There is no shortage of food. The World Food Programme states that the world produces enough food to feed the entire global population. Indeed the UK's waste food alone can provide enough to end UK food poverty, so why do some people still go hungry? The prevailing food system is anchored by the need for money to gain access to food. As Riches and Silvasti outline, food is a commodity, an article of value distributed by free market mechanisms. Affluent consumers are able to choose from an abundant variety of food products, arguably the citizens' right to food is only realised if the citizen has purchasing power.
The UK government's Family Food 2014 Report shows that after housing, fuel and power costs, food is the biggest expenditure for low income households. As the cost of living rises faster than income, this budget is tightly squeezed with low income households buying less food in 2014 than in 2007. The increase in food prices, the implementation of austerity measures and reformation of the Welfare State has cumulatively affected those living on low incomes, diminishing their ability to buy food, no matter how well they budget.
Links between income and diet-related health are well recognised. The term 'Household Food Insecurity'(i), reaffirms these links by not only describing the inability to access enough appropriate and nutritious food but also the anxieties of acquisition, going beyond affordability to include the fear of going hungry and mental stress. The term is used in The Fabian Commission's independent report on food and poverty, Hungry for Change, which explains how food choices are restricted for those on low incomes. According to the report, 'healthy food' is three times more expensive than 'non-healthy food', so, a mother on a low income is more inclined to skip meals in order to feed her child. She is also more likely to prioritise calories over nutrients simply to be able to afford food, choosing items which give a "tummy filling" feeling.
The welfare benefits system is an inconsistent and complex beast. The Government claims that the current reforms to the system will decrease dependency on welfare and move more people into work, but reforms have resulted in dire consequences for the poorest in society. There has been an increase in the severity and number of benefit sanctions and delays where a claimant can have their income stopped altogether thus removing the ability to buy food. These changes are included in the top three primary referral causes to Trussell Trust Foodbanks in 2014-2015 (Fig.1).
Welfare reform has led to a critical discourse from many leading anti-poverty groups(iii). The Joseph Rowntree Foundation discuss the fragility of low income households and outline that whilst the government may increase personal tax allowance, support for childcare and introduce a new basic pay rate named 'National Living Wage' (NLW); other benefits for working-age recipients – for both working and non-working families – shall be frozen until 2019. This exposes a large part of their income to future rises in the cost of living. Fig.2 demonstrates how households earning NLW will not meet even Minimum Standards of Living by 2020. Some food Industry representatives have also reportedly warned that they will lay-off staff if NLW is implemented whilst others have voluntarily committed to the higher pay rate, the Living Wage, which is annually calculated according to the cost of living (not to be confused with the government's NLW!).
Fig 1. The Trussell Trust.
Primary Referral Causes in 2015-2015 to Trussell Trust foodbanks (2015).
Fig. 2. Joseph Rowntree Foundation.
Minimum Income Standards in 2020 (2015).
'Big Society' responses are not working. Adjusting prices to keep food costs low (including supermarket offers and 'essential' ranges) or relying on emergency food providers like food banks for welfare provision, are not solutions to household food insecurity(ii), indeed they are a symptom of failing food and income redistribution policies. These methods exclude low income consumers from freedom of choice and socially acceptable methods of food acquisition, resulting in restricted access to nutritious and appropriate food. These governmental 'responses' arguably demonstrate how the Government is further reducing household income, and failing millions of citizens in their Right to Food.
The right to have regular, permanent and unrestricted access, either directly or by means of financial purchases, to quantitatively and qualitatively adequate and sufficient food corresponding to the cultural traditions of the people to which the consumer belongs, and which ensure a physical and mental, individual and collective, fulfilling and dignified life free of fear.
(The United Nations Special Rapporteur on the right to food, 2000).
Although this right is not an enforceable domestic law, Government is obliged to respect protect and fulfil it under international law.
You Tube – Geoff Tansey. The right to food – An overview by Olivier De Schutter (2014).
The way in which Volunteer Community Services, charities and NGOs have mobilised at an unprecedented scale to protect people as best they can against household food insecurity, demonstrates great concern from the general public. However, these efforts have proved to be unsustainable according to the 'right to food' standard. With the 'right to food' approach, Government should not retreat from its obligation but take central role as duty-bearer to protect access to enough nutritious, affordable and appropriate food for all.
Lambie-Mumford's paper Addressing Food Poverty in the UK ends with recommendations outlining a networked approach with roles for a range of stakeholders including emergency food providers, policy makers, NGOs, the food industry, local communities, individuals and researchers to achieve this goal and hold Government accountable. The Fabian Commission on Food and Poverty outline a detailed approach for Government to begin the journey towards household food security, concluding that there needs to be coordinated action on income not prices. Decent work for decent pay, re-establishing the social security safety net, and protection from price rises could break the link between diet-related illness and income, and protect access to food for low income households.
Previous: Previous post: Government, the food industry and foodbanks. Who's taking the biscuit?
Reblogged this on Food Security and Food Justice.
Great stuff LBA. In Kenya I often work with people who spend pretty much all their money (after rent and kerosene) on food. They are extremely vulnerable to commodity price rises and the whims of the free market. Talking to these people about food insecurity in the UK, they struggle to comprehend that people are food insecure here. How can that be, they say, in one of the richest countries in the world? Maybe there is an article in there somewhere?
I, personally, would be interersted to know where food production fits into this picture – but maybe that's for another post! The poorest people supporting the poorest working conditions and worst quality of food. I've not shown you the Colin Tudge article in Resurgence? It's interesting what kind of a diet he is advocating and how domestic and international producers could meet that.
Government, the food industry and foodbanks. Who's taking the biscuit?


The Warrington Bank is a branch office of The Warrington Bank. They provide the following services: Full Service Office Location and are located at 4093 Barrancas Avenue in Pensacola Florida.
Mobile and traditional directions to this location can be found below along with ratings, lobby hours, their phone number and additional banking information.
The The Warrington Bank location of The Warrington Bank was established Mar 18, 1953 (66 years and 1 months ago). They are one of 2 branch locations operated by The Warrington Bank.
This site is designed to help people locate their bank's nearest branch locations, lobby hours, and online banking information. This site is not run by, endorsed, or associated with The Warrington Bank in any way. All information is provided as-is. Data is updated periodically from the FDIC's databases.


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An E. coli strain that carries the FauI cloned FauI gene from Flavobacterium aquatili (S.K. Degtyarev).
One unit is defined as the amount of enzyme required to digest 1 µg of λ DNA in 1 hour at 55°C in a total reaction volume of 50 µl.


As you may have heard, the California Consumer Privacy Act (CCPA) — a broad data privacy law — was enacted on June 28, 2018, with an original enforcement date of Jan. 1, 2020. Now, lawmakers have already passed the first amendment to the CCPA (SB 1121) just three months after its enactment. Among the most notable changes is a new enforcement date of July 1, 2020, or six months after the publication of final regulations from the CA Attorney General, whichever is sooner.
The CCPA currently imposes requirements on companies that (1) have an annual gross revenue of $25 million or more; (2) collect, share, or sell data of 50,000 California residents or more; or (3) derive at least 50 percent of their annual revenues from selling consumers' personal information. Some of the CCPA's requirements include providing particular notices to consumers about data collection, responding to consumer requests to access, deletion, or correction of their data, and implementing data security measures to safeguard consumers' information.
The CCPA — often compared to the EU's General Data Protection Regulation — was hastily passed this summer in an effort to defeat a more intensive data privacy ballot initiative. Due to the quick pace of passage, lawmakers anticipated that the law would require subsequent amendments prior to 2020. On Sept. 23, 2018, the governor of California signed SB 1121, the first amendment to the CCPA.
While the delay of enforcement by the CA Attorney General is the most notable change for companies, the amendment included other changes. The amendment also clarified exemptions for data regulated by the Gramm-Leach-Bliley Act (GLBA) and the Health Insurance Portability and Accountability Act (HIPAA). Another change removed the requirement that consumers notify the CA Attorney General's office after filing a private action related to a data breach.
During the amendment process, businesses, the Attorney General and consumer groups all weighed in on potential changes. An array of industry groups proposed substantial revisions to the law, but lawmakers did not include a majority of their proposed changes. The amount of lobbying both by consumer protection advocates and businesses on the first amendment signals that SB 1211 is likely just the beginning of changes to the CCPA. In the next year, lawmakers will likely consider a number of amendments to the law before its enforcement date.
Regardless of future changes, companies subject to the law should start or continue working regularly towards compliance, including revising privacy policies and developing internal processes to handle consumer data requests. We will continue to monitor the CCPA through future revisions and provide updates.
If you have any questions about the CCPA and your company's compliance requirements, please contact the Data Security & Privacy Practice Group at Godfrey & Kahn, S.C.


text:
Marsy's Law
About Marsy's Law
Marsy's Story
About Dr. Nicholas
Victims' Stories
I'm a Victim
I'm an Attorney
I'm a Policymaker
Amend The Federal Constitution
State Efforts
Ask Judge Cassell
Marsy's Law Campaign Blog
The latest campaign activity from around the country
Back to All Victims' Stories
Ryan United Founder Stands Behind Marsy's Law for Montana
Blog, Victims' Stories | Breeanne Howe | February 22, 2016
The most powerful voices in support of Marsy's Law are those individuals who have gone through the incredible pain of being victimized by crime and lived to tell about it. We've been sharing their stories with Montanans; here's one of those stories recently published in several Montana newspapers, including this excerpt from the Missoulian:
When I was 17, my 8-year-old brother Ryan was kidnapped, sexually assaulted and murdered by a repeat sex offender. That unthinkable experience is part of the reason I became a police officer, serving for 18 years in Montana.
My experiences also led me to start a national organization called Ryan United, dedicated to helping victims of child sexual assault and abduction. Today Ryan United has trained law enforcement officers in all 50 states on sex offender management, child abduction response, and how to relate with families who are in a painful situation.
And my experiences are also the reason that I'm such a staunch supporter of Marsy's Law for Montana, a proposed amendment to our state Constitution that would establish a Crime Victims' Bill of Rights.
Please click here to read this full story.
Get Involved Now
Click here to help us pass Marsy's Law in your state.
Help Pass Marsy's Law in Your State
We Can't Do This Alone. Join Our Effort To Pass Marsy's Law And Provide Equal Rights To Crime Victims.
Marsy's Law is named after Marsalee "Marsy" Nicholas. Marsy was stalked and killed by her ex-boyfriend in 1983.
Dr. Henry T. Nicholas
Dr. Nicholas has made it his mission to give victims and their families across the country constitutional protections.
Copyright © 2018 Marsy's Law for All.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: CLI Application with docker I building a CLI python application that takes a CSV file as argument input and various options
Example:
 rexona [-h] [-v | -q] [-o] filepath
My question is how to dockerize it in a way that when I run my docker file I can run the above command and pass in the specified arguments?
My current docker file
FROM python:3
WORKDIR .

COPY . .

CMD ["python","app.py"]

Should I also install an os image such as ubuntu, so that I can run cmd commands or is there a way to that in docker?
Apologies, I'm still new to docker.
Thanks

A: You need to add entry point for eg:
# Base image of the docker container
FROM python:3

# Copy the contents of the repo into the /app folder inside the container
COPY . /app
# Update the current working directory to the /app folder
WORKDIR /app

# Add your CLI's installation setups here using the RUN command
# If you have any pip requirements you can do that here
# RUN pip install --user -r requirements.txt

# Provdide a path to your cli apps executable
ENTRYPOINT [ "python", "script.py" ]

A: I also run into similar senario i solved it using Entry point
ENTRYPOINT [ "python", "script.py" ]

run script
docker run arg1 arg2 arg3...

And then in Python Program
import sys
print(sys.argv)

redpajama_set_name: RedPajamaStackExchange


text:
About ECTRIMS
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Can biomarkers help us move towards a more holistic approach to tackling MS?
Go back to ECTRIMS Hub
15 December 2022 • min read
MS Health
MSResearch
The development and validation of biomarkers is essential to furthering our understanding of disease progression and treatment response in individuals with MS. Given the highly variable nature of the MS disease course, reliable biomarkers are essential to facilitate treatment decisions, which can significantly impact long-term patient outcomes, and may, in the future, provide additional evidence in differential diagnoses. At ECTRIMS 2022 [1], several sessions highlighted new and reliable imaging and non-imaging biomarkers currently in development for MS. In addition, a symposium by the European Charcot Foundation [2] examined the importance of placing the patient at the centre of care in MS. Through the integration of patient-reported outcome (PRO) measures into clinical practice, it may be possible to garner further evidence regarding disease progression and treatment effects. When combined with information gathered via the application of biomarkers, this may facilitate a move towards more personalised treatment approaches for MS. In this edition of ECTRIMS Insights, we will examine some of the data presented at the 38th Congress of ECTRIMS [1] and explore the novel biomarkers that could become integrated into routine care of individuals with MS.
Imaging biomarkers in MS
Imaging plays an important role both in the differential diagnosis of MS and in the ongoing monitoring of disease activity and treatment response. Important insights into the underlying neurological pathology of MS, and disease progression, can be gained from imaging findings [3] such as gadolinium enhancements, brain atrophy patterns and chronic lesion phenotyping. Network neuroscience studies have improved our understanding of brain responses to complex cognitive tasks and have demonstrated how coordination among brain regions supporting executive function is required for cognitive flexibility. Brain networks in individuals with MS have been measured by means of structural, diffusion or resting-state functional magnetic resonance imaging (MRI), with longitudinal MRI measures used to study neurodegeneration. In MS, it has been noted that neurodegeneration begins in the thalamus before progressing towards the cortex [4], with network re-routing able to compensate for initial thalamic atrophy and so prevent clinical impairment. However, in later stages of the disease, re-routing becomes impossible and disease progression occurs. Multilayer modelling based on MRI and convolutional neural networks is currently being explored as a means of predicting disability level in individuals with MS.
Perilesional iron rims [5] have also been demonstrated to be a prognostic biomarker for long-term disability in individuals with MS. A longitudinal study conducted in 91 patients showed a correlation between baseline iron rim lesions and disability assessment scores, with greater numbers of lesions being a significant predictor of disability over a 12-year follow-up period (p≤0.05). Updated international consensus guidelines on the use of MRI in MS [6] from Magnetic Resonance Imaging in MS (MAGNIMS), the Consortium of Multiple Sclerosis Centers (CMSC) and the North American Imaging in MS Cooperative (NAIMS) were presented at the 38th Congress of ECTRIMS. Advocacy will be required to ensure dissemination and compliance with these guidelines, which suggest that the addition of spinal cord MRI for monitoring clinically stable relapsing remitting MS (RRMS) could reveal otherwise undetected disease activity.
Non-imaging biomarkers in MS
The search for non-imaging biomarkers in MS has often been hypothesis-driven, with blood panel screens or proteomic examination of blood or cerebrospinal fluid (CSF) being common strategies. Data on novel body fluid biomarkers [7] presented at the 38th Congress of ECTRIMS suggest that CSF biomarkers such as soluble vascular cell adhesion molecule-1 (sVCAM-1) may decrease following treatment, whilst proteomic analyses have demonstrated an upregulation of other proteins following treatment with agents such as natalizumab. Moreover, some CSF biomarkers were found to be associated with progressive forms of MS and so may assist in predicting long-term disease progression; such findings, however, require validation.
Recent studies examining blood-based biomarkers for MS have noted the importance of glial fibrillary acidic protein (GFAP) and neurofilament light (NfL) [8], with NfL being strongly associated with acute inflammatory activity and axonal damage. Findings from a large cohort study of 800 individuals with MS who were followed for over 12 years demonstrated a link between the timing and pattern of disease progression and blood NfL levels. Similarly, GFAP has been shown to be associated with inflammation, with significant decreases in GFAP levels noted following initiation of high efficacy therapies, such as natalizumab.
Patient-centred care and the role of patient-reported outcomes
Despite advances in MS care and the assessment of disease activity and treatment response using biomarkers, there remains an unmet need to more fully understand how MS may be affecting the individual. During the European Charcot Foundation Symposium [2] findings from the Patient-Reported Outcomes for MS (PROMS) project were shared. The use of digital health technologies has increased considerably following the COVID-19 pandemic. In particular, the use of mobile phone-based e-diaries provides MS patients with an opportunity to record and report factors such as daily clinical disease activity, psychological status and quality of life on an ongoing basis to provide a more accurate picture of the course of their disease. This approach could facilitate the integration of PROs into health policy and the everyday life of patients, effectively allowing individuals with MS to become researchers and assist in the quest to advance care and find solutions to the challenges faced when living with MS.
Promoting continued advances in research
ECTRIMS welcomes the continued investigation of potential biomarkers to monitor the progression and treatment of individuals with MS and the integration of PROs into patient care to provide a more holistic treatment approach. ECTRIMS applauds the efforts of the scientific community to constantly improve our understanding of how best to optimise patient care. We remain optimistic that ongoing research will continue to improve our knowledge of how best to treat individuals with all types of MS and how best to provide a personalised approach to care.
ECTRIMS Insights articles are produced with an intent of being a neutral source of information sharing and objective analysis for the MS and neuroscience community. Unless otherwise stated, cited information in our articles does equivocate official endorsement from ECTRIMS.
[1] ECTRIMS 2022. 38th Congress of the European Committee for Treatment and Research in Multiple Sclerosis. Available at: https://2022.ectrims-congress.eu/. Accessed December 2022.
[2] European Charcot Foundation Symposium: The patient at the centre – role of patient reported outcomes. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62739. Accessed December 2022.
[3] Free Commmunications 6: Imaging. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62819. Accessed December 2022.
[4] Scientific Session 2: A network disease. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62754. Accessed December 2022.
[5] Young Scientific Investigators' Session 2: Long-term outcomes and safety. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62785. Accessed December 2022.
[6] Scientific Session 9 MRI: Updated MAGNIMS-NAIMS-CMSC guidelines. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62794. Accessed December 2022.
[7] Hot Topic 3: Novel body fluid biomarkers. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62742. Accessed December 2022.
[8] Scientific Session 17: Blood-based biomarkers – when to implement. ECTRIMS 2022. Available at: https://vmx.m-anage.com/congrex/ectrims2022/en-GB/session/62823. Accessed December 2022.
Congrex


text:
Derailment of Amtrak train going 106 MPH could have been prevented with speed control system, NTSB says
Updated: May. 13, 2015, 11:20 p.m. |
Published: May. 13, 2015, 10:20 p.m.
Rebecca Forand | For NJ.com
If Amtrak train 188 had been equipped with a system that could control its speed, the deadly accident that occurred Tuesday night could have been avoided, the National Transportation Safety Board said Wednesday.
The Northeast Corridor train left Philadelphia's 30th Street station at 9:10 p.m. Tuesday on its way to New York's Penn Station, NTSB board member Robert Sumwalt announced at a press conference Wednesday evening, but shortly after that departure its engine and seven passenger cars all derailed, leaving seven dead and dozens injured.
During the Board's initial investigation, it has been determined that the train was traveling at more than double the 50 mile per hour maximum speed limit of the curve it eventually derailed on.
WATCH: Investigators comb scene of Philadelphia train crash
As the train approached the curve it was running at 106 miles per hour when the engineer applied an emergency braking system that brought it down to 102 mph just before it left the tracks, Sumwalt said.
While Amtrak does utilize a "positive train control system" called an Advanced Civil Speed Enforcement System (ACSES) in many of its trains, this particular one was not equipped with the feature.
"It is designed to enforce a certain speed to keep the train below its maximum speed," Sumwalt said. "We feel had such a system been installed this accident would not have occurred."
The NTSB is expected to be on the scene of the accident for about a week collecting evidence, interviewing the train's crew and passengers and investigating the incident, but they are not expected to rule on a definite cause of the accident until a full investigation is complete.
"Our mission is to find out not only what happened, but why it happened to prevent it from happening again," Sumwalt said.
Rebecca Forand may be reached at rforand@southjerseymedia.com. Follow her on Twitter @RebeccaForand. Find the South Jersey Times on Facebook.


GLOBAL - The World Organisation for Animal Health (OIE) has received reports from all three countries of recent outbreaks of highly pathogenic avian influenza (HPAI) caused by the H5N1 virus.
The outbreak in Nepal started on 26 January in the region of Pokhara. In all, 153 birds died from flocks described as 'backyard ducks and chickens and few commercial farms'.
The veterinary authority in Cambodia sent an Immediate Notification to OIE about a new outbreak of HPAI in village poultry in Takeo province, which is in the south of the country and borders Viet Nam. According to the report, there were 31,070 cases and 16,442 birds died. The outbreak started on 27 January.
The outbreak in Myanmar started on 2 February at Mayangone in Yangon region. The reports says that the farmer purchased the birds as pullets. The production system is battery cages. There are two buildings and each building has chickens. Around 100 out of 2,455 chickens died from 1 February 2010, and the rest of the flock was destroyed.


For three weeks, I had to take 2 mg of Estrace twice a day and during the last week, I had to do the Endometrin progesterone support vaginally. I fully expected to be a hormonal mess, but I felt no different. The last five days, I have had to add in 10 units per day of Lupron injections. The insomnia started almost immediately.
I finished the Estrace and Endometrin doses and am now awaiting my period to start so that I can go in for a baseline and get instructions to start stimming. My period should start on October 9th or 10th.
My mom is very tired but she has all this nervous energy. She has rearranged her closets, sorted clothing to donate, rearranged her sewing studio, and re-did the stuff in the kitchen cabinets. Oh… and she rearranged and organized the garage ! She has WAY too much nervous energy.
In regards to my mom's cancer diagnosis, I have been a bit reflective and very nervous. There are never any guarantees in life and anything could go wrong. I fear getting pregnant and having babies and she not being around to get to know then and for them to get to know her. I worry about meeting Mr. Right and her not being there to walk me down the aisle. My father and grandfather have been gone 14 years and 9 years respectively. So many thoughts rush into one's mind when faced with mortality. There is this quiet voice that keeps saying all will be well. I have to trust that and focus on staying calm through this cycle and being supportive of my mom.
My sisters and I are planning a tea for her the weekend before her surgery. We started this tradition of doing a tea when she had breast cancer 8 years ago and we started a foundation called Tea For 2 Foundation to educate and support persons affected by breast cancer.
With everything going on, I am looking forward to going on a short trip this weekend!
I am still trying to learn the ropes for EHarmony.com. That website is so confusing. I get a little ticked that they keep sending me matches that are 5 ft 6 or 5 ft 8…. I AM 5'11 and I wear ridiculous heels ! Once I am more familiar with the site, it may go a bit easier. With Match.com, I am chatting with a few guys. I will make an effort to go out on a few meet and greets next week when I get back. This is all so nerve wrecking. A few guys have asked me for my number, but I do not feel comfortable giving out my number just yet. It is so hard to get rid of people once they have your phone number. At least my phone has the block feature, but that will not work if they call from other numbers ! UGH. I guess I need to loosen up a bit, but I swear I do not want to meet Chester the Molester and then have to change my phone number. Maybe a burner phone will work?
This entry was posted in Uncategorized and tagged Acupuncture, Breast Cancer, Dating, Eharmony.com, IVF, Lupron, Match.com, Single Mother By Choice. Bookmark the permalink.
I am sending prayers up for your mother's procedures and this cycle of yours. You have a lot to balance here, I can't believe you're taking on dating to boot. You're a champion!
I'm excited for your trip. Enjoy the time away!
Sounds like you are going through a lot. I am going to pray for you and your mother!!


text:
dashing into trouble - why html comments break in firefox
[Or, When Minutiae Attack!]
Update 2011.10.17: a quick test in Firefox 6 and 7 suggests they've finally fixed this issue. With the suggestion that FF 3.6 will reach EOL in the near future, we might finally be able to say goodbye to this curious little problem.
There's a perennial question that pops up on email lists and from other developers. The question goes something like this:
"This page works fine in everything except Firefox and I can't tell why... it's showing an HTML comment as raw code..."
This problem usually boils down to a quirk in the way Firefox handles HTML comments. Most browsers only treat --> as a closing comment in HTML. However, Firefox also treats any instance of -- as a closing comment.
So, if you have a comment with two or more adjacent hyphens, you're in trouble. Both of these are out:
<!-- --------------- Blah --------------- -->
Blah blah blah -- then blah.</p>
Firefox will display the comment as raw code, instead of hiding the comment and its contents. The late Netscape Navigator did this too - in fact I first saw the problem in NN4, back in 2000.
The solution is simple, even if it's not always convenient: don't put adjacent hyphens inside an HTML comment. That's fine and dandy unless you have content authors who have a habit of using two hyphens instead of an em dash!
In any case, you either need to remove the adjacent hyphens, or if it's appropriate you can convert them to more correct characters.
If your page's content includes double hyphens and you're not allowed to modify it, then you're not going to be able to comment blocks of it out. Yes, that is indeed annoying.
is firefox wrong?
Technically, very technically, Firefox is right. The HTML 4 specification defines "--" as the comment delimiters; while "<!" and ">" are the markup declaration delimiters. From the spec:
White space is not permitted between the markup declaration open delimiter("<!") and the comment open delimiter ("--"), but is permitted between the comment close delimiter ("--") and the markup declaration close delimiter (">"). A common error is to include a string of hyphens ("---") within a comment. Authors should avoid putting two or more adjacent hyphens inside comments.
Information that appears between comments has no special meaning (e.g., character references are not interpreted as such).
Note that comments are markup.
...so, Firefox is not "wrong". It's just following the spec to the letter (or hyphen, as the case may be). The other browsers have gone with a more human-friendly interpretation of the spec.
so are all the other browsers wrong?
I don't think the other browsers are definitively wrong either. They still comply with a different interpretation. Personally I read the specification the same way: "any instance of -- followed by > or whitespace and > is a closing comment".
According to this interpretation, "-->" and "-- >" are valid closing comments, but "-- blah" is not. It's also a reasonably logical approach to say that since a closing comment should be "-->", then the browser should ignore anything which is not "-->". That's pretty much what a comment is there for, after all - to ignore stuff.
is the spec wrong?
Well the spec can't really be "wrong" I guess. It is what it is. But in this case I think the specification is a bit illogical:
I don't see the sense in random exceptions to rules - why specify vagueness? "this is the closing comment tag, except when it's not".
Why allow whitespace in the closing comment, when it's not allowed in the opening comment? If whitespace was prohibited the only valid interpretation would have been the complete "-->" and the whole problem goes away.
The "common error" note just confuses the issue. It does not say why including adjacent hyphens is an error, nor does it define any specific error handling method.
The double-hyphen approach can't be a technical requirement for producing a rendering engine, since the other browsers are able to restrict closing comments specifically to "-->".
It's impractical to expect that commented content will never contain multiple adjacent hyphens. Sure, we can live without hyphens in comments; but we shouldn't dictate content based on markup (no matter how small a detail it is).
And finally... it's irritating, so I'm going to be cranky at the spec ;)
Besides that, as the HTML5 spec notes, HTML has always been implemented by browsers as a language in its own right. There's no need to slavishly follow anything else. The more human interpretation could just as easily have been specified.
But then, comments appear to be a blind spot in W3C specs - how I curse the lack of a single-line comment in CSS... but I digress.
will html5 clear it up?
No. HTML5 actually makes things a little harder to remember, by addingdocumenting (hat tip zcorpan) the restriction that a comment can't end with a hyphen either:
Comments must start with the four character sequence U+003C LESS-THAN SIGN, U+0021 EXCLAMATION MARK, U+002D HYPHEN-MINUS, U+002D HYPHEN-MINUS (<!--). Following this sequence, the comment may have text, with the additional restriction that the text must not contain two consecutive U+002D HYPHEN-MINUS (-) characters, nor end with a U+002D HYPHEN-MINUS (-) character. Finally, the comment must be ended by the three character sequence U+002D HYPHEN-MINUS, U+002D HYPHEN-MINUS, U+003E GREATER-THAN SIGN (-->).
What's the saying about laws and sausages?
Perhaps there's some deep-seated syntactical reason for the double hyphen approach. The HTML4 spec's warning about "a common error" hints at some underlying logic without actually revealing it. Maybe it's related to the formatting of DTD comments. Maybe it was just a Netscape quirk which got turned into a standard. Maybe it's totally random.
It seems unlikely that Mozilla is going to change this particular detail, particularly as it's not a "bug" to follow the specifications; and besides, Firefox 3 Beta 2 still has the quirk.
Still, Firefox does correct omitted background colours by defaulting to white - so they're not above "helpful" rendering tricks. So maybe there's some hope on that front.
But in the meantime, no matter what we think we just have to live with it. It's yet another bit of web development minutiae to file away in your head, for the day you see it happen.
Filed under bug, comments, firefox, html, interpretation, netscape, problem, specifications, w3c
X-UA-Compatible: let sleeping intranets lie?
opt-out version targeting is spam
dashing into trouble - why html comments break in ...


text:
LAND DONATED FOR NEW ELEMENTARY SCHOOL IN CROWLEY DISTRICT
Land for a new elementary school for the master-planned community Chisholm Trail Ranch is being donated by developer The Walton Group of Companies, a statement released Tuesday says. The new school will be part of Crowley Independent School District, which has 23 campuses including 10 elementary schools, according to the district's…


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text:
Jason Derulo and Jena Frumes Split 4 Months After Welcoming Baby Boy
Jason Derulo and Jena Frumes Break Up
The pair recently welcomed their baby boy four months ago but have called it quits after dating for about three years. Jason Derulo announced the split on Thursday curiously after Jena Frumes shared that Derulo made her the "happiest girl in the world."
According to Derulo, he and Frumes decided to part ways but will continue to co-parent their 4-month-old son, Jason King.
"She is an amazing mother but we feel being apart at this time will allow us to be the best versions of ourselves and the best parents we could be," Derulo tweeted. "Pls respect our privacy in this time."
Jena and I have decided to part ways.
She is an amazing mother but we feel being apart at this time will allow us to be the best versions of ourselves and the best parents we could be. Pls respect our privacy in this time.
— Jason Derulo (@jasonderulo) September 23, 2021
Jena Frumes apparently was sure things were going well with her and Derulo. On Wednesday, she shared a birthday message sent to him on her Instagram account.
"You are the most handsome, hardworking, talented, silly, loving human ever," the TikTok creator gushed in a since-deleted Instagram post. "You truly make me whole and I'm so grateful for the love we share. You and our mini make me the happiest girl in the world and I can't wait to make more memories with you guys."
She continued, "I know I'm a tough cookie but you make me soft and accept me for who I am and I'm forever grateful for that. Cheers to another year! I love you so much, forever."
The pair started dating around 2019 after meeting at the gym and have shared their lockdown chronicles and their hilarious prank videos on Tik Tok.
Jena Frumes Jason Derulo Credit: Jena Frumes/Instagram
In March, they shared news of their pregnancy and that they were expecting a baby boy born in May 2021.
Jena had previously shared their parenthood journey of Jason Jr. on her Instagram account.
"When we have each other we have everything @jasonderulo," she penned on Instagram. "Baby boy is two months old now. He's the best and is the most smiley squirmy happy baby ever and loves spending time outdoors we are so in love."
Frumes has not addressed the news of the breakup.
A post shared by JENA (@jenafrumes)
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Elly van den Heuvel is an experienced manager, who has had a long career within cybersecurity. In 2014 she was appointed Secretary to the Dutch Cyber Security Council (CSR). The Dutch Cyber Security Council has 18 high level members from government, industry, and the scientific community. The CSR offers both solicited and unsolicited advice to the Cabinet. The Council also facilitates public-private dialogue on the complex matter of cyber security.
From 2008-2014, she was head of the National Cyber Security Centre (NCSC) and its predecessor GOVCERT.NL. During this period she focused on strengthening existing (inter)national joint ventures within the community. The NCSC is formed as a public-private partnership. Building a strong public private partnership had her special attention. Added to her achievements were building a sturdy foundation of trust with all stakeholders. She was responsible for the operational coordination of large incidents (including DIGINOTAR) in the critical infrastructure.


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text:
Q: How to attach a function to my package's namespace after it's loaded? This may seem like a weird question, but I do have a use case for it that I'm trying to figure out.
Suppose I'm writing a package and I have a function that I want to allow the user to alias to something else - the user provides the name of the function. I'm wondering what's the best way to achieve this?
#' @export
foo <- function() "Hello"
#' @export
addAlias <- function(x) assign(x, foo, envir = globalenv())

This is the behaviour I want to get - now the user can call addAlias("bar") and then if he calls bar() it'll be as if he called my function.
Obviously this is not a nice solution because it assigns to the global environment.  Does anyone have feedback on what would be the best way to do this? A few methods I tried:
1. Assigning to globalenv
Just like I showed in the example. This seemed to work.
2. Assigning to the package's environment
addAlias <- function(x) assign(x, foo, as.environment("package:mypackage"))

This worked great for a while until I realized that it only works with devtools and not if the package is loaded properly because of locked environments
3. Attaching a new env to the searchpath
.onLoad <- function(libname, pkgname) {
  assign("aliases", new.env(), envir = parent.env(environment()))
  attach(aliases)
  invisible()
}

addAlias <- function(x) assign(x, foo, aliases)

This I don't like because of the use of attach.  Is it warranted in this case?  When would I detach?
4. Expose a separate named environment
#' @export
#' @keywords internal
aliases <- new.env()

addAlias <- function(x) assign(x, foo, aliases)

This works, but instead of being able to call bar(), the user needs to call alises$bar() or mypackage::aliases$bar().  I don't like that, but it was an interesting experiment. I also don't know if it's ok to export a variable like that?
Any help is appreciated

A: I think a more appropriate way is to use closure.
#' @export
foo <- function() "Hello"
#' @export
getfoo <- function() {
    function(){
        # do anything, including running foo()
        foo()
    }
}

With this, you can do
> bar <- getfoo()
> bar()
[1] "Hello"


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Great news, our one year old Friends of Heaton Chapel Station group were nominated for FOUR ACoRP [Association of Community Rail Partnership] awards this year.
On Friday 29th September 2012, four FofHCS members, Rory Alkin, Karen Allerton, Bob Barlow and Phil Rowbotham were all invited to a Community Rail Awards ceremony at the STEAM museum at Swindon as we'd been nominationed for four awards [there are a total of 15 categories of awards; we'd only applied for 4].
Apparently, no new group has ever been nominated before for so many awards. These awards can be won by any of the hundreds of Friends of Stations groups covering the whole of Britain and it's 2,953 railway stations .
We were delighted to receive awards in each of these four separate categories, particularly winning the Community Art Scheme award for the 'Running Man' , when we were thrilled to win first prize.
This was a community project including children from local schools so we'd like to thank everyone who was involved as well as the local businesses who kindly sponsored this project.


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Originally published as: Alonso, D. (2017). Socioeconomic development in the context of Uruguay: A knowledge-based approach. Competitiveness Review, 27(5), 476-494. Article available here.
Purpose: The purpose of this exploratory study is to examine the relevance and impact of knowledge in the context of Uruguay's present and future socioeconomic development through the lens of the knowledge-based theory of the firm (KBTF). Design/methodology/approach: The perspectives of 47 key informants, predominantly representatives of public and private Uruguayan institutions, including chambers of commerce and producer associations, were gathered through unstructured, face-to-face interviews. Findings: Aligned with the KBTF, the significance of tacit knowledge, complemented with explicit knowledge, was revealed, particularly in the more traditional industries. Indeed, industry-based (tacit) knowledge evolving for generations has been strengthened by innovative practices, enhancing the appeal and image of key commodities and the nation's exports. Additional elements highlighted in the KBTF, such as problem-solving, knowledge integration and application and knowledge specialisation, were identified. Originality/value: Essentially, the study highlights the different associations between the KBTF, the various forms of acquiring knowledge (tacit, explicit), innovation and resulting impacts on food quality and increased product recognition for a developing economy. Moreover, the findings, which illustrate that crucial improvements can be achieved through knowledge-based approaches, could also be considered in the context of other emerging economies that are aiming to attain further socioeconomic development through maximising the benefits of knowledge. In addition, the study addresses a theme that has been sporadically presented in the academic literature, especially when studying developing economies and their industries.


text:
package six.ca.droiddailyproject.drawable;

import android.graphics.Canvas;
import android.graphics.ColorFilter;
import android.graphics.Paint;
import android.graphics.PixelFormat;
import android.graphics.Rect;
import android.graphics.drawable.Drawable;

/**
 * First sample of custom drawable
 * Created by Xiaolin on 2016-05-28.
 */
public class CustomDrawable extends Drawable {
    private Paint mPaint;

    public CustomDrawable(int color){
        mPaint = new Paint(Paint.ANTI_ALIAS_FLAG | Paint.DITHER_FLAG);
        mPaint.setColor(color);
    }

    @Override
    public void draw(Canvas canvas) {
        final Rect bounds = getBounds();
        float cenX = bounds.exactCenterX();
        float cenY = bounds.exactCenterY();
        canvas.drawCircle(cenX, cenY, Math.min(cenX, cenY), mPaint);
    }

    @Override
    public void setAlpha(int alpha) {
        mPaint.setAlpha(alpha);
        invalidateSelf();
    }

    @Override
    public void setColorFilter(ColorFilter colorFilter) {
        mPaint.setColorFilter(colorFilter);
        invalidateSelf();
    }

    @Override
    public int getOpacity() {
        return PixelFormat.TRANSLUCENT;
    }
}

redpajama_set_name: RedPajamaGithub


text:
The Russia 'Fake News' Scare Is All About Chilling Speech
By David Harsanyi
Last week, Republicans began to call for the release of a memo authored by House Intelligence Committee Chairman Devin Nunes that purports to lay out a series of abuses connected to the FBI surveillance of Donald Trump's 2016 presidential campaign. As often happens these days, a Twitter hashtag, #ReleaseTheMemo, evolved around the effort and was widely retweeted by Republicans and elected officials.
It didn't take long for a report to emerge that claimed Russian-sponsored Twitter accounts and bots were the real driving force behind the viral call for the release of the memo. Without worrying about the veracity of this convenient claim, all the usual suspects giddily spread the story across social media — probably because they have such a deep reverence for truth in the Era of Trump.
The report also prompted Sen. Dianne Feinstein and Rep. Adam Schiff, both Democrats, to pull out every fearmongering catchphrase available to demand that Twitter CEO Jack Dorsey and Facebook CEO Mark Zuckerberg perform an "in-depth forensic examination" on the "ongoing attack by the Russian government through Kremlin-linked social media actors directly acting to intervene and influence our democratic process."
It's difficult, it seems, for some people to embrace neutral principles nowadays. But if you genuinely believe that President Donald Trump's distasteful tweets are attacks on the foundations of free expression, how could you not be alarmed by a pair of powerful elected officials demanding that social media companies hand over information about their users? What would they say if the president had sent a letter to Google insisting it give the executive branch an "in-depth forensic examination" of his political opponent's searches?
As it turns out, reports today say that Twitter's internal analysis found it was mostly Americans, not creepy Slavic mind-control robots, who were behind the hashtags. Not that it really matters, anyway. If a group of Americans has a legitimate issue to rally around, how is it supposed to control what outsiders do? It's not as if #ReleaseTheMemo was secret or illegal. Republican politicians were openly using it.
Yet if Feinstein and Schiff had their way, Twitter and Facebook would have moved to quash the #ReleaseTheMemo hashtag for what apparently turned out to be solely partisan reasons. Sounds like a power that can be abused. Even if the two had been genuinely troubled by Russian hashtags — yes, suspend your disbelief — the source of "fake news" is not always easily discernible. Sometimes it comes to you from an anonymous Russian bot, and sometimes it's retweeted by a prominent journalist.
Democrats have manufactured panic over amateurish Russian propaganda to not only claim that Russian President Vladimir Putin was "meddling" in the election but also to argue that interference had the power to turn the election to Trump. With this risible idea in hand, they have created paranoia about social media interactions and rationalized infringements on expression.
Not long before demanding forensic investigations into hashtags, Feinstein was demanding that Twitter, Facebook and Google restrict their content more tightly, threatening, "Do something about it — or we will." Democrats have attempted to control interactions through the Fairness Doctrine or the IRS, and now through the Russia scare. Part of living in a free country is dealing with messy, ugly misinformation.
Lots of people in the United States seem pretty impressed by how they do things in Europe. In Britain, Prime Minister Theresa May is launching a "rapid response unit" run by the state to "battle the proliferation of 'fake news' online." The "national security communications unit" will be tasked with combatting misinformation — as if it has either the power or ability to do so. In France, President Emmanuel Macron is working on a plan to combat "fake news," which includes the power to institute an emergency block on websites during elections. What could possibly go wrong?
Me? I'd rather we live with Russian troll bots feeding us nonsense than authoritarian senators dictating how we consume news. I mean, has anyone yet produced a single voter who lost his free will during the 2016 election because he had a Twitter interaction with an employee of a St. Petersburg troll farm? Or do voters tend to seek out the stories that back their own worldviews?
If your argument is that Americans are uninformed and easily misled, I'm with you. Just look at all the people who believe that a $46,000 buy on Facebook by the Russians was enough to destroy the pillars of our democracy. But if you want to live in a free and vibrant nation, you have to live with the externalities of that freedom.
David Harsanyi is a senior editor at The Federalist and the author of the forthcoming "First Freedom: A Ride through America's Enduring History with the Gun, From the Revolution to Today." To read features by other Creators Syndicate writers and cartoonists, visit the Creators Syndicate webpage at www.creators.com.
opinion conservative social media russia election fisa devin nunes trump campaign fake news meddling releasethememo bots
About David Harsanyi
Contact David Harsanyi


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text:
\section{Introduction}

Topological theory of the band structure began, albeit implicitly, with the work of
Thouless, Kohmoto, den Nijs, and Nightingale on the quantized Hall conductance in
a two-dimensional model of electron motion~\cite{TKNN}. The transverse conductivity of a
filled band was identified with what is known as the first Chern number in mathematics of the same band. It was immediately established afterwards that general non-interacting bands were characterized by Chern numbers~\cite{Simon}. While the original model analyzed by Thouless {\it et al}., namely the Harper's model~\cite{harper}, contained a myriad of sub-bands and Chern numbers at general rational filling factors, Haldane was later able to produce a simple two-band model that contained a non-zero Chern number $\pm 1$~\cite{Haldane}. Three-band generalization in the context of the kagome lattice model was done by Ohgushi, Murakami, and Nagaosa, where the Chern numbers were +1, 0, -1~\cite{OMN}. Later theoretical studies showed how the Chern numbers in their respective models are related to the Skyrmion structure in the Brillouin zone (See Refs. \onlinecite{varma,go-3band} and references therein).

Search for models with higher Chern numbers began in a flurry in recent years employing a diversity of ideas such as extended hopping and the multi-layer extension~\cite{ran,das-sarma,niu}. Without exception, all these models consider extensions of the original Hamiltonian in the {\it real space}. In this paper, we explore the contrasting path to view the Chern-number-changing process in the {\it momentum space}. It is well known, for two-band models, that a given Chern number corresponds to the monopole charge associated with the two-component spinor wave function~\cite{nakahara}. By exploiting this fact, we establish the existence of certain unitary transformations carrying the extra topological numbers in the form of singular gauge potentials. The unitary transformation provides a convenient path for obtaining lattice models with arbitrary Chern numbers by changing the monopole charge.

The idea of topology-changing unitary operation applies to the three-band case as well, but now one manipulates a pair of monopole charges instead of one as in the two-band problem. There is no shortage of condensed matter and cold atom systems that fit within the three-band framework, as recent vigorous investigation of their topological properties have demonstrated (See Ref. ~\cite{jo} and references cited therein). Our scheme can be applied to existing three-band models as a ready recipe for generating their higher-Chern-number derivatives.

\section{Two-band Chern number engineering: review}
\label{sec:two-band}

We begin by summarizing several well-known facts about the two-band Hamiltonian. An arbitrary two-band Hamiltonian in momentum $(\v k)$ space can be written as

\begin{eqnarray} {\cal H} (\v k ) = -\v d(\v k) \cdot \bm \sigma , \label{eq:2.1}\end{eqnarray}
involving the Pauli matrix $\bm{\sigma}= (\sigma^x, \sigma^y, \sigma^z )$ and a smooth three-component vector $\v d(\v k)$, without the uniform part $\varepsilon(\v k)\mathbb{I}_{2\times2}$ that has no effect on the band topology. Any other Hamiltonian related to this one by a unitary
transformation $U(\v k)$,
\begin{eqnarray} {\cal H}' (\v k) = {\cal U} (\v k) {\cal H} (\v k) {\cal U}^\dag (\v k), \end{eqnarray}
must possess the same band energies $\pm |\v d(\v k)|$. Wave functions of the new Hamiltonian, $|\psi'_i (\v k)\rangle$, are related to $|\psi_i (\v k)\rangle$ of the old ${\cal H}(\v k)$ through

\begin{eqnarray} |\psi'_i  (\v k) \rangle = {\cal U} (\v k) |\psi_i (\v k) \rangle, \end{eqnarray}
where $i$ stands for the band index. The geometric connection~\cite{nakahara,Simon} for the new state is obtained by
\begin{eqnarray} \v a'_{i} (\v k) \!=\! \v a_{i} (\v k)  \! -\! i \langle \psi_i (\v k)| {\cal U}^\dagger
(\v k) \partial_{\v k}  {\cal U} (\v k) |\psi_i (\v k) \rangle , \label{eq:vector_potential}\end{eqnarray}
$\v a_{i} (\v k) = -i \langle \psi_i (\v k)|\partial_{\v k}|\psi_i (\v k) \rangle$. The Chern number for the $i$-th band of the new Hamiltonian is therefore to be obtained from integrating the curl of the new gauge potential $\v a'_i (\v k)$ which may, in principle, differ from the old one due to the singular contribution of the unitary matrix.

Writing the two-band model (\ref{eq:2.1}) in the form (dropping the $\v k$ label)
\begin{eqnarray} {\cal H} = - d \left(
                       \begin{array}{cc}
                       \cos \theta & e^{-i \phi} \sin \theta\\

                        e^{i \phi} \sin \theta & -\cos \theta  \\
                       \end{array} \right)\label{eq:twoband_Hamiltonian}\end{eqnarray}
where $d$ stands for the magnitude $|\v d|$ and the unit orientation vector $\hat{d} =
(\sin \theta \cos \phi , \sin \theta \sin \phi , \cos \theta )$ is introduced, the two
eigenstates of the Hamiltonian are
\begin{eqnarray} |\psi_\uparrow \rangle = \left(
                       \begin{array}{c}
                          \cos \frac{\theta}{2} \\
                        e^{i \phi} \sin \frac{\theta}{2} \\
                       \end{array} \right), ~
|\psi_\downarrow\rangle = \left(\begin{array}{c} -e^{-i \phi} \sin \frac{\theta}{2} \\
                        \cos \frac{\theta}{2} \\ \end{array}
                     \right). \label{eq:cp1}
\end{eqnarray}

\begin{figure}[t]
\includegraphics[width=80mm]{fig1.eps}
\caption{(color online) Schematic representation of the monopole charge-changing unitary operation in the two-band model. $U$ operation changes the winding number of the polar angle $\theta$ by $\theta \rightarrow p \theta$ ($p=2$ in the above left). $V$ operation changes the winding number of the azimuthal angle $\phi \rightarrow n \phi$ which increases the Chern number by $n$ ($n=2$ in the above right).}
\label{fig1}
\end{figure}

We now introduce unitary matrices to manipulate the Chern number. The scheme is based on the pedagogical observation that the Hamiltonian ${\cal H}$ is diagonalized with the unitary matrix

\begin{eqnarray} U=\begin{pmatrix} \cos {\theta\over 2} & - e^{-i\phi} \sin {\theta\over 2} \\
e^{i\phi} \sin {\theta \over 2} & \cos {\theta \over 2} \end{pmatrix}, ~~ U^\dag {\cal H} U = -d \sigma^z . \label{eq:2.7} \end{eqnarray}
The diagonal Hamiltonian $-d \sigma^z$ carries trivial eigenstates $(1,0)$ and $(0,1)$ and have no topology associated with it. Therefore, the topological charge of ${\cal H}$ must have been planted there by the unitary matrix $U$. In other words, $U$ is a singular gauge that contributes non-zero flux in Eq. (\ref{eq:vector_potential}). And if one such unitary rotation could turn a non-topological Hamiltonian $-d \sigma^z$ into a topological one, what would be the consequence of implementing the same unitary rotation, say $n$ times?

In order to make the discussion fully general we introduce a second unitary rotation that changes the azimuthal angle $\phi$ in the Hamiltonian by one unit, $e^{i\phi} \rightarrow e^{2i\phi}$:

\begin{eqnarray} V = \begin{pmatrix} e^{-i \phi/2}  & 0 \\ 0 & e^{i \phi/2} \end{pmatrix}. \label{eq:2.14}\end{eqnarray}
We then combine the two unitary transformations as one general operation,

\begin{eqnarray} {\cal U}^{(p,n)} = [V]^{n-1} [U]^{p-1} ,\end{eqnarray}
which results in the change of the Hamiltonian

\begin{eqnarray} {\cal{H}}^{(p,n)}&=& -d {\cal U}^{(p,n)} \begin{pmatrix} \cos \theta  &  e^{-i \phi}  \sin \theta \\ e^{i \phi}
\sin \theta & -\cos \theta  \end{pmatrix} [{\cal U}^{(p,n)}]^\dag \nonumber \\
 %
 ~~ &=&  -d \begin{pmatrix} \cos p\theta  &  e^{-i n\phi}  \sin p\theta \\ e^{i n\phi} \sin p\theta & -\cos
p\theta  \end{pmatrix} .  \end{eqnarray}
In this notation, $\hat{d}=(\sin \theta \cos \phi, \sin \theta \sin \phi, \cos \theta)$ in the original Hamiltonian becomes $\hat{d}^{(1,1)}$. Generally,

\begin{eqnarray} && \hat{d}^{(p,n)} = (\sin p \theta \cos n \phi , \sin p\theta \sin n \phi , \cos p\theta), \nonumber \\
&& {\cal H}^{(p,n)} = -d  \hat{d}^{(p,n)} \cdot \bm \sigma .  \end{eqnarray}
The ${\cal U}^{(p,n)}$-transformed wave functions are

\begin{eqnarray} |{\psi}_\uparrow^{(p,n)}\rangle &=& {\cal U}^{(p,n)} |\psi_\uparrow^{(1,1)}\rangle
=\left(\begin{array}{c}
e^{-i \frac{n \phi}{2}}\cos \frac{p\theta}{2} \\
e^{i \frac{n \phi}{2}} e^{i \phi} \sin \frac{p\theta}{2} \\
\end{array} \right),\\
|{\psi}_\downarrow^{(p,n)}\rangle&=&{\cal U}^{(p,n)} |\psi^{(1,1)}_\downarrow
\rangle
=\left(
\begin{array}{c}
-e^{-i \frac{n \phi}{2}}e^{-i \phi} \sin \frac{p\theta}{2}  \\
e^{i \frac{n \phi}{2}}\cos \frac{p\theta}{2} \\
\end{array} \right)\nonumber. \label{eq:nthVwaveft}\end{eqnarray}
The reference states $|\psi^{(1,1)}_{\uparrow,\downarrow}\rangle$ are the ones given in Eq. (\ref{eq:cp1}). Vector potentials and the magnetic field through the unit sphere~\cite{nakahara} associated with them are

\begin{eqnarray} a^{(p,n)}_{\uparrow,\phi} &=& \frac{1-n\cos p\theta}{2\sin \theta}, ~
a^{(p,n)}_{\uparrow,\theta} =0, \nonumber \\
{\v B}^{(p,n)}_{\uparrow} &=& n p \frac{ \sin p \theta}{2\sin \theta} \hat{r} = -{\v B}^{(p,n)}_{\downarrow} . \label{eq:nthV_vectorpotential} \end{eqnarray}
Charge of the magnetic monopole is obtained by integrating $\v B^{(p,n)}_\uparrow$ over the unit sphere,

\begin{eqnarray} C^{(p,n)}_{\uparrow}= n P = - C^{(p,n)}_{\downarrow}, ~ ~ P = {1- (-1)^p \over 2} .
\label{eq:UV_Chern_number}\end{eqnarray}
Therefore, a series of two-band Hamiltonians ${\cal H}^{(p,n)}$ related by unitary transformations must have identical dispersions and yet possess distinct Chern numbers

\begin{eqnarray} C^{(p,n)}=\frac{1}{4\pi} \int_\mathrm{BZ} ~ \hat{d}^{(p,n)} \cdot  \left(
{\partial \hat{d}^{(p,n)} \over \partial k_x} \times {\partial \hat{d}^{(p,n)} \over \partial
k_y } \right) . \nonumber \end{eqnarray}
The Chern number defined here agrees exactly with the magnetic charge given in Eq. (\ref{eq:UV_Chern_number}). Figure \ref{fig1} summarizes the monopole charge-changing operations discussed in this section.

\section{Three-band Chern number engineering}
\label{sec:three-band}

\subsection{Mathematical preliminary}
\label{sec:three-band-mathematical-preliminary}

Chern numbers are derived from the connection, which in turn is derived from the knowledge of the wave function.  Finding eigenfunctions of a given 3$\times$3 Hamiltonian in closed form is exceedingly difficult. On the other hand, it is much easier to do the reverse: express an arbitrary 3$\times$3 Hamiltonian from the knowledge of all three orthogonal eigenfunctions along with their energies. We build heavily upon the work of Byrd and collaborators~\cite{byrd} to show how to do this, and then apply the idea of unitary transformations to generate arbitrary Chern numbers for the bands.

A Hermitian matrix with three eigenvalues $(e_1 , e_2 , e_3 )$ are
found as the SU(3) rotation,

\begin{eqnarray} {\cal H} = {\cal U} \begin{pmatrix} e_1 &  0 & 0 \\ 0 & e_2 & 0 \\ 0 & 0 & e_3 \end{pmatrix} {\cal U}^\dag , ~
{\cal U} \in \mathrm{SU(3)} . \label{eq:SU(3)-rotation}\end{eqnarray}
The general SU(3) ${\cal U}$ can be expressed as a series of U(1) and SU(2) rotations,

\begin{eqnarray} {\cal U} = {\cal U} (\alpha, \beta, \gamma) e^{i \delta \lambda_5 /2 } {\cal U}
(a, b, c) e^{i d \lambda_8 /2}, \label{eq:SU(3)-Euler} \end{eqnarray}
where ${\cal U} (\alpha, \beta, \gamma)$ is an element of SU(2) given by

\begin{eqnarray} {\cal U} (\alpha, \beta, \gamma ) = e^{i \alpha \lambda_3 /2 } e^{i \beta \lambda_2
/2} e^{i \gamma \lambda_3 /2 }. \end{eqnarray}
Ranges of the parameters are~\cite{byrd}

\begin{eqnarray} && 0 \le \alpha, \gamma, a, c < 2 \pi, \nonumber \\
&&  0 \le \beta, \delta, b \le {\pi},~~ 0 \le d \le 2 \sqrt{3} \pi.
\label{eq:range-of-angles}\end{eqnarray}
Dependence of the parameters in the unitary matrix ${\cal U}$ and the three energies $e_i$ on the two-dimensional momentum $\v k$ of the Brillouin zone will be implicit throughout the discussion.

We display the representation of Gell-Mann matrices used in this paper:

\begin{eqnarray} \lambda_1 = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} ,  &&  \lambda_2 = \begin{pmatrix} 0 &
-i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} , \nonumber \\
\lambda_3 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{pmatrix} , &&
\lambda_4 = \begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{pmatrix} , \nonumber \\
\lambda_5 = \begin{pmatrix} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{pmatrix} , &&
\lambda_6 = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} , \nonumber \\
\lambda_7 = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{pmatrix} , &&
\lambda_8 = {1\over\sqrt{3}} \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{pmatrix} . \end{eqnarray}
Acting out the unitary rotation (\ref{eq:SU(3)-rotation}) reveals that, out of the eight
angles that define the SU(3) matrix, the two angles $c$ and $d$ drop out in the final
expression of the Hamiltonian. The space of 3$\times$3 Hermitian matrices with a fixed set of energies $(e_1  , e_2 , e_3 )$ is equivalent to
SU(3)/(U(1)$\times$U(1)).

Recall that the unitary matrix diagonalizing a particular Hamiltonian consists of the eigenstates of the same Hamiltonian. The matrix elements of ${\cal U}$ in the parametrization (\ref{eq:SU(3)-Euler}), with $c=d=0$, become the three eigenstates of the Hamiltonian,

\begin{eqnarray} |\psi_1 \rangle &=& \cos \frac{b}{2}~ |u
\rangle- \sin \frac{b}{2}~ |v \rangle , \nonumber \\
|\psi_2 \rangle &=& \sin \frac{b}{2}~ |u
\rangle + \cos \frac{b}{2}~ |v \rangle ,\nonumber \\
|\psi_3 \rangle  &=&   | w \rangle,
\label{eq:3-eigenstates}\end{eqnarray}
with energies $e_1, e_2, e_3$, respectively. The three orthonormal basis vectors are

\begin{eqnarray} |u \rangle &=& e^{i \frac{1}{2}a} \begin{pmatrix} e^{i \frac{1}{2}(\alpha + \gamma)} \cos
\frac{\beta}{2} \cos \frac{\delta}{2} \\ -e^{-i \frac{1}{2}(\alpha-\gamma)} \sin \frac{\beta}{2} \cos \frac{\delta}{2} \\ - \sin \frac{\delta}{2} \end{pmatrix} ,\nonumber \\
|v \rangle &=& e^{-i \frac{1}{2} a} \begin{pmatrix} e^{i \frac{1}{2}(\alpha - \gamma)} \sin \frac{\beta}{2}\\
e^{-i\frac{1}{2} (\alpha+\gamma)} \cos \frac{\beta}{2}  \\ 0 \end{pmatrix}, \nonumber \\
|w \rangle &=&\begin{pmatrix} e^{i\frac{1}{2} (\alpha + \gamma)} \cos \frac{\beta}{2}
\sin \frac{\delta}{2} \\ -e^{-i\frac{1}{2} (\alpha-\gamma)} \sin \frac{\beta}{2} \sin \frac{\delta}{2} \\
\cos \frac{\delta}{2} \end{pmatrix}. \label{eq:uvw-basis} \end{eqnarray}
An arbitrary $3\times3$ Hamiltonian having $|\psi_i\rangle$ as eigenstates with energies $e_i$ is

\begin{eqnarray} {\cal H} &=& \sum_i e_i |\psi_i \rangle \langle \psi_i | \nonumber \\
&=& {1\over 2} \Bigl( [e_1 \!+\! e_2 ] + [e_1 \!-\! e_2 ] \cos b \Bigr) |u\rangle \langle u | \nonumber \\
&+& {1\over 2} \Bigl( [e_1 \!+\! e_2 ] - [e_1 \!-\! e_2 ] \cos b \Bigr) |v \rangle \langle v | \nonumber \\
&+& {1\over 2} (e_2 \!-\! e_1 ) \sin b  \bigl(|u\rangle \langle v| + |v
\rangle \langle u | \bigr) \nonumber \\
&+& e_3 |w \rangle \langle w | . \label{eq:4.8}\end{eqnarray}

As we are mainly concerned with the Chern number structure of the three-state Hamiltonian, we proceed to construct a general formula for the curvature of each eigenstate by adopting the projection operator method of Avron, Seiler, and Simon~\cite{Simon}. The
projection operator for each eigenstate $|\psi_i \rangle$ is, $\bm \lambda = (\lambda_1, \cdots, \lambda_8)$,

\begin{eqnarray} P_i &=& |\psi_i \rangle \langle \psi_i |  = {1 \over 3}(1+\sqrt{3} \v n_i \cdot \bm
\lambda) , \nonumber \\
\v n_i &=& {\sqrt{3} \over 2}\langle \psi_i | \bm \lambda | \psi_i \rangle .
\end{eqnarray}
One can check that $\v n_i$ is an object on the unit seven-sphere, $\v n_i \in S^7$. The Berry curvature for each $|\psi_i\rangle$ is conveniently expressed with $\v n_i$,

\begin{eqnarray} {\cal F}_i &=& -i \Bigl(\langle \partial_{x} \psi_i |\partial_{y} \psi_i \rangle \!-\!
\langle \partial_{y} \psi_i |\partial_{x} \psi_i \rangle\Bigr) \nonumber \\
&=&  {4 \over 3 \sqrt{3} }\v n_i \cdot \Bigl( {\partial \v n_i \over
\partial x} \times { \partial \v n_i \over
\partial y}\Bigr) , \label{eq:generalized-MH} \end{eqnarray}
where $(x,y)$ spans the coordinates of the base space. The cross product in the above formula is defined with the aid of structure constants of SU(3),

\begin{eqnarray} \lambda_a \lambda_b &=& {2 \over 3} \delta_{ab} + i f_{abc} \lambda_c + d_{abc} \lambda_c ,  \nonumber \\
(\v u \times \v v )_a &=& f_{abc} u_b v_c. \end{eqnarray}
The inner product $\cdot$ is defined in the usual way of multiplying the matching components. Equation (\ref{eq:generalized-MH}) for the Berry curvature ${\cal F}_i$ in terms of $\v{n}_i \in S^7$ in the three-band Hamiltonian is a new result of our work. The formula derived in Ref.~\cite{galitski} is equivalent to ours, but more complicated in appearance. We note as a further fact of mathematical curiosity that the star product, $(\v u * \v v)_a =\sqrt{3} d_{abc}u_b v_c$, between a pair of $\v n_i$'s obeys the relation

\begin{eqnarray} \v n_i * \v n_j =\delta_{ij} \v n_j + |\varepsilon_{ijk}| \v n_k.
\label{eq:constraintS7}\end{eqnarray}
This is an extension of the result found in Ref. \onlinecite{galitski} which only focused on the $i=j$ case.

This concludes the mathematical preliminary for the discussion of topological number-changing unitary operations in the three-band model. Due to the enormous complexity of the algebra involved in the following discussion, we will be forced to consider a slightly restricted space of Hamiltonians by taking $b=0$ in the parametrization of the unitary matrices. Such restriction will not present any barrier in generating arbitrary Chern numbers for the three-band model.

\subsection{A pair of monopoles in the three-band model}
\label{three band chern number changing}

With the $b=0$ restriction in place, the wave functions become simpler, $|\psi_1 \rangle = |u \rangle$, $|\psi_2 \rangle = |v \rangle$, and $|\psi_3 \rangle = |w\rangle$. The connection for each state is

\begin{eqnarray} -i \langle u | \partial_\mu | u \rangle &=& \frac{1}{2} \partial_\mu a +  \frac{1}{2}
\cos \beta  \cos^2 \frac{\delta}{2} ~ \partial_\mu \alpha +   \frac{1}{2}\cos^2
\frac{\delta}{2}  ~\partial_\mu \gamma, \nonumber \\
-i \langle v | \partial_\mu | v \rangle &=& - \frac{1}{2}\partial_\mu a -\frac{1}{2}\cos
\beta~ \partial_\mu \alpha - \frac{1}{2}\partial_\mu \gamma, \nonumber \\
-i \langle w | \partial_\mu | w \rangle &=& \frac{1}{2}\cos \beta  \sin^2
\frac{\delta}{2}~ \partial_\mu \alpha + \frac{1}{2} \sin^2 \frac{\delta}{2}~\partial_\mu
\gamma. \end{eqnarray}
Their Berry curvatures are

\begin{eqnarray} {\cal F}_u dxdy &=&  {1\over 4} \sin \beta (d \alpha \wedge d \beta) \!+\! {1\over 4} \sin
\delta (d \gamma \wedge d \delta)  \nonumber \\
&& ~~ \!+\! {1 \over 8} \sin [\beta \!+\! \delta]\Bigl(d \alpha \wedge d (\beta \!+\! \delta)\Bigr)  \nonumber \\
&& ~~~~ \!+\! {1 \over 8} \sin [\beta \!-\! \delta]\Bigl(d \alpha \wedge d (\beta \!-\! \delta)\Bigr), \nonumber \\
{\cal F}_v dxdy & = & -\frac{1}{2} \sin \beta (d\alpha \wedge d \beta), \nonumber \\
{\cal F}_w  dxdy &=& {1\over 4}  \sin \beta (d \alpha \wedge d \beta) \!-\! {1\over 4} \sin
\delta (d\gamma \wedge d \delta )  \nonumber \\
&& ~~ \!-\! {1 \over 8}\sin [\beta\!+\!\delta] \Bigl(d \alpha \wedge d (\beta \!+\! \delta)\Bigr) \nonumber \\
&& ~~~~ \!-\! {1 \over 8}\sin [\beta\!-\!\delta] \Bigl(d \alpha \wedge d (\beta \!- \!\delta)\Bigr) . \label{eq:Fxy-uvw}\end{eqnarray}
A wedge product $\wedge$ is defined by

\begin{eqnarray} d \alpha \wedge d \beta \!=\! \Bigl( {\partial \alpha \over \partial x} {\partial
\beta \over \partial y} \!- \!{\partial \alpha \over
\partial y} {\partial \beta \over \partial x} \Bigr) dx dy
\!=\! - d \beta \wedge d \alpha. \end{eqnarray}
The three Berry curvatures add up to zero~\cite{Simon}. Let us introduce four ``integers" (integrals of solid angles over a unit sphere divided by $4\pi$)

\begin{eqnarray} N_1 &=& {1 \over 4\pi}\int \sin \beta (d \alpha \wedge d \beta),\nonumber \\
N_2 &=& {1 \over 4\pi}\int \sin \delta (d \gamma \wedge d \delta ), \nonumber \\
N_3 &=& {1 \over 4\pi}\int \sin [\beta+\delta] \Bigl(d \alpha \wedge d (\beta+\delta)\Bigr),\nonumber \\
N_4 &=& {1 \over 4\pi}\int \sin [\beta-\delta] \Bigl(d \alpha \wedge d (\beta-\delta)\Bigr),
\label{eq:3.18}\end{eqnarray}
and express the Chern number of each band in terms of them as

\begin{eqnarray} C_u &=& {1\over 2} ( N_1 +  N_2 ) +{1\over 4} ( N_3 + N_4 ) , \nonumber \\
C_v &=& - N_1 , \nonumber \\
C_w &=& {1\over 2} ( N_1 - N_2 ) -{1\over 4} ( N_3 + N_4 )\label{eq:3.19} .\end{eqnarray}
Despite its appearance we know only two of the integers can be truly independent~\cite{Simon}. In turn, this observation suggested to us a strategy to parameterize the four angles $(\alpha, \beta, \gamma, \delta)$ as mappings to two independent two-spheres in the manner described below.

\begin{figure}[t]
\includegraphics[width=80mm]{fig2.eps}
\caption{(color online) Schematic representation of a pair of monopole charge-changing unitary operations in the three-band model. $(p_1, n_1) = (1,2)$ and $(p_2, n_2 ) = (3,1)$ in the two spheres, respectively.}
\label{fig2}
\end{figure}

Explicitly, we introduce one stereographic mapping for $(\alpha, \beta)$ by writing

\begin{eqnarray} \hat{d}_1 = (\sin \beta \cos \alpha, \sin \beta \sin \alpha, \cos \beta) \end{eqnarray}
and letting $\hat{d}_1$ wrap the sphere $S^2$. Winding number of $\hat{d}_1$ is precisely the integer $N_1$ defined in Eq. (\ref{eq:3.18}). In the same way we let

\begin{eqnarray} \hat{d}_2 = (\sin \delta \cos \gamma, \sin \delta \sin \gamma, \cos \delta) \end{eqnarray}
wrap another, independent two-sphere with the winding number $N_2$. Under such  prescriptions the third integer $N_3 + N_4$ is not independent, but uniquely fixed by the previous two stereographic projections. To prove this point we borrow the ideas developed from the two-band Chern number engineering and write (see Fig. \ref{fig2})

\begin{eqnarray} (\alpha, \beta) = (n_1 \phi, p_1 \theta) , ~~~ (\gamma , \delta ) = (n_2 \phi, p_2 \theta ), \label{eq:3.25}\end{eqnarray}
using two pairs of integers $(p_1 , n_1)$ and $(p_2 , n_2)$. The angles $(\theta, \phi)$ span the two-sphere just once, $(1/4\pi)\int \sin \theta d\phi \wedge d\theta = 1$, and can be used to define the pristine vector $\hat{d} = (\sin \theta \cos \phi, \sin \theta \sin \phi, \cos \theta )$. According to the language developed for two-band engineering, $\hat{d}_1$ and $\hat{d}_2$ are derived from $\hat{d}$ as

\begin{eqnarray} \hat{d}_1 = \hat{d}^{(p_1 , n_1)}, ~~ \hat{d}_2 = \hat{d}^{(p_2 , n_2 )}. \end{eqnarray}
With the substitution (\ref{eq:3.25}), winding numbers $N_1$ through $N_4$ are worked out as

\begin{eqnarray} N_1 &=& {1 \over 4\pi} n_1 p_1 \int \sin p_1 \theta (d \phi \wedge d \theta) = n_1 P_1 ,\nonumber \\
N_2 &=& {1 \over 4\pi} n_2 p_2 \int \sin p_2 \theta (d \phi \wedge d \theta) = n_2 P_2 , \nonumber \\
N_3 &=& N_4 =  n_1 P_{12}  . \label{eq:3.27}\end{eqnarray}
Indeed $N_3$ and $N_4$ are not independent from other integers.
The ``polarity function" $P_i = [1-(-1)^{p_i} ]/2$ and $P_{12} = [1-(-1)^{p_1 + p_2 } ]/2$ are introduced to keep track of the even ($P_i = 0$) or odd ($P_i = 1)$ polarity of the winding.  The bands' Chern numbers are related to two pairs of integers $(n_1, p_1)$ and $(n_2, p_2)$ used in the stereographic mapping as

\begin{eqnarray} C_u & = & {1\over 2} ( n_1 P_1 + n_2 P_2 ) + {1\over 2}n_1 P_{12} , \nonumber \\
C_v &=& - n_1 P_1 , \nonumber \\
C_w &=&  {1\over 2} ( n_1 P_1 - n_2 P_2 ) - {1\over 2}n_1 P_{12}. \label{eq:3.29}\end{eqnarray}
One can easily convince oneself that arbitrary integers satisfying $C_u + C_v + C_w=0$ can be engineered through judicious choices of $(n_1 , p_1)$ and $(n_2 , p_2)$. Equation (\ref{eq:3.29}) is the central result of our endeavor relating the Chern numbers in the three-band model to a pair of monopole charges, or to be more precise, two pairs of integers governing two singular unitary transformations.

With this general result we propose the following recipe to construct three-band models of arbitrary Chern numbers:

\begin{enumerate}

\item Write $(\alpha, \beta)$ and $(\gamma, \delta)$ in the unitary matrix elements according to Eq. (\ref{eq:3.25}). Other parameters can be set to zero. Choose some energy dispersion for each $e_i$. Make sure different $e_i$'s do not cross anywhere in the Brillouin zone.

\item Choose for the pristine vector $\hat{d}$ the one with a unit winding number. One can take $\hat{d}$ from the Haldane model, for instance.

\end{enumerate}

With the three-band Hamiltonian engineered in this way, Chern numbers of the bands can be read off from Eq. (\ref{eq:3.29}). We have tried the scheme explicitly for the pristine vector taken from the Haldane model. For all the integer combinations $(n_1, p_1)$ and $(n_2, p_2)$ we have tried, explicit computation of the Chern number for the resulting Hamiltonian over the Brillouin zone was found to be consistent with the general formulas of Eq. (\ref{eq:3.29}).

\section{Summary}

The space of unitary matrices that preserve the same set of energies $(e_1 , e_2 , e_3 )$ forms the fiber bundle $\mathrm{SU(3)}/(\mathrm{U(1)}\times\mathrm{U(1)})$. The homotopy map into this space from two dimensions reads~\cite{nakahara}

\begin{eqnarray} && \pi_2 (\mathrm{SU(3)}/(\mathrm{U(1)}\times\mathrm{U(1)} ) \nonumber \\
&& ~~~~~ \simeq \pi_1 (\mathrm{U(1)} \times \mathrm{U(1)} ) \nonumber \\
&& ~~~~~~~~~ \simeq \pi_1 (\mathrm{U(1)} ) \times \pi_1 (\mathrm{U(1)} ) .  \label{eq:3.20}\end{eqnarray}
Two independent integers are thus expected from such mapping. Another relation, $\pi_2 (\mathrm{SU(2)/U(1)}) \simeq \pi_1 (\mathrm{U(1)})$, states that each of these integers is related to the Skyrmion number, or the integer of the map $S^2 \mapsto {\rm SU(2)/U(1)} \simeq S^2$, as we have just proposed.

The goal of our work was to suggest a transparent recipe to generate arbitrary Chern numbers in a three-band model. The idea was based on the equivalence of the topological number of a given band to a certain monopole charge. Monopole charge-changing operations are none other than unitary transformations on the Hamiltonian. For the three-band case we proposed an explicit topology-engineering scheme based on the manipulation of a pair of magnetic monopole charges. Concrete realization of the unitary rotation scheme proposed here in condensed matter systems, both real and artificial~\cite{manoharan}, will be considered in the future.

\acknowledgments{J. H. H. thanks members of the MIT condensed matter theory group for their hospitality during his sabbatical leave. This work is supported by the NRF grant No. 2013R1A2A1A01006430 (JHH) and No. 2013R1A1A2058046 (GG).}

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Over the past year we have been asked to provide shade from the sun and festoon style where build lighting.
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