OpenLLM-France/wikimedia huggingface dataset:
# Incomitant Strabismus/Module 1: Clinical Investigations of Incomitant Strabismus/Part 3: Parks 3 Steps & Bielschowsky Head Tilt Test
### Background

When the head is tilted to either side of the vertical meridian, the eyes undergo physiological cycloduction to compensate. Otherwise, images would be seen as being tilted. The compensatory movements are such that one eye excycloducts (I have a preference for this than the term extorts) while the other incycloducts, eg. when the head is tilted to the left, the RE must excycloduct and the LE must incycloduct.
For the RE to excycloduct, the RIO and RIR must contract (remember that only inferior people extort!)
For the LE to incycloduct, the LSO and LSR must contract.
NB: The opposing vertical (and horizontal) actions of these muscles to maintain orthophoria while the person tilts their head. So, the RIO and RIR both excycloduct, however, one is an elevator the other a depressor…

### 'Step 3' of the Parks 3 Step Method

Remember that by step 3, you have eliminated 6 cyclovertically-acting muscles, leaving you with one oblique and its contralateral antagonist vertical rectus muscle, eg. LIO and RIR, or RSO and LSR.
Head tilt testing is the only way to determine which muscle is palsied.

### An Example

Step 1: R/L (RIR-, RSO-, LIO- or LSR-)
This is self explanatory
Step 2: R/L increases on R gaze (RIR- or LIO-)
The problem obviously involves a muscle which belongs to the 'R gaze family of cyclovertically-acting muscles', so RIR or LIO (the other two being RSR and LSO, but they were excluded after step 1. NB. that these muscles belong to the same 'sequelae')
Step 3: R/L increases on L tilt
How do you interpret this finding?
Both the RIR and LIO excycloduct, one excycloducts the RE the other the LE, so you must produce excycloduction of each eye in turn: R tilt will force the LE to excycloduct (evaluating LIO function), L tilt will force the RE to excycloduct (evaluating RIR function).
In a clinical situation (or in a clinical exam!) just ask yourself:
Where is the problem? …On L tilt.
Which eye excycloducts on L tilt? …The RE.
Which of the suspected muscles belong to the RE? …The RIR.
Therefore, the RIR is the palsied muscle.
(NB. that the LIO has no influence on L tilt, yet this is the problem side. So, the LIO is not involved.)
It's that simple!
The rationale is as follows. On L tilt, the RE must excycloduct (the LE must incycloduct, but neither of the suspected muscles are incycloductors, so the palsy is not in the LE - LIO is automatically excluded). R excycloduction will be produced by RIO and RIR. You know that RIO is intact and is an elevator. The R/L (or R hyper) increases because the RIO is acting unopposed since the RIR is palsied.
NB. that the difference in the vertical deviation on tilting would be less in a vertical rectus palsy than in an oblique palsy because the vertical action of an unopposed oblique would be considerably less than that of an unopposed vertical rectus muscle.
# Incomitant Strabismus/Module 1: Clinical Investigations of Incomitant Strabismus/Part 6: Assessing Diplopia and BSV
### Assessing Diplopia

Interpretation of Diplopia Chart
Description
* The diplopia chart is a record of the position of diplopic images in the 9 positions of gaze.
* It can be used in any co-operative patient with an incomitant deviation who is experiencing diplopia.
Method
* Patient sits still, with head straightened.
* Patient wears red and green goggles (but this is not mandatory) and views a pen torch, held by the examiner at a distance of 50 cms.
* Move the torch into the 9 positions of gaze.
* Question the patient about the position of the diplopic images in each position relative to and commencing in the primary position. If a linear torch is available (or even a pen!), ask about the presence of torsion as patients rarely volunteer this information.
Recording
* Record the results on the grid as if the examiner were the patient, i.e. diplopia recorded on the left hand side of the grid are the diplopic images as seen to the patient's left hand side.
* Record which goggle was in front of the right eye. (It is convention that the red goggle is in front of the right eye).
* Record the distance of the fixation light if other than 50cms (e.g. 1m)
* Record the distance of separation of images and the tilt.
* Record which eye "sees" which image.
# Incomitant Strabismus/Module 2: A/V Patterns
## Characteristics of Alphabet Patterns

An A or V (or alphabet) pattern occurs when there is horizontal incomitance from the primary position to up gaze and/or down gaze.
* V esotropia - an increase in the convergent angle in down gaze
* V exotropia - an increase in the divergent angle in up gaze
* A esotropia - an increase in the convergent angle in up gaze
* A exotropia - an increase in the divergent angle in down gaze
There are modifications of these patterns:
* X pattern - an increase in the divergent angle in up gaze and down gaze
* ◊ pattern - an increase in the convergent angle in up gaze and down gaze
* Y pattern - an exotropia is present in up gaze only
* λ pattern - an exotropia is present in down gaze only

## Causes

There are several theories as to the cause of A/V patterns. Some more common causes are as follows:
* overaction or underaction of the horizontal recti
* paresis of the cyclovertical muscles
* anatomical anomalies, including orbital configuration and muscle insertion

## Clinical Diagnosis

The diagnosis of an A/V pattern can only be made following a measurement (or at least estimation) of the angle in primary position, up gaze and down gaze. As a slight V is a physiological phenomenon, there must be a difference of approximately 15∆ between the angles in up gaze and down gaze before a V pattern is considered significant. A difference of approximately 10∆ is considered significant for an A pattern.

## Management of A/V Patterns

The surgical options are based on whether the A/V pattern is associated with an eso- or exo-deviation, and the likely aetiology or the coexistence of superior oblique overaction or IV CN palsy as two examples. In most cases of A/V patterns, this is obvious. The three choices in the surgical treatment of A/V patterns are operating on the:
* the horizontal recti
* the vertical recti
* the obliques
# Incomitant Strabismus/Module 2: A/V Patterns & Neurogenic Palsies

This enquiry will introduce you to the various neurogenic palsies, including the VIth, IVth, and IIIrd cranial nerve palsies. The focus will be on the characteristics of the eye movement disorders, differential diagnosis and management of each condition.
You will need to work through the online material in preparation for face to face to classes. See your timetable to ensure you have completed the relevant sections prior to your scheduled class.
Upon completion of this enquiry you will be able to interpret clinical findings for the diagnosis and management of various nerurogenic palsies.
1. Introduction
2. Alphabet Patterns
3. IVth CN Palsy
4. VIth CN Palsy
5. IIIrd CN Palsy
# Incomitant Strabismus/Module 1: Clinical Investigations of Incomitant Strabismus/Part 3: Parks 3 Steps & BHTT
### Bielschowsky Head Tilt Test: Rationale and Interpretation

Background
When the head is tilted to either side of the vertical meridian, the eyes undergo physiological cycloduction to compensate. Otherwise, images would be seen as being tilted. The compensatory movements are such that one eye excycloducts (I have a preference for this than the term extorts) while the other incycloducts, eg. when the head is tilted to the left, the RE must excycloduct and the LE must incycloduct.
For the RE to excycloduct, the RIO and RIR must contract (remember that only inferior people extort!)
For the LE to incycloduct, the LSO and LSR must contract.
NB. the opposing vertical (and horizontal) actions of these muscles to maintain orthophoria while the person tilts their head. So, the RIO and RIR both excycloduct, however, one is an elevator the other a depressor…
'Step 3' of the Parks 3 Step Method
Remember that by step 3, you have eliminated 6 cyclovertically-acting muscles, leaving you with one oblique and its contralateral antagonist vertical rectus muscle, eg. LIO and RIR, or RSO and LSR.
Head tilt testing is the only way to determine which muscle is palsied.
An Example
Step 1: R/L (RIR-, RSO-, LIO- or LSR-)
This is self explanatory
Step 2: R/L increases on R gaze (RIR- or LIO-)
The problem obviously involves a muscle which belongs to the 'R gaze family of cyclovertically-acting muscles', so RIR or LIO (the other two being RSR and LSO, but they were excluded after step 1. NB. that these muscles belong to the same 'sequelae')
Step 3: R/L increases on L tilt
How do you interpret this finding?
Both the RIR and LIO excycloduct, one excycloducts the RE the other the LE, so you must produce excycloduction of each eye in turn: R tilt will force the LE to excycloduct (evaluating LIO function), L tilt will force the RE to excycloduct (evaluating RIR function).
In a clinical situation (or in a clinical exam!) just ask yourself:
Where is the problem? …On L tilt.
Which eye excycloducts on L tilt? …The RE.
Which of the suspected muscles belong to the RE? …The RIR.
Therefore, the RIR is the palsied muscle.
(NB. that the LIO has no influence on L tilt, yet this is the problem side. So, the LIO is not involved.)
It's that simple!
The rationale is as follows. On L tilt, the RE must excycloduct (the LE must incycloduct, but neither of the suspected muscles are incycloductors, so the palsy is not in the LE - LIO is automatically excluded). R excycloduction will be produced by RIO and RIR. You know that RIO is intact and is an elevator. The R/L (or R hyper) increases because the RIO is acting unopposed since the RIR is palsied.
NB. that the difference in the vertical deviation on tilting would be less in a vertical rectus palsy than in an oblique palsy because the vertical action of an unopposed oblique would be considerably less than that of an unopposed vertical rectus muscle.
# Incomitant Strabismus/Module 1: Clinical Investigations of Incomitant Strabismus/Part 5: Mapping Ocular Deviations
### Interpretation of Hess/Lees Charts

General points
* Hess (or Lees) chart shows the direction of the deviation; it does not differentiate between a latent and manifest deviation.
* The subjective angle is recorded, not the objective angle, therefore the patient must have NRC.
Position
* Foveal projection is used in this test therefore the position of the field of movement reflects the position of the eyes, e.g. a lower field (or recording point) belongs to the lower eye.
* The position of the central dot indicates the deviation in the primary position, fixing with the RE on the left chart and with the LE on the right chart.
* The left chart indicates the deviation of the LE, the right chart indicates the deviation of the RE.
* The graph is read as if the examiner is the patient.
Size
* Based on Hering's Law of equal innervation the smaller field, plotted with the normal eye fixing, belongs to the eye with the primary limitation of movement. This is the primary deviation.
* Displacements of the recordings interior of the normal template are underactions; displacements exterior of the normal template are overactions.
* After selecting the eye with the primary limitation of movement, the primarily affected muscle is found by selecting the muscle which has the greatest underaction.
* The contralateral synergist will show the greatest overaction in the non-palsied eye.
* The ipilateral antagonist of the palsied muscle will show the next greatest overaction.
* The secondary inhibition of the contralateral antagonist will be seen as an underaction (usually but not always smaller than the primary palsy).
* The outer fields should be examined for small under- and overactions which may not be evident on the inner field.
* The consequent over- and underactions of the muscle sequelae will decrease in size with time as the deviation becomes more concomitant therefore fields of equal size may indicate a long standing palsy or a non paralytic strabismus.
* A narrow field which is restricted in opposing directions of movement shows a mechanical restriction ie. The normal muscle sequelae of a neurogenic palsy are not evident.
Shape
* Sloping fields denote 'A' & 'V' patterns
* Sloping fields should not be interpreted as indicating torsion.
Summary
* The smallest field belongs to the primary affected eye.
* Look for the greatest underactions and corresponding over action of contralateral synergist and other muscle sequelae (NB torsion is noted by the tilt of the torch light NOT by a sloping field).
* Mechanical restriction show fields of restriction in opposing directions and do not follow the normal pattern of muscle sequelae of a neurogenic palsy.
* Fields of differing sizes indicate a recent palsy; fields of the same size indicate either a long standing palsy or a non paraletic squint.
# Exercise and metabolic disease/prostate/diagnosis

The main tests used to help diagnose prostate cancer in Australia are the PSA (prostate specific antigen) blood test and the DRE (digital rectal examination)$^{(2)}$.
* PSA test - This is not a cancer specific test. This blood test examines the number of serum prostate specific antigen. This type of protein is produced by prostate cells, so an increased number of this protein suggests that there has been some sort of growth of the prostate. The higher the number the more chance of a cancer and really high numbers suggest the cancer may have started to spread.
* DRE - This test involves a doctor inserting a gloved finger into the anus of a patient and feeling the prostate for any hard lumps that could be cancerous tissue.
A combination of these two tests is usually recommended.
Abnormalities in these tests leads to the suspicion of prostate cancer, a biopsy may then be recommended to confirm or deny these suspicions. The biopsy involves a small sapmle of tissue being taken by a spring loaded needle. Samples are then analysed to determine the stage and grade of the cancer, this provides a definitive answer as to whether or not the patient has prostate cancer.
Men over 40 with a family history are advised to get tested annually and so are all men over the age of 50. In the early stages of prostate cancer there can be no signs or symptoms in some cases, so getting tested is usually the only way to detect it. Early detection is vital as far as whether or not the cancer can be cured.
# Existentialism

Existentialism is the philosophy of, well, existence. It states that life and existence is without purpose. Life, the universe, and everything is void of any purpose or meaning. Existentialism rejects the use of reason to define some meaning, as it is an attempt to impose a sort of order in the world of phenomena, which is essentially irration, unscrutured, and random. Rationality hinders us from finding meaning--it's "bad faith". To try and suppress our anxiety and dread that we feel in our own freedom and our awareness of death, we confine ourselves in the everyday experience, in which we give up our freedom. In Existentialism, people make decisions based on their interpretation of meaning rather than what's rational. The individual longs for an order, and this conflicts with the world of phenomena's randomness. This means the universe, where people try to be rational in an irrational world, is absurd.
How do we, then, find meaning? In Existentialism, meaning is not provided by some divine order, but rather is created by the individual's actions and interpretations. In the absurdity of the universe, where the universe has you in a void of nothingness and you're feel like you're just thrown into existence, meaning is sought through embracing existence, the individual creates the meaning.
"Existence Precedes Essence"
# Exercise and metabolic disease/prostate/Prevalence

Prostate cancer is the most common form of cancer in Australian men. Each year around 3 300 men die from the diseae. Close to 20 000 men are diagnosed each year and this number appears to be rising$^{(2)}$.
In the period from 1978 to 1992 the incidence of prostate cancer increased from 33.8 per 100 000 to 53.5, in Australia. These rates have tended to increase as the number PSA (prostate specific antigen) tests have increased over the years, suggesting that there may be any number of undiagnosed cases of prostate cancer.
The prevalence of prostate cancer increases greatley as a man gets older, jumping from 1 in 1 000 men in their 40's being diagnosed, up to 80 in 1 000 for men in their 70's. Australian men have a 1 in 5 chance of developing the disease by the age of 85. As mentioned, the likelihood of being diagnosed increases with age and also if there is a family history. The risk is nearly double if a family history exists. Men who live in rural areas also have a 21% higher diagnosis rate when compared to men living in the city..
Androgen deprivation therapy (ADT) is becoming a more and more popular treatment method for men with prostate cancer. From 2003 to 2009 the use of ADT increased by more than 40%. Up to 50% of prostate cancer patients now receive ADT.
# Exercises on the bisection method
## Exercise 1

* Write a Octave/MATLAB function for the bisection method. The function takes as arguments the function $f$, the extrema of the interval $a$ and $b$, the tolerance $\epsilon$ and the maximum number of iterations.
* Consider the function $\displaystyle f(x)=\cos x$ in $\displaystyle [0,3\pi ]$.
** How many roots are there in this interval?
** Theoretically, how many iterations are needed to find a solution?
** With $\epsilon =10^{-10}$, how many iterations are needed? Does the numerical result satisfy this condition?
** With $\epsilon =10^{-20}$, how many iterations are needed? Does the numerical result satisfy this condition?

## Exercise 2

* Consider the function $\displaystyle f(x)=e^{x}-x^{2}$ in $\displaystyle [-2,0]$.
** Show the existence and uniqueness of the root $f(\alpha )=0$.
** Given the tolerance $\epsilon =10^{-8}$, how many iterations are needed?
** Consider the restriction of the interval to $\displaystyle [-2,-1]$. In this case how many iterations are needed?
** With the aid pf the Octave/MATLAB function of exercise 1, compute the root of the function.
** Compute the solution with precision $\epsilon =10^{-15}$ e consider it as the exact solution. Then considering $\epsilon =10^{-8}$, draw a logarithmic plot to represent the average error and the actual error. Comment.

## Exercise 3

Show that the sequence defined by the bisection method with $k\geq 0$ we have
    $|\alpha -x_{k}|\leq {\frac {b-a}{2^{k+1}}}$.
# Exobiology

Welcome to the Wikiversity Center for Exobiology, part of the School of Biology.
Exobiology, also known as xenobiology or astrobiology, is a speculative field within biology concerned with extraterrestrial life.
The Center for Exobiology is a Wikiversity content development project where participants create, organize and develop learning resources about the search for life beyond Earth.

# Where are the data?

Astrobiology is an idea in search of data. Many scientists expect that life is common, probably having come into existence on millions of planets. However, astrobiology is a speculative field within biology; nobody has evidence for extraterrestrial life. Astrobiology includes the concept of artificial life, since any life form with human-like intelligence could conceivably create artificial life in a laboratory. Such artificial life might be more suitable than a biological organism for interstellar travel. While currently funded efforts in astrobiology focus on planetary exploration and attempts to detect planets with Earth-like atmospheres, it has been suggested that we should also look closely at Earth for signs that alien artificial life is already here.

## Possible data

* Search for life on Mars
* Liquid water on Europa
* Replacement of phosphorus by arsenic in living organisms

## Learning resources

* The Drake Equation
* can human like intelligence evolve under water?
* can comets incubate life and seed it to planets?
# Exercise and metabolic disease/prostate/Medical and Clinical Considerations

Androgen deprivation therapy (ADT) has proven to be very effective in treating prostate cancer. This is why so many prostate cancer patients undergo this type of treatment. But ADT has been shown to cause a number of side-effects, all of which need to be taken into consideration when dealing with someone undergoing ADT. Some of the more common side effects are listed below:
As a result of these side-effects quality of life tends to be significantly decreased$^{(1)}$$^{(2)}$.
The majority of these-side effects are due to decreased testosterone levels$^{(7)}$.
All of these factors need to be considered when determining appropriate exercise programs.
# Exercises on the bisection method/Solution
## Exercise 1

* The following is a possible implementation of the bisection method with Octave/MATLAB:
* The solution of the points 1, 2 e 3 can be found in the example of the bisection method.
For point 4 we have
    $k\geq \log _{2}3\cdot 10^{2}0\pi \approx 69.8$,
so we would need at least 70 iterations. The chance of convergence with such a small precision depends on the calculatord: in particular, with Octave, the machine precision is roughly $2\cdot 10^{-16}$. For this reason it does not make sense to choose a smaller precision. The number of iterations, if we don't specify a maximum number, would be infinite.

## Exercise 2

* To verify the existence of a root $\alpha$ we need to show that the hypothesis roots theorem are satisfied. The first hypothesis requires $f$ to be continuous. Obviosly this is a continuous function since it is sum of two continuous functions. The second hypotheses requires the function to have oppiste signs at the interval extrema, and in fact we find
    $f(-2)\approx -3.86,\quad f(0)=1\quad \implies f(a)f(b)<0$.
    Comparison of the average and actual errors computed with the bisection method in logarithmic scale..
    To show the uniqueness of the root we need to prove that the function $f$ is monotone and in fact
    $f'(x)=e^{x}-2x>0\quad \forall x\in [-2,0]$.
* The number of iterations need is given by
    $k\geq \log _{2}{\frac {b-a}{\epsilon }}=\log _{2}2\cdot 10^{8}\approx 25.8$,
    and so we have $k\geq 26$.
* The interval $[-2,-1]$ does not contain aany root as the second hypotesis of the roots theorem fails, in fact
       $f(-2)\approx -3.86,\quad f(-1)=-0.63\quad \implies f(a)f(b)>0$.
* $\alpha \approx -0.7035$
* In the plot we show in red the average errorand in blu the actual error. From the graph, it is clear that the actual error is not a monotone function. Moreover, note that the global behavior of both curves is the same, clarifying the term average error for $\displaystyle e_{k}$.

## Exercise 3

For the solution look at the convergence analysis in the bisection method page.
# Increasing function/R to R/Sequence limit and function limit/Exercise

Let
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
be an increasing function and $b\in \mathbb {R}$. Show that the sequence $f(n)$, $n\in \mathbb {N}$, converges to $b$ if and only if
    $\operatorname {lim} _{x\rightarrow +\infty }\,f(x)=b\,$
holds, i.e. if the limit of the function for $x\rightarrow +\infty$ is $b$.
# Independent variable

This statistics resource is a "stub". Learn how you can help Wikiversity to develop it.
An independent variable is used in statistics to predict or explain a dependent variable.
For example, Age and Gender might be used as independent variables to predict the age of death or life expectancy (dependent variables).
In experimental designs, the independent variables are manipulated by the researcher (e.g., different dosages of a drug). In quasi-experimental and non-experimental designs, the independent variables may be naturally-occurring, non-manipulated variables which are measured and used to predict variations in the dependent variables.
--Example--: Question: Does soda erode rocks just as it does to teeth? Answer: Independent Variable- Whether or not rocks erode in soda. (What are you testing?)
             Dependent Variable- The rate of erosion. (What are you measuring?)