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An analytical essay involves summarizing and evaluating an event by breaking the topic down into parts and providing evidence that supports your claim. The event can be a political situation, a social phenomenon, or a historical event. It can also be a literary work, a movie, or a performance. You can also be asked to analyze an issue or an idea.
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Start by jotting down the relevant information that you have gathered under the relevant section. Figure out the arguments you want to stress on and provide appropriate evidence to back it up.
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Minimal Chords is a free pack by Sample Modern containing 6 midi minimal chords, and 68 wav loops for House, Trap, Club, Trance & many more experimental genres.
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Mkhitaryan Production has released Frutis, a free collection of loops and NI Massive presets for EDM music production. And this is an update of the pack by Sample Modern available for download.
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Event Horizon – Free Loops
Event Horizon is a collection of royalty free loops that are all made from the patches in DUNE 2 soundbank called "Event Horizon" by 123Creative.com.

subset: commoncrawl


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This week Bobbi Conner talks with Dr. Elisha Brownfield about specific vaccinations that are recommended to prevent infectious disease and complications in older adults. Dr. Brownfield is an Associate Professor of Internal Medicine at MUSC.
Health Focus is a production of the Medical University of South Carolina in partnership with South Carolina Public Radio.
About the Author
Bobbi Conner
Keywords: Health Focus, Geriatrics, Healthy Communities


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Weight controlGreen tea extract
Green tea extract
- Helps slim down
- Optimizes the detoxification process (detox)
- Prevents high blood sugar and cholesterol levels
- Keeps blood vessels open
- Stimulates the functioning of the heart
- Very strong antioxidant
The studies on weight loss due to green tea are contradictory. This is because dietary supplements containing decaffeinated green tea extracts have no effect on weight management. In addition, several clinical studies show that the use of green tea extract with caffeine has a positive effect on weight control, weight loss and waist circumference compared to placebo.
- Phung et al. Effect of green tea catechins with or without caffeine on anthropometric measures: a systematic review and meta-analysis. Am J Clin Nutr. 2010 Jan;91(1):73-81.
- Hursel et al. The effects of green tea on weight loss and weight maintenance: a meta-analysis. Int J Obes (Lond). 2009 Sep;33(9):956-61.
- Auvichayapat et al. Effectiveness of green tea on weight reduction in obese Thais: A randomized, controlled trial. Physiol Behav. 2008 Feb 27;93(3):486-91.
Green tea has a beneficial effect on the amount of cholesterol and triglycerides (fatty acids) in the blood. Clinical research shows that the consumption of green tea significantly reduces the total amount of cholesterol and bad or LDL-cholesterol. Conclusion? The daily consumption of green tea standardised at EGCG reduces the risk of arteriosclerosis (arteriosclerosis) and also causes less damage to the vascular endothelium or the inner wall of the blood vessels. Epidemiological research has shown that drinking green tea is associated with a 28% reduced risk of coronary heart disease.
- Miyawaki et al. "Benifuuki" Extract Reduces Serum Levels of Lectin-Like Oxidized Low-Density Lipoprotein Receptor-1 Ligands Containing Apolipoprotein B: A Double-Blind Placebo-Controlled Randomized Trial. Nutrients. 2018 Jul 19;10(7).
- Wang et al. Black and green tea consumption and the risk of coronary artery disease: a meta-analysis. Am J Clin Nutr. 2011 Mar;93(3):506-15.
- Maron et al. Cholesterol-lowering effect of a theaflavin-enriched green tea extract: a randomized controlled trial. Arch Intern Med. 2003 Jun 23;163(12):1448-53.
Epidemiological research suggests that adults who consume green tea daily are less likely to develop type 2 diabetes. This is because green tea has a positive effect on HbA1c. The HbA1c value provides an insight into the average blood glucose value of the past 6 to 8 weeks. Green tea regulates the blood sugar level and lowers the HbA1c value, a risk factor for the development of diabetes.
- Huang et al. Associations of green tea and rock tea consumption with risk of impaired fasting glucose and impaired glucose tolerance in Chinese men and women. PLoS One. 2013 Nov 18;8(11):e79214.
- Toolsee et al. Effectiveness of green tea in a randomized human cohort: relevance to diabetes and its complications. Biomed Res Int. 2013;2013:412379.
- Iso et al. The relationship between green tea and total caffeine intake and risk for self-reported type 2 diabetes among Japanese adults. Ann Intern Med. 2006 Apr 18;144(8):554-62.


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Sexclub Noblesse is not only well known in the Nijmegen and Boxmeer region, but is a concept throughout the Netherlands. We stand for ultimate hospitality and discretion. Our attractive, friendly and extremely sensual ladies come from all over the world.
In our nightclub you can relax at a high level. In a relaxed atmosphere and while enjoying a drink at the bar, you can choose from one of the many attractive ladies who are present that day. We welcome you as a guest in our special ambiance. At Sexclub Noblesse you will find a pleasant mix of personal attention, relaxation, seduction and eroticism, according to your wishes. In this discrete environment you will find ultimate enjoyment, in pleasant company.
Times and days that our ladies are present can vary. Our offer of guest ladies changes regularly, so let yourself be surprised every now and then.
Of course, personal hygiene and discretion are extremely important to us. Our guest ladies are always taken care of to ensure your safety and that of our ladies. Our customers can also expect that their personal hygiene is in order. We work with a permit and in accordance with national guidelines for hygiene and safety.
Our girls decide for themselves which actions they do or do not want to perform. If you have personal wishes, please let our ladies know in advance. They will do everything to fulfill your wishes and let you enjoy from head to toe.
Beautiful blond girl of 27 from Romenia. Maya has a cup size B and she speaks English.
Beautiful dark girl of 26 from the Dominican Republic with black hair and brown eyes. Lola is 165 tall, cup size C and she speaks Dutch.
Enticing slim Hungarian girl of 25 with blond hair and brown eyes. Elvira has a B cup, is 170 tall and speaks Dutch and English.
Slim Romanian girl of 22 with brown eyes and brown hair. Emma is 155 tall and has a B cup. She speaks English and Spanish.
Sexy Russian girl of 30 with red hair and brown eyes. Mira is 160 tall with a slim build and C cup. She speaks Dutch and English.
Polish girl at the age of 21 years with light brown hair and brown eyes. Kelly is 172 tall and has a cup size B. She speaks English.
Rumanian sexy girl of 26 years old with brown eyes. Ela is 165 in size and has a cup size of C. She speaks English and German.
A 34-year-old Brazilian girl with brown eyes and black hair. Ruby is 175 in size and has a cup size of G. She speaks Dutch, English and Spanish.
South American girl, 23 years old. Has brown eyes and brown hair. Tatiana is 160 in size and has a cup size C. She speaks Dutch, Spanish and English.


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Much more than he bargained for… "You want me to find you a wife?" "No. I want you to be my wife." Garrett Song is this close to taking the reins of his family's LA fashion empire…until the Song matriarch insists he marry her handpicked bride first. To block her ... more >
Inspired by the true story of a kleptomaniac cat who stole his way into America's heart . . . KITTENS CABOODLE As a tabby cat with criminal tendencies, MacGyver is always a whisker away from trouble. But when he stumbles upon a litter of four motherless kittens, he really has ... more >
Meet Nina Hill: A young woman supremely confident in her own…shell. The only child of a single mother, Nina has her life just as she wants it: a job in a bookstore, a kick-butt trivia team, a world-class planner and a cat named Phil. If she sometimes suspects there might ... more >
Dear Ms. Guillory, I was on the fence about reading The Proposal because of a controversy regarding this interview with you at Bitch Media. The interviewer presented your debut novel as revolutionary because it was "a romance novel written by a Black woman with a Black woman protagonist that was ... more >
Susan Orlean, hailed as a "national treasure" by The Washington Post and the acclaimed bestselling author of Rin Tin Tin and The Orchid Thief, reopens the unsolved mystery of the most catastrophic library fire in American history, and delivers a dazzling love letter to a beloved institution—our libraries. On the ... more >
Remedial Rocket Science by Susannah Nix I picked up this book when it was available for free, and since I'd heard good things about it, I actually read it, unlike with some freebies that merely clutter my kindle. The blurb describes Remedial Rocket Science as a romantic comedy, with comparisons ... more >


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Six tips to make sure your jog bra fits you perfectly.
Find the bra that will keep you cool and comfortable on your next run.
A bra with multiple fit options and good support.
A breathable bra that provides support and limits bounce.
Running better, from head to toe.
Three no-diet plans for getting a bit thinner, a lot healthier, and fit enough to run a marathon.
Iron-deficient women can boost their aerobic capacity by simply increasing their iron intake.


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Firstly make sure you are at your best today!
Hello visitors and friends,
I will love to share some of my knowledge on "Computer Programming" with some of you who are willing to learn.. If you are a programmer, please let make this interactive for new comers and beginners by dropping your comments or point of view.. Thank you..
Also Read: How To Generate Business Ideas
In my own view - Programming is the process of writing, testing, debugging/troubleshooting and maintaining instructions (source code) for solving a problem with the computer.. Programming can also be said to be "CODING".. (Drop your definition of Programming in the comment box), we are all here to learn, improve our skills and impart one another..
Programming is a lot of fun and extraordinarily useful.. While you learn to program, you'll also develop a host of other analytical and critical thinking skills for tacking all sorts of complex problems (not just ones on computers) and it may just help you start a new career or land a new job in software development..
Computer programming is almost always done in some sort of programming languages. These languages are written so that humans can understands them, but are formal and rigorous enough to input into a computer machine.
I shall continue in "Part 2" ... Drop your view, let's learn together.. Thanks for stopping by...


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BlackBerry and Facebook
BlackBerry devices are perfect for social networking sites like Facebook because of their easy to use keyboard and camera features. There is little you can do on Facebook with a BlackBerry that you can't do with a computer. However, some problems will arise when using this combination, and you may have to reset your Blackberry or try alternate methods for posting photos. In this article, we'll discuss a few common BlackBerry Facebook issues and how to resolve or work around them.
BlackBerry Problems Uploading Facebook Photos
On my own BlackBerry, I have never been able to upload a photo directly to Facebook by using the app. When I take a photo and bring up the menu to 'Send to Facebook', it tries for a few minutes then tells me it failed. As you might expect, I found this very aggravating because I was looking forward to being able to upload photos from my smartphone directly to Facebook. I did finally figure out a way around the problem.
Facebook will actually provide an email address for mobile phone users to send photos to, as opposed to sending them through the Facebook app. Just follow these steps to get your BlackBerry Facebook email:
- On your computer, go to https://www.facebook.com/mobile.
- On the bottom left of the web page, you'll see an 'Upload Via Email' section and it'll list your photo upload address.
- Add that email address to your contacts and give it a name like 'Facebook Photo'.
- Now, when you take a photo, just choose 'Send via email' and send it to the Facebook Photo contact.
- The subject of your email will default to the filename, but you can change it to display whatever you want for the photo caption on Facebook.
- After a couple of minutes, you'll get an email confirmation from Facebook that your photo was received, then it'll show up on your Facebook account under Mobile Uploads in the Photos section.
(Image credit: Facebook.com screenshot)
Update the Facebook App
If you are having BlackBerry Facebook issues, it could be that you're using an older version of the app. I've found that the BlackBerry isn't always good about notifying you of software updates so you may be running an outdated version and not know it.
From your BlackBerry, just go to https://www.facebook.com/mobile and it'll provide a link to download the latest version. After you install it, try getting back on Facebook and see if the issue still exists.
Facebook Locks Up on BlackBerry
Every BlackBerry user should know that you have to pull your battery out and reset the device on a fairly regular basis. I compare this to earlier versions of Windows that needed to be rebooted at least once a day. I have found that the more data transfers I do like with web browsing and utilizing Facebook, the more often I need to perform a battery pull. The one app that causes my BlackBerry to lock up more than anything else is Facebook.
If your BlackBerry seems to be sluggish while accessing Facebook, such as when photos are excessive slow to load or you keep getting the spinning hourglass icon no matter what you click on, it's time for a battery pull. Once the BlackBerry starts doing this with Facebook or any other app, it could mean that you're on the way to a BlackBerry WSOD (White Screen of Death) and then you'll have to do a battery pull, anyway.


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Get the Look: Ombré Bun
There are many ways to wear Cashmere Hair Clip-Ins. Make fuller buns & even change the color of your hair with a little help from Cashmere Hair.
There are many ways to wear Cashmere Hair Clip-Ins. Make fuller buns & even change the color of your hair with a little help from Cashmere Hair.
Trying to find the perfect match for your hair? Now you can with the Cashmere Color Swatch Store we have available for you to choose your perfect color match.
At recent photo shoot with the sexy Jesse Jane & photographer Raquel Rischard, Cashmere Hair in shade CALIFORNIA BLONDE was added to the Bombshells already gorgeous locks for extra fullness and volume. A perfect match that made this sexy lady even more sexy!
CASHMERE HAIR Clip in extensions are the Perfect Accessory for Gorgeous Wedding Day Hair! Every bride wants to look picture perfect on their wedding day, from the perfect wedding dress to the perfect wedding hairstyle.
In a recent issue of Metropolis Nights Magazine, a spread featuring Sunset Blonde interviews her on her new company CASHMERE HAIR, and she is also wearing the gorgeous Clip-In Hair Extensions in the photos: " "
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Day 1: Cairo Airport & Transfer to your Hotel in Cairo
Upon arrival in Cairo representative who will assist you through passport control formalities, luggage identification & portage will greet you. From the airport you will be transferred by a private A/C car or mini-bus to your hotel to check in and overnight.
Day 2: (B+L) Cairo Day Tour
Following breakfast at the hotel your guide for the day will pick you up and transfer you to Giza, legendary as the majestic Pyramids of Cheops, Chephren and Mykerionos to view these spectacular man-made monuments. Afterwards a tour of the great Sphinx; guarding the Royal Burial Chambers and temple of Cheops. After that transfer you to the Egyptian museum of antiquities, which was established in 1902 near the city center in Cairo. On display is a rare collection of 5000 years of art — the largest most precious collection of Egyptian art in the world. Over 250,000 genuine artifacts are presented, including an exhibit dedicated to the Tutankhamen collection of treasures, gold, and jewelry, as it was enclosed in his tomb for over 3,500 years before it was discovered in the 1920's when his tomb was excavated. Next on the itinerary is Coptic Cairo home of some of the oldest Christian churches in the world and retrace the steps where Mary and Joseph walked thousands of years ago. We will visit the Hanging Church, also known as El Muallaqa that was dedicated to the Virgin Mary and it was believed to have been built at the end of the 3rd century. Following is a visit to the Church of St. Sergius, a perfect example of Coptic churches and monasteries. It was founded at the end of the 4th century and it stands on a crypt that is said to have sheltered the holy family during their flight from Egypt. In the afternoon we will visit the Khan El Khalili Bazaars that dates back to 1382. Shops in this district are legendary for fine brassware, copper, perfumes, leather, silver, gold, antiques and more! Everything for sale in these shops is negotiable, be prepared to bargain for goods sold in this exciting maze of shops!
At the end of the day we will transfer you back to your hotel. Overnight in Cairo. Optinal: Cairo Nile Dinner Cruise & Show. OR Sound and Light Show at the Pyramids of Giza.
Day 3: (B) Transfer to Cairo Airport & Final Departure
Following breakfast at the hotel representative will pick you up and transfer you to the airport and assist you at the airport through final departure.


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FanTeam CL Wednesday (11th March) – Free Ticket Giveaway Now I'm not usually one to boast (fantasy cricket aside) (and Ilicic ) but having already had a couple of winners at Cheltenham yesterday I was feeling a bit lucky and so when I got a call from the good people at FanTeam asking if I fancied a few free trial tickets for their Tuesday night CL games I naturally thought 'oh go on then, why not…'. Three hours later and I was suddenly €530.44 richer! And it took me about 2 minutes to enter. And I only came 4th. Seriously… To celebrate this we are offering you all the chance to do likewise. There are two levels of free entry here; NEW USERS* If you are new to FanTeam you can claim a €20 ticket to tonight's CL game simply by clicking here to register and ...[Read More]
CL Tuesday New format: Pursuit (10th March) – Preview Finally, the second legs of the Champions League round of sixteen begin, starting on Tuesday with Leipzig-Tottenham and Valencia-Atalanta. Sign up here! First of all I have prepared a table for you again: Here are the 4 teams that will play this Tuesday. We can see their probability of winning, the probability of them scoring a goal and the probability of them having a clean sheet. It quickly becomes clear that Leipzig outperforms in all categories and Tottenham is the tail light. Leipzig wins by 62%, Tottenham only by 16%, Leipzig scores 86%, Tottenham only by 59%. Accordingly the clean sheet probabilities: As usual, we look at the defensive lines of all 4 teams first. For this we take the average price at Fanteam.com of the 4 most exp...[Read More]
Fanteam announces record-breaking €500,000 Fantasy Event – SCOFF 2020 Our valued partner Fanteam is doing the unbelievable! They are launching a Fantasy Football Event, which has a total guarantee of €500,000. This is by far the biggest Premier League contest in the history of Daily Fantasy Sports! The event is called SCOFF – Spring Championship of Fantasy Football and covers the last Premier League gameweeks. Why we are telling you this now then? Because you can already start to register for it; for the entry fee of €1. Yes, this is right, you are given the chance to turn €1 into €150,000 by playing Fantasy Football. Take some years off from work, buy a Lamborghini, or just use it as a deposit for your house; all sorts of things are possible with this win! It's also possible to safe...[Read More]
WCOFF winner did not tell anyone he was playing the Final The winner of this year´s World Championship of Fantasy Football on Fanteam is from Scotland. User 'fscottl' won the first prize of €30,000 by entering one of our €2 Euro qualifiers and playing his way to the top! The father of 4 boys works offshore on an oil rig and watches Premier League matches on the sea at night with his colleagues. Read our interview with the fresh crowned World Champion of Fantasy Football as he tells us how he approached his way to the top, how he built his winning squad and what he is going to do with all that money! As fscottl answers the phone, he is in a very cheerful state. We notice that he is genuinely happy about his triumph and seems very thankful throughout the entire interview. Hi fscottl! Thanks ...[Read More]
WCOFF 2019 – 'fscottl' turns €2 into €30,000! UK DFS NEWCOMER "fscottl" TURNS €2 TO €30,000 & WINS THE 3RD WORLD CHAMPIONSHIP OF FANTASY FOOTBALL ON FANTEAM You can´t make a story like this one up! An unbelievable effort by new DFS player 'fscottl' is worth a new car now. The UK-based Fantasy-Newbie left everyone behind and made his way up from paying €2 for a qualifier to getting paid €30,000 as the winner of WCOFF 2019! It was a thrilling Finale in the 3rd World Championship of Fantasy Football! 116 participants qualified through satellites or paid the entry fee of €1050. A €100,000 guaranteed prize pool grew to €116,000 while the first prize was endowed with €30,000. After the first round last Saturday, user 'fscottl' took the lead with 88 points, well helped by De Bruy...[Read More]
Guide to 50k Weekly Monster GW 7 – Teams & Players to watch In this week's competition the SHU vs LIV early game is left out so we will not include the likes of Salah, Firmino or Mane in our team. Same goes for Sheffield United players. As the obvious picks from Manchester City should not be worth a long discussion, we will concentrate on the possible differentials, which can produce points for your Fantasy Squad. Tottenham Although Spurs have been mediocre at best, they play Southampton at home on Saturday. They have conceded 9 goals so far which is not that bad, but Spurs are coming off a huge defeat against Leicester last GW. We expect this to be a high scoring game and there is only one guy we would spend our money to get into our team. Son has already bagged 2 goals and 2 assists...[Read More]
Fanteam's €100,000 Champions League Fantasy Game The guys at Fanteam are back with an all new fantasy tournament and this time they are going for Europe's Elite! As advertised the prize pool is a guaranteed €100,000 to be shared between 600 rankings as well as best GW manager and highest round-score of the group stage. This tournament will not run for the whole UCL event but ONLY of the group stage so just for 6 Gameweeks. If I am honest this is better than the original UCL Fantasy where you have a Wildcard at every stage as the teams tend to template. Top 10 managers at the end of the tournament will win 4-digit cash prizes as per below table! Test your knowledge of the game at a European level and use the skills you acquired over the years playing FPL to win some cash. Game Rules •...[Read More]
Beginner's guide to DFS Football Beginner's guide to DFS Football With the top football seasons underway, we are giving you an extended guide to Daily Fantasy Football on Fanteam. As the amount of members on the platform grows and continuously increasing guaranteed prize pools can be seen in the Fanteam Tournament-Lobby, this is your chance to convert your Football expertise into real money. Whether you are a Football expert, stepping into the Fantasy Sports world, or an actual FPL player, who wants to break into the realm of Daily Fantasy Football: this is your guide to begin with! What is Daily Fantasy Sports (DFS)? At first, the general concept of DFS looks very simple: you choose players and receive points for their individual actions on the pitch. In the end, the team with...[Read More]
FanTeam season long €250,000 game; late registration? Why everyone should consider late registration on FanTeam for the Premier League season game? The upcoming reasoning applies for all of the players, no matter if you already have one or more teams in the competition. So, you definitely should read this through. For instance, me myself (and I!) have 6 teams in the competition since the first gameweek, and currently I'm thinking about the number of teams that I will construct before the start of the second gameweek. This all despite that I had a pretty decent first round. From all six teams I scored 77,5 to 100 points, but now let's get to the point. Main reason: Overlay, overlay, overlay… No matter whether you're playing DFS, sports betting, poker, casino games or whatever, you sho...[Read More]
FanTeam GW2; Join the €50,000 Monster game (for free!) Having already launched a ridiculously monied season long game the guys over at FanTeam don't stop there as they have fantastic weekly prizes to feast on too. The catch, you ask? Well, the catch is usually that you have to back yourself a bit by buying in to the game each week. This week's main game has a buy in of €20 but with a prize pool of €50,000 this could be easy money for our experienced FPL'ers. Our patrners are ever generous though and as such we have 5 FREE ENTRIES to give away this week to our community. Each one is worth €20 (obviously). And winning one couldn't be simpler; HOW TO GAIN FREE ENTRY To enter our free prize draw all we ask is that you post your FanTeam handle (nickname/username/call it ...[Read More]
How to play the €250,000 GTD season game on Fanteam This year the season game is even more interesting than usual. The reason is Fanteam's huge game with €250,000 guaranteed to be paid out. If you play well enough, you could exchange €25 with €50,000! There are many interesting aspects of the seasonal fantasy game. In this article we will look at some of them. At the end of the day, what matters is which players YOU decide to pick. But we have some ideas that you may want to consider. Advice number 1: Don't spend too much money on forwards In our experience, the forwards generally are priced too high in the season game. Very few forwards return enough points to justify their high price. Since the expected value is low, mathematics dictate that we should not put in much money for players in...[Read More]
Fanteam offers a €250,000 Fantasy Premier League Season Tournament Dear Community, as the pre-season is getting more interesting and you are already starting your analysis of the prices and fixtures, we have some big news for you. Our new £500 Regulars League sponsor, Fanteam, is offering a Premier League season game with a prize pot of an incredible €250,000. If that already sounds interesting to you, just wait for the following information. The first prize receives €50,000 and to be in the top 20 would still grant you a minimum payout of €1,500 (and that is ignoring the additional weekly and monthly prizes). Now you might think that the entry fee will be extremely high, but you can get a chance for life-changing money with only €25. (Yes, we couldn't believe it at first either). We will ...[Read More]


text:
Please read below current news on the project:
Articles listed on subsequent pages but recent coverage from these outlets (so far ....) :
An inspirational talk by John Davidson, former special forces soldier rowing the Atlantic solo to raise funds for Motor Neurone Disease.
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'Today I was invited to a local school, The Downs School Malvern, to inform the children of my Atlantic Challenge and why I was doing it. I was also lucky enough to take my boat with me so the children could see my home for the 50-60 days at sea.
It was also an honour to be able to talk the School about the Charity (Doddie5 Foundation) I am doing this challenge on behalf and Motor Neurone Disease and why I am fundraising to help find a cure. The school has a great charitable ethos and gets the children involved in regular fundraising efforts.
Alistair Cook, Headmaster, The Downs School Malvern:
'It's absolutely wonderful that John was able to join us on our 'Dress Green for Macmillan Day' today. Not only did the children hear of John's very ambitious challenge to raise money for Motor Neurone Disease, but they were also able to celebrate wonderful fundraising achievements for Macmillan Cancer Support and St Richard's Hospice. We wish John all the very best here at The Downs Malvern.'
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Link to the article can be found here: https://www.worcesternews.co.uk/news/16953994.ex-sas-soldier-tells-malvern-pupils-about-quest-to-row-solo-across-the-atlantic/
John Davidson took his 'Mad Giraffe' boat to The Downs Malvern last week to talk about his epic challenge for the My Name'5 Doddie Foundation which raises funds for research into Motor Neurone Disease (MND).
The 56-year-old, who lives in Worcestershire, is taking part in the Talisker Whisky Atlantic Challenge in December with the aim of raising £1million after being inspired by rugby legend Doddie Weir, who has MND.
John said: "I took my boat with me so the children could see my home for the 50-60 days at sea. I was able to regale them with tales of the sea life I would see –
"The children asked great questions such as: What wildlife will I see in the water? What kind of food will I take? Will the chocolate melt in the boat? And, how do I sleep when it's bumpy on the water? And of course, very importantly, where will I go to the toilet?"
John added: "It was an
"I would ideally like to get as many local schools involved as possible in helping create some giraffes for my boat. The top five can then be turned into stickers to go on my boat so it can help give me a boost as I get across the ocean.
"Any schools who are interested, please do get in touch."
Downs School headmaster Alistair Cook said the pupils were fascinated by John's challenge.
Father-of-four John, originally from Dundee, was inspired to take on the row after meeting fellow Scotsman Doddie.
John, who joined the army aged 19 and served until 1996, and was in the SAS, is one of eight solo rowers taking on the quest this year, which begins on December 12, weather depending.
It will take him one million strokes of the oar to cross the 3,000-mile expanse, and he hopes to reach his £1million target by encouraging everyone who hears his story to donate at least a £1.
"Most people signed up for the challenge two years in advance, but I did it with just six months before it starts, so I'm having to do a lot of catching up with my training," he said.
"I had a '55-year-old sit at a laptop 12 hours a day body' but thankfully muscle memory and determination has meant intensive training sessions have had to kick in and kick start this body back into shape fast. The mental side will be the biggest challenge because you're in a boat on your own for all that time and you have to force yourself to keep
John, who has run a consultancy company since leaving the forces, added: "There's a tendency to think that the adventure in your life is over by the time you hit 50, so it's a great thing to show that you can always do something a bit crazy like this, no matter your age."
See madgiraffeatlanticrow.co.uk for more
With great thanks to HRH Princess Anne for sending me a letter of support for my Atlantic Challenge. As Patron of the MNDA and Scottish Rugby Union this endorsement means a huge amount to me and the My Name Doddie'5 Foundation.
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A Dundee-born veteran wants to raise a £1 million for Motor Neurone Disease by rowing solo across the Atlantic ocean in a death-defying challenge.
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John Davidson, 56, plans to undertake the gruelling journey wearing a kilt and with just 180 days of training, compared to the two years normally required to prepare for the perilous journey.
The former SAS soldier and "proud Fintry boy" said although there have been deaths during the challenge in the past, he is not worried and is ready to face the sea despite never having rowed before.
John, who now lives in Worcestershire, was inspired to sign up for the Talisker Whiskey Atlantic Challenge, beginning on December 12, after meeting with rugby legend Doddie Weir.
All money raised would be donated to the My Name'5 Doddie Foundation, which funds research into MND.
John said: "I met Doddie at a Scotland-England game when I was with my son Hamish.
"Hamish had been told by his school that he was too small to play rugby and Doddie took great offence to that.
"He took him under his arm and gave a truly inspirational speech about how we shouldn't let anything hold us back. Hamish is now 12 and he is playing rugby.
"Doddie was such a great inspiration and it was devastating to hear that he had been diagnosed with MND.
"I decided that I wanted to raise awareness and money for for this cause and with my background, I wanted to do something that would really push the limits.
"I have never rowed before but I'm confident that I will be able to prepare for this challenge."
John will be rowing from the Canary Islands to Antigua in a small boat called the Mad Giraffe.
There has only ever been 85 people who completed the challenge, called 'the toughest endurance race on the planet', which should take an average of 60 days at sea – rowing 18 hours a day and consuming 8,000 calories.
John added: "I expect to lose around 15 to 20kg in body weight. More people have climbed Everest than have rowed the Atlantic Ocean.
"If something goes wrong, it would be three to four days before help would come, so I'd be on my own out there.
"I want to show people that you can still achieve great things when you're over 50 and I want to inspire people in Dundee – I live in Worcestershire now but I'm a proud Fintry boy."
To sponsor John, visit https://www.justgiving.com/fundraising/madgiraffeatlanticrow
Link: https://www.thecourier.co.uk/fp/news/local/dundee/718937/pics-and-map-to-come-sas-veteran-and-proud-fintry-boy-to-row-across-atlantic-for-mnd/
Radio Interview with Justin from BBC Hereford and Worcester
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Justin came across today to see the boat and record an interview to be broadcast on BBC Hereford and Worcester. A tour of the boat and training 'centre' with an inclusion of the Wilson ball (which will accompany me across the Atlantic) from the lovely Perry family. Details on broadcast date to be confirmed.
Worcester News Interview with Michael Purton
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A FORMER special forces soldier will row solo across the Atlantic to raise £1million for charity after being inspired by rugby legend Doddie Weir.
John Davidson, 56, is taking part in the Talisker Whisky Atlantic Challenge to support the My Name'5 Doddie Foundation which raises funds for research into Motor Neurones Disease (MND).
Father-of-four John, originally from Dundee and now living in Worcestershire, was inspired after meeting fellow Scotsman Doddie, who has since been diagnosed with the debilitating disease and set up his foundation with the aim of finding a cure.
John, who joined the army aged 19 and served until 1996, and was in the SAS, said: "I met Doddie at Malvern College three years ago where he was giving an after-dinner speech, which in true Doddie style was funny, warm and full of hilarious anecdotes.
"I then bumped into him at Murrayfield where I was watching Scotland play England. Last minute ticket bookings meant that my son Hamish and myself were in a room with about 95 England supporters, we couldn't get in the Scottish wing with Doddie and fellow Scotsman. Upon hearing this Doddie picked Hamish up under his arm and carried him into the room and gave an inspirational talk about how you can do anything you want to do and how important children are to the future of rugby. It meant a lot to Hamish, who was nine at the time.
"So it just felt right to support his foundation with this challenge."
To call John's Atlantic row 'a challenge' is something of an understatement. It will take him one million strokes of the oar to traverse the 3,000-mile expanse, and he's hoping to reach his £1million target by encouraging everyone who hears his story to donate at least a £1.
John is one of eight solo rowers taking on the quest this year, which begins on December 12 (weather depending) and will take between 50-60 days (again weather dependant!), and although he's playing catch-up when it comes to training, he has no doubt that he will succeed.
"Most people signed up for the challenge two years in advance, but I did it with just six months before it starts, so I'm having to do a lot of catching up with my training," he said.
Link: http://www.worcesternews.co.uk/news/16597494.former-sas-soldier-rowing-solo-across-atlantic-to-raise-money-in-honour-of-doddie-weir/
"I had a '55-year-old sit at a laptop 12 hours a day body' but thankfully muscle memory and determination has meant intensive training sessions have had to kick in and kick start this body back into shape fast. The mental side will be the biggest challenge because you're in a boat on your own for all that time and you have to force yourself to keep rowing even when you're exhausted, but I'm used to that kind of mental test from my time in the special forces. I know I will do it."
John, who has run a consultancy company since leaving the forces, added: "There's a tendency to think that the adventure in your life is over by the time you hit 50, so it's a great thing to show that you can always do something a bit crazy like this, no matter your age."
He said that the rugby community is "a family" and that the sport is "very personal" to him, hence his decision to support Doddie's foundation.
"My best friend was killed in action in 1991 while we were serving in the Gulf War," he said. "David 'Shug' Denburry MM QGM. We made a deal that if anything happened to one of us, we would support each other's teams if they were not playing each other. He was a great rugby player and proud Welshman so I wear a Scotland top and a Wales top to honour this memory.
"That idea of honouring someone special is behind me doing this challenge."
See madgiraffeatlanticrow.co.uk for more on John's challenge and how to donate.
Editor's kind comments on my mad kilted challenge!
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WHAT an inspiration John Davidson is.
As he prepares to row 3,000 miles solo across the Atlantic, the former SAS soldier is living proof that age and having a 'laptop body' is no barrier to adventure.
John, at 56, will push his body to the limit as he takes on the gruelling challenge but, with his experience in the special forces, he's certainly got the mental strength for the task.
His own inspiration is Doddie Weir, the legendary Scottish rugby player who has been diagnosed with Motor Neurone Disease (MND).
Ever the fighter, Doddie decided that rather than wallow in the grief of discovering that he had the debilitating disease, he would do everything possible to find a cure – and so he set up his own charity to fund research, the My Name'5 Doddie Foundation.
After meeting Doddie, John was inspired to take on the Talisker Whisky Atlantic Challenge in his honour – which is all the more amazing when you consider that Doddie is not a relative or close friend of John's, simply someone leading a cause that is worth supporting. Brilliant!
Link: http://www.worcesternews.co.uk/news/16600810.editors-view-ex-sas-soldiers-atlantic-row-is-truly-inspiring/
Interviewed by Ashleigh Carroll on LBC London News
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Listen here:
Ashleigh Carroll kindly gave me a slot on her afternoon show on 2 August highlighting my Mad Giraffe row and fundraiser for MND. Thank you hugely Ashleigh for your support!


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Now that we've gone through a very basic introduction to computational complexity, we're ready
to take a high-level glimpse at some of the more interesting things that arise from it. The one
that you'll hear about most often is "P vs NP", which is what I'm going to write about today.
So, what are P and NP?
P and NP are two very broad classes of computational problems. When we're talking about P and NP, we're talking about the intrinsic complexity of a problem - that is, a minimum complexity bound on the growth rate of the worst case performance of any algorithm that solves the problem.
P is the class of problems that can be solved in polynomial time on a deterministic effective
computing system (ECS). Loosely speaking, all computing machines that exist in the real world are
deterministic ECSs. So P is the class of things that can be computed in polynomial time on real computers.
NP is the class of problems that can be solved in polynomial time on non-deterministic
ECSs. A non-deterministic machine is a machine which can execute programs in a way where whenever there are multiple choices, rather than iterate through them one at a time, it can follow all choices/all paths at the same time, and the computation will succeed if any of those
paths succeed; if multiple paths lead to success, one of them will be selected by some unspecified mechanism; we usually say that they'll pick the first path to lead to a successful result.
The idea of non-determinism in effective/Turing-equivalent computing systems is a tough
thing to grasp. There are two ways of thinking about it that help most people understand what it
means: there's the low-level explanation, and the high level explanation.
The low level explanation is based on the basic concept of the Turing machine. (If you need
a reminder of how a Turing machine works, I wrote an explanation here.) In a Turing machine, you've got a tape full of data cells, with a head that can read and/or write data on
the cell under it, and you've got a state. Each step of the computation, you can look at the contents of the tape cell under the head, and then using the data on that cell and the current state of the machine, and use those to decide what (if anything) to write onto the current tape cell; what state to adopt, and what direction to move the head on the tape. In a deterministic Turing machine, for a given pair (cell,state) of tape cell data and machine state, there can be only one possible (write,state,move) action for the machine. In a non-deterministic machine, there can be multiple actions for a given (cell,state) pair. When there are multiple choices, the machine picks all of them; you can think of it as the machine splitting itself into multiple copies, each of which picks one of the choices; and whichever copy succeeds first becomes the result of the
The high level explanation is a simpler idea, and it's closer to what we use in practice for
specifying when some problem is in NP, but it sounds pretty weird. A problem whose solution can
be computed in polynomial time on a non-deterministic machine is equivalent to a problem where
a proposed solution can be verified correct in polynomial time on a deterministic machine. You can
specify a non-deterministic machine that guesses all possible solution, following all of those paths at once, and returning a result whenever it finds a solution that it can verify is correct. So if you
can check a solution deterministically in polynomial time (not produce a solution, but just verify that the solution is correct), then it's in NP.
The distinction can become much clearer with an example. There's a classic problem called the
subset/sum problem (SS). In the SS problem, you're given an arbitrary set of integers. The question is,
can you find any non-empty subset of values in the set whose sum is 0? It should be pretty obvious that
checking a solution is in P: a solution is a list of integers whose maximum length is the size
of the entire set; to check a potential solution, sum the values in the solution, and see if the result
is 0. That's O(n) where n is the number of values in the set. But finding a solution is
hard. The solution could be any subset of any size larger than 0; for a set of n elements,
that's 2n-1 possible subsets. Even if you use clever tricks to reduce the number of possible
solutions, you're still well into exponential territory in the worse case. So you can non-deterministically guess a solution and test it in linear time; but no one has found any way
of producing a correct solution deterministically in less than O(2n) steps.
One of the great unsolved problems in theoretical computer science is: does P = NP? That is, is
the set of problems that can be solved in polynomial time on a non-deterministic machine the same as the set of problems that can be solved in polynomial time on a deterministic machine? We know for certain that P ⊆ NP - that is, that all problems that can be solved in polynomial time on a deterministic machine can also be solved in polynomial time on a non-deterministic machine. We simple do not know.
For computing devices simpler than Turing-equivalent, we know the relationships between the deterministic and non-deterministic problem families. For example, for finite state machines,
non-deterministic FSMs are no faster or more capable than deterministic ones (So DFA = NFA); for pushdown automata, the deterministic versions are strictly weaker than the non-deterministic ones (D-PDA ⊂ N-PDA). But what about Turing machines, or any other Turing-equivalent ECS? Not a clue. I know people who study computational complexity who think that P=NP, and that we will find a polynomial time deterministic solution to an NP problem any year now. Personally, I suspect that P ≠ NP,
based on intuition from the PDA case; as computing devices get more complex, we start to see more
differences between the deterministic and non-deterministic machines, and I personally think that that
will hold true all the way up to full ECS's. But I have no proof to back that up, just intuition.
Within NP, there are a set of particularly interesting problems which are called NP-complete. An NP-complete problem is one where we can prove that if there is a
P-time computation that solved that problem, it would mean that there was a P-time solution
for every problem in NP, and thus that P=NP. We've identified hundreds (thousands?) of
NP-complete problems, but no one has ever found a P-time solution for any of them.
The SS problem mentioned above is NP-complete. So are a lot of other interesting problems:
graph coloring, the traveling salesman, clique detection in graphs, and many more.
So how do we show that something is NP complete? It sounds like a very difficult thing to do. And doing it from first principles is extremely difficult. Fortunately, once it's been done for one problem, we can piggyback on that solution. The way to prove NP-completeness is based on
the idea of problem reduction. If we have two problems S and T, and we can show that
any instance of S can be transformed into an instance of T in polynomial time, then we say that S is polynomial-time reducible to T. If T is NP-complete, then every problem in NP is polynomial-time reducible to T.
The trick is: once we know a problem T which is NP complete, then for any other problem U, if we can show that T is polynomial-time reducible to U, then U must be NP-complete as well. If we can reduce T to U, but we don't know how to reduce U to T, then we don't just say that U is NP-complete; we say that it's NP-hard. Many people think that if we could show whether or not NP=NP-Hard, then we'd also know whether P=NP; others disagree.
Anyway, there are a lot of problems which have been proven NP-complete. So given a new problem,
there are a lot of different NP-complete problems that you can use as a springboard for proving that
your new problem is also NP complete.
If you trace back, you'll find that most NP-completeness proofs are ultimately built on top of NP-completeness proof of one fundamental problem, whose nature makes it particularly appropriate as
a universal reduction target - and it's also the first problem that was proven to be NP-complete. It's called the propositional satisfaction problem (aka SAT), which was shown to be NP-complete via a rather difficult poof. For any other problem, if we can show that we can translate any instance of a SAT problem to an instance of some other problem in polynomial time, then that other problem must also be NP-complete. And SAT (or one of its simpler variations, 3-SAT) is particularly easy to work with, and show how to translate instances of SAT to instances of other problems.
The SAT problem is a neat one. Take a set of boolean variables of size n,
b1,...,bn, and their complements, not(b1),...,not(bn);
these are called atoms. Now, form an arbitrary logical statement using atoms joined by logical ANDs and ORs. The problem is, can you find an assignment of the boolean variables to true and
false so that the statement is true (satisfied).
The only problem with SAT is that it's so general. The set of all logical equations consisting of
an arbitrary set of atoms joined together in any syntactically valid form - it's an enormous set; but worse, it's got a huge amount of structural variation. To work with it, and show a P-time reduction from SAT to some other problem, and be absolutely sure that you've covered every possible case - that's a tough job. Too tough; it's awfully easy to miss just one little case; and missing one case can
give you an apparent reduction that shows P=NP.
What we typically do, then, is used a constrained version of SAT. Any arbitrary SAT equation can be
P-time transformed into a equivalent equation in a particular form consisting of groups of 3 atoms
(triples), where the members of a triple are joined by logical "OR"s, and triples are joined by logical
"AND"s. Solving the SAT problem for equations in the constrained triple form is called 3-SAT. 3-SAT is NP-complete, just like the general SAT problem; and because it is so constrained, 3-SAT is a much easier basis for constructing reduction-based NP-completeness proofs.
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More like this
After this nice theoretical exposition, one can
practice the concepts in this quiz:
You 've got your troubles I've got mine.
People prefering the topology posts might try:
Farmer Ted and his sheep.
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Concerning SAT
the first problem that was proven to be NP-complete. It's called the propositional satisfaction problem (aka SAT), which was shown to be NP-complete via a rather difficult poof.
I think the first point arguable, though it depends whether you consider the "Does a given non-deterministic Turing machine have an accepting computation within a polynomial time bound on given input" is a "problem", or simply a restatement of the definition!
And having taught the reduction a number of times, I'd like to take issue with "difficult". The main difficulties with most of the proofs (up to and including current textbooks) are:
the mathematician's choice of variable names for the propositional variables (and I'm allowed to say that being one myself) as opposed to naming them for what they stand for; and
the failure to mention that the idea of the proof is to show that we can specify "snapshots" of a TM using propositional variables.
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Many people think that if we could show whether or not NP=NP-Hard, then we'd also know whether P=NP; others disagree.
No, there are definitely problems that are NP-hard but not in NP, in particular many problems requiring super-exponential time. NP-complete = NP-hard and in NP.
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if you can check a solution deterministically in polynomial time then it's in NP.
is the set of problems that can be solved in polynomial time on a non-deterministic machine the same as the set of problems that can be solved in polynomial time on a deterministic machine?
Mark, I find these two sentences contradictory. In one you refer to checking a solution; in the other to finding a solution.
I think this article never makes clear if you are talking about checking or finding solutions. I found it confusing in that regard.
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I'm not sure if I wrote unclearly, or if you're misinterpreting it; when I read it, it seems clear to me, so if you have some idea of how I can clarify, or point out what's specifically making it hard to follow, let me know, and I'll fix it.
In the article, I'm talking about finding solutions to the problems. But any problem that can be solved in polynomial time on a non-deterministic machine (i.e., a problem that is in NP) is also a problem whose solutions can be checked in polynomial time on a deterministic machine. That's why the verification/checking thing comes up: an NP problem is a problem that can be solved in polynomial time on a non-deterministic machine, and checked in polynomial time on a deterministic machine.
Does that help?
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That helps. I guess I found this phrase a bit tough to parse (I needed to read it thrice):
So if you can check a solution deterministically in polynomial time (not produce a solution, but just verify that the solution is correct), then it's in NP.
I would probably rephrase it somewhere along the lines of "If veriftying that the solution to a problem takes polynomial time on a deterministic machine, then that problem is NP". It might seem similar but it makes clear what "it" is in "..., then it's in NP."
BTW, thinking more about this, if that implication is true, then what about P problems? How long does it take a deterministic machine to verify a solution to a P problem? Making a quick guess I'd say it'd probably take O(1) but I'm not sure.
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Maybe I'm wrong, but I believe NP-completeness relies on 1) showing that your problem is no easier than an NP-complete problem (reduction of SAT/whatever into your problem), and 2) showing that your problem is no more difficult than an NP-complete problem (reduction of your problem to SAT/whatever).
With that said, I'm not quite sure that it will be as easy to show that P=NP or that P!=NP as some claim. Why?
If we think of an algorithm to solve an NP-complete problem as being a tree of decisions, similar to the way we think of the N! orderings of a list (and the comparison-based lower bound as O(log(n!)) ), then we can come upon an obvious EXPTIME solution to the NP-complete problem: traverse the decision tree until you come to a solution.
Modern techniques for solving NP-complete problems (at least that I've seen), tend to rely on heuristic prunings of the decision tree in order to skip over portions that may not lead to a solution (depending on the algorithm, this may be more or less strict).
Showing that P=NP would be, from what I understand, equivalent to saying that there exists a universal heuristic for pruning. If this is correct, then it doesn't seem difficult to construct an NP-complete problem for which the "universal heuristic" fails in an inconsistent manner (it's not always right OR wrong).
Regardless, P=NP would imply that inverting any cryptosystem is arbitrarily easy; from prime factorization in RSA, to key inversion in AES. All become easy. Such a simple solution being claimed as correct for entire universe of problems, smells to me a bit like ID (no offense to your friend). Would it be convenient? Of course. But so would ID.
As for P!=NP, I think that is also going to be difficult, for similar reasons.
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A problem that can be verified in P-time on a deterministic machine can also be verified in P-time on a non-deterministic machine. There's no general reduction in complexity class between deterministic and non-deterministic; if there were, we'd probably have the answer to whether or not P=NP.
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I guess what I'm asking is this:
You said that "If solution verification is P, then problem is NP".
Is the converse true? In other words, is it true that:
"solution verification is P iff problem is NP"
If the converse is not true, then verification of a solution to a non-NP problem can't be in P. I guessed it'd be O(1).
I hope I'm making sense.
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Yes, part of the definition of NP is basically that a problem is in NP if/f its solution is verifiable in polynomial time. The implication works both ways; if you know you can verify the solution in polynomial time, then you know that the problem is in NP; if you you know that the problem in NP, then you know that you can verify a solution in polynomial time.
Also, a problem with a complexity of O(1) is in P. (1 is considered a polynomial in x0.)
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OK, that's interesting. Thanks for the explanations.
Also, a problem with a complexity of O(1) is in P. (1 is considered a polynomial in x0.)
I didn't know that, but it makes sense. One question remains, though: how long does it take to verify the solution to a P problem? If it's not polynomial time, what's left?
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Just pointing out the obvious: if verifying the solution to a P problem is P too, and Mark is right, then P=NP.
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Sorry for replying to myself here... I just realised every problem in P is also in NP, so the time to verify the solution to a P problem can be in P too, without any consequence.
Maybe it'd be worth it to point out in the article that P is a subset of NP? For those of us who can't immediately figure it out...
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MiguelB: The article does point out that, "We know for certain that P â NP - that is, that all problems that can be solved in polynomial time on a deterministic machine can also be solved in polynomial time on a non-deterministic machine."
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Yeah, thanks for pointing that out. When dealing with a complex subject, I only start to fully comprehend it when I turn it around in my head and repeat by myself what has just been explained (and by then I've forgotten it was already explained to me). It's hard to describe the process. I'm sorry for doing it in public :) -- on the other hand, this is the first time I feel I have a grasp on the subject. Thanks.
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Verifying the solution to a P problem is in fact only guaranteed to be in P.
And P is a subset of P, but it is not known if P is a proper subset of P. (that's the whole P=NP/P!=NP question.)
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Also, a minor note.
As it's known that any problem in NP can be reduced in polynomial time to an NP-Complete problem, proofs of NP-completeness typically skip showing that it's possible to reduce problem X to a known NP-Complete problem, and simply show it's in NP.
It's usually much easier to "reduce" a simple problem to a complex one than it is to go the other way around... but it's very easy to show something's in NP. (Just display a polynomial-time algorithm to verify solutions. This is usually pretty trivial for problems we care about.)
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MiguelB: The article does point out that, "We know for certain that P â NP - that is, that all problems that can be solved in polynomial time on a deterministic machine can also be solved in polynomial time on a non-deterministic machine."
Now, the fun part is when you consider that we know
P â NP â PSPACE â EXPTIME
We know P != EXPTIME, so AT LEAST ONE of these âs in fact denotes a proper subset.
But we don't know which one!
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"Many people think that if we could show whether or not NP=NP-Hard..."
NP is not equal to NP-Hard. The Halting problem is NP-Hard. It is definitely not in NP.
Also, to prove NP-Completeness, you don't need to do two reductions (although you can). You can reduce SAT or whatever to your problem, then show that your problem is in NP. That's often pretty easy: just show that the answer is polynomial in the length of the input.
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"Many people think that if we could show whether or not NP=NP-Hard, then we'd also know whether P=NP; others disagree."
It occurred to me that maybe you meant NP = NP-Complete. In that case, if P != NP, then there are problems that are in NP but not NP-Complete, so NP != NP-Complete (Richard Ladner proved this in 1975 in the Journal of the ACM). Therefore if NP = NP-Complete, then P = NP. No disagreements allowed!
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One interesting thing that is hidden in the NFA = DFA equality is the complexity of the machine description.
For any regular expression, there is an NFA whose description is linear in the size of the regular expression. (In fact, there's one with exactly the same number of states as there are symbols in the original regular expression, plus one.) However, there are regular expressions such that the number of states of the minimal DFA is exponential in the size of the regular expression.
Why is this interesting? Because while NFAs and DFAs have equal power, but NFAs are not polynomially reducible to DFAs.
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Mark, another comment (great series, by the way). There are fairly complicated classes for which non-determinism makes no difference. These are "space" classes, for example the class of all problems solvable in polynomial space. An old result shows that for any space class, non-determinism doesn't change the power, and so PSPACE (poly-space) = NPSPACE (non-deterministic poly-space) and so on.
It is indeed usually easy to check that a problem is in NP, but there are some well known problems for which this is not true at all. Often, these problems involve calculations with things like square roots, and so verifying that a solution is a certain value is nontrivial.
Also, optimization problems in general are not known to be in NP, because it's difficult to verify in polytime that a given solution is "optimal"; they are often NP-hard, but that's as far as we can go.
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Great knowledge-in-the-gap article, reducing and SATisfying and more. Thanks!
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A distinction that I've heard people talk about, which I'm not sure is exactly the same as the P vs NP distinction is the difference between finding a solution to a problem and checking a solution to a problem. For example, it's harder to figure out the solution to x^5 - x^4 - 16 = 0 than it is to verify that x=2 works. For a hard theorem of mathematics, it's much more difficult to come up with a proof than it is to check to see if the proof is correct. In chess, it's a lot harder to figure how to force a checkmate in 5 moves than it is to check that a particular sequence of 5 moves produces a checkmate.
If P=NP, then that means for many hard problems, there really is no big distinction between producing a solution and checking a solution.
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I'm wondering if you're going to get into quantum complexity here, or if that's to the side of your real interest. My intuition is that NP is in QP, but there's yet to be a proof. Full disclosure: the problem that kicked off my dissertation would have had this proof as a corollary, but it turned out not to work as I'd hoped.
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Suresh: Optimization problems and the definition of NP don't really map well to one another.
But almost any optimzation problem has a simple restatement as a decision problem (which is what NP is really about); If you have an optimization problem that optimizes some variable V given an instance I, you can recast it as a decision problem by saying "Is there any solution to instance I that has a value of V no worse than [insert number here]."
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Mark, I'm new to commenting on this blog, but I can't understand how the solution to the Traveling Salesman problem you linked to can be checked in P. This problem could be trivially checked in P and therefore NP-complete if you specify it as "Is there a route of length less than x" rather than "what is the minimum route". Am I missing something?
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I've been regularly reading your blog for many months now, great work and thanks for writing, I always learn something new! In regards to NP-completeness, I've been independently studying the derivation of the class of NP-complete problems, namely via Cook's SAT reduction(mostly from textbooks like Hopfcroft & Ulhman, Garey & Johnson, etc). You mention that it is a rather difficult proof, and I agree--I am quite stuck on it! But I feel like the only way to really understand NP-completeness is by intuitively knowing why/how SAT is the hardest NP problem, which is really the first step to take in this subject.
Can you or any of the readers here recommend any papers, sites or books that provide an unusually lucid or novel walkthrough of Cook's "SAT is NP-complete proof"? Everything I've found so far, even online lectures from various math depts., don't do a good job of presenting the proof and the step by step reasoning to get through it. I would even request for you to do an upcoming post on taking this proof apart.
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Thanks for the explanation. It's been a while since college, and we never did go into NP-completeness.
I suppose one trivial corollary is that if we have a problem M known to be (at worst) NP, and can in polynomial time enumerate all possible solutions to M, then we can, in polynomial time, iterate over the set of all possible solutions and verify them. So M is really P.
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From the article: Personally, I suspect that P â NP, based on intuition from the PDA case; as computing devices get more complex, we start to see more differences between the deterministic and non-deterministic machines, and I personally think that that will hold true all the way up to full ECS's.
It is known that PSPACE == NPSPACE, and those classes are at least as complex as P.
From lylebot: It occurred to me that maybe you meant NP = NP-Complete.In that case, if P != NP, then there are problems that are in NP but not NP-Complete, so NP != NP-Complete (Richard Ladner proved this in 1975 in the Journal of the ACM). Therefore if NP = NP-Complete, then P = NP. No disagreements allowed!
NP != NP-Complete.
Consider the problem "yes", for which the answer is always yes. This set is obviously in P and NP, but cannot be NP-Complete, because no problem which can be answered "no" can be reduced to it.
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P=NP. Professor Martin Michael Musatov. "If smart people always had Ph.D.'s we would not have light bulbs."
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Great! Prove it.
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What I've found with regards to that problem.
I've been studying the 255 main rules of cellular automaton with a twin bifurcation based numerical system. What I mean by twin Bifurcation is where you have two numbers produced from a Piecewise Equation that as a pair are unique for every value of n.
So for example we'll call this pair x and y
so when n = 1,2,3,4,5,6,7,8,9 ...
x = 1,0,1,2,1,0,1,2,3,1,0 ...
y = 1,2,2,1,3,3,4,2,1,5,4 ... (y being the occurrence count of the pyramidal sequence x)
Any way If I if tell the computer to find the steps for a cellular automata rule between 1 and 255 and I ask it for a range of steps starting at the initial condition being n represented in binary form I find that the X of this outcome - the Y of this out come produces a re-occurring numbers sequence for regardless of which rule is chosen or which n value in binary form acts as the initial value.
This is rather off the wall and odd but true.
When I take this x - y of the each step result pattern and minus that from the true step value that is where I find a different pattern that look much like variable axis in some way.
So as a result of using this twin bifurcation I am somehow splitting the problem into a repetitive sequence and something else. If of course I could mathematically reproduce the result of that something else I could take a the repetitive sequence and simply add that to my reproduction and the two numbers when represented in binary would be equal to the result of any given step.
It's early days by that's where i'm looking.
My recursive sequence is on youtube I am the mad guy wildchildplasma but I have indeed found that recursive sequence result of the steps.
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text:
Sometimes, choosing between candidates for city council elections can feel a lot like those ōfind the differenceö cartoon quizzes.
At first glance, everything appears to be pretty much identical. You have to search for subtle distinctions, the placement of an arm, say, or the pattern on a sweater Ś or approaches to budget cuts and gradations of support for essential city services, as the case may be.
Not so this season in Iowa CityÆs District A, where voters will choose Nov. 8 between two candidates who stand in stark relief.
In one corner, thereÆs family doctor and University of Iowa clinical professor Rick Dobyns.
In the other, local radio station owner and on-air personality Steve Soboroff Ś aka KCJJ-AM 1630Æs Captain Steve.
Both are longtime Iowa City residents by choice Ś both went to school at the UI and decided to return to make the city their home. Both have given back through significant community contributions.
But when it comes to the details, Soboroff and Dobyns are political yin and yang: The gown and the town; the Doctor and the Captain.
Dobyns supported the 21-ordinance back when most city residents thought it was nothing but a big wet blanket. Soboroff still thinks it was a dumb way to go.
Dobyns sees a ōunique city among unique cities,ö which should capitalize on the overlap between the UI campus and downtown.
Soboroff thinks the UI should back off, especially when it comes to off-campus policing.
And as for Iowa City police, well they should focus their attention on the real public safety problem, Soboroff says Ś the break-ins, assaults and gunplay he says still plague Iowa City neighborhoods south of Highway 6.
You almost wonder if the two candidates live in the same town. And technically, they do.
But Soboroff lives on the cityÆs southeast side. Dobyns on the west Ś areas of town that are as night-and-day different as the candidates themselves.
Both Soboroff and Dobyns give you the feeling theyÆd represent their parts of the city well.
But because District A is so sprawling, no matter who is elected, residents from one or another part of the district will once again have to go without a council representative with firsthand knowledge of their neighborhoodÆs challenges and strengths.
So District A voters have a clear choice to make during next monthÆs election. And something else is equally clear: ItÆs time to add a fourth district to Iowa CityÆs city council.Comments: (319) 339-3154; email@example.com


text:
Author bio
Clive Cussler - book author
Cussler began writing novels in 1965 and published his first work featuring his continuous series hero, Dirk Pitt, in 1973. His first non-fiction, The Sea Hunters, was released in 1996. The Board of Governors of the Maritime College, State University of New York, considered The Sea Hunters in lieu of a Ph.D. thesis and awarded Cussler a Doctor of Letters degree in May, 1997. It was the first time since the College was founded in 1874 that such a degree was bestowed.
Cussler was an internationally recognized authority on shipwrecks and the founder of the National Underwater and Marine Agency, (NUMA) a 501C3 non-profit organization (named after the fictional Federal agency in his novels) that dedicates itself to preserving American maritime and naval history. He and his crew of marine experts and NUMA volunteers discovered more than 60 historically significant underwater wreck sites including the first submarine to sink a ship in battle, the Confederacy's Hunley, and its victim, the Union's Housatonic; the U-20, the U-boat that sank the Lusitania; the Cumberland, which was sunk by the famous ironclad, Merrimack; the renowned Confederate raider Florida; the Navy airship, Akron, the Republic of Texas Navy warship, Zavala, found under a parking lot in Galveston, and the Carpathia, which sank almost six years to-the-day after plucking Titanic's survivors from the sea.
In addition to being the Chairman of NUMA, Cussler was also a fellow in both the Explorers Club of New York and the Royal Geographic Society in London. He was honored with the Lowell Thomas Award for outstanding underwater exploration.
Cussler's books have been published in more than 40 languages in more than 100 countries. His past international bestsellers include Pacific Vortex, Mediterranean Caper, Iceberg, Raise the Titanic, Vixen 03, Night Probe, Deep Six, Cyclops, Treasure, Dragon, Sahara, Inca Gold, Shock Wave, Flood Tide, Atlantis Found, Valhalla Rising, Trojan Odyssey and Black Wind (this last with his son, Dirk Cussler); the nonfiction books The Sea Hunters, The Sea Hunters II and Clive Cussler and Dirk Pitt Revealed; the NUMA® Files novels Serpent, Blue Gold, Fire Ice, White Death and Lost City (written with Paul Kemprecos); and the Oregon Files novels Sacred Stone and Golden Buddha (written with Craig Dirgo) and Dark Watch (written with Jack Du Brul).
Clive Cussler died at his home in Scottsdale, Arizona on February 24, 2020.
Clive Cussler is the author of books: Sahara (Dirk Pitt, #11), Inca Gold (Dirk Pitt, #12), Atlantis Found (Dirk Pitt, #15), Raise the Titanic! (Dirk Pitt, #4), Valhalla Rising (Dirk Pitt, #16), Iceberg (Dirk Pitt, #3), Pacific Vortex! (Dirk Pitt, #1), Trojan Odyssey (Dirk Pitt, #17), The Mediterranean Caper (Dirk Pitt, #2), Deep Six (Dirk Pitt, #7)
Author Books
1998, the Andes Mountains of Peru. DIRK PITT dives into an ancient sacrificial pool, saving two American archaeologists from certain drowning. But his death-defying rescue is only the beginning, as it draws the intrepid Pitt into a vortex of darkness and danger, corruption and betrayal. A sinister crime syndicate has traced the long-lost treasure -- worth almost a billion dollars -- from the Andes to the banks of a hidden underground river flowing beneath a Mexican desert. Driven by burning greed and a ruthless bloodlust, the syndicate is racing to seize the golden prize...and to terminate the one man who can stop them: DIRK PITT!
Clive Cussler has long since proven himself one of America's most popular authors--a master of intricate, audacious plotting and "vibrant, rollicking narrative" (Chicago Tribune). But Atlantis Found may be his most audacious novel of all.
September l858: An Antarctic whaler stumbles upon an aged wreck, its grisly frozen crew guarding crates of odd antiquities--and a skull carved from black obsidian.
March 200l: A team of anthropologists gazes in awe at a wall of strange inscriptions, moments before a blast seals them deep within the Colorado rock.
April 200l: A research ship manned by Dirk Pitt and members of the U.S. National Underwater and Marine Agency is set upon and nearly sunk by an impossibility--a vessel that should have died fifty-six years before.
Pitt knows that somehow all these incidents are connected, and his investigations soon land him deep into an ancient mystery with very modern consequences, up against a diabolical enemy unlike any he has ever known, and racing to save not only his own life but the future of the world itself.
The trap is set. The clock is ticking. And only one man stands between earth and Armageddon. . . .
Filled with dazzling suspense and astonishing set pieces, this is Clive Cussler's greatest adventure novel yet.
"I've always had tremendous fun with Dirk Pitt, but nothing has given me more pleasure than the opportunity to send him to that most fabled of lost lands, Atlantis, and to virtually reinvent aspects of its civilization. I hope you have as good a time reading Atlantis Found as I did writing it!"--Clive Cussler
In the middle of its maiden voyage, a luxury cruise ship using revolutionary new engines suddenly catches fire and sinks. Its alarms stay silent; its sprinkler system remains inactive. Nearby NUMA special projects director Dirk Pitt notices smoke and races to the rescue. He's too late to save the engineer behind the ship's new technology, but helps the man's daughter, Kelly Egan, escape with her father's work in a leather briefcase.
While Ms. Egan strives to uncover the hidden value in her father's inventions, Pitt is hired on by maritime insurers to investigate the wreckage. Neither are prepared for the mechanical marvels they'll soon be forced to confront. The machines could only be the stuff of legend, described in the tales of Viking explorers or the accounts of Jules Verne. And they may be Pitt and Egan's only hope when an oil tycoon with a plan of his own appears on the scene.
Before journey's end, Pitt will take on a power-mad millionaire, tread upon territory previously known only to Verne's illustrious Captain Nemo, and make shocking discoveries about his own past.
In the final pages of Valhalla Rising, Dirk Pitt discovered, to his shock, that he had two grown children he had never known-twenty-three-year-old fraternal twins born to a woman he thought had died in an underwater earthquake. Both have inherited his love of the sea: the girl, Summer, is a marine biologist; the boy, himself named Dirk, is a marine engineer. And now they are about to help their father in the adventure of a lifetime.
There is a brown tide infesting the ocean off the shore of Nicaragua. The twins are working in a NUMA(r) underwater enclosure, trying to determine its origin, when two startling things happen: Summer discovers an artifact, something strange and beautiful and ancient; and the worst storm in years boils up out of the sky, heading straight not only for them but also for a luxurious floating resort hotel square in its path.
The peril for everybody concerned is incalculable, and, desperately, Pitt, Al Giordino, and the rest of the NUMA(r) crew rush to the rescue, but what they find in the storm's wake makes the furies of nature pale in comparison. For there is an all-too-human evil at work in that part of the world, and the brown tide is only a by-product of its plan. Soon, its work will be complete-and the world will be a very different place.
Though if Summer's discovery is to be believed, the world is already a very different place...
On an isolated Greek island, a World War I fighter plane attacks a modern U.S. Air Force base--a mysterious saboteur preys on an American scientific expedition--and Dirk Pitt plays a deadly game of hunter and hunted with the elusive head of an international smuggling ring.
A deadly tide of poison flows into ocean waters. A ghost ship drifts across the empty northern Pacific. A luxury Soviet liner blazes into a funeral pyre. The Presidential yacht cruises the Potomac night—and the President disappears without a trace.
Dirk Pitt takes on a sinister Asian shipping empire in an intercontinental duel of nerves. In his most dangerous, fast-paced adventure, he fights to save the US government—and to seize one desperate moment of revenge!


text:
Whats your opinion on this wakizashi i bought a few years back?
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Posted 01 April 2019 - 05:05 AM
Whats your opinion on this wakizashi i bought a few years back?
Martin L.
Posted 01 April 2019 - 09:55 AM
Dear Martin.
Welcome, please add your name to all your posts as we all do here. I am not sure what you want to hear about your sword. It is a perfectly genuine antique sword, an unsigned wakizashi in older polish with low end but genuine mounts which is papered to a Takada school smith. I think Teruyuki of which there were four generations between 1650 and 1800.
The Takada school is not generally highly regarded, it is suggested that they are not art swords. I have always found that a rather strange statement and individual swords are often very good.
Hope this helps.
All the best.
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Eyes on Africa is becoming Eyes on Adventure and adding exciting new destinations - new and expanded website coming soon!
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ZAMBEZI SUN HOTEL RATES: Zambezi Sun
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a World Heritage Site by UNESCO.
Accommodation For
images of The Zambezi Sun, click Zambezi
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Twin beds alongside each other
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age. Children between the ages of 2 - 4 must be accompanied by an adult,
or babysitter (available at an extra cost), if they are not potty-trained.
Babysitters can be arranged through your hotel and are also available
during the evening.
Staff are specially selected and undergo extensive training in child-care
and first aid, ensuring that the child and the parent feel protected
and secure.
The Royal Salon - International Hair and Beauty
Enjoy the peace and tranquillity
of the mighty Zambezi River while having a luxurious outdoor body massage
or sit back and enjoy the healing power
of a magnificent foot massage while relaxing next to the swimming pool.
Try any of the internationally renowned hair and beauty services: paraffin
wax manicures and pedicures, personalised facials, hair removal, hair
care for ladies and gents.
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of Zambia Camps For
History and General information about Zambia, click More
further information about the National Parks of Zambia, click Zam
Parks For
History and General information about Victoria Falls, click More
further information about the National Parks of Zimbabwe, click Zim
History and General information about Zimbabwe, click More