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Liberty University's educational philosophy is based on the integration of fundamental Christian beliefs and the liberal arts tradition.
Our programs are designed to prepare students to assume leadership roles in society.
At the undergraduate level, Liberty University defines a degree program as a major. Concentrations and cognates within given majors are listed under the major. Liberty University defines a Concentration as a specific grouping of 18 or more credit hours that may be offered within the requirements for an Undergraduate Major or Graduate Program. A Cognate/Specialization is defined as a specific grouping of 9 to 17 credit hours that may be offered within the requirements for an Undergraduate Major or Graduate Program.
The requirements for graduation for all undergraduate programs are listed in this Catalog and on Degree Completion Plans (DCP) which can be accessed at http://www.liberty.edu/dcps.
A course planning schedule is provided in order for students to plan their classes for upcoming semesters. The planning schedule presents every class offered and the terms where it is scheduled to be taught. This schedule is sorted alphabetically by class. You can find the course planning schedule by viewing the last page in the degree completion plan links.
Undergraduate students declare a major when they are accepted to Liberty. They may process a change of major at any time following matriculation through the College of Applied Studies and Academic Success (CASAS). Exceptions are majors which require acceptance into the program, i.e., Athletic Training, Education, Individualized Studies, Interdisciplinary Studies, and Nursing majors.
A complete listing of the majors and minors offered at Liberty follows. Concentrations and cognates within given majors are listed under the major. Liberty University defines a Concentration as a specific grouping of 18 or more credit hours that may be offered within the requirements for an Undergraduate Major or Graduate Program. A Cognate is defined as a specific grouping of 9 to 17 credit hours that may be offered within the requirements for an Undergraduate Major or Graduate Program.
Unless published in this Catalog, no other undergraduate degree programs or major and minor fields can be offered by Liberty and students must be aware that Liberty has no responsibility to offer any degree program, major, or minor unless such information is found in this publication. At least 50% of the semester hours in the major for any program of study or minor must be earned at Liberty University with the exception of the A.A. in Interdisciplinary Studies.
To view Academic Programs choose the appropriate school or college and programs offered in the school will appear below. Please note: (O) indicates the program is available Online; (R) indicates the program is available Residentially; * indicates that the program is available for Teacher Licensure.
College of Applied Studies and Academic Success
Technical Studies (A.A.S) (R)
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English (B.A.) (R) *
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Fashion (B.S.) (R)
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Concentration: Fashion Merchandising
History (B.A./B.S.) (O,R)
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Mathematics (B.S.) (R) *
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Philosophy (B.A.) (R)
Social Sciences (B.S.) (R) *
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Teaching English as a Second Language (B.S.) (O)
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Social Work (B.S.) (O,R)
Psychology (A.A.) (O)
Christian Counseling Minor (O)
Dobson Center Family Advocacy, Public Policy and the Future Minor (O)
Dobson Center Marriage and Family Studies Minor (O)
Dobson Center Parenting and Child/Adolescent Development Minor (O)
Psychology Minor (O,R)
Sociology Minor (R)
Military Resilience Certificate (O)
Accounting (B.S.) (O,R)
Business Administration (B.S.) (O,R) *
Concentration: Finance
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Cognate: Automotive Dealership Management
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Cognate: Green and Sustainable Management (O)
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Coaching (B.S.) (R)
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Cognate: Application and Database Development
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Cognate: Sport Administration
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Accounting (A.A.) (O)
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Information Systems (A.A.) (O)
Accounting Minor (O,R)
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Accounting Certificate (O)
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School of Communication and Creative Arts
Communication (B.S.) (R)
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Journalism (B.S.) (R)
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Cognate: Social Media Management
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Digital Media – Audio Minor
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Rawlings School of Divinity
Biblical and Educational Studies (B.S.) (O)
Biblical Studies (B.A.) (R)
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Cognate: Global Studies
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Early Childhood Education Interdisciplinary Studies (Non-Licensure) (B.S.) (O)
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Cognate: English
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Cognate: Spanish
Elementary Education Interdisciplinary Studies (With Fifth-Year Option for M.A.T. and Licensure) (B.S.) (O)
Special Education Integrated Studies (B.S.) (R)
Special Education Interdisciplinary Studies (With Fifth-Year Option for M.A.T. and Licensure) (B.S.) (O)
Early Childhood Education (Non-Licensure) (A.A.) (O)
Education (Non-Licensure) (A.A.) (O)
Autism Minor (O)
Special Education (Non-Licensure) Minor (O,R)
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Computer Engineering (B.S.) (R)
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Environmental Biology (B.S.) (R) *
Exercise Science (B.S.) (R)
Cognate: Fitness Specialist
Cognate: Therapeutic Science
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General Biology (B.S.) (R) *
Physical Education and Health (B.S.) (R) *
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Concentration: Health Promotion
Concentration: Pre-Clinical
Respiratory Therapy (B.S.) (Post-Licensure) (O)
Zoo and Wildlife Biology (B.S.) (R)
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Biology Minor (R)
Biomedical Sciences Minor (R)
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Kinesiology Minor (R)
Public Health Minor (R)
Health Sciences Certificate (R)
Helms School of Government
Criminal Justice (B.S.) (O,R)
Cognate: Business Administration and Management (O)
Cognate: Crime Scene Investigation
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Cognate: Homeland Security
Cognate: Juvenile Justice (R)
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Government (B.A./B.S.) (O,R)
Concentration: National Security (R)
Concentration: Politics and Policy
Concentration: Public Administration (O)
International Relations (B.A.) (R)
Concentration: International Politics and Policy
Concentration: Strategic and Intelligence Studies Concentration
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Criminal Justice (A.A.) (O,R)
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Homeland Security Minor (O)
International Relations Minor (R)
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Public Administration Certificate (O)
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Paralegal Studies (A.A.) (O)
Paralegal Studies – Certificate (O)
Music – Instrumental (B.A./B.S.) (R)
Music – Vocal (B.A./B.S.) (R)
Music and Worship (B.S.) (R)
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Cognate: Business
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Worship Studies (B.S.) (O)
Choral Music (B.M.) (R) *
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Commercial Music (B.M.) (R)
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Music in World Cultures (B.M.) (R)
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Vocal Performance (B.M.) (R)
Woodwind, Brass, or Percussion Performance (B.M.) (R)
Worship Leadership (B.M.) (R)
Music – Brass, Woodwind, or Percussion Minor (R)
Music – Liberal Arts Minor (R)
Music – Performance: Voice, Keyboard, Guitar or Strings Minor (R)
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RN to BSN (O) *
School of Visual and Performing Arts
Cinematic Arts (B.S.) (R)
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Acting (B.F.A.) (R)
Graphic Design (B.F.A.) (O, R)
Musical Theatre (B.F.A.) (R)
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Cinematic Arts Minor (R)
Cinematic Arts Production Minor (R)
Graphic Design Minor (R)
Photography Minor (R)
Studio Art Minor (R)
Theatre Arts Minor (R)
Willmington School of the Bible
Biblical Studies (Th.G.) (O)
Liberty University offers teacher licensure programs which are approved by the State of Virginia Department of Education.
Those who enter the teacher licensure program must complete the academic major, be subject to the same general education requirements as all other students, and complete academic and practicum experiences related to professional teacher training.
Those wishing to pursue teacher-related programs should seek information from the Teacher Licensure Office in the School of Education. Licensure information is also available at http://www.liberty.edu/uguide.
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Each course is identified by a four-letter prefix and a three digit number. The letters represent the academic area. The first digit will be 1, 2, 3, or 4 to indicate that the course is a freshman, sophomore, junior, or senior level course, respectively. Graduate course numbers begin with 5 and above.
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A full list of course prefixes can be found under the course search on the Courses of Instruction - Undergraduate Programs webpage.
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Is The Success Of 'Moana' An Indication Of The Empowering Direction Disney Will Steer Toward?
Although it seems as if the Disney Princess model is what dominates among animated female characters being produced by Disney studios, every now and then they surprise us by launching a powerful story featuring a young girl or woman who goes against the narrow standards thrust upon women (aspire to marriage and babies only) and shows us what it looks like when a female Disney character is empowered beyond the norms.
The latest of these anomalies is Moana, the young Polynesian girl (who also happens to be a princess) on a mission to save her tribe and community's culture from extinction. It is the type of adventurous and heroic role normally reserved for male characters, which is why 'Moana' is a cut above the rest, especially for young female audiences.
In the film, the titular character is torn between her heart's mission, and respecting her father's wishes to stay closer to home. It is a battle not doubt many women are familiar with, even today. Also a rarity in this film is the presence of a love interest for Moana. This is is also a very important decision which was made by veteran Disney directors Ron Clements and John Musker ('The Little Mermaid' and 'Aladdin').
It was released just before Christmas and topped the US box office 3 weeks in a row. So far it has amassed over $480 million in international box office sales, proving what a hit this film is, on par with the intense popularity of 'Frozen' a couple of years ago.
The character was voiced by Auli'i Cravalho, an Hawaiian-born American actress who lends quite the air of authenticity to the life of Moana. Her sidekick Maui was voiced by Dwayne Johnson. This is the first Disney film set in Polynesia, and Moana is the first Disney female character of color to take the lead without taking on the dynamic of romance.
As TheConversation.com points out, it has been a long road from seeing the standard Disney Princess go from disempowered woman whose story is hinged on her acceptance by a man, to female characters who work, go on adventures, fight battles, and defy the norms. Characters such as Mulan, Pocahontas and Merida from 'Brave' started to show cracks in the heavily built-upon romantic foundation (although some of the aforementioned were warriors as well as love interests). In 'The Princess and the Frog', audiences got to see Tiana as a career woman, a restaurant owner, and in 'Zootopia', lead character Judy Hopps is determined to become the city's first bunny rabbit police officer (spoiler alert: she is successful!).
In 'Frozen', although there were 2 love interests for Anna, the pivotal relationship upon which the film's story rested was between her and her sister, Elsa. This was a clear departure from anything we had seen from Disney. Some of the criticisms about this film, however, were that the animation specifics were still the usual unrealistic, tiny waist, big eyes and perfect physique that is not found on a single woman in this world.
Yet everything about Moana shows that Disney is either listening to the voices of critics and audience-members who want to continue seeing more empowered female characters, or they too are bored with the same old.
Head animator for the film, Amy Smeed, spoke to Screen Arts & Cultures and Art & Design students at the University of Michigan about the formation of the characters, and what she particularly wanted to see in Moana's scenes.
"She's very courageous and fearless, and I love that about her. And she's very athletic … The scenes that I got to animate, I picked Moana," said the Michigan native.
To understand why this film is so different to other Disney animated films and why Moana is not your typical female character, we have to go back to the two directors Ron and John, who made a point of making Moana into a heroine.
"We saw this as a hero's journey, a coming-of-age story, in a different tradition than the princess stories. I don't know that any of the other princesses we've been involved with we'd describe as badass," they told TIME magazine.
The two men wanted to draw upon Polynesian mythology from a distinct Polynesian perspective, as they saw most of the stories about Pacific Islander culture being told from Western storytellers and writers. They traveled to Fiji, Samoa, and Tahiti five years ago, and spoke with local village chiefs and archeologists. They learned some of the key components of the culture's stories and myths were sailing and navigation, yet these seemed to have been forgotten 2000 years ago.
Central to many of these mythical stories were male characters and demigods, but directors Ron and John thought it would be far more interesting to put a teen girl at the center of a story about reclaiming lost culture, and make the demigod, Maui, her sidekick instead.
"We thought it would be very appealing to do a female empowerment story that didn't center on any sort of romance,. We saw it as sort of a 'True Grit'-type story: the determined girl who teams up with a washed-up guy. They have this adventure and she finds her true calling—and saves the world in the process," they said.
The directors were also determined to base her physical features on a realistic portrayal of an Islander girl who embarks on the type of physical activities similar to what we see Moana doing. It is a journey of self-discovery that has far more long-lasting appeal among young audiences than a princess model. The messages and themes seen throughout 'Moana' can have a far greater impact in the life of a young girl, than, say, 'Cinderella'.
"The film offers us a vision of a powerful and wilful young lady who will take on everything that comes at her to be successful. She is the epitome of the modern working woman," write Martyn Griffin, Mark Learmonth, and Nancy Harding who all contributed to the article on The Conversation about Disney's inclusion of careers in the lives of their female characters in more recent years.
Writing for MichiganDaily.com, Sydney Cohen says the film's focus on nature, culture and storytelling lay an empowering foundation for a character like Moana to embark on an adventure without being stereotyped to fit a narrow mold.
"'Moana' is a refreshing break from classic tropes in the lineage of Disney princess movies. With the absence of a male love interest, the film is another success in providing feminist cinematic role models, especially in a tradition of passive female heroines," she writes.
If this is the direction Disney animated studios will be taking for its female characters from now one, we are totally on board with this. The attention to detail and making conscious decisions from casting, all the way to how the foliage in the background is portrayed is what is going to keep audiences coming back for more, especially if we can now start to see female characters as heroines and adventurers alongside men, instead of just objects of romance.
Tags: animation × disney × female character × female empowerment × moana

redpajama_set_name: RedPajamaCommonCrawl


We have identified a 13 gene set that predicts renal transplant fibrosis and graft loss in patients. Interestingly some of these genes are donors as well as recipient related. In this project we aim to investigate these gene pathways in cell lines and animal models to better understand how the cause of renal fibrosis after transplantation.


Smartphones have been around for nearly a decade and yet founders still declare mobile the most underhyped technology, according to First Round's State of Startups Survey. And, within mobile, the potential of push notifications reigns supreme. Entrepreneur Ariel Seidman captures this well: "It's hard to over-hype the power of mobile push notifications. For the first time in human history, you can tap almost two billion people on the shoulder." That's why Slack's Noah Weiss is a true believer in a world coming closer together through smarter pings.
Before Slack, Weiss worked at Foursquare when it monetized the service with native ads and boldly split into two apps in 2014. During that time, monthly active users more than quintupled. Weiss was also Google's lead product manager on structured data-related search projects. Recently, Weiss joined Slack to build out its New York office and lead its new Search, Learning and Intelligence Group with a mandate to develop features that make companies more productive the more they use Slack.
In this interview, Weiss maps out the dynamic evolution of push notifications — revealing critical paradigm shifts in the era of smartwatches and app-filled homescreens. Here, he also shares tips for startups seeking to build out their push notification strategy and the inputs, metrics and guidelines to instate. Any startup that wants to command this high-risk, high-reward channel will benefit from Weiss' wisdom.
A great push notification is three things: timely, personal and actionable.
An in-depth notification strategy can weigh and weave together several factors, such as nearby wifi, personalization, social factors and real-time snapping to places to power its push notifications. But for startups that are just embarking on their push notification technology, there are fundamentals to consider. From the basics to more advanced tips, Weiss outlines the essential lessons he's learned while developing push notification systems.
Boost retention outside the app.
Customer acquisition propels an app. User retention builds a business.
Don't mistake a download with permission.
Asking for the authority to send notifications is not only good form, but technologically necessary. "If you're building on iOS, sending notifications is a permission the user must authorize. Unlike on Android, downloading the app does not give you that authority. You have to prompt users for it," says Weiss. "This is the pivotal moment. If users decline permission, there's no way for the app to reach out to pull them back in, which drastically decreases the likelihood that they'll be active users down the line. Even if they accept, it is not a binding contract."
To assess your notification strategy, nail down three metrics: 1) the rate of users opting out of your notification permissions, 2) the uninstall rate and 3) actions per hundred pings.
...but calibrate them to compare performance on iOS and Android.
Fill your notifications with personalized tidbits, so they sound like they came from a close friend.
Run experiments with notifications for a minimum of six weeks but 12 weeks is a good sweet spot. Weiss has learned that conducting tests for a longer period of time is necessary to surface any negative effects. "The average user will ignore unwanted pings for about a month without taking action, such as altering settings or uninstalling the app. There's a threshold that's passed where annoyance surprasses the ease of quick dismissal," says Weiss.
Experiment with how, when and where.
Magicians bring your card to the top of a deck. Apps with smart notifications will have this sleight of hand, lifting their service to the front of people's phones at the right time.
You'll always be able to navigate to an app, but notifications will be your steadfast sherpa.
The best apps will be the ones you don't have to remember to use. They'll remind you. Soon that'll be the only type of app.
A comprehensive approach to leveraging sensors on mobile can be challenging, but there are basic ways to get started. "While most developers cannot easily build this type of location understanding, it's fairly trivial to build a model for understanding when a person is at home or work based on background location. Those are two very rich contexts for triggering relevant pings," says Weiss.
While notifications are great for boosting retention and engagement rates, don't start off by looking at them as a growth hacking tool. They have the potential to be the most intuitive and intimate way to interact with your users. In order to build that trustworthy relationship, they must be timely, personal and actionable. A notification strategy must ask permission from users and be measured by their opt-outs, uninstalls and actions per 100 pings. The more that notifications can be customized actively via user input and passively through contextual awareness, the better.


By the time we arrived back at our hotel on the eve of our last day in Disney (remember? magical-ish princess day?) the question of me catching Ephraim's stomach bug was no longer an "if" but a "when". I knew it was coming for me. And it was going to be ugly.
Now for a quick aside. I rarely get sick. In fact, I so rarely get sick that sometimes I long to be sick so I can have an excuse to lay in bed and watch Doomesday Preppers all day (don't judge. I see you Miss I-Love-Sister-Wives).
But there are a few notable times that I've fallen gravely ill. The most unfortunate being the time I contracted a rather nasty strain of rotavirus upon returning home from the hospital, three days postpartum with Ephraim. Thank you again for that, Sarah. You haven't had diarrhea until you've had postpartum diarrhea.
Skip ahead three years and I picked up what must have been that same nasty strain the day B-Ro turned three. I spent the entirety of the super hero birthday party that I'd carefully planned hugging the toilet and praying for a quick and easy death.
So it should come as no surprise when I tell you that the eve of our last day in Disney was also the eve of my only son's fifth birthday. And as the waves of nausea started to hit at about midnight I knew that I would once again be celebrating my boy's birthday by becoming one with the porcelain.
Brent and the kids woke up at 7 after I'd had an on again, off again battle with the bug all night long. I knew I wasn't heading to Magic Kingdom with my birthday boy, and I was devastated. By this point Brent was beginning to wonder if he too was coming down with something. But he swore it off and hauled both kiddos on to the park, donning his Superdad cape once again.
Then I settled in for a long miserable day of Doomesday Preppers.
After about an hour I decided I wasn't going down without a fight. As I said on Facebook that morning, if I could push an 8 pound human being out of my body then I could surely power through this junk to spend the day with that birthday boy.
Which is how I ended up almost hurling on a Disney transit bus, the Disney ferry and in the line to get in. And this time I didn't have ziplocs.
Now that's the stuff fantasies are truly made of. Can I get an amen from the married ladies in the audience?
Our first stop together was for lunch. Um, yum?
But I enjoyed watching B-Ro map out the rest of our day.
And I sure as heck enjoyed just being there with my littlest love.
After lunch the next stop was to cash in the boys' fast pass for Splash Mountain. Sarah opted to just watch.
And I think it goes without saying that so did I.
Live and learn, buddy. Live and learn.
and then I made a beeline to the smoothie stand. Purees have never tasted so delicious.
In fact I was in such a state of smoothie nirvana that I curled up on a Magic Kingdom bench and fell asleep for the next 30 minutes while my little fam took off for another ride. True story. If Magic Kingdom gave out tickets for loitering I would most definitely have been fined.
I was even happier when to be heading back to the hotel that afternoon.
But I was happiest to know that in times like these, this guy's always got my back.
You poor things!!! Very much a Griswolds vacation! Glad super dad was able to take the kiddos & that you were able to power through it. Thank you for sharing your crazy adventure!
You are a better woman than I! I'm not sure I could've mustered that energy. I hope that was the extent of the illness and it's awesome how superdad saved the day!
And Splash Mountain is the best ride ever – sorry B-Ro didn't think so.
I am so sorry you and Ephraim got sick on your trip! It sounds like your kids have 2 Superparents to brave the parks with the stomach flu!
We just got back from Disneyworld Friday. Luckily, the stomach flu hit our house the week before we left! I did the same thing on Splash Mountain but somehow got 50 pictures of strangers and entirely missed my family! lol I have no idea how I managed that.
Thanks for sharing your pictures with all of us and I hope you all are feeling better now!
yay for superdad! i love that you have a husband that steps up to the plate! they are definitely a rare find. you looked pretty good to be so sick! happy late birthday to ephraim!
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IB's Professional of the Week is the premier way to meet Dane County's professionals. This week features John Seamon, architectural director, Iconica.
Because design profoundly impacts people's lives, the most rewarding aspect of my job is getting to know clients on a personal level. Knowing what makes them tick and why they do what they do leads to crafting design solutions that provide the most powerful outcomes. Those relationships are meaningful to me and the work we do together is hopefully meaningful for others long after we are gone. The most challenging aspect of my job can be helping others see the benefits of exploring what could be. We can't create a new reality while looking at the current reality.
Simon Sinek, as he best articulated the single most important aspect of any business — it's not what you do or how you do it that matters most, it is why you do it. Eric Schmidt, as he understands how to keep business culture and innovation completely scalable. Elon Musk, as his why truly drives the how and what he and his companies do. He was a client for a very short time and I believe he can move through or around obstacles more quickly and efficiently than perhaps anyone I've ever met.
I've had many high points, so there is not one that stands out. I've worked with some great people and minds so far. Working closely with Jeff Kipnis over a number of years had the most impact on me. It was transformational. Starting and growing a small firm in San Francisco was incredibly meaningful and rewarding. Years of working/living in a studio with those that cared as much as I did was amazing. I don't separate my career from my life, or my life from my career. Life is fun, is work, is fun, is life. It's all wrapped together for me. This is how I have designed my life, you could say. I have basically allowed my "why" to get me to where I have been, and I want to continue to let it guide my direction and decisions.
Explore and stay the course for what inspires you — not your friends, your parents, or your teachers, you. Surround yourself with winners and don't compromise. Say "yes, and" rather than "yes, but" most of the time to get the best out of your team. Be more of problem seeker not a problem solver.


With its sleek glossy finish and matte accents, the Textures kettle will make a stylish addition to any kitchen. It is equipped with a large 1.7L capacity with enough space for up to six cups, which makes it ideal for family kitchens. If you are only making one cup, then the rapid boil zone markers will ensure you only fill the ideal amount to save energy. It also features a perfect pour spout to prevent drips and spills, together with a removable washable filter to keep the water pure and scale-free.


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Thanksgiving is right around the bend, and with it comes the joys of those tasty autumn treats... pumpkin, winter squash, cranberries, chard, apples, sweet potatoes... yum yum yum! Though I love the summer harvest with its delightful fruits and brightly colored vegetables, there's something earthy and comforting about fall and winter produce.
My CSA food drop this month brought me a medley of autumn delights, including yams! They were mixed in with the potatoes and I almost missed them, but once found, I couldn't pass up the opportunity to whip up something delightful after work. Not only that, but I came up with a recipe that is both healthy and sweet... the perfect combo to get you in the autumn mood!
Peel the yams and boil in a pot of water. Depending on the size of the yams, and whether or not you cube them, they could take anywhere from 10-30 minutes to cook. I used three large yams and they boiled for 30 minutes or so. Test with a fork -- when you can easily push the fork through the yam, it's finished.
Let the yams cool a little and then puree them in a food processor or with a blender until creamy. Preheat the oven to 350 degrees.
Place eggs, applesauce, sugar, vanilla, and pureed yams into a large bowl. Beat until light and fluffy.
Sift flour, baking soda, baking powder, cinnamon and salt together in a small bowl. Stir dry ingredients into the yam mixture until just combined. It should thicken to a heavy paste.
Get a hold of yourself and grease a muffin tin. Pour the delicious-smelling yam mixture into each cup, about 2/3 of the way full.
Cook muffins 17-20 minutes, or until toothpick inserted into middle comes out clean. I left them a little on the underdone side, and this made them pumpkin-pie creamy on the inside. Mmmmmmm.
Let muffins cool ten minutes. Butter the tops of the muffins and sprinkle a cinnamon-sugar mixture on top for sweetness. Enjoy!


Wednesday night marked two occasions for AGT -- Howard's final night as a judge and the crowning of a Season 10 champion.
Wednesday night marked two occasions for "America's Got Talent" -- Howard's final night on the show and the crowning of a Season 10 champion.
From the December 2011 announcement that the King of All Media would be replacing Piers Morgan as a judge on the reality TV series, on through the four seasons that cemented him as "America's Judge," it has been a wild and rewarding journey.
Check out some of the great moments from his run on the show in the retrospective above and be sure to congratulate Howard on Twitter and Facebook!


Flott guide til dette unike naturområdet på grensen mellom Hellas og Bulgaria. Boka dekker Rodopifjellene og lavlandsområdene på gresk side. Et område som ikke dekkes på en slik god helhetlig måte i forhold til alle naturverdier i noen andre guider.
The Nature Guide to Eastern Rhodopes har relasjoner til.
The Eastern Rhodopes lie on the border of Greece and Bulgaria. Both sides boast a splendid, authentic and little visited landscape with a rich flora and fauna. The Bulgarian Eastern Rhodope mountains are wild, with a large numbers of birds of prey, wolves and jackals hide in the woodlands, while scores of butterflies and wildflowers grace the meadows. The lowlands of Greece, with famous areas like Dadia, Evros and Nestos, are a birding hotspot with attractions like pelicans, Pygmy Cormorants and Spur-winged Plovers.


Staying Connected focuses on the importance of relationships with family, friends, work colleagues and your local community. It is designed to help Defence families throughout their ADF career from enlistment, training and deployment, through to transitioning into civilian careers.
ADF members who have different careers and life experiences share their personal stories about how staying connected helped them and their families, including through difficult times. It also provides advice from a mental health professional and DCO on the importance of supporting each other and getting help when you need it.
In this video Australian Defence Force members with very different career and life experiences will share their perso0nal stories of how staying connected has helped them and their families, including through the tough times. It also provides advice from a mental health professional and the Defence Community Organisation on the importance of supporting each other and seeking assistance for any concerns.


text:
\section{Introduction}

Pulsars have long provided a rich source of astrophysical information
due to their compact emission and predictable timing. One of the
least well constrained parameters for most pulsars is their
distance.  For some pulsars, timing parallax or VLBI parallax has
resulted in direct distance determination.
For most pulsars, the
distance is a major uncertainty for precision timing interpretations,
including mass, moment of inertia \citep{2006Sci...314...97K,2012hpa..book.....L}, and
gravitational wave direction \citep{boyle2012}.

Direct VLBI observations of PSR B0834+06 show multiple images lensed
by the interstellar plasma.
Combining the angular positions and
scintillation delays, the authors \citep{2010ApJ...708..232B} (hereafter B10) published the derived effective
distance (defined in Section \ref{21}) of $1168\pm 23$ pc
for apexes on the main scattering axis.
This represents a precise
measurement compared to all other attempts to derive distances to this
pulsar.  This effective distance is a combination of pulsar-screen and
earth-screen distances, and does not allow a separate determination of
the individual distances.  A binary pulsar system would in principle
allow a breaking of this degeneracy \citep{2014MNRAS.442.3338P}. One
potential limitation is the precision to which the lensing model can
be understood.

In this paper, we examine the geometric nature of the lensing screens.
In B10, VLBI astrometric mapping directly demonstrated the highly
collinear nature of a single dominant lensing structure.  First hints
of single plane collinear dominated structure had been realized in
\citet{2001ApJ...549L..97S}.   While the nature of these structures
is already mysterious, for this pulsar, in particular, the puzzle is compounded by an offset group
of lenses whose radiation arrive delayed by 1 ms relative to the bulk of the pulsar flux.  The mysterious nature of
lensing questions any conclusions drawn from scintillometry as a
quantitative tool \citep{2014MNRAS.440L..36P}.

Using archival data we demonstrate in this paper that the lensing screen
consists of nearly parallel linear refractive structures, in two
screens.  The precise model confirms the one dimensional nature of the scattering geometry, and
thus the small number of parameters that
quantify the lensing screen.

The paper is structured as follows. Section \ref{sec:lensing}
overviews the inclined sheet lensing model, and its application to data.
Section \ref{sec:astrometry} presents new VLBI proper motion and
distance measurements to this pulsar.
Section \ref{sec:discussions} describes the interpretation of the
lensing geometry and possible improvements on the observation.
We conclude in Section \ref{sec:conclusions}.

\section{Lensing}
\label{sec:lensing}
In this section, we map the archival data of PSR 0834+06 onto the grazing incidence sheet
model.  The folded sheet model is qualitatively analogous to the
reflection of a light across a lake as seen from the opposite
shore.
In the absence of waves, exactly one image forms at the point
where the angle of incidence is equal to the angle of reflection.  In
the presence of waves, one generically sees a line of images above and
below the unperturbed image.  The grazing angle geometry simplifies
the lensing geometry, effectively reducing it from a two dimensional problem to
one dimension.  The statistics of such reflections is sometimes called
glitter, and has many solvable
properties \citep{LonguetHiggins1960}.  This is illustrated in
Fig. \ref{fig:water_reflection}.

\begin{figure*}
\centering
\includegraphics[width=1.0\linewidth, angle=0]{toronto-skyline.png}
\caption{Reflection of lights on surface waves.  At grazing angle,
 each wave crest results in an apparent image, causing a linear
 streak of images centred on the unperturbed image location.  For
 example, the red light streak would consist of a single image at its
 center in the absence of waves. The inclined sheet model for  pulsar
 scintillation is analogous, with reflection replaced by refraction.
Image copyright Kaitlyn McLachlan,
 licensed through shutterstock.com image ID 45186139.}
\label{fig:water_reflection}
\end{figure*}

A similar effect occurs when the
observer is below the surface.  Two major distinctions arise: 1. the
waves can deform the surface to create caustics in projection. Near
caustics, Snell's law can lead to highly amplified refraction
angles\citep{2006ApJ...640L.159G}.  2. due to the odd image theorem, each caustic leads to two
images.  In an astrophysical context, the surface could be related to
magnetic reconnection
sheets \citep{2015MNRAS.450.3201B}, which have finite widths to
regularize these singularities.  Diffusive structures have Gaussian
profiles, which were analysed in \citet{2012MNRAS.421L.132P}.  The
lensing details differ for convergent (under-dense) vs divergent
(over-dense) lenses, first considered by \citet{1998ApJ...496..253C}.

The typical interstellar electron density $\sim 0.02$ cm$^{-3}$
is insufficient to deflect
radio waves by the observed $\sim$ mas bending angles.  At grazing
incidence, Snell's law results in an enhanced bending angle, which
formally diverges.  Magnetic discontinuities generically allow transverse surface waves, whose restoring force is the difference in Alfv\'en
speed on the two sides of the discontinuity.  This completes the
analogy to waves on a lake: for sufficiently inclined sheets the waves
will appear to fold back onto themselves in projection on the sky.  At
each fold caustic, Snell's law diverges, leading to enhanced
refractive lensing.  The divergence is cut off by the finite width of
the sheet.  The generic consequence is a series of collinear images.
Each projected fold of the wave results in two density caustics.  Each density
caustic leads to two geometric lensing images, for a total of 4 images
for each wave inflection.  The two geometric images in each caustic are
separated by the characteristic width of the sheet. If this is smaller
than the Fresnel scale, the two images become effectively
indistinguishable.
The geometry of the inclined refractive lens is shown in Fig. \ref{fig:sheetgeom}.
\begin{figure*}
\vspace{-0.8in}
\includegraphics[width=1.0\textwidth, angle=0]{sheetgeom.pdf}
\vspace{-7.0in}
\caption{Refractive lensing geometry
(reproduced from \citet{2014MNRAS.442.3338P}
  fig. 1).  The pulsar is on the right, observer on the left.  Each
  fold of the sheet leads to a divergent projected density, resulting
  in a lensed image as indicated by the dotted line. See text for details.
}
\label{fig:sheetgeom}
\end{figure*}

A large number of sheets might intersect the line of sight to any
pulsar.  Only those sufficiently inclined would lead to caustic
formation.  Empirically, some pulsars show scattering that appears to be dominated by a
single sheet, leading to the prominent inverted
arclets in the secondary spectrum of the scintillations \citep{2001ApJ...549L..97S}.

\subsection{Archival data of B0834+06}
\label{21}
Our analysis is based on the apex data selected from the secondary
spectrum of pulsar B0834+06 in B10, which was
observed as part of a 300 MHz global VLBI project on 2005 November 12, with
the GBT (GB), Arecibo (AR), Lovell and Westerbork (WB) telescopes.  The GB-AR and AR-WB
baselines are close to orthogonal and of comparable lengths, resulting
in relatively isotropic astrometric positions.
Information from each identified apex includes delay $\tau$,
delay rate (differential frequency $f_{\rm D}$), relative Right Ascension,
$\Delta\alpha$, and relative declination, $\Delta\delta$.
Data of each apex are collected from four dual circular polarization $8$ MHz wide sub-bands spanning the frequency range $310.5$--$342.5$ MHz.
As described in B10, the inverse parabolic
arclets were fitted to positions of their apexes, resulting in a
catalogue of apexes in each sub-band, each with delay and differential
frequency.
In this work, we first combine the
apexes across sub-bands, resulting in a single set of images.  We focus on
the southern group with negative differential frequency: this
grouping appears as a likely candidate for a double-lensing screen.  However, two groups (with negative differential frequency) appear distinct in both the VLBI angular positions and the secondary spectra.  We divide the apex data with negative $f_{\rm D}$ into two
groups: in one group, time delays range from $0.1$ ms to $0.4$ ms,
which we call the $0.4$ ms group; and in the other group, time delay at
about $1$ ms, which we call the $1$ ms group.  In summary, the
$0.4$ ms group contains $10$ apexes in the first two sub-bands, and
$14$ apexes in the last two sub-bands; the $1$ ms group, contains $5$,
$6$, $5$ and $4$ apexes in the four sub-bands subsequently, with
center frequency of each band $f_{\rm band}=314.5, 322.5, 330.5$ and $
338.5$ MHz.  The apex positions in the secondary spectrum are shown
in Fig. \ref{fig:apex_pos}.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{apex_pos.pdf}
\caption{Distribution of the apex positions in the sub-band centred at
  314.5 MHz.  The apexes that belong to the 1 and 0.4 ms groups are marked.}
\label{fig:apex_pos}
\end{figure}

We select the equivalent apexes from four sub-bands.  To match the same apexes in different sub-bands, we scale the differential frequency in different sub-bands to $322.5$ MHz, by $f_{\rm D} (322.5/f_{\rm band})$ MHz.  A total of $9$ apexes from the $0.4$ ms group and $5$ apexes from the $1$ ms
group, were mapped.  This results in an estimation
for the mean referenced frequency $f=322.5$ MHz and a standard
deviation among the sub-bands, listed in Table
\ref{table:apex}.  The $f_{\rm D}$, $\tau$, $\Delta\alpha$ and $\Delta\delta$
are the mean values of $n$ sub-bands
($n=3$ for points 4 to 6 and points $1^\prime$, $2^\prime$ and $4^\prime$, while 4 for the remainder of the points), listed
in Table \ref{table:apex}.

\begin{table*}
\centering
\begin{tabular}{c|llllll}
\hline
label & $\theta_{\parallel}$(mas) & $f_{\rm D}$(mHz) & $\tau$(ms)  & $\Delta\alpha$(mas) & $\Delta\delta$(mas) & $t_0$(day)\\
\hline
1& $-17.22$   & $-26.1(4)$    & 0.3743(6)         & 6.2    & $-11.9$      & $-107$                               \\
2& $-16.36$  & $-24.9(4)$      & 0.3378(3)         & 8.0(4)  & $-14.5(8)$      &$-101$                                \\
3& $-16.08$   & $-24.6(4)$       & 0.327(3)   & 7.2(6)  & $-13.9(4)$       & $-99.0$                                \\
4& $-14.45$   & $-22.3(5)$      & 0.2633(3)    & 6.1(4)  & $-13.1(7)$     & $-88.1$                                \\
5& $-13.68$ & $-21.6(6)$        & 0.236(2)    & 5.1(4)  & $-12.7(5)$      & $-83.3$                                \\
6& $-13.27$ & $-20.4(5)$      & 0.222(3)     & 5.8(4)  & $-11.8(1)$    & $-81.4$                                \\
7& $-12.21$   & $-18.9(2)$      & 0.188(2)   & 5.5(6) & $-10.8(6)$      & $-74.2$                        \\
8& $-10.58$   & $-16.8(3)$      & 0.1412(9)  & 3.9(6) & $-10.0(4)$      & $-62.8$                                \\
9& $-8.18$   & $-12.9(2)$      & 0.0845(5) & 2.8(3)  & $-8.6(4)$      & $-48.7$
\\ \hline

1'&$ \cdots$ & $-43.1(4)$      & 1.066(5)    & $-8(3)$     & $-24(2)$   & $-185$   \\
2'&$\cdots$ & $-41.3(5)$    & 1.037(3)   & $-14(1)$     & $-23(3)$   & $-188$                                   \\
3'&$\cdots$ & $-40.2(6)$  & 1.005(8)    & $-14(1)$       & $-22.3(5)$  & $-187$                                   \\
4'&$\cdots$ & $-38.3(6)$  & 0.9763(9)   & $-14(1)$       & $-20.6(3)$  & $-190$                                    \\
5'&$\cdots$& $-35.1(5)$  & 0.950(2)   & $-15(1)$  & $-21(1)$   &$-202$                                   \\
 \hline
\end{tabular}
\caption{ $0.4$ ms and $1$ ms reduced apex data.
We list the $0.4$ ms group data in the upper part of the table, while the $1$ ms group lie in the lower part of the table.
Observation data include the differential frequency $f_{\rm D}$, time delay
$\tau$ ($\tau_1$ for $0.4$ ms group and $\tau_2$ for $1$ ms group);
$\Delta\alpha$ and $\Delta\delta$ are from the VLBI measurement (there is only one matched position for point 1, thus no error).
$t_0$ is the time at constant velocity for an apex to intersect the
origin at constant speed along the main scattering parabola.  More
details in Section \ref{21} and Section \ref{222}.
}
\label{table:apex}
\end{table*}
We estimate the error of time delay $\tau$, differential frequency
$f_{\rm D}$, $\Delta\alpha$ and $\Delta\delta$  listed in Table
\ref{table:apex} from their band-to-band variance:
\begin{equation}
\sigma^2_{\rm \tau, f_{\rm D},\Delta\alpha, \Delta\delta} = \frac{1}{n}\sum^{n}_{i=1}\frac{(x_i-\bar{x})^2}{n-1},
\end{equation}
and $n$ is the number of sub-bands. The outer $1/n$ accounts for the expected variance of a mean of $n$ numbers.

\subsection{One-lens model}
\subsubsection{Distance to the lenses}
In the absence of a lens model, the
fringe rate, delay and angular position cannot be uniquely related.  To interpret the data, we adopt the lensing model of
\citet{2014MNRAS.442.3338P}.  In this model, the lensing is due to projected fold caustics of a thin sheet closely aligned to the line of sight.  We will list the parameters in this lens model in Table \ref{tab:parameters}.

\begin{table}
\caption{Parameters for double-lens model}
\begin{threeparttable}
\begin{tabular}{cl}
\hline
$D_{1\rm e}$  &
Effective Distance of $0.4$ group data\\
$D_{2\rm e}$
	&  Effective Distance of $1$ ms group data\\
$D_1$ 		&  Distance of lens 1 \\
$D_2$	& Distance of lens 2 \\
$\gamma$ &  Scattering axis angle of $0.4$ ms group\tnote{a} \\
$\phi$	& Angle of the velocity of the pulsar\tnote{a}\\
$\theta$ & Angular offset of the object \\
\hline
\end{tabular}

\begin{tablenotes}
\item[a]{The angle is measured relative to the longitude and east is the positive direction.}
\end{tablenotes}
\label{tab:parameters}
\end{threeparttable}
\end{table}

We define the {\it effective distance} $D_{\rm e}$ as
\begin{equation}
D_{\rm e} \equiv \frac{2c\tau}{\theta^2}.
\end{equation}
The differential frequency is related to the rate of change of delay
as $f_{\rm D}  =-f\frac{\rm d\tau}{\dif t}$.
In general, $D_{\rm e}={D_{\rm p} D_{\rm s}}/({D_{\rm p} - D_{\rm
    s}})$ for a screen at $D_{\rm s}$.
    The effective distance
corresponds to the pulsar distance $D_{\rm p}$, if the screen is exactly halfway.
Fig. \ref{fig:Singledegeneracy} shows two sets of $D_{\rm p}$ and $D_{\rm s}$ with common $D_{\rm e}$.

\begin{figure}
\centering
\hspace*{-0.4in}\includegraphics[width=3.9in]{single_degeneracy.pdf}
\caption{A single refracted light path showing the distance
  degeneracy.  The primed and un-primed geometries result in the same
  observables: delay $\tau$ and angular offset $\theta$.
$O$ denotes the observer; $A$ and $A'$ denote the positions of the
pulsar; $D$ and $D'$ denote the positions of the refracted images on the
interstellar medium. The un-primed geometry corresponds to a pulsar
distance $D_{\rm p} = |AO| = 620$ pc, while the primed geometry has the same $D_{\rm e}$ but twice the
$D_{\rm p}.$}
\label{fig:Singledegeneracy}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=1.0\linewidth, angle=0]{Theta_tau.pdf}
\caption{${\theta}$ vs ${\sqrt{\tau}}$.  Two separate lines through the
  origin were fitted to the points sampled among the $0.4$ ms group
  and $1$ ms group.  The solid line is the fitted line of the $0.4$ ms
  positions, where $D_{1\rm e}=1044\pm 22$ pc. The dashed line is
  the fitted line of the $1$ ms
  position, where $D_{2\rm e}=1252\pm 49$ pc.
}
\label{thetatau}
\end{figure}

When estimating the angular offset of each apex,
we subtract the expected noise bias:
${\theta}^2=({\Delta\alpha}\cos(\delta))^2+({\Delta\delta})^2-\sigma^2_{\Delta\alpha}-\sigma^2_{\Delta\delta}$.
We plot the $\theta$ vs square root of $\tau$ in Fig.
\ref{thetatau}.  A least-square fit to the distance results in
$D_{1{\rm e}}=1044\pm 22$ pc for the  $0.4$\ ms group, which we call
lens 1 (point 1 is excluded since VLBI astrometry was only known for
one sub-band, thus we cannot obtain the variance nor weighted mean for that point), and
$D_{2{\rm e}} = 1252 \pm 49$ pc for the $1$\ ms group, hereafter lens 2.
The errors, and uncertainties on the error, preclude a definitive
interpretation of the apparent difference in distance.  However, at face value,
this indicates that lens 2 is closer to the pulsar, and we will
use this as a basis for the model in this paper.
The distances are slightly different from those derived in
B10, which is partly due to a different subset
of arclets analysed.  We discuss
consequences of alternate interpretations in Section \ref{sec:degeneracy}.
The pulsar distance was directly measured using VLBI parallax to be
$D_{\rm p} = 620 \pm 60$ pc, described in more detail in Section \ref{sec:astrometry}.
We take $D_{1{\rm e}}=1044$ pc,  and the distance of lens 1 $D_{1}$,
where $0.4$ ms group scintillation points are refracted, as $389$
pc. Similarly, for $1$ ms apexes, the distance of lens 2 is taken as $D_2=415$ pc,
slightly closer to the pulsar.

For the 0.4 ms group, we adopt the geometry from
B10, assigning these points along line $AD$ as
shown in Fig. \ref{Doublelens} based solely on their delay, which is
the best measured observable.  The line $AD$ is taken as a
fixed angle of $\gamma=-25\degree.2$ east north.  We use this axis
to define ${\parallel}$ direction and define ${\bot}$ by a $90\degree$ direction clockwise
rotation.

\begin{figure*}
\centering
\includegraphics[width=7.5in]{Double_lens_xy.pdf}
\caption{Positions of $0.4$ ms and $1$ ms group data in the one-lens model and double-lens model.
The axes represent the relative transverse distances to the un-refracted pulsar in Right Ascension (calculated by $x= \Delta \alpha \cos(\delta)D_i$ with $D_i$ represent the distance of the object to the observer: for point $A$, $D_i=D_{\rm p}$; for points $H$ and $J$, $D_i=D_2$; for points $B$ and $D$, $D_i=D_1$.) and declination (calculated by $y=\Delta \delta D_i$) directions, on a 2D plane that is transverse to the line of sight.
On the left side, the points marked with letter $D$ labelled from 1 to 9, are the derived
positions from the time delays of $0.4$ ms group in
the one-lens
model.  At a distance $389$ pc from the observer, the green solid line
demarcates the scattering axis for the
$0.4$ ms apexes positions, with an angle $\gamma=-25\degree.2$ east of
north.  The points on the right side mark the first and second
refraction points in double-lens model.
The unobservable points
denoted by the letter $H$, are the calculated positions on lens 2 from the
1
 ms group; the observed apparent positions denoted by the letter $B$, are the
second refraction on lens 1.  They are connected by short solid lines.  The long
dash dotted line passing through $J$ is the inferred geometry of the second
lens.  Its thicker portion has formed a full caustic, while the
thinner portion are sub critical.
The dash
dotted lines, constructed perpendicular to the $AD$ scattering axis,
denote the caustics of lens 1.  The dotted line on the top right is
perpendicular to the magenta dash dotted line, intersecting at $J$.
The relative model pulsar-screen velocity is $185.3$ km $\rm s^{-1}$, with an angle $\phi=-3\degree.7$ east of north, is marked with an arrow from the star, at point $A$, at the top of the figure.}
\label{Doublelens}
\end{figure*}

\subsubsection{Discussion of one-lens model}
\label{222}
The $0.4$ ms group lens solution appears consistent with the premise
of the inclined sheet lensing model \citep{2014MNRAS.442.3338P}, which
predicts collinear positions of lensing images.  The time in the last
column of Table \ref{table:apex}, which we denote as $t_0
=-2{\tau}f/{f_{\rm D}}$, corresponds to the time required
for the arclet to drift in the secondary spectrum through a delay of zero.

The collinearity can be considered a post-diction of this model.  The
precise positions of each image are random, and with 9 images no
precision test is possible.  The predictive power of the sheet model
becomes clear in the presence of a second, off-axis screen, which will be discussed below.

\subsection{Double-lens model}
\label{doublelensmodel}

The apparent offset of the $1$ ms group can be explained by a second lens
screen.  The small number of apexes at $1$ ms suggests that the second
lens screen involves a single caustic at a different distance.  One
expects each lens to re-image the full set of first scatterings,
resulting in a number of apparent images equal to the product of
number of lenses in each screen.
In the
primary lens system, the inclination appears such that typical waves
form caustics.  For the sake of discussion, we consider an inclination
angle for lens 1 $\iota_1 = 0.1^o$, and a typical slope of waves
$\sigma_\iota = \iota_1$.   Each wave of gradient larger than
1-$\sigma$ will form a caustic in projection.
The number of sheets at shallower inclination
increases as the square of this small angle.  A 3 times less-inclined $\iota_2=0.3^o$
sheet occurs 9 times as often.  For the same amplitude waves on this
second surface, they only form
caustics for 3-$\sigma$ waves, which occur two hundred times less
often.  Thus, one expects such sheets to only form isolated caustics,
which we expect to see occasionally.  Three free parameters describe a
second caustic: distance, angle, and angular separation.  We fix the
distances from the effective VLBI distance ($D_1$ and $D_2$), and fit the angular
separations and angles with the 5 delays of the $1$ ms group.

\subsubsection{Solving the double-lens model}

Apexes 1'--5' share a similar 1 ms time delay, suggesting they are lensed by
a common structure.
We denote the position of the pulsar point as point $A$, the positions of the lensed image on lens 2 as point $H$, positions of the lensed image on lens 1 as point $B$, position of the observer as point $O$, and the nearest point on lens 2 to the pulsar as point $J$.
The lines $AJ\perp HJ$ intersect at point $J$, $HF\perp BD$ intersect at the point $F$, and $BG\perp HJ$ intersect at the point $G$.

A 3D schematic of two plane lensing by linear caustics is shown in
Fig. \ref{fig:3D_image}.
\begin{figure*}
\hspace*{-1in}\includegraphics[width=9in]{3D_image.pdf}
\caption{A 3D schematic of light path when light is doubly-refracted.
Two planes from left to right are the plane of lens 1,
  and the plane of lens 2.  The dash dotted lines represent the
  projected line-like fold caustics.
Light goes from $A$ (pulsar) to the first
  refracted point $H$ on lens 2 (line $HJ$, magenta dash dotted line), and
  then the second refracted point $D$, the image we observe, on lens 1
  (line $BD$, cyan dash dotted line), and finally the observer $O$.  Dash
  dotted lines show the light path of singly-deflected light path
  ($A-D-O$).  The crosses ($A_1$ on plane 1, and $A_2$ on
  plane 2) denote intersection of the un-deflected light through the
  lensing sheet.  $D$ and $J$ are the closest point of the lens caustic
  to the un-deflected path, which are the loci of single deflection
  images.  Thus, $A_2J\bot
  HJ$, and $A_1D\bot BD$.  The thick line on plane 2 indicates the
  real caustic, while the thin continuation indicates the extrapolated
  continuation beyond the cusp/swallowtail.
}
\label{fig:3D_image}
\end{figure*}

First, we calculate the position of $J$.  We estimate the
distance of $J$ from the $1$ ms $\theta$--$\sqrt{\tau}$ relation (see
Fig. \ref{thetatau}).  We determine the position of $J$ by
matching the time delays of point 4' and point 1', which is
marked in Fig. \ref{Doublelens}.  The long dash dotted line on the right side of Fig. \ref{Doublelens}
denotes the inferred geometry of lens 2, and by construction vertical
to $AJ$.

The second step is to find the matched pairs of those two lenses.
By inspection, we found that the 5 furthest points in $0.4$ ms group match naturally to the double-lens images.  These five matched lines are marked with cyan dash dotted lines in Fig. \ref{Doublelens} and their values are listed in the second column in Table \ref{table:double_lens_compare}.
\begin{table*}
\centering
\begin{tabular}{c|llllllll}
\hline
label&$\theta_{\parallel}$ (mas)  & $\tau_2$(ms) & $\sigma_{\rm \tau}$(ms)  & $\tau_{\rm M}$(ms) & $f_{\rm D}$(mHz)  &$\sigma_{f}$(mHz)      &  $f_{\rm M}$(mHz)& $t_1$(day) \\ \hline
1'& $-17.22$  &  1.0663     &0.0050    & 1.0663*        & $-43.08$    &0.84   & $-42.26$           & $-78$\\
 2'& $-16.36$  &    1.0370     &0.0059    & 1.0362       & $-41.27$    & 0.88   & $-41.04$          & $-73$\\
3'& $-16.08$  &   1.005    &0.011   & 1.027          & $-40.17$    &   0.87     & $-40.64$          & $-72$\\
 4'& $-14.45$  &   0.9763    &0.00088   & 0.9763*       & $-38.31$     &0.64    & $-38.31\dagger$  & $-63$\\
5'& $-13.68$  &    0.9495     &0.0094    & 0.9550       & $-35.06$     &0.78    & $-37.21$          &$-59$\\
 \hline
\end{tabular}
\caption{Comparison of time delay $\tau$ and the differential
  frequency $f_{\rm D}$ of the observation and the model fitting result in the
  double-lens model.  $\theta_{\parallel}$ denotes the angular offsets
  of the corresponding images at lens 1.
The values with star symbols on them are the points that we use to
calculate the position of $J$ and the point with a $\dagger$ symbol is
the point that we use to calculate the transverse velocity of the
pulsar $v_{\bot}$.  They agree with data by construction.  The last
column, $t_1$ is the time the lensed image on lens 2 takes to move
from point $H$ to point $J$, which is also defined in Section
\ref{subsec:doublelens}.}
\label{table:double_lens_compare}
\end{table*}
They are the located at a distance $389$ pc away from us. Here we define three distances:
\begin{equation}
\begin{aligned}
D_{\rm p2}&=620~{\rm pc}-415~{\rm pc} =205~{\rm pc},\\
D_{21}&=415~{\rm pc}-389~{\rm pc} =26~{\rm pc},
\end{aligned}
\end{equation}
where $D_{\rm p2}$ is the distance from the pulsar to lens 2, and $D_{21}$ is the distance from lens 2 to lens 1.

Fig. \ref{first_reflect} and Fig. \ref{second_reflect} are examples of how light is refracted on the first lens plane and the second lens plane.  We specifically choose the point with $\theta_{\parallel}=-17.22$ mas, which refer point 1' on lens 1 as an example.
Equality of the velocity of the photon parallel to the lens plane before and after refraction implies the relation:
\begin{equation}
\begin{aligned}
\frac{JH}{D_{\rm p2}}&=\frac{HG}{D_{21}},\\
\frac{FB}{D_{21}}&=\frac{BD}{D_{1}}.
\end{aligned}
\end{equation}

\begin{figure}
\centering
\includegraphics[width=1.0\linewidth,scale=1.0]{First_reflection.pdf}
\caption{Refraction on lens 2.
$A$ is the position of the pulsar.  $H$ is the lensed image on lens 2.  $B$ is
the lensed image on lens 1.  $AJ\bot HJ$ and $BG\bot HJ$.  We illustrate the scenario for point 1'.}
\label{first_reflect}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=1.0\linewidth]{Second_reflection.pdf}
\caption{Refraction on lens 1.
$H$ is the lensed image on lens 2.  $B$ is the lensed image on lens 1.  $O$ is the position of the observer. $HF\bot DF$ and $OD\bot HJ$.  As in the previous figure, we illustrate the scenario for point 1'. }
\label{second_reflect}
\end{figure}

We plot the solved positions in Fig. \ref{Doublelens}, and list
respective time delays and differential frequencies in
Table \ref{table:double_lens_compare}.
We take the error of the time delay $\tau$
in the double-lens model as
\begin{equation}
\begin{aligned}
(\frac{\sigma_{\tau_i}}{\tau_{2i}})^2 = (\frac{\sigma_{\tau1i}}{\tau_{1i}})^2+(\frac{\sigma_{\tau2i}}{\tau_{2i}})^2 + (\frac{\sigma_{\tau2j}}{\tau_{2j}})^2,
\end{aligned}
\end{equation}
where $\tau_1$ and $\sigma_{\tau1}$ represent the time delay and its
error from the $0.4$ ms group on lens $1$, and $\tau_2$ and
$\sigma_{\tau2}$ represent the time delay and its error from
the $1$ ms group on lens 2.  And $\tau_{2j}$ is the $\tau_2$ for
the nearest reference point in Table
\ref{table:double_lens_compare} with error $\sigma_{\tau2j}$.
Specifically,
for point $i=5'$ and $3'$, $j=4'$ is the nearest reference point; while for point $i=2'$, $j=1'$ is the nearest reference point.  The reference points are marked with star symbols in the fifth column in Table \ref{table:double_lens_compare}.

For the error of differential frequency $f_{\rm D}$, we add the error of the reference point (point 4') to the error of each other measured point:
\begin{equation}
\begin{aligned}
(\frac{\sigma_{f_i}}{f_{{\rm D}i}})^2=(\frac{\sigma_{f_{{\rm D}i}}}{f_{{\rm D}i}})^2+(\frac{\sigma_{f_{{\rm D}4'}}}{f_{{\rm D}4'}})^2
\end{aligned}
\end{equation}
where $f_{{\rm D}4'}$ and $\sigma_{f_{{\rm D}4'}}$ are the differential frequency
and we list its error of the point in the fourth row in Table
\ref{table:double_lens_compare}.

\subsubsection{Comparing with observations}
In order to compare $\tau$, we calculate model time delays $\tau_{\rm M}$ for these five
points, and list the results in Table
\ref{table:double_lens_compare}.  For points 4' and 1', they fit by
construction since we use these to calculate the position of $J$; for the remaining three points, all of the results are within 3-$\sigma$ of the observed time delays.

To compare differential frequency $f_{\rm D}$, we need to calculate the velocity of the pulsar and the velocity of the lens. We take the lenses to be static, and solve the velocity of the pulsar relative to the lens (in geocentric coordinates).  The pulsar has two velocity components, and the two 1-D lenses effectively determine one component each.
For $v_{\parallel}$, we derive the velocity $172.4 \pm 2.4$ km $\rm s^{-1}$,
which is $58.7$ mas/yr in a geocentric system,
from $f_{\rm D}$ of point $1$ in $0.4$ ms group.  The direct observable is the time to crossing of each caustic, denoted $t_0$ in Table \ref{table:apex}.

To calculate $v_{\bot}$, we choose the point 4', which has the smallest errorbar of differential frequency.
This gives a value of  $67.9\pm 2.8$ km $\rm s^{-1}$ for $v_{\perp}$,  which is $21.4$ mas/yr in geocentric system, with an angle
$\phi=-3\degree.7 \pm 0\degree.8$ west of north.  This represents the
pulsar-screen velocity relative to the Earth.  We can further
transform this into the local standard of rest (LSR) frame to
interpret the velocities in a Galactic context.
The model derived and observed velocities (heliocentric and LSR) are listed in Table \ref{Table:velocity}.  The
direction of the model velocity is marked on the top of the star in
Fig. \ref{Doublelens}.

\begin{table*}
\centering
\begin{tabular}{c|cccccc}
\hline
Parameter & $\mu_{\alpha*}$(mas yr$^{-1}$) & $\mu_{\delta}$(mas yr$^{-1}$) & $\mu_{l*}$(mas yr$^{-1}$) & $\mu_b$ (mas yr$^{-1}$) & $v_{l*}$ (km $\rm s^{-1}$) & $v_b$ (km $\rm s^{-1}$) \\
\hline
model pulsar-screen velocity & $-5.30 \pm 1.11$  & $61.97 \pm 1.11$  & $-56.45$ & 22.23 &  $\cdots$ & $\cdots$\\
VLBI pulsar proper motion & $2.16 \pm 0.19$ & $51.64 \pm 0.13$ & $-46.69$ & 28.02 & -137.24 & 82.34 \\
Screen motion & $\cdots$ & $\cdots$  & 9.76 & 5.79 & 18.00 & 10.68\\
\hline
\end{tabular}
\caption{Summary of velocities in double-lens model.  The velocities
listed in equatorial coordinates are the relative velocity in
heliocentric system, while the velocities in Galactic coordinates are
the relative velocities in LSR (Local Standard of Rest). $\mu_{\alpha*}=\Delta\alpha\cos(\delta)/t$ and $\mu_{l*}=\Delta l\cos(b)/t$, for we moved the center position from $(\Delta\alpha,\Delta\delta)$ or $(l,b)$ to (0,0).  $v_{l*}$ and $v_b$ are the linear velocities relative to the LSR.  The screen is
only moving slowly ($\sim 21$ km $\rm s^{-1}$).  Ellipses reflect the
unobserved and frame dependent parameters.
}
\label{Table:velocity}
\end{table*}

With this velocity of the pulsar, we calculate the model differential frequency $f_{\rm M}$ of points 5',3',2' and 1'. Results are listed in Table \ref{table:double_lens_compare}. The calculated results all lie within the 3-$\sigma$ error intervals of the observed data.

The reduced ${\chi}^2$ for time delay $\tau$ is $1.5$
for $3$ degrees of freedom
and $2.2$ for $f_{\rm D}$ for $4$ degrees of freedom.  This is consistent with the model.

Within this lensing model, we can test if the
caustics are parallel.  Using the lag error range of double-lensed point 4 (the best
constrained), we find a 1-$\sigma$ allowed angle of 0.4 degrees from
parallel with the whole lensing system.  This lends support to the hypothesis of a
highly inclined sheet, probably aligned to better than 1 per cent.

\subsubsection{Discussion of double-lens model}
\label{subsec:doublelens}
For the $1$ ms group, lens 2
only images a subset of the lens 1 images.  This could happen if
lens 1 screen is just under the critical inclination
angle, such that only 3-$\sigma$ waves lead to a fold caustic.  If the lens 2 was at a critical angle, the chance of encountering a
somewhat less inclined system is of order unity.
More surprising is the absence of a single-refracted
image of the pulsar, which is expected at position $J$.  This could
happen if the maximum refraction angle is just below critical, such
that only rays on the appropriately aligned double refraction can form
images.
We plot the refraction angle $\beta$ in the
direction that is transverse to the first lens plane in Fig.
\ref{vtrans}.
The fractional bandwidth of the data is about 10 per cent, making it unlikely that single lens
image $J$ would not be seen due to the larger required refraction
angle.  Instead, we speculate that the fold caustic terminates
near double-lensed image 5', and thus only intersections with the closer
lens plane caustic south of image 5' are doubly-lensed.

This is a generic outcome of a swallowtail
catastrophe \citep{Arnold1990}.  In this picture, the sheet just
starts folding near point 5'.  North of point 5', no fold appears in
projection.  Far south of point 5', a full fold exhibits two caustics
emanating from the fold cusp.  Near the cusp the magnification is the
superposition of two caustics, leading to enhanced lensing and higher
likelihood of being observed.

We denote $t_1$ the time for the lensed image on lens 2 to move from point
$H$ to point $J$.  From our calculation, we predict that on 2005 September 14, which is 59 days before the observation, the lensed image would have appeared overlayed on point $H_5$; and on 2005 August 26, which is 78 days before the observation, the lensed image would have appeared overlayed on point $H_1$.
The
model predicts the presence of a singly-lensed image refracted at
these points, in addition to the doubly-lensed images.

\begin{figure}
\centering
\includegraphics[width=1.0\linewidth]{Reflection_angle.pdf}
\caption{Deflection angle $\beta=\pi-\protect\angle AHB$ on lens 2.  Point $J$ denotes the expected position to form a single refraction image, which was not
  observed.   The small change in angle relative to the observed
  images precludes a finite refraction cut-off, since the data spans
  10 per cent bandwidth, with a 20 per cent change in refractive strength.  We
  propose a swallowtail caustic as the likely origin for the
  termination of the second lens sheet.
}
\label{vtrans}
\end{figure}

The generic flux of a lensed image is the ratio of the lens transverse
size to maximum impact parameter \citep{2012MNRAS.421L.132P}.  Near
the caustic, the lensed flux can become very high.  The 1 ms group is
about a factor of 4 fainter than the 0.4 ms group.  The high flux of
the second caustic suggests it to be relatively wide, perhaps a
fraction of an AU.  Due to the odd image theorem, one generically
expects two distinct set of double lensed arcs.  We only see one
(generically the outer one), which places an upper bound on the
brightness of the inner image.  In a divergent
lens\citep{1998ApJ...496..253C}, the inner image is generically much
fainter, so perhaps not surprising. For a convergent Gaussian lens,
the two images are of similar brightness, but a more cuspy profile
will also result in a faint inner image.  In gravitational lensing,
the odd image theorem is rarely seem to hold, generally thought to be
due to one lens being very faint.

One can try to estimate the chance of accidental agreement between
model and data.
We show the data visually in Fig. \ref{fig:tau-fD}.
\begin{figure}
\centering
\includegraphics[width=1.0\linewidth, angle=0]{tau-fD.pdf}
\caption{Model comparison.
Points with subscripts are derived from the double-lens model, see
Table \ref{table:double_lens_compare}.
Rectangles mark the 1-$\sigma$ error region.
Points 1' (only for $\tau$) and 4' were used to fit the model, and
thus do not have an error region.  The rectangles cover $10^{-3}$ of
the area in the dotted region bounded by the parabolic arc and the
data points.  We interpret this precise agreement
between model and data
is unlikely to be a random coincidence.
}
\label{fig:tau-fD}
\end{figure}

To estimate where points might lie accidentally, we conservatively
compare the area of the error regions to the area bounded by the
parabola and the data points, as shown by dotted lines.  This results
in about 10$^{-3}$, suggesting that the model is unlikely to be an
accidental fit.

\subsection{Distance degeneracies}
\label{sec:degeneracy}
With two lens screens, the number of observables increases: in
principle one could observe both single refraction delays and angular
positions, as well as the double reflection delays and angular
positions.  Three distances are unknown, equal to the number of
observables.  Unfortunately, these measurements are degenerate, which
can be seen as follows.  From the two screens $i=1,2$, the two single
deflection effective distance observables are
$D_{i{\rm e}} \equiv 2c\tau_i/\theta_i^2=D_i^2(1/D_i+1/D_{{\rm p}i})$.  A third
observable effective distance is that of screen 2 using screen 1 as a
lens, $D_{21{\rm e}}=D_1^2(1/D_1+1/D_{21})$, within the triangle that is formed by lens 1, lens 2 and the observer.  That is also algebraically
derivable from the first two relations:
$D_{{21}{\rm e}}=D_{1{\rm e}}D_{2{\rm e}}/(D_{2{\rm e}}-D_{1{\rm e}})$.
We illustrate the light path in Fig. \ref{fig:double_degeneracy}.
\begin{figure*}
\centering
\hspace*{-1in}\includegraphics[width=9in]{double_degeneracy.pdf}
\caption{Illustration of double-lens degeneracy.  As in
  Fig. \protect{\ref{fig:Singledegeneracy}}, all observables are identical
  for both the prime and un-primed geometries, including all pairwise
  delays and angular positions.  This degeneracy also holds in three dimensions.}

\label{fig:double_degeneracy}
\end{figure*}

In this archival data set, the direct single lens from the further
plane at position $J$ is missing.  It would have been visible $59$ days
earlier.  The difference in time delays to image $J$ and the double
reflection images would allow a direct determination of the effective
distance to lens plane 2.  Due to the close to $90 \degree$ angle $\angle~DAJ$
between lenses, the effect would be about a factor of 10 ill
conditioned.  With sufficiently precise VLBI imaging one could
distinguish if the doubly-refracted images are at position $B$ (if
lens 1 is closer to the observer) or position $H$ (if lens 2 is closer to the observer).  As described above, we interpret
the effective distances to place screen 2 further away.

\section{VLBI astrometry}
\label{sec:astrometry}

The model kinematics can be compared to direct measurements of pulsar
proper motion to infer the absolute motion of the lensing screen.

PSR B0834+06 was observed 8 times with the Very Long Baseline Array (VLBA), under the project code BB269, between 2009 May and 2011 January.  Four 16~MHz bands spread across the frequency range 1406 -- 1692 MHz were sampled with 2 bit quantization in both circular polarizations, giving a total data rate of 512 Mbps per antenna.  The primary phase calibrator was J0831+0429, which is separated from the target by 2.1 degrees, but the target field also included an in-beam calibrator source J083646.4+061108, which is separated from PSR B0834+06 by only 5 \arcmin.  The cycle time between primary phase calibrator and target field was 5 minutes, and the total duration of each observation was 4 hours.

Standard astrometric data reduction techniques were applied
\citep[e.g.,][]{deller12b,deller13a}, using a phase calibration
solution interval of 4 minutes for the in-beam calibrator source
J083646.4+061108.  J083646.4+061108 is weak (flux density $\sim$4 mJy)
and its brightness varied on the level of tens of percent.  The
faintness leads to noisy solutions, and the variability indicates that
source structure evolution (which would translate to offsets in the
fitted target position) could be present.  Together, these two effects
lead to reduced astrometric precision compared to that usually
obtained with VLBI astrometry using in-beam calibration, and the
results presented here could be improved upon if the observations were
repeated using the wider bandwidths and higher sensitivity now
available with the VLBA, potentially in conjunction with additional
in-beam background sources.

While a straightforward fit to the astrometric observables yields a pulsar distance with a formal error $<$1 per cent, the reduced $\chi^2$ of this fit is $\sim$40, indicating that the formal position errors greatly underestimate the true position errors, and that systematic effects such as the calibrator effects discussed above as well as residual ionospheric errors dominate.  Accordingly, the astrometric parameters and their errors were instead obtained by bootstrap sampling \citep{efron91a}.  These results are presented in Table~\ref{tab:vlbi}.

\begin{table}
\caption{Fitted and derived astrometric parameters for PSR B0834+06.}
\begin{threeparttable}
\begin{tabular}{ll}
\hline
Reference right ascension (J2000)\tnote{a}
							&  08:37:5.644606(9)\\
Reference declination (J2000)\tnote{a}
							&  06:10:15.4047(1)\\
Position epoch (MJD)			& 55200 \\
$\mu_{\mathrm{R.A.}}$ (mas yr$^{-1}$)	& 2.16(19) \\
$\mu_{\mathrm{Dec}}$	(mas yr$^{-1}$) & 51.64(13)  \\
Parallax (mas)	 				& 1.63(15) \\
Distance (pc)					& 620(60) \\
$v_{\mathrm T}$ (km s$^{-1}$)	& 150(15)\\
\hline
\end{tabular}
\begin{tablenotes}
\item[a]{The errors quoted here are from the astrometric fit only and do not include the $\sim$1 mas position uncertainty transferred from the in--beam calibrator's absolute position.}
\end{tablenotes}
\end{threeparttable}
\label{tab:vlbi}
\end{table}

\section{Discussions}
\label{sec:discussions}
\subsection{Interpretation}

The relative motion between pulsar and lens is directly measured by
the differential frequency, and not sensitive to details of this
model. B10 derived similar motions.  This
motion is in broad agreement with direct VLBI proper motion
measurement, requiring the lens to be moving slowly compared to the
pulsar proper motion or the LSR.  The lens is $\sim200$ pc above the
Galactic disk.  Matter can either be in pressure equilibrium, or in
free-fall, or some combination thereof.  In free fall, one expects
substantial motions.  These data rule out retrograde or radially
Galactic orbits: the lens is co-rotating with the Galaxy.  In pressure
equilibrium, gas rotates slower as its pressure scale height
increases, which appears consistent with the observed slightly slower
than co-rotating motion.  The modest lens velocities also appear
consistent with the general motion of the ISM, perhaps driven by
Galactic fountains \citep{1976ApJ...205..762S} at these latitudes above
the disk.  In the inclined sheet model, the waves move at Alfv\'enic
speed, but due to the high inclination, will move less than one percent of this
speed in projection on the sky, and thus be completely negligible compared to
other sources of motion.

Alternative models, for example, evaporating
clouds \citep{1998ApJ...498L.125W} or strange
matter \citep{2013PhLB..727..357P}, do not make clear predictions.  One
would expect higher proper motions from these freely orbiting sources,
and larger future scintillation samples may constrain these models.

In order to incline one sheet randomly to better than 1 per cent requires of
order $10^4$ randomly placed sheets, i.e. many per parsec.  This sheet
extends for $\sim$ 10 AU in projection, corresponding to a physical
scale greater than $1000$ AU.   These two numbers roughly agree,
leading to a physical picture of magnetic domain boundaries every
$\sim 0.1$ pc.  B0834+06 has had noted arcs for multiple years,
perhaps suggesting this dominant lens plane is larger than typical.
One might expect to reach the end of the sheet within decades.

A generic prediction of the inclined sheets model is a change in rotation
measure across the scattering length.  Over 1000 AU, one might expect
a typical RM (rotation measure) change of $10^{-3}$ rad/m$^2$.  At low frequencies, for
example in LOFAR\footnote{http://www.lofar.org/} or GMRT\footnote{http://gmrt.ncra.tifr.res.in/}, the size of the scattering screen extends
another order of magnitude in angular size, and the RM in different
lensed images are different, increasing to
$\sim 0.01$, which is plausibly measurable.  Even for an un-polarized
source, the left and right circularly polarized (LCP, RCP) dynamic spectra will
be slightly different.  Usually a secondary spectrum (SS) is formed by
Fourier transforming the dynamic spectrum and multiplying by its
complex conjugate.  To measure the RM, one multiplies the Fourier
transform of the LCP dynamic spectrum by the complex conjugate of the
RCP Fourier transform.  This will display a phase gradient along the Doppler
frequency axis.  In the SS, each pixel is the sum of correlations of
pairs of scattering points with corresponding lag and Doppler
velocity.  The velocity is typically linear in the pair separation,
which is also the case for differential RM.   This statistic is
analogous to the cross gate secondary spectrum as applied in
\citet{2014MNRAS.440L..36P}.

\subsection{Possible improvements}

We discuss several strategies which can improve on the solution
accuracy.  The single biggest improvement would be to monitor the speckle pattern over
several months, as the pulsar crosses each individual lens,
including both lensing systems.  This allows a direct comparison of
single lens to double-lens arclets.

Angular resolution can be improved using longer baselines, for example
adding a GMRT-GBT baseline doubles the resolution.  Observing at
multiple frequencies over a longer period allows for a more precise
measurement: when the pulsar is between two lenses, the refraction
angle $\beta$ is small, and one expects to see the lensing at higher
frequency, where the resolution is higher, and distances between
lens positions can be measured to much higher accuracy.

Holographic techniques \citep{2008MNRAS.388.1214W,2014MNRAS.440L..36P}
may be able to measure delays, fringe rates, and VLBI positions
substantially more accurately.  Combining these techniques, the
interstellar lensing could conceivably achieve distance measurements
an order of magnitude better than the current published effective
distance errors.  This could bring most pulsar timing array targets
into the coherent timing regime, enabling arc minute localization of
gravitational wave sources, lifting any potential source confusion.

Ultimately, the precision of the lensing results would be limited by
the fidelity of the lensing model.  In the inclined sheet model, the
images move along fold caustics.  The straightness of these caustics
depends on the inclination angle, which in turn depends on the
amplitude of the surface waves.  This analysis concludes a high degree
of inclination, and thus high fidelity for geometric pulsar studies.

\section{Conclusions}
\label{sec:conclusions}
We have applied the inclined sheet model \citep{2014MNRAS.442.3338P}
to archival apex data of PSR B0834+06.  The data is well-fit by two
linear lensing screens, with nearly plane-parallel geometry.  The
second screen provides a precision test with 10 observables (5 time delays and 5 differential frequencies) and 3 free
parameters (the marked points in Table \ref{table:double_lens_compare}).  The model fits the data to $\sim$ percent accuracy
on each of 7 data points.
This natural consequence of very smooth
reconnection sheets is an unlikely outcome of ISM turbulence.  These
results, if extrapolated to multi-epoch observations of binary
systems, might result in accurate distance determinations and
opportunities for removing scattering induced timing errors.  This
approach also opens the window to measuring precise transverse motions
of the ionized ISM outside the Galactic plane.

\section{Acknowledgements}

We thank NSERC for support. We acknowledge helpful discussions with
Peter Goldreich and M. van Kerkwijk.
We thank Michael Williams for photography help.
Siqi Liu thanks Robert Main and JD Emberson for helpful discussions on
improving the expression of the content.
The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

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redpajama_set_name: RedPajamaArXiv


text:
Venezuela's Teachers And Students Skip School For Survival Amid Venezuela's catastrophic economic meltdown, education experts say that it's getting much harder for children to get a good grasp of history, geography and their ABCs.
Venezuela's Teachers And Students Skip School For Survival
Venezuela's Teachers And Students Skip School For Survival 3:55
John Otis
Venezuelan Leidy Navarro (left) walks with her daughter Valentina Caceres back to their home in Ureña, Venezuela, after picking her up at school in Cúcuta, Colombia, in March. Juan Pablo Bayona/AFP/Getty Images hide caption
Juan Pablo Bayona/AFP/Getty Images
Venezuelan Leidy Navarro (left) walks with her daughter Valentina Caceres back to their home in Ureña, Venezuela, after picking her up at school in Cúcuta, Colombia, in March.
At a primary school in a middle-class neighborhood of Caracas, Venezuela, the students' parents play an outsize role.
Gasoline shortages have collapsed public transportation, making it hard for teachers to get to work. Others skip class to scrounge for food and medicine, both of which are in short supply in Venezuela. Due to low salaries, some teachers have quit.
That's why Karen Benini, the mother of a sixth-grader, often steps in to substitute even though she lacks a teacher's certificate.
"I'm not a teacher. I never studied to be a teacher. I'm a graphic designer," says Benini, 41, who volunteers two to three days per week.
Amid Venezuela's catastrophic economic meltdown, education experts say that it's getting much harder for children to get a good grasp of history, geography and their ABCs.
School staff are resigning in droves. Legions of students and teachers are among the 4 million Venezuelans who have fled the country in recent years. Those still going to school in the country often find that classes have been canceled due to power outages, water shortages and other breakdowns.
Some school buildings are falling apart, have been taken over by homeless squatters or are used by pro-government militias for training, says Nancy Hernández, a founder and board member of FENASOPADRES, a national association of PTAs.
In 2016, the last year the Venezuelan government released enrollment figures, about 8.5 million Venezuelan children were attending K-12 schools. Now, that figure may have dropped to about 6.5 million, according to rough estimates provided by Hernández.
One independent education group in Aragua state, just west of Caracas, reported that at the start of the current school year more than half of all students were no longer going to classes.
In a TV interview in May, Education Minister Aristóbulo Istúriz acknowledged problems but blamed them on U.S. economic sanctions and pointed out that, in spite of the government's challenges, public school remains free.
To make up for lost class time, Istúriz announced that the 2018-19 academic year, which normally ends in June, would be extended through July.
But Hernández, who is also a former national elections official, says that will make little difference.
"We, as an organization, have determined that the 2018-19 academic year has been lost," she says of the PTA group.
Many of the challenges faced by students and teachers are glaringly obvious in Ramo Verde, a mountainside slum on the outskirts of Caracas, where María Pérez has taught geography at a public school for the past 18 years. She's one of just four teachers still showing up for work. The other eight recently resigned because they couldn't survive on their $5 monthly salaries.
Pérez scrapes by peddling cellphone accessories on weekends. She also crosses the border into Colombia to stock up on food, which she resells on the streets and sometimes distributes to her malnourished students.
Raquel Castaño stands to the right of the entrance to her home in Ramo Verde, a poor neighborhood on the outskirts of Caracas, Venezuela, is a mother of five. She says her 15-year-old son often skips school to work delivering water to the community. John Otis for NPR hide caption
John Otis for NPR
Raquel Castaño stands to the right of the entrance to her home in Ramo Verde, a poor neighborhood on the outskirts of Caracas, Venezuela, is a mother of five. She says her 15-year-old son often skips school to work delivering water to the community.
The school is supposed to provide a midday snack but often there are no provisions in the cafeteria. Three of her students recently fainted, including one girl who had not eaten dinner the night before or breakfast that morning and collapsed during gym class.
"It makes me want to cry," Pérez says.
Many of her students skip school to help feed their families by doing odd jobs — such as hauling water.
During frequent electricity cuts in Ramo Verde, water pumps don't work. So residents must fill up buckets and containers at mountainside springs and lug them back to their homes. Some of Pérez's students now spend their days going door to door delivering spring water.
As she walks through the slum, Pérez spots one of them, Roynel Riso, a skinny 14-year-old. In exchange for about 5 gallons of water, families will pay Riso with a bag of rice or pasta. He prefers payment in kind because hyperinflation has rendered the bolívar, Venezuela's currency, nearly worthless.
Riso skips two days of school per week and laments: "I miss going to math class."
Yureibis Coronado, a mother of three who lives in a three-room shack in Ramo Verde, says shortages of water and soap promote absenteeism because many parents refuse to send their children to school in dirty uniforms.
"It's very worrisome," she says, "because kids go to school today so they can be somebody tomorrow."
Despite professing loyalty to her students, Pérez is thinking of joining the exodus of Venezuelan educators.
This summer she plans to visit friends in the United States who have set her up with part-time work. She'll still be teaching — but this time as a spinning instructor at a gym in North Carolina.
Venezuela crisis


text:
Izhmorsky () is an urban locality (an urban-type settlement) in Izhmorsky District of Kemerovo Oblast, Russia. Population:

References

Urban-type settlements in Kemerovo Oblast

redpajama_set_name: RedPajamaWikipedia