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But in 2010, Miami Beach banned short-term rentals in most areas of the city and Nichols was fined about $3,000 for her properties. Still, because her rentals were her primary source of income, Nichols kept renting her properties. She kept them well-maintained, she said, and they were not subject to any nuisance enforcement action.
"I just sort of had to make sure that I had nice groups of people that weren't disturbing the neighbors, and for the most part it worked out," she said.
That is, until March 2016, when Miami Beach passed a new ordinance raising the first violation fine for a resident caught renting short-term to $20,000. Each subsequent fine increases by another $20,000 and can be as high as $100,000. By contrast, Nichols used to make about $14,000 a month from short-term rentals, she said.
Since March 2016, Miami Beach has issued $12.1 million in fines, but only $174,000 have been paid, according to city records. Nichols stopped renting short-term when the fines increased, she said, and her properties have not been fined the higher penalty.
But Miami Beach created an exception in October 2016, when it made it legal for short-term rentals to be conducted in historic buildings that front Harding Avenue, a move preservationists and developers supported in the hopes it would encourage property owners to improve the aging buildings.
That exception, Nichols alleges in her suit, is discriminatory and "not rationally related to any legitimate government interest." At the time the ordinance was passed, Miami Beach said that the buildings where short-term rentals are now allowed are considered as "contributing" to the architectural character of the North Shore National Register Historic District.
Ross Milroy, a Miami Beach real estate expert who runs an advocacy group in support of rental reform, said the lifting of the ban in North Beach is actually proof that short-term rentals are lucrative businesses for residents — and the city.
"These properties now bring tourists, tourist dollars, and jobs to the local community and taxes to the city," said Milroy. He worked for more than a year with the Goldwater Institute, a national nonprofit civil rights organization, to bring the lawsuit against Miami Beach.
Nichols also alleges in the suit that the fines are "so great as to shock the conscience of reasonable people and are patently and unreasonably harsh and oppressive."
"Of all the laws I have ever seen a political body pass, this has been the most hurtful for me and other people," she said. "... In the 10 houses around me, I know three of them have been fined $20,000. People who haven't been caught yet don't even want to sign a petition because they don't want to be targeted."
Miami Beach has heavily policed short-term rentals in the past two years in an attempt to stop tourists from overrunning residential neighborhoods and causing disturbances. The city's fines are the highest in the country, higher even than other cities like San Francisco and New York City, where some of the most contentious battles against short-term rentals have been waged.
Nichols believes the fines are already preempted by state law, which limits the fines the Beach's zoning board can impose to $1,000 per day for the first violation and $5,000 per day for the repeat violation. "Per day" refers to each day after the initial fine is imposed that the illegal activity continues, said Matthew Miller, senior attorney at the Goldwater Institute, who is representing Nichols. The Institute also filed short-term rental lawsuits against Seattle, Washington, and Pacific Grove, California.
"[In Miami Beach], it's immediately $20,000," Miller said. "That's enough to ruin most property owners."
But Miami Beach spokeswoman Melissa Berthier said in an email that Miami Beach is authorized to "create an alternative code enforcement system (which it has done so) and thus, is not obligated to comport to those monetary limitations set forth in Chapter 162 of the Florida Statute." The city declined to comment more generally on the lawsuit.
Nichols is asking a judge to overturn the city's policy.
Nichols believes there are solutions to the issue of problematic short-term rentals other than banning the practice outright. Police should be called when there are instances of loud tenants and disturbances, she said, and homeowners will typically cooperate because most don't want parties in their homes.
"There are all kinds of ways to control parties and crowds and noise that don't involve length of stay," she said. "I'm generating a lot of extra revenue for the city as are all the other investors and they are showing us no respect for the investment we've made and the contributions we've made."
Chabeli Herrera: 305-376-3730, @ChabeliH
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Poudre School District starts spending 2016 bond money on new furniture
Poudre School District Board of Education approved $2 million to be used for new furniture, more than $1.6 million for asphalt improvements.
Poudre School District starts spending 2016 bond money on new furniture Poudre School District Board of Education approved $2 million to be used for new furniture, more than $1.6 million for asphalt improvements. Check out this story on coloradoan.com: https://www.coloradoan.com/story/news/education/2019/03/29/poudre-school-district-board-education-approves-2016-and-2010-bond-projects-sutherland/3288341002/
Kelly Ragan, Fort Collins Coloradoan Published 1:50 p.m. MT March 29, 2019 | Updated 4:42 p.m. MT March 30, 2019
Cash is starting to flow to various projects as Poudre School District begins using money from a bond voters approved in 2016.
The district's board of education approved $2 million to be used for furniture renovations and updates for existing buildings, according to materials provided by the school board at Tuesday's meeting.
The district plans to buy classroom furniture — such as seating, desks, carts, and whiteboards — office furniture, library furniture and more. It plans to use 10 vendors to get the best deal, according to materials provided by the board.
Voters approved the $375 million bond and $8 million mill levy override in 2016. Ongoing litigation delayed the district from using the funds for two years, but the Colorado Court of Appeals ruled in the district's favor in February 2018.
After the Colorado Supreme Court denied a request to hear the case in August, the school district was allowed to move forward with its plans for the funds.
Of the money, $40 million was earmarked for improvements to existing schools — $12 million going to improvements based on school requests and $28 million going to facilities' deferred maintenance.
The district is also using the money to build new schools and facilities, including one middle/high school in Wellington, one middle/high school east of Interstate 25, one elementary school, a new athletic complex, a transportation maintenance facility, and an addition to Zach Elementary School.
The new middle/high schools are set to open in fall 2022. The new elementary school is set to open in fall 2021.
The 2016 bond money isn't the only money moving in the district.
The board also approved spending 2010 bond money to replace aging asphalt. Rocky Mountain High School's French Field, Lincoln Middle School, Poudre Community Academy and Putnam Elementary School can expect to see improvements. Lincoln, Poudre Community Academy and Putnam projects are set to cost no more than $721,711. Rocky's French Field project is set to cost no more than $941,772.
The 2010 bond provided $120 million for improving, equipping and furnishing district buildings and other properties, according to the district's website. So far, the money has helped spur on 450 projects, totaling $81 million.
The improvements include new technology in classrooms, improved safety and security, and upgrades — such as Americans with Disabilities Act compliance, roofs, electrical systems and more.
Read or Share this story: https://www.coloradoan.com/story/news/education/2019/03/29/poudre-school-district-board-education-approves-2016-and-2010-bond-projects-sutherland/3288341002/
What Supreme Court inaction on topless ban means
Flu cases increase in Larimer County

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Home Video Get ready for a second wave: Ranil
Get ready for a second wave: Ranil
1 July 2020 11:12 pm - 12 - {{hitsCtrl.values.hits}}
Sri Lanka should be prepared to face a possible second wave of COVID-19 pandemic without delay, former Prime Minister Ranil Wickremesinghe said today.
Speaking during a gathering at UNP Headquarters Sirikotha today, Mr. Wickremesinghe said the government did not seemed to have focused on it.
"President Gotabaya Rajapaksa took several steps to control the first wave of COVID-19. UNP also came up with some proposals which were accepted by the government. The pandemic was successfully controlled due to this reason. Some accused us of getting into deals with the government. We only intervened on behalf of the people," Mr. Wickremesinghe said.
"There was an opportunity to bring in a new legislation to control COVID-19. We, in the UNP made several proposals in this regard. We called for the increase of testing. This was ignored," he added.
"Sri Lanka should ready itself to stand up to a possible second wave even at this moment. Health is a major issue faced by the Sri Lankan people currently. It is also a major issue for other countries as well. It is everyone's duty to prevent a second wave. UK is greatly affected by COVID-19. It is questionable whether the UK could get out of this crisis. How could Sri Lanka get out of it if a country like the UK is unable to get out of it?" the former Premier questioned.
"The second wave has already been found in the USA and in China. Over 100,000 have died of COVID-19 in the USA, despite claims made by President Trump that it was not a major issue. It is also spreading in New Delhi and Mumbai and rampant in some parts of Europe. Some parts of the UK have gone into a lockdown once again. The WHO had warned of a second wave," he cautioned.
The Former Prime Minister then questioned about how Sri Lanka had utilized the funds received from the WHO. "The government received these funds at a time when it went on saying there were no funds to carry out testing. WHO claimed that it had given US$ 230 million to Sri Lanka. However, Minister of Health claimed the government only received US$ 1.9 million. Government should come up with a clarification on it.
Mr. Wickremesinghe also said it was not fair to blame the navy for the COVIV-19 spread in Sri Lanka and said the sailors were not given protective equipment.(Yohan Perera)
Roshan Wednesday, 01 July 2020 11:15 PM
I wish the second wave hits you.
Muzamil Wednesday, 01 July 2020 11:27 PM
Once you get it we will believe you.
ChanakaJ Thursday, 02 July 2020 12:05 AM
Perhaps concentrate on the Central Bank bond scam and sort that mess out first!
Johan Thursday, 02 July 2020 12:07 AM
First wave against Srikotha finished now second Wave is on move must get ready.
Hiran Thursday, 02 July 2020 08:10 AM
Sajith has already organised many waves for you. You will need a place to hide.
A Thursday, 02 July 2020 08:43 AM
I think the wave has hit you already u arr nuts
Sambo Thursday, 02 July 2020 08:46 AM
From politics to health. did politics let you down or you let it down.
Sokrates Thursday, 02 July 2020 09:07 AM
As one can see from the comments here, the people of Sri Lanka are so stupid that it cannot be described. They won't believe the danger until they die in front of a hospital because it's overcrowded with corona patients. There is no testing in this country (not even half a percent of the population has been tested), otherwise the number of infected people can no longer be kept secret. The Rajapaksa Mafia clan and its military go over dead bodies because of the election.
Sando Thursday, 02 July 2020 11:25 AM
You only wish Doom. There will be no second wave here.
Sri Lankan Thursday, 02 July 2020 11:37 AM
6 August second wave will totally wipe you out this time.Be cautioned and get ready now.
P Daniel Thursday, 02 July 2020 12:10 PM
Very valid questions raised by RW on very low testing rate and what happened to the money given by WHO.
nadisha Thursday, 02 July 2020 01:37 PM
Yes. but people are so blinded by party and colour they cannot see whats under their very nose. typical frog in the well sri lankans!


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Q: $this->authorize('gate-name') in laravel 9 with 2 parameters I'm learning authorization in laravel 9 using 'gate'. In my case, I want to protect my controller so who can access the controller only users who have "delete" and "edit" 'gate'.
Then I created 2 new gates in 'App\Providers\AppServiceProvider' defined as follows:
Gate::define('edit', function (User $user) {
    return $user->permission === 'edit';
});

Gate::define('delete', function (User $user) {
    return $user->permission === 'delete';
});

Then, I need to add $this->authorize('edit') and also $this->authorize('delete') in the controller, unfortunately it can't be done, laravel only accept once of $this->authorize('edit') or $this->authorize('edit').
The problem is, I have to add 2 conditions there, I also can't write an array as a parameter.
What I want is like this:
$this->authorize('edit' && 'delete')

Or:
$this->authorize(['edit', 'delete'])

Unfortunately, I can't add both.
Basically, the user have to pass 2 checks (must have "edit" AND "delete' gate) using the laravel 'gate' feature in my controller.
The check is like this:
"Does that user have edit access"? OR "Does that user have delete access"? if "yes/true", allow entry to the controller, else "return 403"
FOR EASIER EXAMPLES:
I have this controller to delete a post on my web:
public function destroy(Post $post)
   {
       $this->authorize('edit'); // I want not only check 'edit', I want to check 'delete' too
       $post->delete();
   }

How to apply it?
I have checked this question but no answer

A: You can use the Gate facade to interact with the authorization system and without throwing an exception (just checking gates):
if (Gate::check(['edit', 'delete'])) {
    // has all these permissions
} else {
    // does not have all these permissions
}

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Video: Migrants From Ebola-Stricken Congo Marched Through Streets of San Antonio
Video footage shows migrants from ebola-stricken Congo being marched through the streets of San Antonio at night as one of their chaperones assaults a cameraman for filming the scene.
The clip shows migrants being led to a nearby church by city workers. Some of the illegal migrants hide their faces while one of the individuals leading the group assaults an Infowars cameraman in an attempt to stop him from filming.
"What country do you think you're in, man?" asks the cameraman.
As we highlighted yesterday, large groups of migrants from the Democratic Republic of the Congo have been arriving in the U.S. after they initially fled to Brazil. Congo has been hit by one of the biggest ebola outbreaks in history, with 2,000 recorded cases in the last 10 months.
Some cities say they are overwhelmed with the number of migrants arriving and are sending them to other areas of the country.
Border Patrol officials said that 500 people from African countries had been arrested by Border Patrol's Del Rio Sector in Texas alone in the six days after May 30.
Infowars reporters documenting the processing and transfer of the migrants were assaulted by both city workers and a waitress working at a nearby restaurant simply for covering the story.
The ebola virus can remain dormant within humans for three weeks.
Meanwhile, Dr Michael Ryan, the executive director of the WHO's health emergencies program, told BBC News that the global spread of deadly diseases is becoming "a new normal" thanks to "large and highly mobile populations".
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These custom banners for business are generally very durable and affordable. Moreover, the material these custom banners for business are made from is specifically designed for UVC inkjet. We can design the posters with high quality image printing, with enhances color quality. The vinyl contained in it ensures that the custom banners for business remain protected from UV and extreme high temperature. They can even survive for 3-5 years with constant exposure to sunlight. The flexibility of the material makes it suitable for eyelets and welding to help users fix them up easily.
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GENERAL ENTERTAINMENT ARTS & CULTURE COMMUNITY BUSINESS SPORTS TRAVEL HEALTH & WELLNESS EDUCATION TECHNOLOGY THINGS TO DO
Gulf crown princes dealt with Washington lobbyists to smear Qatar -- GCC Crisis Updates Week 51
Khadiza Begum
Here's what's happened since last week's updates.
Amir participates in extraordinary OIC summit
The Amir His Highness Sheikh Tamim bin Hamad al Thani attended on Friday, along with their highnesses and majesties head of Islamic delegations, the opening session of the Extraordinary Summit of the Organization of Islamic Cooperation (OIC) at the Conference Center in Istanbul, Turkey, QNA reported. The summit discuss the serious developments taking place in the State of Palestine. The meeting was attended by the members of the official delegation accompanying HH the Amir, and their Excellencies, members of the official delegations and guests of the Summit, the report said.
Anti-Qatar lobby
Photo credit: iStock by Getty Images
The crown prince of Saudi Arabia and the UAE have been dealing with a pair of controversial Washington lobbyists to influence the US government against Qatar, according to a new report revealed by Associated Press.
The former Republican Party official Elliott Broidy and businessman George Nader – supposedly promoted anti-Qatar policies at the maximum levels of US government in exchange for Saudi and Emirati favor.
In return Broidy and Nader tried to secure huge military and consulting contracts from Riyadh and the UAE.
This findings came out of the investigation by Associated Press(AP), based on interviews with more than two dozen people and hundreds of pages of leaked emails between the two men. The emails reviewed by the AP included work summaries and contracting documents and proposals.
Qatar-Australia trade ties reviewed
Photo credit: Peninsula Qatar
Minister of Economy and Commerce, H E Sheikh Ahmed bin Jassim Mohammed Al Thani, met the visiting Australian Minister for Agriculture and Water Resources, David Littleproud, and his accompanying delegation,Peninsula Qatar reported. During the meeting, they reviewed the bilateral relations and discussed aspects of joint cooperation, especially in the field of economic, trade and investment, and means of developing them. The meeting also discussed developments on the subject of Australian livestock exports to the Middle East.
What are your thoughts on these latest developments in the ongoing GCC crisis? Drop us a line and tell us your opinion in the comments below. Also, don't forget to like and share this article?
(Cover Photo credit: Michael Reynolds/European Pressphoto Agency)
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Dee and I and Dee's son Russ Granger will be traveling from Oregon to Austin Texas to watch the MotoGP and MotoAmerica races, and to promote my book "Racing the Gods." Most of you have probably seen the cover art but here it is again.
We are going a day early. On Thursday evening there will a meet and greet at Ducati Austin and I'll sign copies of books for folks. There will also be sales and signings at the racetrack on Friday, Saturday, and Sunday, but we don't yet know exactly where or when. I'll keep you posted. We have finalized the artwork for the full dust jacket. Just click on the link below — it's an Adobe .pdf file so you'll need to have Adobe reader to view it.
I hope to see at least some of you there. It will be fun.


2000 Chevy Malibu MAF Ground problem.
1996 Chevy Van G1500 5.7L Computer Problems.
In this video I will show you how to test a GM 3-wire MAF sensor using a lab scope.
Follow along and let me teach you some fundamental tests that I use on every vehicle that has a low power complaint.


In early April, Trimble launched Farmer Core, a new entry-level Trimble Ag Software subscription that enables farmers to connect all aspects of their farm operation. Available online and on any mobile device, Farmer Core is a powerful yet affordable software-as-a-service (SaaS) that integrates machine-generated data from precision ag displays to simplify farm setup and streamline farm operations.
Farmer Core leverages the new AutoSync feature, which automatically syncs guidance lines, field names, boundaries, landmarks and operator information across Trimble Ag Software and Trimble displays using the Precision-IQ field application. Precision-IQ is used to collect and manage data from in-field activities. By reducing human error and eliminating the need to manually share data via USB, this new AutoSync functionality improves overall farm record integrity.
AutoSync is included with Trimble Ag Software subscriptions to Farmer Core, Farmer Fit or Farmer Pro. With AutoSync, Farmer Core significantly reduces duplication, data re-entry and human error because the creation and ongoing management of field and operator information—whether online, via the Trimble Ag mobile app or on the display—is automatically synced within minutes across the entire farm operation.
Farmer Core is a powerful addition to the Trimble Connected Farm® solution, a unified suite of precision ag applications covering all aspects of modern agricultural management. From the office to the field, all year round, Trimble Connected Farm enables growers to perform critical farm work smarter, faster and more cost-effectively. Through universal vehicle and implement integration, seamless data transfer and analysis as well as the ability to leverage Trimble's leading satellite-delivered positioning correction services, farmers can connect as much or as little of their operation as they choose, with easy options for expanding and upgrading as desired.
In addition, Farmer Core, Farmer Fit and Farmer Pro subscriptions enable users to work with precision ag data in real time, including data imported via APIs from third-party displays.
Simplify Farm Setup: Create client/farm/field names, import or draw field boundaries and map landmarks with Trimble Ag Mobile, which will then sync across connected devices such as laptops, smartphones, tablets and Trimble displays using the Precision-IQ field application.
Streamline Farm Operations: Manage guidance lines boundaries, field names, landmarks and operator data across connected devices in a farm operation, integrating all machine-generated data from Trimble displays and other sources via APIs.
Improve Reliability of Farm Records: Track purchases and costs by field, improve consistency of precision ag data and generate reliable 'proof-of-placement' reports for a farmer's own farm records and for third parties.
A Farmer Core subscription is $199 per year. Connecting to Trimble displays with AutoSync requires a Display Connection, which is $99 per display per year. For more information or to purchase Farmer Core, visit: https://agriculture.trimble.com/product/farmer-core.


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The Pros and Cons of Kangaroo Leather
Quick, where does your leather come from? Cow, calf, or sheep, usually, but there's another option that you need to know: kangaroo. Kangaroo leather, also sometimes called K-leather, is what most people would call an exotic leather, though that term typically brings to mind rare and exalted animals. In truth, kangaroos are to Australia like deer are in North America, where they outnumber humans two-to-one — many consider them pests and they're far from rare.
That might make you feel better about picking up some kangaroo boots and contributing to controlling their population. When we saw the release of Viberg's new Kangaroo Chelsea boot, we decided to take a closer look at this unusual leather and explain why it's worth adding to your collection.
Strong and Supple
Kangaroo leather is lighter, stronger, and more flexible than goat or cow hide. It's usually thinner too, given you can make tough-as-nails kangaroo boots with skin that's barely a millimeter thick. (Cowhide boots are usually 1.4 to 2 millimeters.) Unsurprisingly, this means that they make a much lighter final product: kangaroo leather boots usually weigh half as much as comparable cow-leather ones.
All that's because the skin of the animals themselves are very different. The collagen fibers that make up kangaroo hide are fine, concentrated, highly uniform, and parallel to the surface of the skin, unlike cow skin's irregular, bundled structure. Kangaroo hide also has very low fat content and a thin grain layer, without sweat glands and erector pili muscles, which means it doesn't require the splitting and shaving that some other leathers require (hence the resulting thin, supple, strong leather). Plus, elastin is evenly distributed throughout the skin, which means it's uniformly stretchy. All of these factors give kangaroo leather a ton of tensile strength: it can stand being pulled apart.
One of the most common uses of kangaroo leather is in whips because it's super supple. It's flexible enough to be easily braided and whipped through the air. Another popular use for kangaroo leather? Motorcycle suits, where it's highly valued for its resistance to tearing and abrasion. And that's a serious testimonial to k-leather's toughness. Think about it, in the kind of sport where a mistake leaves you smeared across the asphalt, you want the only thing between your skin and a bloody, bloody disaster to be as tough as possible. Kangaroo leather is that thing.
Kangaroo leather comes in both chrome-tanned and veg-tanned varieties, so you'll want to check out the difference between the two before you buy.
Image via Viberg.com
The Downsides of Kangaroo Leather
K-leather has a noticeable grain and does crease easily, though that creasing doesn't usually lead to cracking because of the strength of the collagen fibers. Unless it's corrected, it's usually not the smoothest leather — almost all kangaroo leather has scars. It's not the shiniest either, kangaroo has a matte texture that develops a patina quickly and it darkens faster than other leathers as well.
This is, of course, all a matter of preference, and there are plenty of folks who happily trade off a shiner, more perfect-looking leather for a lighter, stronger, more flexible one that will develop character quickly. We can't make that call for you, it just depends on what you're looking for and what's already in your wardrobe.
The Big Con
The real con of kangaroo leather is the fact that it comes from kangaroos and people have a lot of feelings about kangaroos. Adidas' most popular soccer shoe of all time, the Copa, is made from kangaroo leather — but their marketing typically calls them "k-leather" to avoid putting anybody off. That said, there's a lot of people who argue kangaroos are pest animals whose numbers are reasonably kept down with annual culling. Which means eating the meat and turning the hides into leather for, say, your new boots, is the responsible thing to do.
On the other hand, there are lots of environmental activists who strongly disagree. A quick google and you'll find lots of phrases like "the Australian killing industry," concerns about how humane the culling process really is, and lots and lots of photos of kangaroos looking plaintively cute.
We can't really make this call for you except to say that kangaroos are not an endangered species and leather is always made from dead animals. If you're okay wearing leather, then you're more than likely to be fine wearing kangaroo leather.
Kangaroo is a strong, supple, durable, light and long-wearing leather that makes boots that will last you for years. If you're the kind of guy who's looking for the character of an easy patina and doesn't mind explaining the fact that kangaroos are certainly pest animals, then it's definitely worth investing in a pair.
Featured image via Viberg.
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Mel Compo
Mel Compo is a writer, editor, and general word-geek from Brooklyn, New York. When they're not writing about the finer side of men's footwear they can be found lurking around the streets, trains, and museums of NYC, ostensibly doing something urgent but actually just looking around for menswear style inspiration.
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8 thoughts on "The Pros and Cons of Kangaroo Leather"
Interesting and helpful article. I've been thinking about getting Kangaroo RM Williams, happy to learn that it's not too delicate or weak of a leather, and why it is so.
Awesome! Hope you enjoy them, Armin.
Your article is informative.
Since kangaroo leather is strong, supple, durable, light and long-wearing, I think it may be quite suitable for jackets.
Where in Australia people can buy kangaroo leather jackets? (cities? stores?)
You'd have to Google that one, Sam!
I was issued kangaroo skin boots in the Australian Army and can guarantee that the leather is tough and light. Pretty much scuff proof as well.
Haha that is excellent, and of course the Australian army would issue them. Thanks for the comment, Nathan!
Hey Nick, I like roo shoe leather and jumpin' jacket leather too! Has anybody thought about making rat wraps? Went to NY once and there was some size 13s with xtra wide soles near the hotel climbing out of a drain! Just a thought of shoes there…. Great article!
hahaha! Thanks for brightening my morning, Kevin.


Vitamin C, also known as ascorbic acid, is an important and powerful antioxidant. Many parts of the human body, such as the immune system, require it to function properly. The RDA (Recommended Daily Allowance) for adults is no less than 60 milligrams a day.
Citrus fruits contain the most Vitamin C among fruits and vegetables. Most purchased citrus juices or canned fruits are labeled with the amount of Vitamin C per serving. However, there are two easy methods to measure which juices have higher contents of Vitamin C, if you want to do it yourself.
Use a Vitamin C Test Strip for Method #1. These small papers are chemically treated to measure the amount of Vitamin C in fruit juices, and are typically used in labs. They are easy to use and can be purchased online in amounts of 50 to 100 strips per box. Follow the manufacturer's directions for how to use and dispose of them.
Make a Vitamin C testing solution for Method #2. Measure 1 teaspoon of cornstarch into a drinking glass and add 1 to 2 tablespoons of cold water. Stir well, making a paste, and then add an additional 1/2 cup boiling water. Stir this mixture until the cornstarch dissolves.
Pour 1 cup (75 ml) of water into a second glass and add 10 drops of the cornstarch solution, using an eyedropper. With the second eyedropper, add iodine to the mixture a drop at a time, until the solution turns dark blue or purple. The amount of iodine needed will vary; pause for a few seconds between drops to allow the iodine to mix with the solution, stopping once it has reached the indicated color.
Remove 1/10 cup (5 ml) of the iodine and cornstarch solution. Pour this into a third glass, and add 10 drops of any citrus fruit juice. The solution will become clear, as ascorbic acid causes iodine to lose color. The clearer the solution, the stronger the concentration of Vitamin C.
Make sure eyedroppers are washed before using on a second experiment.
Vitamin C esting strips can only be purchased online at this time from select companies.


text:
\section{Introduction}
Well-defined machine learning tasks have been crucial for machine learning researches.
Major deep learning breakthroughs in the field of computer vision such as AlexNet \cite{alexnet}, VGGNet \cite{vgg} and ResNet \cite{he2016deep} could not be possible without Imagenet dataset and challenges \cite{imagenet}.
In the field of reinforcement learning, open-source platforms like MuJoCo \cite{mujoco} and Deepmind Lab \cite{deepmindlab} provide challenging environments for the studies.
However, it is hard to find machine learning task suite for algorithmic reasoning although reasoning has always been a significant subject for many machine learning studies.

It is theoretically proven that carefully designed neural network models can simulate any Turing machine \cite{siegelmann1995computational}.
Hence, there have been studies applying neural network models to solve algorithmic tasks such as learning context-sensitive languages \cite{gers2001lstm}, solving graph questions \cite{graves2016hybrid}, and composing low-level programs \cite{reednpi}.
Also, there have been attempts to train neural networks with simple numerical rules such as copy, addition or multiplication \cite{stackrnn,neuralgpu,gridlstm,neuralturing}.
However, it has been unclear whether the proposed models express computational powers equivalent to Turing machines in practice.
To provide a method to test the computational powers of neural network models, we propose a set of number sequence prediction problems designed to fit deep learning methods.

A number sequence prediction problem is a kind of intelligence test for machine learning models inspired by number series tests, which are conventional methods to evaluate non-verbal human intelligence \cite{nonverbal}.
A typical number series test gives a sequence of numbers with a certain rule and requires a person to infer the rule and fill in the blanks.
Similarly, a number sequence prediction problem requires a machine learning model to predict the following numbers from a given sequence.
The numbers are represented as a sequence of digit symbols; hence the model has to learn discrete transition rules between the symbols such as carry or borrow rules.

To be specific, we suggest two types of number sequence prediction problems: the number-level problems and the digit-level problems.
A number-level problem provides a two-dimensional grid of digits as an input where each row of the grid represents a multi-digit number.
The target would be a grid of the same format filled with the following numbers.
Solving a number-level problem is equivalent to constructing the combinatorial logic for the transition rules.
On the other hand, a digit-level task provides a single digit as an input per each time step.
A model needs to simulate a sequential state automaton to predict the outputs.
The type of the state machine required can vary from a finite state machine to a Turing machine, depending on the generation rule of the sequence.

The number sequence prediction problems are good machine learning tasks for several reasons.
First, typical deep learning models can easily fit into the problems.
Generative models for 2D images can be directly applied to solve the number-level problems, and recurrent language models can fit into the digit-level problems after minimal modifications.
Next, it is possible to define the complexity and difficulty of the problem.
Like Kolmogorov complexity \cite{chaitin1977algorithmic}, we can define the complexity of a problem with the structure of the minimal automaton needs to be simulated.
Finally, we can generate an arbitrarily large number of examples, which is hard for many machine learning tasks.

To empirically prove that the number sequence prediction problems can effectively evaluate the computational capabilities of machine learning models, we conduct experiments with typical deep learning methods.
We apply residual convolution neural network (CNN) \cite{he2016deep} models for the number-level problems, and recurrent neural network (RNN) models with GRU \cite{gru} or LSTM \cite{hochreiter1997long} cells to the digit-level problems.
We also augment RNN models with stack \cite{stackrnn}, external memory \cite{neuralturing} and attention \cite{bahdanau2014neural} which might help models solve more complex digit-level sequence prediction tasks.
One-dimensional CNN models can be applied to digit-level sequences, but it is not equivalent to solving digit-level problems because for the CNN models the data needs to be given at the same time in parallel, losing the sequential nature of the problems.
For each type of sequences, we measure the complexity of it by designing an automaton equivalent to the generation rule.
In the experiments of the number-level problems, sequences are generated by various linear homogeneous recurrence relations.
Since the digit transition rules of the relations can be implemented with combinatorial logic, we measure the complexity and the difficulty of a sequence from the width and the depth of the logic.
Experiments show that CNN models are capable of learning the compound operations of number-level sequence generation rules but limited to certain complexity.
Digit-level sequence prediction problems can be solved with state automata.
Therefore, we define the complexity of a problem with the computing power of the automaton and choose sequences with complexities of finite state automata, pushdown automata, and linear bound Turing machines.

The contributions of this work are as follows:
\begin{itemize}
\item We propose a set of number sequence prediction problems for evaluating a machine learning model's algorithmic computing power.

\item We define methods to measure complexities and difficulties of the problems based on the structure of automata to be simulated, which can predict the difficulty of training.

\item Number-level sequence prediction experiments show that CNN models can simulate deep combinatorial logics up to certain depth.

\item Digit-level sequence prediction tasks reveal that the computational powers of existing recurrent neural network models are limited to that of finite state automata or pushdown automata.

\end{itemize}

Overall, the set of our problems can be a well-defined method to verify whether a new machine learning architecture extends the computing power of previous models.
There are some possible directions to extend the computational capabilities of neural network models.
The first way is to apply training methods other than the typical methods we used in the experiments.
For instance, reinforcement learning methods can be applied to the algorithmic tasks \cite{zaremba2016learning}.
Next, non-backpropagation methods such as dynamic routing \cite{capsnet} might help neural network models learn more complex rules.
Our number sequence prediction tasks would provide a well-defined basis for those possible future works.

\section{Problem Definition}

\subsection{Number-level Sequence Prediction}

\begin{figure}[htbp]
  \centering
    \includegraphics*[width=0.65\linewidth]{fig_numberproblem}
\caption{
Input and target sequence examples of a number-level problem with the Fibonacci sequence. The number-level sequence example is with length $n=4$, shift $s=2$ and digit $l=4$. A number in a cell is represented by an one-hot vector.
\label{fig_numberproblem}
  }
\end{figure}

Figure~\ref{fig_numberproblem} illustrates a number-level sequence prediction problem.
The model is given with an input sequence $A_{1} \cdots A_{n}$ which is formatted as a two-dimensional grid with $n$ rows.
Each row corresponds to a term $A_{i}$ which is a multi-digit number of $l$ digits.
A digit cell is a one-hot vector where the number of channels is equal to the base $b$ of the digits.
The target data $A_{n+1} \cdots  A_{n+s}$ is a sequence of following numbers with the length shift $s$ with the same data layout.
In the experiments, we use sequence data of $n=8$, $l=8$ and $s=4$.
We denote this $\{0,1\}^{l\times b}$ binary one-hot row tensor representation of a natural number $A$ as $\langle A\rangle$.

We use various order-$k$ homogeneous linear recurrence of the form $A_n=c_1 A_{n-1}+\cdots+c_k A_{n-k}$ with constant integer coefficients $c_1, \dots, c_k$ to generate number sequences starting from randomly selected initial terms $A_1, \dots,  A_k$.
For instance, $k=2, \ c_1=1, \ c_2=1$ imply a general-Fibonacci sequence and $k=2, \ c_1=2, \ c_2=-1$ give an arithmetic progression.
Likewise, a progression with arithmetic sequence as its difference whose recurrence is $A_{n}-A_{n-1}=A_{n-1}-A_{n-2}+c$ can be re-written in $A_{n}=3A_{n-1}-3A_{n-2}+A_{n-3}$.
In the perspective of combinatorial logic, the generation rules of the sequences can be seen as $k$-ary operations of the binary tensors.
For example, the generation rule of arithmetic sequences can be represented with a binary operation of $(\langle A\rangle, \langle B\rangle) \mapsto \langle 2A-B\rangle$.
Since all inputs and outputs of an operation are binary, there exists a shortest disjunctive normal form (DNF) for the operation.
We first define a combinatorial width of an operation with its disjunctive normal form, i.e. sum of minterms\footnote{A logical AND of literals in which each variable appears exactly once in true or complemented form \cite{logicdesign} }.

\begin{definition}
If the smallest DNF of a function $f : \{0,1\}^n \rightarrow \{0,1\}^m$ has $\Theta(w)$\footnote{$w$ is a function of input and output dimensions} minterms, $\Theta(w)$ is called the \textbf{combinatorial width} of the function. If functions $f_1, \dots, f_k$ have corresponding widths of $\Theta(w_1), \dots, \Theta(w_k)$, the \textbf{compound width} of a composition $f_1 \circ \dots \circ f_k$ is defined as $\Theta(w_1+\dots+w_k)$.
\end{definition}

\begin{figure}
  \centering
  \includegraphics*[width=0.7\linewidth]{fig_comb}
  \caption{
Conceptual schema of a binary operation (left), a ternary operation (middle) and an equivalent composition of two binary operations (right). The formulas represent combinatorial widths.
\label{fig_logic}
  }
\end{figure}

The decimal digit addition, for example, requires at least $\Theta(10^2)$ products since it has to memorize the consequences of all possible digit pair inputs.
Therefore, the combinatorial width of a linear binary operation is $\Theta(b^2)$ where $b$ is the base of the digits.
Note that the compound width of a function is not unique.
Consider a logical circuit for the ternary operation of $(\langle A\rangle, \langle B\rangle, \langle C\rangle) \mapsto \langle 2A-B+C\rangle$.
As seen in Figure~\ref{fig_logic}, the operation can be implemented with a single function of combinatorial width $\Theta(b^3)$, or a compound of two binary operations resulting in the compound width of $\Theta(b^2)$ in at the cost of a deeper data path.
This depth of the path can define the complexity of the operation.

\begin{definition}
The \textbf{complexity} of a function $f : \{0,1\}^n \rightarrow \{0,1\}^m$ is the minimum number $n$ of functions which make the compound width of $f_1 \circ \dots \circ f_n = f$ the smallest. Such smallest compound width is called the \textbf{difficulty} of the function.
\end{definition}

For example, the length of a row $l$ is the complexity of the carry rule since the carry digit of the most significant digit sequentially depends on all other digits.
To eliminate the dependence on the dimensions, we ignore the carry or borrow rule while calculating a complexity.
Since a logical product can be approximated with a neuron with a nonlinear activation, the difficulty should correspond to the number of neurons in the network.
Also, since the complexity reflects the depth of a logical circuit, it should correspond to the number of layers in the network.
Note that it is possible to compromise the width for the depth as seen in Figure~\ref{fig_logic}.
We expect deep neural networks to learn narrow but deeper representations.

\subsection{Digit-level Sequence Prediction}

\begin{figure}[htbp]
  \centering
    \includegraphics*[width=0.8\linewidth]{fig_digitproblem}
\caption{
Input and target sequence examples of a digit-level problem with the Fibonacci sequence. The example is with $n=8$ and $s=4$. The order of the digits is little-endian (least significant digits first).
\label{fig_digitproblem}
  }
\end{figure}

Figure~\ref{fig_digitproblem} illustrates a digit-level sequence prediction problem.
The model is given with sequential inputs of $a_{1} \dots a_{n}$, each of which is an integer number corresponds to a character.
With the base of $b$, the numbers $0 \dots b-1$ correspond to the digits.
The second last number $b$ is a blank, and the last number $b+1$ is a delimiter.
After $n$ inputs, we give delimiters as inputs for $s$ time steps.
The target sequence consists of $n$ delimiters followed by $a_{n+1} \dots a_{n+s}$.
Because digit calculations must start from the smallest digit, we order the digits in the little-endian order which is the reverse of the typical digit order.
In the experiments, we use sequences of $n=12$ and $s=12$.

The sequential nature of the data makes it more difficult to solve the problems.
Since the model has to retain information from the previous inputs, solving the problem is equivalent to modeling a sequential state automaton of the generation rule.
The computing power of a state automaton falls into one of the four categories: finite state machine, pushdown automaton, linear bounded automaton, and Turing machine.
All Turing machines are linearly bounded in the problems because the computation time is linearly bounded to the length of the sequence.
Therefore, three levels of state automata are possible in the digit-level sequence prediction problems.
We define the complexity of a sequence by the smallest state automaton required.

\begin{definition}
The \textbf{complexity} of a number sequence prediction problem is the complexity of a state automaton which can simulate the sequence generation rule with the smallest number of states. The \textbf{minimal grammar} of the sequences is the formal grammar can be recognized with the automaton.
\end{definition}

To illustrate, we can think about the most straightforward sequence of number counting.
If the numbers have at most $l$ digits of base $b$, the counter can be implemented with $\Theta(lb)$ shift registers which can be translated to the same number of non-deterministic finite state automaton.
Hence, the complexity of counting numbers is the complexity of finite state automata, and its minimal grammar is a regular grammar.
In the experiments, we use progressions with a fixed difference because they can be understood as generalized forms of number counting sequences.
Arithmetic, geometric and general-Fibonacci sequences can also be represented as digit-level sequences.
The most straightforward automata capable of generating them are queue automata, which share the same computational powers with Turing machines.
Since Turing machines must be linearly bounded in the digit-level problems, the minimal grammars of both arithmetic and general-Fibonacci sequences are context-sensitive grammars.

\begin{figure}[htbp]
  \centering
  \includegraphics*[width=0.9\linewidth]{fig_fsm}
  \caption{
Nondeterministic finite state automaton that can solve reverse-order task with $n=2$ and $b=2$. Automata for fixed difference arithmetic sequence can be built in similar manners.
\label{fig_fsm}
  }
\end{figure}

Between regular and context-sensitive languages, there are context-free languages which require pushdown automata.
Palindromes are proper examples of context-free languages which cannot be expressed by lesser languages.
Therefore, we add the experiment of a reverse-order task where the target sequence is the reverse of the input sequence.
The input data consists of $n$ random digits followed by $n$ delimiters, and
the target data is $n$ delimiters followed by $n$ digits, which is the reverse of the input sequence.
If $n$ is limited, it is possible to solve the reverse-order task with a finite state automaton as seen in Figure~\ref{fig_fsm}.
Therefore, we train the models with $n=1 \dots 12$ and validate with $n=16$ to force the complexity of the problem equivalent to a pushdown automaton.

\section{Method}

\subsection{Model Architecture}
\begin{figure}[htbp]
  \centering
  \includegraphics*[width=0.8\linewidth]{fig_cnnmodel}
  \caption{
Schematic of number-level CNN models. The number of neurons in the convolution layers can be one of ${64, 128, 192}$. The residual blocks can be repeated once, twice or thrice, making 12, 21 or 30-layer CNN model.
\label{fig_cnnmodel}
  }
\end{figure}

The number-level sequence prediction models described on Figure~\ref{fig_cnnmodel} are based on WaveNet model \cite{wavenet} which is also a generative model for sequential data.
Since the data layout of number-level sequences is two-dimensional, we use 3$\times$3 convolution kernels with dilation on the second dimension of the kernels where large receptive fields are necessary for the carry rules.
Unlike WaveNet, we use ReLU activation because we empirically observe that the gate activation slows down the training speed but shows no improvement on the accuracy.
The number of neurons per convolution layer can be 64, 128 or 192, which can correspond to the difficulty of a problem.
Inspired by the bottleneck architectures of residual CNN \cite{he2016deep}, the first layer of each residual block has half the number of neurons.
By stacking more residual blocks to the model, we can change the depth of the model.
The base 12-layer model has three residual blocks of dilation (0,2,4), and they can be repeated to make 21-layer and 30-layer models.
BatchNorm \cite{batchnorm} and Dropout \cite{dropout} methods are applied to all residual blocks.

The digit-level sequence prediction models on the left side of Figure~\ref{fig_rnnmodel} are based on the simple character-level RNN language model \cite{char-rnn} with minimal modifications.
LSTM \cite{hochreiter1997long}, GRU \cite{gru}, Stack-RNN \cite{stackrnn} and Neural Turing Machine (NTM) \cite{neuralturing} are used for the recurrent modules in the middle.
A Stack-RNN module uses a number of stacks equal to the base $b$, and an NTM module uses 4 read and write heads.
A digit-level model with attention \cite{bahdanau2014neural} follows the encoder-decoder architecture on the right side of  Figure~\ref{fig_rnnmodel}.
The first half of an input sequence and the second half of a target sequence begun with the delimiter ($\langle$Go$\rangle$ symbol) are fed into the encoder and the decoder.
We use both unidirectional and bidirectional LSTM modules for the models with attention.
We set the number of neurons in all hidden layers to 128.

\begin{figure}[htbp]
  \centering
  \includegraphics*[width=0.9\linewidth]{fig_digitmodel}
  \caption{
Schematics of digit-level neural network models. A recurrent module in a digit-level model can be either LSTM, GRU, Stack-RNN or Neural Turing Machine. Unlike other digit-level models, an attention model must follow the encoder-decoder structure which is illustrated on the right side.
\label{fig_rnnmodel}
  }
\end{figure}

\begin{figure*}[tbp]
  \centering
  \includegraphics*[width=\linewidth]{plot_deepwide}

  \caption{
Validation error curves of the deep and wide models on the sequences generated by a ternary relation (left), the mixture of the four types of binary relations (middle) and the quaternary relation with different base digits (right). Y-axes are validation error rates, and the X-axes are training example counts. The value following the number of layers denotes the number of neurons in a convolution layer. The third experiment uses a 30-layer model with 128 neurons per layer.
\label{fig_mixlv3}
  }
\end{figure*}

\subsection{Training and Validation Method}

We follow the end-to-end training fashion.
Thus the models have to learn the logical rules without any domain-specific prior knowledge.
A batch of size 32 is randomly generated for each iteration by choosing the initial numbers and applying the generation rules.
The space of all possible training sequences should be large enough to avoid overfitting.
We evaluate the validation prediction error rate with a pre-defined validation dataset after every 32 iterations.
We define a prediction error rate as a ratio of wrong predictions to the total predictions.
The total predictions are counted as $l\times s = 32$ in number-level sequences and $s = 12$ in digit-level sequences.
A prediction is determined by the digit channel with the maximum output value.
Both number-level and digit-level models are trained to minimize the cross-entropy loss function.
The validation dataset is also randomly generated from the space outside of the training data space.
For example, we choose the first two terms of number-level arithmetic sequences from the range of $(0,20000)$ for the training dataset, but we choose them from the range of $(20000, 30000)$ for the validation dataset.

\section{Experiment}

\begin{figure}[htbp]
  \centering
  \includegraphics*[width=0.9\linewidth]{plot_lv2}
  \caption{
The learning curves of the 12-layer number-level model with 64 neurons on the five types of the basic sequences. $(p,q)$ denotes the coefficients of binary operations $(A,B) \mapsto pA+qB$. $(1,0,1)$ denotes the relation of $A_n=A_{n-1}+A_{n-3}$.
\label{fig_lv2}
  }
\end{figure}

\subsection{Number-level Sequence Prediction Experiment}

\paragraph{Setup}
The objective of the experiments is to verify that complexity and difficulty of a number-level problem correspond to the depth and the parameter size of a CNN model.
Total eight types of sequences are used in this part of the experiments.
First four types of the sequences have recurrence relations in the form of $A_n=p A_{n-1}+q A_{n-2}$ where $(p,q)\in \{ (1,1),(2,-1),(3,-2),(1,2) \}$.
These four sequences represent binary operations with the complexity of one.
The fifth type of sequences has a relation of $A_n=A_{n-1}+A_{n-3}$ which represents a binary operation with the complexity of two because the model has to see through at least two layers to catch the relation between $A_{n-1}$ and $A_{n-3}$ with $3\times3$ convolution kernels.
The sixth type of the sequences is a mixture of the first four types of the sequences.
This is equivalent to building a ternary combinatorial logic with four times more width.
For comparison, the seventh type of sequences is generated by a recurrence relation of $A_n=2A_{n-1}-A_{n-2}+A_{n-3}$ which can be a compound of two binary operations.
The last type sequence is a progression with a relation of $A_n=4A_{n-1}-6A_{n-2}+4A_{n-3}-A_{n-4}$ whose general term can be calculated with a fourth-order polynomial.
For the training data, the first $k$ terms\footnote{$k$ is the order of a recurrence relation} of the sequences are chosen from $(0,20000)$, while they are chosen from $(20000,30000)$ in the validation dataset.
We compare the learning curve patterns over various model configurations.

\begin{figure}[htbp]
  \centering
  \includegraphics*[width=0.7\linewidth]{fig_lv2err}
  \caption{
The error examples from number-level model trained with general-Fibonacci sequences. Shaded cells show the locations of the errors. The numbers are shown in little-endian order.
\label{fig_lv2err}
  }
\end{figure}

\paragraph{Result}
Figure~\ref{fig_lv2} and Figure~\ref{fig_lv2err} show the validation error curves and the error examples of a CNN number-level model during the training on the five types of sequences generated by the binary operations.
Although the numbers of possible sequences exceed a hundred million, the model can achieve error rates near zero in less than a hundred thousand examples.
Since the validation data comes from the outside of the training data space, we can conclude that the model can learn the exact logic rules for the operations.
The error examples show that it is hard to catch long-term carry rules, which is expected because the carry rules have complexities equal to $l=8$.
Deploying deeper models reduce the errors from those long-term carry rules, occasionally achieving a zero prediction error.
The fifth sequence of rule $A_{n-1}+A_{n-3}$ shows a different learning curve pattern since $3\times3$ convolution kernels force the model to simulate the logic with the complexity of two.
The results show that complexities of number-level sequence prediction problems can effectively predict the hardness of learning.

Figure~\ref{fig_mixlv3} compares the learning curves of the models with various configurations and sequence data.
The models successfully learn the rules from both the mixed set of primary sequences and the sequences generated by a ternary relation.
However, the patterns of the learning curves are different.
With the mixed set of primary sequences, the learning curves of the models show uniform convexity without a saddle point.
Also, there is no clear advantage of using deeper models.
However, the learning curves with the sequences of a compound rule have saddle points, where we suspect the models find breakthroughs.
Moreover, we can observe the advantages of using deeper models.
Therefore, it can be concluded that deep learning models tend to learn complex but less difficult combinatorial logic, rather than the equivalent shallow but wide representations.
Meanwhile, the last learning curves show that the CNN model finds it hard to learn the logic with the complexities more than three.
The quaternary operator with base 5 has a smaller combinatorial width than a decimal ternary operator, but the model cannot learn the rule of the former.

\begin{table*}[tbp]
\centering
\def1.5{1.5}
\begin{tabular}{|l|rrrr|}
\hline
Tasks     & Reverse-order (training) & Geometric & Arithmetic & Fibonacci \\ \hline
LSTM      & 28.4\% (1.2\%)	& 79.4\%    & 77.1\%     & 80.5\%    \\
GRU       & 51.9\% (0.9\%)	& 69.0\%    & 77.1\%     & 79.3\%    \\
Attention(unidirectional) & 42.0\% (8.8\%)  & 62.8\%    & 77.0\%     & 69.3\%    \\
Attention(bidirectional) & 0.0\% (0.0\%)  & 51.0\%    & 72.9\%     & 60.9\%    \\
Stack-RNN & \textbf{0.0\%} (0.0\%)     & 64.1\%    & 63.8\%     & 69.4\%    \\
NTM       & \textbf{0.0\%} (0.0\%)     & 57.1\%    & 65.7\%     & 68.1\%    \\ \hline
\end{tabular}
\caption{Test error rates of the digit-level sequence prediction experiment. Identical training methods are applied to the models except the attention model. Parenthesized numbers in the reverse-order task column are training error rates with $n=1\dots12$.}
\label{table_err}
\end{table*}

\begin{figure}[htp]
  \centering
  \includegraphics[width=0.9\linewidth]{plot_count}
  \caption{
Validation error curves of LSTM and GRU digit-level sequence prediction models on the arithmetic sequences with fixed difference of 17.
\label{fig_count}
  }
\end{figure}

\begin{figure}[htp]
  \centering
  \includegraphics[width=0.9\linewidth]{fig_lstmfiberr}
  \caption{
Error examples from the digit-level LSTM model trained with general-Fibonacci sequences. The numbers are shown in little-endian order. Shaded cells show locations of the errors.
\label{fig_digitfib}
  }
\end{figure}

\subsection{Digit-level Sequence Prediction Experiment}

\paragraph{Setup}
The purpose of the digit-level sequence prediction experiments is to find complexity limits of the models.
The first type of the sequences is a progression with a fixed difference, which can be understood as a variation of number counting sequences.
We use the difference of 17 to observe the carry rules more often.
The first term of a training data is chosen from the range of $(0,9000)$, and that of a validation data is chosen from $(9000,9900)$.
In the second experiment, we use arithmetic sequences or general-Fibonacci sequences.
The first two terms are chosen from the range of $(0,4000)$ during the training and $(4000,6000)$ for validations.
Since it is impractical to build finite state automata for all cases, the model must simulate queue automata to solve the problems.
The third experiment uses rounded geometric sequences with the relation $A_{n+1} = \lfloor1.3A_n\rfloor$ where
the first terms are randomly chosen from $(0,4000)$ during the training and $(4000,6000)$ for validations.
The task also requires a smaller queue automaton since it has to remember only one previous number at a time.
The last experiment tests the models with the reverse-order task, which has the complexity of a pushdown automaton.
Since a reverse-order problem of fixed length can be solved by a finite automaton, we train the models with $n\in\{1 \dots 12\}$ and validate the models with $n=16$ to force the models to learn a pushdown automaton.

\paragraph{Result}
Figure~\ref{fig_count} shows that GRU and LSTM based models are capable of simulating finite state automata.
Although the GRU model shows better performance than the LSTM model, both are not able to solve the problems that require queue or pushdown automata as seen in Table~\ref{table_err}.
Training error rates of GRU and LSTM models on reverse-order task converges around 0.01 suggesting that the models are capable of simulating finite state automata for generating palindromes with a limited length.
The error examples from the general-Fibonacci sequence prediction task in Figure~\ref{fig_digitfib} show the strategies of the models.
The models remember relationships between the most significant digits, while relationships between the least significant digits are more critical for the digit computations.
We can conclude that the computational powers of typical RNN models are limited to those of finite state automata if they are trained with typical training methods.
Encoder-decoder model with attention, Stack-RNN and NTM models are capable of solving reverse-order task, but they are no better than typical RNN models in problems that require queue automata.
The model with attention doesn't show significant differences if the model uses unidirectional LSTM.
Using bidirectional LSTM seems to be crucial for simulating pushdown automata in the models with attention.

\section{Conclusion}

We introduced effective machine learning problems of number sequence prediction which can evaluate a machine learning model's capability of solving algorithmic tasks.
We also introduced the methods to define the complexities and difficulties of the number sequence prediction problems.
The structure of a combinatorial logic measures the complexity and the difficulty of a number-level sequence prediction problem.
Experiments with the CNN models showed that they are effective ways to predict the hardness of learning, and they correspond to structures of neural network models.
The complexity of a digit-level sequence prediction task could be defined as the complexity of a minimal state automaton which can solve it.
The experimental results showed that the computational powers of typical RNN models are limited to those of finite automata.
While models augmented with external memory could solve the problems that require pushdown automata, none of the models were capable of simulating queue automata which are equivalent to Turing machines.
To sum up, our number sequence prediction tasks were proven to be effective and well-defined for testing neural network models' computational capabilities.

There are a few possible ways we suggest to proceed with the problems.
The first way is to propose and test a new network architecture to solve the tasks could not be solved in this study.
If a neural network model can solve digit-level arithmetic and geometric sequence prediction tasks, we can say that the model extended the computational capabilities of neural networks.
Another way is applying training methods other than typical methods we used in the experiments.
Sequence-to-sequence training methods for the digit-level prediction problems limit the capability of models to linear bound automata since the computation time is linearly bounded to the length of a sequence.
The training methods that decouple computation time and the number of outputs might expand the capability of the neural network models.
Finally, non-backpropagation methods such as dynamic routing \cite{capsnet} might be able to expand the computing power of neural network models.
Our number sequence prediction tasks would provide a well-defined basis for those possible future works.
\bibliographystyle{aaai}

redpajama_set_name: RedPajamaArXiv


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Edison-Ford Winter Estates in the city of Fort Myers offers tours including the museum, which has Edison's phonographs, electric lights, and some of his other inventions.


text:
<?php
/**
 * Created by PhpStorm.
 * User: niu
 * Date: 13-12-19
 * Time: 下午6:58
 */

if ( ! defined('BASEPATH')) exit('No direct script access allowed');

class Safe extends CI_Controller {
    public function __construct(){
        parent::__construct();
        $this->load->model('user');
        $this->load->helper('message');
        $this->user->if_login();
    }

    public function index(){

    }

    public function cash_password(){
        $this->load->view('flat/cash_password.tpl');
    }

    public  function change_cash_password(){
        $this->load->library('validation');
        $this->load->model('code/securimage');

        $code = $this->input->post('code');
        if ($this->securimage->check($code) == false){
            show_msg(0,'验证码错误');
            exit();
        }
        $password = trim($this->input->post('old_password'));
        $new_password = trim($this->input->post('new_password'));
        if (!$this->validation->password_validator($new_password)){
            show_msg(0,'新密码必须是6位以上且同时包含数字与字母');
            exit;
        }
        if ($this->user->change_cash_password($password,$new_password)){
            show_msg(1,'资金密码修改成功');
            exit;
        }else{
            show_msg(0,'原始密码不正确');
            exit;
        }
    }

    public function login_password(){
        $this->load->view('flat/login_password.tpl');
    }

    public function change_login_password(){
        $this->load->library('validation');
        $this->load->model('code/securimage');

        $code = $this->input->post('code');
        if ($this->securimage->check($code) == false){
            show_msg(0,'验证码错误');
            exit();
        }

        $password = trim($this->input->post('old_password'));
        $new_password = trim($this->input->post('new_password'));
        if (!$this->validation->password_validator($new_password)){
            show_msg(0,'新密码必须是6位以上且同时包含数字与字母');
            exit;
        }
        if ($this->user->change_login_password($password,$new_password)){
            show_msg(1,'登陆密码修改成功');
            session_destroy();
            exit;
        }else{
            show_msg(0,'原始密码不正确');
            exit;
        }
    }

}

redpajama_set_name: RedPajamaGithub


text:
1(81). rev 1
spaces/ – admin 30 Mar 2016, 6:15 p.m. link
initial content
A number of vector spaces are discussed below and widely used in 3D graphics to place objects in a common scene. Transformation [matrices](/9/rendering/matrices/) both define and transform [vectors](/10/rendering/vectors/) between spaces. Either objects are projected into a discretized image for rasterization or rays are projected from the image into the world for raytracing. See [projection matrix](https://www.heuristic42.com/11/rendering/matrices/projection/). **Object space** is the name given to the coordinate system that objects, i.e. triangle mesh vertices, are defined in. Each mesh has its own object space, and the data typically remains static with animation applied on the fly during vertex processing. Exceptions include deformable objects and dynamically defined meshes such as isosurfaces. Object space operations (as opposed to image space, below) commonly refers to the use of triangle data, without specific reference to the vector space, and can also imply more global operations on all instantiated objects in world space. **World space** is the space the scene is constructed in, instantiating objects and placing them in relation to one another by defining an object-to-world space transformation. These and other transformations can be efficiently stored in 4 × 4 [homogeneous matrices](https://www.heuristic42.com/9/rendering/matrices/#homogeneous-matrices) and applied by multiplying vertex coordinates. By pre-multiplying and combining transformations, a vertex can be transformed to a desired space with a single operation. World space is common to all instances and provides view-independent relative positions to objects in the scene. With the scene defined, a viewer is necessary to relate a 2D image to the 3D world. Thus, a virtual camera model is defined, somewhat implicitly in some cases, and is split into two parts: a view and projection. **Eye space**, or camera space, is given by the [camera](/8/rendering/cameras/)'s view, commonly position and direction. The transformation can be thought of as moving the entire world/scene to provide the viewer location and rotation, which despite appearances is mathematically inexpensive. This analogy works for other transforms but may be more intuitive here. Like the previous spaces, eye space is linear and infinite, with viewing volume bounds or projection yet to be defined. **Clip space** exists after a projection has been applied and is 4D. A typical projection for a virtual environment is a perspective projection, which computes intersections between a plane and lines to each vertex. An alternative interpretation is that the x and y coordinates are divided by $z$, due to the following normalization, to shrink distant objects in the image. Clip space defines bounds for a viewing volume, where triangles outside can be discarded and those intersecting can be clipped. Clipping is particularly necessary for triangles that cross the $w = 0$ plane where points would otherwise cause a division by zero when normalized. Perspective-correct vertex interpolation must be performed in clip space, before normalization. **Normalized device coordinates** (NDC) are a result of the perspective divide, where 4D homogeneous vectors are normalized, $\mathsf{NDC} = \mathsf{clip}_{xyz}/\mathsf{clip}_w$, after the perspective transformation to clip space. The 3D components of visible points commonly range between -1 and 1. This really depends on the projection matrix. A notable case is a difference in the $z$ range between the projections created by OpenGL and DirectX software. To undo a perspective divide when transforming from NDC to eye space, simply transform by the inverse projection matrix and re-normalize with the same divide, rather than attempt to compute and scale by $w$. **Image space** linearly scales NDC to the pixel dimensions. For example, $\frac{\mathsf{NDC_{xy}} + 1}{2} \mathsf{resolution}$ This is where rasterization would be performed. Alternatively, points in image space can be projected into 3D rays in world space (from the near to the far clipping planes for example), multiplying by the inverse projection and view matrices for raytracing.


This page features campaign advertisements from Michigan's 2016 state supreme court elections.
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This ad says Larsen and Viviano "keep violent criminals behind bars."
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This ad highlights Larsen and Viviano's values and respect for the law.
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Can we get a thanks button? Allows us to give a thumbs up for good posts.
There is one. Up on top of the topic, there is a rating system.
But that's hard to implement per post.
I was thinking a "thanks" for each post. I'm pretty sure IPB allows for this, but if it's difficult to implement I understand.


text:
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Published April 13th, 2007 | by Coco Forsythe
The Jane Austen Book Club Review
Classification: 12 Director: Robin Swicord Rating: 3.5/5
The Jane Austen Book Club is what used to be known, in the golden age of Hollywood, as a 'women's picture', and back then would have starred Bette Davis, Joan Crawford, Olivia DeHavilland and Joan Fontaine. But even this modern day equivalent is a pleasurable little treat.
The film opens with a montage of characters pitted against the speed of modern life – the heartless, soulless machines which, supposedly making life better for us, make it so much worse. Jocelyn (Bello) is in mourning – one of her champion ridgebacks has died. Her friends share her hour of grief, though some take it more seriously than others. Daniel Avila (Smits) scoffs; people need people, and he more than most as he informs his wife Sylvia (Brenneman) over dinner that he has been seeing another woman and is leaving her. Sylvia's daughter and friends decide that she needs distracting; as fans of Jane Austen they decide to form a book group, dedicated to Austen's works. Six members, six books, six months: the group includes Sylvia, Jocelyn, Sylvia's daughter Allegra (Grace), Bernadette (Baker) and Prudie (Blunt), an unhappily married schoolteacher with a crush on one of her students (Zegers). Jocelyn happens to meet Grigg (Dancy), who she thinks may be just the thing to distract Sylvia from her misery, and invites him along.
And that's really about it, plotwise. Characters fall for each other, and argue, and resist temptation, and talk about Jane Austen. They all resemble Austen characters in some way, or at least learn from her writings – it's all sense, sensibility, pride, prejudice, and most of all persuasion. Jocelyn is Emma, matchmaking for others and failing to see love under her own nose; Allegra is Marianne Dashwood, always falling impetuously in love; Prudie has her very own embarrassing mother, like Elizabeth Bennet, and clearly has many many issues, not least of which is being married to the wretched Dean (Blucas), Riley from Buffy The Vampire Slayer, sporting a hideous rodent on his chin and upper lip.
Anyway, not a lot really happens, but it's all rather lovely nevertheless. Because there isn't much plot, for once there is time to actually develop the characters who behave implausibly and inconsistently and generally like real people. Jocelyn clearly likes Grigg, but because she has decided that he is for Sylvia – even though Sylvia isn't interested and Grigg makes it clear how he feels about Jocelyn – she just seethes quietly instead of just asking him out (what is she thinking? He's GORGEOUS!). When they finally get together over Ursula LeGuin, it feels completely right. (And how refreshing to have great sci-fi authors name-checked in a film about Jane Austen.) Kevin Zegers is, it has to be said, worth losing your job for.
Ahem! Sorry. Anyway, this is not a film that will change your life but it's charming, funny and sweet, and just the sort of thing to curl up under a duvet with on a wet Sunday afternoon. And it's a film that says that reading is the next best thing to sex. Words to live by.
Last modified on April 13th, 2007
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