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Tottenham vs Southampton Betting Tips & Predictions
Tottenham Hotspur might have enjoyed a fantastic 2-0 win over Manchester City on Sunday although we're surprised that the bookies make Jose Mourinho's team such hot favourites to overcome Southampton on Wednesday night.
While Mourinho would dearly love to win silverware during his first season at White Hart Lane, we're not entirely convinced they are banker material to beat a Saints side who were a lot better at Anfield than the 4-0 scoreline suggested.
Ralph Hasenhuttl's side have recently worked their way out of trouble and they have been especially potent on the road in recent weeks, landing victories at Aston Villa, Chelsea, Leicester City and Crystal Palace.
Southampton don't have another game for eleven days after this fixture, so the visitors are likely to be at full-strength and that team is likely to include the talented Moussa Djenepo along with the in-form Nathan Redmond and Danny Ings.
Tottenham will be missing Harry Kane and Dele Alli for this encounter, while the team have quite a short turnaround time after facing City on Sunday and we think they can be opposed for an FA Cup encounter which is likely to be close.
New signing Steven Bergwijn is likely to continue in midfield, with Heung-Min Son and Lucas Moura continuing to lead the line although this could be a tough ordeal against a Southampton team who seem to have the blueprint for away matches at the moment.
You can back the Saints with a one-goal start and that means money back if they lose the game by a single goal, although we think they are capable of either forcing extra-time or alternatively simply winning in normal time.
Southampton +1 @ 1.65 with bet365


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Surely we all know that we need to listen to our customers? That way we will know how best to serve them and delight them, right? Well maybe not! Shocking as it might seem, we might find that we risk losing our customers if we do what they ask us to. So here are 3 reasons why Listening to your Customer can be a Bad idea and, to balance the perspective, 3 reasons why it could be Good. Let's do the good stuff first.
Listening to your Customer is Valuable because:
1. You find out where you are Failing.
Complaints records and customer satisfaction surveys can deliver deep insight into where you may wish to invest time or resources into improving things. This may have nothing to do with your product offer (I'm including Services as a product here), but may be all about how your customer wishes you to do business with them. This can be about the way you transact business, but also the service you provide to your customer Before, During and After the sale. Winning a new customer is harder than getting repeat business, so finding out how to make doing business with you a positive experience throughout the cycle will pay dividends.
2. They tell you what they Want…
…and you can work out how to give them more of that. This increases customer satisfaction. You are going to want to find the things that give high satisfaction for low effort and/or low cost for your business and save the harder stuff for later. Finding out customer 'wants' also gives you an insight into their emotional state. Bearing in mind that all purchase decisions are made on the basis of wants (and then subsequently justified by needs), finding these out helps you bring products to market that hit those targets on the want side of the equation.
3. They tell you what you are doing well.
If you want to improve your business, you will need to make changes – right? So take care not to take out or worsen the things that your customers value. You'll need to find a way to preserve the cherished aspects of your business; at least until the customers switch to that new thing you just brought to market. Knowing what to keep is just as valuable as knowing what to change, and if you really have to get rid of a thing that people like, at least find out why they like it so you can work out how to give them something that they will love even more.
Listening to your Customers is a Waste of Time because:
1. They usually can't see past the present. So when they say what they want, it relates to where they are now, not where you might want to take them. As Henry Ford said: "If I had asked my customers what they wanted , they would have asked for a faster horse." In fact Henry asked himself a far better question: What is the challenge that the customer thinks can be solved by a faster horse?" And so a more useful answer starts to emerge.
Thinking about your customer in this way is all about seeing things from their perspective, and then working laterally to develop alternative solutions. Don't forget – if you also talk to people who aren't your customers [yet] then you may get another perspective.
2. Customers don't see Trends, they participate in them.
So they can't tell you what the next big thing should be. But they do have expectations that are constantly evolving. Uber has created an expectation that you can get things you want Conveniently and Safely using your mobile phone. When a competitor works out how to do something like that in your market, you will find customers ready to buy. But they won't have predicted this or asked for it.
3. Customers don't always tell the truth!
There are many reasons for this: They may not like to give you personal information that could help you understand them. They may not tell you that your product/price/performance offer is just fine, because they want to get a better deal from you. They will certainly come up with any number of false objections about why they can't say 'yes' to the deal. So do your research around the customer to better understand their position. Find out what is really going to be good for them and when you present it, study their body language and facial expressions. That way you'll have a better appreciation of how they feel. Which is not something many customers talk about.
So what is the conclusion?
As ever it is a bit of a compromise: Yes, talk to your customer and listen to what they say but then go and find out the rest of the picture. Oh, and if you are going to have a dialogue with your customers, make sure they know you have been listening. Active feedback here is essential. No lip-service please. Check your understanding, Thank them for their input and time, Respect their opinion and don't argue or justify.
Good Luck!

subset: commoncrawl


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Altran Rated in the Leadership Zone by Zinnov
- Altran placed in the leadership zone in Entertainment industry segment
- Altran positioned as one of the emerging players in New Media, Gaming and Broadcasting
Bangalore, March 15, 2016 - Altran today announced that it has been positioned in the leadership zone for entertainment segment, according to Zinnov Global Service Provider Rating (GSPR) study 2016.
Altran and its portfolio company frog, a global leader in innovation and design, bring in a depth of services, innovation and contribution to the Media & Entertainment ecosystem, the company has been placed in the leadership zone in the entertainment industry. Altran rates in the execution zone across three major industry segments-New Media, Gaming and Broadcasting.
"This recognition from Zinnov is of great value to Altran and mirrors our consistent effort in delivering best-in-class solutions for the Media & Entertainment product segment. Being in the leadership position for this particular category fuels our market leadership, and reflects our diversification strategy into newer verticals and markets," said Frank Kern, Altran's Chief Executive Officer.
Altran was also recognized as a leader in the semiconductor and telecommunication industries according to Zinnov Global Service Provider Rating for Product Engineering Services 2015. The above recognitions are a testament of Altran's consistent performance and capabilities in realizing go-to-market strategy in the product engineering service space across industries.
Altran is one of the largest product engineering services company, with recognized depth across nine industries: Semiconductor, Telecommunications, Automotive, Industrial Automation, Consumer Electronics, Consumer & Enterprise Software, Networking, Internet Services and Media & Entertainment.
"We extend our heartiest congratulations to Altran and recognize the company as one of the emerging players in New Media, Gaming and Broadcasting. Today, industries are challenged with ever-changing technologies, product engineering, development, and design costs and it has become imperative for companies to stay ahead of the market. Altran has been at the forefront of bringing the best of offerings to the market and foster innovation," said Sidhant Rastogi, Partner & Practice Head, Zinnov.
Zinnov's annual GSPR study is an exhaustive analysis that covers more than 50 companies in the engineering R&D space, across multiple verticals and geographies including India, China, APAC, Eastern Europe and Russia. R&D service providers were assessed across key parameters including strategy, human capital, product development capabilities, financials, ecosystem connect, infrastructure and innovation/IP creation, lab infrastructure, R&D practice maturity, and customer relationships. The analysis process involved data collection from participating companies, interviews with end customers, and inputs from domain experts.
About Altran
Altran is a global design and engineering company innovating for customers for what comes next in North America and beyond. We lead our clients into the future by solving their most complex engineering services needs and mission-critical software framework solutions. For decades, we have helped companies connect new things and scale with intention. We bring differentiated value to market faster in focused industries to help transform products, brands, companies, and start-ups. Based in San Francisco, frog, the global leader in innovation and product design, is also part of Altran.
Learn more about Altran at https://northamerica.altran.com
About Zinnov
Zinnov assists clients to improve organizational efficiency, innovation, and revenue by leveraging global resources and markets. The company offers deep expertise in Engineering, Digital, and Globalization. Zinnov has been at the forefront of innovation and thought leadership. With over a decade of experience in globalization, it helps us in understanding customer problems and coming up with viable solutions. Zinnov assists clients in addressing globalization challenges by offering customers insights, data, and implementation support to address their challenges. The company's in-depth experience is driven by its focus on engineering and digital practice areas. Visit us at https://zinnov.com/
# # #
Media and Analyst Contact:
Altran North America Media
Contact: firstname.lastname@example.com
Analyst Contact:
Pragya Vaishwanar


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Question #7588c
1 Answer
Dec 23, 2016
Any multiple of 5 greater than 20 is a possible number of marbles.
There are many, many possible answers to this question.
If there are exactly 20 marbles in the bag, how many of each colour are there?
There will be 8 white and 12 blue marbles, meaning 20 altogether.
Remember that a ratio can be written as a fraction:
We can write the following equivalent fractions:
The possible number of marbles in the bag could be:
(Note that 2+3 = 5)
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By Mark Jurkowitz | Outer Banks Voice on July 28, 2020
On a day when the numbers tracking the spread of COVID-19 in North Carolina showed some signs of "stabilizing," Gov. Roy Cooper announced an Executive Order that mandates an 11 p.m. curfew on the sale of alcohol in restaurants. The Order also applies to breweries, wineries and distilleries, and bars in the state remain closed. The curfew will take effect on Friday, July 31.
"We want to prevent restaurants from turning into bars after hours," said Cooper at a July 28 media briefing. Noting that bars are venues for COVID-19 transmission, the governor added that, "We're getting some reports about restaurants that are essentially turning into bars later at night," with more mingling and less social distancing.
Cooper added that Alcohol Law Enforcement (ALE) and the Alcohol Beverage Control (ABC) Commission would have the authority to enforce the Order and potentially revoke liquor licenses. Cooper characterized the alcohol curfew as part of an effort to "double down" on efforts to combat the spread of COVID-19, efforts that may be starting to show some success.
Stating that "some of our metrics are showing early signs of stabilizing," North Carolina Health and Human Services Secretary Mandy Cohen talked about some of the key trends monitoring the virus' trajectory in the state at the briefing. The number of individuals showing up in emergency rooms with COVID-like symptoms, an early indicator of possible infections, has starting to level in the past two weeks, she said, adding that the number lab-reported COVID-19 cases is also "leveling in the past fourteen days." The percentage of positive tests out of all COVID-19 tests administered, while still higher than the desired 5% goal, has also dropped recently from about 10% to about 8%.
The one notable outlier in these somewhat encouraging trends is the number of COVID-19 hospitalizations in the state — and a new record high was reported on July 28 with 1,244 people in the hospital. But Cohen characterized that as a "lagging indicator," meaning hospitalizations follow infection by days, if not by several weeks. She also indicated that the state still has "capacity" for more patients in its hospitals.
While generally expressing a cautious wait-and-see attitude toward the stabilizing numbers, Cohen asserted that she did "see a direct correlation [between that stabilization] and the start of the statewide mask requirement in June." Cooper announced that face covering mandate on June 24.
What's new today: Record number of hospitalizations reported. (See most recent Today's NC coronavirus numbers for interactive charts)
Note: Every morning, the NC Department of Health and Human Services posts updates o number of reported cases of coronavirus. That number reflects positive results from all tests, including the NC State Laboratory of Public Health and all hospital and commercial labs. There may be other reports, from the media and elsewhere, that will include different numbers during a given day, but this is an effective way of tracking numbers from the same source on a day-to-day basis.
What a joke this fool is. Because, you know, the virus is less dangerous before 11:00 p.m. and is especially attracted to those drinking alcohol after 11:00 p.m. I'm relieved that I'm safe before 11:00 p.m. doing whatever I want and after 11:00 p.m. I'm golden, as long as all I'm doing is drinking sweet tea. So if you chug a half bottle of bourbon at 10:45, you'll be fine…. What scientific basis is there for this kind of cherry-picking? When will people get that all the good guv wants to do is impose more and more restrictions on free people.
Do what is needed Mr. Cooper, take the restaurants back to take out only.
Typical liberalism; symbolism over substance. When Cooper 'closed bars' bars in restaurants were not included in the closure. Bars that were not restaurants began serving food. Since all bars tend to be where people congregate w/out social distancing, all bars should have been closed. So now congregating in restaurant bars before 11PM is less risky than after 11PM. DUH!
HAHA. i know who will be voted out this election. Ive seen so many polls- VOTE HIM OUT! this is a damn joke! WE ARE NOT PUPPETS. We ARE NOT PART OF YOUR AGENDA. Look at the numbers people. Yes, theres a virus. You know what kills more people than this? DRUGS, CANCER, FLU, OTHER VIRUSES. now that the white house has gotten statistics, guess what numbers have went so far down its crazy. the survival rate is now at 99.6% AND IF MASKS WORKS SO DAMN WELL, Y SHUT EVERYTHING DOWN? O THATS RIGHT..ALL THIS IS BULL! come on. Even front line nurses are speaking out and saying all of this now. WAKE UP.
I am so thankful for Governor Cooper, a Democrat who is doing everything he can to battle this very dangerous virus. I honestly think we need to go back to a complete lockdown until December so we can show the country how great North Carolina is. People are terrified about this virus and going outside is so dangerous and risky. People are dying left and right in North Carolina!
I agree because this virus is not stopping and our numbers are astounding in NC. IT IS SO BAD PEOPLE, OPEN YOUR EYES. I would honestly support a new stay at home order and closing the malls and beaches until January. Also restaurants need to be takeout only because sitting inside a restaurant is killing people at alarming rates. 500 children have died in NC from this unforgiving virus and all of the hospitals in the state are at full capacity with coronavirus patients. It is extremely sad but it is true.
Agreed, anotherobxman. This is getting out of hand. Phase one…
I guess we're still doing the delusional nonsense thing where people think this is all just a ploy to take away freedom.
Dems are seeing how many sheep are out there! Man up lockdown is a joke,
Cooper is the typical Liberal coward.
I for one didn't vote for him last time & sure as hell won't next time either!


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A vaginal yeast infection is not considered to be a sexually transmitted disease (STD), since Candida may be present in the normal vagina, and the condition does occur in celibate women. Vaginal yeast infection prevention, aside from the discomfort of persistent itching, you can't assume that a yeast infection will simply go away. Health news, or your doctor may prescribe a medicine to treat the infection. If you don't want to risk the scent-ual side effects of garlic, consider a no-odor garlic supplement. Risk factors include pregnancy, diabetes mellitus, and systemic antibiotics.
- It also describes which antibiotics can cause these infections and how to treat them.
- Many medications have possible side effects that can be unpleasant and uncomfortable.
(3°C) along with a vaginal discharge. The prescription medication, fluconazole, is a single pill that is taken by mouth (6). Having leukemia or AIDS, both conditions that damage the immune system. Fungal infections: when to see the doctor, here's one of my favorite suppository blends for treating vaginal yeast infections. A small amount of Candida fungus is usually present in the vagina, and beneficial bacteria help keep this fungus in check. Clothing that is too tight or made from harsh synthetic material could be causing your body to develop yeast infections. The use of probiotics in the vagina or by mouth along with using an antifungal medication may slightly increase the chance of curing a yeast infection, compared to using an antifungal medication alone (10).
When to Contact a Medical Professional
Signs and Symptoms: What causes yeast infections? Fluconazole is an effective antifungal medication. Medical and science glossaries, garlic (Allium sativum) strengthens immunity by aiding white blood cells, and it has shown significant antifungal activity against Candida albicans in animal and test tube studies. People, for providers with more than one physical location, this is the primary location. Your doctor may also take a sample of the vaginal discharge for quick examination under a microscope in the office.
If you get symptoms of infection, such as warm, reddened skin or drainage, tell your healthcare provider. Two cloves per day. Localized infection[edit], sounding familiar? Can vaginal yeast infections be prevented? Antibiotics kill some of this friendly bacteria, which allows yeast to overgrow.
Girls who have diabetes that isn't controlled are more likely to get yeast infections. This is important now that there are over-the-counter medications for yeast infections. What treatments are available for vaginal yeast infection? The dryness isn't permanent, of course, but it can be uncomfortable. If you are pregnant, do not use vaginal boric acid treatment.
If you have never been diagnosed with a vaginal yeast infection, see your doctor.
You're Not Getting A Full Night's Sleep.
You can also try adding some yogurt containing live active cultures to your diet. Related, and some medicines that you use in your vagina have oil in them, which can cause condoms to break. A woman's vagina maintains its own balanced mix of yeast and bacteria. These infections can either be superficial, affecting the skin and mucosal membranes or slightly more serious causing diseases like oral thrush and vaginitis.
There is no evidence to support the use of special cleansing diets and colonic hydrotherapy for prevention. Yeast cells that normally live in the vagina are kept in careful check by the minimally available nutrients in the acidic environment of the vagina. Taking antifungal medication and antibiotics simultaneously is safe, though they cautioned against doing so if you're pregnant. Only take antibiotics when and how they're prescribed for you.
People Keep Making Fun Of Kylie Jenner's Toes And She's Not Having It
What is bacterial vaginosis? Your body will thank you. Avoid douching, as this can change the conditions in the vagina and promote yeast growth. Women with poorly controlled blood sugar are at greater risk of yeast infections than women with well-controlled blood sugar. While eating yogurt can help to replenish good bacteria, applying it near your vagina may also offer a little help. Genital candidiasis, yeast can grow out of check when a person is stressed, has recently used antibiotics or has a weakened immune system. They're not considered sexually transmitted infections. Treatment will depend on the cause of the vaginitis. Talk with your doctor about any drugs you are now taking—you are more likely to get a vaginal yeast infection if you are taking certain drugs such as antibiotics, steroids or birth control pills.
The risk of developing this infection is increased by certain conditions, such as the following: Candidiasis (vulvovaginal). These medicines upset the normal balance between yeast and bacteria in the vagina. A sample of vaginal discharge can be taken during a wet mount test. A healthy immune system and some "good" bacteria keep the amount in a person's body under control. If you want to take your health to the next level, try out our audio-based fitness app, Aaptiv. And yes, you can do something to lower this risk. We know that while some women simply get yeast infections once in a great while, others are susceptible to them because of certain risk factors.
Lizzo calls out TikTok over apparent removal of her bathing suit videos: 'TikTok we need to talk'
These infections occur in up to 75% of women during their reproductive years. Prescription antibiotics are very effective at treating a sinus infection, strep throat, or other bacterial infection. Once the patient is able to recognize the symptoms of a typical yeast infection, future infections can be treated using nonprescription vaginal antifungal medication, such as clotrimazole or miconazole. Another option is to not take a decongestant drug and try to clear your nasal passages with natural decongestant strategies, such as drinking hot liquids and taking a steamy shower. Follow us:, use plain, whole-milk yogurt with live cultures. Pregnant women are also more prone to yeast infections. Lopez JEM (2020).
Change pads or tampons often. No RCTs compare the incidence of culture-confirmed VVC among women receiving antibiotics or placebo. These conditions can trigger yeast overgrowth by altering the delicate balance among microbes living in the vagina. Did your illness result in, or come about because of, a compromised immune system? You are not sure that yeast is the cause of your symptoms. What is candida (oral thrush)? People who are taking inhalers or steroid tablets are also at risk of oral thrush. Patients are more likely to comply when antifungal therapy is administered orally, but oral treatment carries a greater potential for systemic toxicity and drug interactions.


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Getting to Net-Zero Emissions: Lessons from Latin America and the Caribbean
Latin American countries (Costa Rica, Mexico, Colombia, Ecuador, Peru, Argentina) in planning long-term decarbonization strategies, which contribute to the preparation of climate policies in line with the Paris Agreement. The first phase of this project is nearing completion and a report on the initial
Published in December 2019
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Committed emissions and the risk of stranded assets from power plants in Latin America and the Caribbean
power plants that are announced, authorized, being procured, or under construction would result in 6.7 Gt of CO2 of additional commitments (for a total of 13.6 Gt of CO2). Committed emissions are above average IPCC assessments of cumulative emissions from power generation in LAC consistent with
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Three Oceans Strategy
largest in the world – covering 11 million km². The territories are located in three large ocean basins that span a broad diversity of countries. Given its longstanding and unique ties both with the French Overseas Territories and with their neighbouring foreign countries, AFD has a singular
Published in October 2019
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Kel Greenough was hoping for a regulation grade 5 for Houdini Boy's 595m debut. Instead, he'll meet a field worthy of a group race.
Despite having just 11 career starts to his name, Houdini Boy will meet a field stacked with big race experience. Headlining the race is dual group 1 winner Hooked On Scotch, the Sandown Park 515m track record holder who stepped up to the distance himself two weeks ago and won in 33.81 – the second fastest time by a greyhound on his 595m debut.
That time eclipsed Rockstar Prince's 33.82 mark as fastest of 2020 and he too will also line up on Thursday night, as will three time group race finalist Mepunga Maggie after her 34.11 victory last Thursday night and Perfect Marshall, a group 1 winner over 600m at The Meadows.
"I would have liked an easier race!" said trainer Kel Greenough.
"But I don't think there are any easy ones – it's ridiculous the standard of racing now – I think it's as good as it's ever been."
Houdini Boy has quickly emerged as one of the country's most exciting greyhounds thanks to his distinctive racing style. His customary lack of box speed – despite Greenough's best efforts to reeducate him – but brilliant closing section has captured the imagination of many in the sport. He was placed in his first five career start, each at Sandown Park, including three wins despite averaging a pedestrian 5.39 first split (the average first split of a winner over 515m in 2020 is 5.16, or almost four lengths faster).
He then came from last to win the Cranbourne Winter Cup, made the group 1 Vic Peters at Wentworth Park, and ran third in a heat of the group 1 Maturity, settling at the tail of the field before flashing home on each occasion.
While Houdini Boy gives every indication he'll be well suited to the step up in distance, Greenough wasn't sure what to expect from his charge. But like many greyhound racing fans, he is looking forward to finding out.
"I don't really know. You never really know what he's going to do or if he'll get a clear run because of his habits, but you don't get many dogs that chase as hard as he does from behind. He'll ride a bump and take off again, he weaves in and out, he's an amazing dog to watch.
"I would have liked an easier step up to 595m but it is what it is so we'll see how it goes. I know he always tries his best, but he wouldn't want to do much wrong on Thursday night."
TAB.com.au opened Houdini Boy the $4 second elect for race 6 on Thursday night. Hooked On Scotch is the presumptive favourite at $1.75.
Elsewhere on what is shaping as an outstanding night of racing, Shima Shine $1.90 and Tiggerlong Tonk $2.15 dominate the market in the Free For All in race 8, while Mister Harlewood is the $1.80 top pick in an outstanding 715m staying event.
Click here for your free Watchdog form guide
Click here for the latest market from TAB.com.au


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Clustering, K-Means, Mixture Models, Expectation Maximization
Clustering is an unsupervised form of learning. We have data but no labels and we want to infer some sort of labels from the data alone. So what does clustering do? Say we have a bunch of data points $ x $ that look like below.
Clearly, the green, red, and blue data points represent three different clusters. The goal of clustering is to be able to determine these clusters meaning figure out which data point belongs to which cluster.
Clustering is an important concept because it is an unsupervised method that can provide labels to an otherwise label-less dataset. Group similar data points using clustering. Say your $ x $ values are customer data points you can then group customers into similar groups using clustering.
Intuitively we want to group data points that are close together in a single cluster. The first and simplest clustering algorithm that leverages this property is the k-means algorithm.
Say that the center of cluster $ k $ is defined as $ \mu_k $. Sometimes $ \mu_k $ is called the prototype vector of cluster $ k $. Intuitively, data points that belong to cluster $ k $ should be closest to the center of cluster $ k $, $ \mu_k $ relative to all the other cluster centers.
Let's start with $ r_{nk} $ being 1 if point $x_n$ belongs to cluster $ k $ or 0 otherwise. Like all other things in machine learning we need a cost function that we can minimize. Define the cost as the distance between each point and it's assigned cluster. We can use $ r_{nk} $ to write this cleanly.
$$ J = \sum_n \sum_{k} r_{nk} \lVert x_n - \mu_k \rVert_2^2 $$
First, let's minimize this cost function with respect to $ r_{nk} $ to find the optimal cluster assignments. Fix $ \mu_k $ and take the partial derivative of $ J $ with respect to $ r_{nk} $ and set it equal to zero to find the optimal cluster assignments $ r_{nk}^{*} $. We find that:
$$ r_{nk}^{*} = \begin{cases} 1 & \text{if $k = \text{argmin}_j \lVert x_n - \mu_j \rVert_2^2$} \\ 0 & \text{otherwise} \end{cases} $$
$\text{argmin}_x f(x)$ returns the value of $ x $ that minimizes $ f(x) $. The optimal cluster assignment for $ x_n $ is simply the closest cluster prototype vector to point $ x_n $.
Next let's do that same process of taking the derivative of the cost function with respect to the cluster centers $ \mu_k $ to find the optimal cluster centers $ \mu_k^{*} $. Doing so gives:
$$ \mu_k = \frac{\sum_n r_{nk} x_n}{\sum_n r_{nk}} $$
This should also be pretty intuitive. The best center of the cluster is just the average of the points in that cluster.
The k-means process is listed below:
- Initialize $ \mu_k $ to a random points in the dataset.
- Update the cluster assignments through the equation: $$ r_{nk}^{*} = \begin{cases} 1 & \text{if $k = \text{argmin}_j \lVert x_n - \mu_j \rVert_2^2$} \\ 0 & \text{otherwise} \end{cases} $$
- Update the cluster means through the equation: $$ \mu_k = \frac{\sum_n r_{nk} x_n}{\sum_n r_{nk}} $$
- Compute the cost $ J $. If the cost has not changed much since last iteration stop.
- Repeat
Turns out it can be difficult to reach a global maximum of the cost function $ J $ through this process. Therefore, the common practice is to use multiple random initializations and see which gives the best lowest $ J $ in the end and use that clustering.
Overall, this is a pretty straight forward algorithm. However, things get more complicated if you look at the example of clusters below.
In the above picture the data points do not necessarily stay close to their cluster centers but it is easy to see there are three distinct clusters. Making the statement about data points should stay close to center clusters was just a stipulation on how we think the data should be distributed about a cluster. It is possible generated data does not obey this rule. Like in the above case the data appears normally distributed around the cluster center. We can then model each cluster not with the points closest to it but with a generalized probability distribution.
Gaussian Mixture Models
Think of a Gaussian mixture model (GMM) as a generalized form of k-means (we will prove that it is later). GMM assumes that the data is generated from $ k $ distinct Gaussian distributions.
The above image shows data that has been generated from a combination of two normal distributions. We can write the final distribution for a generalized GMM as the following.
$$ p(x) = \sum_k \omega_k N(x \lvert \mu_k, \Sigma_k) $$
$$ \sum_k \omega_k = 1, \omega_k > 0 $$
Note that this is for the multinomial distribution, a generalized version of the normal distribution for multiple dimensions. We therefore, write the covariance matrix $ \Sigma_k $ and the mean vector $ \mu_k $ as parameters of the model. Don't let this confuse you, think of $ \Sigma_k $ as the variance and $ \mu_k $ as the mean. The stipulation on $ \omega_k $ is just to ensure the combined probability distribution is a valid distribution.
With k-means we leveraged knowledge about how data in a cluster should be distributed. We were utilizing data about not just $ p(x) $ but also the additional random variable of $ z $, the cluster index that we were modeling. So we were actually using marginal distribution of the joint distribution $ p(x, z) $ to model $ p(x) $ in k-means. We can rewrite the joint distribution using Bayes rule.
$$ p(x,z) = p(z)p(x \lvert z) $$
In our case of GMM we have.
$$ p(z=k) = \omega_k $$
$$ p(x \lvert z=k) = N(x \lvert \mu_k, \Sigma_k) $$
Therefore, we have:
$$ p(x,z=k) = p(z=k)p(x \lvert z=k) = \omega_k N(x \lvert \mu_k, \Sigma_k) $$
Then finding the marginal distribution of the data
$$ p(x) = \sum_k p(x,z=k) = \sum_k \omega_k N(x \lvert \mu_k, \Sigma_k) $$
Which is what we had before.
Now how we do we go about learning the parameters of each Gaussian distribution $ \Sigma_k, \mu_k $ We want to find $ \theta $ (where $ \theta = (\Sigma_k, \mu_k, \omega_k )$) that maximizes the conditional probability $ p(x \lvert \theta) $. Starting with:
$$ p(x \lvert \theta) = \sum_z p(x,z \lvert \theta) $$
Then express the joint distribution of the entire dataset and take the log of it to find the maximum likelihood estimator of $ \theta $ (If you don't know what maximum likelihood estimation (MLE) is check out this article from towards data science)
$$ \theta = \text{argmax}_{\theta} \log \prod_n p(x_n, \lvert \theta) = \sum_n \log \sum_z p(x_n, z_n \lvert \theta) $$
Turns out taking the derivative of this expression to analytically solve for the argmax of $ \theta $ is intractable because we are taking the logarithm of a sum. This problem has no analytical solution. Instead, we will use an iterative method to solve this. We call this method Expectation Maximization (EM).
Expectation Maximization (EM)
Essentially, the trick of EM is to take the expectation of the variable $ z_n $ instead of summing over all possible values. More generally, this variable $ z_n $ is called a latent variable. In the case of clustering it is the cluster index. The variable is not directly observed which is why we call it latent.
Let's define a new expression the expected log likelihood with respect to $ q(z_n) $. In this case $ q(z_n) $ is just some distribution of $ z_n $ don't worry too much about it for now we will see what $ q(z_n) $ should be soon.
$$ Q(\theta) = \sum_n \mathbb{E}_{z_n ~ q(z_n)} \log p(x_n, z_n \lvert \theta) $$
$$ Q(\theta) = \sum_n \sum_{z_n} q(z_n) \log p(x_n, z_n \lvert \theta) $$
Now the log is outside of the sum and we can solve this problem. What is $ q(z_n) $ all about though? Turns out if we want to bound the loss of the Q function to the original MLE problem we should use the following choice:
$$ q(z) = p(z \lvert x; \theta) $$
This should seem pretty intuitive as well (this is about the most basic choice of a distribution over the latent variable). This is the distribution of the latent variable given our data. So now we have
$$ Q(\theta) = \sum_n \sum_{z_n} p(z \lvert x; \theta) \log p(x_n, z_n \lvert \theta) $$
Now let's think about how we could actually evaluate this expression. How are supposed to know the value of $ \theta $? This expression depends only on information that we do not know. Let's alter this expression a little bit to include stuff we do know.
$$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{z_n} p(z_n \lvert x; \theta^{t-1}) \log p(x_n, z_n \lvert \theta) $$
Remember the EM is an iterative algorithm. We will iteratively be updating our guesses for $ \theta $ For our next time step prediction of $ \theta^{t} $ we select $ \theta^{t} $ such that:
$$ \theta^t = \text{argmax}_{\theta} Q(\theta, \theta^{t-1}) $$
We know our previous value of $ \theta $ which is $ \theta^{t-1} $. However, we don't know $ \theta $ in the Q function. We can then maximize that function by choosing a value of $ \theta $.
Now let's lay out the complete steps for the EM algorithm.
- Randomly initialize the initial values of $ \theta $.
- Remember our complete Q function is given by $$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{z_n} p(z_n \lvert x; \theta^{t-1}) \log p(x_n, z_n \lvert \theta) $$
- The first step is expectation. Evaluate the expression $ p(z \lvert x;\theta^{t-1} )$ using the already known value of $ \theta^{t-1} $. When actually evaluating this probability we can use Bayes rule to make it a little easier to compute. $$ p(z_n=k \lvert x; \theta^{t-1}) = \frac{p(x_n \lvert z_n = k) p(z_n = k)}{\sum_{k'} p(x_n \lvert z_n = k') p(z_n = k')} $$
- Next step is maximization. $$ \theta^t = \text{argmax}_{\theta} Q(\theta, \theta^{t-1}) $$ Then set $ \theta^{t-1} = \theta^t $.
This algorithm has theoretical guarantees that the loss of the loss will be minimized each step. However, like k-means this algorithm can often reach local minima and it is best to randomly start the algorithm multiple times to get the best loss.
Let's see what EM looks like for our GMM problem.
- Expectation step: $$ p(z_n=k \lvert x; \theta^{t-1}) = \frac{p(x_n \lvert z_n = k) p(z_n = k)}{\sum_{k'} p(x_n \lvert z_n = k') p(z_n = k')} $$
$$ p(z_n=k \lvert x; \theta^{t-1}) = \frac{\omega_k^{t-1} N(\mu_k^{t-1}, \Sigma_k^{t-1})}{\sum_{k'} \omega_{k'}^{t-1} N(\mu_{k'}^{t-1}, \Sigma_{k'}^{t-1})} $$
- Maximization step: $$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{z_n} p(z_n \lvert x; \theta^{t-1}) \log p(x_n, z_n \lvert \theta) $$
$$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{k} p(z_n=k \lvert x; \theta^{t-1}) \log p(x_n, z_n \lvert \theta) $$
$$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{k} p(z_n=k \lvert x; \theta^{t-1}) \log p(z_n = k) p(x_n \lvert z_n=k ; \theta) $$
$$ Q(\theta, \theta^{t-1}) = \sum_n \sum_{k} p(z_n=k \lvert x; \theta^{t-1}) \left( \log(w_k) + \log(N(x_n \lvert \mu_k, \Sigma_k)) \right) $$
And then of course plugging in the value for $ p(z_n=k \lvert x; \theta^{t-1}) $ found from the expectation step.
- We then take the derivative of this expression with respect to our parameters and set it equal to zero to solve for the optimal value of the parameter to minimize $ Q(\theta, \theta^{t-1}) $. $$ \frac{\partial Q}{\partial \mu_k}=0, \frac{\partial Q}{\partial \Sigma_k}=0, \frac{\partial Q}{\partial \omega_k} = 0 $$ Solving for the respective parameters in each of the cases gives the following.
$$ \omega_k^{*} = \frac{\sum_{n} \gamma_{nk}}{\sum_{k} \sum_{n} \gamma_{nk}} $$
$$ \Sigma_k^{*} = \frac{1}{\sum_{n} \gamma_{nk}} \sum_{n} \gamma_{nk} (x_n - \mu_k)(x_n-\mu_k)^T $$
$$ \mu_k^{*} = \frac{1}{\sum_{n} \gamma_{nk}} \sum_{n} \gamma_{nk} x_n $$
Where $ \gamma_{nk} = p(z_n=k \lvert x_n; \theta^{t-1}) $
GMM is a more general form of k-means if we set $ \Sigma_k = \sigma^2 I $ then as $ \sigma^2 \rightarrow 0 $ the Q function becomes the same cost function used in k-means.
We can use EM to solve the GMM problem and to find complex clusters in our data. This can be very useful for finding how your data is structured or finding unsupervised labels.


text:
A 17th Century Louis XIII Walnut French Four Door Two Drawer Cupboard
From Streett Marburg
This very early antique French walnut cupboard is a wonderful colour. The doors and sides have decorative moulded panels and the top and bottom are in two parts, making it easy to transport and install. This would make a great kitchen larder, linen cupboard or dining room cupboard.
Dimensions: 186cm h x 130cm w x 64cm d
Condition: Excellent antique condition
Origin: France
Circa: 1640
Ref: C905


text:
Girls in baby oil
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Relájate, hermanita, que ya está la mitad dentro!
Uauu eu gostaria de fuder com essa senhora... eu lamberia a vagima dela sem problemas.. so levantar aqueles pneuzinhos e lamber a noite toda
I practiced during this video
she is colombian ella es colombiana ella me chupo la verga a mi
Ellen it must hold taken a charge of courage to speak so honestly with w


text:
She's already upset quite a few people for just being herself . We presume this appointment will just add to the chatter.
Marijuana Moment write..
The former director of federal policy for the Marijuana Policy Project (MPP) has joined the staff of newly sworn-in Rep. Alexandria Ocasio-Cortez (D-NY) as a senior counsel and policy advisor.
Dan Riffle, who most recently served as communications director to former Rep. Keith Ellison (D-MN) and a legislative aide to former Rep. John Conyers (D-MI), will bring his expertise on health care and tax reform to the freshman congresswoman's team at a time when her proposal to raise the top marginal tax rate is dominating headlines.


text:
|3221 Brunswick Pike, Lawrenceville, NJ 08648, USA
|+1 609-896-1515
|8AM–6PM 8AM–6PM 8AM–6PM 8AM–6PM 8AM–6PM 8AM–3:30PM Closed
vinit parkar
STAY AWAY from these crooks. Especially Jim who works at Midas Lawrenceville. I doubt if they get much work and hence are always on the lookout to rip people off. I have a 2006 Benz and I suddenly started getting a flashing engine light and my engine was misfiring. Since the Benz dealership did not have any appointment until next week, i decided to goto Midas Lawrenceville which was 2 miles from my place. First Jim and his guys checked the error codes and told me that it would cost between 400 to 1000 bucks since they will need to change all 6 Spark plugs and Cam Shaft sensors. Next morning they called me and told that it would be 1500 bucks. He said 2 Cam sensors were bad & he was pushing me to replace all 4 sensors as apparently the other 2 will also go bad soon according to him. Since I had no option, I said fine & the car was supposed to be done in 2 hrs. Later in the eve he called and said that the car wont be ready as he is unable to get rid of 1 error code and will look at it tomm. Finally the next day, he called me and told me to goto the Benz Dealership which fortunately is within 2 miles of his garage. He said that its an issue with the engine and it will cost anywhere from 3K to 6K depending on the actual work .. I was shocked. Also he did not charge me anything and said all 4 Cam sensors and Spark Plugs are new and they will write it off. SUSPICIOUS. I towed the car to Benz dealership and they fixed the issue with 2 hours of labor only .. no part was bad. I got LUCKY as these crooks did not know how to fix the high end cars with complex error codes. I also checked with Benz if the Cam sensors and sparkplugs were new .. and as SUSPECTED .. they had not done any work and all parts unchanged. I would have appreciated if they had been upfront about everything. Nevertheless their plan to rip me did not work. I am writing this review to ALERT other gullible people who live in the Lawrenceville area might go there in the future .. Please be aware ... this place is not worth getting your car fixed.
Leandro Francisco
Im really impressed with their organization and friendly assistance. Before making my appointment Id looked for several different mechanics, and this Midas office had a 4 star rating. So, I though it would worth it to visit them and check the cost to replace some pieces of the suspension of my car. Their organization is, in my opinion, something unusual for this kind of service providers, where sometimes people do not devote sufficient attention to their costumes (that are not mechanics experts), and are badly organized with their schedules (last week I gave up from another mechanic after waiting for more than 2 hours, despite of the fact that I had arrived on time, as scheduled 3 days before!). The staff is outstanding as well. The mechanic who fixed my car (David) is excellent. He showed the problems and gave me honest advices in terms of what would be urgent or not. Based on his behavior and genuine interest in helping me, I approved the complete service. Mr. Gene, in the front desk/management, is friendly and very polite. He manages the office very well, being able to accommodate new demands and kindly scheduling more complex orders (I noticed that while waiting for the completion of the service in my car). I would definitely recommend these folks if a someone asked for my advice.
Anonymous User
Ive been to these guys twice. Gene, the forman, has treated fairly on both occassions where another auto shop couldve have taken advantage and over-charged. I had problems with my brakes that I thought the pads and roters needed to be replaced. Gene said that he might be able to repair the roters (which would save me around $150) and did! On my next visit I had issues with my power steering which was either going to be a $250 or $950 repair. Gene called me once the car was on the lift and assessed the problem. It ended up being the cheaper repair and when I went to pick the car up he show me the broken part and explained what happened. Very good service, fair shake, recommend.
Anonymous User
Ive been to this particular Midas several times and have to say that I am impressed with the level of service. The manager is friendly and gives honest advice. For example, Pep boys down the road wanted to replace my entire cooling system (and timing belt) for a cool $1200 or so. The guys at midas only saw a crack in the radiator ($600 to fix). However, it wasnt leaking at the time so he told me to keep an eye on it and to come back if it gets worse. The mechanics here had no qualms showing me the crack in the radiator, and discussing my options. Thanks!
mitesh chheda
Had a 02:30 pm appointment today for an oil change and its been 03:04 pm and my car is still sitting in the parking lot to be serviced bye hey.... people came after me got their car right in there before me.... Is it negligence, lack of attention to details or something else... I dont know...... Whats the point of making the appointment prior to walk-ins PS: - Even though I had 02:30 pm appointment. I arrived at 02:10 pm so technically its almost getting to an hour before my car is even taken in for the work.... BEST OF LUCK
Anonymous User
Friendly, prompt, and offers quality service. Ive been here several times for oil changes and other maintenance, and have always come away happy with the service I received. The manager not only remembered my name (!), but he also gave frank advice without being pushy. Ill admit I was skeptical the first time I came here, being a chain and all, but the team has always fought to win my business. Im sorry that Ill be leaving the area, since Ill be leaving such a great place to have my car service. Highly recommend.
Anonymous User
I went there and was told that my car required synthetic oil and that I would need 7 quarts of oil. I was skeptical so I walked out and checked the owners manual. The owners manual does not state that my car requires synthetic oil and it doesnt even say that it is recommended. The owners manual also stated that the engine oil capacity is 5.8 quarts. I was disappointed so I called them back the next day, and they stated that is what their manual said and that they would get it updated.
Eric Mattessich
Ive never been to a Midas before but was very happy with my experience with this Lawrenceville shop. The employees are what make it great - Ken and Gene were friendly and charismatic at the front desk and Ramon was the craftsman who worked his magic on my not-typical 3" diameter exhaust modification request. Very affordable and very accommodating - I will definitely return when I need work done in the future.
Anonymous User
I have used them for oil changes, exhaust replacement, and broken cam shaft. They are friendly enough, honest, and I was happy with the results of the work. They even found dangerous mistakes the dealership garage had made. When I brought in the broken camshaft, they suggested that It was not worth the expense to fix, and didnt charge me for the diagnostic. Good people, I think.


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(1) Kenwood KMR-M322BT Marine Media Player. (1) Scosche Harley Radio Kit HD7000AB.
(1) Scosche Harley Thumb Control Interface HDSWC1. Marine digital media receiver with Bluetooth (does not play CDs). You can also enjoy your favorite Pandora or Spotify playlists. Marine digital media receiver (does not play CDs). Built-in MOSFET amplifier (22 watts RMS/50 peak x 4 channels).Plays MP3, WAV, WMA, and FLAC music files. Control your music with Kenwood's remote app. Anti-glare 1.5 line LCD display. Covered USB and AUX inputs. Enjoy music from Pandora and Spotify.
Android rapid-charge for your smartphone. Connect two phones at once. IPod/iPhone direct connection with optional cable.
Android Open Accessory protocol works with cables or Bluetooth. Drive EQ improves sound to compensate for exterior noise. Sound Reconstruction restores fullness to compressed digital files.Low-pass filter and sub level control. Speaker Setting function for different sizes and types of speakers. Compatible with SiriusXM satellite radio tuner. Inputs: front USB and AUX inputs. Outputs: 6-channel preamp outputs (4-volt front, rear, sub). Works with up to three Kenwood marine remotes. Choose English- or Spanish-language display. Retain handlebar audio controls with a compatible new radio in select 1998-13 Harley-Davidson models. All motorcyclists know that it's safer to use convenient handlebar controls to adjust the radio instead of reaching over and fumbling with knobs and buttons. Scosche's HDSWC1 interface allows you to keep all the handlebar control functions of your Harley-Davidson when you add an aftermarket stereo. Fits select 1998-13 Harley-Davidson motorcycles. Works with Alpine, Clarion, JVC, Kenwood, Sony, Pioneer, and Panasonic receivers with 3.5 mm wired remote input or steering wheel control input.
Works with Scosche HD7000A mounting kit. The package includes a mounting plate to trim out your new radio, along with brackets to hold it in place. The item "FOR 1998-2013 HARLEY DAVIDSON TOURING PLUG & PLAY BLUETOOTH MP3 AUX RADIO STEREO" is in sale since Sunday, July 19, 2015. This item is in the category "eBay Motors\Parts & Accessories\Motorcycle Accessories\Other Motorcycle Accessories". The seller is "a2z-car-audio-superstore" and is located in United States.This item can be shipped to United States, Canada, United Kingdom, Denmark, Romania, Slovakia, Bulgaria, Czech republic, Finland, Hungary, Latvia, Lithuania, Malta, Estonia, Australia, Greece, Portugal, Cyprus, Slovenia, Japan, China, Sweden, South Korea, Indonesia, Taiwan, South africa, Thailand, Belgium, France, Hong Kong, Ireland, Netherlands, Poland, Spain, Italy, Germany, Austria, Bahamas, Mexico, New Zealand, Philippines, Singapore, Switzerland, Norway, Saudi arabia, United arab emirates, Qatar, Kuwait, Croatia, Malaysia, Brazil, Colombia, Antigua and barbuda, Aruba, Belize, Dominica, Grenada, Saint kitts and nevis, Saint lucia, Montserrat, Turks and caicos islands, Barbados, Bangladesh, Bermuda, Brunei darussalam, Bolivia, Ecuador, Egypt, French guiana, Guernsey, Gibraltar, Guadeloupe, Iceland, Jersey, Jordan, Cambodia, Cayman islands, Liechtenstein, Sri lanka, Luxembourg, Monaco, Macao, Martinique, Maldives, Nicaragua, Oman, Peru, Pakistan, Paraguay, Reunion, Viet nam, Uruguay.


text:
Gotta be firm with the womenfolk.
Gotta be firm with the womenfolk.
I got the 2gm memory today, RAM. I went from 512mb to 2gb. So far no difference. I opened an empty spread sheet and browsed the web and there is no noticeable difference. I suppose if I had a heavy operating system it would be more noticeable. I don't think I want to get Windows 7 or Vista for this machine. Any thoughts on that are appreciated.
Don't even think about Vista. I've had Windows 7 for a year and a half and it's about as good as it gets. But then I have a 64bit and you might have 32bit and that might be one difference. And that's all I know about that.
I just upgraded an XP machine from 512M to 2 G and it made a huge difference. I'm surprised that you did not see any improvement.
Life's different here ... It's a whole 'nother pace.
Well tom, I have not had it very long and it never really was slow. I have never used it for anything so far other than browsing so I have no real base point. I opened an empty spreadsheet, and that was fast enough. So maybe it did improve and I just don't know it. Memory is cheap on Ebay and what I got was brand new and worked okay. The vendor is Memory Chick.
I would never install Vista, but maybe 7. I am not sure what I was thinking when I said that. I think XP runs nice, but it seems like an antique laptop after using Vista and 7 for a couple of years. I really liked 7. Hope new software will work with XP. It is the favorite operating system for a lot of serious people so that shouldn't be a problem. But you know how it is with Microsoft, they call the shots for the world with what they will buy and use.
Come to think of it....mine ran OK at first but slowly degraded over time even with CCleaner and AVG, but the bigger memory really helped.
Life's different here ... It's a whole 'nother pace.
I got the "XP Virus Scan 2011" scam virus yesterday.
Now I have had trouble with this one in the past and was able to stop it in it's tracks with control alt delete, task manager, stop the process and delete the file... However, the virus has evolved. It now takes over administrative control and accepts commands that are administrative as agreeing to the software. It shut me down in minutes.
Fortunately I didn't have any important files in my laptop yet and just fixed it with a clean instal of the operating system. Others may not be so lucky.
I got this virus looking for movies that Robert DeNiro was in from what would appear a safe site. Java started running and next thing you know I had it.
Everyone beware.
Installed Windows 7 Professional today. I love it, and 2gb ram works great.
Randude I have a draft to a book I am working on with a couple of pictures thrown in goofing around.
It is done in Micro soft office word 7 and some of my friends can't open it, am I behind times or ahead of times with it?
To be called a "Has Been" I must surmise, is much Greater than to be called a "Nevah Been"... JW...
JW I am not familiar with word 7. Are you talking about 2007?
The thing about some of these programs is a thing called Upward Compatibility. You cannot open a document in version 1997 if the file was created in version 2007. You can open a file with 2007 that was created in 1997 though. Lots of programs work that way and that may be the problem. If you find that is your problem you can use the Save As funtion and save it as an earlier version.
Hope that helps.
Last edited by randude; 06-01-2011 at 02:57 AM.
It is Microsoft office word 2007 something about 3rd edition, mine is pirated and in Spanish I don't like that part but I can live with it, I do like it so and it is what e-book publishers want things in, I am not ready to publish yet. I have a lot of friends and family procrastinating to me with a request of pictures from the past that I must get on their butts again tonight over it, I was promised and so I expect.
To be called a "Has Been" I must surmise, is much Greater than to be called a "Nevah Been"... JW...
Might be worth a google..
Of course there is nothing that stops you from writing it in Microsoft Turd and then opening it in Microsoft Turdpad and submitting that to the publisher..
Anyways.. Just FYI..
Dude !!!.... Its a Canal !!! Can you Dig it ??
I think you're referring to the file extension .docx.
Download OpenOffice from www.OpenOffice.org and you'll never need Microsoft Office ever again.
JW Open office is completely free. It looks and feels a lot like Microsoft Office or in your particular case MS Word. It is great. At the cost of MS Office now days it is a real relief. You can open MS Office files with it and save them as MS Office files.
Here is a link so you don't have to go looking for it.
OK I got it going about 3 or so hours to load and am doing it, I don't know if getting back on here slows it down or not but, I will try it.
Thanks ya'll.
To be called a "Has Been" I must surmise, is much Greater than to be called a "Nevah Been"... JW...


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Unicompartmental Knee Arthroplasty
Nanne P. Kort, MD, PhD
Unicompartmental knee arthroplasty has had varying degrees of acceptance since its introduction approximately 30 years ago. Frequent and early failures were cited in initial studies. By the late 1990s, however, unicompartmental knee arthroplasty for the treatment of localized knee arthritis was becoming more common, and early outcome reports were favorable.
Theoretical advantages of the procedure include preservation of uninvolved tissue and bone, reduced operative time, better range of motion, improved gait, and increased patient satisfaction. With appropriate patient selection, careful surgical technique, and proper implant design, unicompartmental knee arthroplasty can now be viewed as a procedure with reliable medium to long-term success.[1, 2]Unicompartmental knee arthroplasty. The minimally invasive technique with a paramedial skin incision. Extension of the minimally invasive skin incision for a total knee arthroplasty. The mobile-bearing unicompartmental prosthesis. Unicompartmental knee arthroplasty. When a mobile-bearing prosthesis is used, the bearing can become dislocated.
In the late 1950s and 1960s, MacIntosh and McKeever reported on the placement of a prosthetic disk into the diseased tibial plateau.[3, 4] The prosthesis was inserted into the affected side of the knee joint without cement. MacIntosh first used an acrylic prosthesis but later employed a metal one with a concave surface. The McKeever prosthesis had a small, T-shaped keel on its undersurface to improve fixation.
In the early 1970s, Gunston and Marmor independently introduced the cemented unicompartmental knee arthroplasty. Gunston employed a circular runner of stainless steel and a track of high-molecular-weight polyethylene, for use as either a bicompartmental or unicompartmental replacement.[5]
In 1988, in a 10- to 13-year follow-up of 97 cases,[6] Marmor reported 21 treatment failures attributed to development or progression of arthritis in the other compartments or to loosening, with subsidence of a thin (6-mm), all-polyethylene tibial component.
In a 2-year follow-up of patients using the Marmor modular knee replacement, Laskin found that 35% of the knees had a fair or poor result, with high incidence of loosening of the implant and degeneration of the opposite tibiofemoral component.[7] The revision rate was 22%.
Insall published a series in which the conversion rate to a total knee arthroplasty was 28%.[8]
Consequently, by the late 1980s, the popularity of unicompartmental knee arthroplasty had waned. However, after recognizing the need to avoid overcorrection of the mechanical axis, surgeons ultimately were able to reduce the risk that pain in the "normal" compartment would cause early failure.
With the publication of several studies in the late 1980s and 1990s reporting 10-year survivorship rates exceeding 93%, enthusiasm for unicompartmental knee arthroplasty again increased, the survivorship rates being comparable to those for total knee arthroplasty.
Although, in 1994, the Swedish Joint Replacement Registry reported a high percentage of poor results for unicompartmental knee arthroplasty, these outcomes mainly reflected the fact that the surgery was performed on patients with chronic inflammatory arthritis.[9]
Interest in unicompartmental knee arthroplasty was also stimulated by the introduction of the mobile-bearing form of the procedure. Goodfellow and O'Connor, along with others, published excellent long-term survivorship rates associated with this technique.[10] Their rationale for the procedure's success was clearly stated: a mobile bearing (also called a meniscal bearing) provides the unique combination of complete congruency of the articular surface (to minimize wear and creep) and total freedom of movement (to accommodate the preferred motion pattern of the retained natural compartment).
The past few years have again seen a heightened interest in unicompartmental arthroplasty, particularly because of the introduction of the minimally invasive parapatellar technique. This form of the procedure potentially can reduce morbidity, complications, and length of hospital stay.
Many now view unicompartmental knee arthroplasty as preferable to high tibial osteotomy (HTO) in relatively young patients with medial compartment arthritis.
Because unicompartmental knee arthroplasty is typically performed for medial osteoarthritis, this condition is the focus of this article.
For patient education information, visit eMedicine's Foot, Ankle, Knee, and Hip Center and Arthritis Center, as well as Knee Joint Replacement.
Careful patient selection is critical for unicompartmental knee arthroplasty if reliable results are to be achieved. The arthritis should be predominantly confined to a single compartment. (Medial compartment osteoarthritis is usually on the anteromedial aspect of the tibial plateau, and lateral compartment osteoarthritis is typically on the femoral side.) No significant degenerative changes in the other (medial, lateral, or patellofemoral) compartments should be present, and both cruciate ligaments should be intact.
Absence of the anterior cruciate is a contraindication; the anterior cruciate ligament (ACL) makes the combined rolling and sliding at the meniscal femoral and meniscal tibial interfaces possible, which may yield near-normal joint kinematics and mechanics.
The operation is also indicated in patients with osteonecrosis of the femoral condyle. Not all of the unicompartmental replacements are suitable for the lateral side, because the ligaments of the lateral compartment are more elastic than those of the medial side.
Malalignment of the limb should be passively correctable to neutral and not beyond. This usually is possible in patients with a varus deformity less than 15° or a valgus deformity less than 20°.
The deformity of the knee should be only mild; therefore, a flexion contracture should be less than 15°. Unicompartmental knee arthroplasty with excision of osteophytes in the notch cannot correct moderately severe flexion contractures.
Ideally, the knee can be flexed to 110°. This is important for the preparation of the femoral condyle during the operation.
Contraindications to a unicompartmental knee arthroplasty include the following:
Unicompartmental knee arthroplasty is controversial in the presence of patellofemoral joint arthritis, youth and high activity level, obesity, chondrocalcinosis, and crystalline arthropathy.
Progression of osteoarthritis in the patellofemoral joint after unicompartmental knee arthroplasty is rare, according to some studies. In the Swedish Registry, no unicompartmental knee arthroplasties have required revision for patellofemoral problems.[9]
Murray, Weale, and colleagues reported that residual postoperative pain was independent of the state of the patellofemoral joint, and no knee surgery was revised because of patellofemoral problems.[11, 12, 13] Unicompartmental arthroplasty improves the mechanical axis and patellar tracking and allows more normal kinematics and rapid quadriceps rehabilitation. For these reasons, osteoarthritis of the patellofemoral joint may not be considered an absolute contraindication.
However, other investigators and surgeons have reached the opposite conclusion; thus, many consider patellofemoral disease to be an absolute contraindication for unicompartmental knee replacement. For more information, see Patellofemoral Joint Arthritis.
Because younger patients tend to be more active than older individuals, they would also seem likely to have a higher revision rate for unicompartmental arthroplasty than older individuals. However, although some studies have found such differences in revision rates, others have not.
Minimally invasive techniques may reduce morbidity, complications, and length of hospital stay, which may favor the use of unicompartmental knee arthroplasty in younger patients.
Technical difficulties and increased risk of complications are associated with obesity. However, obesity is not considered a contraindication particularly for the unicompartmental knee arthroplasty mobile-bearing design. This is because a correlation has not been found between obesity and wear.
It may be necessary to differentiate between patients with a generalized chondrocalcinosis with synovitis and, effectively, an inflammatory condition in the knee (which is a contraindication for unicompartmental knee arthroplasty) and patients with calcification in the meniscus without generalized evidence of inflammation.
Many patients with osteoarthritis have calcium pyrophosphate crystal deposition in their articular surfaces and suffer from crystalline inflammatory arthropathy. Although Brumby and Thornhill indicated that crystalline arthropathy is a contraindication to unicompartmental replacement, Murray and colleagues disagreed.[14, 11]
Careful patient selection is critical for unicompartmental knee arthroplasty if reliable results are to be achieved. The arthritis should be predominantly confined to a single compartment. (Medial compartment osteoarthritis is usually on the anteromedial aspect of the tibial plateau, and lateral compartment osteoarthritis is typically on the femoral side.)
No significant degenerative changes in the other (medial, lateral, or patellofemoral) compartments should be present, and both cruciate ligaments should be intact. Absence of the anterior cruciate is a contraindication; the ACL makes the combined rolling and sliding at the meniscal femoral and meniscal tibial interfaces possible, which may yield near-normal joint kinematics and mechanics.
The operation is also indicated in patients with osteonecrosis of the femoral condyle. Not all of the unicompartmental replacements are suitable for the lateral side, because the ligaments of the lateral compartment are more elastic than those of the medial side.
Malalignment of the limb should be passively correctable to neutral and not beyond. This usually is possible in patients with a varus deformity less than 15° or a valgus deformity less than 20°.
The deformity of the knee should be only mild; therefore, a flexion contracture should be less than 15°. Unicompartmental knee arthroplasty with excision of osteophytes in the notch cannot correct moderately severe flexion contractures.
Ideally, the knee can be flexed to 110°. This is important for the preparation of the femoral condyle during the operation.
Unicompartmental Knee Arthroplasty Versus High Tibial Osteotomy
Resurfacing methods are gaining popularity. Results comparing HTO with unicompartmental knee arthroplasty favor the latter.
Broughton et al demonstrated good results in 76% of patients in a replacement group and in 43% of patients in an osteotomy group.[15] Range of motion, speed of rehabilitation, and perioperative morbidity were significantly better for unicompartmental knee arthroplasty, and no signs of late deterioration were present.
Weale and Newman, after a 12- to 17-year follow-up period, also reported better function and longer survival in the unicompartmental group.[16]
Other publications have similarly shown more favorable results with arthroplasty.[17, 18] The functional benefits of unicompartmental knee arthroplasty over HTO have also been demonstrated using gait analysis, with patients displaying a more normal gait and better stair-climbing ability following unicompartmental knee arthroplasty than they did after HTO.
If a revision to a total knee arthroplasty becomes necessary, the results are now believed to be generally better if the revision occurs after a failed unicompartmental knee arthroplasty than they are following a failed HTO. (Previous HTO is a contraindication for a unicompartmental knee arthroplasty.)
Unicompartmental Knee Arthroplasty Versus Total Knee Arthroplasty
In the late 1980s, unicompartmental knee arthroplasty waned in popularity, largely because of problems with patient selection, operative technique, and polyethylene wear. Later, as understanding of the procedure and the associated prostheses improved, the long-term results of unicompartmental knee arthroplasty became comparable to those of total knee arthroplasty.[19, 20]
Functional outcome with unicompartmental knee arthroplasty is superior to that with total knee arthroplasty, with the former providing better range of motion and ambulatory function.
Laurencin et al found that unicompartmental knee arthroplasty also results in less pain, more stability, and better stair-climbing ability than does total knee arthroplasty.[21]
In addition, the cost of the unicompartmental procedure is about 57% that of total knee arthroplasty.
In a study, Dalury et al found little or no difference in outcome between patients who received a total knee arthroplasty and those who received a unicompartmental knee arthroplasty, except for a slightly improved range of motion with unicompartmental knee arthroplasty over the total knee procedure (123º ± 9º vs 119.8º ± 7º, respectively). In their investigation, the authors identified 23 patients with osteoarthritis who had undergone a total knee arthroplasty on one side and a unicompartmental knee arthroplasty on the other, for medial compartment disease, and measured Knee Society scores, radiographic analysis, and patient preferences. Average follow-up was 46 months for total knee arthroplasty and 42 months for unicompartmental knee arthroplasty.
Of the 23 patients, 11 expressed no preference between either knee and 12 preferred the unicompartmental knee; no patient preferred the total knee.[19
The patient is placed in a supine position, with the draped leg set on a thigh support or in a legholder. When positioning the patient, it is necessary to ensure that the knee is free to flex to at least 120°.
A sandbag or other bump is affixed to the table to help maintain flexion of the knee. A strap placed around the thigh and leg may serve the same function. The leg is draped free, and it is helpful to place a mark or ball of tape over the anterior superior iliac spine or the femoral head.
A history of trauma should alert the surgeon to the possibility of a remote fracture or articular or ligamentous damage. A history of pain in multiple joints should draw attention to the possibility of inflammatory arthritis.
The physical examination is crucial for appropriate patient selection for unicompartmental knee arthroplasty (see Indications and Contraindications). The integrity of the ACL, the mechanical alignment and range of motion of the knee, and collateral stability must be assessed.
The concept behind unicompartmental knee arthroplasty is the replacement of only the damaged part of the knee and the preservation of as much normal tissue and bone as possible, to allow the restoration of normal kinematics.
In the past, unicompartmental knee arthroplasty was performed through a standard anterior approach with dislocation of the patella, as used for total knee arthroplasty. However, the minimally invasive form of unicompartmental arthroplasty has gained popularity. The smaller incision and arthrotomy of this technique causes less damage to the extensor mechanism, because the patella is not dislocated and the suprapatellar synovial pouch remains intact.
Follow-up research has demonstrated decreased morbidity, faster rehabilitation, and reduced length of hospital stay among patients who have undergone the less invasive medial unicompartmental arthroplasty. With appropriate pain control, the surgery can safely be done as an outpatient procedure, providing substantial cost savings, and patients have reported feeling less pain postoperatively than they did preoperatively. Nevertheless, surgeons utilizing the minimally invasive approach must contend with a restricted visual field, making unicompartmental knee arthroplasty a demanding procedure.
The minimally invasive technique can also be used for lateral unicompartmental arthroplasty, although some authors prefer the standard total knee approach. With the less invasive technique, the exposure is limited, so positioning the prosthetic components is more difficult.
Advances in instrumentation for unicompartmental arthroplasty have increased the surgeon's ability to implant the components in proper alignment and should theoretically increase the longevity of the arthroplasty. Instrumentation is crucial for proper alignment and orientation with some types of unicompartmental knee arthroplasty systems, such as the Oxford Phase III prosthetic. Other prosthetic systems, such as the Repicci II, rely more on anatomic landmarks to ensure proper component placement.
The optimal tibiofemoral alignment following unicompartmental arthroplasty has yet to be determined. Extremes of overcorrection and undercorrection are undesirable. Overcorrection may result in medial or lateral subluxation and increased loading of the unreplaced compartment (medial or lateral).
Undercorrection causes varus or valgus alignment of the leg and can potentially overload the implant.[22] Most surgeons advocate undercorrection of the mechanical axis by 2-3° to avoid overloading the normal compartment.
In general, medial and lateral soft-tissue releases are contraindicated, because knees requiring these have too much preoperative deformity for unicompartmental knee arthroplasty. Angular correction is usually obtained with removal of peripheral osteophytes that tent the capsule and the collateral ligaments.
Computer-assisted surgery can improve the postoperative alignment of medial unicompartmental knee arthroplasty over that of conventional techniques. Real-time information about the leg axis at each step of the operation should diminish the danger of overcorrection or undercorrection.
The navigation system may also be helpful in achieving a more precise component orientation. However, all investigations into the navigation system's use have consisted either of bone-saw or of cadaver studies. As a result of the limited exposure and restricted visual field in vivo associated with the minimally invasive procedure, it is difficult to apply the studies' results to the optimal positioning of components. Further development of the navigation technique will prove if it is more accurate thanthe conventional method.[23, 24, 25]
Mobilization of the knee and patient can start on the day after surgery. Recovery of knee function is usually rapid, with considerably less pain than that which occurs with a total knee replacement. Early mobilization is encouraged, and passive assistance by the physical therapist is advised. The patient can frequently be discharged after 2-3 days. In some centers, the procedure is now performed in day care.
Mechanical prophylaxis against deep vein thrombosis is recommended for the duration of the hospitalization. Postdischarge prophylaxis is at the discretion of the surgeon.
When nonoperative and, possibly, arthroscopic procedures fail, the surgeon may consider HTO, unicompartmental arthroplasty, or total knee arthroplasty. Unicompartmental knee arthroplasty appears to result in better function and pain relief, less morbidity, and higher patient satisfaction than do HTO and total knee arthroplasty.
The long-term survival rate for unicompartmental knee arthroplasty is better than that for HTO and comparable to the long-term survival rate for a total knee arthroplasty. With strict indications, newer prostheses, and attention to surgical technique, unicompartmental knee arthroplasty has become a valuable treatment for unicompartmental knee arthritis.
In a prospective study, Berger et al found that in a 3-month period following knee arthroplasty, no patients in the investigation who had undergone the unicompartmental knee procedure required hospital readmission, compared with 9% of patients who received total knee arthroplasty. In the study, the authors looked at 111 patients who had undergone primary knee arthroplasty, 25 of whom had unicompartmental knee arthroplasty and 86 of whom underwent total knee arthroplasty. Of the 111 patients, 104 (24 with unicompartmental knee arthroplasty and 80 with total knee arthroplasty) met discharge criteria and were discharged directly to home.[26]
Saenz et al evaluated the clinical and radiographic outcomes of the EIUS unicompartmental prosthesis and found it to be associated with higher revision rates than were metal-backed implants. The implant survival rate was 89%, with 16 knees either revised or scheduled for revision. The reasons for revision included aseptic loosening of the tibial component, progressive symptomatic patellofemoral disease, and tibial component subsidence.[27]
Converting a unicompartmental knee arthroplasty to a total knee arthroplasty, shown in the images below, is somewhat more difficult than performing a primary total knee arthroplasty. The results are acceptable but debatably not as good as they are with primary total knee arthroplasty. Despite the benefit of the conservative bone cuts used for unicompartmental knee replacement, stemmed components and augments may be needed for bone loss associated with component removal or osteolysis.Revision to a total knee arthroplasty; view after removal of the unicompartmental prosthesis. Revision to a total knee arthroplasty. The earlier femoral-condylar bone cut/milling of the unicompartmental knee arthroplasty is usually less or the same as that for total knee replacement distal femoral (medial and lateral condyle) resection. Revision to a total knee arthroplasty. The medial or lateral proximal tibial plateau resection of the unicompartmental knee arthroplasty is usually at the same level as the proximal tibial plateau resection for total knee arthroplasty.
Bone defects, if present, usually can be treated with a local autograft. The cumulative revision rate at 10 years is more than 3 times higher for patients in whom a failed unicompartmental knee arthroplasty has been revised to a further unicompartmental knee arthroplasty than for those in whom it has been revised to a total knee arthroplasty.[18]
Early complications
Infection, superficial and deep, is possible. With lateral unicompartmental arthroplasty, palsy of the common peroneal nerve may occur, although this is more common with total knee arthroplasty in patients with severe flexion and valgus deformity.
A tibial plateau fracture, shown below, may result if too much stress is applied with cementation of the tibial component. The vertical tibial cut may act as a stress riser. In general, forceful impaction of the component is minimal, and this complication should be unusual.Unicompartmental knee arthroplasty. A tibial plateau fracture may occur when too much stress is applied with cementation of the tibial component or after adequate trauma. The vertical tibial cut may act as a stress line.
Ligamentous instability is rarely a problem in properly selected patients and with an intact ACL. Soft-tissue releases should be minimal. Knee joint stiffness may occur.
Late complications
Late infection may occur, usually from hematogenous seeding. In addition, prosthesis failure or loosening is possible.
The bearing of a mobile-bearing unicompartmental knee prosthesis may become dislocated, as shown in the image below, especially with lateral unicompartmental arthroplasty. A high, proximal, varus tibial angle along with damage to or overdistraction of the lateral soft-tissue structures is thought to contribute to this problem.Unicompartmental knee arthroplasty. When a mobile-bearing prosthesis is used, the bearing can become dislocated.
Polyethylene wear can occur, but it may be less with a mobile-bearing design.
Undercorrection or overcorrection of the deformity and malpositioning of the components may cause late complications. In the case of overcorrection, excessive load on the opposite compartment might accelerate degenerative changes. Undercorrection places excessive load on the prosthesis, and loosening and failure may result. Improper placement of the components can cause subluxation of the tibia on the femur or impingement of the patella on the femoral component.
Most patients develop a radiolucent line in the tibial bone-cement interface. If these lines are less than 1 mm, they usually do not progress. The appearance of a similar line under the femoral component is expected but is not easily demonstrated because of the nonplanar form of the femoral bone-cement interface.
Borus T, Thornhill T. Unicompartmental knee arthroplasty. J Am Acad Orthop Surg. Jan 2008;16(1):9-18. [Medline].
Jamali AA, Scott RD, Rubash HE, Freiberg AA. Unicompartmental knee arthroplasty: past, present, and future. Am J Orthop. Jan 2009;38(1):17-23. [Medline].
MacIntosh DL. Hemiarthroplasty of the knee using a space occupying prosthesis for painful varus and valgus deformities. J Bone Joint Surg Am. 1958;40A:1431.
McKeever DC. Tibial plateau prosthesis. Clin Orthop. 1960;18:86-95.
Gunston FH. Polycentric knee arthroplasty. Prosthetic simulation of normal knee movement. J Bone Joint Surg Br. May 1971;53(2):272-7. [Medline].
Marmor L. Unicompartmental knee arthroplasty. Ten- to 13-year follow-up study. Clin Orthop Relat Res. Jan 1988;(226):14-20. [Medline].
Laskin RS. Unicompartmental tibiofemoral resurfacing arthroplasty. J Bone Joint Surg Am. Mar 1978;60(2):182-5. [Medline].
Insall J, Aglietti P. A five to seven-year follow-up of unicondylar arthroplasty. J Bone Joint Surg Am. Dec 1980;62(8):1329-37. [Medline].
Knutson K, Lewold S, Robertsson O, et al. The Swedish knee arthroplasty register. A nation-wide study of 30,003 knees 1976-1992. Acta Orthop Scand. Aug 1994;65(4):375-86. [Medline].
Goodfellow J, O'Connor J. The mechanics of the knee and prosthesis design. J Bone Joint Surg Br. Aug 1978;60-B(3):358-69. [Medline].
Murray DW, Goodfellow JW, O'Connor JJ. The Oxford medial unicompartmental arthroplasty: a ten-year survival study. J Bone Joint Surg Br. Nov 1998;80(6):983-9. [Medline].
Murray DW. Mobile bearing unicompartmental knee replacement. Orthopedics. Sep 2005;28(9):985-7. [Medline].
Weale AE, Murray DW, Crawford R, et al. Does arthritis progress in the retained compartments after 'Oxford' medial unicompartmental arthroplasty? A clinical and radiological study with a minimum ten-year follow-up. J Bone Joint Surg Br. Sep 1999;81(5):783-9. [Medline]. [Full Text].
Brumby SA, Thornhill TS. Unicompartmental Osteoarthritis of the Knee. In: Laskin RS, ed. Controversies in Total Knee Replacement. Oxford, UK: Oxford University Press; 2001: 285-312.
Broughton NS, Newman JH, Baily RA. Unicompartmental replacement and high tibial osteotomy for osteoarthritis of the knee. A comparative study after 5-10 years' follow-up. J Bone Joint Surg Br. May 1986;68(3):447-52. [Medline].
Weale AE, Newman JH. Unicompartmental arthroplasty and high tibial osteotomy for osteoarthrosis of the knee. A comparative study with a 12- to 17-year follow-up period. Clin Orthop Relat Res. May 1994;(302):134-7. [Medline].
Stukenborg-Colsman C, Wirth CJ, Lazovic D, Wefer A. High tibial osteotomy versus unicompartmental joint replacement in unicompartmental knee joint osteoarthritis: 7-10-year follow-up prospective randomised study. Knee. Oct 2001;8(3):187-94. [Medline].
Rees JL, Price AJ, Lynskey TG, et al. Medial unicompartmental arthroplasty after failed high tibial osteotomy. J Bone Joint Surg Br. Sep 2001;83(7):1034-6. [Medline].
Dalury DF, Fisher DA, Adams MJ, Gonzales RA. Unicompartmental knee arthroplasty compares favorably to total knee arthroplasty in the same patient. Orthopedics. Apr 2009;32(4):[Medline].
[Best Evidence] Newman J, Pydisetty RV, Ackroyd C. Unicompartmental or total knee replacement: the 15-year results of a prospective randomised controlled trial. J Bone Joint Surg Br. Jan 2009;91(1):52-7. [Medline].
Laurencin CT, Zelicof SB, Scott RD, Ewald FC. Unicompartmental versus total knee arthroplasty in the same patient. A comparative study. Clin Orthop Relat Res. Dec 1991;151-6. [Medline].
Gulati A, Pandit H, Jenkins C, Chau R, Dodd CA, Murray DW. The effect of leg alignment on the outcome of unicompartmental knee replacement. J Bone Joint Surg Br. Apr 2009;91(4):469-74. [Medline].
Cossey AJ, Spriggins AJ. The use of computer-assisted surgical navigation to prevent malalignment in unicompartmental knee arthroplasty. J Arthroplasty. Jan 2005;20(1):29-34. [Medline].
Keene G, Simpson D, Kalairajah Y. Limb alignment in computer-assisted minimally-invasive unicompartmental knee replacement. J Bone Joint Surg Br. Jan 2006;88(1):44-8. [Medline].
Lonner JH. Indications for unicompartmental knee arthroplasty and rationale for robotic arm-assisted technology. Am J Orthop. Feb 2009;38(2 Suppl):3-6. [Medline].
Berger RA, Kusuma SK, Sanders SA, Thill ES, Sporer SM. The feasibility and perioperative complications of outpatient knee arthroplasty. Clin Orthop Relat Res. Jun 2009;467(6):1443-9. [Medline].
Saenz CL, McGrath MS, Marker DR, Seyler TM, Mont MA, Bonutti PM. Early failure of a unicompartmental knee arthroplasty design with an all-polyethylene tibial component. Knee. Jan 2010;17(1):53-6. [Medline].


text:
Zinc Batteries
Basics, Developments, and Applications
1. Edition June 2020
272 Pages, Hardcover
Wiley & Sons Ltd
Battery technology is constantly changing, and the concepts and applications of these changes are rapidly becoming increasingly more important as more and more industries and individuals continue to make "greener" choices in their energy sources. As global dependence on fossil fuels slowly wanes, there is a heavier and heavier importance placed on cleaner power sources and methods for storing and transporting that power. Battery technology is a huge part of this global energy revolution.
Zinc batteries are an advantageous choice over lithium-based batteries, which have dominated the market for years in multiple areas, most specifically in electric vehicles and other battery-powered devices. Zinc is the fourth most abundant metal in the world, which is influential in its lower cost, making it a very attractive material for use in batteries. Zinc-based batteries have been around since the 1930s, but only now are they taking center stage in the energy, automotive, and other industries.
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Inamuddin, PhD, is an assistant professor in the Chemistry Department, King Abdulaziz University, Jeddah, Saudi Arabia and is also an assistant professor in the Department of Applied Chemistry, Aligarh Muslim University, Aligarh, India. He has extensive research experience in multidisciplinary fields of analytical chemistry, materials chemistry, electrochemistry, renewable energy and environmental science. He has published about 150 research articles in various international scientific journals, 18 book chapters, and 60 edited books with multiple well-known publishers. His current research interests include ion exchange materials, a sensor for heavy metal ions, biofuel cells, supercapacitors and bending actuators.
Abdullah M. Asiri is the Head of the Chemistry Department at King Abdulaziz University and the founder and Director of the Center of Excellence for Advanced Materials Research (CEAMR). He is placed on the list of prestigious highly cited (Hi-Ci) researchers' of the year 2018 powered by Web of Science. He serves on the editorial boards of multiple scientific journals and is the Vice President of the Saudi Chemical Society (Western Province Branch). He holds multiple patents, has authored many books, more than one thousand publications in international journals, and multiple book chapters.


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