecological resources the planet can regenerate during an entire year.
The 100 days referenced in the initiative's name mark the time left until the start of the 26th annual UN Climate Conference (COP26), when government officials from around the globe will gather in Glasgow, Scotland, to try to agree on effective actions to combat climate change.
The solutions highlighted by the project underpin its key message: Companies, governments and individuals can act now –there is no need to wait for decisions to be made at COP26.
Opportunities and solutions across all sectors will be revealed each day leading up to COP26 at 100DaysofPossibility.org These will highlight the many ways that everyone can #MoveTheDate of Earth Overshoot Day. Examples include proposals for 100% renewable power grids, smart homes and food waste reduction.
Schneider Electric, named world's most sustainable corporation by Corporate Knights Global 100 Index showed its support of the initiative by submitting six of its climate solutions to the "100 Days" list. Other partners in the project include the Scottish Environment Protection Agency (SEPA) and Drawdown Europe.
One of the scalable solutions Schneider has contributed is the integration of a microgrid with an electric vehicle (EV) charging infrastructure in a Maryland-based smart energy bus depot in the US. It will be the first of its kind and help #MoveTheDate of Earth Overshoot Day by reducing carbon emissions by 62% among other benefits.
Another example is with Schneider's office building, IntenCity, in Grenoble, France. IntenCity demonstrates how public and private sectors have joined forces to build cleaner and healthier communities. The building is designed to consume 7 kilowatt-hours per square meter each year — nearly 10 times less energy than the average European building consumes. Rooftop solar panels, two onsite wind turbines, the use of groundwater, and smart technology solutions enable the complex to consume and produce equal amounts of electricity over one year. A unique microgrid partnership facilitates energy sharing and coordination with the surrounding community.
Another contribution is Schneider's recent agreement with the Egyptian Electricity Holding Company, the country's national utility provider. It will be the Middle East's first ever country-wide smart grid and help Egypt meet future energy demands while advancing its sustainability strategy.
All three solutions will be highlighted during the launch of the "100 days" initiative and Schneider's remaining three contributions will be featured throughout the project.
Schneider Electric and the Global Footprint Network partner on "100 Days of Possibility" initiative to promote solutions to fight climate change (.pdf)
Contact press
Global PR Central Team
global.pr@se.com


We are pleased to announce that BritishAmerican Business presented Tradeweb CEO, Lee Olesky with an Entrepreneurial Award at their annual Transatlantic Business Awards Dinner on October 13th. The evening celebrated great strides in innovation and shared successes for businesses bringing the U.S. and U.K. closer together.
The award highlights Tradeweb's entrepreneurial spirit and drive to navigate new challenges and deliver real innovation not only to clients, but across the fixed income and derivatives markets. In our dynamic industry, it's special moments like these that allow us to pause and reflect on how far we've come, and what exciting opportunities lie ahead. As a firm, we remain committed to moving markets forward across the more than 25 markets we support through our offices in the U.S., Europe and Asia.
We would like to thank our employees, clients and the industry for their continued support and for sharing in this gracious recognition. More details on the award can be found here.


The Personal License of Event Espresso provides an easy-to-use interface for creating and managing event registrations right from within the WordPress administration panel.
Event Espresso 4 is the most advanced event registration and ticketing management plugin for WordPress. This fully-featured events plugin for WordPress allows even basic users to turn your existing blog or website into a event registration and ticketing management website.
With custom registration forms, integrated gateways, multiple ticket options, popular gateways, etc., Event Espresso can help any small company be more successful with each event. Event Espresso is also fully-supported with dedicated support staff and developers and they're launching a new website soon to provide the best customer service offered by commercial WordPress plugins.
If your organization offers classes, workshops, events, trainings or conferences for which participants need to register in advance, Event Espresso can make you a hero. Why? Because this online event registration system will help: reach a wider audience, generate more revenue, save your organization countless hours of administrative time, create a "green" and paperless event registration process, reduce costs and be available to take sign-ups 24/7.
Our mission is to be your technology partner and give you the tools to be more successful and we're confident we can help you.


President Trump fired Director Comey to disrupt the FBI's investigation into ties between his campaign and the Russian government.
After President Trump's latest exercise in abuse of power, Doris and House Democrats are demanding that an independent investigator be appointed to lead the investigation. Chip in today to keep up the pressure.


text:
Alabama–Louisiana–Mississippi Division Headquarters
Southern Territory Headquarters
— Main Menu —About Programs	- Corps Community Center - Youth Programs Services	- Social Services - Emergency Shelter - Recovery - Thanksgving Outreach - Christmas Assistance Family Store Get Involved	- Donate - Schedule a Pick Up - Planned Giving - Resource Development - Volunteer Events	- Calendar News Community Partners Contact
Corps Community Center
Thanksgving Outreach
Still Serving Strong to the Greater Baton Rouge
by mdailey
A new billboard sign stands along Airline Highway – to announce to all who pass by that The Salvation Army, serving the Greater Baton Rouge Area since 1905, is still here, still serving strong. Although we never stopped meeting the needs of the community during the 2016 flood, the waters did force us to move temporarily from our long-time home. Renovations were completed in October 2018 on the Administrative and Social Services Offices, the Corps Recovery Center and the Center of Hope Emergency Shelter – it is good to be back!
In May of 2018, we celebrated the opening of a brand-new Family Store on Coursey Boulevard. Eddrick Hawkins, The Salvation Army's Director of Operations, has focused his energies on efficiently processing donated goods and keeping the Coursey Boulevard and Gonzales stores regularly stocked with fresh goods for sale. Eddrick noted, "The Family Stores sales are vitally important to the work of The Salvation Army. We are really looking forward to the re-opening of our largest store on Airline Hwy later this year!"
Returning to our facilities on Airline has also made it easier for clients to access a wide range of Social Services offered by The Salvation Army. We were especially encouraged to see 13 families participate in The Pathway of Hope Initiative in 2018. Seven of those families have now "graduated" and are living new lives of hope, having broken free from inter-generational poverty.
The 53 bed Corps Recovery Center graduated 83 men in 2018 and continues to accept men seeking support in their recovery from substance abuse. The Center of Hope Emergency Shelter regularly offers room and board to 40-50 homeless men per night.
It is good to see The Salvation Army's Airline facility busy again – staff, board members and volunteers working hard to meet urgent and long-term needs of our neighbors in the Capital Area, people finding help in their time of need and hope for a better day.
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