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# Math Help - Difference Quotient

1. ## Difference Quotient

I'm new to calculus and haven't had pre-calc. I have a question regarding a certain problem.

I'm to compute the derivative of a given function using the difference quotient.

This is the function: $f(x)= -2/x$

I only got as far as plugging the function into the formula before I got lost. Can someone please help?

2. Originally Posted by gstyzzer
I'm new to calculus and haven't had pre-calc. I have a question regarding a certain problem.

I'm to compute the derivative of a given function using the difference quotient.

This is the function: $f(x)= -2/x$

I only got as far as plugging the function into the formula before I got lost. Can someone please help?
Let $f(x) = \frac{-2}{x}$, then:

$\frac{df}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{\frac{-2}{x+h} - \frac{-2}{x}}{h}$ $= \lim_{h \to 0} \frac{\frac{-2x}{x(x+h)} + \frac{2(x+h)}{x(x+h)}}{h}$

Can you finish it off from here? (Rest is in the spoiler.)

Spoiler:
$\lim_{h \to 0} \frac{-2x +2x +2h}{hx(x+h)} = \lim_{h \to 0} \frac{2}{x(x+h)} = \lim_{h \to 0} \frac{2}{x^2+xh} = \frac{2}{x^2}$

f'(x)=g(x)h'(x)-h(x)g'(x)
[g(x)]^2

let -2=h(x) and x=g(x)
f(x)=h(x)/g(x)

f'(x)={xd(-2)-(-2)d(x)}/(x)^2
dx d(x)
=0+2
x^2
=2/x^2


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Possibly naive question about quantized space-time

In Quantum Mechanics, discrete values of measurements occur only in relation to bound states. This is because of the general solution for the time-independent Shroedinger's equation.

Similarly, in order to quantise space-time, do we need to make space-time compact? How would a compact space-time look like? Would we simply need close it by including $\infty$? Is that physical (infinity doesn't sound very physical to me)?

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# What is the equation of the line with slope  m= 7/25  that passes through  (4/5 3/10) ?

Jan 18, 2016

$y = \frac{7}{25} x + \frac{19}{250}$

#### Explanation:

.

Standard form: $y = m x + c$ ....................(2)

Given: m=color(green)(7/25) ; color(white)(....) "a given point on the line" P->(x,y)->(color(brown)(4/5),color(blue)(3/10))

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substituting the information we are given into equation (1)

$\textcolor{b l u e}{\frac{3}{10}} = \left(\textcolor{g r e e n}{\frac{7}{25}} \times \textcolor{b r o w n}{\frac{4}{5}}\right) + c$

$\implies \frac{3}{10} = \frac{28}{125} + c$

Subtract $\frac{28}{125}$from both sides

$\frac{3}{10} - \frac{28}{125} = c$

$c = \frac{19}{250}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~
So the equation $y = m c + c$ becomes

$y = \frac{7}{25} x + \frac{19}{250}$


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Integration By Parts

This chapter explains how to mentally do integrations which must be solved by integration by parts. As you read, it may seem that you have to keep an unreasonable amount of information in your head. How am I supposed to keep track of all this? It's not possible.'' What you are learning to do is work with your internal representation of the math. If you visualize an equation, that is one possible internal representation. The more efficient the representations you employ inside of you, and the more efficient your methods for working with them, the more complex the math you can easily do. One thing talented mathematicians have working for them is that they have discovered how to internally represent math expressions in ways that are both efficient and amendable to mathematical manipulation. This lets them use the mental energy they have very, very effectively. As mentioned earlier, if a person's ability to visualize is good enough, they can just imagine a whiteboard in their mind's eye, and imagine each step written out exactly as they would write it out on a real whiteboard. That's certainly one possible internal representation, and one that requires a LOT of mental work! Mathematicians learn to represent expressions in more minimal ways, making them much easier to manage. That is precisely what you are learning to do here!

Ease into it gradually. Use the techniques to skip single steps that you would normally write out. For a problem that you might typically write six steps to solve, do one of them mentally and write five steps. After you have done this enough that it seems straightforward, look for opportunities to do two steps in a row mentally. Bite off what you can chew. It's very likely that there will be times when you attempt to do something mentally, and partway through it discover that it was too much. No problem; I do that all the time. So does every mathematician and engineer I know of. Just back off to where you started that step and write it out instead, or break it up into smaller, more manageable pieces.

What's written below is presented in the most extreme case: how you would evaluate the whole expression mentally. You can always use it partially, writing out as many steps as needed. When evaluating a mathematical expression, the most important thing is to understand what you are doing. Do as much or as little mentally as it takes to support that goal.

Most modern calculus textbooks use the symbols u and v when teaching integration by parts. The equation you memorize is probably , not , even though mathematically they are the same. In addition, the position of the symbols is always the same: you typically see and write the right hand side as , and not like or .

You can use this consistency to help you do integration by parts mentally. We'll demonstrate with the integral

First, you want to rearrange the symbols so that you can work with the expression more clearly. You might end up visualizing something like this:

In this form, the expression is organized in a more minimal way, and will be easier to work with.

(Note: while doing algebra mentally is not explicitly covered in this work, it can be done with the techniques covered in the first few sections - visualization, using chunks, and so on. The book Inner Algebra (http://hilomath.com/inneralgebra/html/), and the upcoming book Higher Mental Math, teach mental algebra in detail.)

When doing integration by parts, you divide the integrand into two parts - one of which will be differentiated, the other integrated. The next step is then to divide up the integrand and differential into two chunks like that:

This is what you might visualize. There are a few things to point out. We have mentally moved some of the symbols around. Also, we have decorated the chunks, by putting a little u'' or dv'' on top of them. You can actually visualize these labels over each chunk. Yet you don't have to: the other thing to notice is that we put the u chunk on the left and the dv chunk on the right. Now, as we mentioned earlier, when you learn integration by parts, typically the formula you use has a left-hand side of , rather than . Even though mathematically both versions have the same meaning, you have made a habit of using the first form. (Or if you are taking your first calculus course right now, you will be taught to make it a habit.) You can exploit this habit; all you have to do is divide the expression into two chunks, and put the one corresponding to u on the left of the chunk corresponding to dv. So you can visualize the expression like this:

While the chunks are not labelled, you know which is which by its position in the expression. The position itself acts as the label! Having fewer symbols, it is easier to visualize and work with mentally. The fewer symbols an expression has, and the simpler they are, the greater the ease with which you can work with that expression.

You can harness this positioning in a powerful, interesting way. Visualize the right side of the integration-by-parts rule:

Now, replace that with this image:

You are visualizing empty chunks, arranged in a pattern like the reference image. Obviously, each of these empty chunks corresponds to u, v, or dv. What you want to do is be able to switch between both images in your mind's eye. Practice this a few times right now.

So now you have two images you are working with: the first one, containing , and the second one, containing empty chunks. You mainly work with the second image, filling in the chunks. When you need to remember what goes in each chunk, you visualize the image, so that each symbol (u, v, and dv) overlaps the chunk they correspond to. This can be done in a way that efficiently reminds you of the meaning of each chunk.

Let's examine how this can be done with , step by step. Once you have sorted the expression into two chunks, visualize something like this:

At any time, to remind yourself of the meaning of each chunk, you can replace that image with this one:

Swap between them in your mind's eyes. This may or may not be easy for you at first. If not, practice!

Since some of the chunks repeat - e.g., u and v both appear twice - you can just copy the chunks to those spaces. Moving left to right, you would first visualize

(This image is split up into two lines, so that it can fit on the page you are reading. As you visualize it internally, you can either keep it as one long line or split it up like this. If you do, you may want to split up the image of similarly.) We don't have to think much for this first substitution, since we are simply copying the contents of one chunk to another. Schematically, it works like this:

You are taking a part of the mental image you have, and reproducing it in another location. To fill the next chunk on the right hand side, you will have to integrate the contents of the dv chunk on the left-hand side. You would end up visualizing something like this:

At this point, you can remind yourself of what to do next by swapping back to this image:

Since the v'' chunk appears twice on the right hand side, and we filled the first one, we know what to put in the second one. Switching back to the other image,

Note that we only visualize the right hand side here, since for this step that is all we need. Switching again to this image,

we see that the last chunk to fill is the differential of . While mental differentiation is not covered in this book, it is based on all the same principles you have learned so far. (Mental differentiation will be detailed in the upcoming book, Higher Mental Math.) Differentiating an expression is often easier than integrating it, fortunately. To finish, copy the u chunk, differentiate its contents, and move it into the last space:

This is a good place to simplify the expression. If you intend to write down the final result, you can simplify and write down the first term on the right-hand side at this point. In fact, you can do it even before now, so that you have less to remember. Let's say you have done this - you have just written something like , and now you are visualizing this:

(This is all you have to visualize now, since you have written down the rest and have finished with it.) We still have the chunks there. At this point, though, we no longer need them. So just visualize the expression without them:

You can simplify it, and perhaps end up visualizing something like this:

To evaluate this mentally, first recognize that this expression fits the rule

(plus a constant, but since we are doing integration by parts, we can set this constant to 0.) To mentally integrate a monomial like this, begin by visualizing the expression and chunking the exponent:

Then, drop the integral sign and the differential dx from the image:

(By the way, this is what we call an intermediate image - an image you visualize that has no (correct) mathematical meaning, but is something you use as a step when moving from one valid image to another.) Now, add one to the exponent (the chunk's contents):

There is one more step, which can be done in a couple of ways. In the first way, you would make a fraction, copying the chunk and moving it into the denominator:

From this point you just de-chunk and simplify:

The second way for the last step also involves copying the chunk. But you don't create a fraction; instead, you invert the chunk's contents and insert it multiplicatively in the expression:

Then, you just de-chunk and simplify. Obviously, these are both mathematically the same. The second way is useful when the exponent is a fraction. The first way is better when the exponent is not a fraction. While you will use both, you will probably use the first way more often.

After all this talk about the internal process, it may be helpful to step back and see what all this looks like from the outside. If you are watching yourself, after you have learned and mastered these techniques, what would you be doing? Imagine you are evaluating an integral that is written on a whiteboard (or written on a sheet of paper, typed into a computer, etc.). You glance at the expression several times as you evaluate it. You may rewrite the expression once with the symbols sorted into two groups, u on the left and dv on the right. Or you may not rewrite it at all, relying on your mental image instead. You write an equal sign, followed by a term that corresponds to uv: it's a simplified expression, with the product of u and v reduced to its simplest form. Next you write an integral, whose argument corresponds to v du. Alternatively, you write the result of evaluating the integral directly, evaluating it internally first.

#### Footnotes

... this
By extension, this works with polynomials also.


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Intermediate Algebra for College Students (7th Edition)

$-\text{ }\text{ }7$
The given expression can be written as: $=x^2-2(x)(7)+7^2$ RECALL: The perfect square trinomial $a^2-2ab+b^2$ can be factored as $(a-b)^2$. Factor the trinomial using the formula above with $a=x$ and $b=7$ to obtain: $=(x-7)^2$ Thus, the missing expression in the given statement is: $-\text{ }\text{ }7$


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Top

# Ratio Comparison

Comparison of quantities by division is ratio and the symbol ":" express a ratio. Ratio as the comparison made on the basis of how many times a quantity is that of the other quantity. A ratio may be used to convey an idea that cannot be expressed as a single number.
Let us study about ratio comparison:
Consider a and b as two different quantities, Then
the quotient a/b  is called as the ratio between a and b. It can be mentioned as a : b.
The ratio comparison is nothing but comparing the two different ratios as they are equal to one another or not.

 Related Calculators Calculate Ratio Ratio to Fraction Ratio to Percent Compare Fractions Calculator

## How to Compare Ratios?

The ratios do not have any unit. Then a and b are said to be as terms of ratio, where ‘a’ is the first term which is termed as antecedent and ‘b’ is the second term which is termed as consequent. Always ratios are used to express in their lowest terms.

The inequality of ratios are also considered as greater inequality, lesser inequality and the other as equality, which are as follows:

Greater inequality as if a > b

Lesser inequality as if a < b

Equality as if a = b

If a:b and c:d are said to be two different ratios then their ratio comparison will be as follows:

a:b > c:d if ad > bc

a:b < c:d if ad < bc

a:b = c:d if ad = bc

## Ratio Problems

Below you could see problems on ratio

### Solved Examples

Question 1: Consider the two ratios as 3:4 and 1:2. Find which one of the two ratios is greater.
Solution:
The two given ratios are a : b = 3 : 4 and c : d = 1 : 2.

Multiply the value ‘a’ with ‘d’ and the value ‘b’ with ‘c’ as follows:

3 x 2 = 4 x 1

6 = 4

Compare the value 6 and 4 as follows:

6 > 4 (that is ad > bc).

Therefore the ratio 3:4 is greater than the ratio 1:2 according to the ratio comparison rules.

Question 2: Consider the two ratios as 2 : 3 and 3 : 5. Find which one of the two ratios is smaller.
Solution:
The two given ratios are a : b = 2 : 3 and c : d = 3 : 5.

Multiply the value ‘a’ with ‘d’ and the value ‘b’ with ‘c’ as follows:

2 x 5 = 3 x 3

10 = 9

Compare the value 10 and 9 as follows:

10 > 9 = 9 < 10 (that is bc < ad).

Therefore the ratio 3 : 5 is smaller than the ratio 2 : 3 according to the ratio comparison rules.

### Practice Problems

Question 1: Consider the two ratios as 1:3 and 2:3. Find which one of the two ratios is smaller.
Question 2: Consider the two ratios as 3:4 and 2:3. Find which one of the two ratios is greater.
Question 3: Consider the two ratios as x:4 and 1:2. If these two ratios are equal then find the value of ‘x’.
 Related Topics Math Help Online Online Math Tutor
*AP and SAT are registered trademarks of the College Board.


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# How to prove $\int^{\infty}_{0}\frac{\sin x}{x}\mathrm{d}x=\frac{\pi}{2}$ [duplicate]

How to prove $$\int^{\infty}_{0}\frac{\sin x}{x}\mathrm{d}x=\frac{\pi}{2}$$ Do you have a simple method ?

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# Determining existence of a solution for a system of linear inequalities

I have a set of vectors $\mathbf{v}_1,\mathbf{v}_2,...,\mathbf{v}_m\in\mathbb{R}^n$ and I want to know if there exists a nonzero vector $\mathbf{x}$ such that $\mathbf{x}\cdot\mathbf{v}_i\le0$ for any $i$. This is the same as saying the equation $\mathbf{x}^TV\leqq\mathbf{0}$ has a nonzero solution, where $V$ is an $n\times m$ matrix whose columns are $\mathbf{v}_i$.

Geometrically, a solution exists if a plane can be drawn through the origin such that all of the vectors are on one side (on contained within the plane).

One can show using Stiemke's Theorem that a solution exists if and only if $V\mathbf{y}=\mathbf{0}\ ,\ \mathbf{y}>\mathbf{0}$ does not have a solution.

I have found a few sources on feasibility problems in linear programming, but none that have allowed me to find a solution to this problem. Any help would be appreciated.

• Do you want a nonzero vector $x$ with that property? – Sungjin Kim Aug 11 '16 at 3:49
• Yes, I forgot to specify that. Thanks. – Kajelad Aug 11 '16 at 3:51
• Let us consider an extreme case: $n=1$, $m=2$, $v_1=1$, $v_2=-1$. Then what happens? This would give you some sense of what must be satisfied to guarantee the existence. – Sungjin Kim Aug 11 '16 at 4:08

Sounds really similar to Farkas's lemma. In order to prove that your problem has a solution, you must show that the problem

$$(P)\quad A\underline{x}=\underline{b}, \quad \underline{x}\geq \underline{0}$$ has no solution (in your case $\underline{b}=\underline{0}$ and $A=V$). To this end, you can use the simplex method to verify that there is no admissible solution to problem $(P)$.

Edit: this is how you use Linear Programming (LP) to determine if there is a feasible solution. Consider the LP problem

$$\min f(\underline{y})=\sum y_i\\ \\ s.t. A\underline{x} + \underline{y} = \underline{b}\\ x_i\geq 0,y_i\geq 0,b_i\geq 0$$

Then, if (one of) the optimal solution(s) verifies $f(\underline{y})=0$, then that means that $y_i=0$ for all $i$, that is, your original system is feasible. This is the first phase of the so called two-phases simplex method, where you try to determine an initial solution for a LP problem. Notice that this problem (the first phase) always has the trivial initial solution $\underline{y}=\underline{b}$.

• Thanks. I have been doing a bit of research on linear programming, but I still have more to figure out. If you know of any, would it be possible to point out some sources on how to implement the simplex method on a feasibility problem like this? – Kajelad Aug 15 '16 at 21:22
• Well, there is already plenty of software that does LP out there. To stay in the open-source world, you could use the linear programming in Octave: gnu.org/software/octave/doc/v4.0.0/Linear-Programming.html. I'm adding a comment on how to use LP. – bartgol Aug 16 '16 at 15:37

You can setup and solve a sequence of $2n$ LP's. For each variable $x_{i}$, first maximize $x_{i}$ subject to the constraints $x^{T}V \leq 0$, then minimize it.

If there was a nonzero vector $\hat{x}$ that satisfied the constraints, then there would be some $k$ such that either $\hat{x}_{k}<0$ or $\hat{x}_{k}>0$. When we minimized or maximized $x_{k}$ we would get a nonzero optimal value. Alternatively, if $x=0$ is the only solution that satisfies the constraints then all optimal values will be 0.

In terms of implementation, you can use any LP solver that you like. Depending on the size and structure of the problem it might be better to use a simplex code or it might be better to use an interior point solver.

• Would it be possible to elaborate this answer? It is still not clear to me how to implement this approach, and why it will produce the desired result. – Kajelad Aug 11 '16 at 17:24
• I've expanded the answer a bit. – Brian Borchers Aug 12 '16 at 3:21

An alternative approach based on Stiemke's theorem would involve the solution of a single somewhat larger LP.

Solve the LP

$\max z$

Subject to

$Vy=0$

$y_{i} \geq z, i=1, 2, \ldots, n$

If the optimal solution has $z=0$, then $Vy=0$, $y > 0$ has no solution.

If a set of vectors belongs to a hyperplane, then the normal vector of the hyperplane perpendicular to each of the vectors of the set. And vice versa: if a vector is perpendicular to each of a set of vectors, these vectors belong to the same hyperplane.

The nesessary and sufficient condition of hyper-coplanarity is the rank of the matrix $r$ is less than $n$.


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GRE Subject Test: Math : Roots of Polynomials

Example Questions

Example Question #1 : Algebra

What are the roots of the polynomial: ?

None of the Above

Explanation:

Step 1: Find factors of 44:

Step 2: Find which pair of factors can give me the middle number. We will choose .

Step 3: Using  and , we need to get . The only way to get  is if I have  and .

Step 4: Write the factored form of that trinomial:

Step 5: To solve for x, you set each parentheses to :

The solutions to this equation are  and .

Example Question #2 : Algebra

Solve for

Explanation:

Step 1: Factor by pairs:

Step 2: Re-write the factorization:

Step 3: Solve for x:

Example Question #3 : Algebra

Find

No Solutions Exist

Explanation:

Step 1: Find two numbers that multiply to  and add to .

We will choose .

Step 2: Factor using the numbers we chose:

Step 3: Solve each parentheses for each value of x..

Example Question #1 : Roots Of Polynomials

Explanation:

Based upon the fundamental theorem of algebra, we know that there must exist 3 roots for this polynomial based upon its' degree of 3.

To solve for the roots, we use factor by grouping:

First group the terms into two binomials:

Then take out the greatest common factor from each group:

Now we see that the leftover binomial is the greatest common factor itself:

We set each binomial equal to zero and solve:

Example Question #5 : Algebra

Find all of the roots for the polynomial below:

Explanation:

In order to find the roots for the polynomial we must first put it in Standard Form by decreasing exponent:

Now we can use factor by grouping, we start by grouping the 4 terms into 2 binomials:

We now take the greatest common factor out of each binomial:

We can see that each term now has the same binomial as a common factor, so we simplify to get:

To find all of the roots, we set each factor equal to zero and solve:

Explanation:

Example Question #2 : Roots Of Polynomials

What are the roots of ?

Explanation:

Step 1: Find two numbers that multiply to  and add to ...

We will choose

Check:

We have the correct numbers...

Step 2: Factor the polynomial...

Step 3: Set the parentheses equal to zero to get the roots...

So, the roots are .

Example Question #3 : Roots Of Polynomials

Find all of the roots for the polynomial below:

Explanation:

In order to find the roots of the polynomial we must factor by grouping:

Group into two binomials:

Take out the greatest common factor from each binomial:

We can now see that each term has a common binomial factor:

We set each factor equal to zero and solve to obtain the roots:


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Medicine » Urology and Nephrology » "Hemodialysis", book edited by Hiromichi Suzuki, ISBN 978-953-51-0988-4, Published: February 27, 2013 under CC BY 3.0 license. © The Author(s).

# Implementation and Management of Strategies to Set and to Achieve Clinical Targets

By Bernard Canaud, Ciro Tetta, Daniele Marcelli, Guido Giordana, Stefano Stuard, Katrin Koehler, Flavio Mari, Carlo Barbieri, Miryana Dobreva, Andrea Stopper and Emanuele Gatti
DOI: 10.5772/53041

Article top

## Overview

Figure 1. Example of SOMs of different variables (Weight, Height, Body Mass Index – BMI –, and Fat) for 251 patients.

Figure 2. Two component planes (relative to the HDF online KPI and to the Treatment Adequacy KPI, respectively) of an SOM trained on BSC data from Portuguese clinics of the NC network. The dashed rectangles superimposed on the planes indicate regions of the SOM where interesting groups of clinics can be found (see discussion in the text). SOM training and visualization were performed in MATLAB using the SOM toolbox [39]. The SOM is shown as a collection of neurons (hexagons) placed in a two-dimensional grid, where the focus is on the relative, rather than the absolute, position of each neuron: that is, the main information content lies in the neighborhood relationships among neurons, as adjacent neurons contain similar KPI records. We can therefore compute the average score for a given KPI in each neuron: this is represented by a color code (colorbar shown on the right) in the component plane relative to that KPI

Figure 3. Two component planes from the SOM for the Portuguese clinics of the NC network. The shown planes refer to the Patient Growth and New Patient Inflow KPIs, respectively.

Figure 4. The High Flux and Treatment Growth component planes of an SOM trained on data from Turkish clinics of the NC network.

# Implementation and Management of Strategies to Set and to Achieve Clinical Targets

Bernard Canaud1, Ciro Tetta1, Daniele Marcelli1, Guido Giordana2, Stefano Stuard2, Katrin Koehler1, Flavio Mari3, Carlo Barbieri3, Miryana Dobreva2, Andrea Stopper2 and Emanuele Gatti4

## 1. Introduction

Today health care and care provider organizations are facing new challenges. They must continually improve their services to provide the highest quality at the lowest cost. Pressures to increase the quality and lower the costs are coming from accreditation and certification boards, public health authorities and the media that publish comparisons and rank facilities by performance. In addition, new demands on health care systems require action accountability with hard outcome data based on morbidity and mortality. Quality control, quality assurance and continuous quality improvement (CQI) processes derived from the manufacturing and industrial world have been progressively applied with success to medicine and in particular to the treatment of end stage renal disease.

[1,2]. It is generally accepted that quality control describes the process for reviewing and checking that targets according to whether a defined set of criteria has been achieved, while quality assurance is the process in which systematic monitoring, collecting and evaluating the performance of a facility or a care network are assessed to ensure that standards of care are met [3]. CQI describes the action that takes place after analyzing outcomes with the intent of improving the results and reducing variation from the target. In this respect, renal replacement therapy by dialysis represents a particular field of application where quality control and quality assurance processes have been shown to be very efficient tools for optimizing treatment adequacy and improving patient outcomes.

Today, national health care systems worldwide are expected to deliver more and better services to a greater number of patients, while dealing with ever more reduced economical resources on the one hand and increased costs on the other hand. Major challenges posed to healthcare systems include global ageing and increase in so-called civilization diseases, growing budget deficits and slowing economic growth, worldwide health care workers shortage and commodity shortage. The need to provide innovative and high-quality, innovative products and treatments should able to contribute to improving outcomes and to be in balance with new perspectives addressing the health care change. Innovation has to contribute to solving the challenge of the economic pressure, though innovation will need standardization according to the rules of good clinical practice and proved by evidence-based medicine. Perverted incentives may also contribute to rising costs as well as reimbursement as providers are reimbursed for performed procedures rather than achieved ones. Moreover, a common weakness of health care systems is linked to the low level of responsibility for the costs generated by the patients at the time they require the medical service. The costs for renal replacement therapy is exceedingly high and are consuming a significant proportion of health care budgets. The global prevalence of kidney failure continues to rise, and treatment is costly; thus, the burden of illness is growing and the resources allocated to treatment are increasing. According to the U.S. Renal Data System (USRDS) Annual Report 2011, total Medicare costs in 2009 rose 8%, to $491 billion; costs for ESRD rose 3%, to$29 billion, accounting for 6% of the total Medicare budget. ESRD data for 2009, however, do not include Part D (costs of drugs), which amounted to \$2 billion in 2008 (Best Dialysis Centres at [25]. In European health care systems, the costs of treatment for the growing population of chronically ill patients (including those requiring renal replacement therapy) are considered an emerging public health problem. Indeed, renal failure persists as a chronic worldwide epidemic with an exponential growth trend on a global scale. Over the last decade, the prevalence of ESRD in Europe grew by an annual average rate of 5%. By the end of 2011, the number of ESRD patients in Europe was estimated to be 657,000 and, of these, approximately 433,000 (around 66%) received dialysis treatment [26]. Currently, many healthcare systems in Europe try to address the growing budget pressures by savings. Savings alone can provide relief to the challenged financial situation only to a very limited extent. Providers and payors turn to simplistic actions such as across-the-board cuts in expensive services, staff compensation, and head count. Imposing arbitrary spending limits on discrete components of care, or on specific line-item expense categories, achieves only marginal savings that often lead to higher total systems costs and poorer outcomes. The inability to properly measure cost and compare cost with outcomes is at the root of the incentive problem in health care and has severely retarded the shift to more effective reimbursement approaches. Moreover, poor measurement of cost and outcomes also means that effective and efficient providers go unrewarded preventing them from making systemic and sustainable cost reductions. A broad consensus exists regarding targets for best medical practice in renal care [27]. Concepts regarding how to achieve these targets in the most efficient way, however, vary significantly. The variety of solutions, reflected by different national models of renal care as well as ongoing reforms and recent reform proposals, suggest that the search for an optimum is still ongoing.

Achieving the right balance between high-quality service for chronically ill patients and its cost is now one major challenge for the health care industry. It is crucial to recognize the benefit of collecting and analyzing large amounts of data, comparing treatment modalities and opting for the highest quality. The wide use of evidence-based medicine and the implementation of national and international guidelines for optimal care play a very important role in this process of improvement of care, drawing a clear line of effective treatment. A recent study by the DOPPs emphasizes how quality of treatment may diverge among centers [28]. In the present context of an ever-growing number of patients requiring treatment in a system of scarce available resources, the optimization of care protocols in terms of “improved care for less money” has become a very complicated challenge. Standardized guidelines coupled with innovative models for process improvement have made it possible to accomplish this otherwise herculean task.

Fresenius Medical Care, has included QPI in an elaborate system called Balanced Scorecard, aimed at evaluating and comparing clinics, countries and regions, providing the stakeholders with an important tool allowing an insight into what is the actual level of care provided in the clinics, besides from the usual financial data [29]. Fresenius Medical Care’s approach to ‘optimal care’ is being applied in more than 3,000 dialysis clinics in North America, Europe, Latin America, Asia-Pacific and Africa. NephroCare, the service provider for Fresenius Medical Care in Europe, coordinates the clinics in Europe, Middle East, Africa and Latin America, that use state-of-the-art dialysis products, renal pharmaceuticals and therapies (all of which are constantly being improved), as well as care from qualified, motivated clinic personnel who regularly participate in training programs. In every country of its European network, NephroCare adapts its care model to reflect the national health care architecture and to further develop concepts within the predefined regulatory frame [29]. To impact the quality and efficacy of a health care service, patient and cost related information must be captured, updated, and shared with all stakeholders in a timely and effective manner to not only ensure universal access to quality data, but also to extend essential information to key clinical decision makers [30]. The Balanced Scorecard tool has allowed NephroCare to promote the collaboration between public institutions and the private provider in more than 20 European countries, giving in the hands of the public a way to control the quality outcomes achieved in the clinics [31,29]. This has been an important achievement for quality in the European healthcare context where dialysis is still mainly provided by public hospitals. It has to be noted that all this would not be possible without the implementation of the electronic medical record EMR). Like in the rest of the health care context, the use of a specialized software to keep track of the patients’ medical history has made it possible for the nephrologist to have immediate access to an enormous amount of patient information. In the last few years, a large number of software platforms have been proposed and some of them offer personalized versions, which could be customised to the needs of the nephrologist (The DoctorsPartner Nephrology EMR, by DoctorPartner LLC ectectect).

## 2. The Electronic Medical Record (EMR): Benefits of the worldwide web, quick and simple data collection and analysis, statistics as a tool to predict outcomes

Paper-based records are still by far the most common method of recording patient information for most hospitals and practices in the world. A critical aspect of paper-based records is legibility. Handwritten paper medical records can be associated with poor legibility, which can contribute to medical errors [32]. Pre-printed forms, the standardization of abbreviations, and standards for penmanship were encouraged to improve reliability of paper medical records. The majority of physicians still find it easier to handle paper-based records and consider entry of data into an EMR tedious. However, paper-based data require a significant amount of storage space and to retrieve information is quite difficult and time-consuming [2]. This is particularly true in the case of person-centred records, which are impractical to maintain if not electronic. For this reason, retrospective analysis based on large historical case series and programs based on data, as Continuous Quality Improvement, are only recently becoming popular with the deployment of EMR. Because of these many "after entry" benefits, governments, insurance companies and large medical institutions are heavily promoting the adoption of EMR. The benefits can be especially high considering the different uses of the same information, i.e. for monitoring a patient, CQI requirements, for reporting purposes or for billing a service. A critical aspect of EMR is the codification of information. In human communication, free text is the natural approach used not only for oral communication but also for written medical records. Free text offers the option to maximize the benefit of a given language to describe situations well, but it may be difficult to maintain the same content once translated into another language. Additionally, it cannot be used for statistical purposes. Codification is somehow universal, and a code is a kind of ideogramme readable by people of different languages. To get more out of an EMR, information has to be codified as much as possible, allowing an easier use. In general electronic records help with the standardization of forms, terminology and abbreviations, and data input. However, the increased portability and accessibility of electronic medical records may also increase the risk of unauthorized access and theft by as acknowledged by increased security requirements. The ability to exchange records between different EMR systems ("interoperability") facilitates the co-ordination of health care delivery in non-affiliated health care practices. Nowadays it is very common to see primary physicians working with computerized systems in their practice. However, very often they use systems which could be described as minimally functional since they include only orders for prescriptions, orders for tests, viewing laboratory or imaging results, and clinical notes. A more sophisticated use, including further analytical elaboration of the data as required by the CQI approach, is normally not part of the routine. To ensure the quality of care delivered to patients treated in its dialysis units, Fresenius Medical Care continuously monitors its dialysis services. The overall quality management system of the company, which is based on CQI, provides the necessary framework. CQI programs, incorporating the implementation of clinical practice guidelines and CPM by dialysis providers, demand the development of computerized monitoring systems in order to collect and supply information on the dialysis treatment. Therefore, Fresenius Medical Care developed a specific clinical database as a tool to monitor critical aspects of dialysis care and improve the quality of care.. This central database is called EuCliD, the acronym for European Clinical Database as the database was first developed in Europe. EuCliD collects the most-important medical information on the treatment of dialysis patients. The data provide a basis for clinical trials and help improve the treatment of dialysis patients by comparing the different treatments. The description of the first version of the database has already been published [33]. Right from the outset, EuCliD was structured to follow a logical information flow. During the last years the software has been updated and a new project based on an enlarged scope has been initiated. EuCliD 5 now includes daily treatments performed throughout European, Latin American and African Countries. The new project was aimed not only at supporting quality assurance, but also to facilitate the day-to-day work of the clinical staff. As a result, EuCliD 5, is a multilingual and fully codified software using, as much as possible, international standard coding tables (ICD10, WHO: International Statistical Classification of Diseases and Related Health Problems 1992; ISCED, UNESCO, 1997;ISCO-88, International Standard Classification of Occupations 1988 etc.). EuCliD 5 collects and handles sensitive medical patient data, and ensures the confidentiality of these data [34]. EuCliD 5 has been approved by the respective national or regional authorities prior to data entry and the initiation of data transfer. Of course, the transfer of private patient data out of the dialysis center is not permitted. The availability of EuCliD 5 data, as well as the increasing interoperability of data present in other systems has allowed the practical implementation in a clinical environment of tools like the Balanced Scorecard, a tool developed in the scientific domain of complex system management. Key characteristic of Balanced Scorecard is the aim of maximizing concurrent interests of different stakeholders in a balanced form, concentrating on KPIs able to describe variables whose improvement can improve the overall system behavior [29,30]. Each KPI is not a reported value only, but much more the headline of a project or program to improve performance in a strategic relevant, target oriented way. KPIs are dynamic and when they approach saturation need to be substituted by new ones in a continuous development process of quality improvement and know-how and operational excellence Related to the use of a Balanced Scorecard, there are certain caveat to consider: since the Balanced Scorecard is nothing else than a model of stege 5 chronic kidney disease management, Wrong or inadequate model design and definition and wrong or inadequate implementation (or execution) can lead to erroneous conclusions. In this sense the right selection of KPI and the appropriateness of the derived actions are of crucial importance as well as the validation of data and their causal relationships with outcomes. It is fundamental to understand how to manage and not just measure performance and this will not happen without regular review sessions at all levels

## 3. Self-organizing maps for continuous quality improvement

In order to derive improvements from the clinical data Self-Organizing Maps (SOMs), an innovative approach recently introduced by Fresenius Medical Care, could complement standard statistical methods used to extrapolate information. A brief description of SOMs follows: As an example, let us consider a dataset containing the values of four variables (Weight, Height, Body Mass Index – BMI –, and Fat) for 251 patients, for which we built a SOM with 84 neurons (Fig. 1). In this case, each neuron is characterized by a vector of four elements, one for each variable: each neuron can be seen as an “average patient”, whose height is the average height of all patients associated with that neuron, and the same goes for the other three variables. Neurons that are close in the SOM represent patients that are similar from the point of view of the considered variables. Once the SOM has been configured, different effective views of the distribution of the data can be obtained. In particular, one can focus on a specific variable of the input data by color-coding each neuron of the SOM based on the value of that variable. This kind of plot is called component plane of the SOM (see, for instance, Fig. 1). By comparing different planes (i.e., different variables) it is possible to identify relations existing among the variables. Notice that each given neuron (depicted in Fig. 1 as a hexagon) always represents the same subset of data, over all the different component planes. For example, in Fig. 1 it can be noticed that the same units in the top left of the four component planes represent patients with large weight, medium to small height, large BMI, and large percentage of fat. The units in the bottom right of the graph represent patients with small weight, medium to small height, small BMI, and small percentage of fat. It should be noted that, although the SOM algorithm is not aware of how the BMI is computed, the relation between height and weight that determines the BMI clearly emerges from the component planes. This example shows how the SOM can be effectively used to extract the relations among the variables of interest.

#### Figure 1.

Example of SOMs of different variables (Weight, Height, Body Mass Index – BMI –, and Fat) for 251 patients.

To ensure the implementation of CQI policies, extensive data collection from the care units, and their reassembly into meaningful performance indexes need to be put in place. Such processes generate massive amounts of data, which carry information that is not always easily extracted by means of standard statistical approaches. On the other hand, the wealth of the available data allows the application of machine learning approaches, which are able to find structure in complex datasets, even in the absence of an a priori hypothesis about what should be looked for. In other words, the data-driven approach of such techniques lets the data speak for themselves, allowing interesting, possibly unanticipated information to emerge. In turn, such information can be used by the management to discover areas of excellence, or clinics where a margin for improvement exists, as well as strategies for achieving such improvement. In the context of the Balanced Scorecard, the available data are organized as vectors of KPI scores, one per clinic-month. Given these data, it is of particular interest to extract the relations existing among different KPIs for particular groups of clinics, in order to identify clusters that share a similar performance pattern, as characterized by correlated scores on specific KPIs.

For this reason, we have recently introduced the use of SOMs to analyze BSC data [34]. SOMs have already been validated as reliable tools in health care, for instance for population studies [35](Basara H, Yuan M, 2008) and for organization [36] or economic evaluations [37]. A Self-Organizing Map is a machine learning paradigm mainly used for clustering and visualization of data in high dimensional spaces (ie, data with a large number of variables) [38]. The SOM model is composed of units, often referred to as neurons, organized in a low dimensional reticular structure (generally in bi-dimensional or tri-dimensional space), which act as prototypes of the input data in such lower-dimensional space. The SOM learns in an unsupervised way to assign each input data point to the neuron that is most similar to it, by means of a training procedure that aims at preserving the topological characteristics of the input space – that is, similar input vectors are mapped to close regions in the SOM. Once the SOM has been configured, different effective views of the distribution of the data can be obtained. In particular, one can focus on a specific dimension of the input vectors (in our case, one specific KPI) by colour-coding each neuron of the SOM based on the value that the prototype takes on that particular dimension. This kind of plot is called component plane of the SOM (Fig. 2).

#### Figure 2.

Two component planes (relative to the HDF online KPI and to the Treatment Adequacy KPI, respectively) of an SOM trained on BSC data from Portuguese clinics of the NC network. The dashed rectangles superimposed on the planes indicate regions of the SOM where interesting groups of clinics can be found (see discussion in the text). SOM training and visualization were performed in MATLAB using the SOM toolbox [39]. The SOM is shown as a collection of neurons (hexagons) placed in a two-dimensional grid, where the focus is on the relative, rather than the absolute, position of each neuron: that is, the main information content lies in the neighborhood relationships among neurons, as adjacent neurons contain similar KPI records. We can therefore compute the average score for a given KPI in each neuron: this is represented by a color code (colorbar shown on the right) in the component plane relative to that KPI

Many interesting insights can be achieved when running an SOM-based analysis on BSC data. For instance, Fig. 2 shows two component planes obtained from an SOM trained on the BSC data of Portuguese clinics (33 clinics, monitored for 28 months, from January 2008 to March 2010). By comparing different planes (i.e, different KPIs), it is possible to identify groups of data (in our case, clinic-month KPI vectors) that share a similar pattern of performance (as they are located in the same region of the map) and characterize such patterns in terms of specific KPI relations. Thus, for instance in Fig. 2, all KPI vectors that are assigned to the upper left corner of the SOM share a similar structure, which is characterized, among other things, by a high score both on the HDF Online and the Treatment Adequacy KPIs (positive correlation). From these planes one can notice that, while these two KPIs are positively correlated for most clinics in the dataset, there are also cases where treatment adequacy is low (see marked unit on the right side of the map), and cases where a good treatment adequacy is achieved (bottom part of the map). These groups of clinics thus show an interesting performance pattern that might prompt further investigations, and possibly corrective measures. To this end, one can easily trace back the clinics falling into these regions of the map to retrieve all relevant information about them. Similarly, in Fig. 3, two different component planes from the same SOM as above are shown: as expected, the patient growth and new patient inflow KPIs are, in general, directly correlated. However, it is also possible to identify groups of clinics that show a moderately high new patient Iinflow while maintaining a low patient growth score (upper left corner).

#### Figure 3.

Two component planes from the SOM for the Portuguese clinics of the NC network. The shown planes refer to the Patient Growth and New Patient Inflow KPIs, respectively.

This observation can allow to quickly identifying those clinics where, presumably, there is a relevant outflow of patients and, therefore, there might be the need for corrective measures. As a final example, consider Fig. 4 where two component planes of a different SOM, trained on data from Turkey (46 clinics monitored during the same period as those in Portugal), are shown.

#### Figure 4.

The High Flux and Treatment Growth component planes of an SOM trained on data from Turkish clinics of the NC network.

Here, it can be noticed, in particular, that an interesting group of clinics exists (bottom part of the map) where high Treatment growth is observed but the use of High Flux dialysis is low. This means that patients may be referred to this group of clinics for reasons different than quality of treatment (i.e. proximity) as expressed by this KPI. These were just a few examples of benefits from an SOM-based analysis on performance data; other results are extensively described [35]. Together, these results show how SOMs have the potential to unveil significant relationships among KPIs and to identify groups of clinics with different performance patterns, which in turn may require different corrective actions. Thus, SOMs offer valuable hints on the potential areas of intervention in the context for CQI. Information about correlated features emerges directly from the data, without the need for the management to specify a working hypothesis in advance; in this way, also relationships that were not previously advanced can be unveiled, which underlines the greater power of the SOM approach with respect to more traditional statistical analyses. Moreover, it should be remarked that another attractive feature of SOMs is that they can be visualized in an intuitive way so as to immediately convey the correlation structure of the data: this is an extra value of the approach that makes it particularly suited for prompt communication at the management level. This innovative approach to intelligent analysis of clinical data could be a contributing factor to more effective guidance of disease management.

## Acknowledgement

The authors are grateful to Ms Gerdi Klinkner for the revision of the text.

## References

1 - D. C. Mendelssohn, M. Benaroia, 2008The modern haemodialysis factory: must quality improvement trump personalized care? Nephrol Dial Transplant X: 13
2 - J. Hegbrant, G. Gentile, G. F. Strippoli, 2011The quest to standardize hemodialysis care. Contrib Nephrol 1713949
3 - D. Marcelli, V. Moscardó, H. Steil, M. Day, J. Kirchgessner, A. Mitteregger, G. C. Orlandini, E. Gatti, Data Management and Quality Assurance for Dialysis Network (2002Ronco C, La Greca G (eds): Hemodialysis Technology. Contrib Nephrol., Karger (Basel) 137
4 - B. Canaud, L. Tong, F. Tentori, T. Akiba, A. Karaboyas, B. Gillespie, T. Akizawa, R. L. Pisoni, J. Bommer, F. K. Port, 2011Clinical practices and outcomes in elderly hemodialysis patients: results from the Dialysis Outcomes and Practice Patterns Study (DOPPS). Clin J Am Soc NephrolJul;67165162
5 - Robinson BM, Joffe MM, Pisoni RL, Port FK, Feldman HI2006Revisiting survival differences by race and ethnicity among hemodialysis patients: the Dialysis Outcomes and Practice Patterns Study. J Am Soc Nephrol. 171029108
6 - F. K. Port, R. L. Pisoni, J. Bommer, F. Locatelli, M. Jadoul, G. Eknoyan, K. Kurokawa, B. J. Canaud, M. P. Finley, E. W. Young, 2006Improving Outcomes for Dialysis Patients in the International Dialysis Outcomes and Practice Patterns Study. Clin J Am Soc Nephrol 12246255
7 - B. Canaud, P. Wabel, C. Tetta, 2010Dialysis prescription: A modifiable risk factor for chronic kidney disease patients. Blood Purif.29436674
8 - B. Canaud, L. Chenine, H. Leray-Moragués, H. Wiesen, C. Tetta, 2006Residual renal function and dialysis modality: is it really beneficial to preserve residual renal function in dialysis patients? Nephrology (Carlton) 1142926
9 - A. Di Benedetto, N. Richards, D. Marcelli, A. Basci, S. Cesare, P. Ponce, L. Scatizzi, P. Marotta, 2008Is it necessary to check outcomes to improvequality of care? The example of anemia management. J Nephrol 21 (suppl 13): S146S152
10 - L. J. Ng, F. Chen, R. L. Pisoni, M. Krishnan, D. Mapes, M. Keen, BD Bradbury, 2011Hospitalization risks related to vascular access type among incident US hemodialysis patients. Nephrol Dial Transplant 2611365966
11 - Rayner HC, Pisoni RL2010The increasing use of hemodialysis catheters: evidence from the DOPPS on its significance and ways to reverse it. Semin Dial 231610
12 - F. Tentori, J. Zhang, Y. Li, A. Karaboyas, P. Kerr, R. Saran, J. Bommer, F. Port, T. Akiba, R. Pisoni, B. Robinson, 2012Longer dialysis session length is associated with better intermediate outcomes and survival among patients on in-center three times per week hemodialysis: results from the Dialysis Outcomes and Practice Patterns Study (DOPPS). Nephrol Dial Transplant Mar 19. [Epub ahead of print]
13 - H. Zhang, D. E. Schaubel, JD Bragg. Kalbfleisch-Gresham, J. L. Robinson, BM R. L. Pisoni, B. Canaud, M. Jadoul, T. Akiba, A. Saito, F. K. Port, R. Saran, 2012Dialysis outcomes and analysis of practice patterns suggests the dialysis schedule affects day-of-week mortality. Kidney Int 8111110815
14 - Robinson BM, Port FK2009International Hemodialysis Patient Outcomes Revisited: The Role of Practice Patterns and Other Factors. Clin J Am Soc Nephrol. 4 Suppl 1:S1217
15 - AA Bragg. Lopes-Gresham, J. L. Ramirez, S. P. B. Andreucci, V. E. Akiba, T. Saito, A. Jacobson, S. H. Robinson, BM F. K. Port, N. A. Mason, E. W. Young, 2009Prescription of antihypertensive agents to hemodialysis patients: Time trends and associations with patient characteristics, country, and survival in the DOPPS. Nephrol Dial Transplant 2428092816
16 - F. Tentori, 2010Mineral and bone disorder and outcomes in hemodialysis patients: Results from the DOPPS. Semin Dial 10; 2311014
17 - MJ Tentori. F. Blayney, 2009Trends and Consequences of Mineral Bone Disorder in Hemodialysis Patients: Lessons from the Dialysis Outcomes and Practice Patterns Study (DOPPS). Invited paper for Supplement to the Journal of Renal Care. J Ren Care 35: (Suppl 1) 7-13
18 - T. Hasegawa, J. L. Bragg-Gresham, R. L. Pisoni, BM Fukuhara. S. Robinson, T. Akiba, A. Saito, K. Kurokawa, T. Akizawa, 2011Changes in anemia management and hemoglobin levels following revision of a bundling policy to incorporate recombinant human erythropoietin. Kidney Int 79340346
19 - P. A. Mc Farlane, R. L. Pisoni, MA Wald. R. Eichleay, F. K. Port, D. Mendelssohn, International trends in erythropoietin use and hemoglobin levels in hemodialysis patients. Kidney Int 2010782215223
20 - B. Canaud, J. L. Bragg-Gresham, M. R. Marshall, S. Desmeules, B. W. Gillespie, T. Depner, P. Klassen, F. K. Port, 2006Mortality risk for patients receiving hemodiafiltration versus hemodialysis: European results from the DOPPS. Kidney Int 6920872093
21 - B. Canaud, J. L. Bragg-Gresham, M. R. Marshall, S. Desmeules, B. W. Gillespie, T. Depner, P. Klassen, F. K. Port, 2006Mortality risk for patients receiving hemodiafiltration versus hemodialysis: European results from the DOPPS. Kidney Int 6920872093
22 - J. Hornberger, R. A. Hirth, 2012Financial implications of choice of dialysis type of the revised medicare payment system: an economic analysis. Am J Kidney Dis 6022807
23 - N. Richards, J. A. Ayala, S. Cesare, C. Chazot, A. Di Benedetto, J. P. Gassia, J. Merello, R. Rentero, L. Scatizzi, D. Marcelli, 2007Assessment of Quality Guidelines Implementation Using a Continuous Quality Improvement Programme. Blood Purif 25221228
24 - Hirth RA2010International economics of dialysis: Lessons from the DOPPS. Semin Dial 20; 2311618
25 - http://dialysis-centers.findthebest.com/, 2012
26 - Fresenius Medical Care Market & Competitor Survey, 2011
27 - Directive 95/46 of the European Parliament and of the Council, 1995
28 - R. L. Pisoni, J. L. Bragg-Gresham, DS Morgenstern. H. Fuller, B. Canaud, F. Locatelli, Y. Li, B. Gillespie, R. A. Wolfe, F. K. Port, BM Robinson, 2011Facility-level interpatient hemoglobin variability in hemodialysis centers participating in the Dialysis Outcomes and Practice Patterns Study (DOPPS): Associations With mortality, patient characteristics, and facility practices. Am J Kidney Dis 572266275
29 - S. Stopper, C. Amato, S. Gioberge, G. Giordana, D. Marcelli, E. Gatti, 2007Managing Complexity at Dialysis Service Centers across Europe. Blood Purif 257789
30 - A. Stopper, A. Raddatz, A. Grassmann, S. Stuard, M. Menzer, G. Possnien, L. Scatizzi, D. Marcelli, (2011, 2011Delivering Quality of Care while Managing the Interests of All Stakeholders. Blood Purif 32432330
31 - A. L. M. de Francisco, C. Piñera, 2011Nephrology around Europe: organization models and management strategies: Spain. J. Nephrol. 24443845
32 - Institute of Medicine1999To Err Is Human: Building a Safer Health System (1999)". The National Academies Press. http://fermat.nap.edu/catalog/9728.html#toc.
33 - D. Marcelli, J. Kirchgessner, C. Amato, H. Steil, A. Mitteregger, V. Moscardo, C. Carioni, G. Orlandini, E. Gatti, 2001EuCliD (European Clinical Database): a database comparing different realities. J Nephrol 14 (Suppl 4): S94S101.
34 - I. Cattinelli, E. Bolzoni, C. Barbieri, F. Mari, JD Soria. Martin-Guerrero-Olivas, E. Martinez-Martinez, J. M. Gomez-Sanchis, J. Amato, C. Stopper, A. Gatti, E. , 2012Use of Self-Organizing Maps for Balanced Scorecard analysis to monitor the performance of dialysis clinic chains, Health Care Manag Sci 157990
35 - H. Basara, M. Yuan, 2008Community health assessment using self-organizing maps and geographic information systems. Int J Health Geogr 7:67
36 - M. Lloyd-Williams, T. Williams, 1996A neural network approach to analyzing health care information. Top Health Inf Manage 1722633
37 - M. Montefiori, M. Resta, 2008A computational approach for the health care market. Health Care Manag Sci 124344350
38 - T. Kohonen, 2001Self-organizing maps, Springer, 3rd edition.
39 - J. Vesanto, J. Himberg, E. Alhoniemi, J. Parhankangas, 2000SOM Toolbox for MATLAB 5, Technical Report, Helsinki University of Technology.


text:
## Inorder Tree Traversal without Recursion: GeeksforGeeks

Problem Statement:
It is easy to traverse a binary tree in-order using recursion. Do it without using recursion.

## Lowest Common Ancestor in a BST: GeeksforGeeks

Problem Statement:
Given values of two nodes in a Binary Search Tree, write a c program to find the Lowest Common Ancestor (LCA). You may assume that both the values exist in the tree. You can assume that the nodes are present in the tree.

## Extract Leaves of a Binary Tree in a Doubly Linked List : GeeksforGeeks

Problem Statement:
Given a Binary Tree, extract all leaves of it in a Doubly Linked List (DLL). Note that the DLL need to be created in-place. Assume that the node structure of DLL and Binary Tree is same, only the meaning of left and right pointers are different. In DLL, left means previous pointer and right means next pointer.

## Boundary Traversal of Binary Tree : GeeksforGeeks

Problem Statement:
Given a binary tree, print boundary nodes of the binary tree Anti-Clockwise starting from the root.

## LittleElephantAndBooks: TopCoder Problem 12112

[The problem appeared in TopCoder SRM 592 (Div-2, Level-1)]

Problem Statement:
Little Elephant from the Zoo of Lviv has a bunch of books. You are given a int[] pages. Each element of pages is the number of pages in one of those books. There are no two books with the same number of pages.

You are also given a int number. As a homework from the teacher, Little Elephant must read exactly number of his books during the summer. (Little Elephant has strictly more than number books.)

All other elephants in the school also got the exact same homework. Little Elephant knows that the other elephants are lazy: they will simply pick the shortest number books, so that they have to read the smallest possible total number of pages. Little Elephant wants to be a good student and read a bit more than the other elephants. He wants to pick the subset of books with the second smallest number of pages. In other words, he wants to pick a subset of books with the following properties:

1. There are exactly number books in the chosen subset.
2. The total number of pages of those books is greater than the smallest possible total number of pages.
3. The total number of pages of those books is as small as possible (given the above conditions).

Return the total number of pages Little Elephant will have to read.

## Little Elephant and Lemonade : CodeChef Problem LELEMON

Problem Statement:

When Little Elephant visits any room, he finds the bottle of the lemonade in that room that contains the greatest number of litres of lemonade and drinks it all.

There are n rooms (numbered from 0 to n-1), each contains $C_i$ bottles. Each bottle has a volume (in litres). The first room visited by Little Elephant was $P_0$th, the second $P_1$th, …, the m-th $P_{m-1}$th room. Note that Little Elephant may visit a room more than once.

Find for Little Elephant the total volume of lemonade he has drunk.

## Detect HTML Tags: Hackerrank

Problem Statement:
In this problem you will use regular expressions to help you detect the various Tags used in an HTML document.

Here are a few examples of tags:

The “p” tag for paragraphs:

`<p>This is a paragraph</p>`

It is also okay to have one or more spaces before or after the tag name:

`<  p >This is also a paragraph</p>`

Then, there is also something called a void or an empty tag such as:

`<p></p>`

Some tags can also have attributes. For example, here we see the “a” tag which is used for adding links to a document.

`<a href="http://www.google.com">Google</a> `

There are also tags such as this which haven’t been split into an opening and closing tag:

In the above case, “a” is the tag and “href” is an attribute, the value of which is “http://www.google.com”. Ignore any attributes. Your task is to find out all the tags present in the given document.