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Managed Services Mergers & Acquistions: Tips From Pros
Written by Charlene O Hanlon 1
Get a group of managed services providers in a room together and the talk invariably turns to mergers and acquisitions. It's one of the ultimate goals for some small-business owners – that another company would find enough value in their business to actually want to acquire it.
Get a group of managed services providers in a room together and the talk invariably turns to mergers and acquisitions. It's one of the ultimate goals for some small-business owners – that another company would find enough value in their business to actually want to acquire it. As a result, it's no surprise M&A was a topic of two panel discussions at the 2011 N-able Partner Summit last week in Scottsdale, Ariz.: One from the buyer's point of view (acquirer) and the other from the seller's point of view (acquiree).
The conversation was surprisingly candid on both panels, ranging in topics from the best way to value your business to the role company founders should play once their company has been acquired. The panels included Carey Balzer of White Glove Technologies, Dan Holt of Computer Services Inc. (who also served on the acquiree panel), Todd Croteau of Konica-Minolta and Tim Brien of OKI Data Americas on the acquirer panel. (And no, it did not escape me that two of the panelists were from document management companies.)
Brian Ellison of All Covered sat with Holt on the acquiree panel – which, ironically, was smaller because two of the panelists were pulled away by their new bosses to take care of other tasks.
"I think for a successful acquisition to occur, you have to have the right culture from the very beginning," Croteau said. "The harder thing is merging of the processes. At the end of the day our deliverables are very similar, but the actual bits and bytes – the actual mechanics – of how each company goes about getting those deliverables to the customer is one of the biggest challenges."
But how do MSPs even start the acquisition process? For starters, make sure your company is buttoned-up financially – your paperwork is up to date, you can back up your facts and figures with documents, and you've forecasted your company's business out at least 18 months. "When you forecast out 18 to 24 months, you're showing proof that every month or every year you've hit your forecast," Holt said.
And for those MSP owners looking to get acquired, Holt noted it's not a detriment to put the word out. And Holt should know – his company, Heit, was in the middle of its own acquisition spree when it was itself acquired by Computer Services Inc.
"I don't think it's a bad idea to reach out to someone — I don't think it impacts my valuation if I call them know I'm interested in being acquired." And working with an investment banker will help the MSP "prepare and package" itself for an acquisition, he said, as well as determine how much the business is actually worth.
Also part of the value equation is the profitability of an MSP's customers. "Contracts are important – and certainly a five-year contract looks better on paper than a one-year contract – but what's also important is how profitable your customers are. A good company knows that information," Balzer said.
The process of being acquired can take as few as six to eight weeks or as long as a year, depending on the situation and how prepared the MSP is for the process, the panelists noted.
And once the acquisition has occurred, what of the former owner? Is there a place within the company and, more importantly, can the owner go back to answering to a higher power once he or she has built a successful company?
"I would be would hard-pressed to do a deal if the owner doesn't want to come over," Croteau said.
Balzer noted White Glove Technologies is upfront with the owner about his or her role in the larger company, and the response to that role can be helpful when determining the structure of the deal. "We prefer to buy the talent but sometimes the talent doesn't want to totally engage," he said. "And when you get the big check, sometimes it gets hard to get up in the morning."
Investment bankers have told Holt that about 75 percent of owners who sell a company don't stick around beyond three years. (CSI's track record for retaining owners is quite strong, Holt adds.) Brien, meanwhile, noted his company looks for owners to stay for about a year. "After they are paid the check, it's difficult for those who still have the entrepreneurial spirit to deal with the demands of new owners and adjust to the corporate culture," he said.
The very fact that N-able hosted not one but two panels of the subject of mergers and acquisitions tells a lot about the managed services environment, but it also tells a lot about the uncertainty and trepidation that can accompany such as large business dealing. Many times business owners of companies of all flavors enter into life-changing deals with little more than a leap of faith. Being able to benefit from the experience of others can be a priceless gift.
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Russell makes a Note, then makes six more. Yasmine's outruns a haboob even though her Nougat joke making license has expired. Andy turns an odd shade of Fuchsia. We also attempt to pronounce German town names, because at this point, why the heck not?
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What are the warning signs that your Lexus ES300h Hybrid Battery or Lexus ES300h Hybrid Battery is failing? 'Poor gas mileage,' warning light illuminated, poor acceleration, these are all direct warning signs that its time for hybrid battery replacement. The Lexus ES300h Hybrid Battery is built up of 34 modules that contains several items such as the battery cells, bus bars, and a charging controller. We recommend replacing the entire battery pack when attempting to correct any of the failure symptoms of the battery. We also offer options to repair, depending on your budget.
Our Lexus ES300h Hybrid Battery Repair and Rebuilds have a 5 Year Pro-Rated warranty. This includes parts and labor so that you can drive worry free for the next 5 years. Our Lexus ES300h Hybrid Replacement price is much less than the Lexus Dealer while providing a better warranty and better service. The battery that Lexus ES300h Hybrids have is a 245V battery that consists of 34 nickel-metal hydride modules. Why not save thousands and have a better warranty?
Give us a call to receive a competitive price on ES300h hybrid battery repair and reconditioning in Escondido and San Diego county. Check our reviews on Yelp and Google and see how many satisfied customers we have helped over the years. Not only do we offer ES300h hybrid batter repair, we offer all hybrid repairs. There may be other underlying issues with your vehicle that may need to be diagnosed. All of our hybrid battery repairs start with a thorough diagnosis of the problem. We are a fully functional automotive repair facility, and one stop shop for your repair or maintenance needs. If your looking for a quality ES300h hybrid battery pack then contact us and we will give you the best option for your hard earned money!


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Women's Health & Leadership
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Department of Neurobiology & Anatomy
Medical & Graduate Teaching
Medical Microanatomy
Summer Remediation Course for MD Students Medical Microanatomy
Course Director: Dr. Haviva Goldman
Medical Microanatomy Course Description
We have developed a web-based summer remediation course for medical students who have received a failing grade during their initial course in Medical Microanatomy.
Students take the course online while remaining at their own institution.
The course consists of materials from the Microanatomy course at Drexel University College of Medicine (see syllabus below) and is presented in a fashion that allows the students to progress at their own rate within established limits.
Some modular options will be available for remediation involving multidisciplinary integrated courses. Please contact us for pricing and availability.
To review the structure of cells, tissues and organs at the microscopic level, with an emphasis on clinical relevance.
To demonstrate the principle that structure reflects function, and to introduce the idea that derangements in function (pathologies) often result from or cause changes in structure.
To serve as a bridge that conceptually connects the molecular events learned in Biochemistry and Physiology to the macroscopic structures studied in Gross Anatomy.
To provide the background necessary for success in the study of pathology.
To certify by means of written and practical exams that, upon successful completion of this course, the student has demonstrated an acceptable level of competency in the subject matter.
The course is open only to students registered in an accredited U.S. medical or dental school, or equivalent.
Students must provide written approval from their administrator (usually the dean of students) in order to take the course.
Students must also supply written assurance from their administrator that a proctor will be supplied to administer the midterm and final exams.
Prerequisite: Completion of a first-year medical school curriculum that included Microanatomy (Cell Biology and Histology).
Course name: Summer Remediation Course in Medical Microanatomy
Offered by the Department of Neurobiology & Anatomy at Drexel University College of Medicine.
Tuition fee: $2,200 (please contact us for pricing and availability for remediation involving integrated multidisciplinary modules).
The course material is available from June 13 until July 15 with a midterm exam on June 27 and a final exam on Friday, July 15, 2022.
The course includes:
Approximately 57 lecture hours presented as streaming video.
Lecture notes that can be downloaded or viewed simultaneously with the streaming video.
A virtual microscopy lab experience based on annotated digitized glass slides.
A lab manual that can be downloaded or viewed simultaneously with the slides.
Section exams that will not count toward the final grade but will provide feedback to the students as they progress through the course, and also serve as practice for the midterm and final exams.
A medical school faculty member available for questions and answers via telephone or email.
The course is divided into seven sections (see detailed syllabus below):
Introduction to Microscopy & Cell Biology
Epithelium, Connective Tissue & Skin
Muscle & Nerve, Cartilage & Bone
Respiratory and Endocrine Systems
Blood, Cardiovascular System & Lymphoid Organs
Urinary System, and Male & Female Reproductive Systems
Midterm and Final Exams:
There will be a midterm exam and a final exam. These are the ONLY exams that will count toward the final course grade.
The midterm will be on June 27, 2022, and will cover the material from Sections 1-3 and contribute to 45% of the course grade. This exam has 50 questions and lasts for 70 minutes (1.4 minutes per question)
The final exam will be on July 15, 2022, and will cover only the material from Sections 4-7 and contribute to 55% of the course grade. This exam has 75 questions and lasts 105 minutes (1.4 minutes per question)
All questions are in a multiple choice format, and approximately half will include images.
Both the midterm and final exams will be taken online through Blackboard Learning System at the student's home school. If online arrangements cannot be made, paper exams will be mailed to an administrator designated by the student who can proctor the exam and return it to us by mail for grading, along with the test booklets.
Section Exams:
At the end of each section there will be a section exam. These will help students assess their understanding of the material from that one section but WILL NOT count toward the final grade.
Each section exam is taken through Blackboard LMS and requires a computer with the Respondus Lockdown browser installed.
Each section exam is composed of 50 questions and lasts for 70 minutes.
Passing a section exam will allow the student to start the next section. If a student fails to obtain a grade of 70% or more in a section exam, they must retake the exam the following day. A second failure on a section exam will not affect the course grade or prevent the student from moving on to the next section, but it will be reported to the student's home institution along with the final course grade.
A feedback questionnaire will be requested from each enrolled student to evaluate the course resources (lecture notes, streaming video lectures, lecturers, virtual microscopy resource, exams, help provided by the course directors, overall quality of the course, areas for improvement, etc.)
Success on the final exam will indicate that the student has reached a level of proficiency in Medical Microanatomy, similar to that of other medical students in this institution.
Since the material taught and the tests used in this course are equivalent to those used in our regular Microanatomy course, we expect that students passing this summer remediation course in Medical Microanatomy will be well-prepared to continue their medical education.
The course is packaged and administered using the Blackboard LMS.
The course is offered through the Department of Neurobiology & Anatomy, and all administrative tasks related to the course will be handled by the course director.
Final grades will be sent to the student's dean for confirmation of course completion as well as to the student.
Medical Microanatomy Course Syllabus
All lectures are approximately 50-60 minutes long unless otherwise indicated. Labs are to be completed online by virtual microscopy, using annotated digitized glass slides and the online lab manual.
Sections 1, 2 and 3 must be completed between June 13 and June 26, 2022.
Section 1 (Introduction to Microscopy & Cell Biology):
Introduction to Light Microscopy (1.5 hrs)
Cell Junctions
Lysosomes & Peroxisomes
Nucleus, Endoplasmic Reticulum & Golgi
The Differentiated Cell
Lab 1: Microscopy, Stains & Organelles
Section Exam: Section 1
Section 2 (Epithelium, Connective Tissue & Skin):
Epithelia & Glands (1.5 hrs)
Lab 2: Epithelia & Glands
Connective Tissue (2 hrs)
Lab 3: Connective Tissue
Integument (1.5 hrs)
Lab 4: Integument
Slide Review Lecture: Section 2 (2 hrs)
Section 3 (Muscle & Nerve, Cartilage & Bone):
Cardiac & Smooth Muscle
Lab 5: Muscle
Peripheral Nerve & Ganglia
Motor & Sensory Nerve Endings
Lab 6: Nerve
Slide Review Lecture (2 hrs)
Lab 7: Cartilage & Bone
Bone Formation & Joints (1.5 hrs)
Lab 8: Bone Formation & Joints
Slide Review Lecture: (1 hrs)
Midterm Exam: Sections 1, 2, 3
Sections 4, 5, 6 and 7 must be completed between June 27 and July 14, 2022
Section 4 (Endocrine Organs and Respiratory System):
Hypophysis
Thyroid & Parathyroid
Lab 9: Endocrine Organs
Lab 10: Respiratory System
Section 5 (Blood, Cardiovascular System, & Lymphoid Organs):
Blood (2 hrs)
Hematopoiesis
Lab 11: Blood & Hematopoiesis
Cardiovascular System (1.5 hrs)
Lab 12: Cardiovascular System
Lymph Nodes & Spleen
Lab 13: Lymphoid Organs
Slide Review Lecture: Section 5 (2.5 hrs)
Section 6 (Digestive System):
Upper GI Tract (2 hrs)
Lab 14: Upper GI
Lower GI Tract (1.5 hrs)
Lab 15: Lower GI
Liver, Gall Bladder & Pancreas (1.5 hrs)
Lab 16: Liver, Gall Bladder & Pancreas
Section 7 (Urinary System, and Male & Female Reproductive Systems):
Urinary System (1.5 hrs)
Lab 17: Urinary System
Female Reproductive Tract
Lab 18: Female Reproductive System
Mammary Gland
Lab 19: Placenta & Mammary Gland
Testis
Male Reproductive Tract
Lab 20: Male Reproductive System
Slide Review: Section 7 (3 hrs)
Final Exam: Sections 4, 5, 6 & 7
Final exam is on July 15, 2022, and covers Sections 4, 5, 6 and 7.
Haviva Goldman, PhD
Summer Remediation Course in Medical Microanatomy
Department of Neurobiology and Anatomy
Drexel University College of Medicine
2900 W. Queen Lane
hgoldman@drexelmed.edu
Quick Links & Resources
Postdocs & Research Associates
Follow College of Medicine:
Drexel University, College of Medicine, 2900 W. Queen Lane, Philadelphia, PA 19129, 215.991.8100, © All Rights Reserved

redpajama_set_name: RedPajamaCommonCrawl


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Q: New version of PHP file upload times out. Old one fine.? Maybe I have a mental block of some kind but this problem is bugging me...
I have an app, for a photography club, whereby images files are uploaded and moved to a folder, and the titles store din a MySQL database. his all works fine.
Recently the requirment changed, so I am amending the app. To do this while leaving the existing app running I copied the PHP files and renamed then with a suffix of X. I also duplicated a couple of the MySQL tables with a suffix X.
Obviously, I then modified the 'X' code.
The problem is that when I reach the stage of inputting a file name and submitting it falls over with a timeout. The log says:
"[Sun Dec 11 00:08:57 2016] [warn] [client 82.20.120.43] Timeout waiting for output from CGI script /var/www/cgi-bin/cgi_wrapper/cgi_wrapper, referer: http://www.rdps.co.uk/comp/en-entriesX.php"
"[Sun Dec 11 00:08:57 2016] [error] [client 82.20.120.43] Script timed out before returning headers: cgi_wrapper, referer: http://www.rdps.co.uk/comp/en-entriesX.php"
'EntriesX.php' is the prog that puts up the form for the users to fill in with file names. This feeds into 'EntriesUpdX.php'.
The original version of the app still runs fine. I've gone over the code a lot, but I can't see what's wrong. Any ideas?

A: Change [max_execution_time][1] in php.ini

Or in php code: set_time_limit()

redpajama_set_name: RedPajamaStackExchange


What gives? This beautiful, collectible glass bowl filled to the brim with all sorts of Ghirardelli treats like chocolates, cookies and cocoa. "How sweet" is what you're likely to receive in return for presenting this classic holiday gift.


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Nawal Al Ramahi
Emirati jobseekers more interested in opportunities than salary and working hours, says labour minister
Those seeking work have 'matured' and don't meet unfavourable stereotypes of the past
Emiratis speak to recruiters at the Tawdheef jobs fair. Silvia Razgova / The National
The attitude of many Emirati jobseekers has "matured" and does not match unfavourable stereotypes of the past, the UAE's labour minister has said.
Many young people seeking work are more interested in good opportunities and having the right skills than simply good pay and short working hours, Nasser Thani Al Hameli, Minister of Human Resources and Emiratisation, said on Monday.
He was speaking at a press conference about a recent three-day career fair organised by the ministry.
At the end of the event, which more than 1,600 people attended, 860 had received job offers from 80 public and private sector companies. He said a further 71 have already signed contracts already.
"Emiratis are becoming more mature in the way they approach job offers and conduct interviews," he said.
"The conversation between interviewees and employers has become more mature, discussing ways to sharpen their skills and the nature of work.
"Employers who interviewed Emiratis were surprised about their attitude toward embracing different kinds of jobs and skills. Employers said that Emirati job applicants were not asking about salaries or working hours. They were more interested in methods to learn about job requirements and get more experience in the field and the mechanism of work."
Earlier this month, the minister, who was newly-appointed in October, unveiled a new drive to push more UAE nationals into the private sector.
He said the government will ask companies to prioritise Emiratis over expats for jobs in about 2,000 companies.
Companies will not be compelled to take UAE nationals on - but give them an interview or opportunity they may not have otherwise been given.
The fair sought to encourage more jobseekers to go into aviation, transportation, telecommunication, technology, and real estate.
"We have attracted young Emirati talents through various channels before the three-day career fair, such as advertisements in newspapers, social media, advertisements in influential personnel accounts. Also, we interviewed employers," he said.
Part of the push means working with Emiratis who are looking for jobs to make sure they are ready for the workplace.
"More than 633 received training and guidelines about interviews. We made sure that jobseekers were well prepared for interviews following training," said Mr Al Hameli.
Saif Al Suwaidi, general manager of the Civil Aviation Authority, who was part of the job fair, said that the push to encourage more Emiratis away from government jobs has come a long way.
"I am very proud about the recent results. There are around 200,000 people from various nationalities working in the aviation field in the UAE. In this vital sector, we want to recruit more Emiratis," he said.
There are several upcoming recruitment events, the next one being in Fujairah on February 28.
Updated: February 20, 2018 07:31 PM
Jimmy Neesham's high school coach died watching him in World Cup final
IMF urges Tunisia to reduce inflation further to boost growth
Egypt to restore Tutankhamun's golden-plated coffin


Hey Love: Finds Under $40! Get The Look!
Finds Under $40! Get The Look!
Hey dolls! Welcome to this week's Finds Under $40! Get The Look: Emma Roberts Edition! I saw this look and immediately set out to replicate it! I love the simplicity and overall put together feel of it. I can see myself walking around wearing this and it's brilliant! It can go from vintage shopping to happy hour at your favorite outdoor bar! Plus, it lends itself to wearing it as is, with bermudas, boyfriend jeans, or skinnies! The possibilities are endless!
Loving this look guys! I'm obsessed with the top and the shoes! I cannot believe they are Steve Madden for less than $40!
I love this!! I could see myself in this outfit as well. Those sunnies are perfection.
I can completely see using all the clothes I have right now to make this outfit! Great and adorable!
Love this look girl! I love that you find such reasonably priced things too.
Have a great weekend, doll!
Great finds!! The shoes are amazing!!
the shoes is really beautiful.
oh i love this look, too!! so classic!
Emma Roberts knows her to rock a high pair of heels and itsy shorts, she looks amazing. Great finds to steal her style!
Very cute picks! Love the bag!
Great finds, great style, great price. Can't go wrong!
Oh I love love this feature of your blog!
I love white crisp shirts in the summer!
Oh man! You nailed it! Great job!
I love when simple outfits look so chic! Totally want to recreate this one too!
LOVE those shoes too!! this whole outfit is amazing!
great finds! this outfit is so great!
Love her simple and stylish look, especially those shoes!
Totally in love with those shoes!
Great find and can't believe that they are all under $40!
Such a versatile outfit! Love Steve Madden shoes!
I so need those $13 sunnies!
I am such a fan of Emma Robert's style. She's grown up so much & always looks simple but fashionable.
She's adorable and has great style! Her shoes are the popular platforms and I've been wanting a pair!!
I love this look! I cannot believe all these great items are under $40, what a steal. Great post luvvy.
Emma Roberts has a great style. Like this look.
She looks so cute!! thanks for the tips!!
I've just discovered your lovely blog!!
I'm loving heels and shorts lately for a dressed up daytime look. Those heels are great!!
These are great essential pieces for summer. At such a great price too.
Emma is such doll...she belongs to the 40s, such a sweet and glamourous style. Love how easy but still feminine this outfit is.
absolutely adore this look. she is too perfect!!
I love this post, such a great look and well recreated. The shoes are FAB are they Steve Madden?
love Emma Roberts! this is such a great board, excellent picks :) loving the posts!
I want those bags!!! esp the pink one!!!!
really amazing choices, thank you for sharing I love useful blogs!
Thanks for visiting my blog, I would love to see you again, check my new post!
Great outfit idea, totally love how chic and casual it is for summer! Emma Roberts has great, effortless style.
Amazing finds and ..under 40!


Two of Finland's heavyweight hard rock acts combine for what has been an extremely well received tour around the UK. With Reckless Love also going down a storm at Hard Rock Hell in Wales, the Finns are riding high in the popularity stakes at the moment.
Clearly excited (cough) to be here tonight, Olli Herman is a ball of energy from the get go. As the band kick off the opening intro to 'Night on Fire', Olli bounds on with a smile as wide as the stage he will inhabit for the next 90 minutes.


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For this reason, those negatively affected should seek experienced legal counsel.
Recently, the Ethicon Medical Safety Team announced an urgent field safety notice to stop the use of Ethicon Physiomesh® due to the high rates of failure. This recall comes as a result of an analysis conducted by the Ethicon Medical Safety Team, which proved many patients had been negatively affected by the Ethicon Physiomesh® implants. Patients who have received such implants should seek medical attention right away. Those who have been harmed by such products should seek legal help immediately.
If you received a hernia mesh implant and suffered negative side effects, we urge you to contact our legal team. We can examine the details of your case and determine who should be held liable for your injuries, medical expenses, and other damages suffered as a result of the defective product implant. From there, we can build a case in order to pursue maximum financial compensation.
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Welcome to Bourton, Dorset
Our Village ↓
Dorset Alert – Neighbourhood Information
Dorset Police – Information for Bourton
A Brief History of Bourton
Footpaths & Bridleways
Short Village Walks
Useful Emergency Contacts
Bourton Village Diary
Latest News – Posts Page
Parish Council ↓
Agenda & Minutes – 2020
Parish Council – Introduction
Agendas & Minutes 2012 to 2019
Agendas & Minutes – 2019
Planning – NDDC weekly application and grant list for planning
Bourton Village Cemetery
Village Hall – Welcome ↓
Trustees & Management
New Village Hall Project
St George's Church
Youth – Schools
Accommodation & Attractions
This two hundred year old church was built to commemorate The Golden Jubilee of King George III in 1810. It is one of four churches in the Parish of Upper Stour. Almost unique, the living is invested in the care of 12 local trustees who are responsible for the welfare of the Church and the appointment of the Incumbent.
The mainstay of worship is the 10 am Parish Communion, which is held in one of the Churches in rotation. The service in Bourton is usually on the 1st Sunday of the month but the pattern can change due to festivals so please check the Parish magazine or see the link below.
A core of worshippers moves from church to church, while others choose to attend the services in their own village. A variety of other styles of Worship such as Taize, Healing Services and Songs of Praise happen at other times. We welcome people of all ages.
For further information on services, local places of worship, events, history and general information please refer to the latest Parish of Upper Stour monthly magazine or the Parish of Upper Stour website www.upperstour.net
Worshipping with Children
Children's Ambassadors
Children are welcome at all of our services. At each church there is a volunteer to help families with children to share in the worship. Depending on demand child centred activities are available.
Formerly a Sunday Club (School) ran alongside the main service, this may be restarted so please let us know if this would appeal to your family.
Children's workshops are held in school holidays on a weekday when the Christian story behind the festivals is expanded and the children's creativity is encouraged to enhance the worship at our all age celebrations. E.g. Mothering Sunday, Easter.
There are close links with the "Outstanding" Village School, which is adjacent to the Church. The school worships in Church at the beginning and end of each term and as a Foundation School has a strong Christian ethos. The Rector and other approved members of the Church lead the School Assembly on a regular basis. There are areas for prayer and reflection in each classroom.
St. George's 100 Club
The St George's 100 Club is a Small Societies Lottery as defined by the Gambling Commission and registered with North Dorset District Council. It's objective is to raise funds for the St George's Church in Bourton. Originally set up by Mrs Sibley back in 1997, it has helped to raise over £10,000 towards maintenance of the structure and fabric of the Church building. In 2015, £1000 was transferred towards the Diocese annual contribution as the Church was in severe financial difficulties.
The subscription year runs from 1 April to 31 March and costs £1 per month, payable in a lump sum of £12. It is possible to join at any time with a reduced fee. Members will be reminded that their annual subscription is due for renewal. Numbers will be allocated as subscriptions are received and all members will be notified of their numbers before their first draw. Of the total monies collected, 50% will be given to the Church and 50% is used for cash prizes. There are two prizes each month and 60% is used as 1st Prize and the remaining 40% as 2nd Prize. For example, if 100 members join, then the total revenue collected would be £1200. £600 of this would be given to the Church and the other £600 would be given as prizes, giving a monthly prize fund of £50 so the 1st prize would be £30 and the 2nd Prize would be £20.
The draw will usually take place on the last Saturday of each month, in the Forge Garage shop at Bourton. Notices giving the names of the prize winners will be placed on the noticeboard by the Post Office at Forge Garage and in the entrance to St George's church within 5 days of the draw taking place. A notice will also be entered into the "About Upper Stour" Magazine as well as shown on this webpage.
The current volunteer organiser is Mrs Ruth Burrows who took over in March 2015, after the quite sudden and untimely death of Mrs Pat Lawes. Each year the accounts are audited by Mr Tony Moorby, Treasurer of the St George's LCC. Anyone wishing to view them can of course do so. If you would like to subscribe, Ruth can be contacted on 01747 840371.
Music and Church
A small choir contributes to our weekly worship and it is always keen to welcome enthusiasts . The regular choir is swollen for the Festivals to make an impressive contribution.
Although our worship is usually traditional, we are keen to try other styles and would value any offers from other musicians in the hope that a music group could be formed to be used on occasions.
St George's Church Flower Team
The team was officially established in 2012 following the Queen's Diamond Jublilee Celebrations. A group of enthusiastic ladies (men are not excluded but as yet none have come forward) got together to commemorate the Diamond Jubilee with a spectacular flower festival at St Georges Church. This was very much a team approach of mixed abilities, from novice to expert; everyone prepared to support and share their experiences working with a 'buddy' thereby promoting confidence and a learning experience plus hard work!
We had developed into a 'team' and the enthusiasm was such that it was decided to continue in this manner. We work on a paired rota system for flower arrangement and maintenance. We are financially independent through fund-raising initiatives, such as coffee mornings, Church decoration for weddings, funerals including a specifically designated pedestal to commemorate, anniversaries of bereavement, special occasions; to commemorate All Souls Tide a rose pedestal was introduced which includes an 'in memory book'.
The team is very much a community approach and we welcome anyone who would like to support us in any way, clearing –up at festivals, making that welcome cup of coffee or offering positive feedback. Experience is not essential, we are not sexist a DIY man is often essential for props, advertising at festivals offer enthusiasm or just want to get the feel of how we operate please contact:
Barbara Borwell – 01747 840141 or borwellbarbara@yahoo.co.uk.
At a dinner to Commemorate the Golden jubilee of King George III, on 25th October 1809, it was decided to build a Chapel for the population of Bourton. This Village was industrial, involved in the growing and processing of Flax, with a population of around 1000 at that time. A Committee of twelve men was chosen and money was raised by public subscription. The land was bought for the village by John Jeans the Publican of the Red Lion for a sum of £5, held in trust for the villagers .
On April 23rd 1810 – St George's Day – the foundation stone was laid . Two years later the Chapel was built and was open for divine service, finally being consecrated in August 1813.
Initially the Church was run as a Chapel of Ease, attached to the Church in the nearby town of Gillingham. It later became a parish in its own right.
In the 1870s, George Glover became the incumbent and found a building in a sorry state of repair and a village without School or Vicarage. He appealed to the Church Commissioners and raised funds to improve the Church, to build a school and a Vicarage. His 'improvements' followed the fashion of the day, turning the church into a more acceptable 'Gothic –like' structure with arched windows, a high roof and an octagonal chancel. The tower at that time only reached roof level. It was during the incumbency of the Rev J.C. Sparrow that the church was finally completed, in 1905, with the addition of a handsome pinnacled tower, designed by Ponting and a set of six bells.
Contact & Update Information
Priest in charge Graham Perryman – 01747 840221
Church Wardens:
Harry Allen 01747 840948
Margaret Martin 01747 840433
Location of Church: Church Track, Bourton, Gillingham Dorset, SP8 5BW
You'll need Skype CreditFree via Skype
©2020 Bourton Village


Howdy folks, this post is about 8x10 Sheds #8 Backyard Discovery. It is a image/jpeg and the resolution of this picture is 840 x 840. It's file size is only 163 KB. Wether You want to download It to Your laptop, you could Click here. You could also see more images by clicking the following picture or see more at this post: 8x10 Sheds.
Can be your 8x10 Sheds? I am aware first. Toiletries and make-up at the back of the sink. The medication case was dirty with creams abnormal bottles, and gels. The closet under the sink was stuffed in spots with moves of toilet-paper and everything was not ideal elsewhere.
If even that appears like more work than you wish to handle, start by considering tiny. How could you increase the area you already have? One of the suggestions is to arrange the area. Everyone has a cabinet there, but items only throw in there until the chaos is not arranged. Alternatively, are you currently considering benefiting from storage boxes that are tiny and labeling them?
Among the best 8x10 Sheds #8 Backyard Discovery I've identified lately requires, not remodeling, but simply rethinking your bathroom style. For those who have a space, you're able to enter concealed shelves that exhibit and can shop sets from your makeup for some pretty knickknacks. And if you need to produce your toiletries invisible, you can constantly place cupboards and hidden cabinets.


Swiss Meet-Up of the Hackteria network in Lausanne. Join us to discuss biohacking and DIY biology, help us setting up a new community bio-lab, have fun with self-made PCR thermocyclers and open-sourced Taq polymerases.
We cultured some Rosetta e.coli strain in the teaching labs of EPFL. Seems our first try went wrong due to the fact that we added the ampicillin antibiotics to early after the transfection, so the cells werent ready yet to cope with it. Then we did another try and got the cultures growing nicely. Added the IPTG after we reached a good density of the culture and let them produce the Taq… Havent tested the product yet.
Making dilutions of pOpenTaq to share with friends.
Crisis at Hack-a-Taq, nothing grew….
Waiting for the bacteria to grow. Biology needs patience… and soft pillows!
Hack-a-Taq welcome party at EPFL….
Visit to EPFL for some Taq hacking. Nice sponsors they have at the RLC.
Checking some regulations about the use of GMO in closed systems.
Hmmmmm, loading these gels is not so easy….
Testing the products of the MyPersonalOpenPCR. It's looking good….
Who needs a transilluminator anyway.
this will be amazing! super cool prototyping work, very advanced!
I am curious to see if all protocolls work out.


text:
Q: I need to lock my headers so that no one can edit those columns but I want to enable autofilter on that using xlsxwriter I need to apply protection on header rows of my spreadsheet but at the same time I want to enable autofilter.
I am able to apply protection based on the below code, but it disables autofilter too.
df.to_excel(writer_template, sheet_name='inputs')

worksheet = writer_template.sheets['inputs']

unlocked = workbook.add_format({'locked': False})
locked   = workbook.add_format({'locked': True})

worksheet.set_column('A:S', None, unlocked)

# Turn worksheet protection on.
worksheet.protect()
worksheet.set_row(0, None, locked)
worksheet.set_row(1, None, locked)

worksheet.autofilter('B2:I500')

My headers look like the below:

A: In Excel you can set the worksheet protection but allow the user to change individual elements such as autofilters. In XlsxWriter you can specify which worksheet elements you wish to protect by using the options argument in protect() (see the docs).
For example:
import pandas as pd

df = pd.DataFrame({'Data1': [10, 20, 30, 20, 15, 30, 45],
                   'Data2': [11, 21, 31, 21, 15, 31, 45]})

writer = pd.ExcelWriter('pandas_filter.xlsx', engine='xlsxwriter', )

df.to_excel(writer, sheet_name='Sheet1', index=False)

workbook  = writer.book
worksheet = writer.sheets['Sheet1']

worksheet.protect(options={'autofilter': True})
worksheet.autofilter('A1:B8')

writer.save()

Output:


The African National Congress rejects with the contempt they deserve false, malicious and mischievous reports being peddled about the proceedings of the Special National Executive Committee (NEC) meeting of the ANC currently underway at the St. Georges Hotel, Irene, Gauteng.
Accordingly and because of the serious nature of the rumours, the ANC has decided to depart from normal procedure and issue this statement which unequivocally dismisses claims made by nameless and faceless sources that there are discussions underway to remove from his position the Secretary General of the ANC, Comrade Gwede Mantashe. These rumors are peddled to sow confusion and division within the movement and are indicative of the media's laziness and total disregard for proper journalistic ethics in favor of populism and sensationalism.
The Special National Executive Committee meeting has resumed today, following an adjournment to allow the National Working Committee to refine the report to the NEC on the ANC Eastern Cape 8th Provincial Conference. The NEC will today discuss such report as well as the draft Organizational Report to be tabled at the 54th National Conference from the 16th to the 20th December 2017.
The ANC calls upon its members, supporters and South Africans at large to resist and reject the frenzy of fake news peddled by so-called insiders and analysts and rather await formal communication from the NEC on the outcomes of this Special NEC.


SPOKES chips are made by a Canadian Mom who wanted a Better-For-You snack for her family. This air puffed potato snacks are made with Non GMO Project Verified simple ingredients. It is gluten-free and free of 11 major allergens including dairy, gluten, wheat, soy and egg. SPOKES do not contain trans fat or cholesterol, artificial preservatives or colours. They are made in a peanut free facility in Calgary, Alberta.
It is priced at $3.99 for a regular size bag and available across Canada in most natural, conventional and independent grocery and drugstore retailers including: Whole Foods, Kardish, Goodness Me!, Planet Organic, Blush Lane, Safeway, Sobeys (Western Canada), Thrifty Foods, Metro (Quebec), London Drugs and Bed Bath and Beyond. See which store is close to you on their site.
We tried a few of the flavours from their collection of nine different flavours - Sea Salt, Mango Habanero, Sea Salt and Vinegar, Barbecue, Dill Pickle, Salt and Pepper, Fiesta Salsa, Sea Salted Caramel, and Simply Bare.
SPOKES are a potato snack everyone can love. Each of the flavours have a different taste, so you must try them all to pick your favourite. In our home, everyone had their favourite.
One person in Canada can win free product coupons valued at $60. Enter the giveaway through the rafflecopter below before December 8. Please leave comments and follow my social media networks to be eligible to win.
Newfoundland Canada. Yes I have tried these before. They are good. Healthy snacks are great!
I do prefer healthy snacks but have not tried these yet. I live in Nova Scotia.
I live in Ontario. I do try to eat healthy snacks (sometimes, haha). I haven't rried Spokes snacks yet but they look yummy.
I live in NL. I enjoy healthy snacks and I have not tried Spokes yet.
I am from Ontario and have not tried these before, but they sound wonderful.
i live in Ontario - i love healthy snacks - i have tried Cheecha Puffs but have not had the pleasure yet, of trying Spokes ! I haven't seen them yet in stores.
I am in BC and while I try to snack healthier, crunchy chips are still a favourite. Maybe these will help!
I live in Ontario. We haven't tried these chips yet but do love healthy snacks. We air pop our popcorn and bake kale chips.
I'm from Ontario. I love eating healthy snacks. I have tried these before and love them.
I'm in Alberta and it depends very much on what the snack is as to whether I like it or not. I've not tried these before but they sound similar to Pombaeren, which was a snack in Germany when we lived there.
I'm in BC and I've never had the chance to try this product! I do love a healthy snack!
I live in NL. I do enjoy healthy snacks,I haven`t tried these,but they sound delicious!
I am from Alberta and have not tried these before, but they sound delicious!
I live in Ontario and I haven't tried these snacks yet.
I'm from Ontario and I love eating healthy snacks, but I haven't tried Spokes yet. Thanks very much for the review, I'll be looking for them.
I am in Canada. I do enjoy healthy snacks. I haven't tried Spokes before.
I like in Saskatchewan. I enjoy snacking! I have not tried this brand yet!
We live in Ontario. I try to make healthy snacks a big part of our school lunch routine. I have not tried these snacks before.
I'm in Alberta. I enjoy healthy snacks if they taste as delicious as unhealthy snacks. I've had Chee Cha Puffs in different before by the same company but I haven't tried the Spokes.
I live in southern Ontario. I do enjoy healthy snacks and serving them to my family. I have not tried these yet, but I would love to!
Gatineau QC . Yes I have tried these before. They are good. Healthy snacks are great!
I live in Newfoundland.We enjoy healthy snacks nd no we have not tried these chips before.
ON here! We love trying new products, these looks yummy!
I live in Ontario! I love healthy snacks and I'd tried these before!
I live in Ontario. I try to eat healthy snacks but get tired of them. These look liken a good snacking product. I need to try these, its the first time I have seen them.
Ontario, yes we enjoy healthy snacks but have not tried these yet.
I'm in Ontario and I've never heard of these before.
I live in Ontario. I have not tried Spokes before but I am trying to snack healthier.
I live in Nova Scotia. I have heard of these but have never tried them. I prefer to enjoy healthier snacks like these.
I live in Manitoba and do like healthy snacks. I have tried these chips.
I live in Nova Scotia. I haven't tried these, but I'm always on the lookout for healthier snacks, so I'm looking forward to trying Spokes.
I live in Ontario and have never seen these before.


text:
Latvia - Sarlote & Sea Stones - Viva La Dance (impression of first rehearsal)
Powered by junioreurovision.tv Sarlote Lenmane, who will represent Latvia at the 2010 Junior Eurovision Song Contest, is 12 years old and she comes from Riga. She studies singing from the age of 9 at the vocal studio Rigas Akmentini, taught by Liva Bondare. Sarlote is the winner of the music festival Majowa Nutka in Poland and Euro Pop contest Berliner Perle in Germany. Laura Luse, Emils Kalenda, Liva Zvirgzdina, Elvis Liede will help her with the backing vocals in Minsk. They are from the pop group Juras Akmentini (Sea Stones) from the city of Ventspils. This year the vocal studio celebrates their 15th birthday. There are more than 50 participants at the age from 3 to 20. Who helped with the song? Arturs Palkkevics, the co-composer of the song, graduated from the Daugavpils music college in 1994, studied the speciality of the choir conductor and piano. The active musical career in the field of the arrangement and production started in 2001. Arturs works together with such musicians as Raimonds Pauls, Guntars Racs, Arnis Mednis and many famous rock groups. The lyricist of the song is Guntars Racs, who's writter over 500 songs - 200 written together with the multi-million selling composer Raimonds Pauls. He's also co-wrote songs with Molly Ann Leikin (who's written songs for Cher, Tina Turner, Anne Murray, Placido Domingo and Billy Preston) as well as Ainars Virga, Tomass Kleins, Janis Lusens etc). And he has released over 30 award winning songs and albums. He's also produced music for artists like the former Eurovision Song Contest participants Brainstorm and Fomins & Kleins.
tags Latvia JESC2010 REH


text:
.:TesfaNews:.
Daily News and Views Related to Eritrea
Horn News
ERI-TV (Live)
Al Jazeera English (Live)
Eritrea on Track Achieving Six out of Eight Millennium Development Goals
Posted on July 11, 2012 by TesfaNews
A UN representative has said relying on foreign aid to achieve the Millennium Development Goals did a disservice to Africa, and has called on African governments to find alternative funding sources and clean up their act
By Madote.com,
Eritrea is on pace to achieve six of the eight UN Millennium Development Goals (MDGs) by the target date of 2015, according to the London-based think tank, Africa Research Institute[1] and the United Nations Development Programme.[2]
The six MDGs Eritrea is on track in achieving are from MDG 2-to-7 that are Universal Primary Education, Gender Equality and Empowering Women, Reducing Child Mortality, Improvement of Maternal Health, Combating HIV/AIDS, Malaria and other Disease and Ensuring Environmental Sustainability.
Since the MDGs were introduced in late 2000, reports indicate Eritrea has reduced its maternal mortality rates by 69 %, declined child mortality levels under five by 57 %, slashed HIV prevalence levels by 49 %, and reduced Malaria infections by 90%.
In striving to provide adequate and cost-effective health service, Dr. Mismay Gebrehiwet, an advisor to the Ministry of Health, disclosed Eritrea has started producing its own antiviral drugs to combat HIV/AIDs.
"The government is committed to provide the drug free of charge to all HIV infected persons."[3], Dr. Gebrehiwet said in an interview with ERI-TV.
The MDGs are a comprehensive framework endorsed by 189 countries at the UN Millennium Summit in September of 2000. They were introduced as a road map for developing nations to reduce poverty, hunger, ill-health, improving education, and environmental sustainability by 2015.
MDG 1
Eradicate Extreme Hunger and Poverty
Off Track ✗
Achieve Universal Primary Education
On Track ✓
Promote Gender Equality & Empower Women
Reduce Child Mortality
Improve Maternal Health
Combat HIV/AIDS, Malaria & other Disease
Ensure Environmental Sustainability
Develop a Global Partnership for Development
Sources: Africa Research Institute, UNDP, Dr. Gibrehiwet
– – – – – – – – – – –
[1] Princes' Progress: Reconstruction and authority in Eritrea and Rwanda, Africa Research Institute, March 2011, page 3
[2] On page 16 of Eritrea's comprehensive response to the Somalia and Eritrea Monitoring Group, a senior government official; citing UNDP officials, said Eritrea is on track to achieve six of the eight MDGs
[3] Dr. Mismay Gebrehiwet's interview with ERI-TV, FEB 15, 2012, via Eastafro.com
This entry was posted in News and tagged Africa Research Institute, Child Mortality, Combating HIV/AIDS, Developing Nations, Dr. Mismay Gebrehiwet, Egypt, Empowering Women, Environmental Sustainabilit, Eri-TV, Eritrea, Ethiopia, Gender Equality, Gender Equality and Empowering Women, HIV/AIDS, hunger, Improvement of Maternal Health, Kenya, Malaria, Maternal Health, MDG, Millennium Summit, Poverty, Primary Education, Reducing Child Mortality, Somalia, Sudan, Uganda, UN Millennium Development Goals, United Nation, Universal Primary Education. Bookmark the permalink.
TesfaNews@wordpress
1) This blog serves as a backup for the parent website www.TesfaNews.net
2) We only update this site on a weekly basis. We advise you to visit www.TesfaNews.net daily for the latest positive news on Eritrea.
An Ethiopian and Susan Rice Semiannual Ritual at the UN Security Council
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African Union turned into Handmaiden for Pax Americana
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Eritrea: The Perfect Scapegoat for Somalia Debacle
Eritrea Urges Respect of AU Rules and Procedures, Again
GreenEdge Rider Teklehaymanot Prepares for London 2012 in Eritrea
BHP Bowed to South Boulder of Eritrea to Abandon Ethiopia Potash Project
BADME – A Political Pawn for the Eritrean Quislings League (EQL)
Ethiopia Ranks 17 in Failed States Index
June 20: Remembering Eritrea's Courageous Heroes
Sixty Percent of the $100m Worth Copper Plant in Eritrea Committed
Abu Dhabi Approves $50m Loan to Promote Development in Eritrea
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Eritrea: Price of cereals drops significantly; Ethiopia's inflation reaches 15%
Eritrea's national team wins tour of Rwanda, Daniel Teklehaimanot crowned 2010 champion
Eritrea's Progress in health: Cost-effective inter-sectoral interventions and a long-term perspective
Ethiopia reportedly plans to balkanize Eritrea
Eritrean-American, Meb Keflezighi, wins U.S. Olympic Marathon Trials


text:
\section{Introduction}
Despite of the fact that positive maps are essential ingredient in a description of quantum systems, a characterization of the structure of the set of all positive maps has been a long standing challenge in mathematical physics. The key reason behind that is the complexity of this structure. In particular,
the convex structure of the positive maps, $\Phi : \cB(\cH) \to \cB(\cH)$, is highly complicated even in low dimensions of the Hilbert space $\cH$.

In the sixties it was shown \cite{St1} (see also St{\o}rmer's book \cite{St} and references given there) that every positive map for 2D case, i.e. for $\dim \cH = 2$, is decomposable. The first example of non-decomposable map was given by Choi \cite{Choi}, see also \cite{Choi1} and \cite{Wor}, for 3D case, i.e. for $\dim \cH = 3$. Since then, other examples of non-decomposable maps were constructed. In particular, by results of Woronowicz \cite{Wor} and St{\o}rmer \cite{St1}, if $\dim \cH_1 \cdot \dim\cH_2 \leq 6$, all positive maps $T:\cB(\cH_1) \to \cB(\cH_2)$ are decomposable but \textit{this is not true in higher dimensions.} On the other hand, the emergence of non-decomposable maps may be considered as a huge obstacle in getting a canonical form for a positive map.

The present work being a continuation of our previous papers \cite{WAM2}, \cite{LMM}, \cite{WAM3}, \cite{WAMT}, and \cite{WAM4}, provides an analysis of the origin of non-decomposable maps. We emphasize that
an explanation of emergence of these maps seems to be a necessary step in the understanding the structure of positive maps.
In particular, we wish to see what is behind the construction of Choi's, Robertson's, Hall-Breuer and others non-decomposable maps.

This paper is organized as follows: first we give necessary preliminaries in Section 2. Next, in Section 3, elementary maps are described. In Section 4, we indicate how Radon-Nikodem type theorems may be used for a characterization of such subtractions which are leading to a positive map. Examples of illustrative maps are studied in Section 5. Conclusions and final remarks are given in Section 6.

\section{Definitions and notations}
For any $C^*$-algebra $\mathfrak{A}$, by $\mathfrak{A}^+$ we denote the set of all positive elements of $\mathfrak{A}$.
If $\mathfrak{A}$ is a unital $C^*$-algebra then a state on $\mathfrak{A}$ is a linear functional $\phi: \mathfrak{A} \to \Cn$ such that $\phi(a) \geq 0$ for every $a \geq 0$ ($ a \in \mathfrak{A}^+$) and $\phi(\jed) = 1$, where $\jed$ is the unit of $\mathfrak{A}$. The set of all states on $\mathfrak{A}$ will be denoted by $\cS_{\mathfrak{A}}$.

A linear map $T: \qA_1 \to \qA_2$ between $C^*$-algebras $\qA_1$ and $\qA_2$ is called positive if $T(\qA_1^+) \subseteq \qA_2^+$. For $k\in \Nn$ we consider a map $T_k: M_k(\Cn) \otimes \qA_1 \to M_k(\Cn) \otimes \qA_2$ where $M_k(\Cn)$ denotes the algebra of $k\times k$ matrices with complex entries and $T_k = id_{M_k} \otimes T$. We say that $T$ is k-positive if the map $T_k$ is positive. The map $T$ is said to be completely positive if $T$ is k-positive for every $k \in \Nn$.

For a Hilbert space $\cH$ by $\cB(\cH)$ we denote the $C^*$-algebra of all bounded linear operators acting on $\cH$. Unless otherwise stated we assume that $\dim \cH = d < \infty$. In other words, $\cB(\cH)$ can be identified with $M_d(\Cn)$. Let $\{e_i\}_{i=1}^d$ be an orthonormal basis in $\cH$. By $\tau$ we denote the transposition map on $\cB(\cH)$ associated with the basis $\{e_i\}$. We note that for every finite dimensional Hilbert space $\cH$ the transposition $\tau: \cB(\cH) \to \cB(\cH)$ is a positive map but not completely positive (in fact it is not even 2-positive).

The set of all unital completely positive maps of $\mathfrak{A}$ into $\cB(\cH)$ will be called the generalized state space, cf. \cite{SWard}, and it will be denoted by $S_{\cH}(\mathfrak{A})$. Obviously, it is a convex set. However, there is also a noncommutative convexity approach to $S_{\cH}(\mathfrak{A})$, see \cite{FM}, where the term noncommutative convexity refers to a form of convexity in which operator-valued convex coefficient are assumed.
In particular, a map $T \in S_{\cH}(\mathfrak{A})$ is called $C^*$-extremal if whenever $T$ is written as a noncommutative convex combination:
\begin{equation}
T(\cdot) = \sum_{i=1}^n t^*_iT_i(\cdot)t_i, \quad t_i \in \cB(\cH), \quad \sum_{i=1}^nt_i^*t_i = \jed,
\end{equation}
where $t_i^{-1}$ exists for all $i$ and $T_i \in S_{\cH}(\mathfrak{A})$,
then for each $i=1,...,n$, $T_i$ is unitarily equivalent to $T$ (so $T_i(\cdot) = uT(\cdot)u^*$, $u$ unitary).
It was shown by Farenick and Morenz, see \cite{FM}, that when $\cH$ is finite dimensional one has:
\begin{enumerate}
\item $C^*$-extreme points exist.
\item there exists a decomposition $\cH=\oplus_{i=1}^k\cH_i$, pure unital completely positive maps $T_i:\mathfrak{A} \to \cB(\cH_i)$ (pure means that $T_i$ are of the form $T_i(\cdot)= W^*_i \pi_i(\cdot)W_i$, where $\pi_i$ stands for irreducible representation of $\mathfrak{A}$ in $\cB(\cK_i)$, $W_i: \cH_i \to \cK_i$) and  unitary $u \in \cB(\cH)$ such that
\begin{equation}
uT(x)u^* = T_1(x) \oplus T_2(x)\oplus ... \oplus T_k(x)
\end{equation}
for every $x \in \mathfrak{A}$.
\item the set of $C^*$-extreme points is sufficiently large to generate  a $C^*$-convex subset that is dense in $S_{\cH}(\mathfrak{A})$; for details see \cite{FM}.
\end{enumerate}
\begin{remark}
We emphasize that the concept of noncommutative convexity is a nice indicator that various structures of $\mathfrak{A}$ as well as  various structures of the set $\{ T: \mathfrak{A} \to \cB(\cH)\}$ should be taken into account, see next section.
\end{remark}
A positive map $T: \cB(\cH_1) \to \cB(\cH_2)$ is called decomposable if there are completely positive maps $T_1, T_2: \cB(\cH_1) \to \cB(\cH_2)$ such that $T= T_1 + T_2 \circ \tau$. As it was shown by St{\o}rmer \cite{StPams} that a linear map $T: \mathfrak{A} \to \cB(\cH)$ is decomposable if and only if for all $n \in \Nn$
\begin{equation}
T(x_{ij}) \in  M_n(\cB(\cH)^+ {\quad \rm{whenever}} \quad (x_{ij})\  {\rm{and}} \ (x_{ji}) \in  M_n(\mathfrak{A})^+.
\end{equation}
$\mathfrak{A}$, as before, stands for a $C^*$-algebra.

Let $\cP, \cP_C$ and $\cP_D$ denote the set of all positive, completely positive and decomposable maps from $\cB(\cH_1)$ to $\cB(\cH_2)$, respectively. There are the following inclusions
\begin{equation}
\cP_C \subseteq \cP_D \subseteq \cP.
\end{equation}
Complete positive maps are relatively easy to handle due to the fundamental theorem of Stinespring \cite{stines}. It states that for any normal completely positive map $T: \qA \to \cB(\cH)$ there exists a Hilbert space $\cK$, a $^*$-homomorphism $\pi : \qA \to \cB(\cK)$ and a bounded operator $V:\cH \to \cK$ such that
\begin{equation}
T(a) = V^* \pi(a) V,
\end{equation}
for any $a \in \qA$.

If $\mathfrak{M}$ is a von Neumann algebra on a Hilbert space $\cH$, it stems from Stinespring's theorem, cf. \cite{kraus}, that $T: \mathfrak{M} \to \mathfrak{M}$ is completely positive if and only if $T$ has the form
\begin{equation}
\label{kraus}
T(a) = \sum_{\alpha} V^*_{\alpha} a V_{\alpha}, \quad a \in \mathfrak{M},
\end{equation}
for a suitable set $\{V_{\alpha}\} \subset \cB(\cH)$ where the convergence is in the weak operator topology. The set can be taken finite if $\cH$ is finite dimensional.

We wish to close this section with definition of spin factor. We remind that among subsets of $\cB(\cH)$, spin factors are playing an important role, cf. the next section. They are constructed in the following way. Firstly, one defines spin systems as a collection $\mathfrak{S}$ of nontrivial symmetries, i.e. anticommuting operators on a Hilbert space such that
\begin{equation}
s \cdot s = \jed, \quad s=s^*, \quad s\neq\pm \jed, \quad st + ts = 0,
\end{equation}
for any $s,t \in \mathfrak{S}$. Clearly, on two dimensional Hilbert space $\Cn^2$, Pauli matrices provide an example of spin systems. The spin factor $\mathfrak{F}$ is defined as the smallest unital JC algebra containing the spin system, for details see \cite{HS}.

\section{Elementary linear maps}
To understand the origin of non decomposable maps, as the first step, we carefully review various structures of $\cB(\cH)$, where $\cH$ is a finite dimensional Hilbert space, $\dim \cH =  d< \infty$. Here and subsequently, elementary maps denote basic transformations defined on the considered fixed structure.
More particularly, we describe a family of maps such that a positive map, defined on a fixed structure, is sequentially built from these basic maps.
For examples, see next subsection, for a (finite dimensional) Hilbert space, one-rank operators are elementary maps. Lastly, it should be added that extreme positive maps are not good candidates for elementary maps as, in general, their classification seems to be a hopeless task, cf.  \cite{WAM3}, \cite{WAMT} and references given there.

\subsection{$\cB(\cH)$ as a Hilbert space.}
A Hilbert space structure is defined by the following inner product
\begin{equation}
\cB(\cH) \times \cB(\cH) \ni \langle a,b \rangle \mapsto (a,b) = \Tr a^*b \in \Cn.
\end{equation}
The elementary maps, for this space, are of the form
\begin{equation}
\label{2.2}
\ket{a} \bra{b}c = (\Tr b^*c)a,
\end{equation}
where $a,b,c \in \cB(\cH)$. In particular, for $a\geq0$, $b\geq 0$ one gets a positive map. As $a,b$ are fixed, then the range of $\ket{a} \bra{b}$, determined by $a$, is contained in a commutative algebra. Hence $\ket{a} \bra{b}$, $a\geq 0$ and $b \geq 0$, leads to a completely positive map.

\subsection{$\cB(\cH)$ as a $C^*$-algebra}
Firstly, we note that the involution ``$^*$'' is another example of an elementary (\textit{non-linear!}) map. Let us consider this map in a matrix representation. To this end, let $\{e_i\}$ be a basis in $\cH$. It is well known that there is the following one-to one
correspondence
\begin{equation}
\cB(\cH) \stackrel{1-1}{\rightarrow} \{a_{ij} \equiv (e_i, a e_j) \}.
\end{equation}
It is easily seen that $\{a_{ij}\} \mapsto \{a_{ij}\}^*$ can be written as
\begin{equation}
\{a_{ij}\} \to J\{a_{ij}\}^TJ,
\end{equation}
where $T$ stands for the transposition associated with the basis $\{e_i\}$, $J$ is the conjugation on the Hilbert space $\cH$. The conjugation $J : \cH \to \cH$ is defined as
\begin{equation}
Jf = J\sum_i (e_i,f)e_i = \sum_i \overline{(e_i,f)} e_i, \quad f \in \cH.
\end{equation}
Consequently, the (matrix) transposition is another elementary linear map.

\skip0,5cm
Secondly, in $\cB(\cH)$ one can distinguish the Jordan structure (to be more precise we restrict ourselves to JC-algebras), i.e. one can consider $\cB(\cH)$ as a linear space with the Jordan product
\begin{equation}
a\ast b \equiv \{a,b\} = \frac{1}{2}(ab +ba).
\end{equation}
Our interest in Jordan structures  is stemming from the following observations:
\begin{enumerate}
\item Positive maps are defined on selfadjoint elements, and the self-adjoint part of $\cB(\cH)$ can be equipped with the Jordan structure.
\item The very deep St{\o}rmer's result states that the nature of positivity of a certain class of linear maps on an algebra can be linked with algebraic properties of their images \cite{Stormer}, see also \cite{ES}. St{\o}rmer has proved that a linear unital positive map $P$ on the algebra $\qA$ such that $P \circ P = P$ (a projection) is a decomposable map if and only if the Jordan algebra associated with the image of the map $P(\qA)$ is the reversible one (so it is closed with respect to the product $\{a_1,a_2,...,a_n\} \equiv a_1a_2...a_n + a_n...a_2a_1$, $n=1,2,..$).
\item
Spin factors of dimension less than four are reversible. The six-dimensional spin factor admits both reversible and non-reversible representations. The rest are non-reversible, for details see \cite{HS}. Consequently,
a projection onto spin factor of dimension larger than six is a positive non-decomposable map.
\end{enumerate}
Therefore, projections $P$ are also elementary maps, and among them there are non-decomposable maps. It is worth pointing out that non-decomposable projections can be used to construct non-decomposable dynamical maps, for details see
\cite{WAM1}. We end this subsection with a remark that obviously both $^*$-homomorphisms and Jordan homomorphisms are also elementary maps on $\cB(\cH)$. It is worth pointing out that these homomorphisms are decomposable maps.
\subsection{$\cB(\cH)$ as a Hilbert $C^*$-module}\label{3.3}
$\cB(\cH)$ can be considered as a Hilbert $C^*$-module with the inner product defined as
\begin{equation}\left\langle a,b\right\rangle = a^*b, \quad a,b \in \cB(\cH).
\end{equation}
Following ``the recipe'' given in \ref{2.2} we define the following elementary maps
\begin{equation}
\label{2.8}
\left\|a><b\right\|c = b^*ca, \quad a,b,c \in \cB(\cH).
\end{equation}
Obviously, if $a=b$ then (\ref{2.8}) gives another type of elementary positive maps. Furthermore, this type of elementary maps plays a crucial role in noncommutative convexity.
\vskip 0,5cm
\begin{corollary}
To sum up, let us restrict ourselves to elementary maps considered in this section. Then, taking convex combinations of elementary maps as well as their compositions, one gets decomposable maps. For higher dimensions than $3$ there are also non-decomposable maps originating from non-decomposable projections.
\end{corollary}
However, there are non-decomposable maps on $M_3(\Cn)$ (cf. Introduction) as well as, for higher dimensions, maps having different structures. Moreover, the structures of these maps can not be explained by arguments mentioned above. Therefore, there is the necessity for other tools. This point will be clarified in next sections.

\section{Radon-Nikodym type results}
We have seen in the previous section that decomposable maps are positive maps originating from convex combinations of elementary maps. Obviously, this stems from the well known fact that the set of positive maps is a convex set. The important point to note here is that for given two positive maps in $\cP$, in certain cases, their difference is also a positive map. Moreover, this operation can be used to obtain some non-decomposable maps. But, in order to prevent any risk of misunderstanding we give the following remarks:
\begin{remark}
There is the (isometric isomorphic) correspondence between the set of all linear bounded maps  $T: \mathfrak{A} \to \mathfrak{A}$ and  functionals on the specific tensor product. This is a result of Grothendieck's theory. Its very special case is known, in quantum information community, as Choi-Jamiolkowski isomorphism \cite{Gro}, \cite{Stor1a} and for details see Lemma 4 and Remark 5 in
\cite{WAM3}. In particular, using Grothendieck's approach it is easily seen that any linear bounded map $T$ can be written as a linear combination of two positive (completely positive) maps.
However, here, we wish to examine whether a positive (completely positive) map can be written as a difference of two completely positive maps. To achieve this specified goal a new tool should be employed. This will be done in this section.
\end{remark}

 Now to the point: assume $T_1$ and $T_2$ are positive maps, i.e. $T_i \in \cP$, $i=1,2$. We wish to have
\begin{equation}
\label{3.1}
T_1 - T_2 \in \cP.
\end{equation}
This is equivalent to
\begin{equation}
\label{3.2}
\forall \varphi \in \cB(\cH)^{*,+} \quad \varphi \circ T_1 \geq \varphi \circ T_2,
\end{equation}
where $\cB(\cH)^{*,+}$ stands for the set of all linear positive functionals on $\cB(\cH)$.

In other words, we are interested is positive maps $T_1, T_2$ satisfying: $T_1\geq T_2$, i.e. $\forall a \geq 0, \quad T_1(a) \geq T_2(a)$. As this reminds the starting point of the classical Radon-Nikodym theorem for measures, results stemming from the assumption (\ref{3.1}) may be called Radon-Nikodym type results.

An application of generalization of Radom-Nikodym theorem (given in terms of $W^*$-algebra, see Theorem 1.24.3 in \cite{sakai}) to inequality (\ref{3.1}) says that there exists a positive element $t_{\varphi}$ in $\cB(\cH)$, with $0\leq t_{\varphi} \leq \jed$ such that for any $a \in \cB(\cH)$ one has $\varphi \circ T_2(a) = \varphi \circ T_1( t_{\varphi} a t_{\varphi})$.
As any $\varphi$ is of the form ($\cH$ is of finite dimension!) $\varphi(\cdot) = \Tr\rh (\cdot)$ one gets
\begin{equation}
\Tr \rh T_2(a) = \Tr\rh T_1(\rt a \rt).
\end{equation}
So for any $a\geq 0$
\begin{equation}
\Tr T^d_2(\rh)a = \Tr\rt T_1^d(\rh) \rt a,
\end{equation}
where $T^d$ stands for the dual map ($\Tr a T(b) \equiv \Tr T^d(a) b$).
Hence, we arrived at the following local relation between $T_1$ and $T_2$: for any state given by a density matrix $\rh$
\begin{equation}
T^d_2(\rh) = \rt T_1^d(\rh) \rt.
\end{equation}

In that way we got a local (depending on state $\varphi$) characterization of the relation $T_1\geq T_2$. However, it seems that in certain cases it is possible to get a more stronger characterization of (\ref{3.1}).
To present results in this direction, we need a version of Radon-Nikodym theorem which is formulated in terms of positive maps entirely.
Under, additional (strong) assumption of complete positivity: $T_1 - T_2 \in \cP_C$, such theorems were considered by Arveson \cite{arveson}, Belavkin-Staszewski \cite{BS} and Raginsky \cite{raginsky}. Unfortunately, the requirement $T_1 - T_2 \in \cP_C$ appeared to be too restrictive - it admits only a small family of maps, see Theorem III.5 and Proposition IV.1 in \cite{raginsky}. In particular, see \cite{raginsky}:
\begin{proposition}
\label{rag}
Let $T$ and $S$ be two completely positive maps. Then $T - S$ is a completely positive map if and only if there exists a (Krauss) decomposition of the form (\ref{kraus}), $T(a) = \sum_{\alpha} W^*_{\alpha} a W_{\alpha}$, and the set $\{\lambda_{\alpha}; \lambda_{\alpha} \in [0,1] \}$ such that $S(a) = \sum_{\alpha} \lambda_{\alpha} W^*_{\alpha} a W_{\alpha}$.
\end{proposition}

This state of affairs is changed dramatically if, in the above argument, one replaces the requirement $T_1 - T_2 \in \cP_C$ by $T_1 - T_2 \in \cP$.

In doing so, we will examine conditions guaranteeing that
\begin{equation}
T^{(1)}_1 + T^{(1)}_2 \circ \tau - \left(T^{(2)}_1 + T^{(2)}_2 \circ \tau \right) \equiv \left(T^{(1)}_1 - T^{(2)}_1\right) +\left(T^{(1)}_2 - T^{(2)}_2 \right) \circ \tau \in \cP,
\end{equation}
where $T^{(i)}_j$, $i,j = 1,2$, are completely positive. In other words, we wish to have
\begin{equation}
T^{(1)}_1 - T^{(2)}_1 \in \cP \quad {\textstyle and} \quad \left(T^{(1)}_2 - T^{(2)}_2 \right) \in \cP.
\end{equation}
The conditions guaranteeing positivity of $T - T^{\prime}$, where $T$ and $T^{\prime}$ are completely positive maps were found by Jin-Chuan Hou, see \cite{hou}. To describe them we need some preliminaries, cf. \cite{hou}.

Let $a_1,...,a_k$ ,and $c_1,...,c_i$ be in $\cB(\cH,\cK)$ ($\cH, \cK$ stand for Hilbert spaces). If for each $x \in \cH$, there exists an $l\times k$ complex matrix $\{(\alpha_{i,j}(x) )\}$ such that
\begin{equation}
c_ix = \sum_{j=1}^k \alpha_{i,j}(x) a_j x, \quad i= 1,...,l,
\end{equation}
$(c_1,...,c_l)$ is said to be a locally linear combination of $(a_1,...,a_k)$. If coefficients $\{\alpha_{i,j}(x)\}$ can be taken in such way that the norm $\| \alpha_{i,j}(x)\| \leq 1$, for every $x$, then $(c_1,...,c_l)$ is said to be a contractive linear combination of $(a_1,...,a_k)$.  Thus, \textit{a form of locality is assumed} (dependence on $x$). Hou has been proved (see Corollary 2.6 in \cite{hou})
\begin{proposition}
\label{4.1}
Let us consider a linear map $\Phi:\cB(\Cn^n) \to \cB(\Cn^m)$ of the form $\Phi(\cdot) = \sum_{i=1}^n a^*_i (\cdot)b_i$,
where $b_i, a_j : \Cn^m \to \Cn^n$. $\Phi$ is positive if and only if there exist $(c_1,...,c_k)$ and $(d_1,...,d_l)$ in $\cB(\Cn^n, \Cn^m)$ such that $(d_1,...,d_l)$ is a contractive locally linear combination of $(c_1,...,c_k)$ and
\begin{equation}
\Phi(v) = \sum_{i=1}^k c_i v c_i^* - \sum_{j=1}^l d_j v d_j^*,
\end{equation}
for all $v \in \cB(\Cn^n)$.
\end{proposition}

\begin{remark}
\label{uwaga}
\begin{enumerate}
\item
In that way we have a characterization when a subtraction of one completely positive map from another one is still a positive map.
\item Note, that Proposition \ref{4.1} is also saying that for a large class $\mathfrak{R}$ of positive maps, an addition of carefully chosen completely positive map to a positive map from $\mathfrak{R}$ leads to a completely positive map. This clearly indicates that the form of a positive map could be highly non-unique.
\item It is easily seen that conditions given in Proposition \ref{rag} are nothing else but the very particular case of that used in Proposition \ref{4.1}.
\item It is worth pointing out that Proposition \ref{4.1} is about elementary maps emerging from $C^*$-module structure, see Subsection \ref{3.3}.
\item The non-decomposable maps can be selected by St{\o}rmer's criterion, see Section 2. However, we emphasize that frequently it could be difficult to utilize this criterion.
\end{enumerate}
\end{remark}

The last comment related to the above Proposition is so important that it is given separately.
\begin{corollary}
\label{hej}
Let $T$ and $S$ be two decomposable maps, i.e. $T= T_1 + T_2 \circ \tau$ and $S= S_1 + S_2 \circ \tau$ where $T_i, S_i$, $i=1,2$ are completely positive maps. Let $T-S \in \cP$. Assume that $S_i$ does not fulfill relations described in Proposition \ref{rag}. Then $T_i-S_i$  $i=1,2$, is either a decomposable map or non-decomposable map. $T-S$ and $T_i - S_i$ is not decomposable if it does not satisfy St{\o}rmer's criterion.
\end{corollary}
We wish to end this section with a remark concerning $2$D case. This remark is another Hou's result, see Corollary 3.4 in \cite{hou} and it will be used in the discussion on the Choi's map.
\begin{proposition}
\label{hou2}
A non-completely positive linear map $\Phi : M_2(\Cn) \to M_2(\Cn)$ is positive if and only if it has the form
\begin{equation}
\Phi(\cdot) = \sum_{i=1}^3 c_i (\cdot) c^*_i - v(\cdot)v^*,
\end{equation}
where $\{c_1, c_2, c_3, v\}$ are linearly independent and $v$ is a contractive locally linear combination of $\{c_1, c_2, c_3 \}$, i.e., for every $x \in \Cn^2$, there exist scalars $\lambda_i(x)$, $i=1,2,3$ such that $\sum_{i=1}^3|\lambda_i(x)|^2 \leq 1$ and $vx = \sum_{i=1}^3\lambda_i(x)c_i x$.
\end{proposition}

\section{Examples}
In this section, we indicate how techniques presented in the previous section may be used to produce maps which are celebrated in Quantum Information. We begin with the Choi map.
\subsection{The Choi map}
Going into the discussion of concrete maps on low dimensional structures let us begin with the general form of the following family of maps $\gamma_{n,k}: M_n(\Cn) \to M_n(\Cn)$ given by Tanahashi and Tomiyama \cite{TT}, see also \cite{Ha}:
\begin{equation}
\gamma_{n,k}(a) = (n - k) \epsilon(a) +\sum_{i=1}^k \epsilon(s^i a s^{i*}) - a,
\end{equation}
where $n\geq1$, $1 \leq k \leq n-2$, $\epsilon$ is the projection on the diagonal part of $M_n(\Cn)$, and finally $S$ is the rotation such that $Se_i = e_{i+1}$ (mod $n$; $\{e_i\}$ is a canonical basis in $\Cn^n$).

Obviously, $\gamma_{n,k}$ is a difference of two completely positive maps. As we wish to consider the original Choi map (so $3$-dimensional case) we restrict ourselves to the case $n=3$. Consequently, we will examine the map
\begin{equation}
\gamma_{2,1}(a) \equiv \gamma(a) = 2\epsilon(a) + \epsilon(SaS^*) - a,
\end{equation}
where $S \begin{pmatrix}
                e_1\\
                e_2\\
                e_3\\
                \end{pmatrix} = \begin{pmatrix}
                e_2\\
                e_3\\
                e_1\\
                \end{pmatrix}, \ \rm{etc.}$

An easy computation shows that $\gamma$ can be rewritten as
\begin{equation}
\gamma(a) = \sum_{i=1}^6 V_i a V^*_i - a,
\end{equation}

where
$V_1 = \sqrt{2}  \begin{pmatrix}
                1, 0, 0\\
                0, 0, 0\\
                0, 0, 0\\
                \end{pmatrix}, \ V_2 = \sqrt{2} \begin{pmatrix}
                                                0, 0, 0\\
                                                0, 1, 0\\
                                                0, 0, 0\\
                                                \end{pmatrix}, \ V_3 = \sqrt{2} \begin{pmatrix}
                                                                               0, 0, 0\\
                                                                               0, 0, 0\\
                                                                               0, 0, 1\\
                                                                               \end{pmatrix},$

and

$V_4 =    \begin{pmatrix}
                0, 1, 0\\
                0, 0, 0\\
                0, 0, 0\\
                \end{pmatrix}, \   V_5 =  \begin{pmatrix}
                                                0, 0, 0\\
                                                0, 0, 1\\
                                                0, 0, 0\\
                                                \end{pmatrix}, \ V_6 =  \begin{pmatrix}
                                                                               0, 0, 0\\
                                                                               0, 0, 0\\
                                                                               1, 0, 0\\
                                                                               \end{pmatrix}.$

Obviously, $\jed \in \{$contractive locally linear combinations of $V_i, \ i=1,...,6 \}$. Hence, $\gamma$ is a positive map by Proposition \ref{4.1}. On the other hand, it was shown by Choi and Lam \cite{Choi}, \cite{Choi1}, \cite{Choilam}, that $\gamma$
is non decomposable (and extremal in the cone of positive maps). It is worth pointing out that non decomposability of $\gamma_{2,1}$ follows directly from St{\o}rmer's criterion. It is enough to apply the criterion to the matrix $\{V_iV_j^* \}_{i,j=3}^6$.

Thus, it is clear now that a difference of two completely positive maps can lead to a non-decomposable map. In other words, by taking a subtraction of identity map from convex combinations of elementary maps one can arrive at a non-decomposable map.

One may ask what is changed in the above arguments when the dimension of $\cH$ is equal to $2$. To answer this question we note that Proposition \ref{hou2} gives the general form of non-completely positive maps for this case:
\begin{equation}\Phi(a) = \sum_{i=1}^3c_i a c^*_i - vav^*,
\end{equation}
where $v$ is not a linear combination of $\{c_i\}$ (only local! combinations are performed). Therefore, the Choi's construction can not be carried out (for 2 dimensional case). Obviously, in this case any positive map is decomposable, cf. Introduction.

\subsection{Reduction map}
The reduction map $R: M_d(\Cn) \to M_d(\Cn)$ is given by
$$R(\varrho) = \Tr\varrho \jed - \varrho$$
It seems that $R(\cdot)$ is arising from the family of maps $R_{\lambda}(\varrho) = \lambda \frac{1}{n} (\Tr\varrho) \jed + (1 - \lambda)\varrho$, $\lambda \in \Rn$, see \cite{Tom}. In particular, the map $R_C(\varrho) = (n-1) \Tr(\varrho) \jed -\varrho$ was first used by Choi as an example of a map which is $n-1$ positive but which is not $n$ positive, \cite{Choicad}, and than $R_{\lambda}$ were examined by Tomiyama \cite{Tom}. Further, the reduction map was studied by Horodeckis \cite{H1} in the context of quantum information.

Define $W_{i,j} \in \cB(\cH)$ ($\dim \cH = d$) as
\begin{equation}
W_{ij}x \equiv \ket{e_i}\bra{e_j}x = (e_j,x)e_i,
\end{equation}
where $\{e_i \}$ is a basis in $\cH$. We note:
$$\sum_{i,j} W_{ij} \varrho W^*_{ij} = \sum_{i,j} \ket{e_i}\bra{e_j}\varrho\ket{e_j}\bra{e_i} = \Tr\varrho \sum_i\ket{e_i}\bra{e_i} = \Tr \varrho \ \jed.$$
Thus, the positivity of $R$ is a simple consequence of Proposition \ref{4.1}. As $R$ is a decomposable map, this example shows that a difference of two completely positive maps being a positive map can be decomposable.

\subsection{Robertson map}
The first example of non-decomposable map on $M_4(\Cn)$ was obtained by Robertson \cite{Rob}. To give its definition some preliminaries are needed, see \cite{Rob}. Let
$u: M_2(\Cn) \to M_2(\Cn)$ stands for the quaternionic flip
$$ u \begin{pmatrix}
                \alpha, \beta\\
                \gamma, \delta\\
                \end{pmatrix} \  =  \begin{pmatrix}
                                            \delta, - \beta\\
                                             - \gamma, \alpha\\
                                                  \end{pmatrix}. $$

 Then, by $\sigma$, the following antiautomorphism of order $2$ on $M_4(\Cn)$ is denoted
 $$ \sigma \begin{pmatrix}
                a,b\\
                c,d\\
                \end{pmatrix} =  \begin{pmatrix}
                                        u(a), u(c)\\
                                        u(b), u(d)\\
                                        \end{pmatrix}
                                        ,$$

 where $a,b,c,d \in M_2(\Cn)$.
 Finally, let $\theta$ be the following Jordan automorphism
 $$ \theta\begin{pmatrix}
                \alpha, q\\
                q^*, \beta\\
                \end{pmatrix} =  \begin{pmatrix}
                                       \beta, q\\
                                        q^*, \alpha\\
                                        \end{pmatrix}.$$

 It was shown, see \cite{Rob2} that $\theta \circ \frac{1}{2}(\iota + \sigma) : M_4(\Cn) \to M_4(\Cn)$ is not decomposable positive map ($\iota$ denotes the identity map). It can be rewritten in ``pure'' matrix form as
\begin{equation}
\begin{pmatrix}
                a,b\\
                c,d\\
                \end{pmatrix} \to  \begin{pmatrix}
                                         tr(d)\jed, \frac{1}{2}(b + u(c))\\
                                         \frac{1}{2}(c + u(b)), tr(a) \jed\\
                                         \end{pmatrix},
\end{equation}

where $tr$ is the normalized trace on $M_2(\Cn)$. Thus, a positive non-decomposable map can be constructed by elementary maps and Jordan structure is playing the important role.

\subsection{Hall, Breuer map}

The next example is the Breuer-Hall map, see \cite{Breu}, \cite{hall}. It is defined on $M_{2d}(\Cn)$ by
\begin{equation} \Lambda(\varrho) = \frac{1}{2d - 2}((\Tr\varrho \jed - \varrho - U\varrho^T U^*),
\end{equation}
where $U$ is  an antisymmetric unitary operator on $\Cn^{2d}$ and $d>2$ is even and $\varrho^T \equiv \tau(\varrho)$. It was shown see \cite{hall}, that this map is non-decomposable. The novelty of this map lies in subtracting co-completely  positive map $U\varrho^T U^*$.

Let us examine this point more carefully. Let $\alpha$ be a $^*$-antimorphism of order $2$ of the von Neumann algebra $\mathfrak{M}$ (i.e., $\alpha \circ \alpha = id$). Then, see \cite{HS} (Chapter 7), the self-adjoint part of the set $\mathfrak{M}^{\alpha}$ of fixed points under $\alpha$ is a \textit{reversible Jordan} (more precisely JW) algebra. Define
$$\beta(\varrho) = \varrho + \beta_0(\varrho) \equiv \varrho + U\varrho^T U^*,$$
where $U$ is an antisymmetric unitary operator. We note $\beta_0 \circ \beta_0 (\varrho) = \beta_0(U \varrho^T U^*) = U(U \varrho^T U^*)^T U^* = U U^{*, T} \varrho U^T U^* = U (-U^*) \varrho (-U) U^* = \varrho$. Consequently, $\beta_0$ is an $^*$-automorphism of order $2$ and $(\iota +\beta_0)(a) \in \cB(\cH)^{\beta_0}$. Furthermore, $\frac{1}{2}(\iota +\beta_0)$
is a projection on a reversible Jordan algebra. Consequently Hall-Breuer map is the subtraction of the projection $\frac{1}{2}(\iota +\beta_0)$ from a slight modification of the reduction map. In other words, there is  the subtraction of two decomposable maps and, in general, this operation can be controlled by Proposition \ref{4.1}. Again, Jordan structures are important.
\subsection{Others examples}
We have noted that Corollary \ref{hej} provides the recipe for plenty examples of non-decomposable maps. To implement this programme one has to consider the difference of two completely positive maps which satisfy conditions given in Proposition \ref{4.1} but not that given in Proposition \ref{rag}. Then, an application of St{\o}rmer criterion shows whether this map is decomposable or not. It is worth pointing out that Choi's, reduction and Hall-Breuer's maps are nice examples of this strategy.  We hope that in that way, one can get plenty of such maps.

\section{Concluding remarks}
In this paper we studied some aspects of the structure of the set of positive maps from the space $\cB(\cH)$ of linear operators on a finite dimensional Hilbert space $\cH$ into itself. In particular, we were interested in the origin of non decomposable maps.

Most of our work relied on the simple and fine idea that, in certain cases, the difference of two positive maps is again a positive map. Intuitively, a difference of two vectors in a convex set is ``localized'' out of the origin of these vectors. In other words, contrary to taking a convex combination, such difference seems to be close to the ``boundary'' of the considered set. Hence, one can expect that such differences can exhibit properties different from those obtained by taking plain convex combinations.

Working in this direction and utilizing Hou's results we got a recipe for a large family of non decomposable maps. In particular, we argued that Radon-Nikodym type results are extremely powerful and versatile tools in the study of origin of non-decomposable maps.
We do not claim that, in this way we are getting a canonical form of a non decomposable map. It is enough to note that there are non decomposable projections, cf. Section 3. Furthermore, our results shed some new light on the structure of non-decomposable maps which are used in Quantum Information.

However, some questions still remain unanswered. For instance, one may ask whether there is a generalization of Hou's result for positive maps of the form
$$T(a) = \sum_i V_i a V_i^* - \sum_jW_i a^{\tau}W^*_j \in \cP $$
where $a \mapsto a^{\tau}$ denotes the transposition.

In addition, one can examine positive maps $T: \cB(\cH) \to \cB(\cH)$ using the detailed analysis of the Hilbert space $\cH$ in the following sense. Let $\cH = \oplus_i \cH_i$. Then, having certain concrete maps $\{ T_{ij}: \cB(\cH_i) \to \cB(\cH_j)\}$ one can study new map $T: \cB(\cH) \to \cB(\cH)$ and this new map $T$ can exhibit new properties, cf. Remark \ref{uwaga}(2). The important point to note here is that the form of $C^*$-extreme completely positive map provides a motivation for such studies, see Section 2. For a deeper discussion on this topic we refer the reader to \cite{MR}, see also \cite{Mil}.
\section{Acknowledgments}
This work was begun in Chennai when the author was attended ``Non-Commutative Analysis'' conference and workshop organized by Institute of Mathematical Sciences in Chennai and the work was completed in Gdansk. He is grateful to Anilesh Mohari for wonderful hospitality and Tomasz Tylec for remarks.

redpajama_set_name: RedPajamaArXiv


text:
Q: Looking for pattern/approach/suggestions for handling long-running operation tied to web app I'm working on a consumer web app that needs to do a long running background process that is tied to each customer request. By long running, I mean anywhere between 1 and 3 minutes.
Here is an example flow. The object/widget doesn't really matter.

*

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*When the long running process is complete the customer is able to complete the last few steps before conversion.

Steps 3 and 4 aren't really important. I just mention them because we can buy some time while we are doing the long running process.
The environment we are working in is a LAMP stack-- currently using PHP. It doesn't seem like a good design to have the long running process take up an apache thread in mod_php (or fastcgi process). The apache layer of our app should be focused on serving up content and not data processing IMO.
A few questions:

*

*Is our thinking right in that we should separate this "long running" part out of the apache/web app layer?

*Is there a standard/typical way to break this out under Linux/Apache/MySQL/PHP (we're open to using a different language for the processing if appropriate)?

*Any suggestions on how to go about breaking it out? E.g. do we create a deamon that churns through a FIFO queue?

Edit: Just to clarify, only about 1/4 of the long running process is database centric. We're working on optimizing that part. There is some work that we could potentially do, but we are limited in the amount we can do right now.
Thanks!

A: Consider providing the search results via AJAX from a web service instead of your application.  Presumably you could offload this to another server and let you web application deal with the content as you desire.
Just curious: 1-3 minutes seems like a long time for a lookup query.  Have you looked at indexes on the columns you are querying to improve the speed?  Or do you need to do some algorithmic process -- perhaps you could perform some of this offline and prepopulate some common searches with hints?

A: As Jonnii suggested, you can start a child process to carry out background processing. However, this needs to be done with some care:

*

*Make sure that any parameters passed through are escaped correctly

*Ensure that more than one copy of the process does not run at once

If several copies of the process run, there's nothing stopping a (not even malicious, just impatient) user from hitting reload on the page which kicks it off, eventually starting so many copies that the machine runs out of ram and grinds to a halt.
So you can use a subprocess, but do it carefully, in a controlled manner, and test it properly.
Another option is to have a daemon permanently running waiting for requests, which processes them and then records the results somewhere (perhaps in a database)

A: This is the poor man's solution:
exec ("/usr/bin/php long_running_process.php > /dev/null &");

Alternatively you could:

*

*Insert a row into your database with details of the background request, which a daemon can then read and process.

*Write a message to a message queue which a daemon then read and processed.

A: Here's some discussion on the Java version of this problem.
See java: what are the best techniques for communicating with a batch server
Two important things you might do:

*

*Switch to Java and use JMS.

*Read up on JMS but use another queue manager.  Unix named pipes, for instance, might be an acceptable implementation.

A: Java servlets can do background processing. You could do something similar to this technology in a web technology with threading support. I don't know about PHP though.

A: Not a complete answer but I would think using AJAX and passing the 2nd step to something thats faster then PHP (C, C++, C#) then a PHP function pick the results off of some stack most likely just a database.


The defending state champion Sierra College men's swim & dive team captured its second consecutive Big 8 conference title in dominating fashion last weekend in Stockton. Coach Chris Breitbart's Wolverines outdistanced second place San Joaquin Delta 913-594, capturing eight individual races and all five meet relays. Michael Crouch won the 50 Free in a school record 20:85 and Stetson Tate, a late-season addition at 1 Meter diving was named the Diver of the Meet. Breitbart was named Coach of the Year for the second straight season. Sierra heads to East LA College in Monterey Park for the CCCAA State Championships May 4-6.


text:
Rexroth Expands Non-Contact Transfer Units to Include High-Grade Polymer Version
Bosch Rexroth Corp. Jun 06, 2011
Addition to standard aluminum version
Ideal for food and beverage industry applications
The Non-Contact Transfer (NCT) unit from Rexroth is a unique picking device that operates on the Bernoulli principle, which applies airflow under the device to create a vacuum and lift force between the center and circumference. The line is now expanded to include a high-grade polymer version.
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The Rexroth NCT unit provides a solution to many handling challenges where suction cups are not feasible because good contact cannot be made with an object's surface. Another advantage of the NCT is that a machine with mechanical grippers can be easily converted to the NCT, since it does not require a vacuum generator, unlike other devices that operate using vacuum pressure. The NCT series is available in four sizes accommodating lift capacities up to 2 pounds (0.9 kg) each, and multiple NCTs can be used together for lifting larger weights.
Bosch Rexroth AG is one of the world's leading specialists in the field of drive and control technologies. Under the Rexroth brand name, the company supplies more than 500,000 customers with tailored solutions for driving, controlling, and moving. Bosch Rexroth is a partner for Mobile Applications, Machinery Applications and Engineering, Factory Automation and Renewable Energies. The company provides customized solutions tailored to the needs and specifications of each individual market. As The Drive & Control Company, Bosch Rexroth develops, produces, and sells components and systems in over 80 countries. As part of the Bosch Group, Bosch Rexroth and its 34,900 associates generated approximately 5.1 billion euros in revenue ($6.8 billion) in 2010. To learn more, please visit www.boschrexroth-us.com
The Bosch Group is a leading global supplier of technology and services. In the areas of automotive and industrial technology, consumer goods, and building technology, some 285,000 associates generated sales of 47.3 billion euros ($62.7 billion) in fiscal 2010. The Bosch Group comprises Robert Bosch GmbH and its more than 350 subsidiaries and regional companies in over 60 countries. If its sales and service partners are included, then Bosch is represented in roughly 150 countries. This worldwide development, manufacturing, and sales network is the foundation for further growth. Bosch spent 3.8 billion euros (approximately $5 billion) for research and development in 2010, and applied for over 3,800 patents worldwide. With all its products and services, Bosch enhances the quality of life by providing solutions which are both innovative and beneficial.
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