Complete your holiday decoration needs with our exclusive variety of Musical Snow Globes by BestPysanky. Originally created in 1889 in France, Snow Globes have been a common household decoration for many years. This exclusive charming hand-painted snow globe will amaze and inspire your family for the seasons!
Two happy children, with a polar bear sitting next to them, are decorating a Christmas tree with the glittery bulbs, mint candy canes, flowing ribbons and beautiful golden star right on top of the tree.
The base is decorated with the wreath, golden bells and red ribbons all around.
Classy red sleigh with the golden design is full of holiday gifts waiting for obedient kids.
Two boys are waiting for Santa to come to the town!
Shake the figurine and create a glittery, snowy blizzard inside the globe!
This charming Christmas Snow Globe features children decorating Christmas tree with ornaments and garlands.
The hand painted intricate base depicts different toys including the teddy bear, rocking horse, nutcracker, etc. It plays a holiday tune "We Wish you a Merry Christmas" when wound-up. Two color changing LED lights are hidden in the base figurine. The snow is blowing automatically when music plays.


After director Ali Abbas Zafar revealed that Priyanka has dropped out of the film, there were various reports that were circulating about Salman Khan being upset with the actress. That's not it. It was also reported that Salman has vowed to never work with the actress again.
She further talked about the incident when a producer of Bharat called Priyanka 'unprofessional'. She called those rumours off too, saying that nothing like that has happened and everything is good.
A few days back, Ali Abbas Zafar took to his twitter account to share about Priyanka's exit. Going by his tweet, it seemed like there is no hard feelings between the two. His tweet also hinted at Priyanka & Nick's engagement, a topic which still hasn't been touched by Priyanka.
Recently, it was also announced that Katrina has taken up Priyanka's place in the movie. Katrina will be playing the love interest of Salman in Bharat, which is an adaptation of 2014 South Korean Drama, An Ode To My Father. Apart from Salman & Katrina, the movie also stars Disha Patani, Tabu and Nora Fatehi in pivotal roles. The film is being co-produced by Salman Khan's brother-in-law Atul Agnihotri and is slated for an Eid 2019 release.
On the other hand, Priyanka, who recently finished shooting for her upcoming Hollywood flick Isn't It Romantic, will make her Bollywood comeback with Shonali Bose's directorial The Sky Is Pink. According to reports, Priyanka has also signed a film opposite Chris Pratt named Cowboy Ninja Viking.


As is true in every business, location can determine whether your medical practice will be a massive success or a nightmarish blunder. Landlords know this and will do everything they can to wring money out of a potential tenant for an ideal space. So to get the perfect location for a medical office space without being taken advantage of, learn these quick tricks before your next negotiation.
Want to lock down your piece of prime real estate? Make sure you don't fall for the standard lease agreement trap. If your office space truly is in a wonderful spot, other doctors and medical practitioners will want to slide in and most likely be willing to pay a higher price for the privilege! So sign a renewable lease, most of which will allow tenants to pay an established rent price for a period of time, and also have a predetermined amount of time in which new negotiations can occur.
It'd be great if we could trust everyone to be honest, but when it comes to making decisions regarding money and the future of your practice, its best to err on the side of caution. This is why it's important to visit in person with an agent at your side, and take the little bit of extra time to ensure the measurements are actually what they claim to be.
Don't sign a lease with a blind eye and discover there are structural problems (or worse!) with what is supposed to be your new office, the face of your business. Obviously it's imperative for a medical office space to be clean and sterile. But getting a commercial inspection done can also be a great negotiation tool for either lowering the price of the lease so you can fix any problems on your own, or have it explicitly stipulated that the landlord take care of any issues which arise from the inspection.
Review these tips before your next negotiation, and remember not to allow yourself to be pushed around. If it truly is a desirable piece of property, expect to face some resistance; they know what they have is good, and they will fight to make you pay more!


More than 150 people packed into Shepreth Village Hall yesterday evening for the latest CamBedRailRoad meeting on the proposals for the East West Rail Link from Oxford to Cambridge.
The think tank was set up by Sebastian Kindersley and others, who introduced the plan for a northern corridor option from Bedford to Cambridge as an alternative to the current 'C-corridor' proposal which incorporates the area around Sandy and Shepreth.
Problems with unclear plans, moving freight, traffic and population increase, cost and the notion of nimbyism were all raised at the meeting.
Chairman Mr Kindersley, who was joined by panelists Brian Bell and James Paxman, said their process started after the story broke of a proposed new town at Bassingbourn at the end of last year.
He said the C-corridor was likely to have been chosen because it was deemed the best performing with the highest benefit-to-cost ratio.
But he said it would reach a much lower number of people than their proposed northern route, which incorporates Bedford Wixams, and new developments at Cambourne, Northstowe and St Neots.
The group also said East West Rail's preferred route, which passes through land between Sandy and Biggleswade and through South Cambridgeshire, would cause a widespread planning blight, wouldn't serve communities and would pass through the "best and most versatile agricultural land".
Mr Kindersley said they had met with many parties including MPs Heidi Allen and Alistair Burt, and the East West Rail Company themselves, and want their proposal to be "given a fair crack of the whip" like the C-corridor.
To a question from the audience regarding cost, Mr Kindersley said that their northern route option would be more expensive – but they "believe that the social value and economic benefits of our route would far outweigh the pounds, shillings and pence" it would take to create it.
There was also a question of why their proposal should be chosen when it wasn't fully-costed, and the response was that this was an opportunity they had to take and if it was considered they would want a delay in the decision making process to address this.
Mr Kindersley said there's nothing like volume and asked the audience to spread the word, sign the online petition and, at the very least "tell your neighbours".


Homemade Vanilla Pudding: Need a Quick but Delicious Dessert?
You Can't Go Wrong with a Simple but Delicious Vanilla Pudding Recipe!
Pudding recipes are really easy to follow and are a great way to enjoy a creamy, soft and sweet dessert. If there are kids at home, you can be sure they will love this recipe. This is a very easy and delicious option — the best part is you probably already have all the ingredients in your kitchen, and you can make as many servings as you want. Let's get started!
Place a cooking pot on medium heat and add the milk along with the vanilla. Bring to a boil. Remember to stir continually.
In the meantime, in a small bowl mix the remaining milk along with the sugar, salt and cornstarch. Mix all the ingredients and then add the yolks. Continue mixing until well combined.
When the milk starts boiling, bring the heat to low and add the mixture you prepared in the last step. Stir continually for about 5 minutes or until mixture is soft.
Put it in the fridge for 2 hours and then serve.
No one in your house will want to sleep in on the weekends if you make this cinnamon French toast recipe for breakfast! Start your weekend with a treat.


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INSTITUT DE LA BIENHEUREUSE VIERGE MARIE
GÉNÉRALAT DE LORETO
ONG associée à l'ECOSOC aux Nations Unies
Sélecteurs génériques
Recherche dans le titre
Recherche dans l'extrait
Stages IBVM/CJ ONU
IBVM/CJ à l'ONU
Notre apport
Le département du monde
Communication (DGC)
Economique et Social
Conseil (ECOSOC)
L'égalité des sexes
Élimination de la violence sexiste
Éradication de la pauvreté
Accès à une éducation et à une santé de qualité
Élimination de la traite des personnes
Prendre soin de l'environnement
Financement du développement
DÉCLARATIONS ET PUBLICATIONS
Exposés de position
Mises à jour de l'ONU
Mises à jour sur la citoyenneté mondiale
Nouvelles et informations
Nouvelles mise à jour
Être impliqué
Plaidoyer scolaire
Campagnes IBVM/CJ de l'ONU
Campagnes de l'ONU
IBVM Spain Alumni: Dialogue on Sustainable Development Goals
On June 14, IBVM's Youth Representative in Spain (Carlota Gayo) organised a small virtual event with a group of Alumni from the schools in Madrid, Bilbao and Seville. The aim of this initiative was to create a space for young people to express themselves on international issues related to the United Nations (UN) and to try to attract participants to get involved in upcoming activities/events.
The organisation of this dialogue between Alumni and the Youth Representative was structured in different sections.
The event started with a brief presentation of the participants and a big thank you for participating in the survey launched in May in which potential attendees were asked about their knowledge and interests regarding UN's SDGs. Then Cecilia O'Dwyer explained the IBVM/CJ's mission at the UN as an NGO. The office plays a significant role within the civil society group at the Economic and Social Council (ECOSOC) and the Department of Global Communications.
We then discussed the following SDGS:
Social: Peace, Justice and Strong Institutions (SDG 16)
The situation in Ukraine was one of the main issues addressed in terms of global peace and stability. The two sides of the coin, multilateralism and unilateralism, are in dispute today with Russia exerting force against the attacked Ukrainian territory. Moreover, young people participating were concerned about war crimes being committed by Russian troops. With this scenario, it is extremely difficult to find a peaceful solution. However, it is key to set preventive measures aimed at avoiding violence and war.
Economic: Decent Work and Economic Growth (SDG 8)
Despite the effect of covid-19 on the economy, attendees emphasised the role that digitisation will play in the upcoming years in which technology will either create new jobs or destroy some that are existing nowadays. Thus, they all agreed that adapting to fast-changing machines and technological advances is a must. Additionally, they stressed the importance of women's work and the fight to strive for equal job opportunities without any kind of gender gap (also in line with SDG 5: Gender Equality).
Environmental: Clean Water and Sanitation (SDG 6), Affordable and Clean Energy
(SDG 7) and Sustainable Cities and Communities (SDG 11)
Access to basic water is a fundamental right which must be enjoyed by every human being. Nevertheless, participants agreed that in many countries that is not the case. One of the girls shared her experience towards contributing to the deployment of water purification plants in India during her volunteering work three years ago. Consequently, developed countries (the Global North) must help those in urgent need of help (the Global South) to have access to water that is not polluted. For this, good governance should be a guiding principle for local governments. When having a look at the last SDGs (nº7 and nº11), they all shared the need to adapt to new sources of renewable energy and apply them in metropolitan and urbanised areas in cities. Generating clean energy and leaving behind fossil fuels should be a priority.
Each participant was able to express themselves comfortably and honestly while listening to each others' views. But time ran out very quickly and we said goodbye, thanking each other for the pleasant time we had!
Auteur: Carlota Gayo Nieto
Photo: Cecilia O'Dwyer ibvm, Carlota Gayo Nieto (Spain Province Intern) and two alumni.
PrécédentPrécédentCongregacio Jesu (CJ) Sisters Assist Refugees from Ukraine
ProchainOur ocean, Our future, Our responsibilitySuivant
Je souhaite m'abonner aux mises à jour de l'IBVM/CJ à l'ONU

redpajama_set_name: RedPajamaCommonCrawl


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Heritage in Hampstead Heath
The Hill Garden and Pergola
The Tumulus
Inverforth House
The Wyldes Farmhouse
Springs, ponds and recreation
Hampstead Heath and the Arts
The fight to save the Heath
Sand digging at the Heath
After a visit to Hampstead Heath, it's not difficult to see why this beautiful location has provided inspiration to many famous writers and artists.
During the Romantic period of the early nineteenth century the village of Hampstead became popular with many influential writers and poets. The poet Leigh Hunt moved to the area in 1815 and mentions Kenwood, Spaniards Road and his home the Vale of Health in his sonnets. Hunt was well connected in literary circles and many of his friends visited him in the Vale including Byron and Shelley. Around the same period Samuel Coleridge the poet, who along with his friend William Wordsworth founded the Romantic Movement in England, lived in Highgate from 1817 until his death in 1834 and wrote about Kenwood describing the 'grand cathedral aisle of giant lime trees' on the terrace.
The great poet John Keats also knew Leigh Hunt and visited him on several occasions at the Vale of Health. It was not long before he moved to Hampstead and it is said that he composed his great "Ode to a Nightingale" after hearing the bird's unique liquid warbled song whilst living in the area. At this time nightingales did nest on the Heath, especially along Millfield Lane where Keats is known to have walked with Coleridge. Keats moved to a house in Hampstead and lived there from December 1818 to September 1820 before moving to a warmer climate in Italy after falling ill with tuberculosis. He succumbed to the disease in February 1921, and died in Rome aged 25.
Keats House in Hampstead was restored as a museum to the poet and is now open to visitors who can learn more about how the Heath inspired him.
Painters, writers
The beautiful landscapes of the Heath also moved painters to capture its dramatic beauty. The most famous of these was John Constable who lived in Hampstead for many years from 1827 and painted numerous landscapes both from sitting in the upper level of his house at nearby Well Walk, and from on the Heath itself. Constable liked the wild and unspoilt landscape of the Heath and his portraits are important historical evidence of what the Heath once looked like. His pictures show a very open landscape, covered in heather and gorse with very few trees. The Heath continued to inspire into the 20th century and CS Lewis was moved to write "The Lion, The Witch and The Wardrobe" after wandering over Hampstead Heath on a snowy winter's day and imagining his fictional land of Narnia.
Philosophers, dancers
It was not just artists and writers who were enthused by the beauty of the Heath. Many brilliant minds from all walks of life have lived around its peripheries and visited its picturesque open spaces, including Karl Marx, whose favourite family outing was a trip to the Heath. Anna Pavlova, the Russian ballerina also chose to live bordering Golders Hill Park when she moved to London in 1912. Her home, Ivy House was featured in the film "Anna Pavlova" and is now the London Jewish Cultural Centre.
The Heath has also been used as a place for the public to enjoy the arts. In 2005 a 30ft sculpture of a table and chair by Italian artist Giancarlo Neri was given a temporary home on Parliament Hill for four months. Thousands of people were captivated by this giant scale model named "The Writer." In the summer of 2012 Sacrilege, a life-sized, bouncy replica of Stonehenge by the artist Jeremy Deller also made a visit to the Heath delighting an audience of all ages.
The same summer, Visitor I, a sculpture, by local artist David Breuer-Weil, of a submerged head also took up temporary residence in the Lily Pond at Golders Hill Park. It is clear to many that the Heath is a very special place and we hope its beauty will continue to inspire for generations to come.
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Burnham Beeches and Stoke Common
City Commons
Open Spaces Annual Report 2012/13
Green spaces >
Hampstead Heath >
> Hampstead Heath and the Arts


Five EU states have urged the bloc to grant visa-free travel to Georgia at the earliest opportunity for the sake of EU "credibility".
Interior and foreign affairs ministers from Bulgaria, Estonia, Latvia, Lithuania and Romania issued the appeal in a letter, seen by EUobserver, on Thursday (9 June) to the Dutch presidency of the EU Council and the EU foreign service.
The letter said they hoped that an agreement could be reached at a home affairs ministers' meeting in Luxembourg on Friday or a foreign ministers' meeting on 20 June.
They spoke out after France, Germany and Italy, at an EU ambassadors' meeting on Wednesday, blocked the move.
Germany, which led the rebellion, cited domestic public concern over an alleged crime spree by gangs of Georgian nationals.
The letter said that since Georgia had fulfilled all EU conditions for the visa waiver "we need to deliver on our side as well".
"Any further postponement to take a decision will undermine our credibility and might have adverse effects on European integration-related reforms in Georgia as well as in other partner countries," the five countries added.
Ukraine has also fulfilled European Commission visa-free conditions, with EU diplomats to discuss its waiver on 14 June.
However, Germany has indicated that it might delay the Ukraine decision as well.
One EU diplomat said Germany delayed the Georgia move because it wanted to grant the waiver to Ukraine at the same time. The diplomat said Germany might delay Ukraine to use the waiver as leverage on the Minsk ceasefire accord.
"Some member states would slow down visa liberalisation for Georgia in order to appease Ukraine," he said. He added that EU visa policy "should help in keeping Ukraine fully on board in the Minsk process".
The Minsk deal, which was brokered by France and Germany last year, obliged Russia to pull out of Ukraine and Ukraine to devolve power to what are today Russia-controlled regions.
The EU diplomat said if things go well, both states should get the visa perks in September.
The European Parliament must ratify the move, but that process would be hard to complete before the summer break even if EU states gave the green light to MEPs, the diplomat said.
Speaking to EUobserver in Brussels on Wednesday, Georgian president Giorgi Margvelashvili said he received "strong support" from MEPs when he visited Strasbourg on Tuesday.
He said the visa move would help "pro-Western and pro-European" parties retain support in Georgia elections in October.
German chancellor after meeting with the Turkish president, said it was likely that conditions would not be met by 1 July as agreed in the EU-Turkey migrant deal.
EU proposal to lift visas for Kosovars created a positive buzz in Pristina. But what will it do to improve ordinary people's lives?
Russia does not have a veto on Georgia's foreign policy and billionaire Bidzina Ivanishvili does not rule the country, the Georgian president has said.
Delaying visa liberalisation for Georgians, after the country has met all the EU benchmarks, would harm our credibility as a soft power.


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Tiranë  er et af Albaniens tolv præfekturer. Administrationscenteret er byen  Tirana, landets hovedstad. 1. januar 2017 havde præfekturet  indbyggere.

Præfekturet består af kommunerne Kamëz, Kavajë, Rrogozhinë, Tiranë og Vorë. Det dækker de tidligere distrikter Kavajë og Tiranë.

Kilder og henvisninger

Websted

Albaniens præfekturer

redpajama_set_name: RedPajamaWikipedia


A crash on Northwest Boulevard sent two people to the hospital.
A crash on Northwest Blvd. sent two people to the hospital Tuesday morning.
Senior Officer Travis Pace said that an 18-year-old man was driving with a 17-year-old woman when his 2008 Mustang veered off, clipping a tractor trailer.
Both people in the Mustang were sent to the hospital. The woman had non-life threatening injuries, while the man had more serious injuries. The driver of the tractor trailer was uninjured.
Pace said the crash happened at 8:25 a.m. in the 1500 block of Northwest Boulevard, causing police to close down the road.
The road has been reopened.


How to Boost your consumer's Lifetime value : Quadruple your Profits !
How to Boost Your Consumer's Lifetime Value (LTV) : Quadruple Your Profits !
Today Market is crowded is lots of brands. and due to a high level of competition new brands are coming to market every day.
It seems that its good for people if new brands their in market-consumers will get more options to buy.
A number of competitors increased their profits are going to decreases dramatically-As per a recent survey by kissmetrics the CAC cost of acquisition of customer is increasing day by day. average CAC is $35.
Imagine you spend $35 on customer and they aught only one product from you. After that, that does not guarantee that he/she will return to you or not!
It's painful right all your marketing & sales efforts will go waste.
So what is the ultimate solution to this?
What if you can engage in such a way that he/she will buy from you again & again.
That's when customer retention comes in picture-Its important but 60% of retailers have 20% of retention rate.well they can achieve more by increasing consumer's lifetime value-(LTV).
As per Econsultancy report, 64% of organizations believe that customer experience is the tactic to boost your Consumer's lifetime value (LTV)-Consumer will stick to your brand when you will delight them with value.
(LTV) Lifetime value is so much important it will provide you an approx idea of revenue that particular consumer will deliver to your company.
It also depends on lots of aspects from sales-marketing–customer delight–customer experience.
Here are 3 fantastic Ways to increase customer's Lifetime value.
Every Business has interaction with people-So companies who succeed to have emotional connections with making their customer's buying experience personalize will have a bigger impact on the customer.
Remember ? When Someone Helps in a Shopping mall to find your size of a pair of shoes or your favorite color of a shirt.
Not only Shopping experience but communication with Customer can also be personalized – It also depends on your customer's age group. i.e. If your customer is between age group 40-54 that person should get communication through SMS or Email.
If your customer is between age group 24-35 they should get a message from Social media. Facebook or Snapchat.
Companies should celebrate loyalty of customers by not giving them special discounts but also give them special gifts or tickets to some concert or shows.
Most of the Companies introduced rewards points who bought with their loyalty card.-73 % of customer remember brands always while they are part of loyalty program.
Companies should recognize their loyal customers and Fans-Company should definitely offer more than discounts-some more valuable by which customer really felt the proud association with Brand.-It will increase Brand Affinity.
The best way to Boost your customer's Life time Value is non another communicate with your team mates who are directly in touch with customers. i.e. your front warriers (Sales team- Customer Support).
Your Sales team is in directly in contact with your customer's so they can understand better why,.where & how they make product experience or customer experience better.
Sometimes All things are going good but the Software which Organization is using for accepting payments are not user friendly.
Sometimes the delivery of product is not at right time or not as per expectation. each & every small observation or feedback will improve your customer experience and ultimate boost your Customer's Life Time Value.
Increasing Customer's Lifetime value is ongoing process-it's not applying big strategies but observing and applying small things which customer is facing problems with-and eliminating them to provide smooth customer buying experience. Ultimately it will delight Customers and it will result into revenue from a customer.
How Feeling Nostalgia Will Improve your Productivity !
How Mind Body & Emotion Will Make You Jaw-Dropping Actor !


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Permanent Collections
johnwjudge
Permanent Collections: First a Car, Then a Bike, Now Some Boats
This is the kind of painting that I would have overlooked when I was much younger. Too gray and too boring, I would have thought. Its subtleties would have been lost on me.
But not any more; today it's one of my favorite paintings at the Museum of Fine Arts, Boston, and so it is the subject of this edition of my series, "Permanent Collections."
Painted around 1679, Rough Sea depicts boats struggling to sail violent waters off the coast of Amsterdam. It is one of a handful of seascapes painted by Jacob Isaacksz. van Ruisdael, who is regarded as one of the greatest Dutch landscape painters of the 17th century. (Take a look at the MFA's View of Alkmaar, and you'll see why Ruisdael's landscapes are so esteemed.)
I remember first seeing Rough Sea nearly twenty years ago, shortly after I had returned to Massachusetts after living elsewhere for a long time. I think I was initially struck by the subject. I saw no other painting in the MFA's Dutch gallery that depicted the ocean, which seemed odd, considering the importance of the sea to life in the Netherlands. As the MFA's website states, "The sea was an integral part of Dutch life and landscape; a powerful navy and ships that traded as far as Asia and the Americas made this small nation one of the wealthiest in Europe."
After considering the scant presence of the sea in the room, I looked closely at the painting's choppy waves, tilting boats, and flapping flags. Ruisdael depicts these elements with such compelling precision, that I could almost feel the strong wind that causes such tumult. I imagined myself on one of the boats cold, miserable, and, above all, afraid.
Nearly two decades later, I still often picture myself in the same predicament when I look at Rough Sea. What a horrible existence, I think. Once you reach the safety of shore, what do you have to look forward to? Another day at sea, another day risking your life.
As if to underscore a seaman's peril, Ruisdael includes weather-beaten logs peeking out of the water at the bottom left of the painting. Sunlight has broken through the clouds there to bathe the logs in a glow that makes that area of the painting almost as bright as the white sail
on the front-most boat. I'm not sure what these logs are--perhaps the remnants of a pier? Whatever their purpose, they seem old and broken, and by making a formal connection between the logs and the white sail, Ruisdael reminds us of the shipwreck the boats will become if they don't weather this storm.
Nonetheless, the situation is not hopeless in Rough Sea. A substantial amount of blue peeks through the clouds, and clear skies seem to be just out of view at the left edge of the canvas. The rightward direction of the gale suggests that the clouds and storm will blow away, and peace will return.
I love that blue sky. It's a hue that, if seen alone on an otherwise blank canvas, would seem dull. But here among Ruisdael's mostly gray clouds, it has a quiet vibrancy, and, most importantly, it looks real. If Ruisdael had chosen a more intense, unnatural blue, the sky would feel artificial, and the painting's optimism less genuine.
Other Ruisdael seascapes are less hopeful. About forty miles to the west of Boston, his View of the IJ on a Stormy Day hangs in the Worcester Art Museum. In this painting, the boats teeter severely, on the verge of capsizing. And the wind seems more likely to blow in a deadly storm than to bring the calm that seems to be moments away in Rough Sea. I imagine if I were on one of the boats in the Worcester Museum's painting, I would huddle in a corner, petrified with fear and useless to everyone else aboard.
In Rough Sea and View of the IJ on a Stormy Day, Ruisdael created two palpably intense and riveting depictions of humans' vulnerability to the capricious whims of nature. I feel fortunate that both these great works found their way to Massachusetts collections.
Permanent Collections: A Tale of Two van Dycks
Permanent Collections: Homer Not Alone
Permanent Collections: Cézanne at the Hammer Museum


10,000 people, 202 miles, two days and one long bike ride! This weekend, Steven and I made the trek across the border into Oregon for the 31st annual Seattle to Portland Bicycle Classic. With riders as old as 87 and as young as 22 months, and from 43 states and over seven different countries, STP proved that age and location don't exclude you from this ride!
While running our photo program at the finish line in Holladay Park, we had the opportunity to watch as thousands of family members and friends supported their loved ones as they finished the ride and caught their breath after pedaling for hours on end. It was at the finish line that we met the Turner family who showed up with a cape for their father who has tackled the STP ride the past four years. "This is the second year we have brought him the Superdad cape," daughter Kaitlin said, beaming with pride as Dad wore it proudly.
Superdad poses with his super family after finishing the grueling ride.
The atmosphere around the park was one of accomplishment and relief as riders traded their biking shoes for bare feet and their spandex for loose fitting clothing. A hot shower and a warm bed were on the cyclists' minds as the ride came to a close Sunday afternoon. The riders deserved that and so much more! The STP was an excellent testament to what can be accomplished when you put your mind to something. Whether they were riding solo, tandem, or three across, all the riders deserve a giant pat on the back.
This trio completed STP in style on their three-person bike.
Rest up from the ride and we'll see you again soon on our own Northwest road trip.


The Employment Relations Authority has upheld a claim for unjustified dismissal following a redundancy process. The employer failed to consult with the employee before making them redundant. The employee was only told of their redundancy without being given any opportunity to respond to the proposal.
In addition the employer tried to justify the redundancy on the basis of allegations of dishonesty and poor performance. Those matters are not ones that support a redundancy but rather should have been raised as allegations of misconduct.
The ERA awarded the employee $19,000 in lost wages and $18,000 for hurt and humiliation for the failure to follow any proper process.


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PCMag UK | News & Analysis | News
Most Google Accounts Don't Use Two-Factor Authentication
18 Jan 2018, 12:30 p.m.
Less than 10 percent of all active Google accounts have adopted the extra layer of protection, according to a company security engineer.
Despite its security benefits, two-factor authentication still isn't popular among Google users.
On Wednesday, a Google security engineer said less than 10 percent of all active Google accounts have adopted the extra layer of protection.
SEE ALSO: Microsoft: Russian Hackers Target US Think Tanks, Political Orgs
"The truth is such obvious security mechanisms just don't get adopted on a wide enough scale," said Grzegorz Milka, who spoke at the USENIX Enigma 2018 conference in Santa Clara, California.
The adoption rate is strikingly low, but it's not a complete surprise. While two-factor authentication can prevent hackers from breaking into your account, it comes at the cost of convenience.
The security feature generally works like this: to access your account, both the password and a special code sent to your phone needs to be entered. Unfortunately, that extra step in the login process can turn people off.
"It's perceived as an unnecessary hassle to setup additional security for one's account," Milka said. Some users are also wary about sharing their phone number with an online service, he added.
But securing your Google account with only a password sometimes isn't enough. Hackers are routinely uncovering login credentials from unsuspecting victims. They can do so by pulling them from past data breaches at major websites, or by targeting victims with malware or email phishing attacks.
Due to password reuse, some of these stolen logins from third-party websites even work on Google accounts. For study purposes, the company has been analyzing lifted passwords sold on digital black markets. It found over 67 million valid login credentials for Google accounts circulating in third-party data dumps.
"The password theft ecosystem is thriving," Milka said. "There are tens of thousands of credentials changing hands everyday."
Fortunately, Google has come up with safeguards that'll kick in with or without two-factor authentication. For instance, the company's internal systems will look for any abnormal activity with the way you login to your account. If detected, Google will try to verify the activity is actually coming from you and not a hacker.
It can do so by issuing a "security challenge" that acts like a one-time two-factor authentication. For example, these challenges can ask you to enter a special code that's been sent to your backup email or to your smartphone.
"Most hijackers are stumped at login, but some do get in," Milka said.
To detect these hackers, Google's safeguards will remain on the lookout for suspicious account activity in places like Gmail. Any attempts to export your contact list, send phishing emails, or delete security alerts sent there by Google can trigger the company to temporarily lock down the account.
Milka indicated the safeguards have been effective at stopping numerous hijack attempts. However, the protections haven't been foolproof. During the 2016 US presidential election, suspected Russian hackers stole personal emails from a Hilary Clinton aide by successfully breaching his Gmail account.
Milka declined to comment on that specific incident. But he said hackers are constantly coming up with ways to outsmart Google's safeguards. In response, the company has come up with its Advanced Protection Program, which is designed to protect high-risk Google users such as politicians and business leaders from the sneakiest of hacks.
But like two-factor authentication, the Advanced Protection Program has to be activated by the user for it to take effect.
Antiphishing
Microsoft: Russian Hackers Target US Think Tanks, Political Orgs
7 Signs You Have Malware and How to Get Rid of It
Google Chrome Feature Pokes Security Hole in YubiKey Product
5 Arrested for Spreading Ransomware in US, Europe
Michael Kan michael_kan@pcmag.com
Michael has been a PCMag reporter since October 2017. He previously covered tech news in China from 2010 to 2015, before moving to San Francisco to write about cybersecurity. See Full Bio
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text:
Q: How to update cell value to "" when other cell value changed? I need if I change the value of cell K2, the value of cell E2 should be equal to "".
I need to do it for all rows, K3 E3, K4 E4, Kn En .. .
Private Sub Worksheet_Change(ByVal Target As Range)

If Target = Range("K2") Then
    Range("E2").Value = ""
End If

End Sub

A: Let try:
   Private Sub Worksheet_Change(ByVal Target As Range)

   If Not(intersect(target,[K:k]) is nothing) Then Range("E" & target.row).Value = vbnullstring

   End Sub

Or better:
Private Sub Worksheet_Change(ByVal Target As Range)

If target.column=[k:k].column and target.cells.count=1 Then Range("E" & target.row).Value = vbnullstring

End Sub

redpajama_set_name: RedPajamaStackExchange


KUALA LUMPUR: The failure of Proton cars to stay competent in the automotive industry was.
KUALA LUMPUR, July 26 — Prime Minister Tun Dr Mahathir Mohamad told the USA news.
KUALA LUMPUR: Umno supreme council member Datuk Seri Tajuddin Abdul Rahman today blames MCA for.


text:
Aphrophorias is een geslacht van halfvleugeligen uit de familie Aphrophoridae. De wetenschappelijke naam van dit geslacht is voor het eerst geldig gepubliceerd in 1910 door Kirkaldy.

Soorten
Het geslacht Aphrophorias  is monotypisch en omvat slechts de volgende soort:
 Aphrophorias inclyta (Walker, 1858)

Aphrophoridae


text:
\section{Introduction}

A Sybil attack, formulated by Douceur~\cite{D02}, is intriguing in its
simplicity. However, such an attack can incur substantial damage to
the computer system. In a Sybil attack, the adversary is able to
compromise the system by creating an arbitrary number of identities
that the system perceives as separate. If the attack is successful,
the adversary may either overwhelm the system resources, thus
channeling the attack into denial-of-service~\cite{WS02}, or create
more sophisticated problems, e.g. routing infrastructure
breakdown~\cite{KW03}.

Ad hoc wireless networks, such as a sensor networks, are a potential
Sybil attack target. The ad hoc nature of such networks may result in
scenarios where each node starts its operation without the knowledge
of even its immediate neighborhood let alone the complete network
topology. Yet, the broadcast nature of the wireless communication
prevents each node from recognizing whether the messages that it
receives are sent by the same or different senders. Thus, an attacker
may be free to either create an arbitrary number of fictitious
identities or impersonate already existing real nodes. The problem
straddles the security and fault tolerance domains as the attacker may
be either a malicious intruder or a node experiencing Byzantine
fault. A fault is Buzantine~\cite{LSP82} if the faulty node disregards
the program code and behaves arbitrarily. For convenience,
in this paper we assume that the attacker is a faulty node rather than
intruder.

\noindent
\textbf{Problem motivation.}  A standard way of establishing
trust between communicating parties is by employing
cryptography. There is a number of publications addressing the Sybil
attack in this manner
\cite{DHM03,pseudonyms,PPG05,TB06,YYYLA05,ZWRN05,ZSJ03}.  For example,
if each node has access to verified certificates and every sender
digitally signs its messages, then the receiver can unambiguously
determine the sender and discard superfluous identities created by the
faulty node by checking the digital signature of the message against
the certificates. However, there are several reasons for this approach
to be inappropriate. A cryptography-based solution pre-supposes a
key-based infrastructure which requires its maintenance and update and
thus limits its applicability.  Moreover, resource constrained
devices, such as sensor nodes in sensor networks, may not be able to
handle cryptographic operations altogether.

Another approach is intrusion detection based on
\emph{reputation}~\cite{BB03,CF05,JMB03}.  Due to the broadcast nature
of wireless communication, the messages from each node are observed by
its neighbors. A fault is detected if the node deviates from the
protocol. It is unclear how reputation-based schemes would fare if the
messages cannot be matched to the sender: the faulty node may
impersonate other nodes or create an arbitrary number of fictitious
nodes and set up its own alternative reputation verification network.

However, there are two unique features of wireless communication that
make defense against the Sybil attack possible. The wireless
communication is broadcast. Thus, the message transmission of a faulty
node is received by all nodes in its vicinity. In addition, the nodes
can estimate the \emph{received signal strength} (RSS) of the message
and make judgments of the location of the sender on its basis. Note
that the latter is not straightforward as the faulty node can change
its \emph{transmission signal strength} (TSS). In this paper we
investigate the approaches to Sybil defense using this property of
wireless communication.

\noindent
\textbf{Related literature.} Newsome et al~\cite{NSSP04} as well
as Shi and Perrig~\cite{SP04} survey various defenses against the
Sybil attack. They stress the promise of the type of technique we
consider. Demirbas and Song~\cite{DS06} consider using the RSS for
Sybil defense.

A line of inquiry that is related to Sybil defense is secure location
identification~\cite{CH06,KZ03,LPC05,SSW03,VN06}. In this case, a set
of trusted nodes attempt to verify the location of a possibly
malicious or faulty node. However, the establishment of such trusted
network is not addressed. Hence, this approach may not be useful for
Sybil defense.

Dela{\"e}t et al~\cite{DMRT08c}, and Hwang et al~\cite{HHK07} consider
the problem where the faulty node operates synchronously with the
other nodes.  Dela{\"e}t et al~\cite{DMRT08c} provided examples of
positioning of faulty nodes and their strategies that lead to
neighborhood discovery compromise. Note that the synchrony assumption
places a bound on the number of distinct identities that the faulty
node can assume before the correct nodes begin to counter its
activities. Even though the faulty node may potentially create the
infinite number of fictitious identities, the correct nodes have to
deal with no more than several of them at a time. However, this
approach simplifies the problem as it limits the power of the faulty
node and the strength of the attack.

Nesterenko and Tixeuil~\cite{NT06} describe how, despite Byzantine
faults, every node can determine the complete topology of the network
despite once each node recognizes its immediate neighbors. Thus, to
defend against the Sybil attack it is sufficient to locally solve
Byzantine-robust neighborhood discovery.

Note that the problem is trivial when the ports are known. In this
case, the receiver may not know the identity of the transmitter of the
message but can match the same transmitter across messages. This
prohibits the faulty node from creating more than a single fictitious
identity or impersonating other real nodes and allows a simple
solution.

\noindent
\textbf{Our approach and contribution.} We consider the problem
of neighbor identification in the presence of Byzantine nodes. The
nodes are embedded in a geometric plane and know their location. They
do not have access to cryptographic operations. The nodes can exchange
arbitrary messages, but the only information about the message that
the receiver can reliably obtain is its RSS. We consider the
asynchronous model of execution. That is, the execution speed of any
pair of nodes in the network can differ arbitrarily. This enables the
faulty node to create an arbitrary number of fictitious identities or
impersonate the correct nodes in an arbitrary way. Moreover, in this
model, the only unique identities that the nodes have are their
coordinates. Hence, the objective of each node is to collect the
coordinates of its neighbors. We focus on local solutions to the
neighborhood discovery. That is, each node only processes messages
from the correct neighbors within a certain fixed distance. We do not
consider a denial-of-service attack or jamming attack~\cite{WS02},
where the faulty nodes just overwhelm resources of the system by
continuously transmitting arbitrary messages. We assume that the
network has sufficient bandwidth for message exchanges and the nodes
have sufficient memory and computing resources to process them.  To
the best of our knowledge, this is the most general model of Sybil
defense considered to-date.

In Section~\ref{SecModel} we provide details for our execution model
and formally state several variants of the neighborhood discovery
problem. Sections~\ref{SecNotSolvable}, \ref{SecDetect},
\ref{SecDensity}, and \ref{SecRange} outline the boundaries of the
achievable.  In Section~\ref{SecNotSolvable}, we formally prove that
this problem is not solvable without outside help. Intuitively, the
faulty node may create a \emph{universe} of an arbitrary number of
fictitious identities whose messages are internally consistent and the
correct node has no way of differentiating those from the universe of
correct nodes.  In Section~\ref{SecDetect}, we introduce
\emph{universe detectors} as a way to help nodes select the correct
universe. The idea is patterned after failure
detectors~\cite{CT96}. Just like failure detectors, universe detectors
are not implementable in asynchronous systems. However, they provide a
convenient abstraction that separates the concerns of algorithm design
and implementation of the necessary synchrony and other details that
enable the solution to Sybil defense. However, unlike failure
detectors, universe detectors alone are insufficient to allow a
solution to the neighborhood discovery problem. If the density of the
network is too sparse, the faulty nodes may introduce a fictitious
identity such that the detector is rendered unable to help the correct
nodes. In Section~\ref{SecDensity}, we prove the necessary condition
for the location of the correct nodes to allow a solution to the
neighborhood discovery problem. However, the faulty node may still be
able to compromise the operation of correct nodes. For that, a faulty
node may assume the identity of a correct node and discredit it by
sending incorrect messages to other nodes. In Section~\ref{SecRange}
we prove another necessary condition for the minimum transmission
range of correct nodes that eliminates this problem.

In Section~\ref{SecSAND} we present a Sybil-attack resilient
neighborhood discovery algorithm $\cal SAND$ that uses the universe
detectors to solve the neighborhood discovery problem provided that
the necessary conditions are met.  In their study of failure
detectors Chandra et al~\cite{CHT96} defined the weakest failure
detector as the necessary detector to solve the problem that they are
deployed to address. With the introduction of $\cal SAND$, we show
that the employed detectors are the weakest detectors necessary to
solve the neighborhood discovery problem. In Section~\ref{SecEnd}, we
conclude the paper by discussing the implementation details of the
algorithm and the attendant universe detectors.

\section{Computation Model  Description, Assumptions,
         Notation and Definitions}\label{SecModel}

A computer network consists of nodes embedded in a geometric
plane. Each node is aware of its own coordinates.  A (\emph{node})
\emph{layout} is a particular set of nodes and their locations on the
plane. Unless explicitly restricted, we assume that the node layout
can be arbitrary. Any specific point on the plane can be occupied by
at most one node. Thus, the node's coordinates on the plane uniquely
identify it. The nodes have no other identifiers.  For ease of
exposition, we use identifiers at the end of the alphabet such as $u$
or $v$ to refer to the particular locations or non-faulty nodes
occupying them. We use $f$ and $k$ respectively to refer to a faulty
node and a location where the faulty node may pretend to be located.
The distance between $u$ and $v$ is $|uv|$. The \emph{neighborhood
set} or just \emph{neighborhood} of a node $u$ is a set of nodes whose
distance to $u$ is less than a certain fixed distance $d_n$.

\noindent
\textbf{Program model.}  We assume the asynchronous model of
algorithm execution. That is, the difference between the execution
speed of any pair of nodes can be arbitrarily large.  Note that this
asynchrony assumption allows any node, including a faulty one, to send
an arbitrary number of messages before other nodes are able to
respond. The nodes run a distributed algorithm. The algorithm consists
of variables and actions. A (\emph{global}) \emph{state} of the
algorithm is an assignment of values to all its variables.  An action
is \emph{enabled} in a state if it can be executed at this state. A
\emph{computation} is a maximal fair sequence of algorithm states
starting from a certain prescribed initial state $s_0$ such that for
each state $s_i$, the next state $s_{i+1}$ is obtained by atomically
executing an action that is enabled in $s_i$. Maximality of a
computation means that the computation is either infinite or
terminates where none of the actions are enabled. In other words, a
computation cannot be a proper prefix of another computation. Fairness
means that if an action is enabled in all but finitely many states of
an infinite computation then this action is executed infinitely
often. That is, we assume \emph{weak fairness} of action
execution. During a single computation, node layout is fixed.

Nodes can be either correct or faulty (Byzantine). A faulty node does
not have to follow the steps of the algorithm and can behave
arbitrarily throughout the computation.

\noindent
\textbf{Node communication.}  Nodes communicate by broadcasting
messages. As the distance to the sender increases, the signal
fades. We assume the free space model~\cite{Rappaport02} of signal
propagation. The antennas are omnidirectional. The received signal
strength (RSS) changes as follows:
\begin{equation}\label{eqnSignalPropagation}
R=cT/r^2
\end{equation}
where $R$ is the RSS, $c$ is a constant, $T$ is the transmitted (or
sent) signal strength (TSS), and $r$ is the distance from the sender
to the receiver. We assume that $r$ cannot be arbitrarily small. Thus,
$R$ is always finite. There is a minimum signal strength $R_{min}$ at
which the message can still be received. There is no message
loss. That is, if a message is sent with TSS --- $T'$, then every node
within distance $r'=\sqrt{cT'/R_{min}}$ of the sender receives the
message. We do not consider interference, hidden-terminal effect or
other causes of message loss. We assume that every correct node always
broadcasts with a certain fixed strength $T_r$. A \emph{range} $r_t$
is defined as $\sqrt{cT_r/R_{min}}$. The relation between range $r_t$
and neighborhood distance $d_n$ is, in general, arbitrary. A faulty
node may select arbitrary TSS. If a node receives a message (i.e. if
the RSS is greater than $R_{min}$), then the node can accurately
measure the RSS.

To simplify the exposition we assume that the nodes transmit three
types of messages: (i) $u$ transmits \emph{announce}, this message has
only the information about $u$ and carries $u$'s coordinates; the
purpose of an announcement is for $u$ to advertise its presence to its
neighbors; (ii) $u$ transmits \emph{confirm} of another node $v$'s
transmission; (iii) $u$ transmits \emph{conflict} with another node
$v$'s transmission if its observations do not match the location or
the contents of $v$'s message. The original message is attached in
\emph{confirm} and \emph{conflict}. Every message contains the
coordinates of the sender.

\noindent
\textbf{Fictitious nodes and conflicts.} Since the only way to
unambiguously differentiate the nodes is by their location, the
objective of every node is to determine the coordinates of its
neighbors. Faulty nodes may try to disrupt this process by making the
correct node assume that it has a non-existent neighbor. Such a
non-existent neighbor is \emph{fictitious}.  A node that indeed exists
in the layout is \emph{real}. Note that a real node can still be
either correct or faulty. Faulty nodes may try to tune their TSS and
otherwise transmit messages such that it appears to the correct nodes
that the message comes from a fictitious node. Moreover, the faulty
nodes may try to make their transmissions appear to have come from
correct nodes.

As a node receives messages, due to the actions of a faulty node, the
collected information may be contradictory. A \emph{conflict} consists
of a message of any type purportedly coming from node $k$, yet the
received signal strength at node $u$ does not match $|uk|$ provided
that the signal were broadcast from $k$ with the TSS of $T_r$.  A
conflict is \emph{explicit} if $u$ receives this conflicting message.
Note that the RSS may be so low that $u$ is unable to receive the
message altogether, even though the RSS at $u$ should be greater than
$R_{min}$ in case the message indeed come from $k$ and be broadcast at
$T_r$. In this case the conflict is \emph{implicit}.  To discover the
implicit conflict $u$ has to consult other nodes that received the
conflicting message. If $u$ detects a conflict it sends a conflict
message.

A \emph{universe} is a subset of neighbors that do not conflict. That
is, a universe at node $u$ contains nodes $v$ and $w$ whose
announcements $u$ received such that $u$ did not receive a conflict
from $v$ about $w$ or from $w$ about $v$.  Note that due to conflicts
the information collected by a single node may result in several
different universes. A universe is \emph{real} if all nodes in it are
real.  A universe is \emph{complete} for a node $u$ if it contains all
of $u$'s correct neighbors. Note that even though a faulty node is
real, it can evade being added to universes by not sending any
messages. Hence, a complete universe is not required to contain all
the real nodes, just correct ones.

\noindent
\textbf{Program locality.}  To preserve the locality of a
solution to the neighborhood discovery problem, we introduce the
following requirement. Each node ignores information from the nodes
outside the range $r_t$ and about the nodes outside the neighborhood
distance $d_n$.

\noindent
\textbf{Problem statement.} We define several variants of the
problem.  The \emph{strong neighborhood discovery problem} $\cal SNDP$
requires each correct node $u$ to output its neighborhood set
according to the following properties:

\begin{description}
\item[safety] --- if the neighborhood set of $u$ is output, the set
  contains only all correct nodes and no fictitious nodes of $u$'s
  neighborhood;

\item[liveness] --- every computation has a suffix in whose every
state $u$ outputs a neighborhood set that contains all correct
neighbors of $u$. In other words, $u$ eventually outputs its complete
neighborhood set.
\end{description}

This problem definition may be too strict. Some correct nodes may be
slow in announcing their presence. However, the safety property of
$\cal SNDP$ requires each node to wait for its slow neighbors before
outputting the neighborhood set.  Hence, we define the \emph{weak
neighborhood discovery problem} $\cal WNDP$. This problem relaxes the
safety property to allow the output neighborhood set to contain a
subset of correct neighbors of $u$. Note that the presence of the
fictitious nodes in the output is still prohibited. Also note that the
liveness property requires that the neighborhood set of $u$ in $\cal
WNDP$ eventually contains all correct neighbors.  Further relaxation
of the safety property yields the \emph{eventual neighborhood
discovery problem} $\diamond \cal NDP$. It requires that the safety of
$\cal SNDP$ be satisfied only in the suffix of a computation. That is
$\diamond \cal NDP$ allows the correct nodes to output incorrect
information arbitrarily long before providing correct output. Observe
that any solution to $\cal SNDP$ is also a solution to $\cal WNDP$,
and any solution to $\cal WNDP$ is also a solution to $\diamond \cal
NDP$.

\section{Impossibility of Standalone Solution to Neighborhood Discovery}
\label{SecNotSolvable}

In this section we demonstrate that in the asynchronous system any
correct node is incapable of discovering its neighborhood if a
faulty node is present. The intuition for this result is as
follows. Since a faulty node is not restricted in the number of
messages that it generates, it can send an arbitrary number of
announcements introducing fictitious nodes. The faulty node can then
imitate arbitrary message traffic between these non-existent nodes.
On its own, a correct node is not able to differentiate these
fictitious nodes from the real ones.

\begin{theorem}\label{trmNotSolvable}
In an asynchronous system, none of the three variants of the
neighborhood discovery problem are deterministically solvable in the
presence of a single Byzantine fault.
\end{theorem}

\par\noindent{\bf Proof:}\indent We provide the proof for the eventual neighborhood discovery
problem. Since this problem is the weakest of the three that we
defined, the impossibility of its solution implies similar
impossibility for the other two.

Assume the opposite. Let $\cal A$ be a deterministic algorithm that
solves $\diamond\cal NDP$ in the presence of a faulty node.  Let us
consider an arbitrary layout $L_1$ that contains a faulty node
$f$. Let us consider another layout $L_2$ containing $f$ such that the
neighborhood $U_1$ in layout $L_1$ of at least one correct node $u$
differs from its neighborhood $U_2$ in $L_2$ and this difference
includes at least one correct node. Without loss of generality we can
assume that there exists a correct node $v$ such that $v\in U_1$ and
$v \not \in U_2$.

We construct two computations of $\cal A$: $\sigma_1$ on layout $L_1$
and $\sigma_2$ on layout $L_2$. The construction proceeds by
iteratively enlarging the prefixes of the two computations. In each
iteration, we consider the last state of the prefix of $\sigma_1$
constructed so far and find the action that was enabled for the
longest number of consequent steps. If there are several such actions,
we choose one arbitrarily. We attach the execution of this action to
the prefix of $\sigma_1$. If this action is a message transmission of
a node $w$ such that $w \in U_1$, we also attach the following action
execution to the prefix of $\sigma_2$: node $f$ sends exactly the same
message as $w$ in $\sigma_1$ with the TSS selected as $T=T_r
|uf|^2/|uw|^2$. Observe that $u$ receives the same message and with
the same RSS in this step of $\sigma_2$ as in the step added to
$\sigma_1$.  If the new action attached to $\sigma_1$ prefix is not by
a node in $U_1$, or it is not a message transmission, no action is
attached to the prefix of $\sigma_1$. We perform similar operations to
the prefix of $\sigma_2$.

We continue this iterative process until maximal computations
$\sigma_1$ and $\sigma_2$ are obtained. Observe that by construction,
both computations are weakly fair computations of $\cal A$. Moreover,
in both cases $u$ receives exactly the same messages with exactly the
same RSS.

By assumption, $\cal A$ is a solution to $\diamond\cal NDP$. According
to the liveness property of the problem, $\sigma_1$ has a suffix where
$u$ outputs its neighborhood in every state and, due to the liveness
property, $\sigma_1$ contains a suffix where $u$'s neighborhood set
contains all correct nodes. In layout $L_1$ of $\sigma_1$, $v$ is
$u$'s correct neighbor. Hence, $v$ has to be included in this
set. That is, there is a suffix of $\sigma_1$ where $u$ outputs a
neighborhood set that contains $v$.  However, $u$ receives the same
messages in $\sigma_2$.  Since $\cal A$ is deterministic, $u$ has to
output exactly the same set in $\sigma_2$ as well. That is, $\sigma_2$
contains a suffix where the neighborhood set also contains $v$.
However, $v$ is fictitious in layout $L_2$ of $\sigma_2$. According to
the safety property of $\diamond\cal NDP$, every computation should
contain a suffix where the neighborhood set of $u$ excludes fictitious
nodes. That is, $\sigma_2$ of $\cal A$ violates the safety of
$\diamond\cal NDP$.  Hence, our assumption that $\cal A$ is a solution
to the weak neighborhood discovery problem is incorrect. The theorem
follows.  \hfill$\Box$\par\vskip1em

\section{Abstract Universe Detectors}\label{SecDetect}

\textbf{Definitions.}  The negative result of
Theorem~\ref{trmNotSolvable} hinges on the ability of a faulty node to
introduce an arbitrary number of fictitious nodes. A correct node
cannot distinguish them from its real neighbors. Still, a correct node
may be able to detect conflicts between nodes and separate them into
universes. However, it needs help deciding which universe is
real. This leads us to introduce the concept of a universe detector
that enables the solution to the neighborhood discovery problem in the
asynchronous computation model. A \emph{universe detector} indicates
to each correct node which universe is real.  It takes the universes
collected by the node as input and outputs which universe contains
only real nodes. That is, a universe detector \emph{points} to the
real universe. Note that the algorithm still has to collect the
neighborhood information and separate them into universes such that at
least one of them is real. If the algorithm does not provide a real
universe, the detector does not help.

Depending on the quality of the output, we define the following
detector classes. For each node $u$, a \emph{strongly perfect universe
detector} $\cal SPU$ has the following properties:
\begin{description}
\item[completeness] --- if a computation contains a suffix where in
     every state, $u$ outputs a real and complete universe, then this
     computation also contains a suffix where $\cal SPU$ at $u$ points
     to it;
\item[accuracy] --- if $\cal SPU$ points to a universe, this
     universe is real and complete.
\end{description}

The strongly perfect universe detector may be too restrictive or too
difficult to implement.  Unlike $\cal SPU$, a \emph{weakly perfect
universe detector} $\cal WPU$ may point to a real universe even if it
is not complete. That is, the definition of accuracy is relaxed to
allow the detector to point to a real universe that is not
complete. Note that $\cal WPU$ still satisfies the completeness
property and has to eventually point to the real universe if it is
available. A further relaxation of completeness and accuracy yields an
\emph{eventually perfect universe detector} $\diamond {\cal PU}$ which
satisfies both properties in a suffix of every computation. Observe
that the relationship between these detector classes is as follows:
${\cal SPU} \subset {\cal WPU} \subset \diamond {\cal PU}$

Observe that these universe detectors enable a trivial solution to the
neighborhood discovery problems: each node composes a universe for
every possible combination of the nodes that claim to be in its
neighborhood.  Naturally, as the node receives announcements from all
its correct neighbors, one of these universes is bound to be real and
complete. Hence, the detector can point to it. However, such an
approach essentially shifts the burden of separating fictitious and
real nodes to the detector while we are interested in minimizing the
detector's involvement. This leads us to introduce an additional
property of the algorithms that we consider. An algorithm that solves
the neighborhood discovery problem that uses detectors is
\emph{conflict-aware} if for each universe $U$ of node $u$, if nodes
$v$ and $w$ do not have a conflict and $v$ belongs to $U$ then $w$
also belongs to $U$. That is, the algorithm does not gratuitously
separate non-conflicting neighbors into different universes. In what
follows we focus on conflict-aware solutions.

\section{Necessary Node Density}\label{SecDensity}

Theorem~\ref{trmNotSolvable} demonstrates that to solve the
neighborhood discovery problem, any algorithm requires outside help
from a construct like a universe detector. However, the availability
of a universe detector may not be sufficient. Faulty nodes may take
advantage of a layout to announce a fictitious node without generating
conflicts. Then, a correct node running a conflict aware algorithm
never removes this fictitious node from the real universe. A universe
detector then cannot point to such a universe.

To illustrate the idea we start with a sequence of fictitious node
placement examples.

\subsection{Fictitious Nodes Placement Examples}

For this discussion we consider the neighborhood of a certain correct
node $u$ and a faulty node $f$ that tries to compromise $u$'s
neighborhood discovery. We denote $x$, $y$, $z$ --- the correct nodes
in the neighborhood of $u$ that that are respectively first, second
and third nearest to $f$. Note that to affect $u$, the faulty node $f$
does not itself have to be the neighbor of $u$. Our analysis proceeds
according to the number of correct receivers of messages sent by $f$.

\begin{figure}
\centering
\epsfig{figure=oneReceiver,width=.7\textwidth,clip=}
\caption{Deception field with a single correct node
$x$.}\label{figOneReceiver}
\end{figure}

\noindent
\textbf{Single correct receiver.}  Refer to
Figure~\ref{figOneReceiver} for illustration. Note that due to the
broadcast nature of radio signal propagation, if any correct node
receives a message sent by $f$, $x$ also receives this message because
it is closest to $f$. Therefore, the single correct receiver may only
be $x$. Note, that for $y$ to not receive the signal from $f$, the
transmission signal strength should be sufficiently low. Recall that a
correct node always broadcasts with pre-defined signal strength
$T_r$. Thus, to deceive $x$, $f$ has to select the location of $k$ and
the TSS such that: (i) the RSS at $x$ is the same as if $k$
transmitted with $T_r$ and (ii) the RSS at $y$ is below $R_{min}$. For
the received signal strength at $y$ to be less than $R_{min}$, $k$
cannot be closer to $x$ than $|fy|$. On the other hand, the location
of $k$ cannot be outside the range $r_t$ (or else $x$ generates
conflict) or outside the neighborhood distance $d_n$ (or else $x$
ignores it). Thus, the possible location of $k$ is a ring around $x$
with the inner radius $|fy|$ and the outer radius --- $min(r_t,d_n)$.

\begin{figure}
\centering
\epsfig{figure=twoReceivers,width=.7\textwidth,clip=}
\caption{Deception field with a two-node retinue. Correct nodes $x$
and $y$ receive transmissions of faulty node $f$, while $z$ does
not.}\label{figTwoReceivers}
\end{figure}

\noindent
\textbf{Two correct receivers.} If there are exactly two correct
receivers, they are the two nodes $x$ and $y$ nearest to $f$. Assume
that $f$ makes two transmissions at signal strengths $T_1$ and
$T_2$. For these transmissions, the RSS at $x$ and $y$ are $R_{x1}$,
$R_{y1}$ and $R_{x2}$, $R_{y2}$ respectively. From the signal
attenuation in Formula~\ref{eqnSignalPropagation} we obtain:
\[
 \frac{|fy|}{|fx|}=\sqrt{\frac{R_{x1}}{R_{y1}}}=
\sqrt{\frac{R_{x2}}{R_{y2}}}
\]
That is, regardless of transmission power, the ratio of received
signal strengths at $x$ and $y$ does not change. Hence, $f$ may select
the location of the fictitious node $k$ such that it preserves this
ratio. Such locations form an arc of a circle. Refer to
Figure~\ref{figTwoReceivers}. The center of the circle lies on the
line whose segment is $(xy)$. The radius of the circle is $ba/(b-a)$
where $b$ and $a$ are the portions of $(xy)$ such that
$b/a=|fy|/|fx|$. This circle is the \emph{deception circle}. Note that
$f$ may not be able to use all of the deception circle for fictitious
node placement: to get both $x$ and $y$ to receive the signal without
generating conflicts the points on the arc have to lie within
$min(r_t,d_n)$ of both $x$ and $y$.  Moreover, similar to the
single-receiver case, the portion of the arc that is closer to $y$
than $|fz|$ cannot be used without $z$ also receiving the message.
\begin{figure}
\centering
\epsfig{figure=manyReceivers,width=.7\textwidth,clip=}
\caption{The location of a snare in case of multiple faulty nodes. The
retinue of $f_1$ is $x$ and $y$. The retinue of $f_2$ is $z$. The
intersection of deception fields produces area where a snare can be
placed.}\label{figManyReceivers}
\end{figure}

\noindent
\textbf{More than two correct receivers.} Note that if there are
more than two correct receivers, they can be considered pairwise. Each
pair of correct receivers forms its own deception circle. Note that
$k$ can only be placed at the intersection of all these circles. Note,
however, that the circles intersect in the same place only if the
recipients are co-linear.

\noindent
\textbf{Snare.} A faulty node may affect the correct nodes around
it.  A set $E_f$ of correct nodes is the \emph{retinue} of a faulty
node $f$ if the following holds: if a correct node $u$ belongs to
$E_f$, then every correct node $v$ such that $|vf| \leq |uf|$, also
belongs to $E_f$. The faulty node is the \emph{leader} of the
retinue. For example, assume there are two faulty nodes $f_1$ and
$f_2$ and three correct nodes $u$, $v$ and $w$ such that $|f_1u| <
|f_1v| < |f_1w|$ and $|f_2w| < |f_2v| < |f_2u|$. Refer to
Figure~\ref{figManyReceivers} for illustration. All three correct
nodes can be either in the retinue $E_{f1}$ of $f_1$ or $E_{f2}$ of
$f_2$. However, if $v$ belongs of $E_{f1}$, so does $u$, and if $u$
belongs to $E_{f2}$, so do $v$ and $w$.

A \emph{deception field} for a retinue of a faulty node $f$ is the
area such that for each point $k$ of the field there exists a TSS that
the leader of the retinue can use to transmit a message. The message
so transmitted generates the RSS at each member of the retinue as if
the message was sent from $k$ with transmission strength
$T_r$. Intuitively, a deception field is the area where $f$ can place
fictitious nodes without generating conflicts at its retinue members.

A point $k$ in a neighborhood of a correct node $u$ is a
(\emph{simple}) \emph{snare} for $u$ if there exists a set of faulty
nodes and a retinue assignment for them such that: $u$ is in one of
the retinues and the intersection of the deception fields of the
retinues includes $k$. Note that the nodes in range of $k$ are either
in the retinues or not. Intuitively, a snare is a point where faulty
nodes can jointly place a fictitious node without generating explicit
conflicts at any of the correct neighbors of $u$.  Refer to
Figure~\ref{figManyReceivers} for illustration. Note that some of the
nodes may have implicit conflicts with $k$. That is, they are within
range $r_t$ of $k$ and $u$ but not in one of the retinues. That is,
they should receive a message from a node at $k$ but they do not. Note
that a snare transmission from faulty nodes may still generate
conflicts outside the range of $u$.  However, due to the locality
assumption, $u$ ignores this conflict.

A point $k$ is a \emph{perfect snare} for $u$ if it is a snare and all
nodes within the transmission range of $u$ and $k$ are in the retinues
of the faulty nodes participating in the snare.  That is, if faulty
nodes broadcast in a perfect snare, neither explicit nor implicit
conflicts are generated at the neighbors of $u$.

\begin{figure}
\centering
\epsfig{figure=grid,width=.7\textwidth,clip=}
\caption{The possibility of a snare in a grid layout with $d_n=1.5s$.}
\label{figGrid}
\end{figure}

\noindent
\textbf{Evaluating fault tolerance of a layout.} To illustrate
the concept of a snare, let us discuss a square grid layout (refer to
Figure~\ref{figGrid}). Let $s$ be the distance between the nodes in
the grid. Note that for a node to have any neighbors, the neighborhood
distance $d_n$ has to be no less than $s$. Let $ s \leq d_n < s
\sqrt{2}$. For simplicity, let $r_t = d_n$. Then each node has exactly
four neighbors. Note that the failure of a single node creates a
wedge-shaped deception field around the faulty node. Thus, with this
distance the layout is not fault tolerant.

Let us consider the case where $s\sqrt{2} \leq d_n < 2s$ and again
$r_t=d_n$. In this case, the neighborhood can withstand a failure of
exactly one node. Indeed, assume that a single node failed. Note that
we have to consider the collusion of this faulty node with arbitrary
faulty nodes outside the neighborhood. Let us focus on the
neighborhood of node $u_5$. For $u_5$ to consider a fictitious node,
the transmission of at least one faulty node has to reach
$u_5$. However, if a signal from a faulty node, either inside or
outside the neighborhood of $u_5$, reaches $u_5$, then this signal is
received by at least two more correct neighbors of $u_5$.  Moreover,
the three correct nodes that receive this signal are
non-collinear. This means that their pairwise deception circles
intersect only in the sender itself. Thus, the neighborhood of $u_5$
does not contain a snare.

Let us determine if this grid layout can withstand simultaneous
failure of two nodes in the same neighborhood.  Let $d_n=r_t$ be
$1.5s$. Suppose nodes $u_1$ and $u_4$ fail.  The deception field of
$u_1$ with $u_2$ in its retinue is a disk with outer circle radius
$1.5s$ and inner --- $s\sqrt{2}$. That is, the outer disk is the range
for correct nodes $r_t=d_n$ and the inner is the distance to the next
nearest node --- $u_5$. A similar disk is a deception field of $u_4$
for $u_5$. The intersection of the two disks forms the area where a
perfect snare for $u_5$ may be located. To use the snare, $u_1$ sends
messages to $u_2$, and $u_4$ to $u_5$ with the appropriate TSS
pretending that the messages come from a fictitious node located in
the snare. Thus, the grid layout with such $d_n$ cannot withstand a
two-node failure.

\subsection{Necessary Node Density Condition}

Having described the required instruments, we now demonstrate that the
availability of the universe detectors alone is not sufficient to
enable a solution to any of the neighborhood discovery problems if the
node layout is too sparse. That is, if the nodes are not properly
positioned on the plane.

To simplify the proof we consider solutions that are
\emph{well-formed}. An algorithm is well-formed if (i) the action that
transmits \emph{announcement} is always enabled until executed; (ii)
the receipt of a message may enable either \emph{confirm} or
\emph{conflict}, this action stays enabled until executed.

\begin{theorem} \label{trmNoSnare}
There is no conflict-aware well-formed deterministic solution to any of
the neighborhood discovery problems despite the availability of the
universe detectors if one of the considered layouts contains a perfect
snare.
\end{theorem}

\par\noindent{\bf Proof:}\indent In the proof, we focus again on the weakest of the problems:
the eventual neighborhood discovery.  Assume the opposite: there is a
conflict-aware well-formed algorithm $\cal A$ that uses a detector and
solves the problem even though in one of the layouts $L_1$, the
neighborhood of a correct node $u$ contains a perfect snare $k$.

Consider a layout $L_2$ that is identical to $L_1$ except that there
is a correct node at location $k$ in $L_2$. We construct a computation
$\sigma_2$ of $\cal A$ on $L_2$ as follows. Faulty nodes do not send
any messages in $\sigma_2$.  We arrange the neighbors of $u$,
including $u$ itself, into an arbitrary sequence $Q$. We then build
the prefix of $\sigma_2$ by iterating over this sequence. Since $\cal
A$ is well-formed, each node in the sequence has \emph{announcement}
enabled. We add the action execution that transmits
\emph{announcement} to $\sigma_2$ in the order of nodes in $Q$.  Since
$\cal A$ is well-formed, these transmissions may enable \emph{confirm}
actions at the neighbors of $u$. Note that since $v$ is correct,
\emph{conflict} actions are not enabled by these transmissions. We now
iterate over the nodes in $Q$. For each node $v$ we add the execution
of these \emph{confirm} actions at $v$ to $\sigma_2$ in arbitrary
fixed order, for example in the order that the original senders the
appear in $Q$.  We proceed in this manner until the sequence $Q$ is
exhausted. Note that these transmissions may potentially generate
another round of \emph{confirm} messages at the nodes in $Q$. We
continue iterating over $Q$ until no more messages are generated.  We
then complete $\sigma_2$ by executing the actions of nodes in an
arbitrary fair manner. Note that the remaining messages deal with the
nodes outside $u$'s neighborhood. Therefore, $u$ ignores them.

Now, the liveness property of all the detectors states that a detector
points to a universe if it is output for a suffix of the
computation. Since $\cal A$ is a solution of $\diamond\cal NDP$ and
$\sigma_2$ is a computation of $\cal A$, $\sigma_2$ has to contain a
suffix where $u$ outputs a real universe in every state. Since $k$ is
a correct neighbor of $u$, $k$ is included in the real universe.

Recall that in layout $L_1$, point $k$ is a perfect snare. This means
that there is an arrangement of retinues and the TSS for the faulty
nodes, such that when the faulty nodes transmit, each node in the
neighborhood of $u$ in the distance $d$ from $k$ receives a message
with the same RSS as if a node at $k$ broadcast with $T_d$. Moreover,
none of the nodes in the neighborhood of $u$ detect conflicts.

We construct a computation $\sigma_1$ of $\cal A$ on layout $L_1$ as
follows. We iterate over the same sequence $Q$ as in $\sigma_2$. Note
that $k$ is also present in the sequence even though it is fictitious
in $\sigma_1$. To build the prefix of $\sigma_1$ we execute similar
actions as for $\sigma_2$.  The only difference is that when node $k$
broadcasts in $\sigma_2$, in $\sigma_1$ we have the faulty nodes that
constitute the snare broadcast at the appropriate TSS. Note that in
the computation thus formed, the correct neighbors of $u$ receive
messages at the same RSS and with the same content from the faulty
nodes as in $\sigma_2$ from $k$. Thus, these transmissions do not
generate conflicts. Observe that this means that node $u$ receives the
same messages with the same RSS, and in the same sequence in
$\sigma_1$ and $\sigma_2$. Since $\cal A$ is deterministic, $u$ has to
output the same universes in $\sigma_1$ and $\sigma_2$. Note also,
that this means that $u$ does not record conflicts. Since $\cal A$ is
conflict aware, all $u$'s universes of $\cal A$ include $k$ together
with the correct neighbors.

However, $k$ is a fictitious node in $L_1$. This means that $\sigma_1$
contains a suffix where $u$ does not output a real universe. According
to the safety property of the detectors, none of them provides output
in a suffix of $\sigma_1$. Which means that $\cal A$ does not output a
neighborhood set in a suffix of $\sigma_1$. This violates the liveness
property of a solution to $\diamond\cal NDP$. Therefore, our
assumption that $\cal A$ is a solution to $\diamond\cal NDP$ is
incorrect. The theorem follows.\hfill$\Box$\par\vskip1em

\section{Necessary Transmission Range}\label{SecRange}

In this section we provide another required condition for the
existence of a solution to the neighborhood discovery
problem. Essentially, if the nodes in the same neighborhood are out of
range, the faulty node may introduce a conflict between them. This
forces the algorithm to mistakenly split the correct nodes into
separate universes and renders the failure detector powerless.

\begin{theorem}\label{trmRange}
There is no conflict-aware deterministic solution for any of the
neighborhood discovery problems despite the availability of universe
detectors and lack of snares if the node transmission range $r_t$ is
less than double the neighborhood distance $d_n$.
\end{theorem}

\par\noindent{\bf Proof:}\indent Consider the eventual neighborhood discovery and assume that
there is an algorithm $\cal A$ that solves the problem in the presence
of detectors on any layout without snares yet the transmission range
of the correct nodes $r_t$ is less than $2d_n$. Consider the layout
$L_1$ where the neighborhood of a correct node $u$ contains two nodes
$v$ and $f_1$ as well as a point $k$ with the following properties.
Refer to Figure~\ref{figRange} for illustration.  As usual, $v$ is
correct, $f_1$ is faulty and there is no node at point $k$. Even
though point $k$ is in the neighborhood of $u$, it is out of range of
$v$.  That is, $r_t < |vk|$.  Recall that this is possible since, by
assumption, $r_t < 2d_n$. Node $f_1$ is such that $|uf_1|=|uk|$ and
$r_t > |vf_1|$. The rest of the correct nodes in range of $u$ are
located such that, with the exception of $v$, $k$ forms a perfect
snare for $u$. That is, if $f_1$ sends a message from a fictitious
node $k$, the only node that generates conflict is $v$. Certainly,
with the presence of $v$, $k$ is not a snare so the assumptions of the
theorem apply.

\begin{figure}
\centering
\epsfig{figure=range,width=.7\textwidth,clip=}
\caption{Insufficient range for recognition of faulty node. Illustration
to the proof of Theorem~\ref{trmRange}.}\label{figRange}
\end{figure}

Consider that $f_1$ indeed sends \emph{announcement} pretending to be
a fictitious node at $k$. Nodes $f_1$ and $k$ are equidistant from
$u$. Thus, if $f_1$ does not want $u$ to detect a conflict, $f_1$ has
to send the signal with the TSS of $T_r$. However, with such TSS, $v$
is in range of $f_1$ but out of range of $k$. This means that $v$
receives the announcement ostensibly coming from $k$ and detects a
conflict. The RSS at $v$ is $cT_r/|vf_1|^2$.  Since $\cal A$ is a
solution to the neighborhood discovery problem and $v$ is the only
node that is aware of the conflict, $v$ has to send \emph{conflict} to
$u$ which removes the fictitious node $k$ from the real universe of
$u$.

Consider a different layout $L_2$ (refer to Figure~\ref{figRange})
which is similar to $L_1$, only point $k$ is occupied by a correct
node and there is a faulty node $f_2$ near $v$. Specifically, the
distance $|vf_2|$ is such that there are no correct nodes within the
following range of $f_2$:
\[
\frac{|vf_2|}{|vf_1|}\sqrt{\frac{c}{R_{min}}}
\]
This ensures that when $f_2$ is going to imitate node $k$, none of
the nodes besides $v$ receive the messages from $f_2$. Note that $f_2$
and $k$ still do not form a snare because $v$ is aware of the
conflict. Note also, that such location of $f_2$ can always be found
if the faulty node can be placed arbitrarily close to $v$.

Assume that if the node $k$ in $L_2$ sends a message, $f_2$ replicates
this message with TSS
\[
\frac{T_r|vf_2|^2}{|vf_1|^2}
\]
Observe that in this case all nodes, including $v$ and $u$, receive
exactly the same messages as in layout $L_1$. Since $\cal A$ is
deterministic, the nodes have to act exactly as in the previous
case. That is, $v$ has to issue a conflict with the message of node
$k$. However, after receiving this conflict, $k$ is separated from
$u$'s real universe. Recall that $k$ is correct in layout $L_2$. Note
that in this case $k$ is never going to be added to the output of $\cal
A$ at $u$. However, this violates the liveness property of the
neighborhood discovery problem since $k$ is a correct neighbor of $u$.
Thus, $\cal A$ is not a solution to this problem as we initially
assumed.  \hfill$\Box$\par\vskip1em

\section{The Sybil Attack Resilient Neighborhood Discovery
         Algorithm $\cal SAND$}\label{SecSAND}

Our description of the algorithm proceeds as follows. We first
motivate the need to frugally encode the universes to be passed to the
universes detectors. We then describe the operation of the
neighborhood detection algorithm itself. Then, we define the concrete
implementations of the abstract detectors specified in
Section~\ref{SecDetect}. These concrete detectors should operate with
our algorithm. On the basis of the algorithm and detector description
we state the theorem of algorithm correctness and detector optimality.

\noindent
\textbf{Encoding universes.} Observe that a na\"{i}ve solution
for representing universes by the algorithm results in an exponential
number of universes. Indeed, assume that node $u$ compiled a set of
nodes $U$ that do not conflict with two nodes $v$ and $w$. Suppose now
that $u$ records a conflict between the two nodes. They thus have to
be placed in separate universes: $U \cup \{v\}$ and $U\cup\{w\}$. Let
us consider another pair of conflicting nodes $x$ and $y$ that are
different from $v$ and $w$. Then, there are four possible universes:
$U \cup \{vx\}$, $U \cup \{vy\}$, $U \cup \{wx\}$, and $U \cup
\{wy\}$. Hence, if there are $N$ nodes in the neighborhood of $u$, the
potential number of conflicting pairs is $\lfloor N/2 \rfloor$ and the
number of universes is $2^{\lfloor N/2 \rfloor}$.

Therefore, our algorithm encodes the universes in the conflicts that
are passed to the detector. That is, the algorithm passes a set of
conflicts for the detector to generate the appropriate universe on its
own.

Recall also that in an asynchronous radio network the receiving node
can not distinguish one sender from another or decide if the two
messages were sent by the same node. This task has to be handled by
the detector.

\noindent
\textbf{Algorithm description.} We assume that the necessary
conditions for the existence of a solution to the neighborhood
discovery problem are satisfied: the layout does not contain a
(simple) snare and transmission range is at least twice as large as
the neighborhood distance $d_n$.

The $\cal SAND$ algorithm operates as follows. Every message
transmitted by the node contains its coordinates.  Each node sends
\emph{announce}. After receiving an \emph{announce}, a node replies
with a \emph{confirm} message. Each \emph{confirm} contains the
information of the announcement. If a node receives a message whose
coordinates do not match the received signal strength, the node
replies with a \emph{conflict} message. The \emph{conflict} also
contains the information of the message that generated the
conflict. Observe that \emph{confirm} can only be generated by
\emph{announce} while \emph{conflict} can be generated by an arbitrary
message.  Note that according to the locality assumption every node
ignores messages from the nodes outside of its neighborhood distance
$d_n$.

Each node $u$ builds a message dependency directed graph
\emph{DEP}. For each \emph{confirm}, $u$ finds a matching
\emph{announce}; for each \emph{conflict} --- a matching message that
caused the conflict. Note that this message dependence may not be
unique. For example a faulty node may send a message identical to a
message sent by a correct node.  Since a node cannot differentiate
senders in asynchronous radio networks, identical messages are merged
in \emph{DEP}. Note also, that a match may not be found because the
faulty node may send a spurious conflict message or the conflict
message is in reply to the faulty node message that $u$ does not
receive. Node $u$ removes the unmatched message. Also, $u$ removes the
cycles and sinks of \emph{DEP} that are not \emph{announce}. Observe
that \emph{DEP} may grow indefinitely as faulty nodes can continue to
send arbitrary messages.

Due to no-snare and transmission range assumptions, for every correct
process $u$ the following is guaranteed about \emph{DEP}:
\begin{itemize}
\item Eventually, $u$ receives an announcement from every correct node
in its neighborhood. An announcement from each correct node will be
confirmed by every correct node. There will be no messages from the
correct nodes that conflict with any other messages from the correct
nodes.
\item Eventually, every message from a fictitious node will be
followed up by at least one \emph{conflict} message sent by one of the
correct nodes from the neighborhood of $u$.
\end{itemize}

\noindent
\textbf{Concrete universe detectors.} We define the
\emph{concrete} detectors $c\cal SPU$, $c\cal WPU$ and $\diamond
c{\cal PU}$ as the detectors that accept the \emph{DEP} provided by
$\cal SAND$ as input and whose output satisfies the specification of
the corresponding abstract detectors described in
Section~\ref{SecDetect}. That is, for each correct node $u$, $c\cal
SPU$ only outputs complete and real universe, $c\cal WPU$ may output a
real universe that is not complete, while $\diamond c{\cal PU}$ may
provide arbitrary output for a fixed number of computation
states. However, all three detectors eventually output the complete
and real universe for $u$.  Observe that the detectors have to comply
with the specification even though \emph{DEP} may grow infinitely
large.

In $\cal SAND$, each process $u$ observes the output of the detector
and immediately outputs the universe presented by the detector without
further modification. By the construction of $\cal SAND$ proves the
following theorem.

\begin{theorem} \label{trmSAND} Considering layouts without simple
snares and assuming that the transmission range is at least twice as
large as the neighborhood distance, the Sybil Attack Neighborhood
Detection Algorithm $\cal SAND$ provides a conflict-aware
deterministic solution to the Neighborhood Discovery Problem as
follows: $\cal SNDP$ if $c\cal SPU$ detector is used; $\cal WNDP$ if
$c\cal WPU$ is used; and $\diamond {\cal NDP}$ if $\diamond c{\cal PU}$
is used.
\end{theorem}

Similar to Chandra et al~\cite{CHT96} we can introduce the concept of
a weakest universe detector needed to solve a certain problem.  A
universe detector $\cal U$ is the \emph{weakest} detector required to
solve a problem $\cal P$ if the following two properties hold:
\begin{itemize}
\item there is an algorithm $\cal A$ that uses $\cal U$ to solve $\cal P$;
\item there is another algorithm $\cal B$ that uses the input of an
arbitrary solution $\cal S$ of $\cal P$ to implement $\cal U$.

\end{itemize}

\noindent
That is, $\cal B$ uses the output of $\cal S$ and provides the
computations expected of $\cal U$. The intuition is that if any
solution can be used to implement $\cal U$, then every solution needs
the strength of at least $\cal U$. Hence, the idea that $\cal U$ is
the weakest detector.

Observe that $\cal SAND$ provides the solutions using these detectors
to the respective problems.  Note also that the outputs of the
neighborhood discovery problems that we defined $\cal SNDP$, $\cal
WNDP$ and $\diamond\cal NDP$ can be used as the respective universe
detectors $\cal SPU$, $\cal WPU$ and $\diamond\cal PU$. For example,
if a process $u$ in $\cal SNDP$ outputs its neighborhood set, this
neighborhood set can be used to point to the real universe. Hence the
following proposition.

\begin{proposition}
Concrete universe detectors $c\cal SPU$, $c\cal WPU$ and $\diamond
c{\cal PU}$ are the weakest detectors required to solve $\cal SNDP$,
$\cal WNDP$ and $\diamond\cal NDP$ respectively.
\end{proposition}

\section{Detector Implementation and Future Research}\label{SecEnd}

\textbf{Detector implementation.} According to
Theorem~\ref{trmNotSolvable}, the universe detectors employed by our
solution to the neighborhood discovery problem are not themselves
implementable in asynchronous systems. The actual implementation of
the detectors can depend on the particular properties of the
application. Here are a few possible ways of constructing the
detectors. The nodes may be aware of the bounds on faulty nodes
speed. That is, the detectors will know the maximum number of
fictitious nodes they have to deal with.  The nodes may contain some
topological knowledge of the network. For example, the nodes may know
that the network is a grid. Alternatively, the nodes may have secure
communication with several trusted neighbors to ensure their presence
in the selected universe.

\noindent
\textbf{Future research.} We conclude the paper by outlining
several interesting areas of research that our study suggests. Even
though the concrete detectors we describe in the paper are minimal
from the application perspective, it is unclear if the input that
$\cal SAND$ provides is optimal. That is, is there any other
information that can be gathered in the asynchronous model that can help
the detector decide if a certain universe is real. We suspect that
$\cal SAND$ provides the maximum possible information but we would
like to rigorously prove it.

In this study, we assume completely reliable communication within a
certain radius of the transmitting node $R_{min}$. However, in
practice the propagation patterns of low-power wireless radios used in
sensor and other ad hoc networks are highly irregular. See for example
Zhou et al~\cite{ZHKS04}. The problem of adapting a more realistic
communication model is left open.

Another question is the true relationship between the universe and
fault detectors. Observe that unlike fault detectors, the universe
detectors require additional layout properties to enable the solution
to the neighborhood discovery. It would be interesting to research if
there is a complete analogue to fault detectors for this problem.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


I listen to a lot of music. While I will listen to some albums a few times and move on, some stay with me. This post quantifies the albums from 2017 that stayed in my life in 2018.
Each December, I compile a list of my favorite recent albums from the past year. People really enjoy reading lists, so pretty much every music publication also releases a end-of-year list around the same time 1.
As fun as it is to parse through yearly lists, liking an album is no guarantee of future streams. Sometimes there are albums like Sufjan Steven's Carrie & Lowell which, although exceptional, are do not exactly make the best background music for homework. Other times I might really en joy an album on repeat for a period of time, but I eventually move on the something else. I might get a nice feeling of nostalgia looking back at the record and how I now associate it with that time period, but there would be no way to replicate that initial infatuation.
In the streaming era, my music library is sometimes a bit like a midnight refrigerator run: there's always plenty inside, but at the moment I might just be looking for something quick and easy. Thus this list is probably best described as my musical comfort food. There are the albums from 2017 I had on repeat in my head and in my ears throughout 2018.
Now I'll say a few words about some of the albums on this list.
The prolific UK-based singer-songwriter has released a masterpiece. Featuring production from the likes of A.G. Cook and SOPHIE, Pop 2 is a celebration of future-facing pop music with catchy hooks and hyper-glossy production.
I was completely blown away by this on my first listen. Jack Antonoff joined Lorde as executive producer and together they crafted a record full of unexpected hooks and sleek arrangements. The fact that this album is even being compared to Kate Bush's Hounds of Love is a testament to the songwriting chops of the young singer-songwriter.
Honestly I really wish that XCX3 got released last year as planned, but these two mixtapes are possibly the greatest consolation prize possible. PC Music-era Charli XCX just plain works. Perhaps the most impressive accomplishment in these mixtapes is her ability to feature so many other artists while at the same time not being overshadowed in the slightest.
I love the sound and aesthetic of pop music from the late 90's and early 2000's. It's hard for me to describe, but there's just a level of confidence to it that is difficult to reproduce. While Rina Sawayama by no means tries to replicate the sound, she channels it perfectly in this Clarence Clarity-produced EP.
Does Hayley Williams have one of the best voices in today's music industry? Yes. Does Paramore keep getting better and better over time? Also yes.
This was late release (early December) and it did not receive very much attention from the music press. Nonetheless, I found it to be a very enjoyable winter album with a raw yet removed approach to its emotional subject matter.
Heartland synthpop drenched in irony and social commentary. Cameron is simultaneously hilarious and thought-provoking.
Bubbly production and chippy songwriting. It's a concept album. I still don't quite get the concept, but that's okay.
I didn't really get into this release until late this year. Wow, there are some good songs in here! Another great winter album with a lot of sad subjects, but also some intimate and emotional arrangements.


The Sigelei 100W box mod does exactly what it says it does. It provides you with a huge 100W of power resulting in huge vapour and great flavour. Perhaps not the most stylish of box mods, but it certainly packs a huge punch.
The SIGELEI 100W BOX MOD. This extremely advanced device allows for wattages up to 100 watts and has sub-ohm compatibility for more advanced vapers. Attractive and small, this box mod is very powerful for its size. Adjustable up to 50.0 Watts in 0.1 W increments, and between 50 and 100 watts in 1.0 watt increments.


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UV Safe introduces tabletop sanitizer under 'MY' for locations with heavy usage
Coimbatore, 3rd December 2020: The country has seen multiple lockdowns and lifting of the same in the efforts to stop the Covid-19 in its tracks. The opening of malls, theatres, and corporate offices triggered whoops of joy among the public at large. There's a lot of awakening around the need for safety and sanitization that is now an integral part of every individual's lifestyle. 'MY' UV Safe, a made in India product comes with a 40-litre table top sanitizer and has a one-touch safety knob with interactive LCD Screen.
Featuring a polycarbonate Glass Top, wrapped around a metal grill, 'MY' UV Safe allows sanitization of anything from grocery to shoes with ONE touch. The inbuilt feature allows for setting a timer and sanitizing objects on all sides, killing the bacteria and viruses in one go.
Commenting on the product, Mr Kavin Kumar Kandasamy, Co-founder and CEO of 'MY' said, "We are happy to introduce our products that should be integral to everyone's life. Safety is now a critical factor while stepping out of the house. MY UV Safe can be used anywhere, from your house or at restaurants and corporate offices. You can sanitize your entire grocery, laptop bags, takeaway food items, the packages delivered at home. We live in times when sanitizing everything we touch has become an important part of our lifestyle. We are sure that UV Safe will only make this process easier."
Current: UV Safe introduces tabletop sanitizer under MY for locations with heavy usage