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Home » Education » Mentors Like Us: Expanding Diversity Research Program Curricula
Mentors Like Us: Expanding Diversity Research Program Curricula
Posted by Christian Cazares on September 1, 2016 in Education, Outreach | Leave a comment
As a Mexican immigrant, I'm finding a career in science academia to be more and more unlikely and difficult to pursue as I realize that not many who share my ethnic and economic background have made it to full professor status. Thankfully, a continued minority student under-representation in STEM-related graduate programs has led to governmental funding initiatives aimed at increasing the inclusion of individuals from these backgrounds. For example, The National Institutes of Health (NIH) currently funds diversity research programs such as Minority Access to Research Careers (MARC), Initiative for Maximizing Student Development (IMSD). While there are promising measures of success for these undergraduate training grants, some of which have been directly experienced by the recent acceptance of all three members of my UC Berkeley MARC 2014 cohort into STEM graduate programs, there is a common sentiment among those targeted by these initiatives: there are still a few key components missing from the curricula of these programs that have yet to be formally addressed.
In short, students eligible for these funding opportunities include those who, according to the NIH, are:
Members of racial and ethnic groups nationally underrepresented in health-related sciences, as well as women in some disciplines
Physically and/or mentally disabled
From a disadvantaged background, where educational access was inhibited by low family income and a rural or inner city resource impoverished environment
The intent of these programs often comes down to increasing research participation of individuals that fall under these criteria to ultimately address their lack of membership in academia as research faculty. This goal is believed to be achieved by providing students with incentives such as a financial stipend, a network of peers, a research mentor, and a structured program that aids students' path to graduate school and beyond.
Degrees earned by underrepresented minorities
The resources these programs provide are invaluable, yet retention strategies for these students often gets separated from the cultural and ethnic identity of the students. This is a tricky situation for those with the power to change this. The admission that these factors play an integral part in academic career advancement would dispel the popular idea that science is beholden solely to merit. However, while there is an increasing number of STEM Ph.Ds from underrepresented minorities, they are nonetheless a paltry percentage of tenured faculty. For many, race is a significant part of their identity, so an environment where discussions on ethnic identity is inhibited ignores the elephant in the room: institutional discouragement, tokenism, and lack of role models in academia make other career options more attractive beyond a financial standpoint. Diversity research programs already provide a vehicle in which to create an ambiance where these discussions are possible, so why not capitalize?
Strategies to Increase Minority Student Retention in Academia
Big Siblings: Alumni from diversity research programs should be held accountable to continue efforts on increasing STEM minority representation. If students benefit from these programs, they should be actively encouraged to pay it forward. A Big Siblings component would provide a valuable mentorship experience for both graduate students and undergraduates, providing the basis for a long-term connection that could serve as an outlet for casual, comfortable discussion of barriers impacting underrepresented students' success in academia. In addition, this would serve as a way of providing undergraduates the details of graduate life that may often go unmentioned in program-organized meetings, such as work-life balance, research mentor selection, and honest conversations about the non-professional pressures of academic careers. Finally, this partnership would connect a pair of students at different stages of their career that come from backgrounds often not found in abundance within graduate research programs, mitigating cultural and ethnic-based perceptions of isolation that may be experienced as they navigate undergraduate and graduate school.
Inclusive Social Events: Organized social events by these programs would do much to cement the networks they establish. From experience, interactions between students are limited by strictly informative meetings in program curriculums. The auspicious potential created by getting groups of 10+ minority students from different research backgrounds and hectic schedules together for weekly meetings can be misspent by going over dry PowerPoint presentations containing easily Googled information, such as graduate funding opportunities. Why test the attention span of young students by dispersing this information in a classroom setting? Instead, diversity research programs should include social events, such as BBQs, dinners, happy hours, etc., as a way to foster a sense of community outside the academic setting and to promote positive student mental health. The almost inherent introversion of STEM students makes clear why these events should be organized and required by the program; mere exposure within these settings break comfort barriers and boost social skills beneficial to public speaking and future science collaborations. At these early career stages, a majority of students are unaware of the responsibilities involved in being a professor. Therefore, by occasionally inviting faculty into this casual setting, social events can do much to inform and change perceptions about the tenure track.
Private Access Database of Alumni Network: Protracted, career-long interactions within these diverse groups and their programs can be bolstered by providing a platform that keeps everyone's updated contact information. The Gates Millennium Scholars web portal includes ways to contact current students, staff, and alumni, with the addition of discussion forums where feedback for graduate school and fellowship applications can be freely given. A directory where current student and alumni email addresses can be filtered by discipline and career stages could be continuously updated by yearly automated e-mail questionnaires.
Guest Minority Faculty Talks: Strategies to inspire and motivate students from disadvantaged backgrounds into academia could be more effective if enacted by successes who share a disadvantaged background and, most importantly, look like them. The previously mentioned student-faculty interactions can be facilitated through introductory talks during which invited faculty candidly talk about their research and career path, as well as their strategies to remain professionally and emotionally resilient as an ethnic minority in academia. Hearing from those who shared your upbringing and its struggles may alleviate unrealistic concerns about research career success requirements as well as feelings of impostor syndrome and stereotype threat. Faculty-student interactions during follow-up Q&A can increase a student's confidence in making direct contacts with future research advisers and mentors, as well as for initiating conversations with their current primary investigators.
Well-Being Workshops: With depression being prevalent among graduate students, it would be remiss for programs aimed at getting students into graduate school to do so without introducing them to prevention strategies. If the health-sciences are making efforts to remove the social stigma of mental health treatment, then these research programs should reciprocate and include Well-Being management into their curricula. An invitation to staff from the institution's psychological counseling services should be extended to lead this workshop, as well as to serve as a future point of contact for students.
These proposed additions may come across to you as being based on common sense. However, program administrators may find themselves dealing with a lot more stringent, logistical limitations than what is evident to a participating student. Nonetheless, from a student's perspective, these are the discernible barriers impeding these initiatives from being part of the curriculum of diversity research programs.
Overcoming Limitations
Money: An alumni database and social events could be exacting on the budget of these programs. Funding is appropriately prioritized to provide multiple staff and facilitator salaries, as well as the student stipend themselves. However, these events may go a long way in creating a strong sense of community that would prove as a worthy venture. Results from a Google Form questionnaire can be exported onto a shared Google Drive Excel sheet as a frugal option for an alumni contact database. A Slack channel can provide a real-time communication outlet for the entire network of students and alumni. Budgets may not have enough room for social events, however, there is little reason to doubt that stipend-funded, of-age undergraduates and graduate students would be shy about getting a pint or some wings over a casual conversation about science and their experiences navigating the academic setting. The hardest part would be getting them to make time in their busy schedule to socialize with the program, hence the previous suggestion that program coordinators willingly set a time and place to congregate, so that one of the already mandatory meetings can take place outside of the discourse-stifling classroom setting. It doesn't need to be fancy or expensive. The perceived effort by these programs to make students feel welcome and comfortable inside the academic setting, as well as supported by their peers over beers, will undoubtedly affect their future career decisions.
Faculty: Research suggests that faculty of color face unique barriers on their way to academic promotion. It is daunting to try to inspire and convince underrepresented students to stay in a career that lacks role models. This is a cycle that diversity research programs aim to break. It is a tough endeavor, one that requires genuine effort from program staff to not only search for minority faculty speakers and mentors, but also to present to them the case about the necessity of their participation. Nonetheless, their unavailability might not necessarily stem from a lack of interest; research faculty have greater priorities in a competitive academic climate. Faculty from underrepresented backgrounds already have a lot on their plate: in the STEM disciplines, they are less represented than White faculty, with women from these groups having the least representation . With the pressures of academic careers in mind, diversity research programs have to find incentives beyond polite e-mail contact to get faculty invested in a generation of researchers in dire need of mentors, to be willing to have the tough conversations on overcoming racial barriers in academic careers. For longer-term programs, the opportunity to apply to the NIH Research Supplements to Promote Diversity in Health-Related Research can be presented to both the student and their eligible faculty mentor, with a commitment from the program to walk the student and the PI through this process. Unfortunately, until the proportion of minority research faculty increases, or better incentives are promoted, mentoring responsibility will fall onto the few gracious enough to get fully involved in these programs.
Beginning to Experiment
The academic experience for ethnically underrepresented students is different from the rest. Research programs with the specific goal of increasing ethnic representation in academia need to make greater effort into looking how this difference plays into students' career choices. What this article proposes can be applied to both undergraduate and graduate research diversity initiatives, with some of them having the specific intent to address the lack of race discussions in STEM academia. Ultimately, the goal of creating a community within a sub-population of students vulnerable to isolation is shared across all of these curriculum additions. Funding agencies and their diversity research programs have already spent several years tackling the lack of financial and academic resources underrepresented students have on their way to a Ph.D. The time has come to experiment, create open dialogue between these students, humanize and listen attentively to find out what it is exactly that keeps dissuading them from the prospects of a career in academic research.
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A state-of-the-art new £7million medical centre in Worcestershire has opened its doors to its first patients following a 10-year campaign to deliver improved facilities for local people.
The impressive new facility at Dog Lane, Bewdley, includes a pharmacy, 25 consulting and treatment rooms, meeting spaces, administration offices, and the latest medical technology which will allow doctors to carry out minor operations.
The 25,000 sq ft, three-storey building, will be a community hub housing the town's relocated library and a public café – with additional space set aside for future expansion.
Leading law firm Emms Gilmore Liberson advised specialist healthcare property developer Matrix Medical throughout the planning and construction process.
The Birmingham-based lawyers advised on a land swap deal that made the development possible. The GPs' existing clinic together with adjacent land owned by NHS Property Services was acquired by Wyre Forest District Council to create a new car park for the town.
Emms Gilmore Liberson property lawyer, associate Beth Margetson, said: "It's fantastic to see such a wonderful project reach completion and begin delivering excellent care to hundreds of patients. Our role was to oversee land swap arrangements involving two separate parcels of land to make the development possible.
The new medical centre has had overwhelming public support since plans for the Dog Lane site were first tabled in December 2012.
Construction was set underway last year by Wyre Forest MP Mark Garnier and district councilor John Campion. It marked the culmination of 10 years' hard work by local stakeholders to secure a new medical centre development in the town.
Dr Matt Davis, who led the project for Wyre Forest Health Partnership alongside development partner Matrix Medical, said the people of Bewdley now have a "world-class" medical facility.
Dr Davis said: "It is wonderful to finally get the keys to the new medical centre which we are confident will deliver 21st century facilities for Bewdley and exactly what local people want – a modern medical facility in the heart of the town.
The surgery in Load Street will now be demolished by Wyre Forest District Council and replaced with a new 49-space car park.
Matrix Medical is an innovative and forward-thinking developer specialising in healthcare premises. Established in 1999, the company has delivered over 40 bespoke medical centres for GPs and NHS bodies and other healthcare providers across England and Wales, all of which are managed in-house.
Emms Gilmore Liberson, based at Lancaster House, Newhall Street, Birmingham, was established in 2011. The three founder directors – Greg Emms, Stephen Gilmore and Martyn Liberson – joined forces to create a practice based on giving highly experienced professional advice to established and new clients. Real estate specialist Mark Dakeyne then joined the company two years ago and leads the growing commercial property team.


SEO vs PPC. Which should you be using?
Home » Blog » SEO » SEO Strategy » SEO Vs PPC: Which Should You Be Using?
Question: What is the difference between SEO and PPC?
Answer: In short, SEO stands for search engine optimization, which is a method used to increase your ranking in search engines without paying the search engines. PPC, on the other hand, is pay-per-click advertising, where you're literally paying a search engine for clicks resulting from the placement of your website in the "Ads" section in search results.
Digital marketing strategies can be confusing, especially for newcomers. With so many choices out there, how do you know which methods will work best for your business? Will your company get a better ROI (return on investment) from social media marketing or pay-per-click advertising via Google Ads (previously Google AdWords)?
We often hear the question, "Which is better: SEO or PPC?" The answer to that question really depends on the client's product, budget, and goals.
I'm going to help by illuminating some of the main differences between these SEM strategies. Even if you're working with an SEO agency to develop a custom campaign, it's important to understand the pros and cons of each approach.
If you've read any of our other posts, you may already have a good idea of what SEO entails. Search engine optimization involves the implementation of strategies (like keyword research, website optimization, content development, link building, and more) that are meant to improve your organictraffic and search rankings. Typically, the best SEO campaigns are built around a content marketing strategy. If you can provide helpful content and a great user experience, you'll be rewarded with more traffic, better rankings, and increased sales. Ultimately, a successful SEO campaign will result in a reliable inbound lead flow.
"PPC" stands for Pay-Per-Click advertising. You'll see these ads regularly when you conduct a search query in Google — even if you weren't completely aware of their presence. These paid search ads show up above and below organic search results. They're displayed above the local map pack in local searches, which means that Google gives them priority. That makes sense, as they're Google's primary revenue source. They're called pay-per-click ads because the advertiser is charged each time a user clicks an ad. With PPC, you're hoping to generate traffic to your website through paid listings that boost your visibility. PPC ads are the only way to guarantee a spot on Page One of Google searches. If you know what you're doing, or if your digital marketing firm does, you can fine-tune your PPC ads until you achieve a positive ROI.
Because search engine optimization is a complex process, it also takes longer to execute a successful SEO campaign. That can be a drawback for companies that need to get off the ground quickly or that want an immediate boost in traffic. While SEO can generate lasting, long-term traffic, some people grow impatient when they don't see the results they're after right away. It takes time to build organic traffic through SEO — for highly competitive keywords, it may take three to six months to get onto page one. In addition, Google's algorithm and search guidelines are constantly changing, which means you're at the mercy of the latest Google update.
So if SEO is a time-consuming process with no guarantees, why are SEO services so popular? Because if you want to generate organic online traffic, then SEO services are essential to long-term success. Today, most consumers use Google to find new businesses. Without page one visibility, you'll lose out on a lucrative lead source. Google is the modern day phone book, and if you want new customers to find you in the digital age, you need an SEO strategy.
When you improve your SEO, there's no guarantee that you'll be featured on page one of the search results — even if you do everything right. With PPC, you know for certain that you'll be highlighted prominently on page one of key search results. That means you can start generating leads immediately. However, like we've mentioned, this can be costly. And if you don't improve your web design and user experience, those clicks might not actually convert to leads or sales! On top of that, 70% to 80% of internet users totally ignore paid advertisements. While the PPC ads you see in Google search results aren't nearly as obvious as banner or sidebar ads on websites, there's still a good chance that educated web users simply won't click on your ad unless they feel it's extremely relevant.
That said, it can be an easier way for small firms or startups to get noticed, particularly if they've had trouble jumpstarting their SEO efforts. It's also a bit more scaleable than SEO; you can spend as much or as little as you want on ads without affecting user experience. But, of course, if you decide to discontinue this marketing effort, your leads will drop off suddenly. With SEO, your site remains optimized (though best practices do evolve).
Both SEO and PPC are search engine marketing tactics that are meant to bring traffic to your website. But if this is all brand new territory to you, you might be confused about which will yield better results for your business. If you can answer the following questions, the answer may be much clearer.
The amount you're able to spend on marketing will play a big role in determining which tactic you want to use. If you can afford to spend a certain amount daily on advertising, PPC could be a great option. That might also apply if you're able to experiment with a larger budget for a short amount of time. But if you can spend only a small amount per month on marketing, SEO might be a more cost-effective option. That's especially true if you run a law firm, technology company, or insurance firm. These industries are notoriously expensive for pay-per-click ads. Unless you have a sizeable budget (think $5,000 per month and up), SEO may be your best bet.
Can you wait to see results?
There's no doubt that PPC produces immediate results while SEO takes more time. When you opt for SEO, you may not feel like you're seeing results right away. That's the way it's supposed to work with an organic strategy, so don't panic or accuse your SEO agency of falling asleep on the job. Have faith in their abilities (provided they're a well-regarded firm) and have patience. On the other hand, if you want or need immediate, guaranteed clicks, and can afford to pay for them, PPC can be a good way to go.
What's your average revenue per customer?
Here's one major advantage of PPC advertising: you can precisely calculate ROI. Google Ads will tell you exactly how much you spent acquiring your leads, which makes it easy to calculate cost-per-acquisition. However, not all products and services are ideal for PPC ads. Let's say you sell an inexpensive product like an umbrella. Your average sale is only $20, but each time someone clicks on your ad, Google charges you $2. Even if you close one out of every 10 leads, you'll probably still lose money from your advertising campaign. However, if you sell expensive electronics and generate $2,000 per sale, you can achieve a very high ROI with those same $2 clicks.
Do you want targeted or time-sensitive leads?
One interesting difference between SEO and PPC is that PPC ads allow you to target specific demographics. You can choose an age range, a location, a gender, level of education, or even an income bracket to ensure your ads are being seen by the right people. With PPC, you can also focus on more time-sensitive information like limited time offers or more seasonal promotions. Because SEO is such a long-term strategy, it's not ideal for those uses. SEO also doesn't discriminate; while local SEO is a fantastic way to appeal to web users in your area, you aren't really able to narrow it down further by demographic. If you want to have mass appeal to people in your area and aren't as concerned with time-sensitive promotions, you'll likely want to improve your SEO instead of relying on expensive PPC ads. But when you want to really target customers of specific ages or backgrounds or you want to drive traffic in time for a particular offer, SEO may be better.
Would you rather increase your site's value or dominate a keyword?
When you improve your SEO, it's entirely possible to generate a lot of traffic for one or two organic keywords. But it's definitely not as easy to see marked results on those keywords right away, particularly if there are a lot of other businesses that currently rank on those competitive keywords. With PPC, your results for a given keyword will be displayed above all organic rankings for that keyword. Despite the fact that your result will be designated as an ad, many users will actually look to you first. If you aren't utilizing PPC ads for those keywords, you might be giving up a lot of traffic to businesses that are using them. When you see no movement on a really important keyword through SEO efforts, you may want to consider PPC. On the flip side, PPC will do nothing to improve your site's overall value or authority. Instead of spending all your money on marketing your web property and gathering traffic, you can spend time fixing up your site so that you can actually convert leads into customers.
Many businesses don't actually choose between these two options. Instead, they will use both methods together to make their digital marketing strategy even stronger. That's often the best way to go, as a diversified strategy will usually yield better results. That way, you won't be putting all your digital eggs in one basket. If you improve your SEO and spend a bit of money on Google Ads, you'll have more control over the results of your campaign. A combined approach is often the best of both worlds. Your PPC ads can instantly generate leads while you wait for your SEO campaign to bear fruit.
Of course, most businesses simply aren't equipped to execute such a complex strategy on their own. That's where your Dallas SEO agency comes in. To find out more about how we can help you craft a search engine marketing strategy that addresses all of your needs, please get in touch with us today. When you can't decide between SEO and PPC, let our team of experts craft a custom digital marketing plan that works for your budget.


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Average number of goals in meetings between Lokomotiv Plovdiv and FK Septemvri Sofia is 3.3.
Lokomotiv Plovdiv won 1, drew 0 and lost 2 of 3 meetings with FK Septemvri Sofia.
Lokomotiv Plovdiv have conceded at least one goal in each of their last 5 home matches.
Lokomotiv Plovdiv had 9 goals in their last 3 home games.
Lokomotiv Plovdiv had 1 of the 3 previous games ended over 2.5 goals.
FK Septemvri Sofia had 14 goals in their last 3 away games.
In the previous game, FK Septemvri Sofia had 2 goals in total for the entire game.
FK Septemvri Sofia had scored in 2 of the last 3 games.
FK Septemvri Sofia had 2 of the 3 previous games ended over 2.5 goals.


Since re-emerging last month from a yearlong absence, Kanye West has sparked outrage by throwing his lot with Donald Trump and calling slavery a choice. Yet the rapper has succeeded spectacularly in one key goal -- staying at the center of attention.
If West's newfound politics have baffled some longtime fans, the 40-year-old has clear stylistic affinities with Trump -- a bombastic round-the-clock presence on Twitter, with musings that appear to be stream-of-consciousness but manage to commandeer each news cycle.
A self-described Renaissance man with interests in music, fashion and politics who has unironically compared himself to Michelangelo, West had long been given a pass by the entertainment world for his rowdier tendencies such as disrupting award ceremonies as few dispute his talents.
Since breaking through in 2004 with "The College Dropout," West has produced lavish hip-hop albums that blend in soul and electroclash. He is tied with Jay-Z as the rapper who has earned the most Grammy Awards with 11.
But whereas West's early work explored his insecurities, the Chicago native has come to epitomize the Los Angeles celebrity lifestyle and in 2014 married reality television star Kim Kardashian, with whom he has three children.
After the chaotic release of his last album "The Life of Pablo," West suffered a mental breakdown and cut short his tour. He reappeared in public in December 2016 when he suddenly walked into Trump Tower in New York to meet the president-elect.
Returning last month to Twitter -- where he also announced two upcoming albums and promoted a shoe line -- West revealed that he feels "love" for Trump and sported one of his "Make America Great Again" caps.
Trump -- who rose to prominence promoting unfounded conspiracy theories on his predecessor Barack Obama's birthplace -- quickly cited West as evidence of rising support among minorities.
West -- whose first visible foray into politics came in 2005 when he said president George W. Bush "doesn't care about black people" after Hurricane Katrina ravaged New Orleans -- acknowledged he has not followed Trump's policies closely.
But the rapper said he admired the real estate mogul's audacity to run -- and West himself has indicated, with an unclear level of seriousness, that he plans to seek the White House in 2024.
"When I see an outsider infiltrate, I connect with that," West told radio host Charlamagne tha God, adding that he was upset Obama invited other rappers to the White House.
But West made bigger headlines during a free-wheeling appearance at TMZ Live, part of the Hollywood gossip site.
"You hear about slavery for 400 years. For 400 years? That sounds like a choice," West said.
His flippant remarks on America's original sin drew a quick and harsh reaction on social media and West was taken to task live in the newsroom of TMZ.
"My brother, OUR ancestors did not choose to be stolen from Mother Africa. OUR ancestors did not choose to be ripped of OUR religion, language, culture," director Spike Lee wrote on Instagram.
In another Trumpian touch, West later took to Twitter to criticize media coverage of his remarks, saying he meant "we can't be mentally imprisoned for another 400 years."
Jeffrey Q. McCunes, an associate professor of African American studies at Washington University in St. Louis who is writing a book on West, called the rapper's remarks a "hiccup" but said he clearly was speaking of "mental slavery."
"Unless Kanye chooses to have much more staged interview moments, we have to ignore some of the stupidity while paying attention to the moments of genius," McCunes said.
"We have a Kanye West who is coming back onto the scene and trying to be his most honest self in public. And that honest self is like a fugitive who is trying to be free. But he's trying to be free in this kind of high-tech, social media, soundbite culture," he said.
West also for the first time explained his hospitalization. He said he had been suffering stress for factors that included low airplay for "The Life of Pablo" and the armed robbery of his wife in her Paris hotel room.
Calling his hospitalization a "breakdown -- or breakthrough," West said his experience was "incredible" and that he wanted to draw awareness to mental health issues.
"Best believe, I'm going to take the stigma off the word 'crazy.'"


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Tag: Maria Grazia Rosin
A Commentary on the 2018 Venice Glass Week
We have been busy. Very busy actually. If you did not know, Venice Glass Week – Festival Internazionale del Vetro was held a couple of weeks ago.
Perhaps the most important event in the world of Murano glass. Venice Glass Week brings together glass artists, glass houses, buyers, resellers, media and official entities and various commercial and cultural representations. All of them united by the love of the art of blown Murano glass.
The event ran from 9 to 16 September and its activities included exhibitions, guided tours, workshops & demonstrations, lectures and award ceremony, as well as performances, special openings, and of course, many openings, parties and leisure or sports activities.
The event is perhaps the second best pretext to enter this world of fragile and transparent beauty. Thus we could not find a better excuse than to comment again on our partnership with the house Ongaro e Fuga.
In case you could not read it before, or if you want to read it now, here is the link, although you may have to have a subscription to the Financial Times to read it. In any case, here's our summary of said article.
The Venice Glass Week 2018 – FT Weekend
Traditional Mirror Market Current Situation
Despite being a millenarian and exclusive technique of incomparable beauty, the Murano world is currently facing a crisis.
It is a crisis caused by the modern world in fact. Given the globalization and other commercial impacts of the present times.
There is greater access to suppliers, vendors and markets, as well as greater competition. In addition to this, there is a lack of appreciation for the Murano technique compared to that which existed a few years ago.
However, all is not lost. There are new houses, new ideas, and new talents that are attracted to the Murano world and the charm of Venice.
Such is the case of the artists, architects or designers Elena Mazzi, Mario Bellini, Carlo Scarpa and Maria Grazia Rosin, which will be discussed today.
All of them, past and contemporaries, in one way or another have brought a vitality to the Murano world, not seen very often, but extremely necessary to revitalize the art.
Since we have previously covered several profiles of creators related to the Murano glass. We will use this chance to showcase the work of these creators.
1. Elena Mazzi
Venetian based visual artist whose Murano inspiration is evident from her short film "Reflecting Venice", a project that investigates the possibility of responding to recent year's increase in environmental issues affecting Venice and the world alike.
Perhaps she was one of the first to document this decline in the Murano world in an artistic way.
She has also collaborated with the house Ongaro e Fuga dating from 2014, with the creation of Murano's artistic glass.
Elena Mazzi Murano glass mirror
Elena Mazzi "Reflecting Venice"
2. Mario Bellini
Milan-born architect and designer, best known for his collaboration with Rudy Ricciotti, building the Islamic arts department of the Louvre, as well as his Milano Convention Center.
Mario Bellini architecture
Milano Convention Center
The work of the renowned architect has not only remained in the design of buildings, his career also includes development of products for the automotive industry, electronics and communications.
The exhibition of Mario Bellini in Murano – "The architecture of glass, the glass of architecture", gives us a 360 degree view of the work of the master in this field.
Mario Bellini Murano glass vases
Mario Bellini Murano glass blue vase
3. Carlo Scarpa
Another retrospective that took place during Venice glass week, and that deserves its own space, is what was done with the Italian architect Carlo Scarpa.
Born in Venice in 1906, the career of the architect was influenced by both Venetian and Japanese culture.
Carlo Scarpa architecture
Brion Cemetery
Brion Cemetery staircase
His most recognized work is in the art of glass and furniture, where the artist demonstrates his interest in history, regionalism, and inventiveness in traditional techniques.
Even before Scarpa began his career as an architect, he preferred to study with the master glass workers of Murano (one of the islands in the Venetian lagoon) rather than follow the traditional path of academia.
Carlo Scarpa Murano glass vases
Vase in coral red pasta vitrea with amethyst decoro fenicio and finishings in coral-red pasta vitrea. Photography: Enrico Fiorese
Corroso a bugne
Carlo Scarpa Murano glass chandelier
4. Maria Grazia Rosin
Finally, we will return to the present with a contemporary exhibition by the hand of Maria Grazia Rosin, resident artist in Venice whose work mixes pop and fantastic influences, elaborated with the traditional technique of blown Murano glass.
Among her most relevant Murano glass modern chandeliers we can mention its Octopus candelabra, Loredan chandelier, and Cosmospora.
Octopus chandelier
Cosmospora chandelier
De Majo chandelier
Loredan chandelier
In addition to her chandeliers, Maria Grazia has developed a series of works in jewelry, object art and decoration inspired by the Murano technique.
I leave some pictures of your work.
Maria Grazia Murano glass art objects
Maria Grazia jewelry
Ossessione tentacolare
Ossessione tentacolare candleholders
Resilience (noun)
the capacity to recover quickly from difficulties; toughness. "the often remarkable resilience of so many British institutions"
the ability of a substance or object to spring back into shape; elasticity. "nylon is excellent in wearability, abrasion resistance and resilience.
We have presented two scenarios to you. While on the one hand the world of Murano seems to be in decline, in the face of new competitors and less harsh and hybrid techniques.
On the other hand, the last decades have seen a kind of renaissance in this millenary art. Artists and creators of all fields are still inspired by the appeal of Murano and its exquisite technique.
It is your decision if you want to continue supporting the resilience of Murano glass.
Author GiulianoPosted on September 28, 2018 March 15, 2019 Categories ZeitgeistTags 2018, Art, Carlo Scarpa, Elena Mazzi, Maria Grazia Rosin, Mario Bellini, Murano glass market, Murano glass week, Traditional Mirror Market, Venice, Venice glass weekLeave a comment on The Fragility and Resilience of Murano Glass

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text:
Q: Back Linear Substitution I have an equation set Ax=b and A(n*m),n<m . To lower down the dimension, I express some vars by other vars, which gives By=c. After some calculation, the values of y is achieved and I want to get x back. How can I accomplish this work?
The main aim is to get the substitution and back substitution, instead of solving the equations.
Remark: n and m are not fixed, the code need to be general for different scales.
For example:
x[1]+x[2]+x[3]==1&&x[2]+x[4]==1

Then we have:
x[1]==x[4]-x[3]&&x[2]==1-x[4]

And after some calculation, I get {x[3],x[4]}=={0,1} and I want to get:
{x[1],x[2],x[3],x[4]}=={1,0,0,1}

I know it's silly to use x[i], as I can't handle matrices well. I believe there is a way to finish all these in the language of matrices.

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text:
\section{Introduction}

	 The conceptual formulation of dynamical $A$ and $B$ forms was pioneered by Sudarshan and coworkers 60 years ago~\cite{ECGS1,Jordan1}. The $A$ and $B$ matrices play an important role to identify if the open system dynamics of finite dimensional quantum systems is completely positive or not~\cite{NC,Breuer,simon,Vinayak}. In this article we study the dynamical $A$ and $B$ forms in detail. In particular we investigate the canonical structure of the $A$ form and its properties. We show that there is a one-to-one connection between the canonical $A$ form and the $B$ form. We also construct the canonical $A$ form associated with some important physical examples of qubit channels~\cite{NC}.

In Sec.~II we introduce the $A$ and $B$ forms and discuss their properties~\cite{ECGS1,Jordan1}.  We present the canonical structure of the $A$ form and establish its equivalence with the $B$ form in Sec.~III.  The canonical structure of the $A$ form is explicitly constructed for several qubit channels in Sec.~IV. Concluding remarks are given in Sec~V.

\section{Properties of $A$ and $B$ maps}

Consider a $n$ dimensional Hilbert Space $\mathcal{H}_n$.  State of a quantum system is described by a density matrix $\rho\in \mathcal{H}_n$, defining properties of which are given by
\begin{enumerate}
	\item Hermiticity:  $\rho^\dag=\rho$.
	\item Unit trace:  ${\rm Tr}\,\rho=1$.
	\item Positivity: $\langle\,\psi\vert \rho\vert\psi\rangle\geq 0\,$\ for all \ \ $\vert\psi\rangle\in \mathcal{H}.$
\end{enumerate}
For a qubit (two-level quantum system) we have
\begin{equation}
\label{q1}
\rho=\frac{1}{2}\,\left(I +\vec{\sigma}\cdot\, \vec{p}\right)
\end{equation}
where $I$ denotes $2\times 2$ identity matrix, $\vec{\sigma}=(\sigma_1,\sigma_2,\sigma_3)$ are  Pauli matrices:
\begin{equation}
\sigma_1=\left(\begin{array}{cc} 0  & 1 \\
	1 & 0  \end{array}\right), \ \
\sigma_2=\left(\begin{array}{cc} 0  & -i \\
i & 0  \end{array}\right), \ \
\sigma_3=\left(\begin{array}{cc} 1  & 0 \\
0 & -1  \end{array}\right), \ \
\end{equation}
 and the real qubit state parameters given by  $\vec{p}=(p_1,p_2,p_3)$  satisfy the condition $\vert\vec{p}\vert=\sqrt{p_1^2+p_2^2+p_3^2}\leq 1$. Thus, the state space of a qubit corresponds to a unit ball in $\mathbb{R}^3$. The vector $\vec{p}$  is called the Bloch vector.

Now we consider a linear map $A$ transforming density matrices in $\mathcal{H}_n$:
 \begin{eqnarray}
 \label{defA}
 A:&&\,\rho_i\rightarrow\rho_f = A(\rho_i),  \nonumber \\
 \left(\rho_f\right)_{r's'}&=&\left(A\,\rho_i\right)_{r's'}=\sum_{r,s=1}^n\, A_{r's';rs}\, \left(\rho_i\right)_{rs}, \ \ \  r',s'=1,2,\ldots, n.
 \end{eqnarray}
 \begin{itemize}
 \item The $n^2\times n^2$ matrix $A$ is called a trace-preserving positive map if, for every input density matrix, the
output $\rho_f = A(\rho_i)$ is also a legitimate density matrix~\cite{ECGS1,Jordan1}.
\end{itemize}

Writing the qubit density matrix (\ref{q1})  explicitly  (in the standard basis $\vert 0\rangle=(1,0)^T$, $\vert 1\rangle=(0,1)^T$) as
\begin{equation}
\label{qrho}
\rho=\left(\begin{array}{cc} \rho_{00}  & \rho_{01} \\
\rho_{10} & \rho_{11}  \end{array}\right)=\frac{1}{2}\left(\begin{array}{cc} 1+p_3 & p_1-i\, p_2 \\
                                 p_1+ip_2 & 1-p_3  \end{array}\right)
\end{equation}
one may identify the action $A:\ \rho_i\rightarrow\rho_f = A(\rho_i)$ (see (\ref{defA})) as follows:
\begin{eqnarray}
\label{qfAqi}
\left(\begin{array}{c} \left(\rho_f\right)_{00} \\ \left(\rho_f\right)_{01}\\ \left(\rho_f\right)_{10}  \\ \left(\rho_f\right)_{11} \end{array}\right) &=&
\left(\begin{array}{cccc}  A_{00;00} & A_{00;01} & A_{00;10} & A_{00;11}  \\
                           A_{01;00} & A_{01;01} & A_{01;10} & A_{01;11}  \\
                           A_{10;00} & A_{10;01} & A_{10;10} & A_{10;11}  \\
                           A_{11;00} & A_{11;01} & A_{11;10} & A_{11;11}
                           \end{array}\right)
\left(\begin{array}{c} \left(\rho_i\right)_{00} \\ \left(\rho_i\right)_{01}\\ \left(\rho_i\right)_{10}  \\ \left(\rho_i\right)_{11} \end{array}\right) \nonumber \\
{\rm or} \ \ \
\left(\begin{array}{c} 1+\left(p_f\right)_{3} \\ \left(p_f\right)_{1}-i \left(p_f\right)_{2}\\ \left(p_f\right)_{1}+i \left(p_f\right)_{2}  \\ 1-\left(p_f\right)_{3} \end{array}\right) &=&
\left(\begin{array}{cccc}  A_{00;00} & A_{00;01} & A_{00;10} & A_{00;11}  \\
A_{01;00} & A_{01;01} & A_{01;10} & A_{01;11}  \\
A_{10;00} & A_{10;01} & A_{10;10} & A_{10;11}  \\
A_{11;00} & A_{11;01} & A_{11;10} & A_{11;11}
\end{array}\right)
\left(\begin{array}{c} 1+\left(p_i\right)_{3} \\ \left(p_i\right)_{1}-i \left(p_i\right)_{2}\\ \left(p_i\right)_{1}+i \left(p_i\right)_{2}  \\ 1-\left(p_i\right)_{3} \end{array}\right).
\end{eqnarray}

\begin{itemize}
	\item Unitary dynamics $\rho_f=U\,\rho_i\,U^\dag$ defines a trace-preserving positive map
\begin{eqnarray}
\label{defAU}
A_U:&&\,\rho_i\rightarrow\rho_f = A_U(\rho_i),  \nonumber \\
\left(\rho_f\right)_{r's'}&=&\sum_{r,s=1}^n\, \left(U\otimes U^*\right)_{r's';rs}\, \left(\rho_i\right)_{rs}, \ \ \  r',s'=1,2,\ldots, n.
\end{eqnarray}
\item Matrix transposition given by
\begin{eqnarray}
\label{defAUT}
A_T:&&\rho_i\rightarrow\rho_f = A_T(\rho_i)=\rho_i^T
\end{eqnarray}
 is an example of  trace-preserving positive map.
\end{itemize}
Given a positive map $A$ on $\mathcal{H}_n$  one may extend it to the map $A\otimes \mathbbm{I}_d$ acting on the tensor product space  $\mathcal{H}_n\otimes \mathcal{H}_d$  of a composite
$n\times d$ system, where $ \mathbbm{I}_d$ denotes identity map on $\mathcal{H}_d$. Then the positive map $A$ acts only on the  $n$-dimensional  subsystem of the composite state. If the $A\otimes \mathbbm{I}_d$ transforms a composite density matrix into a physical state for any $d$, then the map $A$ is said to be {\em completely positive} (CP). Otherwise, it is called {\em not-completely positive} (NCP).  Thus  a positive map represents a bonafide state to state transformation  if it is  completely positive.

Under the action of a map $A:\rho_i\Longrightarrow \rho_f=A(\rho_i)$, preservation of hermiticity i.e.,  $(\rho_f)^*_{s'r'}=(\rho_f)_{r's'}$ and the unit trace condition $\sum_{r'=1}^n\,\left(\rho_f\right)_{r'r'}=1$  result in the following constraints  on the elements of the $n^2\times n^2$ process matrix $A$:
\begin{eqnarray}
\label{A1}
\left(\rho_f\right)_{r's'}&=&\left(\rho_f\right)^*_{s'r'} \Longrightarrow \sum_{r,s=1}^n\, A^*_{s'r';sr}\, \left(\rho_i\right)^*_{sr}=\sum_{r,s=1}^n\, A_{r's';rs}\, \left(\rho_i\right)_{rs} \nonumber \\
\Longrightarrow &&   \sum_{r,s=1}^n\, A^*_{s'r';sr}\, \left(\rho_i\right)_{rs} = \sum_{r,s=1}^n\, A_{r's';rs}\, \left(\rho_i\right)_{rs} \nonumber \\
\Longrightarrow &&  A^*_{r's';rs} = A_{s'r';sr}
\end{eqnarray}
and
\begin{eqnarray}
\label{A2}
\sum_{r'=1}^n\left(\rho_f\right)_{r'r'}&=&1\Longrightarrow  \sum_{r',r,s}\, A^*_{r'r';rs}\, \left(\rho_i\right)_{rs}  \nonumber \\
\Longrightarrow &&   \sum_{r'=1}^n\, A_{r'r';rs}=\delta_{rs}
\end{eqnarray}
where $\delta_{rs}$ denotes Kronecker delta symbol.

A realigned process matrix $B$ was defined as~\cite{ECGS1,Jordan1}
\begin{equation}
\label{abdef}
B_{r'r;s's}=A_{r's';rs}.
\end{equation}
so that the hermiticity and unit trace conditions (\ref{A1}), (\ref{A2}) on the $A$-form can be expressed as
\begin{eqnarray}
\label{B1}
B_{r'r;s's}&=&B^*_{s's;r'r} \\
\sum_{r'=1}^n B_{r'r;r's}=\delta_{rs} && \Longrightarrow\ \  {\rm Tr}\,B=n.
\end{eqnarray}
Thus a physically valid  $A$-form  requires that the corresponding realigned matrix $B$ (see (\ref{abdef}))  is a $n^2\times n^2$ hermitian matrix  with trace $n$.

Furthermore, positivity of the density matrix $\rho_f=A(\rho_i)\geq 0$ leads to the following constraints on the elements of $A$ and $B$ respectively~\cite{ECGS1}:
\begin{eqnarray}
\sum_{r,s,r',s'}\,x^*_r\,x_s\, A_{rs;r's'}\, y_{r'}y_{s'}^*\geq 0, \nonumber \\
\sum_{r,s,r',s'}\, x^*_r\,y_{r'}\, B_{rr';ss'}\,x_s\, y_{s'}^*\geq 0.
\end{eqnarray}
In other words, positivity $\rho_f=A(\rho_i)\geq 0$ of the density matrix requires that $B\geq 0.$

It is pertinent to point out that    the $B$-form is represented by a hermitian matrix whereas $A$ is not; positivity of the $B$ matrix highlights that the output density matrix is legitimate.  For this reason  Sudarshan, Mathews and Rau~\cite{ECGS1} highlighted that  {\em the matrix $B$ incorporates the kinematical restrictions on the dynamical law in a succint fashion; we shall call $B$ the dynamical matrix}.  The $A$-form was used in Ref.~\cite{ECGS1} to define a linear map from input to output density operators (where the elements of the input and outpur density matrices are arranged in the form of  $n^2$ component  columns). Beyond this initial definition, the $A$ matrix was not recognized to have any clear role.  Our focus here is to unravel the $A$-form to its full potential. We show in the next section  that  the $A$ matrix introduced in the Sudarshan-Mathew-Rau paper exhibits an elegant canonical structure and it reveals itself as a powerful tool in capturing all the dynamical features reflected by the corresponding  $B$-form~\cite{urs}.

\section{Canonical structure of the $A$-form}

Consider an orthonormal set $$\{T_\mu, \mu=0,1,2,\ldots, n^2-1\}$$ of $n\times n$  matrices satisfying
\begin{equation}
\label{tor}
{\rm Tr}[T_\mu^\dag\, T_\nu]=\delta_{\mu,\nu}.
\end{equation}
We then construct a basis set
\begin{equation}
\{T_\mu\otimes T_\nu^* , \ \  \mu,\nu=0,1,\ldots , n^2-1\}
\end{equation}
of  $n^2\times n^2$ matrices and express the  $A$ matrix (see (\ref{defA})) as follows:
\begin{equation}
\label{smalla1}
A=\sum_{\mu,\nu=0}^{n^2-1} \, a_{\mu\nu}\, T_\mu\otimes T_\nu^*
\end{equation}
where the expansion coefficients $a_{\mu\nu}$ are given by
\begin{equation}
\label{asmall}
a_{\mu\nu}={\rm Tr}[A(T^\dag_\mu\otimes T^T_\nu)],\ \ \mu, \nu=0,1,\ldots , n^2-1.
\end{equation}
The matrix elements $A_{r's';rs}$  of the $A$ matrix are then given by
\begin{equation}
\label{a2}
A_{r's';rs}=\sum_{\mu,\nu=0}^{n^2}\, a_{\mu\nu}\, [T_\mu]_{r'r}\, [T^*_\nu]_{s's}.
\end{equation}
Let us examine the hermiticity preserving condition (\ref{A1}) on the expansion coefficients  $a_{\alpha\beta}$:
\begin{equation}
\label{aher}
A^*_{r's';rs} = A_{s'r';sr} \Longrightarrow
a^*_{\mu\nu}=a_{\nu\mu}
\end{equation}
In other words the coefficients $a_{\mu\nu}, \mu,\nu=0,1,\ldots, n^2-1$ constitute a $n^2\times n^2$ hermitian matrix, which we denote by  $\mathcal{A}$.

Let $\mathcal{U}$ be a unitary matrix which diagonalizes $\mathcal{A}$ i.e.,
\begin{equation}
\label{uaudag}
\mathcal{U}\, \mathcal{A}\, \mathcal{U}^\dag=\mathcal{A}_0=\left(\begin{array}{lllll}\lambda_0 & 0 & \ldots & \ldots &  0 \\
                                                                                0 & \lambda_1 & \ldots & \ldots &0 \\
                                                                                \vdots & \vdots & \ddots &  & \vdots \\
                                                                                0 & 0 & \ldots & \ldots & \lambda_{n^2-1}   \end{array}\right)
\end{equation}
where $\lambda_\mu, 0\leq \mu\leq n^2-1$ denote the eigenvalues of $\mathcal{A}$. Thus we obtain
\begin{eqnarray}
\label{ael}
a_{\mu\nu}&=&\left(\mathcal{U}^\dag\, \mathcal{A}_0\, \mathcal{U}\right)_{\mu\nu}\nonumber \\
&=&\sum_{\alpha}\lambda_\alpha\,  u^{*}_{\alpha\mu}\, \, u_{\alpha\nu}.
\end{eqnarray}
Substituting (\ref{ael}) in (\ref{smalla1}) we obtain the following canonical structure of the $A$ matrix:
\begin{eqnarray}
\label{canA}
A&=&\sum_{\mu,\nu,\alpha}\,\lambda_\alpha\, u^*_{\alpha\mu}u_{\alpha\nu}\, \left(T_\mu\otimes T_\nu^*\right) \nonumber \\
&=& \sum_\alpha\, \lambda_\alpha\,\left( C_\alpha\otimes C_\alpha^*\right),
\end{eqnarray}
where we have denoted
\begin{equation}
C_\alpha=\sum_{\mu=0}^{n^2-1}\,  u^*_{\alpha\mu}\, T_\mu.
\end{equation}

\begin{itemize}
\item Using (\ref{canA}) we can express the matrix elements of $A$ as
\begin{equation}
\label{canA2}
A_{r's';rs}=\sum_{\alpha=0}^{n^2-1}\, \lambda_\alpha\, (C_\alpha)_{r'r}\,(C_\alpha^*)_{s's}.
\end{equation}
Substituting (\ref{canA2}) in (\ref{defA}) and simplifying, we obtain the following elegant structure for the action of the linear $A$-map on the column vector consisting of the elements of the  input density matrix $\rho_i$:
\begin{eqnarray}
\label{ele}
(\rho_f)_{r's'}&=&\sum_{r,s}\, A_{r's';rs}\, (\rho_i)_{rs} \nonumber \\
&=&  \sum_{r,s,\alpha} \, \lambda_\alpha\, (C_\alpha)_{r'r}\,(C^*_\alpha)_{s's}\,(\rho_i)_{rs}     \nonumber \\
&=& \sum_{r,s,\alpha}\, \lambda_\alpha\, (C_\alpha)_{r'r}\,(\rho_i)_{rs}\,(C_\alpha^\dag)_{ss'}\, \nonumber \\
& =&\sum_{\alpha} \lambda_\alpha\, \left(C_\alpha\, \rho_i\, C^\dag_\alpha\right)_{r's'} \nonumber \\
\Longrightarrow  \ \ \  \rho_f&=&\sum_{\mu}\lambda_{\mu}\, C_{\mu}\, \rho_i\,C^\dag_{\mu}.
\end{eqnarray}
\item From (\ref{ele}) the trace preservation condition (\ref{A2}) assumes the form
\begin{eqnarray}
\label{tp2}
{\rm Tr}(\rho_f)=1\ \ \ &&\Longrightarrow  \sum_{\alpha}\lambda_{\alpha}\, {\rm Tr}\,\left(C_{\alpha}\, \rho_i\,C^\dag_{\alpha}\right)=
\sum_{\alpha}\lambda_{\alpha}\, {\rm Tr}\,\left(C^\dag_{\alpha}\,C_{\alpha}\, \rho_i\,\right)=1 \nonumber \\
&&\Longrightarrow  \sum_{\alpha}\lambda_{\alpha}\,C^\dag_{\alpha}\,C_{\alpha}=I_{n}.
\end{eqnarray}
\item  From (\ref{abdef}) and (\ref{canA2}) we may identify the elements of the realigned $B$ matrix as
\begin{equation}
\label{bac}
B_{r'r;s's}=  \sum_\alpha\, \lambda_\alpha\, (C_\alpha)_{r'r}\, (C_\alpha^*)_{s's}
\end{equation}
which happens to be the spectral decomposition of the dynamical $B$ matrix with  $\lambda_\mu$ being its eigenvalues.
\end{itemize}
Highlighting point here is that (\ref{bac}) brings out an explicit  connection between the hermitian (coefficient) matrix $\mathcal{A}$ (see (\ref{smalla1}) and (\ref{aher}))  and the dynamical matrix $B$ of Ref.~\cite{ECGS1}:
 \begin{enumerate}
 \item The eigenvalues of the coefficient matrix  $\mathcal{A}$ associated with the $A$-form are identically same as those of  $B$.
 \item A completely positive map requires that the coefficient matrix $\mathcal{A}$ is positive (i.e., the eigenvalues $\lambda_{\alpha}$ are  non-negative whenever the map is completely positive).
 \item In the case of a completely positive map one may define a set $\{E_\alpha,\,\alpha=0,1,\ldots,n^2-1\}$ of  $n\times n$ matrices based on the canonical structure (\ref{canA}) of the $A$-map:
 \begin{equation}
 \label{krE}
 E_\alpha=\sqrt{\lambda_\alpha}\, C_\alpha.
 \end{equation}
Then the transformation $\rho_i~\rightarrow~\rho_f~=~A(\rho_i)$ gets expressed in terms of the Kraus operator-sum representation~\cite{Kraus} i.e.,
  \begin{eqnarray}
  \label{krAmap}
  (\rho_f)_{r's'}&=& \sum_{r,s}\, A_{r's';rs}\, (\rho_i)_{rs} \nonumber \\
  &=&  \sum_{r,s,\alpha} \, \lambda_\alpha\, (E_\alpha)_{r'r}\,(E^*_\alpha)_{s's}\,(\rho_i)_{rs} \nonumber \\
  &=& \sum_\alpha (E_\alpha)_{r'r}\,(\rho_i)_{rs}\, (E^\dag_\alpha)_{ss'}=\sum_\alpha\, \left(E_\alpha\,\rho_i\,E^\dag_\alpha\right)_{r's'}  \nonumber \\
  &&\Longrightarrow \rho_f=\sum_\alpha\, E_\alpha\,\rho_i\,E^\dag_\alpha.
  \end{eqnarray}
  We point out  that the operator sum representation (\ref{krAmap}) was already described (via  the spectral decomposition of the dynamical matrix $B$)  by Sudarshan, Mathews and Rau in  their 1961 paper~\cite{ECGS1} and it was independently proposed by Kraus~\cite{Kraus} after 10 years. The operators  $E_\alpha$ (see  (\ref{krE}),(\ref{krAmap}))  associated with a completely positive map are known as Kraus operators in the literature.
 	\end{enumerate}

 Summarizing, in this section we have shown that the canonical structure (\ref{canA}) of the $A$-form plays a significant role on its own --   bringing forth all the required features of the quantum channel --  without any necessity to invoke the realigned $B$-form.  In the next section  we employ the  $A$-form to elucidate the completely positive or not completely positive behaviour of some familiar qubit channels.

\section{Canonical $A$\,-\,form of standard qubit maps}

In this section we illustrate explicit $4\times 4$ matrix forms of the canonical $A$-form and its equivalence with the dynamical matrix $B$ of some standard qubit transformations.

\subsection{Unitary map}
Under the action of a unitary transformation we have
\begin{eqnarray}
\label{ss21}
\rho_f=U\,\rho_i\,U^\dagger\,\ \Longrightarrow
\left(\rho_f\right)_{r's'}&=&\sum_{r,s}\,U_{r'r}\,U^*_{s's}\,\left(\rho_i\right)_{rs} =\sum_{r,s}\,\left(U\otimes U^*\right)_{r's'; rs}\,\left(\rho_i\right)_{rs}.
\end{eqnarray}
We thus obtain (see (\ref{defA}))
\begin{equation}
\label{ss22}
\left(A_U\right)_{r's';rs}=\left(U\otimes U^*\right)_{r's'; rs} \Longrightarrow A_U=U\otimes U^*
\end{equation}

Let us consider the $2\times 2$ unitary matrix
\begin{eqnarray}
\label{22u}
U&=&e^{i\, (\vec{\sigma}.\hat{n})\theta/2}, \ \ \vert\hat{n}\vert^2=n_1^2+n_2^2+n_3^2=1  \nonumber \\
&=& I_2\, \cos\left(\theta/2\right)  + i\,  \vec{\sigma}.\hat{n}  \, \sin\left(\theta/2\right)  \nonumber \\
&=& \left(\begin{array}{cc}\cos\left(\frac{\theta}{2}\right) +i\, n_3\,\sin\left(\frac{\theta}{2}\right)  & i\,n_-\,\sin\left(\frac{\theta}{2}\right) \\
i\,n_+\,\sin\left(\frac{\theta}{2}\right) & \cos\left(\frac{\theta}{2}\right) -i\, n_3\,\sin\left(\frac{\theta}{2}\right)  \\
 \end{array}\right),\ \ n_\pm=(n_1\pm i\,n_2).
\end{eqnarray}
Then the matrix $A_U$ (see (\ref{defAU}), (\ref{ss22})) associated with the unitary matrix (\ref{22u}) takes the form
 \begin{eqnarray}
\label{amunu}
A_U &=& \left(I_2\otimes I_2\right)\, \cos^2\left(\theta/2\right)   + \left(\vec{\sigma}^*\cdot\hat{n}\otimes\vec{\sigma}^*\cdot\hat{n}\right)\, \sin^{2}\left(\theta/2\right) \nonumber \\
&& \ \  -i\left(I_2\otimes\vec{\sigma}^*\cdot\hat{n}- \vec{\sigma}\cdot\hat{n}\otimes I_2\right)\, \cos\left(\theta/2\right)
\sin\left(\theta/2\right).
\end{eqnarray}
Denoting  $\sigma_0=I_2$ and employing the basis set   $\{T_\mu=\frac{1}{\sqrt{2}}\, \sigma_\mu\}$ of $2\times 2$ matrices satisfying  (see (\ref{tor})) the conditions
$$\frac{1}{2}{\rm Tr}[\sigma_\mu\,\sigma_\nu]=\delta_{\mu\nu},\ \mu,\nu=0,1,2,3,$$ we express (\ref{amunu}) in the following compact form.
\begin{eqnarray}
\label{bau22}
A_U=\frac{1}{2}\,\sum_{\mu,\nu=0,1,2,3}\, (a_U)_{\mu\nu}\, \sigma_{\mu}\otimes \sigma^*_{\nu},
\end{eqnarray}
Observe that
\begin{eqnarray}
\label{amunu2}
(a_U)_{\mu\nu}&=&\frac{1}{2}\,{\rm Tr}\left[A_U\,(\sigma_\mu\otimes\sigma^*_\nu)\right] \nonumber \\
&=& \frac{1}{2}\,{\rm Tr}\left[U\,\sigma_\mu\right]\, {\rm Tr}\left[U\,\sigma_\nu\right]^*
\end{eqnarray}
where ${\rm Tr}\left[U\,\sigma_\mu\right],\mu=0,1,2,3$ is evaluated using (\ref{22u}):
\begin{eqnarray}
{\rm Tr}\left[U\,\sigma_0\right]= 2\,\cos\left(\frac{\theta}{2}\right), \ \
{\rm Tr}\left[U\,\sigma_k\right]= 2i\,n_k\, \sin\left(\frac{\theta}{2}\right), \ \  k=1,2,3
\end{eqnarray}
Then the $4\times 4$ coefficient matrix $\mathcal{A}_U=((a_U)_{\mu\nu})$ (see (\ref{amunu2})) associated with $A_U$  is given by
\begin{equation}
\label{coau}
\mathcal{A}_U= 2\,  X_U\, X_U^\dag,  \ \ \
X_U=\left(\begin{array}{c} \cos\left(\frac{\theta}{2}\right) \\ i\,n_1\, \sin\left(\frac{\theta}{2}\right) \\
i\,n_2\, \sin\left(\frac{\theta}{2}\right) \\ i\,n_3\, \sin\left(\frac{\theta}{2}\right) \end{array}\right).
\end{equation}
From (\ref{coau}) it is seen that the coefficient matrix $\mathcal{A}$ is a rank-1 positive matrix with  eigenvalue 2 and eigenvector $X_U$.
The realigned $B_U$ matrix matches exactly with the coefficient matrix $\mathcal{A}_U$ (see (\ref{coau})) i.e.,
\begin{equation}
B_U=2\, X_U X_U^\dag \equiv \mathcal{A}_U.
\end{equation}

\subsection{Pin map: }

Consider a linear $A$-form mapping every input state $\rho_i$ to a fixed output state $\rho_0$   i.e.,
\begin{equation}
A_{\rm pin}: \rho_{i}\rightarrow \rho_0=A_{\rm pin}(\rho_i) \ \forall\rho_i.
\end{equation}
Sudarshan, Mathews and Rau presented this map in terms of the $B$-form, which was termed as  {\em relaxation generator}. Here we would like to illustrate the canonical structure of the $A$-form associated with the qubit pin-map.

Let the fixed output density matrix of the qubit be given by
\begin{equation}
\label{pinrho}
\rho_0=\frac{1}{2}\left(I_2+ \vec\sigma\cdot \vec{p}_0 \right).
\end{equation}
The $4\times 4$ matrix  $A_{\rm pin}$ corresponding to the pin map is identified as follows:
\begin{eqnarray}
\label{pinex}
\left(\begin{array}{c} 1+\left(p_0\right)_{3} \\ \left(p_0\right)_{1}-i \left(p_0\right)_{2}\\ \left(p_0\right)_{1}+i \left(p_0\right)_{2}  \\ 1-\left(p_0\right)_{3} \end{array}\right) &=&
\left(\begin{array}{cccc}  \left(A_{\rm pin}\right)_{00;00} & \left(A_{\rm pin}\right)_{00;01} & \left(A_{\rm pin}\right)_{00;10} & \left(A_{\rm pin}\right)_{00;11}  \\
\left(A_{\rm pin}\right)_{01;00} & \left(A_{\rm pin}\right)_{01;01} & \left(A_{\rm pin}\right)_{01;10} & A_{01;11}  \\
\left(A_{\rm pin}\right)_{10;00} & \left(A_{\rm pin}\right)_{10;01} & \left(A_{\rm pin}\right)_{10;10} & \left(A_{\rm pin}\right)_{10;11}  \\
\left(A_{\rm pin}\right)_{11;00} & \left(A_{\rm pin}\right)_{11;01} & \left(A_{\rm pin}\right)_{11;10} & \left(A_{\rm pin}\right)_{11;11}
\end{array}\right)
\left(\begin{array}{c} 1+\left(p_i\right)_{3} \\ \left(p_i\right)_{1}-i \left(p_i\right)_{2}\\ \left(p_i\right)_{1}+i \left(p_i\right)_{2}  \\ 1-\left(p_i\right)_{3} \end{array}\right)\ \ \forall \ \ \vec{p}_i \nonumber \\
&& \Longrightarrow  A_{\rm pin}=\frac{1}{2}\,\left(\begin{array}{cccc}  1+\left(p_0\right)_3 & 0 & 0 & 1+\left(p_0\right)_3  \\
\left(p_0\right)_1-i\left(p_0\right)_2 & 0 & 0 & \left(p_0\right)_1-i\left(p_0\right)_2  \\
\left(p_0\right)_1+i\left(p_0\right)_2 & 0 & 0 & \left(p_0\right)_1+i\left(p_0\right)_2  \\
1-\left(p_0\right)_3 & 0 & 0 & 1-\left(p_0\right)_3
\end{array}\right).
\end{eqnarray}
Using the orthonormal basis set of  matrices $\{\frac{\sigma_\mu}{\sqrt{2}}, \mu=0,1,2,3\}$ we expand
$$A_{\rm pin}=\frac{1}{2}\sum_{\mu,\nu}\, \left(a_{\rm pin}\right)_{\mu\nu}\, \sigma_{\mu}\otimes\sigma_\nu^*,\ {\rm where}\  \left(a_{\rm pin}\right)_{\mu\nu}=
\frac{1}{2}{\rm Tr}[A_{\rm pin}\,\left(\sigma_\mu\otimes\sigma_\nu^*\right)].$$
 The coefficient matrix $\mathcal{A}_{\rm pin}=(\left(a_{\rm pin}\right)_{\mu\nu})$ is then found to be
\begin{eqnarray}
 \mathcal{A}_{\rm pin}=\frac{1}{2}\left(\begin{array}{cccc}  1& \left(p_0\right)_1  & \left(p_0\right)_2  & \left(p_0\right)_3  \\
 	\left(p_0\right)_1 & 1 & -i\left(p_0\right)_3 & i\left(p_0\right)_2  \\
 	\left(p_0\right)_2 & i\left(p_0\right)_3 & 1 & -i\left(p_0\right)_1  \\
 	\left(p_0\right)_3 & -i\left(p_0\right)_2 & i\left(p_0\right)_1 & 1
 \end{array}\right).
\end{eqnarray}
The eigenvalues of $\mathcal{A}_{\rm pin}$ are given by
\begin{equation}
\label{evpin}
\lambda_0=\lambda_1=\frac{1}{2}\, (1+\vert\vec{p}_0\vert), \ \  \lambda_2=\lambda_3=\frac{1}{2}(1-\vert\vec{p}_0\vert).
\end{equation}
Clearly, the eigenvalues of $\mathcal{A}_{\rm pin}$ are all positive ensuring that the pin map is completely positive.

 The $B$ matrix associated with the pin map is constructed using the explicit matrix form of $A_{\rm pin}$ (see (\ref{pinex})):
\begin{eqnarray}
	B_{\rm pin}&=&\frac{1}{2}\left(\begin{array}{cccc} 1+\left(p_0\right)_3 & 0 & \left(p_0\right)_1-i\,\left(p_0\right)_2 & 0 \\ 0 & 1+\left(p_0\right)_3 & 0 & \left(p_0\right)_1-i\, \left(p_0\right)_2 \\
		\left(p_0\right)_1+i\, \left(p_0\right)_2 & 0 & 1-\left(p_0\right)_3 & 0 \\
		0 & \left(p_0\right)_1+i\, \left(p_0\right)_2& 0 & 1-\left(p_0\right)_3 \end{array}\right)\nonumber \\
		&=&\rho_0\otimes I_2
		\end{eqnarray}
Eigenvalues of $B_{\rm pin}$ match with those of the coefficient matrix $\mathcal{A}_{\rm pin}$ (see (\ref{evpin})), thus establishing the equivalence between the two.

\subsection{Transpose map:}
 Consider the transpose map $A_T:\rho\rightarrow\rho^T$ on  qubit density matrices (see (\ref{qrho})).
We obtain the associated $4\times 4$ matrix form of $A_T$ as
\begin{equation}
\label{at}
A_T=
\left(\begin{array}{cccc}\,1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0\\ 0 & 1 & 0 &  0 \\ 0 & 0 & 0 & 1 \\
\end{array}\right).
\end{equation}
Employing the  basis set  $\{\frac{\sigma_\mu}{\sqrt{2}}, \mu=0,1,2,3\}$ we express
\begin{equation}
A_T=\frac{1}{2}\sum_{\mu,\nu=0}^3\, \left(a_{T}\right)_{\mu\nu}\, \left(\sigma_{\mu}\otimes \sigma^*_{\nu} \right)
\end{equation}
to obtain the following explicit structure for the coefficient matrix $\mathcal{A}_T$:
\begin{equation}
\label{calat}
\mathcal{A}_T=\mbox{diag}\,\left(-1,\,1,\,1,\,1 \right).
\end{equation}
The matrix $\mathcal{A}_T$ is not positive (one of the eigenvalues of $\mathcal{A}_T$ is -1) which points towards the not-completely positive nature of the transpose map.

From the explicit matrix structure of  $A_T$ (see (\ref{at})) it is easy to see that the realigned dynamical matrix  $B_T\equiv A_T$. The
eigenvalues of $B_T$ match with those of the coefficent matrix $\mathcal{A}_T$ (see (\ref{calat})).

\subsection{Projection of the Bloch sphere onto its equatorial plane:}
A map that projects the entire Bloch sphere onto the equatorial plane is defined by the transformation of the Bloch vector
 $$(p_1,\,p_2,\,p_3)\rightarrow (p_1,\,p_2,\,0).$$ This leads to the following linear transformation
\begin{equation}
\label{pR}
\left(\begin{array}{c}\,\ 1 \\  p_1-i\ p_2 \\ p_1+i\ p_2 \\ 1 \end{array}\right)  =
\frac{1}{2}\left(\begin{array}{cccc}
1 & 0 & 0 & 1 \\
0 & 2 & 0 & 0\\
0 & 0 & 2 &  0 \\
1 & 0 & 0 & 1
\end{array}\right) \left(\begin{array}{c}\,1+p_3 \\  p_1-i\ p_2 \\ p_1+i\ p_2 \\ 1-p_3 \end{array}\right).
\end{equation}
We then  express $A_P=\frac{1}{2}\sum_{\mu,\nu}\,\left(a_P\right)_{\mu\nu}\, \left(\sigma_{\mu}\otimes\sigma_\nu^*\right)$ to obtain
\begin{equation}
\mathcal{A}_P=\frac{1}{2}\mbox{diag}\,\left(3,\,1,\,
1,\,-1 \right).
\end{equation}
Negative eigenvalues of $\mathcal{A}_P$ clearly indicate that projection of the Bloch sphere onto the equatorial plane is not physical as it corresponds to a not completely positive map.  The dynamical matrix $B_P$ is then obtained using the realignment   $(B_P)_{r'r;s's}=(A_P)_{r's';rs}$:
\begin{equation}
B_P=\frac{1}{2}\left(\begin{array}{cccc}\, 1 & 0 & 0 & 2 \\
0 & 1 & 0 & 0\\ 0 & 0 & 1 &  0 \\ 2 & 0 & 0 & 1 \\
\end{array}\right).
\end{equation}
Eigenvalues  of $B_P$ are same as those of $\mathcal{A}_P$.

	\subsection{ Bit flip channel}
		A qubit bit flip channel reverses the state of a qubit from $\vert 0\rangle$ to $\vert 1\rangle$ with probability $1-p$, $0\leq p \leq 1$; the channel keeps the states unaltered  with a probability $p$. This is a completely positive map equipped with the  Kraus operators given by~\cite{NC}
	\begin{equation}
	\label{bf1}
	E_0=\sqrt{p}\left(\begin{array}{cc} 1 & 0 \\ 0 & 1  \end{array}\right), \ \ \
	E_1\equiv \sqrt{1-p}\,\left(\begin{array}{cc} 0 & 1 \\ 1 & 0  \end{array}\right).
	\end{equation}
Using the operator-sum representation  $\rho_f= E_0\,\rho_i E_0^\dagger+
	E_1\,\rho_i E_1^\dagger$  we construct the associated $A$ matrix:
	\begin{eqnarray}
	\label{bitflipA}
A_{\rm BF}	&=&\left(\begin{array}{cccc}\,p & 0 & 0 & 1-p \\
	0 & p & 1-p & 0\\ 0 & 1-p & p & 0 \\ 1-p & 0 & 0 & p  \end{array}\right)
	\end{eqnarray}
	Adopting the  matrix basis $\left\{\frac{\sigma_\mu}{\sqrt{2}},\mu=0,1,2,3\right\}$, as  in all other examples studied earlier, we compute the coefficient matrix $\mathcal{A}_{\rm BF}=\left(a_{\mu\nu}\right)$ associated with  $A_{\rm BF}$:
\begin{eqnarray}
	\mathcal{A}_{\rm BF}&=&\left(\begin{array}{cccc} 2p & 0 & 0 & 0 \\ 0 & 2(1-p) & 0 & 0 \\ 0 & 0 & 0 & 0 \\
	0 & 0 & 0 & 0 \end{array}\right)
	\end{eqnarray}
Note that the  eigenvalues $2p, 2(1-p)$ of   $\mathcal{A}_{\rm BF}$    are  positive and ascertain the completely positive nature of the bit flip channel.

\subsection{Phase flip channel}
 A qubit phase flip channel is equipped with the Kraus operators~\cite{NC}
	\begin{equation}
	\label{pf1}
	E_0=\sqrt{p}\left(\begin{array}{cc} 1 & 0 \\ 0 & 1  \end{array}\right), \ \ \
	E_1=\sqrt{1-p}\,\left(\begin{array}{cc} 1 & 0 \\ 0 & -1  \end{array}\right).
	\end{equation}
The linear map $A_{\rm PF}$ associated with the phase flip channel  is given explicitly as a $4\times 4$ matrix form:
\begin{eqnarray}
	\label{pflipA}
	A_{\rm BF}&=&\frac{1}{2}\left(\begin{array}{cccc}\,1 & 0 & 0 & 0 \\
	0 & 2p-1 & 0 & 0\\ 0 & 0 & 2p-1 & 0 \\ 0 & 0 & 0 &
	1 \end{array}\right).
\end{eqnarray}
	Then the associated coefficent matrix $\mathcal{A}_{\rm BF}$ is found to be
	\begin{eqnarray}
	\mathcal{A}_{\rm BF}&=&\left(\begin{array}{cccc} 2p & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\
	0 & 0 & 0 & 2(1-p) \end{array}\right)
	\end{eqnarray}
The eigenvalues  $2p$, $2(1-p)$ of 	$\mathcal{A}_{\rm BF}$ are necessarily positive and  confirm the legitimacy (complete positivity) of the phase flip channel.

\section{Summary}

The dynamical $A$ and $B$-maps were pioneered by Sudarshan, Mathews and Rau~\cite{ECGS1} in the context of open system dynamics. Unfortunately this seminal 1961 paper did not receive its due attention in the field, although it contained all the details of finite dimensional quantum channels.
In this work we have elaborated on the canonical structure of the $A$-form, establishing that it  offers an alternative approach to recognize the completely positive/not completely positive nature of  quantum channels. We have illustrated the canonical structure of the $A$ map in several standard examples of qubit maps.  A new geometrical representation based on the Lorentz singular value decomposition~\cite{svd} of the canonical $A$-form associated with qubit transformations is being prepared~\cite{KSAR} and it will be presented separately as a sequel to the present work.

We dedicate this tutorial article as a mark of our reverence to Professor ECG Sudarshan.

\section*{Acknowledgement}  ARU,BNK and Sudha acknowledge financial support from the Department of Science and Technology, India (Project No. DST/ICPS/QuST/Theme-2/Q107/2019).

redpajama_set_name: RedPajamaArXiv


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Last edited by jeffmazen on February 7th, 2019, 4:17 am, edited 2 times in total.
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Not to be confused with Physical chemistry.
Chemical physics is a subdiscipline of chemistry and physics that investigates physicochemical phenomena using techniques from atomic and molecular physics and condensed matter physics; it is the branch of physics that studies chemical processes from the point of view of physics. While at the interface of physics and chemistry, chemical physics is distinct from physical chemistry in that it focuses more on the characteristic elements and theories of physics. Meanwhile, physical chemistry studies the physical nature of chemistry. Nonetheless, the distinction between the two fields is vague, and workers often practice in both fields during the course of their research.
The United States Department of Education defines chemical physics as "A program that focuses on the scientific study of structural phenomena combining the disciplines of physical chemistry and atomic/molecular physics. Includes instruction in heterogeneous structures, alignment and surface phenomena, quantum theory, mathematical physics, statistical and classical mechanics, chemical kinetics, and laser physics."
Can we experimentally test quantum mechanical predictions of the vibrations and rotations of simple molecules? Or even those of complex molecules (such as proteins)?
Can we develop more accurate methods for calculating the electronic structure and properties of molecules?
Can we understand chemical reactions from first principles?
Why do quantum dots start blinking (in a pattern suggesting fractal kinetics) after absorbing photons of light?
How do chemical reactions really take place?
What is the step-by-step process that occurs when an isolated molecule becomes solvated? Or when a whole ensemble of molecules becomes solvated?
Can we use the properties of negative ions to determine molecular structures, understand the dynamics of chemical reactions, or explain photodissociation?
Why does a stream of soft x-rays knock enough electrons out of the atoms in a xenon cluster to cause the cluster to explode?


text:
Topic Storage and services
Data Storage Management
Network-Attached Storage (NAS)
Primary and secondary storage
Remote Storage Management
The status of FCoE
Learn about the two major sets of proposed standards that will enable FCoE in data centers – one that defines mapping of Fibre Channel frames and the other that defines Ethernet enhancements -- and how close to final status they are.
Carol Sliwa
You've been hearing about Fibre Channel over Ethernet (FCoE) for more than two years. So what's its status? The answer to that question is a bit complicated. First of all, it's not just one proposed standard; it's two major sets that, applied together, are designed to enable FCoE in data centers. Second, the two sets are at different steps in their process within different standards bodies.
One set of standards -- the fifth version of the Fibre Channel Backbone standard (FC-BB-5) -- defines how to map Fibre Channel frames to run over networks where the physical and the link layer are not Fibre Channel. Its development rested with the T11 technical committee, which is responsible for Fibre Channel interfaces, within the International Committee for IT Standards (INCITS).
More on FCoE
Steps to FCoE readiness
The other set of standards, known as Data Center Bridging (DCB), applies to the Ethernet enhancements necessary to ensure that FCoE traffic can be transported without packet loss and that bandwidth can be effectively shared between FCoE and Ethernet LAN traffic. DCB falls under the purview the Institute of Electrical and Electronics Engineers (IEEE).
Of the two sets of proposed standards, FC-BB-5 is closer to finalization. The T11 technical committee in June approved FC-BB-5 for submission to INCITS for public review and further processing. INCITS is accredited by, and operates under rules approved by, the American National Standards Institute (ANSI), so the final processing steps are designed to result in an ANSI standard.
Under an ideal scenario, the draft standard -- which is now known as INCITS 462-200x -- could move to final-approval status in early 2010, according to Lynn Barra, director of INCITS Standards Operations.
Meanwhile, products claiming to support FCoE have been on the market for months. Bob Laliberte, a senior analyst at Enterprise Strategy Group Inc., said, "Essentially, it's a de facto standard, and no changes need to be made to the hardware that's being shipped today," such as converged network adapters and switches.
On the enhanced Ethernet side, the proposed standards are moving along, but their status isn't as close to finalization as FC-BB-5/INCITS 462-200x. Active projects within the DCB Task Group of the IEEE 802.1 Working Group include Congestion Notification (802.1Qau), Enhanced Transmission Selection (802.1Qaz) and Priority-based Flow Control (802.1Qbb).
Of the trio, Congestion Notification is the farthest along in the standards process. A sponsor ballot is due to end on Nov. 29, but if any concerns or comments surface, they need to be addressed. Recirculation ballots are not uncommon, further extending the time frame.
"It's usually pretty stable at this point, but we won't know for sure until the end of the month," said Patricia Thaler, who chairs the DCB Task Group.
The 802.1Qau proposed standard will allow any point in the network that is experiencing congestion to send notifications to the congestion sources so they can slow the transmission rates. Thaler estimated finalization could happen some time between March and September 2010, with the timing contingent, in part, on when various groups meet.
A draft of Priority-based Flow Control is also up for a vote this month, but the ballot is at an earlier stage in the process, by the 802.1 working group. If interested parties have issues with a proposed standard, they typically raise them at this stage.
Priority-based Flow Control provides the ability to pause traffic, based on its priority, while allowing other traffic to flow. Thaler expressed hopes that the proposed standard will go to sponsor ballot following a March 2010 meeting, with finalization in September or December.
Enhanced Transmission Selection is expected to finish in the same time frame, since parts of Priority-based Flow Control are dependent on it. The 802.1Qaz proposed standard provides a standard way to manage bandwidth allocation to different classes of traffic, so each gets a share.
Another standard, known as Media Access Control Frame for Priority-based Flow Control (802.3bd), defining the frame that is sent for priority flow control, is also in the works. Thaler said she hopes that one will also be done by December 2010.
While some industry analysts advise that IT organizations wait until the standards reach completed status before investing in FCoE equipment, vendors and other analysts disagree. "There's nothing that will be added that will alter the products that are already shipping because we know from the development of standards what is going to be done," claimed Ahmad Zamer, a senior product manager for new technology protocols at Brocade Communications Systems Inc. "This is basically like building a 10-story building. You already built your ninth floor. You know where the 10th floor is going to go in the building."
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text:
El British Antarctic Survey (BAS), traducido como Relevamiento Antártico Británico o Prospección Antártica Británica, es una institución nacional del Reino Unido dedicada a la investigación de la Antártida. El BAS es parte del Natural Environment Research Council (NERC) y tiene más de 400 empleados. Opera cinco estaciones de investigación, dos barcos y cinco aviones en y cerca de la Antártida. Trabaja en proyectos de investigación conjuntos con más de 40 universidades británicas y más de 120 instituciones colaboradoras nacionales e internacionales.

Historia

La Operación Tabarin fue una pequeña expedición británica en 1943 para establecer bases permanentes en la Antártida. Fue un emprendimiento conjunto del Almirantazgo Británico y la Secretaría de Estado para las Colonias (Oficina Colonial). Al finalizar la Segunda Guerra Mundial fue renombrado como Falkland Islands Dependencies Survey (FIDS) y quedó bajo dependencia plena de la Oficina Colonial. En ese momento había cuatro estaciones, tres ocupadas y una desocupada. Para el momento en que el FIDS fue renombrado a British Antarctic Survey en 1962, 19 estaciones y tres refugios habían sido establecidas.

El explorador antártico sir Vivian Fuchs fue director del BAS de 1958 a 1973.

Bases

Bases en la Antártida

El BAS opera cinco bases en el Territorio Antártico Británico (British Antarctic Territory):

 Base Rothera (Rothera Research Station), en la isla Adelaida.
 Base Halley (Halley Research Station), en la barrera de hielo Brunt.
 Base Signy (Signy Research Station), en la isla Signy.
 Base Fossil Bluff (Fossil Bluff Logistics Facility) instalaciones logísticas en la isla Alejandro I.
 Aeródromo Sky Blu (Sky Blu Logistics Facility) instalaciones logísticas en la Tierra de Ellsworth.

De esas bases, solo Rothera y Halley son instalaciones permanentes durante todo el año. Las demás operan solo durante el verano antártico.

La Base Faraday fue mantenida hasta 1996, cuando fue cedida a Ucrania, que la renombró como Base Akademik Vernadsky.

Desde 1996 la histórica base en puerto Lockroy en la isla Goudier ha sido habilitada como Herencia Antártica del Reino Unido durante el verano antártico. Recibiendo cerca de 10 000 visitantes al año, es uno de los sitios más visitados en el continente. Los visitantes pueden realizar un tour por el museo, comprar souvenirs, enviar correo y ver la gran colonia de pingüinos gentoo.

Bases en las islas Georgias del Sur

El BAS también opera dos bases permanentes en las islas Georgias del Sur:

 King Edward Point (King Edward Point Research Station) en la isla San Pedro
 Base Isla Bird (Bird Island Research Station) en la isla Bird

Otros sitios

El cuartel general del BAS está en el Reino Unido, en la ciudad universitaria de Cambridge. Allí se le provee de oficinas, laboratorios y talleres para sostener las actividades científicas y logísticas en la Antártida.

El BAS también opera la Base Ny-Ålesund (Ny-Ålesund Arctic Research Station) en nombre del NERC. Es una base ártica localizada en Ny-Ålesund en la isla noruega de Spitsbergen.

Equipamientos

Barcos

El BAS opera dos barcos en soporte de sus programas de investigación antárticos. Ambos barcos tienen capacidades de investigación adicionales, el RRS James Clark Ross es primeramente un buque de investigación oceanográfica, mientras que el RRS Ernest Shackleton es primeramente un barco logístico usado para el reabastecimiento de las estaciones científicas.

Ambos barcos zarpan del Reino Unido en septiembre u octubre de cada año y retornan al Reino Unido en el siguiente mayo o junio. Ambos barcos son reacondicionados durante el invierno antártico, pero también son usados en otros lugares durante ese período. El James Clark Ross a veces es utilizado para investigaciones científicas para otras organizaciones en el Ártico, mientras que el Ernest Shackleton se alquila para investigaciones comerciales.

Los dos barcos civiles operados por el BAS son complementados por las capacidades del HMS Endurance (A171), patrullero polar de la Marina Real que opera en las mismas aguas. El Endurance tiene dos helicópteros Westland Lynx disponibles para que el personal del BAS puede alcanzar sitios remotos a los que los sus aviones no pueden acceder.

Aviones

El BAS opera cinco aviones en soporte de sus programas de investigación en la Antártida. Estos aviones son cuatro de Havilland Canada Twin Otter y un de Havilland Canada Dash 7. Durante el verano antártico los aviones están basados en la Base Rothera, que tiene una pista de 900 metros. Durante el invierno antártico los aviones retornan al Reino Unido.

El Dash 7 realiza vuelos regulares entre el aeropuerto de Puerto Stanley (Port Stanley) en las Islas Malvinas, o Punta Arenas en Chile, y Rothera. También opera hacia y desde la pista de hielo en el Aeródromo Sky Blu. Los más pequeños Twin Otters están equipados con esquíes para aterrizar en la nieve o el hielo en áreas remotas, y opera fuera de las bases en Rothera, Fossil Bluff, Halley y Sky Blu.

En enero de 2008 los científicos del British Antarctic Survey liderados por Hugh Corr y David Vaughan, informaron (en la revista Nature Geoscience) de que 2200 años atrás, un volcán hizo erupción bajo la capa de hielo de la Antártida (basados en investigaciones aeréas con imágenes de radar). La más grande erupción en los últimos 10 000 años, la ceniza volcánica fue encontada depositada en la superficie del hielo bajo las Montañas Hudson, cerca del Glaciar Pine Island.

Véase también

 Bases antárticas del Reino Unido

Referencias

Enlaces externos
 Página del BAS
 Discovering Antarctica - teaching and learning resources on Antarctica
 Programas científicos del BAS
 BAS research stations
 BAS Online Palaeontology Collection

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