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ShoppingCaret Right
· Updated on Nov 29, 2021
45 Splurge-Worthy Things To Buy On Cyber Weekend
If you've had AirPod Pros, a Barefoot Dreams blanket, or Samsung frame TV, and more on your wishlist, now's the perfect time to buy.
by Abby Kass, Melanie Aman, Sally Elshorafa, Stephanie Hope, Kit Stone
Cyber Week, the week when almost every store has deals (more than you could ever conceivably look through in an ENTIRE LIFETIME), is here.
We waded through mountains of bargains for you and found some of the best deals in every category.
FYI — deals can move quickly. We'll do our best to keep this post and imagery as up-to-date as possible, but we can't catch everything immediately. Check back throughout the week to see our latest updates as the deals change!
1. A Samsung frame TV for $300 off specifically designed to look like it's an actual piece of art when it's not in use so you don't have a black rectangle eyesore in the middle of the wall. Plus, it has 4K ultra HD, works with Alexa, and has amazing picture and sound quality.
Promising review: "I'm loving my new TV! I'm an artist and graphic designer, so I loved the idea of having a TV that doesn't look like a TV when it's not in use. I've had fun choosing different art to showcase in my living room. I love that I can even create my own art and load it on the TV. I think the picture and sound are great too, but I hadn't had a new TV in 12 years, so I can't speak to how it compares to other TVs that are less expensive. Of course, I know that a lot of the cost for this TV has to do with its design and the extra features that make it more than just a TV. It's an art piece, and for me, that makes it totally worth it!" —Yva Lovee'
Get it from Amazon for $797.99+ (originally $999.99+; available in six sizes).
2. A Dagne Dover duffle bag for 20% off made out of neoprene and mesh for a super soft bag you'll be able to fit SO much stuff in that you'll never travel without it again.
Dagne Dover / Via instagram.com, Dagne Dover
Use code HOLIDAZE at checkout.
I've had this duffle for years now, and it's one of my favorite things I own. I'm not exaggerating when I say it is the PERFECT carry-on bag. The neoprene fabric makes it so it can fit so much and slide perfectly under the seat in front of you. The pockets inside make sure everything has a place and stays organized. And one of the coolest features is the small outside pocket that fits your phone perfectly. It's also a great bag for a weekend trip as a duffle. I let my mom borrow mine when she traveled across Europe a couple of months ago, and now I have to get her own for Christmas because she's joined the #TeamDagneDover travel team.
Get it from Dagne Dover for $160 (originally $200; available in five sizes and seven colors).
3. An Instant Pot for 40% off that takes this already stellar gift and makes it even better because it AIR FRIES. Yes, that's right, so now in addition to pressure cooking, sautéing, steaming, slow cooking, sous vide–ing, warming, roasting, baking, broiling, *and* dehydrating it will also whip up some delicious fries in minutes. Talk about a revolutionary kitchen gadget everyone needs in their kitchen.
Promising review: "What else can you say about this product? It will replace three appliances that I use on a regular basis — rice cooker, air fryer, and pressure cooker. That's important to me because at this point kitchen space is at a premium. The packaging is great, the instructions are very clear and well written and it works very well. The first use was to make chicken bone broth using the pressure cooker feature. It worked flawlessly. Two-hour cook time. 10 min prep, 30 min to cool off. Three hours later I had homemade bone broth in the refrigerator. And the whole house didn't smell for 24 hours like it would with an open pot method. Anyway, the instant pot is a huge kitchen innovation IMO. Just get one, and use it." —Josh Brainard
Get it from Amazon for $119.95 (originally $199.99).
4. A Furbo camera for 30% off for pet owners who want help keeping an eye on their pet while they're gone at work or out running errands. You can monitor your pet from your smart device, and toss your pet a treat to give them a little reminder that you're not too far away.
Promising review: "I was always concerned leaving my puppy home alone because he will cry a lot... When I got the Furbo, things got much better! Furbo sent me notifications to my phone when he was crying, so I would log on and talk to him right away. This changed everything!! My puppy knows I'm always there, so his separation anxiety is getting better. He cries less, and I feel much more relieved." —Susan
Get it from Amazon for $118 (originally $159).
5. A UV sanitizer wand for 30% off — the germ-conscious friend who will appreciate the power to quite literally destroy germs with the ~wave of their magic wand~. It can kill 99.9% of bacteria and viruses in seconds 🤯.
Shipping Info: Available on Amazon Prime with free same-day shipping and two-day shipping, non-Prime shipping options will still arrive by Christmas (see Amazon's full shipping information here).
Get it from Amazon for $139.96 (get this price by clipping the "30% off" coupon on the product page; originally $199.95).
6. A handwoven throw blanket for 20% off featuring original artwork for a fun and bright addition to your bedroom or living room you'll love to cozy up under.
The Little Avocado / Etsy
This LA-based woman-owned shop has been creating fun macrame home decor and blankets, as well as other stickers and magnets to add joy to homes since 2013! This throw is made from 100% cotton and can be washed. Plus, the shop has a ready-to-ship section in case you need something ASAP.
Promising review: "I love this blanket so much! It's exactly what I wanted for my room, and it got here so fast!" —Sarah
Get it from The Little Avocado on Etsy for $131.20 (originally $164).
7. A pair of AirPods Pro for 28% off with noise cancellation so clear, you'll be able to focus on your work and not the barking dogs and noisy neighbors (or roommates) around you. Plus, if you don't want to miss all the noise around you, there's transparency mode, which means you won't miss the pilot telling you that you're landing 30 minutes early (Score!).
Emma Lord / BuzzFeed
Promising review: "These little things pack one hell of a punch! Apple's new noise cancellation and transparency modes lay the groundwork for a new generation of wireless headphones. Yes, others may have used similar technology before, but Apple's simplistic UI made for the AirPods Pro make the experience so much better than what other companies offer. Coming from the first generation AirPods, the experience is like night and day. Even though the AirPods themselves are heavier, they feel lighter in the ears and much more comfortable. The audio quality is so good, and this quality is only amplified by Apple's new spatial audio. I definitely recommend these." —Diane G
Get them from Amazon for $179.99 (originally $249).
8. The Golden State Capsule set for 25% off from Brightland, which includes the brand's entire collection of olive oils and vinegar sourced from family farms in California that will make any home-cooked meal taste even better than you thought possible.
Brightland
Brightland Co. is a WOC–owned small business.
The set includes AWAKE and ALIVE extra virgin olive oils, ROSETTE garlic, LUCID lemon, ARDOR chili, and ARISE basil-infused olive oils, PARASOL and RAPTURE vinegars, and a spout for easy pouring.
Promising review: "I kept seeing Brightland ads on Instagram and decided to give it a try, mainly drawn by the beautiful design of the bottles (which are glass). I went all in and purchased the set that came with 5 oils and 2 vinegars. I LOVE THEM SO MUCH. It is wonderful to have different flavor oils depending on what I'm cooking. I love the basil oil for salads and the chili oil for Asian dishes. I couldn't be happier with the purchase and will be a customer for life. The vinegars are also wonderful." —Emily
Get it from Brightland for $199 (originally $270).
9. An "I'm a luxury" sweater for 25% off made famous by the one-and-only style icon Princess Diana. And I can't be the only one who's wanted to emulate her style since I was a little girl, so this sweater is the perfect tribute to the forever royal.
Rowing Blazers
This sweater was created in a collaboration between Gyles & George (the original creator) and Rowing Blazers (the original creator of the iconic sheep sweater, also worn by Diana). Not only is the message totally on-brand (the back says "few can afford") but the colors are amazing. I recently treated myself to this sweater as an early birthday present (my birthday is a week before Christmas), and it's just as great in person as it looks online. It's made of wool, so it's super cozy, and I know I'll be wearing it a lot this winter (and the winter after that, too).
Get it from Rowing Blazer for $221 (originally $295; available in women's sizes XS-XXL and men's sizes XS-XXL, both in three colors).
10. Breville sous vide for 20% off that'll basically be the ~sous~ chef you didn't know that you needed. Attach this to any pot, put the food in, and then it will cook it to perfection using the built-in controls in the app. The future is now.
This unit is pretty small compared to other sous vide machines and lightweight. Plus, it can connect to Wi-Fi via Bluetooth so you can keep tabs on what's cooking (and how long you have left) in an app.
Promising review: "Love it. I've made creme brûlée, egg bites, and a couple rib roasts. I'm saving so much money on NOT buying Starbucks egg bites it was worth it for that alone. I can't compare it to other sous vide units, but it heats quickly, the depth works well (I use my big old All-Clad lobster pot and clip it on the side, but before I pulled the lobster pot out I set it down in my Dutch oven and I loved the magnet that stood it up). The app is okay. It does its job. I like being able to check on the timer from wherever. I would buy again." —erin johnson
11. A pair of Spanx faux leather leggings for 20% off that look so real, your friends might not believe they're not actual leather and have to feel your legs to make sure.
Spanx / Via instagram.com
Promising review: "I have these faux leather leggings in every color offered — they are THE BEST and a staple for my fall and winter closet. I'm currently pregnant and sized up for the fall to be able to continue to wear! I 100% recommend everyone get a pair. They make you look and feel amazing." —aadams10
Get them from Nordstrom for $78.40 (originally $98; available in women's sizes XS–XL, XS–XL Petite and 1X–3X).
12. A Barefoot Dreams throw blanket for 20% off with a cult following that includes Chrissy Teigen and the Kardashians. You'll feel like royalty when you snuggle up under this ultra-soft and cozy blanket and catch up on The Crown.
Barefoot Dreams / Via instagram.com
The blanket is made from 100% polyester microfiber blend that makes it SUPER soft. It can be washed on cold and tumbled dry on low.
Promising review: "I love and enjoy these throws so much that I invested in two of them so far! They are extremely soft and very calming when sick! They also wash well and hold up for a long time! If anyone is on the fence! Jump off — it's so worth it, in my opinion!" —Michael A. Roman
Get it from Nordstrom for $144 (originally $180; available in 12 colors).
13. A super sleek four-drawer dresser for 50% off that would look sleek with pretty much any decor and be a place your very large collection of souvenir T-shirts would be proud to call home.
Deal ends Monday.
Promising review: "A more difficult dresser to build from scratch but the outcome is worth it! Great quality and beautiful style, just the look I was going for!" —Review
Get it from Target for $194.99+ (originally $389.99; available in two colors).
14. A super-chic Bandolier phone case for up to 30% off with a wallet and a strap to keep all your essentials close and with you at all times. Trust me, this may be one of the most useful things you own — I've been using mine every day for almost two years now.
Promising review: "The Bandolier crossbody phone and wallet are perfect for me! No worries about dropping the phone or having it fall out of a pocket, and the added card space provides me with only having to carry one small item! I highly recommend the Bandolier solution!" —Teresa F.
Get it from Bandolier for $73.50+ (originally $105; available in 14 phone styles and 10 colors).
15. An iRobot Roomba i3+ vacuum for $250 off because we only have so much time during the day and there's an ever-growing to-do list where vacuuming might just be at the bottom of said list... That's OK. This handy gadget will help you check that right off your to-do list and leave your floors spotless. You can control it with your phone *and* it empties itself. How ~neat~ is that?
Promising review: "Best roomba I've ever owned. I love that I can use Alexa/Google to start the vacuum and I love that I can use it over and over and over again without ever touching it or needing to empty the bin. I have a 1,000-square-foot open floor plan with tons of furniture and different rugs and the navigation system is fantastic. I love the straight line vacuuming and even better is when it returns to its dock." —miradu
16. A pet mop and vacuum robot for 38% off because you looove your family (especially the four-legged members) but cleaning up after them is such a chore. This lil' robot will do some of the heavy lifting for you.
Promising review: "What can I say!!?!? It was delivered today and I couldn't help but give it a spin after charging it up and connecting to the app. I have a robot mop from another brand but all it does is release water slowly and drag a microfiber pad over the floor. The spinning pads in the back are what sold me on the SpinWave. It vacuums the floor as it mops. It's extremely quiet so I can run it while my kids are sleeping. When it's in the wet mop mode, it avoids my area rugs and random toys left on the floor. I've searched for something like this for a while and couldn't be happier with my purchase." —Wertz83
Get it from Amazon for $249 (originally $399.99).
17. An all-new, glare-free Kindle Paperwhite for 25% off with a user-friendly touch screen that not only can hold thousands of books, but will let you read the *chef's kiss* way you like best — you can customize it with all your favorite fonts and layouts, and organize your virtual shelves to your precise standards. Bonus — its charge lasts weeks (plural!!), and it's waterproof, so you can take this bb in the bathtub 🍷.
Another thing reviewers love that separates it from the 2018 model is that it comes with a warm amber light that's *much* easier on the eyes when you're reading in dim lighting!
Promising review: "Coming from a 1st edition Paperwhite, I couldn't be more impressed. The $25 trade-in credit + 20% off + 4 free months of my current Kindle Unlimited subscription saved me nearly $100. The new Paperwhite screen is crystal clear and very responsive. The addition of the new warm amber lights is awesome, especially if you like to read before bed to help you fall asleep. Battery life is nice too, currently at 72% after 2 weeks of everyday for a few hours." —MD RIstau
18. A Sony glass sound speaker for $101 off so ~bad and bougie~ that any recipient that is particular about the sound quality of their music will gasp at this both stylish and sound-efficient speaker.
@sonyelectronics / Via instagram.com
My family is in the music biz so sound quality is a huge deal when it comes to purchasing anything from headphones to speakers. When I saw this, I thought that it looked pretty but there was probably a sacrifice in sound quality because of its chic design. But let 👏🏽 me 👏🏽 tell 👏🏽 you — baby, this right here is it! I was pleasantly shocked that it looked fantastic literally anywhere I put it in my house, but it also sounds amazing. I mean duh, it's Sony, but I was still happily surprised. If you can swing the price, it's truly a gift for anyone, not just sound snobs like me.
19. A Ninja Foodie indoor grill for $100 off to tackle all of their grilling needs in addition to their air frying, roasting, baking, broiling, dehydrating, and more. I mean seriously, what else could they ask for?
@ninjakitchen / Via instagram.com
Promising review: "I have to say this machine is absolutely amazing. It exceeded my expectations by far. I have cooked ribeyes, shrimp, pork loin, whole chicken, and fried chicken in the past week. I can't believe how well it cooks and you don't have to deal with grease splatter. Cleanup is very easy and it takes less than a minute to put the grate and grease catcher in the dish washer. It radiates almost no heat. If you're wondering if you should buy don't hesitate." —Eezie's Daylily Farm
Get it from Amazon for $199.99 (originally $299.99)
20. The Foreo Luna Mini 2 for 30% off – an amazing face-cleaning brush that vibrates to remove makeup, dirt, and oil, so you'll have amazing skin in as little as 60 seconds.
Maitland Quitmeyer / BuzzFeed
Promising review: "I bought this about a month ago after seeing all the hype it got on BuzzFeed. I have oily, sensitive, acne-prone skin, and have always been wary of chemical exfoliants — most just tend to irritate my skin and make me break out more. The first thing that drew me to the Luna Mini 2 was that I'd never need to buy replacement heads. I was a little concerned about the price tag, but I reminded myself that the upfront cost would be one-and done since there's no brush heads to buy. And honestly, this brush has been worth every penny! After the first use, my skin felt the smoothest it has ever felt! The only (minor) drawback, was that the first week or two, I did see a temporary 'purge' of gunk from my pores that resulted in a temporary spike in breakouts, which other reviewers have mentioned, but this was thankfully short-lived. Now after a nearly a month of use, my skin is more radiant, softer/smoother, breaking out less, and even I'm starting to see a reduction in the size of my huge pores, which no product has ever given me before-. I also have a better oil balance in my skin. So for me, the results have taken a little time have totally been worth the wait! Needless to say, I'm very pleased with this product and have been recommending it to all of my friends. Thanks, Foreo!" —Knonymously
Get it from Amazon for $83.30+ (originally $119; available in five colors).
Read one BuzzFeeder's full review of the Foreo Luna Mini 2.
21. A pair of Sony overhead headphones for 29% off that left reviewers (more than 19,000!!) raving that these are some of the best headphones they've ever used. The 30-hour battery life, quick charging, touch sensors controls, speak-to-chat technology, and more features take these the extra mile.
Promising review: "I've never spent more than 100 dollars on headphones. I was worried about spending this much on headphones. But, WOW, I'm so happy I did. If these are headphones, then my others were garbage. Noise-canceling, features in the app, touch sensitivity, noise cancelation, and pass-through. I'm a fan. All that and AMAZING sound bases hit lows are clear. I don't know how it could get much better. But, it does! They come with an airplane adapter, a USB cable, a headphone cable, and a nice case. I like everything about them. I 100% recommend." —zach2825
Get it from Amazon for $248 (originally $349; available in three colors).
22. A set of lidded stoneware canisters for 25% off you'll actually want to take up your precious counter space because not only are they beautiful but they'll give you more places to store ingredients.
Holistic Habitat
Discount automatically applied at checkout.
Friends Kristin Holler and Rachael Daugherty founded Holistic Habitat in 2017 to curate home decor, furniture, and other items that are fair trade certified and ethically made by artisans around the world. They donate 15% of their profits to different issues, including The ACLU, Together Rising, and Habitat for Humanity.
Get the set of four from Holistic Habitat for $67.50 (originally $90).
23. A chic rolling suitcase for 25% off with a durable aluminum frame, one-click locks, a polycarbonate shell, silent wheels, and a dust cover and stickers for protection and customization.
Promising review: "Used this immediately after receiving for a weekend trip. Decided to get this instead of the Away carry on that everyone has. Love how chic it is and the hardware locks. One side is good for clothes and the other side for toiletries and accessories. I also like the zipper pockets to keep jewelry and undergarments organized. Very pleased!!" —Nicolette D.
Get it from Calpak for $213.75+ (originally $285; available in three sizes and three colors).
24. A foot massager for $50 off here to bring the spa right into your home. If you're on your feet all day, this will be the relief you need after standing for hours on end.
Promising review: "This is an awesome product. This foot massager was a great purchase. I wasn't going to try it but right away everyone in the house wanted to use it. And it is great. Definitely a keeper. Anyone that is on their feet all day, this is for you! Did I mention there's a heat option as well?" —K-METZ
Get it from Amazon for $199.99 (originally $249).
25. Bose QuietComfort noise-canceling earbuds for $80 off you'll probably be talking everyone's ~ear~ off about, because these headphones are worth their weight and more. Even though they're small, they have great noise cancellation, a transparency mode that lets you decide how much outside noise you want to let in, touch controls, noise-rejecting microphones, and a long battery life. These earbuds give a new meaning to the phrase "small but mighty".
Plus, they're weather and sweat-resistant, meaning they can go anywhere with you. The battery is made to last up to six hours in a single charge and the charging case gives you an additional 12 hours. You also get three sizes of eartips so you can customize them to fit perfectly.
Promising review: "I don't often do product reviews but these earbuds are by far the best I have ever owned. The music sounds crisp and clear. The base is just perfect. Very comfortable as well as super easy to hook up to your phone. I love those but usually prefer over the ear headphones. These are my current favorite — they stay put and sound phenomenal." —debra carlsen
Get them from Amazon for $199 (originally $279; available in three colors).
26. A Nespresso Vertuo and Aeroccino bundle for 21% off guaranteed to make your morning better because you'll be able to make a perfect cup of coffee, espresso, or even pour-over. Plus, it includes a milk frother so you can whip up your own lattes at home. Now you can be your own barista.
Promising review: "Admittedly I'm a little bit of a coffee snob. I have a Breville semi-automatic espresso machine and separate Breville espresso grounder in our primary home. Each morning I was used to grinding and brewing a fresh quad-shot latte. However in our vacation home I did not want to replicate that entire setup, so instead ordered a Nespresso Vertuo Next machine. The machine works well, super simply. Insert pod, lock the top down, and press one-time the only button on the machine. Pods are available from one shot espresso to large cup of drip. The amount of options for anyone in the household is really handy. The Vertuo Next machine is fairly loud, not horrible, but when spinning the coffee it's make a good amount of noise and vibration on the counter top. I think it's quiet enough to not wake up household members. The Vertuo coffee pods are not bad! I was pleasantly surprised. I ordered some single and double espresso options to try. The machine also came with a 12 pod assortment, which was fun to try different things and order more if you like. Looking forward to hopefully years of good use." —Anthony L.
Get it from Amazon for $164.96 (originally $209.95; available in four colors).
27. A soil-free AeroGarden Harvest for up to 40% off so you can have fresh herbs picked straight from...your countertop. This hydroponic system removes most of the mess and stress of traditional gardening, plus it alerts you when it's time to water and feed your plants.
Check out my colleague's AeroGarden review for more deets!
Promising review: "I purchased this as a Christmas gift for my boyfriend's sister-in-law who lamented not having a green thumb. I was somewhat apprehensive, having read a few reviews that mentioned pods not spouting. However, in the two months that the sis-in-law has had the AeroGarden, the growth has been tremendous. I'm constantly in awe when she sends me pics of the new growth. Only one pod failed to spout, but she reached out to customer service, and they are sending a replacement for that particular pod. All the others have grown quite large, and last night I received a picture of their dinner using herbs grown with the AeroGarden. Impressive!" —Mary A. Walls
Get it from Amazon for $89.99+ (originally $149.95; available in three styles and three colors).
28. The Mirror for $500 off you can seamlessly add to your wall to bring interactive workout classes right into your apartment while giving you the ability to check your form as you go.
getthemirror / Via instagram.com
Use code BFCM21 at checkout.
The Mirror brings a fitness studio right into your home. It comes with a wall-mount and stand as well as a companion app. Plus, you can sync the heart-rate monitor or Apple Watch to help you track your workout in real-time. There are more than 20 different types of workouts on the device, including boxing, Pilates, weights, and more. It also tracks your progress so you can try and beat yourself to improve.
Promising review: "The thing that makes The Mirror a game-changer a combination of the convenience of working out at home and the awesome personal trainers who guide you through your workouts. I can workout whenever I want. and I don't have to leave the house, and I can take any class I want whether it be focused on cardio, arms, abs, core, legs, etc. There are also tons of classes to give you a lot of variety so you don't get bored, which is a factor for me so I like that you can change it up. I also prefer instructional workouts and the trainers on The Mirror always come with awesome workouts. I like working out with dumbbells but there is a variety of equipment such as resistance bands, kettlebells, or body weight. The instructors are like personal trainers and are very motivating. They know exactly how to make you move your body with said equipment to get a great workout. Overall, the mirror has been a game-changer for me because I use it way more than any gym I used to go to. I see actual results. It helps keep me motivated, and I feel great." —Shawn
Get it from The Mirror for $995 (originally $1,495).
29. A Shark air purifier for $200 off providing both clean air (in rooms up to 1,200 square feet) and six high-speed fans to evenly distribute fresh air around the room. Plus, it has a Clean Sense IQ that auto-adjusts the power to maintain the air's purity.
Promising review: "I love this air purifier! You can actually see it working. Mine is in my bedroom, which is so helpful to my allergies! If I'm cooking something in the kitchen, you can see when the smell of the food reaches my bedroom door. When set on auto, the air quality number drops below 100% (how far it drops depends on the food smell) and the fan turn up and starts cleaning the air. Even with something like burned toast or popcorn, the air is cleaned and the smell is gone very quickly. Where burned popcorn otherwise lasts for hours. I'm very pleased with this product. I would definitely recommend it!" —Donanne Bisbee
30. A towel warmer for 30% off because nothing screams luxury living like stepping out of a warm bath or shower and wrapping yourself up with a warm towel. Oh yes, they won't be able to look at a shower or tub without thinking of you, which could get weird, but think of it as a compliment.
It fits about two towels (or even a towel and a robe or other fabric items) and has a 15-minute adjustable timer.
Promising review: "I bought one for myself, then bought several others as presents because it's so nice. It's fairly small and easy to find space for even in a small bathroom but is also big enough to hold two large towels at a time. There are a few small things to watch for: occasionally the on button takes a bit of finagling to work; it takes about eight minutes to hit 'maximum' towel warmth; if the lid is askew/not fully on the towel loses a lot of heat; there's a bit of a plastic odor that goes away after the first few uses. But if you're aware of those things it's super luxurious and worth every penny, having a super warm towel waiting for you counters all the misery of having to leave the shower in the winter. It also makes a great present, it's the kind of luxury item people don't normally think to get for themselves but makes life so much better. Anybody who says you can't buy happiness obviously hasn't bought a towel warmer." —Heather
31. A Mint mattress for 30% off from Tuft & Needle that's been hailed as the best mattress for couples. Even if your parent is solo, they'll still enjoy the adaptive foam and progressive support so they can wake up more rested and pain-free in the morning.
@tuftandneedle / Via instagram.com
Promising review: "This mattress has really helped me. I had lower back pain that I was seeing a chiropractor for but I no longer had time in my schedule to see. We were also overdue for a new mattress, while my back pain had returned. My back is drastically better since sleeping on this mattress. I went from having my back seize several times per day, to some limited tenderness once or twice per week. I'm basically functional again. And, the mattress wasn't life altering when I first laid on it. But maybe that's the point? It should feel just normal to be aligned normally? I wake up less in the night and I have way less back pain, and for me that's a win." —Another Sarah
Get it from Amazon for $521.50+ (originally $745+; available in five sizes) or from Tuft & Needle for $521.50+ (originally $745+; available in six sizes).
32. A sophisticated catch all with built-in charger to hold their trinkets and keep their phone charged at the same time. You can make it extra special by adding a monogram, too.
Promising review: "This charger is amazing. Already received one in white as a gift and had to pass the aloha since they had the brown in shop. It's the perfect size to sit on the night stand, be used as a catch all. As a bonus this review page wouldn't let me paste until I stated the three magic words, size, bonus and style but just know it's really nice and quality. Well worth your purchase!" —Nate S.
Shipping Info: Free shipping on all orders above $75 in the USA and Canada. Orders placed after 3 p.m. ET will be shipped the following business day. Monogrammed products may take an additional five to seven business days to process.
Get it from Courant for $131.25 (originally $175; available in five colors).
33. A Madewell large leather transport tote for 30% off perfect for everyday use because the simple style holds a lot while still looking professional.
Rachel Dunkel / BuzzFeed
Use code CLICKCLICK at checkout.
BuzzFeed Shopping writer Rachel Dunkel says, "Random canvas totes may come and go, but nothing beats having a permanent, go-to bag. I've had this since college when I used it to carry my heavy load of books, my laptop, and other English major paraphernalia, but it's transitioned flawlessly into my adult life where — OK — I still use it to carry books and my computer. The leather is getting a lovely patina and the structure of the bag is as strong as the day I got it. It has one zippered interior pocket which is perfect for keys, cards, or any other tiny necessities. I received this as a gift, so I can confirm that it makes a good one! My bag is even monogrammed, which made the gift all the more special. (You can add monogramming to almost any Madewell leather or denim item for $10 or for free if you're a Madewell Insider!)"
Get it from Madewell for $124.60 (originally $178; available in three colors).
34. A smart thermostat for 31% off so you can control the temperature of your home from anywhere. Yes, that means you can turn the heat up before you get home from your vacation and won't freeze the second you walk through the door.
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Reviews have been edited for length and/or clarity.


Don't satisfied with Carpet For Ford Expedition results or want to see more shopping ideas? Try to exlore these related searches: mp3 disc player, projector 3d 720p, budweiser speaker.
Expedition update.. Floor carpet done...some wire in..


Over the last few years there seems to have been an awful lot said about getting your "message" out. We all have something vitally important to say and the world needs us to say it, according to the "on trend" marketers. Back in the day it used to be all about passion and purpose and now it's all about "message".
You'd have thought I'd have learned my lesson from all the years spent searching futilely for MY passion and My purpose but no, I bought into the "message" thing, hook, line and sinker.
I searched hard for MY message and paid lots of money to those who were apparently in the know, so they could help me find it. This despite secretly suspecting I didn't have one and, quite honestly, not being that bothered about getting it "out there" if I did!
Initially, I thought I had a problem verbalising what I wanted to say because I noticed that others seemed to be able to articulate my ideas better than I. So, having been inspired by William Keiper's words below, I started collecting quotes, ideas and notes that resonated with my thinking or made me ponder or see things in a new light, and my 'bag of bits' was born.
"I then decided to create an action plan that would embody my unique offer of service. As part of the construction of my plan, I carefully selected words, quotations, references, catalogued "what others say about me" and even found photos that were representative of my uniqueness and my ability to serve others. I put these into an online template at first only accessible by me.
That was 5 months ago and, if you read yesterday's post, you'll know that I've found a use for my 'Bag of Bits' which does not involve the construction of an action plan, as it did for William. If you didn't read it you can catch up here: If I was Writing a Book.
Number 2 of 366 Book Bits.


text:
\section{abstract}

Cuckoo hashing \cite{cuckoo hashing} is a multiple choice hashing
scheme in which each item can be placed in multiple locations, and
collisions are resolved by moving items to their alternative locations.
In the classical implementation of two-way cuckoo hashing, the memory
is partitioned into contiguous disjoint fixed-size buckets. Each item
is hashed to two buckets, and may be stored in any of the positions
within those buckets. Ref. \cite{3.5 way} analyzed a variation in
which the buckets are contiguous and overlap. However, many systems
retrieve data from secondary storage in same-size blocks called pages.
Fetching a page is a relatively expensive process; but once a page
is fetched, its contents can be accessed orders of magnitude faster.
We utilize this property of memory retrieval, presenting a variant
of cuckoo hashing incorporating the following constraint: each bucket
must be fully contained in a single page, but buckets are not necessarily
contiguous. Empirical results show that this modification increases
memory utilization and decreases the number of iterations required
to insert an item. If each item is hashed to two buckets of capacity
two, the page size is 8, and each bucket is fully contained in a single
page, the memory utilization equals 89.71\% in the classical contiguous
disjoint bucket variant, 93.78\% in the contiguous overlapping bucket
variant, and increases to 97.46\% in our new non-contiguous bucket
variant. When the memory utilization is 92\% and we use breadth first
search to look for a vacant position, the number of iterations required
to insert a new item is dramatically reduced from 545 in the contiguous
overlapping buckets variant to 52 in our new non-contiguous bucket
variant. In addition to the empirical results, we present a theoretical
lower bound on the memory utilization of our variation as a function
of the page size.

\section{Introduction}

Cuckoo hashing \cite{cuckoo hashing} is a multiple choice hashing
scheme in which each item can be placed in multiple locations, and
collisions are resolved by moving items to their alternative locations.
This hashing scheme resembles the cuckoo's nesting habits: the cuckoo
lays its eggs in other birds' nests. When the cuckoo chick hatches,
it pushes the other eggs out of the nest. Hence the name {}``cuckoo
hashing.'' As Ref. \cite{3.5 way} explains, analysis of hashing
is similar to the analysis of balls and bins. Hashing an item to a
memory location corresponds to throwing a ball into a bin. Insights
from balls and bins processes led to breakthroughs in hashing methods.
For example, if we throw $n$ balls into $n$ bins independently and
uniformly, it is highly probable that the largest bin will get $\left(1+\textrm{o}\left(1\right)\right)\textrm{log}\left(n\right)/\textrm{log}\textrm{log}\left(n\right)$
balls. Azar et. al \cite{Azar} found that if each ball selects two
bins independently and uniformly, and is placed in the bin with fewer
balls, the final distribution is much more uniform. This led to hashing
each item to one of two possible buckets, decreasing the load on the
most-loaded bucket to $\textrm{log\ensuremath{\left(\textrm{log}\left(n\right)\right)}}+\textrm{O}(1)$
with high probability. In general, if each item is hashed into $d\geq2$
buckets, the maximum load decreases to $\textrm{log\ensuremath{\left(\textrm{log}\left(n\right)\right)}}/\textrm{log}\left(d\right)+\textrm{O}(1).$

Cuckoo hashing \cite{cuckoo hashing} is an extension of two-way hashing.
Each item is hashed to a few possible buckets, and existing items
may be moved to their alternate buckets in order to free space for
a new item. There are many variants of cuckoo hashing. The goals of
cuckoo hashing are to increase memory utilization (the number of items
that can be successfully hashed to a given memory size) and to decrease
insertion complexity. Pagh and Rodler \cite{cuckoo hashing} analyzed
hashing of each item to $d=2$ buckets of capacity $k=1$, and demonstrated
that moving items during inserts results in 50\% space utilization
with high probability. Fotakis et. al. \cite{Space efficient hash tables}
analyzed hashing of each item into more than two buckets. Ref. \cite{Efficient hashing with lookups in two memory accesses}
analyzed a practically-important case in which each item is hashed
to $d=2$ buckets of capacity $k=2$. Refs. \cite{The k-orientability thresholds,The random graph threshold for k-orientiability}
found tight memory utilization thresholds for $d=2$ buckets of any
size $k\ge2$. Specifically, they proved that the memory utilization
for $d=2$ and $k=2$ is 89.7\%.

Ref. \cite{Tight Thresholds for Cuckoo Hashing} proved that the maximum
memory utilization thresholds for $d\ge3$ and $k=1$ are equal to
the previously known thresholds for the random k-XORSAT problem. Ref.
\cite{Maximum Matchings,Orientability of Random Hypergraphs} developed
a tight formula for memory utilization for any $d\ge3$ and $k=1$
and Ref. \cite{Multiple-orientability Thresholds} extended the formula
to any $d\ge3$ and $k\ge1$.

\emph{comment added.} While this work was being completed, we became
aware of Ref. \cite{Cuckoo Hashing with Pages} which proposed a model
where the memory is divided into pages and each key has several possible
locations on a single page as well as additional choices on a second
backup page. They provide interesting experimental results.

In a classical implementation of two-way cuckoo hashing, the memory
is partitioned into contiguous disjoint fixed-sized buckets of size
$k$ . Each item is hashed to 2 buckets and may be stored in any of
the $2k$ locations within those buckets. Ref. \cite{3.5 way} analyze
a variation in which the buckets overlap. For example, if the bucket
capacity $k$ is 3, the disjoint bucket memory locations are: $\left\{ 0,1,2\right\} ,\left\{ 3,4,5\right\} ,\left\{ 6,7,8\right\} ,\ldots$.
whereas the overlapping bucket memory locations are: $\left\{ 0,1,2\right\} ,\left\{ 1,2,3\right\} ,\left\{ 3,4,5\right\} ,\ldots$.

Their empirical results show that this variation increases memory
utilization from 89.7\% to 96.5\% for $d=2$ and $k=2$. However,
many systems retrieve data from secondary storage in same-size blocks
called pages. Fetching a page is a relatively expensive process, but
once a page is fetched, its contents can be accessed orders of magnitude
more quickly. We utilize this property of memory retrieval to present
a variant of cuckoo hashing requiring that each bucket be fully contained
in a single page but buckets are not necessarily contiguous.

In this paper we compare the following three variants of cuckoo hashing:
\begin{enumerate}
\item CUCKOO-CHOOSE-K- the algorithm introduced in this paper. The buckets
are \emph{any} $k$ cells in a page, not necessarily in contiguous
locations. There are $\binom{t}{k}$ buckets in a page, where $t$
is the size of the page.
\item CUCKOO-OVERLAP \cite{3.5 way}- The buckets are contiguous and overlap.
Here we assume that all buckets are fully contained in a single page,
so there are $t-k+1$ buckets in a page. This is a generalization
of Ref. \cite{3.5 way}. Originally Ref. \cite{3.5 way} did not consider
dividing the memory into pages.
\item CUCKOO-DISJOINT \cite{cuckoo hashing}- The buckets are contiguous
and not overlapping. There are $t/k$ buckets in a page. This is a
generalization of Ref. \cite{cuckoo hashing}. Originally Ref. \cite{cuckoo hashing}
did not consider larger buckets.
\end{enumerate}
Note that algorithm CUCKOO-DISJOINT is the extreme case of the CUCKOO-OVERLAP
and CUCKOO-CHOOSE\_K algorithms when the size of the page $t$ equals
the size of the bucket $k$.

We prove theoretically and present empirical evidence that our CUCKOO-CHOOSE-K
modification increases memory utilization. Moreover, using the classical
cuckoo hashing scheme, an item insertion requires multiple look-ups
of candidates to displace. Empirical results show that our modification
dramatically decreases the number of candidate look-ups required to
insert an item compared to Ref. \cite{3.5 way}. In the overlapping
buckets variant \cite{3.5 way}, some buckets are split between two
pages, so that each item resides in up to $2d$ pages. In our variant,
each bucket is fully contained in a single page.

An appealing experimental result is that CUCKOO-CHOOSE-K memory utilization
converges very quickly as a function of the page size $t$. When $k=2$
and $t=16$, memory utilization is 0.9763. This value is almost identical
to memory utilization when $t=2^{20}$ which equals 0.9767. CUCKOO-OVERLAP
memory utilization when $t=16$ is 0.9494, and CUCKOO-DISJOINT memory
utilization is only 0.8970. If we allow a tiny gap of one inside the
buckets $(t=3),$ memory utilization increases from 0.9229 (CUCKOO-OVERLAP)
to 0.9480 (CUCKOO-CHOOSE-K). Table \ref{fig:Number-of-iteration}
specifies the parameters used in our analysis.

\section{Theoretical analysis}

We can determine the success of cuckoo hashing by analyzing the cuckoo
hyper graph. The vertices of the graph are the memory locations. The
hyper-edges of the graph connect all the memory locations where each
item could be placed. Recall that each item can be placed in $d$
buckets chosen uniformly and independently of other items. Each bucket
is composed of any $k$ locations in a page.

It is well known (see, e.g., ref. \cite{3.5 way} for a proof) that
a cuckoo hash \emph{fails}$ $ if and only if there is a sub-graph
$S$ with $v$ vertices and more than $v$ edges. We say that a sub-graph
$S$ has \emph{failed} if it has more edges than vertices.

\begin{table}
\begin{tabular}{|l|l|l|}
\hline
Symbol & Description  & Comments\tabularnewline
\hline
\hline
$n$  & number of vertices  & $n\rightarrow\infty$\tabularnewline
 & (hash table capacity)  & \tabularnewline
\hline
$m$  & number of edges  & $m\leq n$, $m\rightarrow\infty$ \tabularnewline
 & (hashed items)  & \tabularnewline
\hline
$d$  & number of buckets each  & typical value: 2, $dk>2$\tabularnewline
 & item is hashed to  & \tabularnewline
\hline
$k$  & bucket size  & typical value: 2-3, $dk>2$\tabularnewline
\hline
$t$  & page size  & $t\geq k$. $k$ divides $t$. $t$ divides $n$.\tabularnewline
\hline
$g$  & number of pages  & $g=n/t$. \tabularnewline
\hline
$\beta$  & memory utilization  & $\beta=\frac{m}{n}$,$0<\beta\leq1$$ $\tabularnewline
\hline
$V$  & a set of vertices  & $\left|V\right|=v$\tabularnewline
\hline
$S=S\mbox{(V,E) }$  & a sub-graph  & \tabularnewline
\hline
$v$  & $v=\left|V\right|$  & $dk\le v<m$. \tabularnewline
 &  & (if $v\geq m$ or $v<dk$ then $S$ cannot fail).\tabularnewline
\hline
$x$  & $x=\frac{v}{n}$  & $\frac{dk}{n}\le x<\beta$$ $.\tabularnewline
\hline
$\epsilon$ & a small constant & $0<\epsilon\ll1$\tabularnewline
\hline
$\delta$ & a small constant & $0<\delta\ll1$\tabularnewline
\hline
\end{tabular}\caption{\label{tab:Parameter-names-and}Parameter names and descriptions}

\end{table}

We will begin by analyzing the probability of success of CUCKOO-CHOOSE-K
for the case where the page size $t$ equals the array size $n$.
This simple and special case is presented here to introduce the main
ideas applied in the following section, where we analyze the general
case where the page size is a finite constant (independent of $n$).

\subsection{Memory utilization when the page size $t$ equals the array size
$n$}

An analysis of memory utilization has been performed previously in
\cite{Space efficient hash tables}. In their analysis, they assume
$k=1$ and prove that if $d\ge\frac{2}{\beta}\log\left(\frac{\textrm{e}\beta}{1-\beta}\right)$,
then the hashing will be successful with a probability of at least
$1-\textrm{O}(n^{4-2d})$. Here we derive a similar constraint on
memory utilization $\beta$. We solve the constraint numerically for
different values of $k$ and $d$, and obtain a lower bound on possible
memory utilization for the specified values. We perform the analysis
using a modification of the method in \cite{Space efficient hash tables},
which we will later generalize to page sizes being equal to any given
constant.

We will bound the failure probability using the union bound. But first,
we would like to reduce redundant summations. We observe that:
\begin{itemize}
\item If there exists a sub-graph $S\left(V,E\right)$ with $\left|E\right|>\left|V\right|$
and there exists an edge that has exactly one vertex $v_{0}$ outside
of V, then the sub-graph $S'\left(V'=V\cup\left\{ v_{0}\right\} ,E'\right)$
also has more edges than vertices since $\left|E'\right|\geq\left|E\right|+1>\left|V\right|+1=\left|V'\right|$.
\item If there exists a sub-graph $S\left(V,E\right)$, such that $\left|V\right|=v$
and $\left|E\right|>v+1$ then there exists a sub-graph $S'\left(V',E'\right)$
such that $\left|E'\right|=\left|V'\right|+1$. We can find such a
sub-graph simply by adding vertices to $V$ one by one until we get
a sub-graph where the number of edges equals the number of vertices
plus one.
\end{itemize}
For each sub-graph $S$ we define an indicator variable $Z_{S}.$

$Z_{S}=\begin{cases}
\textrm{1} & S\left(V,E\right)\textrm{\,\ has\,}\left|V\right|=v\textrm{\,\ vertices\,\ and\,}\left|E\right|=v+1\,\textrm{edges}\textrm{\,\ AND}\\
 & \textrm{There\,\ is\,\ no\,\ edge\,\ that\,\ connects\,}V\textrm{\,\ to\,\ exactly\,\ one\,\ vertex\,\ from\,\ outside\,\ of\,}V\\
\textrm{0} & \textrm{otherwise}\end{cases}$

If $Z_{s}=1$, then we will say that $S$ is a \emph{bad} sub-graph,
and otherwise we will say that $S$ is a \emph{good} sub-graph. If
the sum over $Z_{s}$ of all sub-graphs is equal to zero then every
sub-graph is good then the cuckoo hash \emph{succeeded}$ $. We will
find the the memory utilization $\beta$ such that the sum over $Z_{s}$
of all sub-graphs is $\textrm{o}(1)$ as $n\rightarrow\infty$.

Let $p_{hit}$ be the probability that a random edge hits $V$. Let
$p_{1}$ be the probability that a random edge connects $V$ to exactly
one vertex from outside of V and let $p_{bad}\left(v\right)$ be probability
that \emph{a given }sub-graph $S\left(V,E\right)$ is bad.
\begin{lem}
$p_{bad}\left(v\right)=\binom{m}{v+1}p_{hit}^{v+1}\left(1-p_{1}-p_{hit}\right)^{m-\left(v+1\right)}$\end{lem}
\begin{proof}
Immediate from the definition of $Z_{s}$. For S to be bad, exactly
$v+1$ edges out of $m$ edges must hit $V$ and all the rest must
miss $V$ and must not connect $V$ to exactly one vertex from outside
of V.\end{proof}
\begin{lem}
The probability that a random edge hits $V$ is $p_{hit}\left(v\right)=\left(\frac{\binom{v}{k}}{\binom{n}{k}}\right)^{d}$\end{lem}
\begin{proof}
Each item is hashed independently to $d$ buckets and the size of
each bucket is $k$. The number of buckets in $V$ is therefore $\binom{v}{k}$
and the total number of buckets is $\binom{n}{k}$.\end{proof}
\begin{lem}
The probability that a random edge connects $V$ to exactly one vertex
from outside of V is $p_{1}=d\frac{\left(n-v\right)\binom{v}{k-1}}{\binom{n}{k}}\left(\frac{\binom{v}{k}}{\binom{n}{k}}\right)^{d-1}$\end{lem}
\begin{proof}
$d-1$ buckets must all fall in $V$ and one bucket must contain any
$k-1$ vertices from $V$ and any of the $n-v$ vertices from outside
of $V$.
\end{proof}
Let $P_{bad}\left(v\right)$ be the probability that there exists
a sub-graph $S$ with $v$ vertices such that $S$ is bad. According
to the union bound, $P_{bad}\left(v\right)<N\left(v\right)\cdot p_{bad}\left(v\right)$,
where $N_{v}=\binom{n}{v}$ is the number of sub-graphs with $v$
vertices. We are going to analyze $P_{bad}\left(v\right)$ as $n\rightarrow\infty$.
If for all $v$, $P_{bad}\left(v\right)=\textrm{o}\left(\frac{1}{n}\right)$,
then $\sum_{v=dk}^{n}P_{bad}\left(v\right)\le\textrm{o}\left(1\right)$
and the cuckoo hash succeeds with high probability. The analysis is
similar to the analysis given in \cite{Space efficient hash tables}.
Let $x_{0}=\exp\left(\frac{-2}{dk-2}\right)$. We divide the analysis
into two sections. In section \ref{sub:x<x0 Analysis} we show that
for any memory utilization $\beta$ and $\forall\frac{dk}{n}\le x<x_{0}$,
$P_{bad}\left(x\right)$ is $\textrm{o}\left(\frac{1}{n}\right)$.
In section \ref{sub:x>x0 Analysis}we find the maximum memory utilization
$\beta$ such that $\forall x_{0}\le x<\beta$, $P_{bad}\left(x\right)$
is exponentially small.

\subsubsection{\label{sub:x<x0 Analysis}\textup{$P_{bad}\left(x\right)$} Analysis
for $\frac{dk}{n}\le x<x_{0}$}

In this section we show that if $dk>2$ then for any memory utilization
$\beta$ and $\forall\frac{dk}{n}\le x<x_{0}$, $P_{bad}\left(x\right)$
is $\textrm{o}\left(\frac{1}{n}\right)$.
\begin{lem}
\label{lem:Pv<c0c1}$P_{bad}\left(x\right)<c_{0}\left(x\right)\cdot c_{1}^{n}\left(x\right)$,

where $c_{0}\left(x\right)=\mathrm{e}\cdot x^{dk-1}$ and $c_{1}\left(x\right)=\mathrm{e}^{2x}\cdot x^{\left(dk-2\right)x}$\textup{.}\end{lem}
\begin{proof}
See appendix \ref{sec:Proof-of-Pv<c0c1}.\end{proof}
\begin{thm}
\label{lem:Pv is good t=00003Dn}

$\mbox{Let}$ $\delta$ be a small constant, $0<\delta\ll$1. If $dk\ge3$
then for any load $\beta$:

1. If $\frac{dk}{n}\le x\le\frac{dk}{n}+\delta$, then $P_{bad}\left(x\right)<\textrm{O\ensuremath{\left(n^{-\left(\left(dk\right)^{2}-dk-1\right)}\right)}}=\textrm{o}\left(\frac{1}{n}\right)$
.

2. If $\frac{dk}{n}+\delta\le x\le x_{0}-\delta$, then $P_{bad}\left(x\right)$
decreases exponentially as $n\rightarrow\infty$.\end{thm}
\begin{proof}
For any memory utilization $\beta$, $P_{bad}\left(x\right)<c_{0}\left(x\right)\cdot c_{1}^{n}\left(x\right)$
,

where $c_{0}\left(x\right)=\mathrm{e}\cdot x^{dk-1}$ and $c_{1}\left(x\right)=\mathrm{e}^{2x}\cdot x^{\left(dk-2\right)x}$.

Note that $c_{0}\left(x\right)$ and $c_{1}\left(x\right)$ are independent
of $\beta$. Recall that $x_{0}=\exp\left(\frac{-2}{dk-2}\right).$
$\forall\frac{dk}{n}+\delta\le x\le x_{0}-\delta$, there exist a
constant $\epsilon$ such that $c_{1}\left(x\right)<1-\epsilon$ .
We obtain that:

1. If $x\rightarrow\frac{dk}{n}$, then $P_{bad}\left(x\right)<\textrm{lim}{}_{x\rightarrow\frac{dk}{n}}c_{0}\left(x\right)\cdot c_{1}^{n}\left(x\right)=\textrm{\textrm{O\ensuremath{\left(n^{-\left(\left(dk\right)^{2}-dk-1\right)}\right)}}}\le\textrm{O}\left(n^{-5}\right)=\textrm{o}\left(\frac{1}{n}\right)$
.

2. If $\frac{dk}{n}+\delta\leq x\le x_{0}-\delta,$ then $c_{1}\left(x\right)<1-\epsilon$,
and $P_{bad}\left(x\right)<c_{0}\left(x\right)\cdot c_{1}^{n}\left(x\right)$
decreases exponentially as $n\rightarrow\infty$.
\end{proof}

\subsubsection{\label{sub:x>x0 Analysis}\textup{$P_{bad}\left(x\right)$} Analysis
for $x_{0}\le x<\beta$}

In this section we are going to find the maximum memory utilization
$\beta$ such that $\forall x_{0}\le x<\beta$, the probability that
there exists a bad sub-graph is exponentially small.
\begin{lem}
\label{lem:Pv<c2c3c4c5}$\forall x_{0}\le x<\beta$, $P_{bad}\left(x\right)<\textrm{O}(1)\cdot c_{5}^{n}\left(x,\beta\right)$
where

$c_{5}\left(x,\beta\right)=\left(\frac{1}{1-x}\right)^{\left(1-x\right)}\left(\frac{1}{x}\right)^{x}\left(\frac{\beta}{\beta-x}\right)^{\left(\beta-x\right)}\left(\frac{\beta}{x}\right)^{x}x^{dkx}\left(1-dk\left(1-x\right)x^{dk-1}-x^{dk}\right)^{\beta-x}$\end{lem}
\begin{proof}
See appendix \ref{sec:Proof-Of-Pv<c2c3c4c5}\end{proof}
\begin{thm}
If $c_{5}\left(x,\beta\right)<1-\epsilon$ for all $x_{0}\le x<\beta$,
then $P_{bad}\left(x\right)$ decreases exponentially as $n\rightarrow\infty$.
Any memory utilization $\beta$ that satisfies the constraint is a
lower bound on the possible memory utilization.\end{thm}
\begin{proof}
The theorem follows directly from the inequality $P_{bad}\left(x\right)<\textrm{O}(1)\cdot c_{5}^{n}\left(x,\beta\right)$.
\end{proof}
Numerical solutions to the constraint $c_{5}\left(x,\beta\right)<1$
indicate that the memory utilization of the CUCKOO-K algorithm is
$\beta_{Choose-2}(k=2,d=2,t=n)>0.937$ and $ $$\beta_{Choose-3}(k=3,d=2,t=n)>0.993$.
Our empirical results show that $\beta_{Choose-2}(k=2,d=2,t=n)=0.9768$
and $\beta_{Choose-3}(k=3,d=2,t=n)=0.9974$. The memory utilization
for $kd>6$ rapidly approaches one. Theoretical analysis performed
by \cite{The random graph threshold for k-orientiability,The k-orientability thresholds}
provided tight thresholds of the memory utilization of the CUCKOO-DISJOINT
algorithm. $\beta_{Disjoint}\left(k=2,d=2,t=n\right)=0.8970$ and
$\beta_{Disjoint}\left(k=3,d=2,t=n\right)=0.9592$. Ref. \cite{3.5 way}
do not provide a theoretical memory utilization threshold for small
$k$. The empirical results of Ref. \cite{3.5 way} show that in the
CUCKOO-OVERLAP algorithm $\beta_{Overlap}(k=2,d=2,t=n)=0.9650$ and
$\beta_{Overlap}(k=3,d=2,t=n)=0.9945$. The theoretical analysis of
the CUCKOO-DISJOINT algorithm performed in \cite{Maximum Matchings,Tight Thresholds for Cuckoo Hashing,Orientability of Random Hypergraphs}
does not apply for $k>1$ and the theoretical analysis of the CUCKOO-DISJOINT
algorithm performed by \cite{Multiple-orientability Thresholds} does
not apply for $d<3$.

\subsection{Memory utilization when the page size $t$ is a given constant}

In this section we analyze the probability that the hashing fails
for the case where the page size $t$ equals a constant. Let $P_{fail}\left(v\right)$
be the probability that there exists a sub-graph $S$ with $v$ vertices
such that $S$ has more edges than vertices and every vertex is in
at least one edge.

Let $x_{1}=\mbox{\ensuremath{\exp\left(\frac{-\left(k+1\right)}{dk-\left(k+1\right)}\right)}}$.
Here again we divide the analysis into two sections. In section \ref{sub:x<x1 Analysis}
we show that for any memory utilization $\beta$ and $\forall\frac{dk}{n}\le x<x_{1}$,
$P_{fail}\left(x\right)$ is $\textrm{o}\left(\frac{1}{n}\right)$.
In section \ref{sub:x>x1 Analysis} we find the maximum memory utilization
$\beta$ such that $\forall x_{1}\le x<\beta$, $P_{bad}\left(x\right)$
is exponentially small.

\subsubsection{\label{sub:x<x1 Analysis}$P_{fail}\left(x\right)$ Analysis for
$\frac{dk}{n}\le x<x_{1}$}

In this section we show that for any memory utilization $\beta$ and
$\forall\frac{dk}{n}\le x<x_{1}$, $P_{fail}\left(x\right)$ is $\textrm{o}\left(\frac{1}{n}\right)$.

The analysis here is similar to the case above where $t=n$, however
now we need to take into consideration the distribution of the vertices
over the pages.

Let $V$ be a given set of vertices, and let $v_{i}$ be the number
of vertices in page $i$. The probability that a random edge hits
$V$ is equal to $p_{hit}\left(V,t\right)=\left(\sum_{i=1}^{g}\frac{\binom{v_{i}}{k}}{g\cdot\binom{t}{k}}\right)^{d}\leq\left(\frac{1}{g}\sum_{i=1}^{g}\left(\frac{v_{i}}{t}\right)^{k}\right)^{d}$.

Let $\widetilde{p}_{hit}\left(V,t\right)=\left(\frac{1}{g}\sum_{i=1}^{g}\left(\frac{v_{i}}{t}\right)^{k}\right)^{d}$
be an upper bound on $p_{hit}\left(V,t\right)$.

We are going to use the following lemma which states that increasing
the page size reduces $\widetilde{p}_{hit}$.
\begin{lem}
\label{lem: low t is bad} For any set of vertices V and any integer
c,$\widetilde{p}_{hit}\left(V,t\right)\ge\widetilde{p}_{hit}\left(V,ct\right)$. \end{lem}
\begin{proof}
Since the function $f\left(v\right)=\left(\frac{v}{t}\right)^{k}$
is convex, for any sequence of $c$ pages, $\frac{1}{c}\left(\left(\frac{v_{1}}{t}\right)^{k}+\ldots+\left(\frac{v_{c}}{t}\right)^{k}\right)\ge\left(\frac{v_{1}+\ldots+v_{c}}{ct}\right)^{k}$,
thus multiplying the page size by a factor $c$ does not increase
$\widetilde{p}_{hit}$. For convenience, we restrict our analysis
to pages of size $t=k\cdot c$, where c is any integer. The worst
case is obtained when $t=k$ which is equivalent to the classical
CUCKOO-DISJOINT hashing.

We will now analyze $P_{fail}\left(x\right)$ and $P_{bad}\left(x\right)$
as $n\rightarrow\infty$. Recall that $\beta=\frac{m}{n}$ $ $ is
the memory utilization, $0<\beta\leq1$ and $x=\frac{v}{n}$. \end{proof}
\begin{lem}
\label{lem:Pv<c6c7}$P_{fail}\left(x\right)<c_{6}\left(x\right)\cdot c_{7}^{n}\left(x\right)$

where $c_{6}\left(x\right)=\mathrm{e}x^{d-1}$ and $c_{7}\left(x\right)=\mathrm{e}^{\frac{\left(k+1\right)x}{k}}x^{\frac{\left(dk-1-k\right)x}{k}}$.\end{lem}
\begin{proof}
See appendix \ref{sec:Proof-of Pv<c6c7}.\end{proof}
\begin{thm}
$\mbox{Let}$ $\delta$ be a small constant, $0<\delta\ll$1. If $\left(d-1\right)dk\ge3$,
then for any load $\beta$:

1. If $\frac{dk}{n}\le x\le\frac{dk}{n}+\delta$, then $P_{fail}\left(x\right)<\textrm{O\ensuremath{\left(n^{-\left(\left(d-1\right)dk-1\right)}\right)}}=\textrm{o}\left(\frac{1}{n}\right)$
.

2. If $\frac{dk}{n}+\delta\le x\le x_{1}-\delta$, then $P_{fail}\left(x\right)$
decreases exponentially as $n\rightarrow\infty$.\end{thm}
\begin{proof}
For any memory utilization $\beta$, $P_{fail}\left(x\right)<c_{6}\left(x\right)\cdot c_{7}^{n}\left(x\right)$

where $c_{6}\left(x\right)=\mathrm{e}x^{d-1}$ and $c_{7}\left(x\right)=\mathrm{e}^{\frac{\left(k+1\right)x}{k}}x^{\frac{\left(dk-1-k\right)x}{k}}$.

Note that $c_{6}\left(x\right)$ and $c_{7}\left(x\right)$ are independent
of $\beta$. Recall that $x_{1}=\mbox{\ensuremath{\exp\left(\frac{-\left(k+1\right)}{dk-\left(k+1\right)}\right)}}$.
$\forall\frac{dk}{n}+\delta\le x\le x_{1}-\delta$, there exist a
constant $\epsilon$ such that $c_{7}\left(x\right)<1-\epsilon$ .
We obtain that:

1. If $x\rightarrow\frac{dk}{n}$, then $P_{fail}\left(x\right)<\textrm{lim}{}_{x\rightarrow\frac{dk}{n}}c_{6}\left(x\right)\cdot c_{7}^{n}\left(x\right)=\textrm{O}\left(n^{-\left(\left(d-1\right)dk-1\right)}\right)\le\textrm{O}\left(n^{-2}\right)=\textrm{o}\left(\frac{1}{n}\right)$
.

2. If $\frac{dk}{n}+\delta\leq x<x_{1}-\delta$, then $c_{7}\left(x\right)<1-\epsilon$,
and $P_{fail}\left(x\right)<c_{6}\left(x\right)\cdot c_{7}^{n}\left(x\right)$
decreases exponentially as $n\rightarrow\infty$.
\end{proof}

\subsubsection{\label{sub:x>x1 Analysis}$P_{bad}\left(x\right)$ Analysis for $x_{1}\le x<\beta$}

In this section we find the maximum memory utilization $\beta$ such
that $\forall x_{1}<x<\beta$, the probability that there exists a
bad sub-graph is exponentially small. We examine the set of sub-graphs
that have a given distribution $\underline{\text{a}}$ of vertices
over the pages. $\underline{\text{a}}=\left(a_{0},...,a_{t}\right)$,
where $a_{i}$ is the number of pages that have $i$ vertices. For
example, when the page size $t$ was equal to $n$ and the number
of pages $g$ was 1, the number of sub-graphs with $v$ vertices was
$\binom{n}{v}$ and the corresponding $\underline{\text{a}}$ of those
sub-graphs was $\left\{ 0,...,0,a_{v}=1,0,...,0\right\} $. by definition
of $\underline{\text{a}}$,

\begin{equation}
\sum_{i=0}^{t}a_{i}=g\end{equation}

\begin{lem}
When the page size $t$ is a given constant, the number of different
possible values of $\underline{\text{a}}$ is polynomial in $n$.\end{lem}
\begin{proof}
We denote by $\#\underline{\text{a}}$ The number of different possible
values of $\underline{\text{a}}$.

$\#\underline{\text{a}}<g^{t}=\left(\frac{n}{t}\right)^{t}$. Since
$t$ is constant, $\#a$ is polynomial in $n$.
\end{proof}
Let $P_{bad}\left(\underline{\text{a}}\right)$ be the probability
that there exists a bad sub-graph with distribution $\underline{\text{a}}$
of vertices over the pages. If $P_{bad}\left(\underline{\text{a}}\right)$
is exponentially small for every $\underline{\text{a}}$, then the
union bound over a polynomial number of all possible values of $a$
is also exponentially small. Let $p_{bad}\left(\underline{\text{a}}\right)$
be the probability that \emph{a given }sub-graph $S\left(V,E\right)$
with $\underline{\text{a}}=\left(a_{0},...,a_{t}\right)$ is bad.

Let $\hat{a}=\frac{\underline{a}}{g}$ be a unit vector. When the
page size $t$ is a constant, the probability that a random edge hits
$V$ is:

\begin{equation}
p_{hit}\left(\underline{\text{a}}\right)=\left(\frac{\sum_{i=k}^{t}a_{i}\binom{i}{k}}{g\binom{t}{k}}\right)^{d}=\left(\frac{\sum_{i=k}^{t}\hat{a}_{i}\binom{i}{k}}{\binom{t}{k}}\right)^{d}\end{equation}
 and the probability that a random edge connects $V$ to exactly one
vertex from outside of V is

\begin{equation}
p_{1}\left(\underline{\text{a}}\right)=d\left(\frac{\sum_{i=k}^{t}a_{i}\left(t-i\right)\binom{i}{k-1}}{g\binom{t}{k}}\right)\left(\frac{\sum_{i=k}^{t}a_{i}\binom{i}{k}}{g\binom{t}{k}}\right)^{d-1}=d\left(\frac{\sum_{i=k}^{t}\hat{a}_{i}\left(t-i\right)\binom{i}{k-1}}{\binom{t}{k}}\right)\left(\frac{\sum_{i=k}^{t}\hat{a}_{i}\binom{i}{k}}{\binom{t}{k}}\right)^{d-1}\end{equation}
 Using the union bound we obtain that

\begin{equation}
P_{bad}\left(\underline{\text{a}}\right)<N\left(\underline{\text{a}}\right)\cdot p_{bad}\left(\underline{\text{a}}\right)\end{equation}
 where $N\left(\underline{\text{a}}\right)$ is the number of sub-graphs
with $\underline{\text{a}}=\left(a_{0},...,a_{t}\right)$.

\begin{equation}
N\left(\underline{\text{a}}\right)=\binom{g}{a_{0},...,a_{t}}\prod_{i=0}^{t}\binom{t}{_{i}}^{a_{i}}\end{equation}
For the asymptotic behavior of $N\left(\underline{\text{a}}\right)$,
we are going to use the following lemma:
\begin{lem}
\label{lem:multinom_bound}$\binom{g}{a_{0},...,a_{t}}\leq\prod_{i=0}^{t}\left(\frac{g}{a_{i}}\right)^{a_{i}}$\end{lem}
\begin{proof}
See Appendix \ref{sec:Proof-of-Lemma multinom_bound}. \end{proof}
\begin{lem}
\label{lem:Pv<c8c9}$P_{bad}\left(\hat{a},\beta\right)<\textrm{O}(1)\cdot c_{8}\left(\hat{a},\beta\right)\cdot c_{9}^{n}\left(\hat{a},\beta\right)$
where

$c_{8}\left(\hat{a},\beta\right)=p_{hit}\left(1-p_{1}-p_{hit}\right)^{-1}\left(\frac{\beta-x}{x}\right)$
and

$c_{9}\left(\hat{a},\beta\right)=\prod_{i=0}^{t}\left(\frac{1}{\hat{a}_{i}}\right)^{\frac{\hat{a}_{i}}{t}}\prod_{i=0}^{t}\binom{t}{_{i}}^{\frac{\hat{a}_{i}}{t}}\left(\frac{\beta}{\beta-x}\right)^{\left(\beta-x\right)}\left(\frac{\beta}{x}\right)^{x}p_{hit}^{x}\left(1-p_{1}-p_{hit}\right)^{\beta-x}$\end{lem}
\begin{proof}
See appendix \ref{sec:Proof-of-Pv<c8c9}.\end{proof}
\begin{thm}
If $ $$c_{9}\left(\hat{a},\beta\right)<1-\epsilon$ for all $\forall\, x_{1}\le x<\beta$,
then $P_{bad}\left(\hat{a},\beta\right)$ decreases exponentially
as $n\rightarrow\infty$ . Any memory utilization $\beta$ that satisfies
the constraint is a lower bound on the possible memory utilization.\end{thm}
\begin{proof}
The theorem follows directly from the inequality $P_{bad}\left(\hat{a},\beta\right)<\textrm{O}(1)\cdot c_{8}\left(\hat{a},\beta\right)\cdot c_{9}^{n}\left(\hat{a},\beta\right)$.
\end{proof}
Theoretical lower bounds of the memory utilization obtained from numerical
solutions of the constraint $c_{9}\left(\hat{a},\beta\right)<1$ are
displayed in figure \ref{fig:Memory-utilization Vs. page size}.

\section{Empirical Results}

\begin{figure}
\includegraphics[scale=0.5]{beta_pageSize_theoEmpi}

\caption{\label{fig:Memory-utilization Vs. page size}}

Memory utilization vs. page size. Empirical CUCKOO-CHOOSE-K (green),
Empirical CUCKOO-OVERLAP (red), approximation formula of Empirical
CUCKOO-CHOOSE-K (blue), and theoretical lower bound of CUCKOO-CHOOSE-K
(black). left: $k=2$, right: $k=3$.$ $
\end{figure}

The experiments were conducted with a similar protocol to the one
described in \cite{3.5 way}. In all experiments the number of the
buckets, $d$, was two. The capacity of each bucket $k$ was either
two or three. The size of the hash tables $n$ was $1,209,600$. The
reported memory utilization $\beta$ is the mean memory utilization
over twenty trials. The random hash functions were based on the Matlab
{}``rand'' function with the twister method. Items were inserted
into the hash table one-by-one until an item could not be inserted.
The results of both CUCKOO-CHOOSE-K and CUCKOO-OVERLAP were notably
stable. In each case, the standard deviation was a few hundredths
of a percent, so error bars would be invisible in the figure. Such
strongly predictable behavior is appealing from a practical standpoint.
Since we added a paging constraint, our results are not comparable
to previous works that do not include a paging constraint.

\begin{figure}
\includegraphics[scale=0.4]{itr_beta_k2_d2_t8_itr_pagesize_k2_d2_beta92}\caption{\label{fig:Number-of-iteration}}

Number of lookups required to insert an item vs. memory utilization
(left) and vs. page size (right). In the left figure the page size
is 8. In the right figure the memory utilization is 92\%. The left
figure was smoothed with an averaging filter. The variance in the
number of lookups required to insert an item was much smallar in CUCKOO-CHOOSE-K.
\end{figure}

Experiments show that CUCKOO-CHOOSE-K improves memory utilization
significantly even for a small page size $t$ and a small bucket capacity
$k$ when compared to the classical cuckoo hashing CUCKOO-DISJOINT.
It outperforms CUCKOO-OVERLAP as well. Recall that CUCKOO-DISJOINT
is the extreme case of CUCKOO-CHOOSE-K and CUCKOO-OVERLAP when the
page size is equal to bucket size $k$. The memory utilization $\beta_{Choose-k}$
converges very quickly to its maximum value. For example $\beta_{Choose-2}(t=16)=0.9763$
is almost equal to $\beta_{Choose-2}(t=1,209,600)=0.9767$. Whereas
$\beta_{Overlap-2}\left(t=16\right)=0.9494$ and $\beta_{Disjoint-2}=0.8970$.

The empirical memory utilization can be approximated very accurately
by the following formulas:

\begin{equation}
\beta_{Choose-2}\left(t\right)\approx0.977\cdot\left(1-(\frac{t}{0.764})^{-2.604}\right)\end{equation}

\begin{equation}
\beta_{Choose-3}\left(t\right)\approx0.997\cdot\left(1-(\frac{t}{1.011})^{-2.998}\right)\end{equation}

The maximum approximation error is 0.0011 for $k=2$ and 0.0015 for
$k=3$.

The empirical results and their approximations are displayed in figure
\ref{fig:Memory-utilization Vs. page size} together with empirical
results of CUCKOO-OVERLAP. The memory utilization for $kd>6$ rapidly
approaches one (not displayed).

CUCKOO-CHOOSE-K outperforms CUCKOO-OVERLAP not only in memory utilization,
but in the number of iterations required to insert a new item as well.
Figure \ref{fig:Number-of-iteration} illustrates the number of iterations
required to insert a new item when the hash table is 92\% full and
we use breadth first search to search for a vacant position. $\#itr_{Choose-2}(t=8)=$52,
whereas $\#itr_{Overlap-2}(t=8)=545$. Note that in these simulations
we did not limit the number of insert iterations and we continued
to insert items as long as we could find free locations. Most applications
limit the number of inserted iterations, and maintain a low memory
utilization in order to find a free location easily. If an empty position
is not found within a fixed number of iterations, a rehash is performed
or the item is placed outside of the cuckoo array.

redpajama_set_name: RedPajamaArXiv


text:
Academic Healthcare Recruitment & Executive Search
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Types of Clients
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Organizations We've Served
Successful Placements
Tenure-Track Assistant/Associate/Professor in Rural Aging and Cognitive Health, University of Minnesota, Duluth
Tenure-track Assistant/Associate/Professor in Rural Aging and Cognitive Health
Dementia, Rural Health, Indigenous Health, Chronic Disease
The Memory Keepers Medical Discovery Team-Health Equity (MK-MDT) at the University of Minnesota Medical School, Duluth is launching a nationwide search for a tenure-track Assistant Professor/Associate Professor/Professor in Rural Aging and Cognitive Health. The faculty member's primary responsibility will be to conduct collaborative research concerning aging and cognitive health in rural populations in Minnesota within the MK-MDT environment.
The Medical Discovery Team seeks a dynamic scholar with demonstrated potential for innovation and leadership. Applicants at all ranks and from varied disciplinary backgrounds (e.g., health sciences, social sciences, psychology, neurology, medicine, and neuropsychology) will be considered. Programs of research with a focus on intervention design and/or implementation science are particularly welcomed. Experience with participatory community-based research is an asset.
The successful candidate will be appointed as faculty to the MK-MDT, with their academic home in the Department of Family Medicine and Biobehavioral Health or Biomedical Sciences, as appropriate, at the University of Minnesota Medical School, Duluth campus.
PhD or MD
Knowledge and Experience in one or more of the following research areas:
Multi-causative disease pathways
Sensitivity to and desire to promote diversity.
Track record of success in NIH grant awards or equivalent.
Experience with community-based participatory research approaches.
Experience and demonstrated interest in working with interdisciplinary research teams.
Experience with, or interest in, small populations research and small samples analyses.
Position Specifics
Memory Keepers Medical Discovery Team
Based at the Medical School's Duluth Campus, the Memory Keepers Medical Discovery Team on Rural and American Indian Health Equity (MK-MDT) is one of four University of Minnesota Medical School Medical Discovery Team's funded by the State of Minnesota legislature. The Memory Keepers Medical Discovery Team is a $15.6 million, ten-year initiative to achieve the state's goals of improving patient and population health, lowering costs, and improving healthcare experiences.
Advancing the boundaries of health equity research to create innovative interventions to support healthy aging in Indigenous and Rural Populations.
The Mission of the Memory Keepers Medical Discovery Team is to suppot an environment of Team Science to conduct community-based participatory action research on dementia in Indigenous and rural communities with the aim of achieving health equity.
To learn more about the Memory Keepers Medical Discovery Team, please visit: www.memorykeepersmdt.com
The Memory Keepers Medical Discovery Team is committed to meaningful partnerships with community stakeholders. We have convened two advisory groups to help guide our mission – the Indigenous Advisory Council and Rural Advisory Council. We also support Elders and advisors in residence to guide our day-to-day activities.
Faculty and staff members use community-based participatory research (CBPR) approaches to respectfully engage Indigenous and rural community members in all phases of planning and research. CBPR builds trust in researchers, boosts recruitment and retention in health disparities research. The results guide approaches to advance community health and foster the translation of new knowledge into community and clinical practice.
We seek to create an ethical research space that brings together University and local expert knowledge to create solutions appropriate to the population they are intended to benefit. Memory Keepers Team investigators and staff have decades of experience conducting Indigenous and rural community-engaged research. They have made significant contributions to the literature concerning ethical community-based participatory research practices within Indigenous and rural populations.
Community-Based Participatory Research Training Lab
Our Community-Based Participatory Research Training Lab includes interview and focus group training rooms, as well as spaces for observation. Our goal is to create a training framework that will build capacity among students, researchers, and faculty to conduct critically engaged, scientifically rigorous health equity research that honors Indigenous knowledge to benefit Indigenous and rural communities.
University of Minnesota, Duluth (UMD)
The University of Minnesota, Duluth (UMD) consistently ranks among the top Midwestern, regional universities in U.S. News and World Report's "America's Best Colleges" issue. Overlooking Lake Superior, UMD provides an alternative to both large research and small liberal arts environments and attracts students looking for a personalized learning experience on a medium-sized campus of a major university. A firm liberal arts foundation anchors a variety of traditional degree programs, as well as professional and graduate students that draw on UMD's many research institutes and labs.
Duluth, Minnesota is a cultural center that boasts a high level of outstanding fine art, performance offerings, and outdoor beauty. Natural history and art museums abound, along with a symphony orchestra and musical talents from numerous performers across many genres.
In 2014, Duluth was voted Outside magazine's best outdoors town in America. Minnesota's City on the Hill claims 6,834 acres of city parkland, 129 Parks, 11,000 acres of green space, 12 miles of paved, accessible trails, 85 miles of bike-optimized, multi-use trails, 150 miles of unpaved hiking trails, and 16 designated trout streams. It is also the southern terminus of the Superior Hiking Trails.
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The University of Minnesota has retained the services of Academic Med, a national leader in academic medicine executive recruitment, to assist with this strategically important search. The search will be led by Gentry Zacheis, Managing Principal for Academic Med. Please direct any initial inquiries, nominations, or applications to Mr. Zacheis via email, gentry@academic-med.com.
The University recognizes and values the importance of diversity and inclusion in enriching the employment experience of its employees and in supporting the academic mission. The University is committed to attracting and retaining employees with varying identities and backgrounds.
The University of Minnesota provides equal access to and opportunity in its programs, facilities, and employment without regard to race, color, creed, religion, national origin, gender, age, marital status, disability, public assistance status, veteran status, sexual orientation, gender identity, or gender expression. To learn more about diversity at the U: http://diversity.umn.edu.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Why isn't 'java Class' working like normal from the current directory? I have a simple program that works fine in a previous environment. I've moved it to a new one with the same OS and Java versions, but have encountered a problem executing the class files.
Never have I had a problem running a java class in the same directory but when I try java Class I get the error could not find or load main class.
I've already looked over all the suggestions, one of the most popular being to add the classpath and run it as java -cp . Class. However this has never been necessary in all the environments I've worked in, including the previous one which was identical to this. Why would this happen and how can I fix it?
Note: In case you wonder, java -cp . Class works for a small test program with no dependencies, but results in a JNI error which has no clear resolution, related to a jar file that is both on the bashrc classpath and the current directory (when specifying -cp .). Regardless, I just want to execute classes like normal.
UPDATE
I'm certain this is an environment issue, but here is the code. I am calling it as java Test, NOT java test or java Test.class.
class Test {
    public static void main(String[] args) {
        System.out.println("Test complete!");
    }
}

A: You need to compile your Java source code with javac Test.java which makes a new file named Test.class before you run it. Otherwise you will get this error message: Error: Could not find or load main class Test as shown below. If you run these commands one at a time, it will show you which command gives unexpected results.
$ cat Test.java
class Test {
    public static void main(String[] args) {
        System.out.println("Test complete!");
    }
}
$ java Test
Error: Could not find or load main class Test
$ javac Test.java
$ ls
Test.class  Test.java
$ java Test
Test complete!
$ java -cp ~/Desktop/ Test # test using classpath
Test complete!
As you can see, the last command has the directory containing the Test executable file after the -cp classpath option, not the Test file itself as you wrote in your question.

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Q: Get a value from the string with regex I have this for example:
<@445288012218368010>

And I want to get from between <@ > symbols the value.
I tried so:
string.replace(/^(?:\<\@)(?:.*)(?:\>)$/gim, '');

But then I don't get any result. It will delete/remove the whole string.
I want only this part: 445288012218368010 (it will be dynamic, so yeah it will be not the same numbers).
Anyway it is for the discord chat bot and I know that there is other methods for check the mentioned names but I want to do that in regex because which I am trying to do can't go the common method.
So yeah how can I get the value from between those symbols?
I need this in node.js regex.

A: You can use String#match which will return regular expression matches for the string (in this case the RegExp would be <@(\d+)> (the parenthesis around the \d+ make \d+ become its own group). This way you can use <string>.match(/<@(\d+)>/) to get the regular expression results and <string>.match(/<@(\d+)>/)[1] to get the first group of the regex (in this case the number).

A: You regex matches but you use a non capturing group (?:.*) so you get the full match and replace that with an empty string. Note that you could omit the first and the third non capturing group and use  <@ and > instead.
You could match what is between the brackets using a capturing group ([^>]+) or (\d+) and use replace and refer the first capturing group $1 in the replacement.

console.log("<@445288012218368010>".replace(/^<@([^>]+)>$/gim, '$1'));


1. Families who lose a child often find themselves involved in complex bureaucracy and may have considerable difficulty obtaining a clear account of why their child died.
2. Families, who have closest knowledge of the lost child, have little opportunity to contribute to review processes. There are numerous anecdotal examples from front-line clinicians that the post-bereavement care, communication, timescales and outcomes of any review, are very unsatisfactory for many families. There continue to be long delays before families are informed of post-mortem findings and involvement of medical practitioners in appropriately 'translating' those findings is not consistent. In stark contrast to a model of professionals working with parents during their child's life, it seems that a family's views, information and questions are sometimes not afforded priority after their child has died. This compounds their grief and loss. The quotes below illustrate some of these parental views.
3. A Child Death Review Working Group was set up to explore current practice in the review of child deaths in Scotland, and to consider whether Scotland should introduce a system for reviewing the circumstances surrounding the death of a child, in order to identify preventable causes of death which could improve child mortality rates in Scotland in the future.
4. The Working Group met 5 times between September 2012 and November 2013. It carried out a mapping exercise of: reviews and audits currently undertaken in Scotland; the deaths examined; data sources and data dissemination; and communication and support for families. The Chair visited the University of Oxford to learn lessons from the MBRRACE-UK system (Mothers and Babies: Reducing Risk through Audits and Confidential Enquiries across the UK) and also visited the Child Death Overview (CDOP) manager in Merseyside (see paragraph 24). The information in this report was also drawn from publicly available online sources, discussions with staff involved in reviewing child deaths in Scotland and from a survey of Child Health Commissioners within Scotland.
Strategic process - learning from deaths and disseminating that learning.
6. The group consisted of representatives from NHSScotland, the Royal College of Paediatrics and Child Health, Police, Crown Office, Procurators Fiscal Service, Scottish Cot Death Trust, University of Dundee and the Scottish Government.


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