Earlier in the month I read this great article by Justin Rondeau, on what CRO is and what it encompasses. The below graphic couldn't sum it up any better.
Whilst AB testing plays a huge role in our CRO strategy, there is significant work which takes place in other areas and help drive our testing hypotheses. The below tools are just a snapshot of some of them.
We use Formisimo to track our purchase page. It is a single tag added to the page, which then tracks all interactions with the form fields on the page. It helps provide data on drop-off points, problem fields and fields which need correcting often. For any form heavy site, it's worth taking a look at.
GoSquared is the latest piece of tracking we've added to the site. It's strengths lie in analysing data in real time and providing a week on week estimate. You can push through revenue data, and from an early stage in the day you can track how you think the site is performing compared to any other previous point in time. We originally looked at GoSquared for it's people analytics, which allows you to tie events to users and report on that. We originally wanted to integrate this with Optimizely, but this specific aspect of GoSquared is still in it's infancy – so we're yet to make use of it.
GA needs no introduction, pretty much every site has used it at some point for the high-level analysis. We use GA heavily to track aggregated user data to see which features are performing, and how. The free version does have it's limitations though, and the sampled data does have to be taken account particularly when dealing with specific events undertaken on the page.
We use UserTesting.com for our user testing. You set up your page(s) that you want testing, select your questions for the test and then within approximately 30 minutes you have a full testing session completed at the cost of $50USD. We've found it particularly useful for competitor comparisons, where we send users to our site and a competitors and we look for struggle points. These tests drive a number of AB test hypotheses, as well as helping future design decisions.
Free 5 second tests, or comparison tests, are available through Usabilityhub.com – this is great for early on in the design process.
Qualaroo is our tool of choice for running on-site surveys. Generally speaking we run them on exit-intent and use them to drive our AB test hypotheses, as well as general business direction. There is also a useful integration with Optimizely, so you can push users into different segments depending on their survey results.
Customer services is the closest we get to a customer at Secret Escapes, and their feedback is essential to our optimisation program. Currently one individual from Product/Tech team spends 1 day each month shadowing our customer service agents at the call centre. The shadowing includes listening into phone calls, working through zendesk issues as well as discussing common issues with the supervisors up there. We are also provided with a weekly update of frequently asked questions from our members, so we can look to find simple tech solutions. This has driven some of our most useful feedback, so far.


Situated just off the A5, the Horse & Jockey is an ideal meeting point, easy to find and has a large car park. We're also close to Dunstable Downs & Whipsnade Zoo, so are perfectly placed for family days out. Our fantastic garden is the ideal spot for a bite to eat during the summer months in which to relax. If you're looking for a venue for a family event or party, look no further - we can accommodate parties up to 22 people.


The equity markets started to experience what stock analysts call a sector rotation, when one or several sectors fall out of favor leading to funds flowing to other sectors. This past month technology stocks fell as markets perceived that the sector may have become overvalued. As this occurred, banking and financial sector stocks rose, as favorable regulatory related news lifted the overall sector.
The S&P 500 index posted its strongest first half of the year since 2013. The Dow Jones industrial average index rose 8% in the first half of 2017, its best performance since 2013, while the S&P 500 was up 8.2% the first half of 2017. The NASDAQ's strong performance for the first six months of 2017 was predominantly led by the technology sector, its best first half since 2009.
Global equity markets had the best first annual half since 2009. Overall improving sentiment in the euro zone as well as increasing international growth prospects helped propel global markets the first half of 2017.


text:
Bruno Rubino, 83, of Woodland Park, passed away on December 20, 2020. He was born in Pacentro, Italy on December 3, 1937 to the late Germano and Gemma (Cercone) Rubino. Bruno immigrated to Paterson, NJ in 1956 where he worked most of his career as a fork-lift operator for Nabisco until his retirement. Bruno was a parishioner of Our Lady of Pompei Church for many years.
Bruno was the beloved husband of Franca (Mitolo) Rubino; the cherished father of Stefano and his wife Kim, Paul and his wife Laura, and Mike and his wife Stephanie; and the adored grandfather of 9 grandchildren. Bruno was predeceased by 5 brothers and 2 sisters and is survived by many nieces and nephews.
Bruno was known for his quiet demeanor, kindness and unselfishness. Bruno touched many people throughout his distinguished life and described by friends as a "true gentleman!" Most of all, Bruno was the ultimate family man who gave everything for his family and wanted nothing in return.
Visitation will be Monday, December 28th from 2-6pm at Santangelo Funeral Home, 635 McBride Ave., Woodland Park. A funeral Mass will be celebrated on Tuesday, December 29th at 10:00am at Our Lady of Pompei Church, 70 Murray Ave., Paterson. Entombment will follow at Laurel Grove Cemetery in Totowa.
Due to the COVID-19 state mandate, a maximum of 50 individuals are permitted in the funeral home at one time. A face covering must be worn by everyone in attendance at all times. In addition, please follow social distancing guidelines. Thank you for your compliance and understanding.

redpajama_set_name: RedPajamaCommonCrawl


text:
Atlanta, GA, US
Funky Bitch
Peaches en Regalia
Poor Heart >
Esther >
Down With Disease >
Hi-Heel Sneakers
Wilson >
Mound >
Sparkle >
Harry Hood
Ginseng Sullivan
Who By Fire
This was Phish's 1st show at the fabulous Fox Theatre in Atlanta – a former movie house and performing arts space opened in 1929 as part of a Shrine temple with opulent Moorish design and a capacity of about 4,700. The stunning auditorium where Phish played was set as an Arabian courtyard complete with a mesmerizing "sky" with a moving projection of clouds and flickering stars overhead. Tickets to the sold-out show cost $18.00 and this was the last show on the tour (along with 4/13/94, 4/14/94, 4/15/94, 4/16/94 and 4/18/94) for which mail order tapers' tickets were offered. The show took place during Atlanta's annual Freaknik celebration resulting in big crowds on the streets and a unique blending of cultures. Trey sang the verses of Fee through his megaphone. The beginning of Esther included a tease of Caravan which was subsequently performed with Merl Saunders on keyboards. Merl stayed onstage after Caravan to sing and play on the 1st and only Phish performance of Hi-Heel Sneakers (Tommy Tucker cover popularized by Merl and Jerry Garcia). Run Like An Antelope included Simpsons and Oom Pah Pah secret language. Ginseng Sullivan was performed without microphones with Trey on acoustic guitar, Mike on upright bass, Page on Melodica and Fish on Madonna washboard. Trey's foot was in a brace due to torn ligaments so You Enjoy Myself featured a guest trampoline jumper from the audience substituting for Trey. YEM included a Rock n' Roll Hoochie Koo jam as well as a guest appearance by Col. Bruce Hampton on piano during a vocal jam that included Who By Fire teases. Col. Bruce stayed onstage for vocal duties on the 1st and only Who By Fire (Leonard Cohen cover) played by Phish. Free Bird was played by request in response to Trey asking (Lynyrd Skynyrd-style) "What song is it you want to hear?" After the show, Page, Mike and Fish sat in with Merl Saunders and the Rainforest Band for "Fever" at the Variety Playhouse in the Little Five Points neighborhood.


text:
package com.healthcit.cacure.model;

import junit.framework.TestCase;

import com.healthcit.cacure.utils.GetterAndSetterTester;

public class ValueLablePairTest extends TestCase {

    private GetterAndSetterTester tester;

    public void setUp(){
        tester = new GetterAndSetterTester();
    }

    /**
     * Test the getters and setters of a the given class.
     * Instantiation is left top the tester.
     *
     */
    public void testAllSettersAndGettersClass(){
        tester.testClass(Answer.class);
    }
}

redpajama_set_name: RedPajamaGithub


When you bring a dog into your home, choosing good food for him/her that you and your wallet will love takes time. Even so, it's pleasant if you know where to start.
That's the reason we've selected the best 10 dry dog food for your canine to try out.
As you may be already aware, what goes through your dog's mouth determines the pet's overall health.
A high majority of dog owners vouch for the food below, for their nutritional value and affordability.
Let your pooch enjoy real organic chicken, the main ingredient in this formula from Organix. It also contains quinoa, a grain with chockfull of nutrients and high levels of dietary fiber.
Plus, it carries traces of flaxseed to supply your dog's body with omega 3 fatty acids.
Feeding your furry friend with this dry food frequently leads to healthy skin and coat. The Organix meets the standards set by the Oregon Tilth, and all its ingredients are from the United States.
Purina isn't dubbed "Pro" for nothing. It is rich in antioxidants to nourish and boost your dog's immune system. It contains DHA for vision and vision development. Because of its unique formulation, it is the best dry dog food for senior pets (seven years or older).
The Purina Pro is highly digestible and provides a maximum protein to fat ration to help your pooch maintain muscles mass. Its main ingredient, as the name suggests, is a shredded blend of rice and chicken.
If you own a sick or large dog, this is the dry food to buy. It contains high-value proteins such as glucosamine and chondroitin to help larger dogs maintain their frame. It also has phosphorous and calcium for healthy bones and joints.
The amino acids and vitamins complete a pack of goodness.
NUTRO adult dry food features a blend of farm-raised chicken, balanced fiber, and whole grains. Your dog will not only enjoy this food but also benefit from a better digestive system that rapidly absorbs nutrients.
Hill's Science promises to help make your dog happy with this dry food. And, looking at what it has to offer, that's indeed the case. A good percentage of veterinarians hail it as the best dry dog food for a healthier pet.
It has adequate doses of minerals, lamb, and salmon. All of its ingredients are natural and clinically proven to contain antioxidants.
There is no artificial colors or chicken by-products. For a meal that's supposed to keep your pooch in the healthiest state possible, the Hill's Science dry dog food is, without doubt, a winner.
Rachel Ray knows what's best for your dog. The recipe used to make this dry dog food says so! It is one of the very few dogs meets that contain wholesome veggies and a mix of seafood.
Other ingredients include beef, minerals and a host of vitamins.
There's even a jumble of carrots and peas to support digestion and perk up dog's ability to fight diseases. And, the Biotin and Zinc sulfate will help keep unhealthy fat in check while ensuring that your dog's organs function optimally.
The makers of this meal understand that dogs prosper in healthy fats and protein. That's why Merrick Grain Free dry dog food offers balanced nutrition of whole food sourced locally.
This is the best dry dog food for pets of all ages, from pups to large breeds.
Its nutritional content seeks to support your furry friend's overall health.
Merrick Grain comprises 70% meat and fish to help build and maintain lean, healthy muscles. Buy this award-winning dry dog food and help your pet foster strong joints and hips.
Purina Beneful is an organic option to fill your dog's bowl with healthy goodness. With real ingredients such as accents of vegetables, chicken, and beef, your best friend will feel great about feeding.
It comes in a variety of flavors to give a broader choice even for picky eaters. Each recipe in this dry dog food provides the nutrients required to keep his/her muscles packed. Purina Beneful is crunchy and tender to ensure that your dog is excited about every meal.
It is cost friendly too!
Diamond Naturals features a healthy blend of ingredients to keep your dogs happy and muscular.
It is the best dry dog food if you want to take your pet's performance to the next level. And the best part, its recipe meet the needs and preferences of all dog stages and level of activity.
It contains human grade meat and natural digestive enzymes. Diamond Naturals has excellent palatability for optimal health and active life. What's more? The crispy kibble helps reduce plaque and tartar.
The Wellness CORE is specially formulated to meet the needs of adult, nonreproducing dog aged one and above. This means you can feed it to your pup, and pregnant or nursing mothers.
It meets AAFCO nutrient profile for adult maintenance.
With a 38% protein matter and 48% carbohydrate content, it is way above average in nutritional value in comparison to most dry dog food. And just so you may know, it contains salmon oil, chicken, turkey, vegetables, and fruits. Yummy!
Taste of the Wild is the best dry dog food for your money.
It is made with roasted meats and supplemented with veggies and fruits. The natural antioxidants deliver the protection your pooch needs to stay disease free. Meanwhile, the garbanzo beans, peas, and flaxseed bring a protein-boosting effect to the meal.
And because it contains no grains, Taste of the Wild is suitable for all life stages. As shoppers note, it will bolster your pup's energy levels. Taste of the Wild is a blend that "your dog will really like" in the words of a happy user.


This new Be My Valentine pose prop is a collaboration between Zedellbee Zuhal of Blonde and Plastic Swords of Dismorph. The pose prop includes 14 different single animations. A lot of them are cute & flirty, they would make great poses for Valentine's Day cards!
The posing prop is scripted to toggle invisibility on and off for the floor, box, lid, or hide all.
by the way nice pictures..


text:
题目描述

Given a collection of numbers that might contain duplicates, return all possible unique permutations.

For example,
[1,1,2]have the following unique permutations:
[1,1,2],[1,2,1], and[2,1,1].

class Solution {
public:
    //时间复杂度O(n!),空间复杂度O(1)
    vector<vector<int> > permuteUnique(vector<int> &num) {
        vector<vector<int> > result;
        sort(num.begin(), num.end());
        do{
            result.push_back(num);
        }while(next_permutation(num.begin(), num.end()));
        return result;
    }

    template<typename BidiIt>
    bool next_permutation(BidiIt first, BidiIt last){
        const auto rfirst = reverse_iterator<BidiIt>(last);
        const auto rlast = reverse_iterator<BidiIt>(first);
        auto pivot = next(rfirst);
        while(pivot != rlast && *pivot >= *prev(pivot))
            ++pivot;
        if(pivot == rlast){
            reverse(rfirst,rlast);
            return false;
        }
        auto point = find_if(rfirst, pivot, bind1st(less<int>(), *pivot));
        swap(*point, *pivot);
        reverse(rfirst, pivot);

        return true;
    }
};


Who do you guys wanna see in BOLA this year? Im hoping Its 16 people again this year, this is my line up.
I liked the one-night 8-man from last year with bonus matches between rounds. 8 first round matches won't get a lot of time to tell a proper story in the ring, even if it's spread over 2 nights.
I think Willie Mack may win it this year. It's all in the presentation for me.
If Strong is in then it's gotta be his year.
Itchypanda wrote: I think Willie Mack may win it this year. It's all in the presentation for me.
Garden State Saint wrote: If Strong is in then it's gotta be his year.
I agree with Itchypand that Mack may win this year, however I would not mind Strong winning.
Roderick is long overdue for a BOLA' win & a PWG title run. It would be cool to see these two in the finals..
I think 12 is better. Night 1 has six matches plus two non-tourny matches. Night 2 has four tourny matches with the semis and the three way final. I think Strong wins this year too. Mack will be in the final for sure with I don't know who yet. Maybe Kyle o Reily? Or Davey?
Mostly I just want to see Johnny Gargano, him vs. Edwards is the match I want to see most out of any two guys in the indys.
The_Sharpshooter wrote: I agree with Itchypand that Mack may win this year, however I would not mind Strong winning.
Strong vs. Mack would be a suitable finals to me. Strong either has to win BOLA this year or the PWG strap before the year is out.
I dunno guys.....think Mack has the stamina/cardio to wrestle 3 quality matches?
I agree with Strong. A guy like him holding the title in PWG will guarantee fresh mains.
camstun187 wrote: I dunno guys.....think Mack has the stamina/cardio to wrestle 3 quality matches?
I believe Mack can have 3 qualtiy matches. Last year he wrestled twice in 1 night at BOLA (both against Hero & Generico) and despite the loss in the 2nd round, he looked good enough after the match to probably go one more if it was necessary.
I'd like to throw out an idea I've had the past few years. Now that Summerslam is happening in LA every August, I think PWG should capitalize on this by running their biggest show of the year, BOLA, that weekend. It could be Friday and Saturday, or just Saturday if it's a one nighttorunament again this time. It'd capitalize on all the extra wrestling fans in town that weekend...could even possibly run a bigger venue than Reseda.
and yes, Kingston and Elgin would make two welcome, WELCOME additions to the tourney. Man, KIngston without a Hero to worry about in PWG would be great.
tristanj13 wrote: I'd like to throw out an idea I've had the past few years. Now that Summerslam is happening in LA every August, I think PWG should capitalize on this by running their biggest show of the year, BOLA, that weekend. It could be Friday and Saturday, or just Saturday if it's a one nighttorunament again this time. It'd capitalize on all the extra wrestling fans in town that weekend...could even possibly run a bigger venue than Reseda.
I pick Callihan. I think Callihan cheating his way to the belt and having Mack chase after it could make for a good story. Then again, I know very little about Callihan.
How about you have it the week after SummerSlam and just flyer the hell out of the Staples Center?
It's worth the trade off to expand such a great company.


text:
Tag: Series
Walmart's fall event series offers fun experiences for families
After a successful run of drive-in movies and virtual day camp this summer, Walmart will continue to offer socially distanced family experiences this month with…
Event Horizon Director Confirms He Has No Interest in Sequel or TV Series
Filmmaker Paul W.S. Anderson is kicking off an all-new universe with his upcoming Monster Hunter, based on the video game series, but if you're hoping…
Color Star Technology in Development of Offline Music Festival Series
NEW YORK, Oct. 13, 2020 /PRNewswire/ — Color Star Technology Co., Ltd. (Nasdaq CM: CSCW) (the "Company", or "Color Star"), a company engaged in the…
Liberty Campus Recreation Kicks off its Trail Series With Races at Hydaway
The Liberty Mountain Trail Series hosted its first race of the season, drawing many runners from the Liberty community and the local area. The Deep…
Color Star Technology in Development of Offline Music Festival Series | Nachricht
Trump plans aggressive travel schedule to reset campaign hit by series of setbacks
President Donald Trump is running out of time to recover from a series of self-inflicted setbacks that have rattled his base of support and triggered…
A look at the upcoming events in NASCAR, other motorsports series
© AP/GERRY BROOME Chase Elliott celebrates last year's victory at the Charlotte Roval. Elliott has seven career Cup Series wins and three of those have…
BioShin, Biohaven's Asia-Pacific Subsidiary, Raises $60M in Series A Funding to Advance Neuroscience Pipeline in Asia-Pacific Region | News
NEW HAVEN, Conn. and SHANGHAI, Sept. 28, 2020 /PRNewswire/ — Biohaven Pharmaceutical Holding Company Ltd. (NYSE: BHVN, "Biohaven") announced today that BioShin Limited ("BioShin") its…
Upcoming events in NASCAR, other motorsports series
The Associated Press | The Daytona Beach News-Journal NASCAR CUP SERIES Bank of America ROVAL 400 Site: Charlotte, North Carolina. Schedule: Sunday, race, 2:30 p.m.…
Virtual workshop series focuses on Ohio immigrant experiences
Daniela Pierre-Bravo, Booking Producer for Morning Joe at MSNBC. Credit: Courtesy of Daniela Pierre-Bravo Immigrant and refugee issues will be front and center in a…
OPPO Reno4 series and OPPO Enco W51 wireless headphones on sale now in Middle East
The Reno4 Series makes it easier than ever for users to express their own unique style and share their creativity with the world. Capture creative…
The Series' Sets Holiday Special at Disney+
Disney+ has lined up a holiday-themed special featuring the cast of "High School Musical: The Musical: The Series," the streamer announced on Wednesday. The 45-minute…
The Series' Holiday Special Set for Disney+
The cast of 'High School Musical: The Musical: The Series' Disney Plus While virtual learning may be the current mandate for many students, the cast…
The Best Sci-Fi Series of the 21st Century Goes Epic
Once upon a time there was a four-year-old girl named Emily who had an English accent and liked playing with toy cars. Do you like her cars? She was just a stick…
'High School Musical: The Musical: The Series' Special Set at Disney Plus
The cast of "High School Musical: The Musical: The Series" is reuniting for holiday special at Disney Plus. The 45-minute special will debut on Dec.…
The Series' sets surprise holiday special
© (Fred Hayes / Disney+) Frankie A. Rodriguez as Carlos in "High School Musical: The Musical: The Series." (Fred Hayes / Disney+) You've heard of…
Netflix 2020 Holiday Lineup: Your Guide to All Festive Movies, Series & More | Television
Dolly Parton's Christmas on the Square (November 22) Starring: Dolly Parton, Christine Baranski, Jenifer Lewis, Treat Williams, Jeanine Mason, Josh Segarra, Mary Lane Haskell Synopsis: A…
Dr. Rangan Chatterjee and YuLife Launch Virtual Wellness Event Series
YuLife's Chief Wellbeing Officer, best-selling author and host of the 'Feel Better, Live More' podcast Dr. Rangan Chatterjee, to promote healthy everyday lifestyle choices in…
Upcoming Events: Science Speaker Series: Dr. Emily Levesque | The Daily Courier
Oct. 7 Prescott Plein Air Art Festival Sales, 12 a.m. to 12 p.m., review and purchase from a selection of works produced during the first…
Tickets for 2020 World Series in Texas already sold out
The first two rounds of the 2020 MLB Playoffs have been played without fans in attendance due to the COVID-19 pandemic. © Jerome Miron-USA TODAY…


Add texture and style to your knitted scarves with these charming and simple fringes. Explore long fringe, bulky fringe, tassels & more!
Learning how to knit a scarf lets you add style and a layered look to your fall and winter wardrobes. From simple scarves to charming cowls, there are thousands of knitted scarf patterns to choose from.
If you're looking to upgrade your latest scarf or add some interest, adding fringe is the way to go!
Fringe at the end of a scarf can add length without adding weight. It can also transform the simplest pattern into something eye-catching and interesting.
Adding fringe to a scarf is insanely easy. While there are about a billion different fringes for scarves, there are basically two ways to add a little something extra to your scarves. The wide variety of fringe ideas come from how long you make the fringe, the weight of yarn you use, and how much yarn is added to the fringe. This makes it easy to personalize a pattern (even as a newbie knitter).
The most popular fringe method for knitted scarves and cowls is attaching the fringe directly to the bottom of the scarf.
To do this, you will need a simple crochet hook. This is done by folding yarn into your stitches before pulling the ends through along the bottom.
Fringe created this way can easily be updated to be longer or shorter, striped by using a variety of colors, or thicker with a bulkier yarn or more strands.
Note: If adding your own fringe to a pattern, do not use a type of yarn that is thicker than the yarn used in your pattern. Pulling chunky or bulky yarn through tight worsted weight or lighter yarn could pull your stitches and cause your scarf to warp.
Adding tassels to the end of a scarf is another great way to create different types of fringe for your knitting patterns. While they might look complicated, it's actually pretty simple to make your own tassels.
Some knitters like to use a tassel maker (we like Clover's Tassel Maker) while others DIY the process with a piece of cardboard. Check out our video below.
Adding fringe to scarves is actually pretty easy. The two basic methods (traditional fringe threaded through the bottom of the pattern and tassels) can easily be updated to transform the look. Varying the length, weight, frequency, and yarn color easily transform a pattern. Check out the ideas below for some stunning scarf fringe ideas to try.
The fringe on this scarf is made by pulling longer cuts of yarn through your stitches. Adjust the length however you would like.
Another simple fringe that adds a gorgeous look to your scarf. I love how this fringe extends the color blocking while softening the over texture.
This extra long and bulky fringe makes this super scarf pattern even longer for a bold and bulky look.
Short and sweet, the chunky yarn on this scarf makes for bold and big tassels that won't tangle.
Alternating small tassels help to continued the striped design of this Harry Potter-inspired accessory.
Featured on a poncho below, this tutorial from Red Heart shows you how to make tassels for knitted projects using yarn and cardboard.
This simple and elegant single strang fringe adds a unique look to this knitting pattern.
This charming fringe features all four colors that are on the base of the scarf, making it a smart and stylish way to use up yarn. You could even add four colors to the ends of a basic one-color scarf for a pop of color.
This fringe idea is a little more complicated than the rest. Ending your scarf with a texture stitch like the bobble stitch and working in fringe can really add some wow to your projects.
Jumbo yarn combined with simple and traditional fringe adds easy texture in this lovely scarf. The gradient look to the end of the scarf is a lovely little touch that really brings out the scarves many shades.
This purposely messy and chaotic look adds so much interest to a simple cowl pattern. If you'd prefer something a little contained or calm, shorten the strings on this fringe and achieve the same look without the threat of tangles.
The long tassels on this shawl elongate the project while highlighting it's intricate stitches. Similar tassels on a simple scarf could easily add length while taking far less time than adding row and row.
I love fringes when your garment just needs a little extra oomph. They can be added to store-bought scarves and shawls as well as the ones you knit. Best part is you get to use your imagination in putting a color pattern together that will fit well with the garment.


I'm looking for a Spanish writer who is able to assist me with content for my web design company in Mexico. You need to be able to create texts based on examples from other websites and compile your own.
If you do a good job this can be a continuous job where I will need 1-2 articles weekly after the initial job is done of around 10 articles.
Empecemos, este parece ser un proyecto a mediano plazo, por lo tanto es complicado calcular los costos aunque eso se puede hacer luego ya que no has indicado la cantidad de palabras que necesitas.
Native spanish journalist and professional translator. Big experience and high quality.
Por favor lee mi perfil y el mensaje privado que te he enviado.
I have done similar work in the past and can help you with your project. Experience researching about different topics and writing 100% original articles. Please, see PM for details.
Spanish is my native language. You can count on me to deliver the work on time.
I am a professional web content writer and journalist. I am native from Spain and have over 20 years´experience.
Hello, Im very interested in your offer. details on message .


Police: 2 shooters target 2 officers at Las Vegas eatery, then kill 1, themselves at Walmart.
Police say two suspects shot two officers at a Las Vegas pizza parlor before fatally shooting a person and turning the guns on themselves at a nearby Walmart.
Las Vegas police spokesman Larry Hadfield says the spree began around 11:30 a.m. Sunday when a man and woman walked into CiCi's Pizza restaurant and shot two officers who were eating lunch.
He says one of the suspects yelled, "This is a revolution," but the motive for the shooting remains under investigation.
Investigators say the two suspects then fled to the Walmart across the street, where they shot a person inside and then killed themselves.
Hadfield says the condition of the two officers wasn't immediately known.


Reality TV star Lisa Oldfield has told friends that she and husband David are getting divorced after 17 years of marriage and two children.
Lisa Oldfield says that she is divorcing her husband, David — for real this time.
The Real Housewives of Sydney star took to Facebook to share the news.
Last year, Lisa Oldfield revealed that she was thinking of divorcing David during a post-elimination interview of I'm a Celebrity … Get Me Out Of Here.
"I feel like he is a boat anchor around my neck, and after 17 years I've had a revelation," she said.
The year before, Lisa Oldfield again threatened divorce. Let's see what happens this time around.


text:
Artios have grown and now promote and manage several product lines. They needed product images that would publish to the web. We talked about the three very different products and the type of images we could get from them. I picked up the products from the offices and we shot the photography in the studio the next day, sent proofs that afternoon and finished the job the next morning. The finished assignment was delivered within 48 hours.
Winton Capital
Winton had commissioned an extremely beautiful garden based on a mathematical formula at the Chelsea Flower Show. They wanted a record of the garden on press day shot in as lively a way as possible. They needed the AM photography edited and distributed by lunch time and the PM photography distributed late that night. The garden was fabulous, the people were lovely and all the work was delivered on time.
EM Ltd
EM Ltd., an international executive recruitment company, had recently redesigned their website and needed their team photographed for the "Who Are We" pages. On a boardroom meeting day we had almost the whole team in one place and a small window of time to photograph everyone. We set up a studio in the park opposite the Piccadilly offices in order use the trees as a background, thrown of focus with a low depth of field. The colours also complimented their website colour scheme. The client was very happy and this is an ongoing project.
Renzacci PLC
Renacci, a leading supplier of dry cleaning equipment in the UK, needed to update their new website with photography of their staff in a boardroom setting. They also commissioned two videos, one to show the office and the work being done and another to show the showroom and products. Backbone were very happy to help with both these projects. The photography was prepared and tests completed very early in the morning so that we could start at 9.00. Everyone was excited, the smiles genuine and the laughter real and we all had a great time on the job.
British American Tobacco, a client of many years, needed an Impact Poster showing how different departments worked. After a careful briefing, we started to shadow and photograph head of the work group throughout the morning, in his meetings, informal discussions, the implementing of work processes and enjoying a coffee break with work friends. BAT has always been an exacting client with a clear idea of what's wanted and the whole project worked very well. It's always been a pleasure working with them over the years.
Ophir Energy
Ophir Energy is a fast growing energy company on the World market. Backbone was commissioned to shoot pictures of the members of the board and senior executives at their London HQ over the course of two days. The brief was that we should light the set in such a way that could be replicated at any time of year. We chose to erect a background across the walls so we could repeat the operation at any time. Everything worked to plan and the client was happy with the results. Job done.
Locksmith Animation
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text:
Michael David Taylor (born 9 June 1955 in Chelsea, Victoria) was an Australian first class cricketer who played for Victoria and Tasmania, and despite never playing Test cricket or One Day Internationals for Australia, also participated in the South African rebel tours. Highlights of his career included 1000 first class runs in a season while playing with both Victoria and Tasmania and an unbeaten 234 for Victoria against the touring West Indians in Melbourne in 1984–85.

Career
Michael Taylor was a right-handed batsman who debuted for the South Melbourne Club in 1972–73. He made his first class debut in the 1977–78 season, making 75 and 107 against Queensland in his first game, but his subsequent form was inconsistent and he only played 5 more matches over the next two seasons.

Taylor's club form remained strong and he won the Ryder Medal in 1981–82 for the best player in the VCA games. He established himself in the Victorian side in the 1982–83 season, making 771 runs at an average of 45.35. The following season he scored 1010 runs at 72.14, including a century against the visiting Pakistanis.

In 1984–85 he scored 801 runs at 50.06, the highlight being 234 not out against the West Indies, an innings that went for eight and a half hours. He was also selected to play for the Prime Ministers XI.

South African Rebel Tours
Taylor decided to join the South African rebel tours for the 1985–86 and 86–87 seasons. He said at the time:
It was easy to agree to go there because I have never played Test cricket for Australia. Because of my age [30 next month], chances were getting limited. It was easier for me than for some of the younger guys, Carl Rackemann for instance. Rackemann could have potentially had five to eight years in which to play Tests. I looked into the South African situation a fair bit before I decided to go. It's a very complex problem which certainly can't be fixed overnight. I have never toured and played against an international team, so I viewed this as my chance; a chance to tour and play against probably one of the best cricketing nations in the world. Though I have never played a Test for Australia, I thought at one stage I might have been fairly close to it. I was hopeful of getting a game at one stage last season. When I look back at my career I will not have any regrets.
On the first tour he was Australia's best batsman with 668 runs at an average of 55.66 an innings. In the first unofficial test at Durban he scored 109 against the South African XI. He returned to South Africa for the second rebel tour of 1986–87, but it was less fruitful for Taylor. He managed 306 runs at 27.81 with a top score of 64.

Return to Australia
The South African rebels were banned from first class cricket in Australia for two seasons, being available for selection in 1987–88. However the Victorian players in particular found it difficult re-integrating into their old team. Graham Yallop says they were "shunned by the Victorian Cricket Association... That's why Mick Taylor went to Tassie, Rod McCurdy stayed in South Africa, and Rodney Hogg and myself [eventually] went back to club cricket. But we knew the VCA wouldn't pick us. It was disappointing, we could've given a lot to the game at that stage; we weren't that old. But we were certainly shunned by the association."

Taylor signed with Tasmania for the 1987–88 summer. He scored 1003 runs, including 216 against South Australia in Adelaide and 85 against New Zealand.

In 1988–89 Taylor failed to get beyond 32 in seven innings and dropped out of senior cricket.

Later career
Taylor won a hat-trick of premierships with North Hobart in 1991/92, 1992/93 and 1993/94, before resuming with South Melbourne in 1994/95.

Australian rules football career
Taylor was also a successful Australian rules footballer, playing 51 games for Victorian Football Association (VFA) club Caulfield from 1975 to 1980.

See also
 List of Victoria first-class cricketers
 List of Tasmanian representative cricketers

References

Sources
 Piesse, K. (2010) The Bears Uncensored, Cricketbooks.com.au: Melbourne.

External links

Michael Taylor at CricketArchive
Michael Taylor at Victorian Cricket

1955 births
Living people
Australian cricketers
Tasmania cricketers
Victoria cricketers
Cricketers from Melbourne
Caulfield Football Club players
People from Chelsea, Victoria

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}

Learning latent representations for graph nodes has attracted considerable attention in machine learning, with applications in social networks~\citep{fan2019graph,perozzi2014deepwalk}, knowledge bases~\citep{trivedi2017know}, recommendation systems~\citep{ying2018graph}, and bioinformatics~\citep{zitnik2017predicting}.
\emph{Textual networks} additionally contain rich semantic information, so text can be included with the graph structure to predict downstream tasks, such as link prediction~\citep{zhang2018diffusion}, node classification~\citep{kipf2016semi}, and graph generation~\citep{kipf2016variational}.
For instance, social networks have links between users, and typically each user has a profile (text).
The goal of \emph{textual network embedding} is to learn node embeddings by jointly considering \emph{textual} and \emph{structural} information in the graph.

Most of the aforementioned textual network embedding methods focus on a fixed graph structure~\citep{tu2017cane,zhang2018diffusion,shen2018improved}. When new network nodes are added to the graph, these frameworks require that the whole model be re-trained to update the existing nodes and add representations for the new nodes, leading to high computational complexity.  However, networks are often dynamic; in social networks, users and relationships between users change over time ($e.g.$, new users, new friends, unfriending, $etc.$). It is impractical to update the full model whenever a new user is added. This paper seeks to address this challenge and learn an embedding method that adapts to a changed graph, without re-training.

Prior dynamic embedding methods usually focus on predicting how the graph structure changes over time, by training on multiple time steps ~\citep{zhou2018dynamic,seo2018structured,du2018dynamic}. In such a model, a dynamic network embedding is approximated by multiple steps of fixed network embeddings. In contrast, our method only needs to train on a single graph and it can quickly adapt to related graph structures.
Additionally, in prior work textual information is rarely included in dynamic graphs.
Two exceptions have looked at dynamic network embeddings with changing node attributes~\citep{li2017attributed,li2018streaming}.
However, both require pre-trained node features, whereas we show that it is more powerful to learn the text encoder in a joint framework with the structural embedding.

We propose \textbf{D}ynamic \textbf{E}mbedding for \textbf{T}extual Networks with a \textbf{G}aussian \textbf{P}rocess (DetGP), a novel end-to-end model for performing unsupervised dynamic textual network embedding. DetGP learns \emph{textual} and \emph{structural} features jointly for both fixed and dynamic networks. The textual features indicate the intrinsic attributes of each node based on the text alone, while the structural features reveal the node relationships of the whole community. The structural features utilize both the textual features and the graph topology. This is achieved by smoothing the kernel function in a Gaussian process (GP) with a multi-hop graph transition matrix. This GP-based structure can handle newly added nodes or dynamic edges due to its non-parametric properties~\citep{rasmussen2003gaussian}. To facilitate fast computation, we learn inducing points to serve as landmarks in the GP \citep{yu2008gaussian}. Since the inducing points are fixed after training, computing new embeddings only requires calculating similarity to the inducing points, alleviating computational issues caused by changing graph structure.

To evaluate the proposed approach, the learned node embeddings are used for link prediction and node classification.
Performance on those downstream tasks demonstrates that learned embeddings capture relevant information. We also perform these tasks on dynamic textual networks and visualize the learned inducing points. Empirically, DetGP outperforms other models in downstream tasks, yielding efficient and accurate predictions on newly added nodes.

\section{Related Work}\label{sec:related_works}
\textbf{Textual Network Embedding}: Many graphs have rich text information for each node~\citep{yang2015network} (\textit{e.g.}, paper abstracts in citation networks, user profiles in social networks, product and costumer descriptions in online shopping, \textit{etc.}), which leads to the problem of \emph{textual network embedding}~\citep{tu2017cane}. Textual network embedding learns enhanced node representations by combining the textual embeddings and structural embeddings together. Textual  embeddings are learnt by encoding raw-text via text encoders. Structural are obtained based  on the connection information on graphs. Recent textual embedding methods~\citep{zhang2018diffusion,shen2018improved,tu2017cane,sun2016general} learn both textual and structural embeddings jointly in an end-to-end training process with neural networks. However, previous methods require all the network connection information before training, which makes them difficult to apply in dynamic network scenarios.

\textbf{Dynamic Network Embedding}: Graph structures are often \emph{dynamic} (\textit{e.g.}, paper citation increasing or social relationship changing overtime), but fixed network embedding algorithms require re-training when graphs change. This issue is addressed by dynamic network embeddings~\citep{trivedi2018representation}. Research on dynamic graphs has usually focused only on \emph{structural embeddings}~\citep{trivedi2018representation,du2018dynamic,guo2018spine} without considering rich side information associate with vertices. While these methods learn how to update the model as the graph changes, they are not real-time algorithms, instead using gradient back-propagation to update representations when new nodes are added or the graph structure changes~\citep{goyal2018dyngem,du2018dynamic}.

\textbf{Gaussian Process}: A Gaussian Process (GP) $f({\bm{x}})$ is a collection of random  variables such that any finite subset of those variables are Gaussian distributed. More specifically, given finite set $\{ {\bm{x}}_1, {\bm{x}}_2, \dots, {\bm{x}}_n \}$ with $n \in \mathbb{N}_+$, the corresponding signal $[f({\bm{x}}_1), f({\bm{x}}_2), \dots, f({\bm{x}}_n)]^\intercal \sim \mathcal{N}([m({\bm{x}}_1), m({\bm{x}}_2), \dots, m({\bm{x}}_n)]^\intercal, [k({\bm{x}}_i, {\bm{x}}_j)]_{n \times n})$, where $m({\bm{x}})$ is a mean function and $k(\cdot, \cdot)$ is a covariance kernel function. GPs are used widely in the Bayesian machine learning literature as priors on functions~\citep{titsias2009variational,rasmussen2003gaussian,titsias2010bayesian}.
To learn the mapping $y = f({\bm{x}})$ with training data $\{({\bm{x}}_i,y_i) \}_{i=1}^N$ and unlabeled testing data $\{ {\bm{x}}'_j \}_{j=1}^M$, with Gaussian process as the prior, $[f({\bm{x}}_1), f({\bm{x}}_2) \dots, f({\bm{x}}_n), f({\bm{x}}'_1), \dots, f({\bm{x}}'_M)]$ follows a multivariate Gaussian distribution. Given observations $f({\bm{x}}_i) = y_i$, the conditional distribution for $[f({\bm{x}}'_1), \dots, f({\bm{x}}'_M)]$ can be easily obtained, which is also Gaussian distributed.
Recently, GPs have been used for node embedding learning on graphs~\citep{ma2018depthlgp,ng2018bayesian}. However, these works require pre-trained node features, leading to a two-step training process. In contrast, our proposed model is an end-to-end framework that can  jointly train the feature extractor (text encoder) with the GP parameters.

\section{Model}\label{sec:model}

We assume the input data are given as an undirected graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$, where $\mathcal{V}= \{v_n\}_{n=1}^N$ is the node set and $\mathcal{E} = \{(v_n, v_{n'}) : v_n,v_{n'} \in \mathcal{V} \}$ is the edge set. Each node $v_n$ has an associated  $L_n$-length text sequence $\bm t_n = \{w_i \}_{i=1}^{L_n}$, where each $w_i$ is a natural language word. The adjacency matrix ${\bm{A}} \in \{0,1\}^{N\times N}$ represents node relationships, where $A_{nn'} = 1$ if $(v_n, v_{n'}) \in \mathcal{E}$ and $A_{nn'} = 0$ otherwise. Our objective is to learn a low-dimensional embedding vector $\Emb_n$ for each node $v_n \in \mathcal{V}$ that captures both textual and structural features of the graph $\mathcal{G}$.

\begin{figure*}[t]
    \centering
    \includegraphics[width=0.8\textwidth]{framework_new2.pdf}

    \caption{The input of the DetGP is the connection information ${\bm{A}}$ of the network and textual side information ${\bm{T}} = \{{\bm{t}}_n\}_{n=1}^N$ for nodes. The model first encodes text ${\bm{T}}$ to a low-dimension representation ${\bm{X}} = \{{\bm{x}}_n \}_{n=1}^N$, then infers the structural embeddings by ${\bm{X}}$ and ${\bm{A}}$ via a Gaussian process. Inducing points ${\bm{Z}} = \{ {\bm{z}}_m \}_{m=1}^M$ are used to reduce computational complexity. The output network embeddings combine the textual and structural embeddings.

}
    \label{fig:framework}

\end{figure*}

Figure~\ref{fig:framework} gives the framework of the proposed model, DetGP. Text $\bm t_n$ is input to a text encoder $\bm g_{{\bm{\theta}} }(\cdot)$ with parameters $\bm \theta$, described in Section \ref{subsec:text_encoder}. The output $\tEmb_n = {\bm{g}}_{\bm{\theta}}({\bm{t}}_n)$ is the \emph{textual embedding} of node $v_n$. This textual embedding is both part of the complete embedding $\Emb_n$ and an input into the structural embedding layer (dotted purple box) that is combined with the graph structure in a GP framework, discussed in Section \ref{subsec:embedding_layer}. In addition, multiple hops are modeled in this embedding layer to better reflect the graph architecture and use both local and global graph structure. The mathematical analysis of the structural embeddings is given in Section \ref{subsec:analysis_of_embedding_layer}. To scale up the model to large datasets, we adopt the idea of inducing points~\citep{titsias2009variational,titsias2010bayesian}, which serve as grid points in the model.  The output structural embeddings are denoted as $\sEmb_n$, which are combined to form the complete node embedding $\Emb_n=[\tEmb_n;\sEmb_n]$.

The model is trained by using the negative sampling loss~\citep{tu2017cane}, where neighbor nodes should be more similar than non-neighbor nodes. The learning procedure is fully described in Section \ref{subsec:algorithm_outline}. When the graph structure is updated, \emph{i.e.} new nodes $v_{new}$ with text $\tTxt_{new}$ are added or links are changed, the node embeddings are updated by a single forward-propagation step without relearning any model parameters. This property comes from the non-parametric nature of the GP-based structure, and it greatly increases efficiency for dynamic graphs.

\subsection{Text Encoder}\label{subsec:text_encoder}

There are many existing text encoders~\citep{melamud2016context2vec,cer2018universal,lin2017structured}, often based on deep neural networks. However, using a deep neural network encoder can overfit on graphs because of the relatively small size of textual data \citep{zhang2018diffusion}. Therefore, various encoders are proposed to extract rich textual information specifically from graphs \citep{tu2017cane,zhang2018diffusion,shen2018improved}. In general,
we aim to learn a text encoder ${\bm{g}}_{{\bm{\theta}}}$ with parameters ${\bm{\theta}}$ that encodes semantic features ${\bm{x}}_n = {\bm{g}}_{\bm{\theta}}({\bm{t}}_n)$. A simple and effective text encoder is the word embedding average (Wavg) ${\bm{g}}_{\bm{\theta}}({\bm{t}})  = \frac{1}{L_n} \sum_{i=1}^{L_n} \bm \nu_{i}$, where $\bm \nu_{i}$ is the corresponding embedding of $w_{i}$ from the sequence $\bm t_n = \{w_i \}_{i=1}^{L_n}$.  This is implemented by a learnable look-up table.
~\citep{zhang2018diffusion} proposed a diffused word average encoder (DWavg) to leverage textual information over multiple hops on the network. Because DetGP focuses mainly on the structural embeddings, we do not focus on developing a new text encoder. Instead, we show that DetGP has compatibility with different text encoders, and our experiments use these two text encoders (Wavg and DWavg).

\subsection{Structural Embedding Layer}\label{subsec:embedding_layer}

The structural embedding layer transforms the encoded text feature $\tEmb$ to structural embedding $\sEmb$ using a GP in conjunction with the graph topology. Before introducing the GP, we introduce the multi-hop transition matrix $\bm P_*$ that will smooth the GP kernel.

\textbf{Multi-hop Transition Matrix}: In a graph, one node can be directly or indirectly connected to others by edges. Only considering direct connections is limiting. For example, in citation networks, cited papers should be closely related to a manuscript, so considering both a neighbor and its neighbors should add information. Following this intuition, we propose to use multiple hops, or multi-step graph random walks, to model both local and global structure.

Suppose $\bm P$ is the normalized transition matrix, $i.e.$ a normalized version of $\bm A$ where each row sums to one and $P_{nn'}$ represents the probability of a transition from node $n$ to node $n'$. If $\bm P$ represents the transition from a single hop, then higher orders of $\bm P$ will give multi-hop transition probabilities. Specifically, $\bm P^j$ is the $j$th power of $\bm P$, where $P^j_{nn'}$ gives the probability of transitioning from node $n$ to node $n'$ after $j$ random hops on the graph~\citep{abu2018watch}.
Different powers of $\bm P$ provide different levels of smoothing on the graph, and vary from using local to global structure. \emph{A priori} though, it is not clear what level of structure is most important for learning the embedding.  Therefore, they are combined in a learnable weighting scheme.
Denoting the weights as $\bm \alpha$, this is
\begin{equation}\label{eq:P*}
   \textstyle \bm P_*=\sum_{j=0}^J \alpha_j \bm P^j , \quad s.t. \sum_{j=0}^J \alpha_j = 1,
\end{equation}
where $J$ is the maximum number of steps considered.
The constraint that $\sum_{j=0}^J \alpha_j = 1$ in \eqref{eq:P*} is implemented by a softmax function. Note that $\bm P^0 = \bm I_N$ is an identity matrix, that treats each node independently. In contrast, a large power of $\bm P$ would typically be very smooth after taking many hops.
Therefore, $\bm \alpha$ can learn the importance of local ($\bm P^0$ or $\bm P^1$) and global (large powers of $\bm P$) graph structure for the node embeddings.  Equation~\eqref{eq:P*} can be viewed as a generalized form for DeepWalk~\citep{perozzi2014deepwalk} or Node2vec~\citep{grover2016node2vec}. In practice, learning the weights appears to be more robust than hand-engineering them~\citep{abu2018watch}.

\textbf{GP Structural Embedding Prior}: To describe the other key components of the structural embedding layer, we describe the GP approach. We define a latent function $f(\tEmb)$ over the textual embedding $\tEmb$ with a GP prior $f(\tEmb) \sim \mathcal{GP}\left( \bm 0, k(\tEmb_n, \tEmb_{n'}) \right)$.  Inspired by~\citep{ng2018bayesian}, instead of using this GP directly to determine the embedding, the learned graph diffusion is used on top of this Gaussian process. For finite samples, the combination of the graph diffusion and the GP yields a conditional structural embedding that can be expressed as a multivariate Gaussian distribution:
\begin{small}
\begin{equation}\label{eq:original_gp}
    p([s_{1i},\dots,s_{Ni}]^\intercal| [\tEmb_1,\dots,\tEmb_N]) = \mathcal{N}\left(\bm 0, \bm P_* ^{\intercal} \bm K_{XX} \bm P_* \right) ,
\end{equation}
\end{small}
where $[\bm K_{XX}]_{nn'} = k(\tEmb_n, \tEmb_{n'})$ and $i$ is a index of our structure embedding feature.
Each dimension of the structural embedding follows this Gaussian distribution with the same covariance matrix $\bm K_{XX}$ smoothed by $\bm P^*$.
In practice, we use the first-degree polynomial kernel
\begin{equation}\label{eq:kernel}
    k\left( \tEmb_n, \tEmb_{n'} \right) = \tEmb_n^{\intercal} \tEmb_{n'}+C , \ C>0
\end{equation}
because it outperforms others due to its numerical stability.
Moreover, the linear kernel in \eqref{eq:kernel} speeds up computation and increases model stability.

\textbf{Inducing Points}: GP models are known to suffer from computational complexity with large data size $N$.
To scale up the model, we use the inducing points based on the Sparse pseudo-inputs Gaussian process (SPGP)~\citep{snelson2006sparse}. Let $\bm Z = [\bm z_1, \cdots, \bm z_M]^{\intercal}$ with $M<N$ denote inducing points (pseudo-textual embeddings) in the same space as the textual features. Assume $\bm U = [\bm u_1,\cdots,\bm u_M]^{\intercal}$ are corresponding the pseudo-structural embeddings of $\bm Z$, which is a function of $\bm z$ following the same GP function.
The structural and textual embeddings of real data samples are denoted as $\bm{S}=[\sEmb_1,\cdots, \sEmb_N]^{\intercal}$ and $\bm{X}=[\tEmb_1,\cdots, \tEmb_N]^{\intercal}$. Given the inducing points, the conditional distribution of our structural embeddings is
\begin{small}
\begin{align}\label{eq:e_x_conditional}
\textstyle
    &p(\bm S_i| \bm X, \bm Z, \bm U)  = \mathcal{N} \left( \bm \mu_{S_i|Z}, \bm \Sigma_{S|Z}\right), \\
    &\bm \mu_{S_i|Z}  = \bm P_*^{\intercal}  \bm K_{XZ}  \left(\bm K_{ZZ} + \sigma \bm I_{M}\right)^{-1} \bm U_i, \nonumber \\
    &\bm \Sigma_{S|Z} = \bm P_*^{\intercal} \bm K_{XX} \bm P_* - \bm P_*^{\intercal} \bm K_{XZ} \left( \bm K_{ZZ} + \sigma \bm I_M \right)^{-1} \bm K_{ZX} \bm P_*, \nonumber
\end{align}
\end{small}
where $[\bm K_{XZ}]_{nm} = k(\tEmb_n, {\bm{z}}_{m})$ and $[\bm K_{ZZ}]_{mm'} = k(\bm{z}_m, \bm{z}_{m'})$. The subscript $i$ indicates the $i$th column of a matrix ($\bm S_i$ is the concatenation of the $i$th element from all node structural embeddings). Each dimension of $\bm S$ has a multivariate Gaussian distribution with unique mean value $\bm \mu_{s_i|Z}$ but the same covariance $\bm \Sigma_{S|Z}$. Note that a small number $\sigma$ is added to the diagonal elements of the kernel ${\bm{K}}_{ZZ}$ to enhance model stability. The relationships of different parameters are given in Figure~\ref{fig:notation_illustration}. The inducing points $\{{\bm{z}}_m\}_{m=1}^M$ and text features $\{{\bm{x}}_n \}_{n=1}^N$ share the same textual embedding space;  the pseudo-textual embeddings $\{ {\bm{u}}_m\}_{m=1}^M$ and the structural embeddings $\{{\bm{s}}_n\}_{n=1}^n$ share the same structural embedding space.

\begin{figure}[t]
\centering
\includegraphics[width=0.6\columnwidth]{variable_illustration.pdf}

\caption{\label{fig:notation_illustration}
Model flow chart. Inducing points are denoted as $\bm z$, with embedding $\bm u$. The final node embedding $\bm h$ is the concatenation of text embedding $\tEmb$ and structural embedding $\sEmb$.
}

\end{figure}

During the training, the textual embedding space is continuously changed, because the text encoder ${\bm{g}}_{\bm{\theta}}({\bm{t}})$ is updated by the gradient descent algorithm iterative. Therefore, the inducing points in the textual embedding space should also be updated correspondingly. To obtain the optimal inducing points ${\bm{Z}}$ with corresponding pseudo-structural embeddings ${\bm{U}}$, we jointly train them using gradient descent with  weights in other layers. To back-propagate through the stochastic posterior distribution $p({\bm{S}}_i | {\bm{X}}, {\bm{Z}}, {\bm{U}})$ in equation~\eqref{eq:e_x_conditional}, we propose the mean approximation strategy.
We use the mean of $p({\bm{S}}_i | {\bm{X}}, {\bm{Z}}, {\bm{U}})$, $\hat{{\bm{S}}} = \bm P_*^{\intercal} \bm K_{XZ} \left(\bm K_{ZZ} + \sigma \bm I_M\right)^{-1} \bm U$, as unbiased estimation of structural embeddings. Then gradients from ${\bm{S}}$ can be easily propagated to ${\bm{Z}}$ and ${\bm{U}}$.

\subsection{Analysis of the Structural Embedding}\label{subsec:analysis_of_embedding_layer}

We analyze the kernel function in \eqref{eq:original_gp} and~\eqref{eq:kernel} to show how the graph structure is used in the embedding layer. Denote $P^j_{nn'}$ in equation~\eqref{eq:P*} as the transition probability from node $n$ to node $n'$ in $j$ hops, then the correlation between node $n$ and $n'$ in \eqref{eq:original_gp} can be expanded as
\begin{small}
\begin{align}\label{eq:analyze_original}
\textstyle
     \text{cov}&(s_{ni}, s_{n'i}) = \alpha_0^2 k(\tEmb_{n}, \tEmb_{n'})+\alpha_0 \sum_{j=1}^J \alpha_j \sum_{r=1}^N P^j_{nr} k(\tEmb_n,  \tEmb_{r})\nonumber \\
     &+\alpha_0 \sum_{j=1}^J \alpha_j \sum_{r=1}^N P^j_{n'r} k(\tEmb_{n'},  \tEmb_{r})  \\
      &+ \sum_{j=1}^J \sum_{j'=1}^J  \sum_{\substack{r=1 \\ r\neq n, n}}^N \sum_{\substack{r'=1 \\ r' \neq n, n'}}^N \alpha_j \alpha_{j'} P^j_{nr} P^{j'}_{n'r'} k(\tEmb_{n'},  \tEmb_{r'}) \nonumber
\end{align}
\end{small}
The covariance is the same for all indices $i$.
The first term in \eqref{eq:analyze_original} measures the kernel function between $\tEmb_n$ and $\tEmb_{n'}$. The next two terms show the relationship between $\tEmb_n$ and the weighted multi-hop neighbors of $\tEmb_{n'}$ and vice versa. $\bm \alpha$ controls how much different hops are used. The last term is the pairwise-weighted higher order relationship between any two nodes in the graph, except $n$ and $n'$.
The covariance structure uses the whole graph and learns how to balance local and global information.
If node $n$ has no edges, then it will not be influenced by other nodes besides textual similarity. In contrast, a node with dense edge connections will be smoothed by its neighbors.

With the inducing points $[{\bm{z}}_1,{\bm{z}}_2,\dots,{\bm{z}}_M]$, equation~\eqref{eq:analyze_original} can be modified as
 $  \text{cov}(s_{ni}, u_{mi}) = \alpha_0 k\left( \tEmb_{n}, \bm z_{m} \right) + \sum_{j=1}^J \alpha_j \sum_{n'=1}^N P^j_{nn'}k\left( \tEmb_{n'}, \bm z_{m} \right) .$

The covariance between node $v_n$ and the inducing points includes the local information $k\left( \tEmb_{n}, \bm z_{m} \right)$, as well as the smoothed effect from $\sum_{j=1}^J \alpha_j \sum_{n'=1}^N P^j_{nn'}k\left( \tEmb_{n'}, \bm z_{m} \right)$. This can also be viewed as feature smoothing over neighbors. Since inducing points do not contain links to other inducing points, there is no smoothing function for them. Each inducing point can be viewed as a node that already includes global graph information.

\subsection{Algorithm Outline}\label{subsec:algorithm_outline}

The structural embedding $\sEmb_n$ and the textual embedding $\tEmb_n$ are concatenated to form the final node embedding $\Emb_n = [\tEmb_n; \sEmb_n]$. If desired, $\Emb_n$ can then pass through several additional fully connected layers; for simplicity, we consider this the final embedding form. To learn the embeddings in the unsupervised framework, most existing works adopt the technique of negative sampling~\citep{zhang2018diffusion,zhang2018nscaching,tu2017cane}, that tries to maximize the conditional probability of one node's embedding given its one- and multi-hop neighbors, while maintaining a low conditional probability for non-neighbors. In the proposed framework, this loss is given for a single hop,
\begin{eqnarray}\label{eq:loss}
\textstyle
    \mathcal{L}=&-\frac{1}{|\mathcal{E}|}\sum_{(v_n,v_{n'}) \in \mathcal{E}} \log \left( \sigma(\bm h^{\intercal}_{n} \bm h_{n'}) \right)\nonumber \\ &- \frac{1}{N_s}\sum_{(v_n,v_{n'}) \not\in \mathcal{E}} \log \left[ 1-\sigma(\bm h^{\intercal}_{n} \bm h_{n'})  \right] .
\end{eqnarray}
$N_s$ is a weighting constant and can be set as  $N_s = \# \{(v_n,v_{n'}) \not\in \mathcal{E} \}$. In practice, using all nodes is infeasible, so a subset of neighbors and non-neighbors will be sampled. Equation~\eqref{eq:loss} maximizes the inner product among neighbors in the graph while minimizing the similarity among non-neighbors.
Our model is trained end-to-end by taking gradients of loss $\mathcal{L}$  with respect to $\bm \theta$, $\bm Z$ and $\bm U$. The inducing points are initialized as the $k$-means centers of the encoded text features. Then, $\bm Z$ and the text encoder are trained jointly to minimize the loss function. Note that our model can also take a mini-batch of nodes as in GraphSage~\citep{hamilton2017inductive}. Adam~\citep{kingma2014adam} is used to optimize the parameters.

For a new node $v_{new}$ with text $\tTxt_{new}$, the transition matrix $\bm P_{new}$ is first updated, and the embeddings can be applied directly without additional back-propagation. Specifically, we first compute $\tEmb_{new} = \bm g_{\theta}(\tTxt_{new})$ from the text encoder.
Then with $[\tEmb, \tEmb_{new}]$, the structural embedding of all nodes can be computed as $[\sEmb, \sEmb_{new}] = \sum_{j=0}^J \alpha_j \bm P^{j}_{new} \bm K_{x_{new}Z} (\bm K_{ZZ} + \sigma \bm I_M)^{-1} \bm U$.
During this process, the structural embeddings of the original nodes also update due to the change in graph structure.

\section{Experiments}\label{sec:experiments}
\begin{table*}[hbt]  \footnotesize
	\centering

	\scalebox{0.93}{

	\begin{tabular}{ccccccccccc}
        \toprule[1.2pt]
        \multicolumn{1}{c}{ }&  \multicolumn{5}{c}{Cora} & \multicolumn{5}{c}{HepTh}\\
        \hline
		\textbf{\%Training Edges} &  	\textbf{15\%} & \textbf{35\%} & 	\textbf{55\%} & \textbf{75\%} & \textbf{95\%} & \textbf{15\%} & \textbf{35\%} & \textbf{55\%} & \textbf{75\%} & \textbf{95\%}\\
		\midrule
		\textbf{MMB}~\citep{airoldi2008mixed}     & 54.7 & 59.5 & 64.9 & 71.1 &75.9 & 54.6 &57.3 & 66.2  &73.6 &80.3 \\
		\textbf{node2vec}~\citep{grover2016node2vec} & 55.9 & 66.1  & 78.7 & 85.9& 88.2 & 57.1 &69.9  &84.3 & 88.4 & 89.2 \\
		\textbf{LINE}~\citep{tang2015line}     & 55.0 & 66.4 & 77.6 & 85.6 & 89.3 & 53.7  &66.5  &78.5  &87.5 & 87.6\\
		\textbf{DeepWalk}~\citep{perozzi2014deepwalk} & 56.0 & 70.2 & 80.1 & 85.3 & 90.3 & 55.2 &70.0& 81.3  &87.6 & 88.0  \\
		\midrule

		\textbf{TADW}~\citep{yang2015network} & 86.6 & 90.2 & 90.0 & 91.0& 92.7 & 87.0  &91.8& 91.1  &93.5 & 91.7 \\

		\textbf{CANE}~\citep{tu2017cane} & 86.8 &92.2 &94.6 &95.6 &97.7 & 90.0  &92.0  &94.2  &95.4 & 96.3\\
		\textbf{DMATE}~\citep{zhang2018diffusion}  & 91.3 & 93.7  & 96.0  & 97.4 & 98.8 & NA & NA & NA & NA & NA\\
		\textbf{WANE}~\citep{shen2018improved}  & 91.7 & 94.1 & 96.2 & \textbf{97.5} & \textbf{99.1} &92.3 & 95.7 & 97.5 & 97.7 & \textbf{98.7} \\
		\midrule
		\textbf{DetGP (Wavg) only Text } & 83.4& 89.1 & 89.9 & 90.9  & 92.3 &  86.5  & 89.6  & 90.2 & 91.5 & 92.6 \\
		\textbf{DetGP (Wavg) only Struct} & 85.4& 89.7 &91.0 & 92.7  & 94.1 &  89.7  & 92.1  & 93.5 & 94.8 & 95.1\\
		\textbf{DetGP (Wavg)} & 92.8& 94.8 &95.5 & 96.2  & 97.5 &  93.2  & 95.1  & 97.0 & 97.3 & 97.9\\
		  \midrule
		\textbf{DetGP (DWavg)} & \textbf{93.4} & \textbf{95.2} & \textbf{96.3}  & \textbf{97.5}& 98.8 & \textbf{94.3} &  \textbf{96.2}  &\textbf{97.7}  & \textbf{98.1} & {98.5}  \\
		\bottomrule[1.2pt]
	\end{tabular}}

	\caption{AUC scores for link prediction on the \emph{Cora} and \emph{HepTh} dataset. The top four models only have structural embedding, while the rest use text information.}
	\label{tab:link_predict_cora_hepth}

\end{table*}
\begin{table*}[htb]  \footnotesize
	\centering

	\scalebox{0.93}{
	\begin{tabular}{ccccccccc}
        \toprule[1.2pt]
        \multicolumn{1}{c}{ }&  \multicolumn{4}{c}{Cora} & \multicolumn{4}{c}{DBLP}\\
        \hline
		\textbf{\%Training Nodes} &  	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%} & 	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%}\\
		\midrule

		 \textbf{LINE}\citep{tang2015line}  &  53.9 & 56.7 & 58.8 & 60.1  & 42.7 & 43.8 & 43.8 &  43.9\\
        \textbf{TADW}~\citep{yang2015network}  &  71.0 & 71.4 & 75.9 & 77.2  &67.6 & 68.9 & 69.2 &  69.5\\

        \textbf{CANE}~\citep{tu2017cane}  &  81.6 & 82.8 & 85.2 & 86.3 & 71.8 & 73.6 & 74.7 & 75.2\\
        \textbf{DMTE}~\citep{zhang2018diffusion}  &  81.8 & 83.9 & 86.3 & 87.9 &72.9 & 74.3 & 75.5 & 76.1\\
        \textbf{WANE}~\citep{shen2018improved}  &  81.9 & 83.9 & 86.4 & 88.1 & NA & NA &NA & NA \\
        \midrule
       \textbf{DetGP (Wavg) only Text  }  &  78.1 &  81.2    & 84.7 &  85.3 &71.4 &	73.3	&74.2	& 74.9   \\
       \textbf{DetGP (Wavg) only Struct}  &  70.9 &     79.7    & 81.5 &  82.3 &70.0&	71.4	&72.6	& 73.3   \\
        \textbf{DetGP (Wavg)}  &  80.5 &  85.4    & 86.7 &  88.5 &76.9 &	78.3	&79.1	& 79.3   \\
      \midrule
        \textbf{DetGP (DWavg)} & \textbf{83.1} & \textbf{87.2 }& \textbf{88.2}& \textbf{89.8} & \textbf{78.0} & \textbf{79.3} & \textbf{79.6}  & \textbf{79.8} \\
        \bottomrule[1.2pt]
	\end{tabular}}

	\caption{Test Macro-F1 scores for multi-label node classification on \emph{Cora} and  \emph{DBLP} dataset.}
	\label{tab:node_classification_cora_DBLP}

\end{table*}

To demonstrate the effectiveness of our DetGP embeddings, we conduct experiments first with static networks as in \citep{tu2017cane,zhang2018diffusion,shen2018improved}, and then on dynamic graphs.
 In the standard setup, learning textual network embeddings requires that all nodes are available in the graph. In contrast, we demonstrate in Section~\ref{subsec:new_node_test} that our proposed model can infer embeddings efficiently after training on newly added nodes. We evaluate the graph embeddings on link prediction and node classification on the following real-world datasets:
\begin{itemize}
\item \textbf{Cora} is a paper citation network, with a total of 2,277 vertices and 5,214 edges in the graph, where only nodes with text are kept. Each node has a text abstract about machine learning and belongs to one of seven categories.
\item \textbf{DBLP} is a paper citation network with 60,744 nodes and 52,890 edges. Each node represents one paper in computer science in one of four categories: database, data mining, artificial intelligence, and computer vision.
\item \textbf{HepTh} (High Energy Physics Theory)~\citep{leskovec2007graph} is another paper citation network. The original dataset contains 9,877 nodes and 25,998 edges. We only keep nodes with associated text, so this is limited to 1,038 nodes and 1,990 edges.

\end{itemize}

For a fair comparison with previous work, we follow the setup in \citep{tu2017cane,zhang2018diffusion,shen2018improved}, where the embedding for each node has dimension 200, a concatenation of a 100-dimensional textual embedding and a 100-dimensional structural embedding. We evaluate our DetGP base on two text encoders: the word embedding average (Wavg) encoder and the diffused word embedding average (DWavg) encoder from \citet{zhang2018diffusion}, introduced in Section~\ref{subsec:text_encoder}. The maximum number of hops $J$ in $\bm P^*$ is set to $3$.

\subsection{Link Prediction}\label{subsec:link_prediction}

The link prediction task seeks to infer if two nodes are connected, based on the learned embeddings. This standard task tests if the embedded node features contain graph connection information. For a given network, we randomly keep a certain percentage ($15\%$, $35\%$, $55\%$, $75\%$, $95\%$) of edges and learn embeddings.
At test time, we calculate the inner product of pairwise node embedding. A large inner product value indicates a potential edge between two nodes. The AUC score~\citep{hanley1982meaning} is computed in this setting to evaluate the performance.
The results are shown in Table~\ref{tab:link_predict_cora_hepth} on Cora and HepTh. Since the DBLP dataset only has 52,890 edges which is far too sparse compared with the node number 60,744, we do not evaluate the AUC score on it as a consequence of high variance from sampling edges.
The first four models only embed structural features, while the remaining alternatives use both textual and structural embeddings. We also provide the DetGP results of with only textual embeddings and only structure embeddings for ablation study.

From Table~\ref{tab:link_predict_cora_hepth}, adding textual information in the embedding can improve the link prediction result by a large margin. Even using only textual embeddings, DetGP gains significant improvement compared with only structure-based methods, and achieves competitive performance compared with other text-based embedding methods. Using only structural information is slightly better than using only textual embeddings, since link prediction is a more structure-dependent task, which also indicates that DetGP~learns inducing points $\bm Z$ that can effectively represent the network structure.
Compared with other textual network embedding methods, DetGP has very competitive AUC scores, especially when only given a small percentage of edges. Noting that for our methods the text encoders come from the baselines Wavg and DWavg \citep{zhang2018diffusion}, the performance gain should come from the proposed structural embedding framework.
\subsection{Node Classification}\label{subsec:node_classification}
Node classification tasks aim to predict the category labels of the nodes based on the network structure and the node attributes. For textual networks,
node classification requires high-quality \emph{textual embeddings} because \emph{structural embeddings} alone do not accurately reflect node categories. Therefore, we only compare to methods designed for textual network embedding.
After training converges, a linear SVM classifier is learned on the trained node embeddings and performance is estimated by a hold-out set.
In Table~\ref{tab:node_classification_cora_DBLP}, we compare our methods (Wavg+DetGP, DWavg+DetGP) with recent textual network embedding methods under different proportions ($10\%$, $30\%$, $50\%$, $70\%$) of given nodes in the training set.
Following the setup in \citet{zhang2018diffusion}, the evaluation metric is Macro-F1 score~\citep{powers2011evaluation}.  We test on the Cora and DBLP datasets, which have group label information, where DetGP~yields the best performance under all situations. This demonstrates that the proposed model can learn both representative textual and structural embeddings. The ablation study results (only textual embeddings \textit{vs.} only structural embeddings) demonstrates that textual attributes are more important than edge connections in classification task.
To describe the effect of learning the weighting in the diffusion, for the experiment on Cora with $10\%$ nodes given for training, the learned weights in $\bm \alpha$ are $[0.58, 0.12, 0.24, 0.05]$. Thus, local and second order transition features are more important.

\subsection{Dynamic Network Embedding}\label{subsec:new_node_test}
\begin{table*}[tbh]  \footnotesize
	\centering

		\scalebox{0.95}{
	\begin{tabular}{lcccccccc}
        \toprule[1.2pt]
                 &  \multicolumn{4}{c}{Cora} & \multicolumn{4}{c}{HepTh}\\
        \hline
		\textbf{\%Training Nodes} &  	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%} & 	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%}\\
        \midrule
        \textbf{Only Text (Wavg)}  &61.2 & 77.9& 87.9 & 90.3 & 68.3 &83.7 & 84.2&86.9\\
         \textbf{Neighbor-Aggregate (Max-Pooling)} & 54.6  & 69.1 &  78.7 & 87.3 & 59.6 & 78.3 & 79.9 & 80.7\\
       \textbf{Neighbor-Aggregate (Mean)} & 61.8  & 78.4 &  88.0 & 91.2 & 68.2 & 83.9 & 85.5 & 88.3\\
       \textbf{GraphSAGE (Max-Pooling)} &  62.1  &  78.6 &  88.6 & 92.4 &  68.4 & 85.8& 88.1 & 91.2\\
       \textbf{GraphSAGE (Mean)} &  62.2    & 79.1 & 88.9  & 92.6 &  69.1 & 85.9& 89.0 & 92.4\\
        \textbf{DetGP} & \textbf{62.9} &
        \textbf{81.1} & \textbf{90.9} & \textbf{93.0} &\textbf{ 70.7} &\textbf{86.6} &\textbf{90.7} & \textbf{93.3}\\
        \bottomrule[1.2pt]
	\end{tabular}}

	\caption{Test AUC scores for link prediction on \emph{Cora} and  \emph{HepTh} datasets.}
	\label{tab:new_node_link_prediction_dwavg}

\end{table*}
\begin{table*}[thb]  \footnotesize
	\centering

		\scalebox{0.95}{
	\begin{tabular}{lcccccccc}
        \toprule[1.2pt]
   &  \multicolumn{4}{c}{Cora} & \multicolumn{4}{c}{DBLP}\\
        \hline
	 \textbf{\% Training Nodes}&  	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%} & 	\textbf{10\%} & \textbf{30\%} & 	\textbf{50\%} & \textbf{70\%}\\
        \midrule
        \textbf{Only Text (Wavg)}  &  60.2& 76.3 & 83.5 & 84.8 & 56.7& 67.9 & 70.4 & 73.5 \\

        \textbf{Neighbor-Aggregate (Max-Pooling)}  &55.8 & 70.2 & 78.4  & 80.5 & 51.8 & 60.5 & 68.3 & 70.6 \\
        \textbf{Neighbor-Aggregate (Mean)}  &60.1 & 77.2 & 84.1  & 85.0 & 56.8 & 68.2 & 71.3 & 74.7 \\

        \textbf{GraphSAGE (Max-Pooling)}  & 61.3 & 78.2& 85.1& 86.3&  58.9 & 69.1 & 72.4 & 74.9 \\

        \textbf{GraphSAGE (Mean)}  & 61.4 & 78.4& 85.5 &  \textbf{86.6}&  59.0 & 69.3 & 72.7  & 75.1\\

        \textbf{DetGP} & \textbf{62.1} & \textbf{79.3} & \textbf{85.8} & \textbf{86.6} & \textbf{60.2} & \textbf{70.1} & \textbf{73.2} & \textbf{75.8}\\
        \bottomrule[1.2pt]
	\end{tabular}}

	\caption{Test Macro-F1 scores for multi-label node classification on \emph{Cora} and  \emph{DBLP} dataset.}
	\label{tab:new_node_classification_dwavg}

\end{table*}

One of the advantages of the proposed model is the ability to quickly estimate embeddings on newly added nodes. To test the effectiveness of our model, we split nodes into training and testing sets. The embedding model is learned only from training nodes with corresponding edges. To evaluate, we embed the testing nodes directly without updating the model parameters. In this section we mainly focus on the performance of dynamic structural embeddings. Therefore, the text encoder is fixed as word embedding average (Wavg) for simplicity.

Previous works \citep{tu2017cane,zhang2018diffusion,shen2018improved} on textual network embedding require the overall connection information to train the structural embedding, which cannot directly assign (without re-training) structural embeddings to a new coming node with connection information unknown during training. Therefore, the aforementioned methods cannot be applied to dynamic networks. To obtain comparable baselines to DetGP, we propose several strategies based on the idea of inductive graph representation learning (GraphSAGE)~\citep{hamilton2017inductive}, which generates embedding for new nodes by aggregating the neighbors' embeddings.  The two embedding assigning strategies are: (a) \textbf{Neighbor-Aggregate}: aggregating the \textit{structural embeddings} from the neighbors in the training set, as the structural embedding for the new node;  (b) \textbf{GraphSAGE}: aggregating the \textit{textual embeddings} from the neighbors, then passing through a fully-connected layer to get the new node's structural embedding. For neighborhood information aggregating, we use the mean aggregator and the max-pooling aggregator as mentioned in \citep{hamilton2017inductive}.

We evaluate the dynamic embeddings for test nodes on link prediction and node classification tasks. For both tasks, we split the nodes into training and testing sets with different proportions ($10$\%, $30$\%, $50$\%, $70$\%).
When embedding new testing nodes, only their textual attributes and connections with existing training nodes are provided. For the link prediction task, we predict the edges between testing nodes based on the inner product between their node embeddings; for node classification, an SVM classifier is trained based on embeddings of training nodes. When new nodes come, we first embed the nodes using the trained model and then use the previously learned SVM to predict the label.

The results of link prediction and node classification are given in Tables~\ref{tab:new_node_link_prediction_dwavg} and~\ref{tab:new_node_classification_dwavg}, respectively. In both tasks, the Neighbor-Aggregate strategy with mean aggregator shows slight improvement to the baseline with only a text encoder. However, it does not work well with the max-pooling aggregator, implying that the unsupervised max-pooling on pre-trained neighbor structural embeddings cannot learn a good representation. The GraphSAGE strategies (with both mean and pooling aggregator) show notable improvements compared with Wavg and Neighbor-Aggregate. Unlike the unsupervised pooling, the GraphSAGE pooling aggregator is trained with a fully-connected layer on top, which shows comparable result to the mean aggregator. The proposed DetGP significantly outperforms other baselines, especially when the proportion of training set is small. A reasonable explanation is, when the training set is small, new nodes will have few connections with the training nodes, which causes high variance in the results of aggregating neighborhood embeddings. However, instead of aggregating, our DetGP infers the structural embedding via a Gaussian process with pre-learned inducing points, which is more robust than the information passed by neighbor nodes.

\subsection{Inducing Points}\label{subsec:inducing_points}

\begin{figure}[htb]
\centering
    \centering
    \includegraphics[width=0.5\columnwidth]{tsne_no_axis.png}
    \caption{t-SNE visualization of learned network structural embeddings of Cora. Unfilled circles are individual nodes and inducing points are denoted as red dots.}
    \label{fig:tsne}

\end{figure}

Figure~\ref{fig:tsne} gives the t-SNE visualization of the learned DetGP structural embeddings on the Cora citation dataset. The model is learned using all edges and all of the nodes with their textual information.  We set the number of inducing points to $M=20$. To avoid the computational instability caused by the inverse matrix ${\bm{K}}_{ZZ}^{-1}$, we update inducing points with a smaller learning rate, which is set to one-tenth of the learning rate for the text encoder. The inducing points $\bm z$ are visualized as red filled circles in Figure~\ref{fig:tsne}. Textual embeddings are plotted with $7$ different colors, representing the $7$ node classes. Note that the inducing points $\bm z$ fully cover the space of the categories, implying that the learned inducing points meaningfully cover the distribution of the textual embeddings.

\section{Conclusions}\label{sec:conclusion}

We propose a novel textual network embedding framework that learns representative node embeddings for static textual network, and also effectively adapts to dynamic graph structures. This is achieved by introducing a GP network structural embedding layer, that first maps each node to the inducing points, and then embeds them by taking advantage of the non-parametric representation. We also consider multiple hops to weight local and global graph structures. The graph structure is injected in the kernel matrix, where the kernel between two nodes use the whole graph information based on multiple hops. Our final embedding contains both \emph{structural} and \emph{textual} information. Empirical results demonstrate the effectiveness of the proposed algorithm.\\

\noindent{\bf Acknowledgements}: The research reported here was supported in part by DARPA, DOE, NIH, NSF and ONR.

\bibliographystyle{aaai}
{\small

redpajama_set_name: RedPajamaArXiv


dealing with mental illness and the many issues associated with it.
The guest speaker is a friend who created the non-profit organization NOSTIGMAS - this podcast is an open, honest, and informative dialog speaking on these issues.
The main points I would like to emphasize are 1. People suffering with mental illness- you are not alone 2.- share your stories/talk with someone. There are many caring ears and hearts out there. 3- mental illness is every part as real and dangerous as the most deadliest cancers or heart conditions. 4. Like other major medical issues help is needed and out there-you can not cure yourself...Think about it; if you have a bad heart you can't perform your own heart surgery?! Get help!


U.S. History I begins in 1763 with the Treaty of Paris, and concludes with World War I. Studies will include domestic changes such as industrialization and the development of cities, and America's emerging role in world events. Students will develop historical thinking skills while working with primary and secondary sources. They will also create and develop original historical claims using relevant historical evidence and effective analysis. Outside classroom preparation and note-taking skills are essential.
Honors U.S. History I contains the same content as U.S. History I, but in greater depth. Outside preparation and research will be required. Students will develop historical thinking skills while working with primary and secondary sources. They will also create and develop original historical claims using relevant historical evidence and effective analysis. Writing will be an integral part of this course.
This course is designed to stimulate your mind about the exciting and frightening times between 1920 and present day. You will express your feelings, backed with facts, through debates about the Sacco and Vanzetti case, the pros and cons of the Treaty of Versailles, dropping the Atomic bombs on Japan, fighting in the Vietnam War, and much more. You will also role play as you will decide how you would have handled the Cuban Missile Crisis, Berlin Crisis, and other international issues. Be prepared as you will investigate the assassination of JFK and conclude who committed this heinous crime—and why? This course will prepare you to think independently as well as with others, come to conclusions supported by facts, write efficiently, and help you understand the roots, controversies and the accomplishments of the United States.
This course is intended to meet the same basic standards of U.S. History II. However, Honors U.S. History II differs from U.S. History II in its level of intensity and additional requirements. A higher level of academic expectation and personal responsibility will be demanded of the student in this course. Students will develop historical thinking skills while working with primary and secondary sources. They will also create and develop original historical claims using relevant historical evidence and effective analysis. Outside classroom preparation, note-taking, and time management are essential.
This college level course involves the study of U.S. history from colonial times to the present. Students will develop historical thinking skills while working with primary and secondary sources. They will also create and develop original historical claims using relevant historical evidence and effective analysis. This course involves a great deal of writing – including both explanatory and documentary essays. Outside reading and note-taking is required in this demanding course. Students who complete the course also are required to take the A.P. examination given by the College Examination Board in May. A summer assignment is assigned in June and submitted in mid-August.
Why is there war and conflict in our modern world? What are the root causes of inequality in our world today? Who has power in our modern society? How is that power wielded? How have humans related to their environment in the past and where does this put us now? Explore these questions and more in this course that focuses on issues and topics in world history from the 18th century to the present. We will critically examine primary and secondary sources and other selected readings. While conducting in-depth analyses, we will work together to try to answer these ongoing questions in modern world history. Perhaps most importantly, we will decide what their implications are for today. Students will play an integral role in formulating further questions, seeking out and creating answers, thinking through possibilities, and evaluating how successful we were in our work.
This course is intended to meet the same basic standards of Modern World History. However, Honors Modern World History will differ in its level of intensity and additional requirements. Students will be asked to create and develop original historical claims using relevant historical evidence and effective analysis. This course involves a great deal of writing – including both explanatory and documentary essays. Outside reading and note-taking is required in this course. A summer assignment is assigned in June and submitted in September.
How do citizens create rules and institutions that allow our nation and the world to flourish? How do we ensure that the world's resources are enjoyed by all segments of society? As students approach the end of the high school career, this course asks students to apply the tools of history, political science and economics to examine answers to these enduring questions. This is a required course designed to develop the student's understanding of the federal government and politics in the United States. This course will be broken into essential parts dealing with the Foundations of Government, the Three Branches of Government, and the Political System as well as the basics of the American economic system and the introductory principles of economics.
This course is intended to meet the same basic standards of U. S. Government & Economics. However, Honors U. S. Government & Economics will differ in its level of intensity and additional requirements. Students will engage in extensive research and work towards developing and defending original claims. Outside reading and research is required in this course.
A.P. U.S. Government and Politics will provide an analytical perspective on government and politics in the U.S. We will study general concepts and interpret U.S. politics. This will require familiarity with terms, institutions, groups, beliefs and ideas that constitute U.S. Politics. We will cover Constitutional underpinnings, political beliefs, political parties, political behavior, interest groups, the institutions of national government, public policy and civil rights. Students taking this class will complete a summer assignment. Students are required to take part in online discussion outside of class throughout the year. Students who complete the course are required to take the A.P exam.
This course gives students an introduction to Law and the Legal System in America. By studying cases and conducting research, students gain a basic knowledge of our court system, lawyers, law enforcement officials, criminal law, civil law and juvenile justice. Guest speakers and field trips will be utilized to enhance the learning when possible. Students will be responsible for writing a number of case studies as well as researching and writing one term paper. Supplemental cases and readings will be used in conjunction with the textbook.
Digital Geography - More than a Jeopardy Category!


text:
medicine -- north carolina -- greensboro -- history (8)
nursing -- study and teaching (1)
university of north carolina at greensboro (1)
cone 10079 moses h. cone memorial hospital collection, 1908-2003 and undated (6)
cone 10082 opie norris smith collection, 1966-1976 (1)
clippings (4)
Greensboro Academy of Medicine minutes 1969
Minutes of meetings of the Greensboro Academy of Medicine from 1969.
[Scrapbook, June 1969 - August 1970]
A scrapbook containing newspaper articles that cover events relating to the Moses H Cone Memorial Hospital, spanning the years 1969 to 1970. Examples of articles found within include "Wesley Long Hospital Passes for Medicare," "Nurses' Image Has...
[Scrapbook, July 1969 - February 1974]
A scrapbook containing newspaper articles that cover events relating to the Moses H Cone Memorial Hospital, spanning the years 1969 - 1974. Articles include "Demand for Nurses Grows" featuring a photograph of Dean Eloise Lewis of UNCG, and articles...
[Medical happenings of 1969]
Several documents from 1969, including a report on the lack of interns to fulfil internship positions, minutes showing considerations of closing local clinics, a joint committee on education meeting's decision to support the Moses H. Cone teaching...
Meditations [September 1969]
An issue of Meditations, the newsletter for the Auxiliary to the Guilford County Medical Society, Greensboro. This issue is labeled ""September 1969,"" likely in error.
Crisis Control Center report
A clipping from the Tar Heel Tandem Winter 1969 reporting on the efficacy of the Crisis Control Center.
Correspondence with Mary B. Taylor
Correspondence with Mary B Taylor of the Moses H Cone Board of Trustees, dated from 1969 to 1984. Some senders include Dennis R. Barry, Harold L. Bettis, and Benjamin Cone. Mostly discuses general board business and includes Taylor's Curriculum...
1965 study
Cone 10082 Opie Norris Smith Collection, 1966-1976
Materials related to a ""study in depth of the total community hospital facilities, needs, and other factors or relationships of long range public interest"" completed some time in 1969.
Moses Cone capers
Program for "Cone Capers" presented by Moses H. Cone Memorial Hospital on December 5, 1969.
The Moses H. Cone Memorial Hospital staff manual
The Moses H. Cone Memorial Hospital staff manual, dated October 1, 1969.
[Dedication of the UNCG School of Nursing Building pamphlet]
A pamphlet for the dedication of the School of Nursing Building at The University of North Carolina at Greensboro, which took place on October 5, 1969.
[Moses H. Cone planning]
Several documents about the state of medicine in 1969 and 1970, including proposals for expansions to the Moses H. Cone Memorial Hospital. This is particularly about serving pediatric needs.
[Report to the medical board and trustees]
A report showing admissions percentages, average stay length, and other statistics about the hospital, spanning a period from October 1, 1968, to March 31, 1969.
[Medical board correspondence and minutes]
Correspondence and minutes related to the medical board. Enclosed are reports on meetings, listings of committees and their members, some correspondence, the Charter of The Moses H. Cone Memorial Hospital, The Moses H. Cone Memorial Hospital Staff...
Miscellaneous articles related to the Board of Trustees
Miscellaneous materials related to the Board of Trustees of the Moses H Cone Memorial Hospital, sometime between 1969 to 1988. Includes newspaper clippings, correspondences, and articles.


MECHANICAL IMAGING SYSTEMS SUCH AS THE SCANNING TUNNELING MICROSCOPE (STM) AND THE ATOMIC FORCE MICROSCOPE (AFM) HAVE TREMENDOUS POTENTIAL FOR IMAGING BIOLOGICAL SAMPLES AND BIOMOLECULES. STM AND AFM HAVE ATOMIC RESOLUTION AND ARE DEMONSTRATED TO WORK IN AMBIENT ATMOSPHERE, LIQUID AND VACUUM. A MAJOR ADVANTAGE OF THESE TECHNIQUES OVER CONVENTIONAL SUBMICRON IMAGING TECHNIQUES SUCH AS SEM IS THAT SAMPLES CAN BE IMAGED IN SITU. THIS PROPOSAL FOCUSES ON DEVELOPMENTS THAT ARE REQUIRED BEFORE STM CAN BE USED ROUTINELY AS A LABORATORY TOOL FOR STUDYING BIOLOGICAL SAMPLES. TOPICS ADDRESSED ARE TECHNIQUES FOR STUDYING NONCONDUCTING SAMPLES, TECHNIQUES FOR STUDYING SAMPLES IMMERSED IN CONDUCTING LIQUIDS, THE EFFECTS OF INTENSE ELECTRIC FIELDS ON BIOLOGICAL SAMPLE, AND INSTRUMENT AUTOMATION.